cer fall 2013 final

The $25,000 Steak

How Revolving Door Lobbyists Gain From Political Connections

Vol. III, No. II Fall 2013

a free lunch on tips?so sue metaperpedicunring the bell? rounding it outmixed messages

Columbia Economics Review


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T A B L E O F C O N T E N T S

Labor Economics4 A Free Lunch on Tips?

Analyzing the Choice of Compensation Structure in New York City Restaurants

Law and Political Economy12 The $25,000 Steak

How Revolving Door Lobbyists Gain From Political Connections

Monetary and Fiscal Policy

Microeconomic Theory

24 TaperPedicAn Analysis of the Federal Reserve’s Forecasted Asset Losses in the Face of Looming Interest Rate Shocks

32 Rounding It Out

The Effect of Round Number Bias in U.S. and Chinese Stock Markets

16 So Sue MeMarket Reaction to Patent Litigation Verdicts and Patent Appeal Results

29 Unring the Bell?The Threat to Deposit Insurance in Cyprus

41 Mixed Messages

How Firms Should Utilize Private Information

A Free Lunch on Tips?Analyzing the Choice of Compensation Structure in New York City Restaurants

Samuel Zakay

Columbia University

Introduction Restaurant staffs in New York are gen-

erally compensated by hourly wages and derive a majority of their salary from tips. Restaurants in New York City have two main methods of distributing tips. “Pooled houses” are based on a share system. At the end of the shift, each staff member receives an amount equivalent to the value per share multiplied by the total shares allotted to them. In this sys-tem, servers receive the greatest percent-age of shares. In “non-pooled houses,” tips are collected by individual servers. In this system, there could be large differ-ences in the amount a server may be com-pensated on a given night and also large differences between total compensation amounts for different servers.

Barkan, Erev, Zinger and Tzach (2004) argue that in a pooled system, servers are given the incentive to provide good ser-vice and to work as a team. There is no incentive to compete with servers at the expense of other servers’ customers, as each server’s income is dependent on all customers. However, a pooled system is undermined by the problem of free rid-ers. Since servers’ earnings do not solely depend on their own efforts, they can grow reliant on colleagues and become unmotivated to work at a high level.

In an individual tip policy, servers are given an incentive to provide the best ser-vice possible. Servers under this policy may compete with one another and over-use limited common resources. In the

long term, servers do have an incentive to make sure that the customers they are not serving have a good experience as they may serve the customer in the future.

B.E.Z.T (2004) argue that pooling yields better service when there is a greater de-gree of visibility within the restaurant as both management and restaurant staff (mutual monitoring) can more easily monitor the efforts of servers.

In addressing how staff compensa-

tion affects the quality of service in res-taurants, I designed and implemented a survey aimed at collecting restaurant specific information. I surveyed restau-rant managers and owners located on ei-ther the Upper West or Upper East Side of Manhattan. All restaurants that partici-pated had a ZAGAT review.

The survey had two major sections: compensation structure information and general restaurant characteristics infor-mation. In evaluating diner’s percep-tion of a restaurant, I use secondary data from ZAGAT and OpenTable. ZAGAT measures a restaurant by 3 factors: Food, Service, and Décor. Each factor or score is presented as a number between 0 and 30. OpenTable also rates restaurants by “Overall, Food, Ambiance and Service”. Reviewers are strictly people who made a reservation through OpenTable.

The descriptive statistics in the sur-vey are aimed at helping differentiate between restaurants. While two restau-rants may share a similar compensation structure, other features of the restaurant could be responsible for causing restau-rants to produce better service in the eyes of reviewers. Thus, many of the charac-teristics serve as controls in analyzing the specific issue of moral hazard within restaurant. Furthermore, I use the other

“Pooled houses,” are based on a share system. At the end of the shift, each staff member

receives an amount equivalent to the value per share multi-

plied by the total shares allot-ted to them.


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diner observations such as cost range from ZAGAT to examine relationships between restaurants that could cater to different types of customers (socio-eco-nomic class).

I first model restaurant management’s choice of compensation structure using a two task, two servers principal-agent problem framework. I then use the vari-able of a restaurant’s seating capacity as a proxy for visibility (higher capacity implies lower visibility). I find a nega-tive statistically significant relationship between the choice to pool and capacity.

I then examine management’s choice regarding the number of servers hired per shift relative to the capacity of the restaurant. I find a negative yet weak non-statistically significant relationship between servers per capita and pooling, thus failing to support the idea of a team incentive giving management more flex-ibility in the number of servers it hires.

I then investigate whether diners per-ceive differences in the quality of service in pooled establishments. To investigate the relationship over the full data set, I use both ZAGAT and OpenTable’s meas-ure of service quality. I find it difficult to argue that pooling leads to higher qual-ity service than non-pooling even when controlling for other restaurant charac-teristics.

Next, I split the data into pooled res-taurants and non-pooled restaurants, and proceed to look at whether capacity affects service quality within the sub-sets. Although I do not find the relationship to quite reach the level of statistical signifi-cance, within the pooled sub-set, as a res-

taurant’s capacity increases, and hence visibility decreases, its service quality

falls. While the negative relationship is not statistically significant, it remains when controlling for other fixed effects associated with a restaurant’s organiza-tional and compensation structure.

I also examine the relationship be-tween the quality of service and visibil-ity amongst the non-pooled restaurants to see whether non-pooled restaurants yield higher quality service as visibility decreases. I find it difficult to observe any directional relationship with statisti-cal significance that holds when control-ling for other restaurant characteristics. Part of the reason for the lack of results could stem from the small sample of non-pooled restaurants.

Literature ReviewWithin a restaurant, managers and

owners wish to establish a culture amongst the service staff to treat the customer in the best way possible. If the manager chooses to create a group-incen-tive structure, as with pooling, he or she can run into the problem of moral hazard amongst his team.


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Alchian and Demsetz (1972) argued that by bringing in an individual to monitor the actions of workers, a firm can limit the amount of free rid-ing, and thus alleviate the problem of moral hazard. The monitor should be able to renegotiate and terminate contracts with individual workers and hold a residual claim on the profitability of the firm.

Rather than a observ-ing each action, the cen-tral monitor needs only to possess the ability to pro-vide a productivity bonus or terminate a contract of an employee. Similarly restaurant management is faced with the issue of optimizing profits by establish-ing wages based on servers’ efforts. In the case of the restaurant industry the owner and general manager can often be consid-ered a monitor of service staff actions.

The idea of mutual monitoring extends the idea of the monitor as presented by Alchian and Demsetz to a role that isn’t strictly centralized. Service staff may also monitor the actions of their peers to en-sure everyone is working within a pooled system. This is consistent with Lazear and Kandel’s (1992) argument that mu-tual monitoring is more effective when profits are shared amongst a smaller group. According to this logic a smaller restaurant would be a stronger candidate for mutual monitoring.

B.E.Z.T (2004) discuss the problem of free riding within a pooled system. They found that servers in both types of res-taurants were bothered by the problem of free riding. If a restaurant attracts fewer customers, the negative effect of less in-come should reach both high effort and low effort servers in the long run. With regard to the problem of overuse of lim-ited resources, they found that servers in non-pooled restaurants were more both-ered by co-workers relationships with shift managers.

Bandiera, Barankay and Rasul (2008) found that managers who were not given a performance incentive tended to favor workers who they were friendly with. However, when a performance incentive was issued that relationship tended to disappear in favor of giving more tasks and hence more opportunity to those who were better. A residual claim for the

monitor or manager is essentially a per-formance incentive for effective manage-ment, and should thus limit favoritism within the restaurant.

After surveying cafe servers and noting their concerns over free riding and com-petition, B.E.Z.T (2004) tested whether the concerns manifested themselves in the quality of service at the two types of cafes. They recorded the level of visibil-ity, service time and the number of ser-vice problems. As the number of service spaces increases, visibility decreases. A pooled system resulted in a higher quali-ty of service in a higher visibility environ-ment, while a non-pooled system result-ed in a higher quality of service in a lower visibility environment. Increased visibil-ity within a pooled restaurant makes it easier for workers to monitor the actions of their peers and thus discourage free riding, which is consistent with the gen-eral moral hazard literature. They also argue that low visibility alleviates the problem of overuse of limited resources in non-pooled cafes, while the individual tip system alleviates the problem of re-duced-effort associated with free riding. This study is similar to the research done by B.E.Z.T (2004), however I use diner’s actual ratings to measure service qual-ity. In this survey, I also collect the gen-eral compensation structure for multiple types of employees within the restaurant, and general features about the restaurant that were not collected by B.E.Z.T.

One dominant theory as to why cus-tomers tip is a fear of social disapproval. Another dominant as to why customers tip is in order to secure equitable relation-ships. A third theory for why customers tip is in order to receive good service in the future upon returning.

Lynn (2001) performs a meta-analysis on fourteen studies, and determines that although service evaluations are statisti-cally significant when regressed against tip sizes, the correlation between them is 0.11. Lynn, Kwortnik Jr. and Sturman (2011), Shamir (1983), and Harris (1995) support that, even if service quality and tipping are positively related, the cost of expending energy on providing supe-rior service may not be worth the extra reward. This could complicate matters regarding whether servers will even ex-pend the extra effort to secure virtually the same tip. Lynn and McCall (2000), and Ostroff (1993) support the preced-ing notion by showing that servers may be able identify how they are perform-ing with respect to their peers and adjust their effort accordingly.

Theoretical Model of Restaurant Man-agement’s Choice of Compensation Structure Under Moral Hazard

Restaurant management’s choice of compensation structure can be construed as an example of a moral hazard princi-pal-agent problem. In the principal-agent problem, output X can be defined as:

where y is a number transforms effort e into output, and ε ~ N(0, σ2). For simplic-ity, we assume that a worker has CARA preferences and thus their utility can be represented by their certainty equiva-lents. In general a workers wage can be represented as:

where a is a fixed amount and b is a piece rate. A worker is also faced with a cost of effort c(e). Thus, an agent’s utility function according to CARA preferences can be written as:


6 Fall 2013

where rA is the coefficient of risk aver-sion of the agent. A principal pays the wages of the worker and is thus faced with a different utility function:

where rP is the coefficient of risk aver-

sion of the principal. The linear quadratic model also assumes cost to be quadratic or

where θ is an agent’s ability. In the moral hazard problem effort is not ob-servable, and it is assumed that the agent selects effort to maximize her payoff un-der the contract

In the principal-agent framework, both the principal and agent have common knowledge regarding the parameters of the relationship and both agree upon the relationship between effort and output. The principal is in a position to anticipate

h o w t h e a g e n t w i l l

respond to the

compensation contract.The agents are servers, which I will re-

fer to as 1 and 2, and they are tasked with serving two tables, which I will refer to as A and B. The output of table A and B respectively can be expressed as:

where E1A represents the effort of server 1 on table A and where E2A represents the effort of server 2 on table A (the same is true for Table B). As in real life restaurant, I assume each server is assigned a prima-ry table to serve (server 1 is assigned to A and server 2 is assigned to table B). Each server has a wage, which can be repre-sented as:

BP represents the piece-rate that a serv-er collects from his primary table and BS represents the piece-rate that a server collects from his secondary table. Each server is also faced with a quadratic cost associated with effort represented by:

where (theta)i represents the ability of server i (cost decreases as ability in-creases) and generally c1B > c1A and c2A > c2B, the cost of effort of serving your secondary, non-assigned table, is greater than the cost of serving your own table. I use the following cost matrix because each server aims at helping his second-ary table if the ability of the other server is different than his own. Servers seek to supplement the other server only if the other server needs it. Thus if the abilities of the servers differ greatly (θ1 >>θ2), then server 1 can really help out server 2 by putting effort into his secondary table. I also square the difference, as the cost of effort should always be positive. For sim-plicity I assume no minimum effort (how-ever efforts cannot be negative), and also no effort in switching tables. Furthermore in the principal-agent problem each serv-er has a cost associated with risk that can be represented as:

where ri is the coefficient of risk aver-sion for server i and σi is the variance associated with table i. For simplicity, I assume that the covariance between table A and B is zero. The principal, restaurant manager or owner, has a profit column vector, P = [PA PB], that transforms output into profit. The principal agent problem in the context of the two servers and two tables can be stated as follows:

subject to:

where Wi0 is the server’s next best alter-native wage. For simplicity, I assume that each agent choose his effort level inde-pendently of the other. In order to solve the problem, I first solve for the optimal effort of agent 1:

These solutions make sense as the cost of effort associated with each table rises, the effort decreases, and as the wage from a table i increases, effort on table i increases. Likewise I perform the same process for server 2 and conclude:

As MacLeod (Forthcoming) writes the fixed payment ai is adjusted to ensure each IRi is binding, from which the payoff to the principal is:

The optimal [Bp Bs] can be computed by plugging in E*

1A, E*1B, E*

2A, E*2B and maxi-

mizing up (B):

The optimal contract is defined by [Bp Bs]. In the real world, restaurants se-lect between two options: pooling and non-pooling. In a non-pooled house BS


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= 0, a server does not derive any piece rate wage from his secondary table. In a pooled house BP = BS, as each server earns the same fraction of his total wage from each table.

Proposition 1: As the ability of both servers rise, both servers work harder and earn higher wages.

The coefficient on ability in the numera-tor is greater than the coefficient on abil-ity in the denominator in the equation for BP. More skilled workers should be paid a higher wage by the restaurant as they are producing more for the restaurant.

Proposition 2: If the ability of server 2 equals the ability of server 1, each server puts no effort into his secondary table and earns no wage from his secondary table. In this case pooling is not efficient.

If θ2=θ1, then E1B = E2A = 0, hence BS = 0. If each server has equal abilities, then it would be detrimental for each server to devote any effort on a table where they would not actually be helping the other server and expending a greater cost, as the cost of serving a secondary table is larger than the cost of serving a primary table. If this happens, management will choose a non-pooled system as servers will not be putting in any effort to their secondary tables, and thus management will not be deriving any benefit from is-suing a team incentive of pooling.

Proposition 3: If the ability of server 2 differs from the ability of server 1, each server will put some effort into his sec-ondary table. Thus, the optimal contract features a degree of pooling wages across tables.

This result can be seen by observing that E1B, E2A, BS ≠ 0 if θ2≠θ1. In the case of unequal abilities, management wishes to offer a form of pooled wages so the high-er ability server is incentivized to work on both tables. Since management offers the same wage to both servers, both the higher ability server and lower ability server receive a wage from their second-ary table. Thus, both servers have an in-centive to expend effort on serving both tables and the secondary server will seek to supplement the efforts of the primary server. While the optimal contract is a de-gree of pooling, in the real world, restau-rant management will only choose pool-ing if the optimal contract more closely resembles the pooled contract, BP = BS, than the non-pooled contract, BS = 0.

Proposition 4: As the servers become more risk averse, their wages fall and hence effort falls.

This is consistent with economic theory and the idea that risk poses a real cost for the agents. If servers become more risk

averse, r1, r2 >> 1, then the denominators of the optimal contracts grow larger and thus the optimal wages grow smaller. Management can offer lower wages; a server’s total wage becomes closer to the fixed wage, as management is bear-ing the risk. As the wages of the servers grow smaller, servers expend less effort on serving both their primary and sec-ondary tables.

Proposition 5: If the abilities of the serv-ers are not equal, as the capacity within the restaurant grows, restaurant man-agement will be more inclined to choose non-pooling.

Earlier, I assumed that c1B > c1A, which is sensible as it should be more costly for a server to work on a table to which he is not assigned. Assume that the abili-ties of each server are not equal (if so, see Proposition 2). If it is more costly for a server 1 to expend effort serving each person at table B, then as the number of people at table B increases, c1B should in-crease as well. Furthermore, c1B should increase faster than c2B because the cost of serving a secondary table is greater than the cost of serving a primary table. If the number of people at table B increases, or c1B, c2B tends to infinity, then BS will reach

0 faster than BP, that is. Furthermore if the number of people at both tables increases, BS will fall even faster than BP as c2A will also increase fast-er than c1A. Thus, as the number of people that are eating in the restaurant increases the cost of serving a secondary table and thus non-pooling becomes more attrac-tive. While the optimal contract is a mix of non-pooling and pooling, restaurant management can only pick one system and thus chooses the system that the op-

timal contract most closely resembles.DataIn selecting a sample, I chose to focus

on the Upper West Side and East Side of Manhattan to minimize locational vari-ance stemming from population compo-sition that could affect the restaurants’ composition and perception. I assembled a list of rated restaurants by screening the 371 restaurants listed on the ZAGAT website, of which 71 agreed to participate in the study.

Of the 71 restaurants that participated in the survey, 44 were located on the Up-per West Side, while 27 were located on the Upper East Side. Several restaurants chose not to answer certain questions such as service staff’s gross pay per shift. No restaurants participating in the sur-vey were given monetary compensation.

