Labor Market Frictions, Capital Adjustment Costs,

and Stock Prices

Monika Merz

University of Bonn ¤

Eran Yashiv

Tel Aviv University and CEPR y

This version: September 27, 2002z

Abstract

This paper investigates the joint determination of investment in capital and the hiring of

labor and its consequences for stock prices. The model posits that labor market frictions,

adjustment costs for capital and the interaction between them a¤ect …rms’ hiring and investment

behavior. This behavior determines …rms’ pro…ts, including rents from job-worker matches, and

hence …rms’ asset values. The model’s quantitative implications are explored using structural

estimation, with aggregate time-series data for the U.S. corporate sector. The results provide for

(i) better understanding of the stochastic relationship between investment and stock prices, and

(ii) the quanti…cation of the links between labor market variables, physical capital investment,

and stock prices. The results suggest that allowing for labor market frictions to interact with

capital adjustment costs improves the performance of investment and production-based asset

pricing equations. Adjustment costs, and in particular hiring costs, play a role in explaining

mean asset values. Capital adjustment costs account for most of asset value volatility.

Key words: production-based asset pricing, investment, hiring, q-theory, matching.

¤Email: Monika.Merz@wiwi.uni-bonn.de.yE-mail: yashiv@post.tau.ac.il.zUpdated versions of the paper are available online at http://www.tau.ac.il/~yashiv/monika.html.

Labor Market Frictions, Capital Adjustment Costs and Stock Prices 1

1. Introduction

This paper investigates the joint behavior of investment in capital and the hiring of labor and its

relationship to stock price determination. The essential idea is that labor market frictions, ad-

justment costs for capital and the interaction between them a¤ect …rms’ hiring and investment

behavior. This behavior in turn determines …rms’ pro…ts, including rents from job-worker matches,

and hence …rms’ asset values. These connections are formalized in a model and structurally esti-

mated using aggregate data for the U.S. corporate sector. The estimates yield time series of capital

adjustment costs and hiring costs as well as predicted stock prices. The latter are decomposed into

the value of capital, rents associated with labor market frictions, adjustment costs of capital and

hiring costs.

These issues are of interest for a number of reasons. First, the volatile behavior of aggregate

investment has not been well accounted for by traditional models. Second, it has been di¢cult to

link the behavior of stock prices to physical investment patterns. Third, while there is increasing

acceptance of the idea that labor market frictions are useful for the understanding of cyclical

‡uctuations, little empirical work has been undertaken to quantify their e¤ects. In particular,

their operation in conjunction with capital adjustment costs and their implications for the stock

market have not been studied. The contributions of the empirical work reported here include:

better understanding of the stochastic behavior of investment and stock prices (and the relations1 We are indebted to Andy Abel and Masao Ogaki for very useful comments and suggestions. We thank seminar

participants at NYU, the NBER Summer Institute 2002, Tel Aviv University, the London School of Economics,

the CentER in Tilburg, Rice University, the June 2002 CEPR conference on dynamic aspects of unemployment at

CREST, Paris, the 2002 annual meeting of the EEA in Venice, and the December 2001 conference on …nance and

labor market frictions at the University of Bonn for comments on previous versions of the paper. We are grateful to

Craig Burnside, Zvi Eckstein, Peter Hartley, Zvi Hercowitz, Urban Jermann, Martin Lettau, Rody Manuelli, Harald

Uhlig and Itzhak Zilcha for useful suggestions, to Hoyt Bleakley, Ann Ferris and Je¤ Fuhrer for their worker ‡ows

series, and to Darina Vaissman and Michael Ornstein for able research assistance. Any errors are our own.

2

between them), and the quanti…cation of the relationships between labor market variables and both

investment in physical capital and stock prices. One of these relations formulates the ratio between

the …rms’ market value and GDP to be related to convex functions of the investment rate and the

hiring rate. Put simply, the estimated model allows us to draw lessons from the hiring of labor and

investment in capital to …rms’ market value.

The following economic intuition underlies the model: the value of the …rm is usually taken

to equal the value of its capital stock. Labor, adjusted costlessly, receives its share in output

production and, therefore, is not a part of the …rm’s value. However, this approach ignores the

cases in which the …rm has rents from labor. There may be various reasons for the existence of such

rents [see, for example Danthine and Donaldson (2002)]. Here we focus on labor market frictions

which create rents that need to be shared between …rms and workers. The part of the …rm in these

rents compensates it for the costs involved in forming the job-worker match. The expected present

value of the ‡ow of these rents may be termed ‘the asset value of the job-worker match’ and makes

up part of the …rm’s asset value. Thus, the latter is made up of the value of capital, the value of

the technology for adjusting the stock of capital, and the asset value of the match.

The model is taken to the data and estimated using GMM. The data set used has a number

of distinctive features: it makes use of gross worker ‡ow data; data on physical investment and

the capital stock, as well as asset value data, pertain to the non-…nancial corporate business sector

rather than to broader, but inappropriate, measures of the U.S. economy; alternative, time-varying

discount rates are examined; and corporate taxes are explicitly taken into account. In terms of

the estimation methodology, the use of alternative convex adjustment costs speci…cations and non-

linear, structural estimation allow for a more general framework than the quadratic cost formulation

that is prevalent in most of the literature.