The full table of summary statistics are available in Appendix Table 8.1. Within the context of the service staff of the res-taurant, bartenders seem to earn the high-est gross pay per shift. A reason provided by many managers as to why bartenders are compensated more is their job affects the operating margin of the restaurant. Bartenders can more easily give a drink on the house to secure a higher tip than a server can give food on the house.

Servers earn a higher income then other members of the service staff that do not affect operating margins. The only dif-ference between pooled houses and non-pooled houses exists on the server level. After the bartender and server, a runner earns the most in the context of the ser-vice staff. In many restaurants, managers said that they viewed the role of the run-ner as equal to the role of the server and thus established compensation systems where runners and servers earned the


8 Fall 2013

same. A busser out-earns only the host. While many managers often cited that bussers were an important part of the ser-vice experience, a busser never earned as much as a server. Finally, the host often earns the least in a restaurant.

Restaurants tend to hire more servers than other members of the service staff. Furthermore there is a higher stand-ard deviation for the number of servers than number of other members of the service staff, which reflects the greater perceived role that servers play in cus-tomer service. Bussers and runners seem to the longest tenured employees within a restaurant. An extremely high percent-age of them are full-time (nearly 90%). Bartenders spend a similar amount of time relative to servers employed within a restaurant, yet there is a higher prob-ability that a restaurant will have full-time bartenders than full-time servers. Management values honesty amongst the bartenders, and if it finds bartenders that it can trust, it may prefer employing few-er trustworthy bartenders on a full-time basis to seeking outsiders for part-time positions. Within the context of a restau-rants, the host position is by far the most transient.

Of the 71 restaurants that chose to partic-ipate in the survey, 54 can be categorized as pooled houses, while 17 can be cate-gorized as non-pooled houses. This per-centage is consistent with managers who guessed that 80% of New York City res-taurants practiced pooling. This propor-tion is also consistent with the 42 restau-rants that were also rated by OpenTable, where 33 of them practiced pooling. The pooled system appears to be the default

compensation structure both within the sample and across New York City.

The general manager is the primary indi-vidual responsible for monitoring the free riding problem within the pooled system. The vast majority of restaurant owners are involved in the day-to-day operations of the restaurant (over 80%). An active owner can also provide another layer of monitoring.

Within the sample, the mean capacity of restaurants hovers around 100 peo-ple, with much variation. Capacity will be a key variable in examining the free rider problem and the difficulties associ-ated with monitoring. Furthermore, the number of people relative to a server, when the restaurant is completely full, is roughly 27 (the inverse of servers per capita). There is also a large amount of variation associated with servers per capita.

Many of the restaurants surveyed are full service restaurants (41%), meaning that they contain all five types of service staff. The two most expendable positions within the sample are runner (37%) and host (32%). All 71 surveyed restaurants participated in ZAGAT (part of the search criterion), while only 42 participated in OpenTable. The ZAGAT ratings were all lower on average than the OpenTable rat-ings. Furthermore, ZAGAT’s ratings had a higher standard deviation than OpenT-able’s. In trying to test hypotheses dis-cussed by past literature along with new hypotheses, I use both measures of ser-vice quality.

In order to assess whether there is a dif-ference between the two measures of ser-vice quality, I created a correlation ma-

trix between all of the diner perception variables. ZAGAT Service was positively related to all of the ZAGAT measures of restaurant quality. A similar phenom-enon exists when considering OpenT-able Service’s relationship with the other OpenTable variables.

The preceding relationships support the conclusion that restaurants with bet-ter food, higher cost, better decor and bet-ter ambiance tend to provide better ser-vice. When considering whether the two measures of diner perceptions are corre-lated, the results are mixed. ZAGAT Ser-vice is positively correlated to OpenTable Service. Furthermore, ZAGAT Food is positively correlated to OpenTable Food. None of the other cross variables between ZAGAT and OpenTable is directly meas-uring the exact same thing, but all of the variables are positively correlated.

Although ZAGAT has 29 more restau-rant observations than OpenTable, I de-cided to examine both in my analyses. The two measures of service and food are positively correlated, however the corre-lation is far from 1. In several analyses, especially concerning non-pooled restau-rants, OpenTable is less reliable given the relatively small data set.

As part of the survey, managers and owners were asked the amount servers could expect to earn in a shift and the per-centage of a server’s salary derived from tips. A percentage of a server’s income derived from tips can serve as a good measure for how dependent a server is on customer approval. Several managers declined to answer the question.

Common sense suggests that servers who produce better service choose to


Fall 2013 9

work at restaurants where they could earn more. Likewise, servers who pro-duce better service would choose to be at a restaurant where a greater percentage of their income would be derived from tips. Both measures describe whether there is a positive relationship between a server’s earnings and the quality of ser-vice provided. I regressed ZAGAT Ser-vice on a server’s gross pay per shift and found a positive and statistically signifi-cant relationship (t(68) = 2.764). I found a similar positive relationship, although it was not quite statistically significant, when regressing OpenTable Service on a server’s gross pay per shift (t(39) = 1.563). I suspect that if I had surveyed more res-taurants that were rated by OpenTable, the positive relationship would further approach a level of statistical significance.

The positive relationship and hence statistical significance between the qual-ity of service and a server’s gross pay per shift diminished when controlling for cost using ZAGAT Cost in both meas-ures of service quality (ZAGAT (t(68) = 1.112) and OpenTable (t(39) = 0.538)). The positive relationship and relative level of non-statistical significance remains when controlling for other fixed effects that measure organizational and compensa-tion structure.

I regressed ZAGAT service on the per-centage of a server’s income derived from tips and found a positive and statistically significant relationship between them (t(70) = 3.079) as shown in Appendix Ta-ble 8.7. Furthermore, the positive and sta-tistically significant relationship remains even when controlling for cost and the same fixed effects that measure organi-zational and compensation structure as the regressions on server’s gross pay per shift. Curiously enough, the positive re-lationship does not exist when consider-ing OpenTable’s measure of service qual-ity (t(41)= -0.602). The preceding results support common sense that servers who produce better service will tend to work at restaurants that will afford them bet-ter pay.

Results and AnalysisEndogenous Analysis of the Pooling ChoiceGiven the greater difficulty in monitor-

ing free riding in a lower visibility en-vironment, it is interesting to examine whether owners and general managers behave as the theory and literature pre-dict by shying away from establishing a pooled system as the size of the restau-rant increases and visibility decreases. I analyzed the question by perform-ing a series of linear probability regres-sions of the dummy variable of whether

a restaurant was pooled on the variable of the seating capacity of the restaurant. The variable of seating capacity is used as a variable for assessing the visibility within a restaurant. As the seating capac-ity within a restaurant increases, its size increases and its visibility decreases.

Consistent with the theory and lit-erature, capacity is negatively related to whether a restaurant decides to institute a pooled system, and the negative rela-tionship is statistically significant (t(71) = -1.900). The negative relationship per-sists and becomes even more statistically significant when I control for the relative price point of a restaurant by using ZA-GAT Cost (t(71) = -2.600). Although din-ers of the restaurant assess cost, it should be considered an endogenous variable as the management of the restaurant sets the prices. ZAGAT Cost is different from other ZAGAT measures because it is ob-served by customers rather than rated by customers, as is the case with ZAGAT Ser-vice, Food and Decor. Thus across both cheaper and more expensive restaurants, management’s choice to pool is nega-tively related to the size of the restaurant. The negative, statistically significant re-lationship persists when controlling for other fixed endogenous effects of the or-ganizational and compensation structure (as well as cost) of the restaurant such as: whether a restaurant is over three years old, whether ownership is involved on a day to day basis (a dummy variable that suggests a higher degree of monitoring), whether most of the servers are full-time, whether some servers are paid a higher hourly wage than others, whether a res-taurant is a full-service restaurant with all five types of service staff (a dummy variable) and whether the restaurant is located on the Upper West Side.

The negative statistically significant persistent relationship suggests manage-ment is aware that servers are presented with a greater incentive to free ride as the size of the restaurant grows and their income is less and less dependent on the effort they expend at their own table. Furthermore it suggests that restaurant management is aware of the greater chal-lenges of monitoring free riding (in the context of management monitoring and mutual service staff monitoring) within a pooled restaurant consistent with the theory of B.E.Z.T (2004). Aside from ca-pacity, ZAGAT Cost also is related to whether management decides to insti-tute a pooled system. When controlling for capacity, the relationship between pooling and ZAGAT Cost is statistically significant (t(71) = 2.513). The free rid-

ing problem could be less of an issue in restaurants that charge higher prices, where workers earn a higher tip. Servers in more expensive restaurants have less of an incentive to free ride because if they do and are fired, they may have to settle for employment at a less expensive res-taurant with a lower gross pay per shift.

Endogenous Analysis of Hiring Choice and Pooling

In assembling a service staff, if man-agement would like each server to focus on perfecting a smaller responsibility of serving a smaller amount of customers really well, it could hire a higher propor-tion of servers per capita. On the other hand, some talented servers may choose to seek employment elsewhere as they will likely earn less income with fewer tables (in the non-pooled case) or a lesser share in the pool.

An additional layer of complexity is added if a manager institutes a pooled system, which incentivizes teamwork amongst the staff as each staff member benefits from the effort of the group. This allows a manager to hire fewer servers per capita, as other servers have an incen-tive to help each other out.

I analyzed the management-hiring di-lemma in a multivariate regression of servers per capita on the dummy variable of whether a restaurant decides to pool and the pricing of a restaurant measured by ZAGAT Cost, servers per capita was: negatively related to pooling (t(71) = -0.002) at a non-statically significant level and positively related to ZAGAT Cost at a non-statistically significant level (t(71) = 0.962). The relationship between servers per capita and pooling does not support the hypothesis that management feels that the team incentive provided by us-ing a pooled system empowers them to hire fewer servers per capita.

However, the positive non-statistically significant relationship between servers per capita and ZAGAT Cost suggests that management of more expensive restau-rants may tend to hire more servers per capita than management of less expen-sive restaurants. Management of a more expensive may charge higher prices be-cause it believes the restaurant provides a superior dining experience. The increase in prices should attract talented servers to a restaurant as many customers tip based on a percentage of the overall cost of the meal (Lynn and Grassman 1990). The size of the positive non-statistically sig-nificant relationship between servers per capita and cost remains when control-ling for other fixed endogenous effects of the organizational and compensation


10 Fall 2013

structure (as well as pooling) of the res-taurant. Given the relatively small data set, there is merit in further researching the positive relationship between servers per capita and cost to see whether the re-lationship further approaches statistical significance.

Pooling’s Effect on Service QualityPooled restaurants offer a real incentive

on a nightly basis for servers to serve all customers of the restaurant, even ones not at their own table. Prior to analyzing the question, I acknowledge that there is a partial flaw in the methodology of performing a regression of a restaurant’s service quality of (an exogenous variable) and whether the restaurant is pooled (an endogenous variable). In such a regres-sion, I am examining whether pooled res-taurants in general yield a higher service quality.

Although it is difficult to extrapolate causality from such a regression, the re-gression and subsequent analysis can be used to describe whether higher service quality is generally located within pooled restaurants. I regressed ZAGAT Service on a dummy variable for whether the restaurant was pooled and found a posi-tive, yet not statistically significant rela-tionship (t(71) = 1.449). I found a similar positive, yet non-statistically significant result when performing such a regression using OpenTable Service as the depend-ent variable (t(42) = 1.212). The strength of such a relationship decreases when considering restaurants of a similar price point controlling for ZAGAT Cost in both of the analyses, (t(71) = 0.387) for ZAGAT Service and (t(42) = 0.435). This continues when controlling for other endogenous variables that differentiate a restaurant’s organizational and compensation struc-ture. Considering the small t values of the coefficients on pooling, it is difficult to ar-gue that pooled restaurants have higher service quality.

Service Quality and Visibility within

Pooled and Non-Pooled RestaurantsI now examine whether diners perceive

a difference in service quality within pooled and non-pooled restaurants as visibility decreases. I split the data set into pooled restaurants and non-pooled restaurants.

I analyzed this question on the pooled sub-set using both ZAGAT and OpenT-able’s measure of service quality, re-gressing the two measures of service on the variable capacity, controlling for the pricing of restaurants by using ZAGAT Cost. The regressions on ZAGAT’s and OpenTable’s measure of service yield, re-spectively, two negative non- statistically significant relationship for capacity (t(54) = -0.983) and (t(33) = -1.405).

The direction of these relationships hold when controlling for other fixed ef-fects for organizational and compensa-tion structure of a restaurant. The nega-tive relationship seems to remain across restaurants catering to different types of customers (socio-economic classes). The results support B.E.Z.T’s (2004) conten-tion that an increase in visibility within pooled restaurants should yield an in-crease in service quality as monitoring free riding becomes easier. However, the negative relationship between service quality and capacity is not statistically significant.

I also analyzed B.E.Z.T’s (2004) conten-tion that service quality decreases in non-pooled restaurants as visibility increases. I again used both ZAGAT and OpenT-able’s measure of service quality. Analy-sis of the non-pooled data subset suffers from the limited number of observations (only 17 ZAGAT reviewed restaurants and 9 OpenTable reviewed restaurants).

I regressed the two measures of service quality on capacity while controlling for the relative pricing of different restau-rants using ZAGAT Cost. The regressions on ZAGAT’s and OpenTable’s measure of service yield, respectively, two nega-tive non-statistically significant relation-ship for capacity (t(17) = -0.722 and t(9) = -0.669). Both relationships seem to re-main negative across the two measures of service quality when controlling for the same fixed effects for organizational and compensation structure as the pooled sub-set regressions. The results do not support B.E.Z.T’s (2004), though it is dif-ficult to refute B.E.Z.T (2004) completely given the weak relationship and the rela-tively small size of the data subset of non-pooled restaurants.

ConclusionThe relatively higher frequency of

pooled restaurants within the sample

as well as conversations with restaurant owners and general managers suggest that pooling is the dominant form of structuring compensation within New York City restaurants. Pooling’s relative dominance supports the idea that restau-rant management wishes to foster a spirit of teamwork amongst the service staff and discourage competition that could lead to unwanted behavior. However, the empirical results suggest that restau-rant management is less likely to choose pooling as the seating capacity or size of the restaurant increases and visibility decreases. Although non-pooling suffers from the problem of competition, res-taurant management will more likely se-lect it as visibility decreases because the free riding costs associated with pooling dominate as monitoring workers (both management and mutual) becomes more difficult. Furthermore, management’s re-luctance to institute a pooled system in a higher capacity environment is apparent even when one considers restaurants that target different types of customers across the socio-economic spectrum.

In general, diners don’t appear to rate pooled restaurants as providing superior service to non-pooled restaurants. How-ever, when considering only restaurants that choose to institute a pooled compen-sation structure, the results suggest that restaurants with a higher seating capac-ity and hence lower visibility are rated as having inferior service by customers consistent with B.E.Z.T (2004). While the relationship is not statistically signifi-cant across the two measures of service, it remains when controlling for different categories of restaurants such as price, whether the restaurant is over three years old and whether ownership is involved on a day to day basis. The result of in-ferior service within pooled restaurants as capacity increases is further supported by management’s reluctance to institute a pooled system in a higher capacity envi-ronment. Given the relatively small data set, there is merit in further researching the negative relationship of service qual-ity and capacity in pooled restaurants by collecting more data points in order to see whether the relationship further ap-proaches statistical significance. n

Increased visibility within a pooled restaurant makes it

easier for workers to monitor the actions of their peers and thus discourage free riding, which is consistent with the general moral hazard litera-

ture.


Fall 2013 11

The $25,000 SteakHow Revolving Door Lobbyists Gain From Political Connections

Gerard R. Fischetti

Bentley University and University of California, Berkeley


12 Fall 2013

IntroductionLobbyists act on behalf of corporations

and unions to persuade Congress to vote in a particular way.1 In doing so, lobby-ists build relationships with Congressper-sons which have resulted in a “revolving door” between K Street and Capitol Hill, in which staffers become lobbyists, lob-byists become staffers, and Congressper-sons become lobbyists. By examining the revolving door phenomenon, I am able

to understand how these connections are benefiting lobbyists.

This paper examines the robustness of the main results in Jordi Blanes i Vidal, Mirko Draca, and Christian Fons-Rosen (2012). The authors find that a lost con-

1 American League of Lobbyists. “Code of Ethics.” Last modified September 28, 2011. http://www.alldc.org/ethicscode.cfm

nection to a senator results in a 24% de-crease in revenue and a lost connection to a representative results in a 10% decrease in revenue. I use a fixed-effects estimator to arrive at a slightly different conclusion. Additionally, by looking at a politician’s rank in Congress, I provide further evi-dence that revolving door lobbyists are benefitting from their connections when a certain party is in power.

Data My data consists of 10,418 lobbyist-

period observations from 1998-2008. A period (or semester) is defined as six months. There are 1,113 individual lob-byists in my sample. This dataset was assembled by Blanes i Vidal et al. (2012) and consists of the following variables:

— The lobbyist’s name and unique lobbyist ID

— The semester(s) in which the lobbyist worked (1-22) — Lobbyist revenue, reported as the value of the lobbying contract divided by the number of lobbyists who were assigned to the contract — Dummy variables for the periods in which a senator or representative leaves Congress — The party of the politician (Democrat or Republican)2

2 Independents are reported as members of the party

—The chamber of Congress the politician belongs to (House or Senate)—Number of semesters of lobbying experienceFor my extension of the study, I addto

this database the following variables: —The name of the politician the lobbyist is connected to3

—The year the politician first entered Congress —The number of years a politician has been in Washington4 Table 1 lists the summary statistics for

U.S. revolving door lobbyists, including statistics for revolving door lobbyists who are present in the lobbying indus-try from 1998-2008 (Panel A) the types of connections as a fraction (Panel B), and descriptions of the politicians the lobby-ists are connected to, broken down by party and chamber (Panel C).with which they voted most often.

3 Because revolving door lobbyists are, by definition, staffers who have worked in Congress, I define the con-nection as their former boss. This allows me to identify one connection per lobbyist.

4 Some politicians have gaps in their years of service. I construct the variable to be the number of years since first entering Congress – regardless if their service is not continuous. My rationale is that the connection between lobbyist and politician is still relevant the more years they know each other. In thinking about seniority, a politician who leaves still has the level of influence, experience, and other connections when s/he returns.

The authors find that a lost connection to a senator

results in a 24% decrease in revenue and a lost connection

to a representative results


Fall 2013 13

Table 2 shows the seat changes in Con-gress from 2000-2008. I focus on the 109th Congress of 2005-2006 and the 110th Con-gress of 2007-2008 to understand how lobbyists gain from being connected to a politician whose party is in power, as well as how a politician’s seniority affects lobbyist revenue.

The 2004 reelection of George W. Bush corresponds with the 109th Congress and the midterm election of 2006 corresponds to the 110th Congress. I focus on these final four years of the Bush presidency as the multiple seat changes provide a useful case study. The Republicans lost 30 House seats in the 2006 election and Democrats gained 31. The Democrats also gained all six Senate seats that were previously occupied by Republicans. Ideally, I’d like to also include the 2008 election in my analysis, but my dataset does not currently have lobbyist informa-tion for 2009-2010.

Empirical Strategy I outline a replication strategy and in-

troduce my own model for addressing seniority effects in Congress and consider some theoretical limitations of my em-pirical strategy.

Model ReplicationFollowing Blanes i Vidal et al. (2012), I

estimate:(1) Rit=αi+β

SPitS+βHPit

H+Xitθ+γtpc+vit

where is the log of revenue; αi is the in-dividual lobbyist fixed effect; Pit

S denotes a lobbyist who is connected to a senator; Pit

H denotes a lobbyist who is related to a representative; X’it is a vector of con-trol variables such as experience; γt

pc are time period, by party and chamber, fixed effects; and vit is the idiosyncratic error term. I also define a vector:

which is a vector of the variables related to senator and representa-tive. The parameters of interest are βs and βH. Under the assumption that

the esti-mates of the parameters of interest will be unbiased and can therefore be inter-preted as the percent increase in revenue due to being connected to a senator and representative, respectively.

The motivation for including αi in (1) above is that there are unobservable at-tributes (such as natural ability or moti-vation) that are correlated with the con-nection to a Congressperson. Using a fixed-effects estimator eliminates this bias

under the assumption that the unobserv-able attribute of interest is time-invariant. I also de-mean (1) within lobbyists to control for unobserved heterogeneity of lobbyists.

Model Extension I specifically look at the 109th and 110th

Congress, as there was a reversal in pow-er from Republican control of both cham-bers in the 109th to Democratic control of both chambers in the 110th. I consider the following model:

(7)


14 Fall 2013

where Rit is the log of revenue; αi is the individual effects; Majority is a dummy variable that equals one when the politi-cian is a member of the majority party; Majority x Rank is the interaction for ma-jority party and rank percentile; Rank is a percentile-adjusted rank of seniority based on the Congressperson’s years in office; Expit is a control variable for lob-byist experience; γt

pc is a control, across

time, for party and chamber; and ɛit is the error term. I estimate this model to show differences across parties, rank levels and time.

This model shows the relative impor-tance of connections in the lobbyists’ net-works.

I can figure out how important a con-nection is to the lobbyist by looking at the politician’s seniority, measured by years since his/her first election. I apply my model to see how politicians of a major-ity party affect lobbyist revenue through their rankings, a metric I construct. Fixed-effects estimation is used for the same reasons outlined in Section A.

I create an “adjusted rank” which constructs percentiles from one to 100 to normalize all ranks along the same rela-tive scale. Adjusted rank is calculated by sorting the dataset by semester, party, chamber and experience. A lobbyist who has the same rank by any of these di-mensions is grouped together. Thus, for every observation of the same rank, the

variable Rank makes this adjustment ac-cording to the following equation:

(8)

Limitations Blanes i Vidal et al. (2012) compares

two groups of lobbyists: those who lost a political connection and those who did not. Their paper ignores the wider set of connections a lobbyist may have in his/her personal and professional networks, an assumption I also make. A limita-tion of their study is underestimation of the effect of connection, in general, on revenue. Lobbyists who suffered higher revenue losses after a connection was lost were more likely to drop out of the lobby-ing industry and thus were not included in the sample in later time periods. My strategy only includes lobbyists present in the lobbyist industry. This may lead to minor overestimation of results, but since I am only looking at a span of eight se-mesters from 2005-2008, this is not a great issue.

Results Table 3 displays the results of the regres-

sions in which I replicate Blanes i Vidal et al. (2012). All of the lobbyists in this sam-ple are ex-staffers of Congresspersons. I define a connection as the Congressper-son who previously employed the staffer. The result can be interpreted as the per-cent increase in revenue.

In column (1) I control for time but not

for individual fixed effects, αi. Addition-al control variables are added in each col-umn: model (2) adds a control for party (Democrat, Republican), model (3) adds a control for chamber (Senate, House), model (4) adds a control for experience (in semesters) and model (5) adds con-trols for individual fixed effects.

The connection to a senator is not sta-tistically significant until models (4) and (5), while the connection to a representa-tive becomes insignificant in model (5). The addition of controls in models (1) to (5) has little change in the coefficient for senators, which shows that differences across lobbyists were not biasing the ef-fect. However, for representatives, the addition of controls causes the coefficient to drop dramatically; the drop from (4) to (5) is the most notable because the coef-ficient becomes insignificant. This shows that unobserved heterogeneity among lobbyists biases the effect of their con-nections to representatives. Ultimately, I cannot conclude that there is any benefit to being connected to a representative. My findings are consistent with the intui-tion that being connected to a senator is more valuable than being connected to a representative.

For the extension, my dataset includes all 454 Congresspersons who served in the 109th and 110th Congresses.

Table 4 gives the results of the model given by Equation (7) and shows the ef-fects of majority status and rank on lob-byist revenue. The number of observa-tions refers to the number of groups of politicians who share the same ranking. In the first column, model (6), I estimate the effect of rank, majority and their in-teraction. Model (7) adds a control for lobbyist experience. Models (8), (9), (10), and (11) all control for lobbyist experi-ence and control for chamber and party in the following ways: (8) estimates the effects for Republican representatives; (9) for Democratic representatives; (10) for Republican senators and (11) for Demo-cratic senators.

Controlling for lobbyist experience in model (7) shows that being connected to a politician in the majority party leads to 21% higher revenue, significant at the 5% level. The politician’s rank in model (7) is not significant. I consider this the most important model in Table 4 because it es-tablishes that connection to a more expe-rienced politician isn’t necessarily indica-tive of higher revenue.

Interestingly, being connected to a politician in the majority party has signif-icant effects for lobbyist revenue. Table 4 uses the 109th Congress, when Repub-


Fall 2013 15

licans controlled the House and Senate, as its majority party baseline. The effect of being connected to a Republican Con-gressperson (estimated in models (8) and (10)) is 34% in the 109th Congress, while

being connected to a Democrat in either chamber is insignificant. The main con-clusion to draw from Table 4 is that a politician’s standing in a majority party is more important than the politician’s

status as a high-ranking Democrat or Re-publican.

Conclusion My study finds that being connected

to a senator leads to 24% higher revenue, while the value of a connection to a rep-resentative is more complicated. Being connected to a representative is not im-portant unless the representative belongs to the majority party, in which case the lobbyist’s revenue increases (33% in my

case study). More generally, I estimate that being connected to a member of the majority party results in 21% higher rev-enue.

This leads to the conclusion that be-ing connected to a majority party is more important than the politician’s relative rank. n

“Being connected to a member of the majority party results

in 21% higher revenue.”

So Sue MeMarket Reaction to Patent Litigation Verdicts and Patent Appeal Results

Lorna Zhang

Columbia University

IntroductionPatents are one of the most significant legal

instruments that protect intellectual property (IP) rights. A patent gives the inventor the ex-clusive rights to their patented idea for a lim-ited period of time, typically 20 years from the date the patent was filed. A patentable invention must be new, useful, and nonobvi-ous to a person skilled in the field of applica-tion at the time. Though new ideas resulting in useful products have an obvious economic value, these ideas are often pure public goods, rendering them unprofitable for the inventor. Patents alleviate this problem by creating a legal means of conferring excludability upon otherwise non-excludable innovations.

Recently, we have seen a steady rise in pat-ent litigation, with the number of patent liti-gations rising from 2,281 in 2000 to 5,484 in 2012, a 140%1 increase. These litigations are costly affairs, causing an average decrease in firm value of -2% upon the initial litigation announcement for 26 biotechnology suits, representing a median shareholder value loss of $20 million. Additionally, numerous stud-ies have shown that firms often choose not to apply for a patent due to the expected cost and likelihood of defending the patent in court.

Given its high cost, litigation can only serve 1 Statistic obtained from the Lex Machina intellectual prop-

erty (IP) litigation database.

its purpose of protecting valuable innovation, if court rulings are accurate. However, 116 of the 560 cases that went to trial in my sample set had verdicts that were later reversed or vacated upon appeal, a rate of about 20.7%2. In this paper, I examine whether markets, through the aggregation of individual expec-tations, are capable of indicating which cases are more likely to be overturned upon appeal. Given the wealth of information embedded in market responses to events, we would suspect that market reaction to these trials might be an indicator as to whether a verdict will be overturned upon appeal if one of the compa-nies involved is a publicly traded company.

There is ample evidence to suggest that markets have already incorporated expec-tations about the outcome of the litigation into stock prices well before a verdict is an-nounced. The premise of an event study is based on the assumption that financial mar-kets are efficient at aggregating information, and thus stock prices reflect investors’ private expectations of the results of litigation before a verdict is publicly announced. If new infor-mation is revealed at the commencement (or termination) of litigation, we expect markets

2 Statistic calculated using data provided by the Lex Machi-na IP litigation database; this rate is likely to be even higher as firms involved in cases where judgements were rendered in late 2011 or 2012 have likely not yet had enough time to file an appeal, or, if an appeal has been filed, the US Court of Appeals has likely not had the time to deliver a final ruling.

to reevaluate their holdings to reflect new ex-pectations about cash flow and risk, revaluing the firm accordingly.

Any changes in the stock prices of the com-panies involved in the litigation after a ver-dict is publicized will consist of two compo-nents: an “uncertainty removal” component and a “surprise” component. The uncertainty removal portion arises from the fact that af-ter the verdict is made public, the uncertainty surrounding the outcome of the litigation is removed, and stock prices will shift to re-flect that. The surprise component of the stock price change measures whether or not the verdict was in line with investor expecta-tions. Raghu et al finds that, at least for the defendant, the market reaction at the time of a settlement/termination of the IP litigation largely reflects discrepancies between the ex-pectations of the investors and the actual out-come. If we assume that markets are capable of accurately assessing the optimal scope and value of a patent, then any deviations from market expectations would suggest a prob-lematic ruling. The presence and magnitude of a surprise component could indicate that there is something troubling about the ruling and that it might be more likely to be over-turned in the appeals process.

Studying the predictive power of this mar-ket response will allow us to determine both whether or not market reaction is a potential


16 Fall 2013

indicator of the success of a future appeal and to what extent markets accurately assess the optimal scope and value of a patent, if at all.

My results suggest that the impact of mar-ket reaction on the probability of reversal differs significantly between claimant and de-fendant firms. Specifically, markets seem to have some predictive power in determining the likelihood that an initial verdict will be overturned upon appeal when the event study firm is the defendant. An OLS regression in-dicates that a 1 unit increase in the deviation of actual market reaction from the expected market value results in a 7.35% increase in the probability that the verdict will be re-versed upon appeal, with a p-value of roughly 11%. The positive coefficient suggests that the larger the deviation of the actual stock re-turn from the expected return, the more likely it is that the verdict will later be reversed, re-affirming the theory.

It is also possible that this reaction is some-what dampened because markets might be

anticipating an appeal, and have therefore al-ready factored some of that anticipation into the reaction. This is very plausible given the fact that over 80% of the cases in my initial sample were later appealed. However, this is only the case when the event study is done on defendant firms. When I split my sample into claimant and defendant firms and run separate regressions, the coefficient on the market re-action variable when the event study firm is the claimant is insignificant, with a p-value of around 70%. This indicates that only market reaction for defendant firms relates to prob-ability of reversal. This is likely because de-fendant firms have a much larger downside than claimant firms. A defendant firm may experience significant financial distress if it is ruled to have infringed upon the claim-ant’s patents. A decrease in their wealth and competitiveness is inevitable if the ruling is not later overturned. On the other hand, if the claimant loses, it does not have to cease production of its product or pay royalties

to the defendant firm. Thus, the claimant’s downside is essentially capped at the status quo. It is therefore unsurprising that market reactions are much larger for defendant firms. Similarly, the effect of industry character-

istics on probability of reversal is very sig-nificant for defendant firms (p-value ≈ 1%), while extremely insignificant for claimant firms (p-value ≈ 94%). These results suggest

Though new ideas resulting in useful products have an

obvious economic value, these ideas are often pure public

goods, rendering them unprof-itable for the inventor.


Fall 2013 17

that publicly traded claimant and defendant firms have markedly different characteristics and reaction magnitudes to unexpected ini-tial verdicts. Additionally, I found that when the claimant wins the trial, the verdict is sig-nificantly more likely to be overturned upon appeal. This result is very strong (p-value < 0.01 for most regressions) and consistent across regressions with different specifica-tions. Similarly, when both the claimant and defendant are publicly traded, the probability that the ruling will be reversed is significantly higher.

BackgroundPatent litigations are complicated pro-

ceedings with a significant amount of variation between cases. At any point in the process, litigation can be terminated if the parties reach a settlement agree-ment. Additionally, the judge can dismiss the case in a summary judgment if it is determined that either side does not have enough evidence to argue the infringe-ment case further, and both parties can file a motion for a summary judgment any time before the commencement of the trial.

While summary judgment rulings can also be appealed, I chose to only study cases that actually went to trial, as these are the cases that are most heavily con-tested. Additionally, if markets adjust their expectations as new information comes to light during the litigation, as theory suggests, then we would expect to see the market capitalizations of the claimant and defendant firms moving op-posite to each other as information that strengthens the claimant’s case will nec-essarily weaken the defendant’s.

Figure 1 displays the movement in the market capitalization of two firms in-volved in a patent litigation, with refer-ence lines placed at key points in the liti-

gation process. It is clear from this graph that the movement in market capitaliza-tions of the two firms mirrors one anoth-er in the period between the commence-ment of the litigation and the delivery of the jury verdict. This suggests that mar-kets are constantly adjusting their expec-

tations throughout the litigation process and will have formed reasonable expec-tations of the outcome of the litigation before the actual verdict is announced. These market cap adjustments imply that markets find patent litigations to be eco-nomically significant events, consistent with past studies on patent litigation.

Figure 1: Movement in market capi-talization of the claimant and defendant firms during litigation. Graph created using stock price and shares outstanding

data provided by the Center for Research in Security Prices

Research HypothesisIt is evident that intellectual property

rights disputes greatly affect the present value of expected cash flows of the firms involved, causing changes in the valua-tions of said firms, as in Figure 1. More-over, given that markets continuously adjust their expectations as new informa-tion is revealed throughout the course of litigation implies that markets will have

We have seen a steady rise in patent litigation, with the

number of patent litigations rising from 2,281 in 2000 to 5,484 in

2012, a 140% increase


18 Fall 2013

formed expectations about the result of the litigation before a verdict is reached. If the final verdict parallels market ex-pectations, then we would expect to see a relatively small deviation from the ex-pected stock return for both firms. How-ever, if the final verdict is not in line with expectations, then the deviations should be much larger.

Regardless of expectations, the announcement of a verdict will reduce the uncertainty surrounding the litigant firms. This will have a positive effect on all firms involved in the case because when uncertainty decreases, the risk sur-rounding the projected future cash flows of the firm also decreases. When the firm that the market expects to win a case does indeed win, there will certainly be a positive effect on that firm’s stock re-turn; however, the net effect on the other

firm is ambiguous. Though uncertainty has been reduced, the firm has lost the litigation suit. Moreover, investors’ ex-pectations are not identical; those who invest in the defendant firm may be more optimistic about the defendant’s position than those investing in the claimant, and vice versa. Thus, for example, the share-holders of the losing firms are likely to experience a negative shock even if the result is in line with market expectations. However, the magnitude of this surprise component is likely to be much smaller than if the entire market were surprised by a ruling.

Event Study MethodologyThe methodology for evaluating

whether market response to a verdict announcement can be used to assess the probability of an initial verdict being overturned in the appeals process is di-

vided into two parts. The first part is an event study. The second part is a regres-sion utilizing the results from the event study. There are four parts to every event study: (1) Defining the event day(s); (2) measuring the stock’s return during the event period; (3) estimating the expected return of the stock during this period, and (4) computing the abnormal return (actual return minus expected return).

The event date was defined as the first

date where the result(s) of the litigation were accessible to the public. This does not necessarily coincide with the final judgment date, where the results are made official. In those cases, the date of the jury verdict is used as the event date as it is the first date that the mar-kets will receive the news. Additionally, in order to ensure that the abnormal re-turn we calculate embodies the market reaction to the verdict, we use a two-day event window. This window accounts for the day before and after the verdict announcement, because we do not know what time the ruling was released to the public. If it was released after the mar-kets had closed, the reaction would not be seen until the next day.

The expected return, measured in step 3, is the return that would have accrued to shareholders in the absence of the event. There are several models to meas-ure expected return. The most widely used model, and the one used in this study, is the market model which states that, Rit=αi+βi*Rmt+eit

Rit The expected return on the stock of firm i at time t.

αi, βi Firm specific parameters measur-ing how the security varied with the mar-ket portfolio

Rmt The market return for period t.The firm-specific parameters, αi and βi;

were calculated using 200 daily returns in the period leading up the announce-ment. This period of 200 returns must

Any changes in the stock pric-es of the companies involved in the litigation after a verdict is publicized will consist of two components: an “uncer-tainty removal” component and a “surprise” component.


Fall 2013 19

be free of firm-specific shocks that might cause its returns to deviate from its base-line level as these will resulted in biased estimated parameters3. However, it is not necessary that the market as a whole be free of shocks. So long as the shock is not specific to the firm that the event study is being conducted on, then we can expect that the market returns will also reflect the effect of these events.

I used the estimated αi and βi along with the return on the market portfolio to calculate an expected return on the event study firm’s stock. The abnormal return was calculated by subtracting the actual return from the expected return. As I used a two-day event window, for each event study, the abnormal returns for day 0 and day 1 were summed to give a cumulative abnormal return (CAR). The standardized CARs were calculated using the formula CARit/sit, where sit is the standard deviation of the regression residuals.

DataThis study examines both the claim-

ants (the firm(s) seeking damages for in-fringement) and the defendants (firm(s) that have allegedly infringed) of patent infringement litigation. In court docu-ments, the first firm to file a lawsuit is labeled the “claimant” regardless of who owns the patent. For consistency, I define the person or firm that owns the patent in question as the “claimant” and the per-son or firm that has allegedly infringed on the patent the “defendant”, regard-less of who filed first. As we are inter-ested in observing the market reactions to the announcement of a verdict, at least one firm involved in the litigation must be a publicly traded company. I have excluded subsidiaries of publicly traded companies from this study as there is no data readily available that points to the importance of the subsidiary to the par-ent firm.

The data collection process was two-fold: first, litigation data was obtained and the characteristics of the case ascer-tained. Once a useable sample was as-sembled by paring down the dataset to cases where an appeal was filed with at least one publicly traded firm, an event study analysis was done for each pub-licly traded company, for a total of 142 event studies. As there was no consoli-dated list of appealed cases, I created my own dataset using litigation data from the Lex Machina database. I looked at 562 cases from 2000-2012, determining

3 This can be anything from the commencement of a litigation to a change in upper level management of the firm

whether each case had been appealed and the outcome of the appeal.

A large majority (81%) of cases that went to trial were appealed; this is un-surprising given that only cases where both firms felt strongly about their posi-tions would go to trial. The true value is actually probably even higher, as firms involved in cases resolved in 2012 likely have not had the time file an appeal.

Of the 142 event studies, 64 were re-versed upon appeal. Oftentimes, an ap-peal will not result in a simple decision to “affirm” or “reverse”, rather an appeal will be “reversed-in-part”,” affirmed-in-part”, and/or “remanded”. In these cases, I have chosen to denote any case where any portion was reversed or vacated upon appeal as “reversed,” because a re-versal of any part of the original verdict indicates that there was something prob-lematic about the initial ruling that I ex-pect the market to have captured.

AnalysisTable 1 displays three different results

of my regression estimations using a probit regression. Table 2 displays the re-sults of an ordinary least squares (OLS) regression, to interpret the results of Ta-ble 1 only at a specific point.

The OLS regression estimates that there is about a 26% increase in the probabil-ity of reversal when both companies are publicly traded compared to when only one of them is4. Further, all three regres-sion models indicate that this correlation is significant at the p<0.01 level. This re-sult corroborates previous studies which have shown that the impact of patent litigation depends on who the opposing firm is. It is unsurprising that, when both firms are publicly traded, the probability of the verdict being overturned is higher, because it is more likely that both firms will have the resources to fully pursue the expensive appeals process. The event study firm’s market capitalization is also used as a control variable as to whether a case had to be terminated due to finan-cial difficulties.

I further find that when the patent holder wins the trial, there is a much higher probability that the verdict will be overturned upon appeal. In Table 2, I find that there is roughly a 36% higher prob-ability that the case will be overturned on appeal when the patent holder, the claimant, wins the initial trial than when the non-patent holding firm, or defend-ant, wins.

4 I do not have any results for when neither company is publicly traded as in or-der to run my regression and calculate an ab-normal return, at least one company had to be publicly traded


20 Fall 2013

This might be expected when we con-sider that, for two reasons, the burden of proof is much higher for defendants than for plaintiffs. Firstly, over the past few decades, there has been a trend in policy to strengthen patent protection; as a result, patent rates, claimant suc-cess rates in infringement suits, and the number of infringement suits filed have all increased. If a firm knows that there is a high probability that the court will rule either invalidity or non-infringement when it tries to defend its patent in court, then there would be no incentive for the firm to patent their innovation. Thus, nec-essarily, the patent litigation system is be set up so that the probability that an in-valid or non-infringed patent will be de-clared valid and infringed upon is higher than the reverse situation.

Secondly, when a firm is sued for in-fringement, it will often argue that the patent in question is invalid or unen-forceable. However, any patent that has been issued has already been screened by the US Patent Office and as a result of this, proving invalidity is difficult. These two facts mean that when the non-patent holding firm does win, due to the high burden of proof required to achieve such an outcome, the verdict is less likely to be overturned upon appeal.

It is interesting that the magnitude of the defendant firm’s abnormal market re-turns is much more effective in predict-ing the probability that a verdict will be reversed than the claimant’s; however, this is not completely unexpected. As mentioned earlier, studies have shown that the defendant has much more at stake in a patent infringement case than the claimant because there is a much larg-er downside for the defendant. The worst case scenario for the claimant is that their patent is declared invalid and they lose royalties, but they would not have to stop producing their product. Additionally, it is also unclear whether the claimant will be able to take full advantage of the reduced competition should they win. Since there are usually more than two firms competing in single market, it is highly likely that other firms might come in and take advantage of the reduced competition as well.

On the other hand, if the defendant los-es, the firm could experience significant financial distress due to the damages and royalties they would be ordered to pay to the claimant firms. Even if the defendant could afford these costs, they will likely have to cease producing and marketing the offending product. This fact could significantly damage their long-term

profit prospects and cause them to lose market share, in the event that they are not able to reach a licensing agreement with the plaintiff. Given that the defend-ants in these cases have much more at stake than the claimants, the stocks of defendant firms are likely to react more strongly, both positively and negatively, to a verdict the market did not predict, and would therefore be a better indicator than the reaction of the claimant firms.

To explore this possibility, I split my sample based on whether the event study firm was the claimant or defendant, and ran both probit and OLS regressions on each sample set. The results of this re-gression are displayed in Table 3. The p-value on the coefficient of |STDCAR| for the claimant sample is 66.6% for the probit regression and 70% for the OLS regression, indicating that the magnitude

of the standardized CARs is completely insignificant in predicting the probability that the initial verdict will be overturned upon appeal when the event study firm is the claimant. However, for the defend-ant, the p-values are 10.2% and 11%, re-spectively. As mentioned above, it is pos-sible that this result is dampened by the market’s anticipation that an appeal will be filed and that the true market move-ment is in reality much larger. These re-sults suggest that it is only in the case of defendant firm event studies that market reaction is capable of providing us with a useable prediction of the probability that the initial ruling will be overturned upon appeal.

Additionally, it also appears that the effect of whether or not the firm’s indus-try is a complex technology industry on the probability of reversal differs greatly


Fall 2013 21

between claimant and defendant firms. The OLS regression indicates that when a firm is part of an industry with complex technology, there is a 29.3% increase in the probability of reversal when the firm is the defendant. However, when the firm is a claimant, the coefficient on this vari-able is completely insignificant (p-value around 94%). One possible explanation for this discrepancy could be due to the

type of companies or individuals likely to sue large, publicly traded firms. Aside from the 22 out of 83 firms where both the claimant and defendant were public-ly traded, it is possible that that claimant is a much smaller firm that is looking to capitalize on a larger firm infringing on one of their patents or a non-practicing entity (NPE). NPEs are patent owners who use their patents solely for the pur-pose of suing infringers. It is much easier for these plaintiffs to make a case when the defendant firm is in a complex tech-nology industry where the boundaries of a patented invention are less clearly defined and where a single product can consist of hundreds, if not thousands, of different patented parts and processes. At the same time, due to such complexities, it is also less difficult to make a compel-ling case for non-infringement. These cases are thus much less clear cut. All these factors combined make it much more likely that the initial verdict will be reversed upon appeal.

ConclusionUsing a market-based approach, I have

studied the relationship between the characteristics of a patent litigation case and probability of reversal upon appeal. Previous works that have used the same approach have only focused on cases where a settlement is reached, and these studies have shown that markets view patent litigations as economically signifi-cant events. Based on these results, I have chosen to look at a previously unexam-ined set of cases to determine whether market reaction, along with other attrib-

utes of the case, are capable of predicting the probability of reversal upon appeal.

My results suggest that the impact of certain case characteristics is not homoge-neous across all publicly traded firms. In particular, the importance of market reac-tion and industry type on the probability of reversal differs significantly between publicly traded claimant and defendant firms. The results show that market reac-tion is related to the probability that the verdict will be overturned upon appeal when the event study firm is the defend-ant, but is insignificant when the event study firm is the claimant. This difference confirms results from past studies that have shown there to be asymmetric ef-fects of litigation depending on whether a firm is a plaintiff or a defendant.

Additionally, the effect of whether the event study firm is in a complex technol-ogy industry also differs significantly between claimant and defendant firms. This difference suggests that there might

be a divergence in the way large, publicly traded defendant firms deal with claim-ant firms of differing sizes, especially within industries with complex technolo-gies. Given that a single product in a com-plex industry is likely to use hundreds or even thousands of different patents, when both firms are large and publicly traded, it is probable that they both produce products that mutually infringe upon the other’s patents. Rather than going to trial, it is more efficient and beneficial for both firms to enter into a cross-licensing agreement with each other. In fact, sur-veys have shown that firms in complex industries often patent their innovations for the sole purpose of strengthening their negotiating power when forming these agreements. However, when there is a significant discrepancy in the size and importance of the two firms, it is unlikely that the larger firm will have sufficient incentive to enter into a cross-licensing agreement with the smaller one. Thus,

The importance of market reaction and industry type

on the probability of reversal differs significantly between publicly traded claimant and

defendant firms


22 Fall 2013

when the smaller firm is the patent hold-er, it has no recourse but litigation5. The significant difference in the coefficient on whether or not a firm is in a complex technology industry between the claim-ant and defendant firm samples, may in fact be capturing the divergence between how a large, publicly traded firm deals with other firms of varying sizes. Fur-ther work might look into the magnitude and significance of these differences and whether smaller firms choose to litigate because they have no other option or be-cause they want to take advantage of the potential royalties that would result from winning a patent litigation suit against a large, well-endowed firm.

These results further elucidate the re-lationship between patent litigation and financial markets. I have shown that markets exhibit some capabilities in pre-dicting whether an initial verdict will be overturned upon appeal. This suggests that in some cases market forces may be more capable of rendering unbiased rulings than district courts. This is cor-roborated by the fact that my results also show that courts are consistently handing down too many initial rulings in favor of the patent holder. While this is partly due to the way that the court system has been designed, it is in reality counter-produc-tive. If potential patent holders know that there is a significantly higher probability that a ruling in their favor will be over-turned upon appeal than a ruling against them, there will still be incentives against patenting. I would argue that slightly stricter requirements should be placed on claimant firms to prove that the patents in question have been infringed upon so that more accurate rulings will be made more often, thus reducing costs for all parties involved and increasing overall welfare. n

5 When the larger firm is the patent holder, there is a higher possibility that it may determine that the costs of litigation out-weigh the benefits and thus decide not to litigate the infringed patent.


Fall 2013 23

TaperPedicAn Analysis of the Federal Reserve’s Forecasted Asset Losses in the Face of Looming Interest Rate Shocks

Jenna Rodrigues

Princeton University

Introduction The size of the Federal Reserve’s bal-

ance sheet has increased significantly throughout the recent economic reces-sion. In this study, I use data for aver-age coupon returns on mortgage-backed securities, short-term Treasury Bills, and long-term Treasury Bills in order to cre-ate a forecasting model to assess how much the value of the Fed’s core assets will decline when they raise interests rates. Looking at the predicted change in the value of the core assets on the Fed’s balance sheet that will come with an in-terest rate hike will serve as a means of assessing the risk they took on during the crisis when they expanded their holdings of each of these three assets. My empiri-cal results suggest that when the Fed de-cides to raise interest rates in an effort to initiate an exit strategy from the recent balance sheet expansion, the value of their core assets overall will drop signifi-cantly in value, with the majority of loss coming from their holdings of long-term Treasury Bills. If the Fed is still holding a large quantity of these assets when they begin to tighten monetary policy, they will experience a significant decrease in their net income. A drop in net income could have serious negative implications on the economy and the scope of mon-

etary policy. The unconventional policy decisions

that the Federal Reserve made during the recent economic recession have been un-der the microscope for the past few years. While such an active attempt to ease

monetary policy was arguably essen-tial during the peak of the recession, the Federal Reserve had to utilize extremely risky measures that will be matched with a complex exit strategy in the coming years. In its attempt to implement exten-sive easing policies when interest rates

were settled at the zero bound, the Fed significantly expanded the overall size of its balance sheet and altered the composi-tion of its asset portfolio. At first glance, it appears that the Fed made a significant amount of money through their increased holdings of these riskier assets through its balance sheet expansion and portfolio shift, but inflation becomes a concern, the Fed is likely to have to switch its trajecto-ry and begin tightening monetary policy. In initiating its exit strategy, how will the Feds’ raising of interest rate affect the val-ue of its asset portfolio? In examining the potential loss in capital the Fed is likely to undergo as they implement their exit strategy, it is also essential to consider the implications that it will have on the fu-ture of monetary policy decisions.

I plan to perform an econometric as-sessment in attempt to quantify how the value of the three core assets on the Fed’s balance sheet will change when the Fed raises interest rates. Through my fore-casting model, I will generate a series of expected asset returns based on a histori-cal period of monetary tightening. I use the mean values of these forecasted asset returns in each of the three cases to assess the difference between the baseline accu-mulated asset returns and the generated accumulated returns given a case of mon-

Looking at the predicted change in the value of the

core assets on the Fed’s bal-ance sheet that will come

with an interest rate hike will serve as a means of assessing the risk they took on during the crisis when they expanded

their holdings of each of these three assets.


24 Fall 2013

etary policy tightening. Through analyz-ing the difference between the two series of accumulated returns for each asset, I will analyze the forecasted valuation loss that will occur with the Fed’s decision to initiate contractionary monetary policy as it begins to implement their exit strate-gy. After running all three assets through this forecasting model, I will combine the three projections to simulate an overall level of net income loss that the Fed will undergo when it tightens monetary poli-cy. In the case that the model predicts that the Fed will in fact undergo a significant loss, I will proceed to analyze potential macro-level ramifications of the resulting capital loss that can be attributed to the increased risk-taking on behalf of the Fed during the crisis.

Literature ReviewBalance Sheet ExpansionSome top fed officials point to the fact

that the risk is under control and does not pose a huge threat to Federal Reserve. For quite some time, Bernanke attempted to minimize the idea of imposing risk to the public in stating that the Federal Reserve

loans that are collateralized by riskier se-curities are quite small compared with our holdings of assets with little or no credit risk (Bernanke: “The Federal Re-serve’s Balance Sheet” 1). However, In a noteworthy research article, Fed ana-lyst Asani Sarkar sets the stage for the ways in which the Fed portfolio changed throughout different stages of the crisis; beginning with providing short-term li-quidity to sound financial institutions, proceeding to provide liquidity directly to borrowers and investors in key credit markets, and finally expanding to the purchase of longer-term securities for the Fed’s portfolio (Sarkar 3). The au-thor proceeds to briefly discuss the risk associated with some of these programs as they are incorporated in the Federal Reserve’s balance sheet and the differ-ences in the level of credit risk in the dif-ferent stages of portfolio expansion and diversification. In his analysis on changes in the Fed’s balance sheet over time, Ken-neth Kuttner discusses in great depth the massive shift out of Treasuries and into private sector assets, which means the

Fed now has assumed some amount of default risk, although exactly how much is hard to know (Kuttner 3). Rudebusch writes an effective paper that delves into this concern of interest rate risk, which I will be addressing further in my analysis of the implications of the Fed’s changed balance sheet. He specifically states that the Fed’s purchase of longer-term securi-ties have been controversial, in part be-cause of the associated interest rate risk, including the possibility that increases in interest rates will cause the market value of the Fed’s portfolio to fall (Rudebusch 1).

Implications for an Exit StrategyJanet Yellen is much more direct in her

rhetoric as per her speech on March 4th, when she discusses the potential losses the Fed may experience when interest rates increase. Yellen expresses her con-cerns for the agency when she states that “the Federal Reserve has, to be sure, in-creased its exposure to interest rate risk by lengthening the average maturity of its securities holdings. As the economic re-


Fall 2013 25

$$$

$$$

OVER TIME

ASSET VALUE

INTERE

ST RAT

E

ASSET VALUE

covery strengthens and monetary policy normalizes, the Federal Reserve’s net in-terest income will likely decline” (Yellen 1). Losses may particularly occur in the case that “the Federal Reserve’s interest

expenses will increase as short-term in-terest rates rise, while reserve balances initially remain sizable. In addition, poli-cy normalization may well involve signif-icant sales of the Federal Reserve’s agen-cy securities holdings, and losses could be incurred in these sales” (Yellen 1). Yellen suggests that “projections result-ing from this exercise imply that Federal Reserve remittances to the Treasury will likely decline for a time. In some scenari-os, they decline to zero” (Yellien 1). While she concludes that “the Federal Reserve’s purchase programs will very likely prove to have been a net plus for cumulative income and remittances to the Treasury over the period from 2008 through 2025,” how the Fed is going to cope with the net income losses that it will undergo in the early stages of its exit strategy remains a question. (Yellin 1)

Mishkin, Greenlaw, Hamilton, and Hooper further performed a quantitative study to analyze potential losses that the Fed may endure based upon different versions of an exit strategy and the fiscal situation at hand. In examining a poten-tial exit strategy, the economists come to the following conclusion:

“Should it sell assets to shrink its bal-ance sheet as it has indicated is likely, the Fed will realize a capital loss on long-term securities that it bought when in-terest rates were lower. In our baseline assumptions, these forces would result in losses equal to a significant portion of Fed capital by 2018, after which these losses could gradually be worked off. But departures from the baseline, such as large-scale purchases continuing past 2013, or a more rapid rise of interest rates would saddle the Fed with losses begin-ning as early as 2016, and losses that in some cases could substantially exceed the Fed’s capital. Such a scenario would at very least present public relations chal-

lenges for the Fed and could very well impact the conduct of monetary policy.” (Greenlaw, David, et al 4).

The economists demonstrate that one major area of potential loss is “the du-ration (average term to maturity) of the Fed’s portfolio (which) peaks at nearly 11 years in 2013 with the end of new quan-titative easing.... The duration is impor-tant because as it rises, it increases the potential losses on the Fed’s portfolio as the Fed strives to return its portfolio to a more normal level upon exit in a rising rate environment” (Greenlaw, David, et al 65). The authors also focus a signifi-cant amount of energy on this overlap between monetary and fiscal policy, and come to the conclusion that “[a] fiscal risk shock occurring within the next five years would complicate matters greatly for a Fed that will be in the process of exiting from its massive balance sheet expan-sion” (Greenlaw, David, et al 81).

While the economists took a large scale approach to obtain overall loss forecasts given a set of conditions, my model will serve as a means of examining how an interest rate hike could shift the fore-casted expected returns of certain assets in the Fed’s asset portfolio, thus contrib-uting to these levels of losses that many economists have recently been alluding to. Since it is not clear where fiscal policy will be at the time of a rate hike or the stage at which the Fed will precisely be-gin to sell assets and drain reserves, the results of my study will serve as a more narrow lens of examination that can be utilized to provide a starting point for ex-amining potential losses given any set of conditional variables.

Methodology/Data In order to quantify the level of

interest rate risk the Fed took on through its changing asset portfolio over time in a roundabout manner, I constructed an econometric forecasting model to assess how a rise in interest rates could shift the value of the three core assets on the Fed’s balance sheet. Since the Fed is holding a substantial amount of these assets, a decrease in the value of these core assets would contribute to significant losses in the Fed’s net income given that they are still holding a large amount of these as-sets in their portfolio at the time that they raise interest rates. In order to reach my final stage of analysis, I performed a vec-tor autoregression of the core set of assets on the Fed’s balance sheet during the rel-evant time span. I will break up the mod-el that I used into multiple stages in order

to clarify my econometric approach:econometric approachSelecting the period of data In order to simulate a rate environment

that could mirror one that we might see when the Fed begins to raise interest rates in the near term, I will construct a fore-casting model where I will obtain shock values from time series regressions using average coupon return data from the his-torical period of interest rate hikes from ‘04-’06. To simplify potential complica-tions in the forecasting model, I will as-sume that when the FOMC begins to an-nounce an increase in interest rates in the near term, the trend will be generally up-ward sloping for two years at the least (as was the case from 2004-2006). This will al-low me to capture a forecasting segment that is likely to be similarly aligned with the trend in the fed funds rate target from the historical period. While it is unlikely that the looming rate hikes will exactly mirror the historical rate hikes of 2004 to 2006, the model will maintain more con-sistency than not when looking at a pe-riod of time where contractionary policy was implemented in the case that there was not abundant financial turmoil.

Vector Autoregression to Obtain MatrixUtilizing data on the average coupon re-

turns for the three core assets from 2000-2013 on a monthly basis, I performed a vector autoregression in order to esti-mate the expected coefficient matrix (Â). I considered the following types of as-sets in my regression, which made up a significant portion of the composition of the risky assets on the Fed’s balance sheet throughout the span of the crisis:

Short-term Treasury Bills (3-Month Re-turns)

Mortgage-Backed Securities (Barclays US MBS Index)

Long-term Treasury Bills (10-Year Re-turns)

I will assign the following variables to represent the individual asset returns: rs will represent average coupon returns on short-term Treasury Bills; rm will repre-sent average coupon returns on MBS; rl will represent average coupon returns on long-term Treasury Bills. Vector R will represent the vector of returns, taking into account the individual returns of the three assets under examination, where:

Vector R =

In the case of three time series varia-bles, the VAR consists of three equations:

rst = gssrst-1 + gsmrmt-1 + gslrlt-1 + est

The Federal Reserve had to utilize extremely risky meas-

ures that will be matched with a complex exit strategy in the

coming years.

rsrmrl


26 Fall 2013

rmt = gmsrst-1 + gmmrmt-1 + gmlrlt-1 + emt rlt = glsrst-1 + glmrmt-1 + gllrlt-1 + eltwhere the g’s are unknown coefficients

and the ext are error terms. I proceeded to calculate the following

[3 x 3] matrix (Â1) based upon the g coef-ficients after running the vector autore-gression:

γss =.9661373* γsm = -.1582282* γsl = .1150768* γms= .0079022* γmm= .9879826* γml= .0022588γls = .0224532 γlm =

.0490017 γll = .9141076*

The * symbol following the coefficient value is representative of the coefficient being significant at the 5% level.

Using the coefficients obtained from performing the three time series regres-sions above, I constructed the following coefficient matrix Â1 that will be used as a constant through the remainder of the one-year forecasting model, where:

Â1 =

In using the constants from the regres-sion outputs for each of the three time series regressions, I constructed the fol-lowing matrix that will be held constant through the remainder of the forecasting model:

Â0 =

When constructing a one-year fore-casting model for the (r) values of the three assets in consideration, I will look at a case where I will perform a baseline analysis where no shocks are introduced. This will allow me to see where the value of assets would naturally trend without the introduction of shocks to the VAR be-yond monetary policy tightening.

One-year forecasting Model Without Shocks: {Assume et = 0}I will begin my forecasting model us-

ing the (r) values from February of 2013 to construct the Rt-1 matrix in the equation to follow. I will utilize the Â0 and Â1 ma-trices that were constructed above based upon the output from the vector autore-gression.

Rt = Â0 + Â1 * Rt-1

In the first stage of my forecasting

model, I will use February 2013 data to predict March asset return values. The first period (1-month) forecast was per-formed as follows:

Rt = +

* =

The following resulting matrix will then be used as the Rt -1 value when pro-ceeding to the next stage of the model where March predicted returns will be used to predict asset return values for April:

Rt = =

I re-peated this cycle period by period until I obtained a set of predicted asset returns for 120 periods. I will introduce the first set of outputs for a year of forecasts in the results section to follow.

Results In order to assess the effectiveness of

the vector autoregression model overall, I graphed the trajectories for the returns of the three assets on a monthly basis using the projected asset returns from the vector autoregression without the implementa-tion of the vector of shocks. This graph demonstrates the forecasted monthly asset returns for each of the three assets under examination, given that there are no additional shocks to the VAR model. The fact that returns on the three assets all converge over time demonstrates the effectiveness of the VAR model in project-ing forecasted asset returns. This graph extends the timeline of the forecasted re-turns beyond the time frame in the table above, accounting for projected returns for 120 monthly periods. The graph of monthly asset returns demonstrates that even without the introduction of the vec-tor of shocks, all three series of returns on assets are increasing fairly rapidly over time. For further analysis of how asset valuation could fluctuate further, the model could be run again with the incorporation of the vector of shocks based upon the contractionary period be-ginning in 2004. For the purpose of this

study, I will only run the case where the vector of shocks is held at zero.

After the (r) values were obtained for the 120 individual month periods to ac-quire a ten-year forecast for the model without additional shocks introduced, I proceeded to utilize these forecasted (r) values of the individual assets to deter-mine the anticipated projected losses in the values of short-term Treasury Bills, long-term Treasury Bills, and mortgage-backed securities. The implied mean as-set returns for each of the three asset se-ries can be represented as follows:

m = (II – A1)-1 * A0 where the values of m, A1, and A0 are

predicted values. Discussion In examining the accumulated returns

on mortgage-backed securities, it seems that the forecasted accumulated returns are actually marginally lower when the interest rate spike is taken into account, which would make the valuation of MBS slightly higher than under benchmark conditions. Thus this particular asset class would not be negatively affected by monetary policy tightening by the Fed.

Proceeding to short-term Treasury Bills, it seems that at first glance, there is an extremely large difference between the accumulated returns of this asset in the benchmark state verse the VAR forecast-ed state. While this large gap between the VAR model forecast and the benchmark seems quite significant over the 120 pe-riods, only the first three periods of the short-term Treasury Bills are relevant in analyzing the effect an interest rate spike would have on the valuation of this as-set. In looking at the output again with a focus on the first three months of ac-

Yellen expresses her concerns for the agency when she states that “the Federal Reserve has, to be sure, increased its expo-sure to interest rate risk by lengthening the average ma-turity of its securities hold-

ings. As the economic recovery strengthens and monetary

policy normalizes, the Federal Reserve’s net interest income

will likely decline”


Fall 2013 27

cumulated asset returns for short-term Treasury Bills, the gap is significantly smaller between the benchmark and VAR forecast. While the VAR forecast is slightly larger than the benchmark over the first three month period, signifying a slight gain in accumulated returns of this asset (and thus a decrease in valuation) when interest rates are raised, the differ-ential is not large enough to be of great significance. In calculating the value loss of short-term treasuries with more pre-cision, the loss in the value of the three-month security is .0058%, which is some-what insignificant. This valuation can be calculated as follows:

Benchmark: P0 = 1 / [1 + (.001/12) * 1 + (.001/12) * 1 + .001/12)] = .99975

VAR Forecast: P0’ = 1 / [1 + (.001/12) * 1 + (.001293/12) * 1 + .001402/12)] = .99969

Valuation Loss of Asset: P0 - P0’ = .99975 - .99969 = .000058 * 100% = .0058% loss

While it is not the case that an increase in interest rates would have a signifi-cant effect on the accumulated returns of mortgage-backed securities or short-term Treasury Bills, this is not the case for long-term Treasury Bills. In looking at the accumulated asset returns graph below, it becomes apparent that over then ten-year maturity period of a long-term Treasury bill, there is a significant divergence between the benchmark ac-cumulated returns and the VAR forecast. This divergence that occurs as the asset approaches its time to maturity demon-strates that the Fed would undergo sig-nificant gains in the accumulated returns of long-term Treasury Bills when they raise interest rates. Such large increases in accumulated returns of long-Term Treasury Bills would contribute to a sig-nificantly lower valuation of this asset class, and a significant capital loss when the valuation decrease is brought to scale. In examining the degree of divergence on the graph, it seems that the Fed would ex-perience approximately a ten percent loss in the value of their holdings of long-term Treasury Bills.

In examining the degree to which the decrease in valuation will af-fect the Fed’s portfolio value on a larger scale, it is essential to revert back to the discussion of the how the asset distribu-tion and size of the Fed’s balance sheet has changed. Since the vector autoregres-sion does not predict a significant increase in accumulated reserves for short-term Treasuries and actually predicts a slight decrease for mortgage-backed securities in the set of periods relevant to their re-

spective valuations, the majority of losses in reserves to the Fed’s asset portfolio will be attributed to the increase in ac-cumulated returns on long-term Treas-ury Bills. Assuming that approximately fifty percent of the Fed’s asset portfolio is made up of long-term Treasury Bills, and there is a ten percent decrease in the valu-ation of this asset as forecasted through the VAR model, the Fed can anticipate an expected five percent decline in their overall reserves. While a five percent loss in overall reserves may not appear to be significant at first glance, it is essential to examine the overall size of the Fed’s portfolio holdings to see the scale of a five percent loss. Given the significant expansion of the Fed’s overall asset hold-ings and balance sheet size over time, the five percent loss due to their holdings of long-term Treasury Bills alone could lead to billions of dollars in losses.

This forecasted decline in overall re-serves of the Fed is quite substantial and could have significant effects on the Fed’s decision-making process moving forward. The fact that the Fed could and most likely will lose a significant amount of capital when they raise interest rates is a clear indicator that they took on a significant amount of risk through their innovative use of monetary policy tools throughout the crisis.

ConclusionWhile it is highly likely that the Fed is

going to see valuation decreases in their asset holdings when they raise interest rates, it is essential to question whether or not this is a relevant concern to the Federal Reserve. What implications would a significant decrease in the value of the Fed’s assets have on the Fed it-self and the financial system as a whole? Would this undermine the credibility of the Fed in the public’s eyes and shift the lens of monetary policy going forward? A group of economists argue that “[many] observers have expressed concern about the magnitude of balance sheet expan-sion that the Fed and other central banks have engaged in, noting the potential costs in terms of market interference, dis-ruption to the markets upon exit, poten-tial losses effectively resulting in a drain on the Treasury, and rising inflation ex-pectations, eventually leading to rising inflation” (Greenlaw, David, et al 62). A decrease in Federal Reserve net income would leave room open for turmoil in a variety of areas that could raise larger economic concerns.

In Greenlaw’s analysis, the authors con-sider what would happen if remittances from the Treasury became negative with

a decrease in the Fed’s net income into the negative range (Greenlaw, David, et al 74). They conclude that “under the Fed’s new accounting practices adopted in January 2011, when net income avail-able for remittance to Treasury falls be-low zero, this does not eat into the Fed’s contributions to capital or threaten the Fed’s operating expenses. Rather, the Fed would create new reserves against an item called the Fed’s ‘deferred asset’ account on the asset side of its balance sheet” (Greenlaw, David, et al 74). While the Fed seems to be somewhat prepared for a net income loss, there is still the po-tential for significant financial turmoil that could easily result based upon differ-ent potential exit strategies that the Fed may seek to impose.

The fact that the Fed is going to lose a significant amount of capital when they raise interest rates is likely to make them think extremely carefully about what the best time is to raise rates that would mini-mize the level of resulting loss. Beyond a monetary policy shock, “[a] fiscal risk shock occurring within the next five years would complicate matters greatly for a Fed that will be in the process of exiting from its massive balance sheet expan-sion” (Greenlaw, David, et al 81). Thus when strategizing an exit to the recent period of monetary easing, the Fed not only has to consider the implications for monetary policy, but they also must con-sider the fiscal situation at the time that they intend to tighten. With so much at stake, the Fed has a substantial amount of factors to consider when making their upcoming monetary policy decisions. n


28 Fall 2013

When the 2013 Cypriot banking crisis cul-minated in a proposal to tax insured depos-its – an unprecedented violation of Eurozone deposit insurance, policymakers questioned the sacrosanctity of deposit insurance, its role in the macroeconomy, and how depositors across Europe would interpret the unfulfilled threat.

We attempt to answer these questions using the popular framework proposed by Diamond and Dybvig in 1983.1,2 The Diamond-Dybvig model provides an ex-planation of how deposit insurance pre-vents bank runs if all depositors are fully insured. But when the model is applied to the Cypriot case, we find that it cannot capture some essential features: strategic uncertainty and bank run likelihood. For these reasons, we call for an extension of the Diamond-Dybvig model in that direc-tion.

Diamond-Dybvig ModelLiquidity CreationBanks create liquidity by investing in

an originally illiquid asset and offering liquid deposits to consumers. We can de-

1 Diamond, Douglas W., and Philip H. Dybvig. “Bank Runs, Deposit Insurance, and Liquidity.” Journal of Political Econo-my 91, no. 3 (1983): 401-19.

2 Diamond, Douglas W. “Banks and Liquidity Creation: A Simple Exposition of the Diamond-Dybvig Model.” Fed-eral Reserve Bank of Richmond Economic Quarterly 93, no. 2 (2007): 189-200.

scribe the original illiquid asset as (r1=1,

r2=R) and the new, more liquid deposit

as (r1>1, r2<R). The bank allows consum-ers to pool the risk of liquidity shocks—a kind of indirect insurance.

Given this set up, a first best Nash equi-librium is possible. At T=1, the bank gives

fraction π of consumers

r1. The remain-

ing unliquidated assets (1-πr1) be-

come worth (1- πr1)R by T=2. At this

point, the bank gives the remaining (1-π)

fraction of consumers r2 = [(1- πr1)R]/(1- π)

Bank RunEven so, there are multiple Nash equi-

libriums. Most importantly, there is an equilibrium when both Type 1 and Type 2 consumers decide to withdraw at T=1, causing a bank run. Suppose that a frac-

tion f >π of consumers decide to with-draw at T=1. From the perspective of a consumer at T=0, that fraction must be

predicted; f θ <π. If we substitute this new element into our previous deriva-

tion, then r2 = [(1- f θ r1) R]/(1- f θ).Now, consider the decision made by a

Type 2 consumer about when she should

withdraw. If r2 (f θ) ≥ r1 then she should

wait until T=2; but if r2 (f θ) ≤ r1 then she should run to the bank at T=1. Note that the decision depends wholly on her expectation about what fraction of con-sumers will withdraw at T=1. Formally,

the tipping point is when f θ > (R-r1) /

[r1(R-1)]. The change in expectations must be large, and its cause must be com-mon knowledge.

Deposit InsuranceA government has the power to elimi-

Unring the Bell?The Threat to Deposit Insurance in Cyprus

Rahul Singh

Yale University

The Diamond-Dybvig model provides an explanation of how deposit insurance pre-

vents bank runs if all deposi-tors are fully insured. But

when the model is applied to the Cypriot case, we find that it cannot capture some essen-

tial features.


Fall 2013 29

nate the risk of a bank run via full deposit insurance. Because only the government has taxation authority, it is uniquely suit-ed to offer such insurance. It can pass a law that commits itself to pay the amount consumers were promised at T=0. It is a strictly dominant strategy for a Type 2 insured consumer to not run on the bank

if she is guaranteed r2>r1 in T=2. Full deposit insurance redesigns the incen-tive structure for Type 1 and Type 2 con-sumers such that they always prefer to act their type; Type 1’s withdraw at T=1, Type 2’s withdraw at T=2, and the first best Nash equilibrium is achieved.

CyprusProposalThe financial sector of Cyprus suffered

greatly from the Greek sovereign debt restructuring in 2011.3 After Greece, Ire-land, Portugal, and Spain, it was the fifth country to seek financial help from the so-called troika: the International Mon-etary Fund, European Commission, and European Central Bank.4 In accordance with European Union standards, deposits < €100,000 were insured by the state and

3 The Guardian. “Cyprus Eurozone Bailout Prompts Anger as Savers Hand Over Possible 10% Levy.” March 16, 2013.

4 The New York Times. “Cyprus Passes Parts of Bailout Bill, but Delays Vote on Tax.” March 22, 2013.

deposits ≥ €100,000 were not insured.5

On March 16, 2013, the troika proposed a €10 billion bailout to the Cypriot finan-cial system. The plan included an unprec-edented measure: a one-off wealth tax of 9.9% on uninsured deposits and—more radically—6.7% on insured deposits. Depositors would be compensated with equivalent amounts of shares in those banks, a kind of forced equity conver-sion.6

Bank RunOur model can illustrate the consequent

bank run. We revert to analysis without deposit insurance because the proposal rendered all accounts vulnerable. Sup-pose Cypriot ratification of the proposal will happen between T=1 and T=2. Con-sumers who withdraw at T=1 will not face the one-off wealth tax while consum-ers who withdraw at T=2 will. This must modify a Type 2 consumer’s decision about when she should withdraw. Let 0 ≤ t < 1 be the fraction of deposits left af-ter the troika’s tax is imposed. Now, the Type 2 consumer should wait until T=2 if

tr2(f θ) ≥ r1; but she should run to the

5 Reuters. “Cyprus Banks Remain Closed to Avert Run on Deposits.” March 25, 2013.

6 BBC News. “Cyprus Bailout: Parliament Postpones De-bate.” March 17, 2013.

bank at T=1 if tr2(f θ) <

r1.7

Type 2 consumers came closer to the tipping point when the return at T=2 be-came worth some fraction t of what it had been. Fur-thermore, because media outlets broadcasted de-tails of the proposal, con-sumers revised their ex-pectations upward of how many would withdraw at T=1. Thus, we model first order and second order effects in this strategic environment via the in-troduction of t < 1 and the

endogenous increase in f θ, respectively.8 Note that we obtained these results in a framework that does not enjoy the stability af-forded by deposit insur-ance.

Cannot Unring the Bell

Commitment UndoneWhile Cypriot citizens

queued at ATMs, Cyp-riot parliament rejected the proposal on March

19, 2013.9 In its place, a different agree-ment was finalized on March 25. In the words of IMF Managing Director Chris-tine Lagarde, “The plan focuses on deal-ing with the two problem banks and fully protecting insured deposits in all banks;” the most radical measure was eliminated.10,11,12 We argue, however, that

7 We assume for simplicity that consumers were certain that Cypriot parliament would ratify the proposal. More properly, consumers who withdraw at T=1 do not face the one-off wealth tax while consumers who withdraw at T=2 might. We can re-flect this risk with a weighted average.

8 To simplify our analysis, we only explain the intuition behind the endogenous increase in fe. In fact, this increase im-plies a mechanism of signal transmission and belief formation. Consumers receive signals that suggest the state of the world. A consumer may expect that different consumers receive differ-ent signals. Probably, some other consumers received signals worse than the one this consumer received. The likelihood that those consumers who received worse signals will run on the bank is what influences this consumer to revise up her fe.

9 Reuters. “Cyprus Lawmakers Reject Bank Tax; Bailout in Disarray.” March 19, 2013.

10 International Monetary Fund. “IMF Statement on Cy-prus.” News release. March 24, 2013.

11 The problem banks to which Lagarde referred are Laiki and Bank of Cyprus. Under the final agreement, policymakers split Laiki into a “good bank” consisting of its insured deposits and a “bad bank” consisting of its nonperforming loans and uninsured deposits. The good bank assets will transfer to Bank of Cyprus. Shareholders, bond holders, and uninsured deposi-tors of Laiki will take losses as their frozen assets are used to resolve Laiki’s debts. Uninsured depositors in Bank of Cyprus will take forced equity conversions.

12 Eurogroup. “Eurogroup Statement on Cyprus.” News re-lease. March 25, 2013.


30 Fall 2013

demonstrating a legally easy way to de-stroy the value of deposit insurance set a dangerous precedent nonetheless.

We model the signal—the ringing of the bell—as the revelation of a new possible option for the troika at T=0. For simplic-ity, we consider the troika to be a force of nature, so ‘honor’ and ‘violate’ are not strategies but rather probabilistic out-comes. When the troika had only one op-tion, its commitment was credible; now that it has two options, its commitment is not. There is a small probability that the troika will violate deposit insurance. Thus, even if there is full deposit insur-ance, it is dubious deposit insurance and consumers may or may not run on the bank. The possibility of the tax creates de-positor uncertainty and in some sense in-creases the likelihood of bank run—a no-tion that Diamond-Dybvig does not fully articulate. Figure C presents the scenario where consumers are uncertain whether deposit insurance will be honored.

Risk to the EurozoneThe troika is the common arbiter of de-

posit insurance validity in the Eurozone. Thus, we can think of Type 2 insured depositors in not just Cyprus but any Eurozone country. The new uncertainty as to whether deposit insurance will be honored or violated heightens the risk of bank runs in each country with a weak banking system. Moreover, the interre-gional claims that characterize Europe’s financial system suggest that financial crisis in one country of the Eurozone may be contagious.13 Because of this amplifica-tion mechanism, we highlight the signifi-cance of our result.

ConclusionThe Diamond-Dybvig model does es-

tablish a first best equilibrium and a bank run equilibrium, thereby laying a theo-retical foundation. Yet it cannot describe how likely a bank run may be, given that depositors are uncertain whether their in-

13 Allen, Franklin, and Douglas Gale. “Financial Contagion.” The Journal of Political Economy 108, no. 1 (2000): 1-33.

surance will be honored. Intuitively, the troika’s threat to Cypriot deposit insur-ance creates uncertainty and may desta-bilize other weak banking systems in Eu-rope—an essential feature that still needs to be incorporated into the Diamond-Dy-bvig model. n

FIGURE C: Dubious Deposit Insurance

FIGURE B: Violated Deposit Insurance

FIGURE A: Deposit Insurance


Fall 2013 31

Rounding It OutThe Effect of Round Number Bias in U.S. and Chinese Stock Markets

Tiansheng Guo

Princeton University

IntroductionThe exploitation of “round number

bias” is ubiquitous in retail and grocery markets (grocery retailing). Prices are most often set just slightly less than a round number ($9.99, $9.95), exploiting the irrational way in which our minds convert numerical symbols to analog magnitudes for decision-making: prices just below a round number will be per-ceived to be a lot smaller than the round number price due to the change in the

leftmost digit (Thomas and Morwitz, 2005). Because this slight drop in price is perceived by the mind to be proportion-ally more, price is perceived to be lower than the value of a product, causing a dis-continuity around round number prices.

These round number biases extend beyond real assets into financial assets. Aggarwal and Lucey (2005) presented

evidence of barriers in gold prices due to round number bias, with important effects on the conditional mean and vari-ance. Johnson, Johnson and Shanthiku-mar (2008) found significant differences in returns following previous-day clos-ing prices around round numbers in U.S.

stock markets. In China, retail investors dominate the securities market, and we expect round number bias to be more pronounced. These studies suggest in-vestors’ biases for round numbers are a source of irrationality and affect the price levels, which may result in excess returns.

Figure 1

investors’ biases for round numbers are a source of irra-tionality and affect the price

levels, which may result in excess returns.


32 Fall 2013

Here, we will explore round number bias by analyzing price clustering around round numbers and excess returns con-ditional on previous-day round num-bers, for U.S. and China during the time period 2001-2011. We compare the degree of bias between U.S. and Chinese large-cap and small-cap stocks, which few previous studies have done, especially after the decimalization of U.S. stock market in 2001. In order to make the comparison valid, we will choose compara-ble US and Chinese stocks and control for varying amounts of liquidity as well as price levels in the dif-ferent data sets that may affect observed bias.

The results of this paper is interesting both practically and theoretically: a sig-nificant finding for an uneven distribution of price levels (e.g. prices end in round numbers more often) would challenge the price equals value sense of market ef-

ficiency because there is no reason that value should end in certain digits more often than others; even if the effect of round number bias on returns is too small to present arbitrage opportunities,

the findings can still help the precisely time high-frequency trades.

Literature ReviewRound number bias is an innate human

cognitive bias, and is present in prices

Figure 2


Fall 2013 33

and other metrics. Pope and Simonsohn (2010) found that in baseball, the propor-tion of batters who hit . 300 (1.4%) was four times greater than those who hit .299 (0.38%), and there were also more instance of .301 than of .298. Thomas and Morwitz (2005) found that nine-ending prices affect perception when the left-most digit changes, and that these effects are not limited to certain types of prices or products. In financial markets, if the same preferences hold for certain num-bers, we should see certain price levels appear in trades more frequently than numbers that have no preferences, and perhaps even excess returns. In a 2003 paper more germane to our question, Sonnemans examines the Ducth stock exchange from 1990-2001 and concludes that price levels cluster around round numbers, and round numbers act as price barriers. Finally, Johnson, Johnson and Shanthikumar (2008) found that inves-tors were trading differently depending on whether closing prices were margin-ally below or above a round number.

In light of these encouraging findings from past studies, we analyze how the ef-fect of the bias differs in two drastically different countries, U.S. and China. Al-though round number bias is caused by an innate cognitive flaw that is present in societies using Arabic numerals, U.S. and China have very different sets of inves-tors, laws, financial systems and culture, all of which can influence the degree of round number bias present in their re-spective stock markets.

DataTo analyze “price clustering around

round numbers” and “next day returns conditional on round number prices”, we will study daily closing prices and daily returns with cash dividend reinvested, of a set of 36 U.S. stocks traded on NYSE and 36 Chinese stocks traded on the SSE (A shares only), for the decade 6/1/2001 to 5/31/2011, which are all found on Whar-ton Research Data Services. The starting date of 6/1/2001 is after the complete deci-

malization of the U.S. stock market. The data sets exclude financial stock, are cho-sen randomly, and encompass a variety of industries.

Among the 36 U.S. and 36 Chinese stocks, half are large-cap stocks and half are small-cap stocks. The 18 U.S. large cap stocks are drawn from the 50 larg-est U.S. stocks, and the 18 Chinese large cap stocks are drawn from the 50 largest on the SSE. The 18 U.S. small cap stocks are drawn from the market cap range 500M-800M, and the 18 Chinese small cap stocks are drawn from stocks in the SSE SmallCap Index (China Securities Index).

All closing prices that are 1.00 or below were deleted to prevent cases where the leading digits are also the ending digits, to avoid complications with Benford’s Law, which states that leading digits in naturally occurring data is not uniform. Stocks go through mergers and acquisi-tions and become listed under another ticker, yielding extra data, or as with small stocks and Chinese stocks, data for earlier time periods were not available because those companies were not pub-licly traded as early as 2001. Missing or extra data has little impact as long as all observations belong in the correct catego-ry (US Large, Chinese small, etc.).

The reason for using price levels as op-posed to other measures such as P/E, P/B is that prices levels are the final numbers seen when executing trades, although P/E or P/B may have just as much evidence for numerical pricing biases, since they

Figure 3

Figure 4


34 Fall 2013

are especially susceptible to security ana-lyst’s rounding of forecasts or investors’ targets. We use daily closing prices be-cause they attract more investor attention than a random price level during the day, and can linger in the minds of investors after a day of trading, capturing much of the behavioral biases.

The reasons for drawing data from “U.S. or China” and “large cap or small cap”, are that there is plentiful data from the two countries, and the finan-cial markets of these two countries are so different in terms of listed companies, investors, and regulations, that many ex-tensions and further studies can be done based on this finding; we expect different sets of investors to be trading in large cap and small cap stocks, and different num-ber of analysts covering the stocks, so we expect the magnitude of round number biases to differ across market caps and countries. For Chinese stocks, we draw from A shares listed on the SSE because it has a large market capitalization and is not open to foreign investors, unlike the HKSE.

We choose the period June 2001 to June 2011 because the NYSE reported prices in fractions (1/16) before 2001. The benefit of this decade is that we see a rise out of the dot-com bubble and another rise and fall in prices from the Great Recession, which would allow a larger range of price levels and potential for certain prices to cluster. This decade is interesting to analyze be-cause the advent of online trading allows many more unsophisticated traders to participate in the stock market, but at the same time, institutional investors become more sophisticated.

MethodologyThe paper will use a two-part analy-

sis. The first part will analyze U.S. and Chinese stock data for price clustering around round numbers. The second part will analyze next day returns condi-tioning on round number closing price. Round number will be defined as prices ending in one round decimal ($XY.Z0) or two round decimals ($XY.00).

Price clustering is defined as prices lev-

els at which proportionally more trades occur, and abnormal next day returns as a significant regression coefficient on a variable measuring “round number”. If there were no price clustering, then the decimals of stock prices should be distributed uniformly from .00 to .99. If there were no abnormal returns, then a previous day closing price that ended in a round number would have no signifi-cant explanatory power in the next day returns.

The price clustering analysis will be graphically presented in a frequency chart, tallying the occurrences of round number closing price, categorized by country (U.S. vs. China) and size (large cap vs. small cap), followed by a linear regression (with binary dependent vari-able). The next day returns analysis will be conducted with linear regressions, as opposed to probit, for easier interpreta-tion of the coefficients. It uses ‘ifone’ as a binary variable for the last decimal being a round number, ‘iftwo’ for both deci-mals, ‘China’ for Chinese firms, and ‘big’ for large cap stocks. The two binary vari-

ables ‘ifone’ and ‘iftwo’ will be interacted with different combinations of the other variables.

This paper makes a distinction be-tween manifested and inherent bias. Due to fundamental differences in market conditions (liquidity, price levels) be-tween China and the United States, the observed round number bias may be an amplified measure of investor’s inherent bias. A second-round analysis takes this into account and includes measures of li-quidity and price levels to take out their effects from price clustering and next day returns. Due to inaccessibility of big-ask spread data in China, we use ‘volume’ as a crude measure of liquidity for Chinese stocks that may not be valid when com-paring China and U.S., but can be used for internal comparisons..

Figures 1-4 tally daily closing prices by last ending-decimal only, compared to a line of “average” representing the ex-pected number of observations assuming a uniform distribution of price levels.

In all four data sets, there is a robust and persistent clustering around prices of the form WX.Y0 and WX.Y5. Clustering is much stronger in U.S. data sets than in Chinese data sets, and slightly stronger in small cap stocks than in large cap stocks. For U.S. data sets, clustering is especially pronounced in prices that end in ‘5’s, or WX.Y5, much more so than Chinese data sets.

Next, we zoom in the same data sets by tallying closing prices by the last two ending-decimals, compared to a line rep-

Figure 5

Table 1


Fall 2013 35

resenting expected frequency given a uni-form distribution. The findings of “two decimals” analysis support that of “one decimal”: round number bias in U.S. data is manifested much more than in Chinese data, and for Chinese data, bias in small cap stocks is much more than in large cap stocks. Most of the prices ending in a ‘0’ as the last decimal have another ‘0’ or a ‘5’ as the decimal before it, so that much of the occurrences of ‘WX.Y0’ are accounted for by ‘WX.00’ and ‘WX.50’. In the U.S., round number bias is so strong that prices ending in ‘.00’ occurred twice as often as in a uniform distribution. Pric-es ending in ‘.X0’ (.10, .20, .30 etc.), and especially ‘.50’ all occurred more than the uniform distribution in both U.S. and China, and additionally in U.S. only, all prices ending in ‘.X5’ occurred more than uniform.

Note that Chinese investors preferred prices ending in ‘.X0’ and not ‘.X5’, while U.S. investors strongly preferred both. Additionally, in both U.S. large and small

caps, ‘.25’ and ‘.75’ had the greatest oc-currences of all prices ending in ‘.X5’, and are the only two price endings that are greater than their round-number counterparts, ‘.20’ and ‘.70’. This prefer-ence for “quarter” prices in the U.S. and not China can be explained by the perva-sive use of the “Quarter” coin as a cur-rency, which is a foreign concept to the Chinese. Frequent use of the “Quarter” among the U.S. population strengthens their familiarity and affinity for the .25 values. Another explanation for the clus-tering around “quarter” values is the lin-gering effects of the time period prior to decimalization of stock prices, which oc-curred right before our sample period, so U.S. investors are used to trading in 2/8, 12/16.

It is also interesting to see that Chinese data, especially for small caps, had a pref-erence for ‘.99’ and ‘.98’ and ‘.88’ that is not seen at all in U.S. data. In Chinese small cap data in particular, ‘.88’ had more occurrences than any other non-

round number (except .99 and .98). This can be attributed to ‘8’ as a lucky num-ber in the Chinese culture, with ‘88’ being even luckier; however, its unlucky coun-terpart ‘4’ did not show any difference from the average (investors did not avoid trading around that number). The Table 1 summarizes regression results. For ex-ample, in “Chinese Big stocks”, there is a 0.11195 probability of seeing the last decimal as round, and 0.01576 of seeing both as round.

Discussion – Simple Price ClusteringThe manifested bias in the data is sta-

tistically significant, and we can rank the strength of bias (from weak to strong): Chinese large cap, Chinese small cap, U.S. large cap, and U.S. small cap. The result of this initial survey is not surpris-ing, and the significantly more clustering seen in U.S. data does not prove that U.S. investors are inherently more biased than Chinese investors. The probability of see-ing a transaction on a round number is tightly tied to the bid-ask spread: if the bid-ask spread is wide, it has a greater chance of including a round number, giving the same investor more chances of choosing a round price in the neigh-borhood of prices. Also, pure frequency of seeing a round number does not ac-curately measure degree of bias. If the price level of a share is higher, a one-cent difference in price is a smaller fraction of total value traded, so that a biased trader is “penalized” less for his round number bias. Therefore, greater clustering in U.S. data sets may be explained by 1) high bid-ask spread, due to low liquidity, and 2) high nominal price per share, meaning U.S. investors incur less cost for being bi-ased. This means that “manifested bias” does not translate to “inherent bias” of investors. The next section shows price clustering analysis adjusting for liquid-ity and price levels, to analyze “inherent bias” of investors.

Results – Price Clustering Ad-justed for Liquidity and Price

Fig-

Table 2


36 Fall 2013

LevelsFirst, we show that liquidity and price

level effects can confound our price clus-tering analysis. More liquidity should mean less round number bias, while higher price levels should allow for more bias. If data sets with lower liquidity and higher price levels happen to have a higher level of round number bias, then bias can actually be driven by liquidity and price level effects, and not inherent round number bias of investors. If there are confounding effects, we need to ad-just for liquidity and price level. For in-stance, in Table 2 we demonstrate an in-terestingrelationship between US bid-ask spreads and round number closing prices from 2001-2011:

Consequently, to adjust for liquidity and price level effects, we add ‘volume’ into the regression, and use frequency weighted by price level. The weighted frequency variables ‘weightedifone’ and ‘weightediftwo’ are calculated using the following:

The weighted variables reflect degree of bias more accurately: for smaller price levels, weighted variables are greater, representing the higher percentage costs that investors incur for being biased by one-cent.

Table 3 presents a measure of inherent bias in each of the four data sets:. The effects can be seen as a rescaled measure of degree of bias, with higher meaning more bias, though it is hard to interpret. The interpretation is as fol-lows: given the same volume, being a U.S. small-cap stock (weightedifone = 1.86229, weightediftwo = 0.26531) on average increases the chance of seeing the last one (or two) decimals as round, as a one-cent fraction of their closing price, by 1.86229% (or 0.26531%). For example, (holding constant volume), a

U.S. small stock trading around $23 has an increased 10.60% chance of seeing a first decimal round than if it were a U.S. big stock: weightedifone=(100*ifone)/Pricelevel, (1.86229-1.40144)=(100*∆ifone)/23, ∆ifone= .10600.

But if it were trading around $4, the difference would be 1.8434% for a small stock over a big stock. We also notice that volume has a negative coefficient as expected, since it reduces the amount of bias through a tighter bid-ask spread. An increase in a million shares per firm-day on average reduces its ‘weightedifone’ and ‘weightediftwo’ by 0.01464% and 0.00125%. This is a substantial impact given that average volume of the four data sets vary widely.

After controlling for liquidity and price levels, Figure 16 shows that the rank-ing of degree of bias has changed: (from weakest to strongest) U.S. large-cap, Chi-nese small-cap, Chinese large-cap, and U.S. small-cap. The result suggest that in the U.S., small-cap stocks exhibit more bias than large-caps, but in China, it is the reverse. This apparent contradiction is explored in the later “Discussion” sec-tion.

Because volume may not have an equal impact across U.S. and China, for the U.S., we can use bid-ask spread data, which directly measures the window of prices surrounding a possible round number. The variable ‘usbidaskfrac’ and its powers are calculated as:

Regression (2) in Table 4 takes into ac-count that ‘usbidaskfrac’ may have a non-linear effect on degree of round number bias. It also includes interaction variables that accounts for the possibility that bid-ask window may not have an equal im-pact on U.S. large-caps and small-caps. The results here support the previous results that were found using volume as a proxy for liquidity. The negative coef-ficient on ‘big’ means that U.S. big stocks exhibit less bias holding constant price level and bid-ask ratio. Note that the co-efficients on ‘usbidaskfrac’ is positive as expected, so that higher spread induces more bias. However, the coefficients on the interaction term ‘bigxusbidask’ is negative, so that higher bid-ask spread induces bias for small stocks more so than for big stocks, possibly due to the already narrow spread in big stocks. All this is consistent for prices that end in two round decimals or just one.

In conclusion, U.S small-cap investors seem to be inherently more biased to-Figure 7

Table 3


Fall 2013 37

ward round numbers. Discussion – Price Clustering Adjust-

ed for Liquidity and Price Levels It seems contradictory that in the U.S.,

smaller stocks exhibit more bias, while in China, smaller stocks exhibit less bias. This finding can be explained by the fact that investors of large-caps and small-caps are different in U.S. and China, in characteristics and motives. Kumar (2009) shows that in U.S., individual investors with lower income and less education tend to gamble in small and local stocks, giving small-cap stocks more speculative qualities and more room for bias. Also small-cap stocks are more likely to sell-out or buy-in completely; their investors are more likely to take a new position or exit entirely, while turnover in large-caps are driven by existing holders who are merely “trading around” their posi-tions (Cevik, Thomson Reuters). U.S. large-caps have more analyst coverage (Bhushan, 1989) and more information available than small-caps, with prices ad-justing faster to new information (Hong, Lim, Stein 2000), reducing round num-ber bias. On the other hand, Hong, Jiang, Zhao (2012) find that in China, small lo-cal stocks are traded more by richer, more educated households in developed areas for status reasons (“Keeping up with the Wangs”). These investors may actually be more sophisticated than investors who trade large-caps, resulting in less bias in Chinese small-caps.

Despite accounting for liquidity and price level effects, it is surprising to see how overall U.S. data would still be as biased as Chinese data, even when

there should be more noise trading in China. It is very possible that because of different market conditions and laws around trading, volume in U.S. has dif-ferent impact than volume in China, and that volume may not be a good control for liquidity effect in round number bias (see “Discussion- Abnormal Returns”). The most important explanation, howev-er, is probably the time period we chose

to examine. Most of clustering in U.S. occurred earlier in the decade, and de-creased dramatically over the years, with the final few years exhibiting less bias than in Chinese data. This can be due to the narrowing bid-ask spread, or due to investors slowly adjusting to the recent decimal system for trading stocks, which never affected Chinese investors. Further studies can be done with bid-ask spread data for this data set, even using future data to avoid the lingering effects of deci-malization.

Abnormal Returns Like price clustering, abnormal returns

based on round numbers is complicated due to the positive correlation between bid-ask spread and probability of trading on a round number: given that investors gravitate toward round number prices, having a larger bid-ask window (more round numbers to choose from) will allow for more biases. Like in the previous sec-tion, we use ‘volumeCHN’ (measured in millions of shares) as a measure of liquid-ity in Chinese stocks due to the inacces-sibility of bid-ask spreads. Because daily rate of return is small, we scale up to per-centage return, ret =100 * RET , and then take its next day lagged returns. Again, we use weighted frequency, which is frequency of seeing ‘one’ or ‘two’ round decimals weighted by the inverse of their closing price. Variables ‘weightedifone’

Table 5

Table 4


38 Fall 2013

and ‘weightediftwo’ are meant to capture degree of bias net of price levels, so that the greater the variables, the more seri-ous the biases.

The variables ‘weightedifoneCHN’ and ‘weightediftwoCHN’, are not statistically significant in any of the regressions, and has little explanatory power on next day returns. Volume surprisingly has a posi-tive effect on next day returns, and does not seem to be capturing liquidity pre-mium (see later “Discussion”).

For U.S. data sets, we use bid-ask frac-tion instead of volume, with next-day re-turns in percentages. Regression (2) in the Table 6 illustrates that round number bias variables have significant effects on next day returns. For small-caps, more bias (in both one and two decimals) means lower next day returns, with two-decimals hav-ing even more effect. For large-caps, more bias in one-decimal similarly means low-er returns. However, for large-caps, the effect of having both decimals as round is surprisingly large and positive, strong enough to overwhelm the usual negative effect from round number bias, generat-ing higher next day returns.

Due to weighing of the variables, coef-ficients may be hard to interpret. For ex-ample, holding constant bid-ask fraction,

a small-cap stock trading at $23.40 (only last decimal as round) is expected to have a -0.03487% lower next day return than if it were not round. weightedifoneUS=(100*ifone)/23.40, ∆retUS= -0.00816×weightedifoneUS,∆retUS= -0.03487%.

But if it were a large-cap stock: ∆retUS=-.00816×weightedifoneUS-.01467×weightediftwoUS+.03445×weightediftwo×US×big=.01452%

We also observe that next day returns are increasing in bid-ask spread frac-tion, so that our bid-ask measure have captured liquidity premium. This was the opposite when regressing Chinese returns using volume as a liquidity meas-ure, where more volume resulted in high-er next day returns (see “Discussion”).

Discussion – Abnormal Returns In China, round number bias seemed

to have no explanatory power in next day returns in our regression. This could be explained by the use of volume, in-stead of bid-ask spreads, as an indicator of liquidity. According to Mei, Scheink-man, and Xiong (2009), trading volume of Chinese shares is not closely related to liquidity. In our regression, volume had positive and significant explanatory power on next day returns, which failed to take into account liquidity effect in

our data. Our findings on volume are also inconsistent with previous studies. Naughton, Truong, and Veeraraghavan (2007) found no strong link between vol-ume and returns, and Lee and Rui (2000) found that trading volume does not Granger-cause stock market returns on any of China’s four stock exchanges. This analysis can be repeated in the future by someone with access to data on Chinese bid-ask spread as a measure of liquidity.

In the U.S., we saw negative excess returns for round numbers, except for large-cap stocks ending in two round dec-imals, for which it was positive. Negative returns in U.S. small-caps is supported by past literature. Wang (2011) finds psycho-logical bias toward round numbers, and finds positive return for prices ending in $X.01, and negative return for prices just below. It is also supported by Johnson, Johnson, and Shanthikumar (2008), who find returns following closing prices just above a round number are significantly higher than returns following prices just below.

The higher return in large-caps can be explained by disproportionate amount of media attention that the big stocks attract when surpassing an important barrier, usually a round number, driving up senti-

Figure 8


Fall 2013 39

ment. Donaldson and Kim (1993) found support and resistance levels in round numbers in DJIA, which is only an index that is arbitrarily scaled and round num-bers do not say much about fundamen-tals. They also found that there were no support and resistance levels in less pop-ular indices. Future studies can look into this by taking more lagged returns- for example, next day returns may be higher, but excess returns two days or a week later may be negative.

Conclusion Although many previous studies have

found positive results with different data sets and older time periods, we expected to find similar robustness in clustering in newer data. Yet, we were uncertain whether the effect would be weaker or greater. The increase in sophistication and narrowing of bid-ask spread should give investors less chances to manifest round number bias, but may be coun-tered by increase in noise trader partici-pation.

Indeed, price clustering effect was significant and robust, across China and U.S., large and small caps. However, see-ing how U.S. data clustered significantly more than Chinese data indicated the possibility that U.S. investors are inher-ently more biased. After observing each year individually in the 2001-2011 data,

we saw that round number clustering in the U.S. has decreased substantially as the bid-ask spread has narrowed, to match that of the Chinese. After control-ling for liquidity and price level effects that have amplified bias for U.S. data, we see that the degree of round number bias is similar for U.S. and China. However, a contradictory finding is that there is more round number clustering for small-caps in the U.S., but large-caps in China. This suggests that small-cap traders in China may be more sophisticated than large-cap traders, but small-cap traders in U.S. may be more speculative than large-cap trad-ers.

As for excess returns, our findings were inconclusive for Chinese stocks, but for U.S. stocks, findings were consistent with past literature. Generally, small-cap and large-cap stocks showed negative next-day excess return around round num-bers, with the exception of large-caps ending in two round decimals, which was positive. This can justify short-term momentum strategies for U.S. large-caps when they hit significant barriers. The positive excess return can be explained by the disproportionate amount of media attention it receives and the resulting sen-timent.

The findings of this paper open up in-teresting topics for future research. We

have only looked at excess returns for numbers ending in ‘0’s, and future stud-ies can expand the definition of “round number” to include $X.50 or $X.25, and even X.88 for China, which showed clus-tering in our analysis. It would be more interesting to extend past the decimal point, for prices in $X00.00, or X88.88 for China. At the same time, analysis can be done with leading digits to see which at-tracts more bias. Given that clustering in U.S. has decreased dramatically after the decimalization of stock markets, it would be interesting to see whether it is due to increased sophistication of institu-tional traders, due to decreased bid-ask spread due to increased liquidity, or due to steady adjustment to the new decimal system. n

Table 6


40 Fall 2013

Mixed MessagesHow Firms Should Utilize Private Information

Jian Jiao

University of Pennsylvania

IntroductionThe strategic interaction between firms

and consumers can be considered a sign-aling game, in which consumers are not completely aware of the quality of the goods or services they get from a firm. It is worthwhile to study the conditions un-der which firms have enough incentive to fully reveal private information.

The combination of signaling and the real option framework is appropriate for most business situations. The concept behind the real option approach is that a firm’s investment in a project can be characterized as an American call option, where the firm has the right to buy a share of stock at a pre-specified price. The best time to invest in the project is comparable

to the optimal time to exercise the option. Analyzing an asymmetric information game using the real option approach al-lows us to capture firms’ behavior under uncertainty and understand the econom-ic incentives behind their strategies.

In this paper, I examine the effect of private information and market volatility on the firm’s optimal timing decision in the nondurable goods market. Consider a firm that is able to produce apple juice and then sell it in the market. The price of apple juice is a stochastic factor that changes exogenously, and the firm’s ob-jective is to maximize profit by entering the market at the first time the random price reaches a certain level. The firm has private information about the true qual-ity of the product, and the price level at which it starts to sell the product is a sig-nal to consumers. This paper intends to provide a theoretical analysis of and un-derstand the economic intuition behind different equilibriums and market con-ditions. It also serves as a guide to help firms behave properly under different scenarios.

Literature ReviewThe investment and financing decisions

for companies under asymmetric infor-mation have been discussed frequently in the literature. Furthermore, the literature

has increasingly emphasized the real op-tion and its application in financial eco-nomics. The real option approach states that having an opportunity to take on an investment project is similar to hold-ing a perpetual American call option. Moreover, it has been demonstrated that the timing of investment is equivalent to the timing of exercise. Both McDonald and Siegel and Dixit and Pindyck show the optimal timing of an irreversible in-vestment project when future cash flows and investment cost follow geometric Brownian motion (McDonald & Siegel, Dixit & Pindyck). Under the real option setup, the decision no longer depends di-rectly on comparing the present value of the benefits with the present value of the total cost. Rather, one of the models sug-gests that it is optimal to undertake the project when “the present value of the benefits from a project is double the in-vestment cost” (McDonald & Siegel). Re-search done by McDonald and Siegel and by Dixit and Pindyck solves the optimal timing quantitatively under both the risk-neutral and risk-averse cases. However, they do not pursue any signaling game in which firms have various options regard-ing the timing decision.

Grenadier and Wang argue that both the standard NPV rule and the real op-

The firm has private informa-tion about the true quality

of the product, and the price level at which it starts to

sell the product is a signal to consumers.


Fall 2013 41

tion rule described above fail to take into account the presence of information asymmetries. They introduce the idea of optimal contracting into real option studies; in their model, the firm’s owner and manager are two separated inter-est groups. The manager has a contract with the owner, under which he provides costly effort when exercising the option. He also has private information about the true value of the underlying project. The conclusion differs greatly from the case in which there is a single agent. Since the manager only receives part of the op-tion’s payoff, he will exercise the option later than earlier models suggest. My re-search differs from that of Grenadier and Wang since I model the company’s inter-actions with outside buyers rather than the interaction between two parties in-side the company. Even so, their research provides solid background for the inter-action between the information provider and the firm.

Compared to Morellec and Schurhoff, Grenadier and Malenko provide a brand new perspective for the real option sign-aling game. In their model, the firm has private information on the true value of the project while outsiders have to inter-pret the firm’s true type. The company cares about outsiders’ beliefs and will take them into account when making investment decisions. The whole model characterizes the optimal timing of the exercise under both perfect information and asymmetric information. Using the standard real option framework depicted by Dixit and Pindyck, the paper suggests that the optimal timing depends on the sign of a “belief function,” which quan-tifies the firm’s concern about outsiders’ belief of its type.

This paper is the benchmark of my re-search; however, the “outsiders” in my model are a group of consumers, who make decisions after observing the firm’s behavior. Grenadier first does such an analysis in his paper Information Rev-elation Through Option Exercise, where he introduces the component that directly affects the stochastically evolved value, which is also an important factor in my model. The major difference is that his paper characterizes the strategic inter-actions between N > 2 firms, where the signal sent by each individual agent dis-torts other agents’ exercise triggers. In contrast, my research designs a scenario where only one firm and one group of consumers exist. This distinction sheds light on the essence of the real option ap-proach to investment and other corporate finance decisions in financial economics.

The Model SetupA simple market is designed in which

there exists one firm and a number of consumers. The firm possesses an invest-ment opportunity to obtain some non-

durable goods at certain cost and then sell them in the market. The firm could be either low type or high type, meaning that the quality of their product is either low or high. The company’s type is de-noted by θ, which is privately known to the firm. After observing the signal sent by the company, consumers update their belief about the true quality of the prod-

uct. Their belief is denoted by . The whole game is broken down into the fol-lowing steps:

The nature decides which type the com-pany is, with probability distribution: [0.5, 0.5]. This means the company has equal chance of being either type.

The company learns its type. It will then enter the market and begin to sell the product at some price level P*. This action is defined as “exercising the op-tion”..

Consumers are also able to observe the market price P*, which serves as a signal. Immediately afterwards, they update their belief, and decide how many units to purchase.

To simplify the model, the company is assumed to receive lump-sum revenue. The game ends.

At any time t, if the nondurable goods have not become spoiled yet and the company chooses to exercise the option, it will get the profit:

is the quantity demanded by con-

sumers, Cθ denotes the per-unit cost, and ϵ is a zero-mean noise term that reflects the uncertainty over the value of the pro-ject (Grenadier and Malenko 2011). The following assumptions are also made:

It is reasonable to assume that QH > QL and CH > CL. Obviously, consumers prefer a high quality product to a low quality one, but the production of a higher qual-ity product is usually more costly. This investment opportunity is regarded as a perpetual American call option. In this model, the firm will face a random price that evolves based on geometric Brown-ian motion:

(2)

where represents the deterministic trend of this stochastic process, denotes the market volatility, and is the incre-ment of a standard Brownian motion over time. It is assumed that α and σ are constants throughout the game and that the evolution of price is publicly observ-able.

Since the company invests in nondura-ble goods, the “spoil rate” of such goods is denoted:

Since time is a continuous variable, the spoil probability is assumed to follow an exponential distribution with param-eter ρθ with cumulative density function

. As a result, the firm’s objective is to maximize the expected pre-sent value of the project:

(3)

In equation (3), E denotes expecta-tion and T represents the unknown fu-ture time of exercise. The maximization of profit is subject to equation (2) for P, so the optimal strategy for the firm is to exercise the option when P crosses some level P*. Furthermore, α must be less than ρθ. Otherwise the firm will choose to wait forever and never invest. It is assumed

that .The Perfect Information CaseNow the firm’s objective is clear and

the goal is to solve equation (3). Note

that under perfect information,. Methods for solving the maximization problem are taken from (Shreve, 2010). In this case, the only benefit from hold-

Under the real option setup, the decision no longer de-

pends directly on comparing the present value of the ben-

efits with the present value of the total cost. Rather, one of the models suggests that it is optimal to undertake the pro-ject when “the present value of the benefits from a project is double the investment cost”


42 Fall 2013

ing the perpetual American call option is the positive trend of the stochastic price. Meanwhile, if the firm chooses to wait for longer time, the risk of losing the option or of capital depreciation increases dra-matically.

Equation (2) leads to the following equation, presenting the relationship be-tween the current price and any future price:

(4) So that,

(5)Let T* denote the first time X(t) hits cer-

tain level L:

Then by the Laplace transform of drift-ed Brownian motion, Theorem 8.3.2 in (Shreve, 2010):

(6)

Note that T* is interpreted to be infinite if X(t) never hits L.

Now return to the maximization prob-lem. The firm’s objective is to choose the optimal investment trigger P*. As soon as the stochastic market price hits P*, the firm will exercise the option. Let P0 de-

note the current price (assumed to be a nonzero, small value1). As a result, equa-tion (3) becomes:

1 This means the firm will not exercise the option at t = 0, regardless of its type.

(7)

where,

(8)

Note that β is the positive root of the quadratic equation:

(9)

By the pre-specified requirement on parameters in Part II, the positive root of this equation is always greater than 1.

Now the maximization problem in the perfect information case becomes straightforward. Taking the FOC of π(P*)

With private information, the company might fool consum-

ers by exercising at a different output price


Fall 2013 43

in equation (7) with respect to P* gives:

(10)

Meanwhile, the following conditions must be satisfied in order to obtain an op-timal investment trigger,

The first condition implies that the initial market price of the product is not zero. Equation (2) shows that once the price hits zero, it will stay there forev-er. The second and third conditions put constraints on both quantity and cost. It is obvious that the number of units sold and the cost generated are both positive. Based on the property of β discussed be-fore, all these conditions are satisfied.

These conditions lead us to the solution of optimality. By solving equation (10), the following solution is obtained:

(11)

Note that the optimal investment trig-ger depends only on the company’s true type and the per-unit production cost. It is not affected by the interaction between the firm and consumers, so this optimal trigger can perfectly reveal the compa-ny’s type. Plug this result back into equa-tion (7) gives the expected present value of profit,

(12)

Now let us compare the optimal solu-tion for high type and low type respec-tively under perfect information:

(13)

(14)

So which type of company has a higher investment trigger under perfect infor-mation? As for the coefficient β, differ-entiating equation (8) with respect to ρ

yields:

(15)

and,

(16)

Therefore, as quality increases, ρ will decrease, causing a decrease in β and a higher critical investment trigger. Mean-while, CH > CL because the per-unit cost of producing these nondurable goods should increase along with quality im-provement. In other words, the firm should spend more on each unit of the product it invests if the product is of higher quality.

Other comparative statics cases are also interesting to study, as in the following set of equations:

(17)

(18)

Remember in section II, it is assumed that .

Therefore,

.

Together with equation (16), it is now safe to conclude the following proposi-tions.

Proposition 1: In the perfect informa-tion case, the firm exercises the option as soon as the stochastic price crosses the critical level P*, as shown in equation (13) and (14).

Proposition 2: High type company has higher investment trigger than low type

company, or

(19)

Proposition 3: The steeper the upward trend of the stochastic price, the higher the optimal investment trigger.

Proposition 4: The more volatile the stochastic price, the higher the optimal investment trigger.

The intuition behind proposition 2 is quite clear. The high type company must pay a larger amount of money to obtain this call option, so it would like to wait for longer time, expecting a higher market price to recover its cost. Meanwhile, its lower spoil/depreciation rate gives it the opportunity to do so. Proposition 3 im-plies that if the price grows more rapidly over time, company can obtain a higher price without waiting for too long and letting their goods get exposed to the risk of being spoiled. Furthermore, proposi-tion 4 suggests that the firm is not against high volatility because larger variance in price gives the firm opportunity to reach a higher price level in advance. Similar to proposition 3, it also does not necessarily request the firm to wait for longer period.

The classic NPV rule no longer applies in the real option framework. By the NPV rule, the firm should investment as long as π > 0, which implies P (t) > Cθ. How-ever, in the real option framework, exer-cising the option in advance incurs a loss in “opportunity benefit”. These benefits stem from the uncertainty of the market price. By waiting for a shorter period of time, the firm also sacrifices the possibil-ity of obtaining a higher market price.

The Asymmetric Information CaseWith private information, the company

might fool consumers by exercising at a different output price. In particular, a low type company could pretend to be a high type company if it exercises the option at higher price. The firm’s objective is to maximize:

in which, (20)

and B(P*) is the outsiders’ belief fun-tion.

Separating EquilibriumIn a separating Perfect Bayesian Equi-

librium (PBE), each type of company uses a strategy that fully reveals its own type. It is reasonable to assume that the


44 Fall 2013

high type company distinguishes itself from the low type company by waiting longer and exercises the option at PH

*. Meanwhile, the low type firm does not have enough of an incentive to mimic the high type in case the nondurable goods in which it considers investing spoil or depreciate too much. It will exercise the option at PL

*. Therefore, by Bayes’ rule, the consumers’ belief is derived:

And similarly,

What if consumers observe some price between PH

*and PL*? Since such strategy

is not specified in the separating equi-librium, Bayes’ rule no longer applies. The off-equilibrium belief is usually ar-bitrary. In this game, however, as long as consumers observe some price below PH

*, they will regard the firm as low type. This assumption is consistent with the logic behind the separating equilibrium. Consumers believe that high quality firm will not exercise the option at price lower than PH

*. Otherwise, the high quality firm will not be able to fully maximize its prof-it. Therefore, the belief function is sum-marized as the following:

(21)

Consumers are willing to buy QH units of product if the price they observe cor-responds to the high type optimal trigger. Any lower trigger will be considered as low type.

Constraints for obtaining separating equilibria are of the following:

Use the result obtained in equation (12),

(22)Equation (22) specifies the condition

under which neither type has enough incentive to deviate from the original optimal investment trigger. To further demonstrate the separating equilibrium constraint, the numerical example is pro-vided here. Suppose there is a corn mar-ket in which the stochastic price in equa-tion (2) has parameter.

As a result, we have .

With these values, inequality (22) be-comes:

(23)

Both conditions put strict constraints

on the relationship between the quanti-ties demanded ratio and the per-unit pro-duction cost. It has been assumed in the model that low type company sells less than high type company, so the inequal-ity above suggests that the difference in quantities demanded between low type and high type firm should not be too large. Otherwise, the first condition in (22) fails and low type firm will try to mimic the high type by exercising the op-tion later. In fact, if CL is normalized to be 1, the relationship between quantities ratio and per-unit cost ratio can be plot-ted (fig. 1).

For any given value of , as long as ies in the region between two bounds, we will be able to obtain a separating equi-

librium. If is too low, the low type firm will benefit more from waiting be-cause it will be able to sell a much higher quantity than before if it imitates the high quality firm. Note that the upper bound

is always 1. This is because is the assumption of our model. Further-more, the upper bound shows that the high quality firm will never have incen-tive to deviate from PH

*. because for them high trigger strategy strictly dominates the low trigger strategy2.

ConclusionIn this paper, the real option approach 2 Unlike low type firm that can sell more if deviate,

high quality firm does not enjoy such advantage. It will stick to the original optimal trigger.

and the signaling game framework are combined to study how uncertainty af-fects firms’ behavior under perfect and asymmetric information cases. The geo-metric Brownian progression of price is implemented throughout the paper, and it is particularly popular for nondura-ble goods that are frequently traded in the market, such as corn, wheat, etc. As hypothesized in section IV, uncertainty is seen to give firms the opportunity to explore higher prices and allows them to make decisions later. It is also discov-ered that under perfect information, high type firms wait longer, primarily because of the lower risk of losing the option as-sociating with waiting and the firms’ in-centive to obtain higher prices in order to recover cost. Note that under perfect information, firms do not need to consid-er the quantity demanded when making decisions.

With asymmetric information, how-ever, firms’ behavior might be distorted due to consumer’s belief. As pointed out in section V, if the quantity demanded by consumers fails to meet the equilibrium constraints, a low type firm will deviate from its original optimal strategy and choose to mimic a high type firm.

This paper provides rigorous quantita-tive tools for company’s decision making. It gives theoretical suggestions for the company about how to utilize the advan-tage of private information, with the goal of maximizing profits. Further research should explore the empirical side of this real option signaling model to decide what specific factors might affect firms’ strategy in the real world. n


Fall 2013 45

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