The results suggest that allowing for labor market frictions to interact with capital adjust-

ment costs leads to better performance of investment and production-based asset pricing equations.

The key …ndings are that adjustment costs play a role in explaining mean asset values, and in this

context hiring costs play an even bigger role than capital adjustment costs. The latter account for

3

most of asset value volatility.

The paper contributes to three strands of literature which have, for the most part, developed

separately: …rst, it extends search and matching models of the aggregate labor market to incorporate

capital adjustment costs and shows how data on physical capital and on the stock market are

important for the understanding of hiring behavior. Second, it shows that estimation results of

the Q model have been biased by the omission of labor market frictions and demonstrates how the

model’s empirical performance is enhanced when these frictions are catered for. Third, it lends

substantive support to the production-based asset pricing model and shows to what extent it can

account for stock price behavior.

The paper proceeds as follows. Section 2 surveys the related literature and discusses the

novel aspects of the current analysis. Section 3 presents the model. Section 4 discusses the data

and the empirical methodology. Section 5 presents the results, discussing alternative speci…cations.

Section 6 derives the results’ implications with respect to the adjustment costs function, hiring

and investment behavior, and asset values. Section 7 concludes. Technical derivations and data

de…nitions are elaborated in appendices.

2. Related Literature

As noted, the paper refers and contributes to three strands of literature. In this section we brie‡y

survey the relevant papers and the relationship of the current paper to them.

2.1. Search and Matching Models

The search and matching approach to the aggregate labor market centers around the idea that

trade frictions exist in the labor market [see Mortensen and Pissarides (1999) for a recent survey].

Because of these frictions, it takes time and resources for workers and …rms to create a job-match.

Thus, at any given moment there are unemployed workers and un…lled vacancies waiting to be

matched. Two fundamental ideas underlie this approach: (i) optimizing agents undertake costly

4

search; and (ii) matching is time-consuming. The creation of the match involves rents that need

to be shared between the …rm and the worker; rent-sharing is usually modeled as a solution to

a bargaining problem. The empirical implementation of the model has focused mainly on the

estimation of matching functions [see Petrongolo and Pissarides (2001) for a survey]. More directly

related to this paper are the results in Yashiv (2000 a,b) quantifying and testing the model using

Israeli data and structural estimation.

The current paper caters for an oft-neglected issue in this literature – capital adjustment

costs interacting with hiring costs in the formation of job-worker matches. Doing so it is able to link

the asset value of the job-worker match and the asset value of the …rm. This link relates concepts

that have hitherto not been associated with each other, such as gross worker ‡ows and stock prices.

2.2. The Q Model

Models of adjustment costs of capital – in particular, Tobin’s Q [Tobin (1969) and Tobin and

Brainard (1977)] – added the value of adjustment technology to the neoclassical approach, whereby

the asset value of the …rm is the value of its capital stock. These models relate to the …rm’s

…rst-order condition equating the marginal cost of investment with the shadow price Q of installed

capital . Hayashi (1982) presented conditions under which the unobservable shadow price of capital

(marginal Q), is equal to Tobin’s Q, the ratio of the market value of a …rm’s capital stock to its

replacement value, which is observable (average Q). This result led to the use of stock market data

to assess the marginal value of capital. The Q model has been extensively studied empirically [see

Chirinko (1993) for a survey and Section 6 below for a report and discussion of key results]. The

estimated investment equations are estimates of the (inverse of the marginal) cost of adjustment

function, taking into account purchase costs as well as convex adjustment costs. The results were

criticized for a number of reasons: low R2; estimates of excessively high adjustment costs and

the signi…cance of other variables in the equation, such as those related to …nance constraints,

that were not predicted by the model. Later on, the convexity of adjustment costs was called into

5

question [see the discussion in Caballero (1999)]. More recently, several papers have explored the

Q approach within di¤erent broader frameworks with better results: Cochrane (1991, 1996) has

shown that it can account for the behavior of asset prices, provided time-varying discount rates

are applied to future streams; Christiano and Fisher (1998) show that when used as a component

of a DSGE model it accounts relatively well for moments that connect the stock market and the

business cycle; Erickson and Whited (2000) have shown that the model works well if measurement

error in …rms’ value is properly accounted for; Abel and Eberly (2002), using …rms’ panel data,

show that a model with an augmented adjustment costs function, allowing for …xed, linear and

convex costs and catering for disinvestment, performs well; Cooper and Haltiwanger (2002), using

LRD data, show that non-convexities matter for plant-level micro model but that an appropriate

convex model does well in …tting the moments of aggregate investment behavior.

The current paper uses the basic Q framework with a number of essential modi…cations.

First, it allows for the interaction of capital adjustment costs with …rms’ hiring costs:2 Second,

it caters for more general convex adjustment costs than typically used. Third, it uses a data

set that focuses on the business sector (rather than on broader, but inappropriate, parts of the

economy) and on …rms’ asset values that correspond to this sector. Fourth, it uses three equations

– two optimality conditions and an asset pricing relationship – to prescribe restrictions on the data2 Two papers – Dixit (1997) and Eberly and van Mieghem (1997) – provide a theoretical discussion of optimality

conditions for joint hiring and investment behavior in the presence of adjustment costs on both factors. In empirical

work, Nadiri and Rosen (1969) examined both capital and labor adjustment costs, and since then a number of

papers have done so. The most notable contribution in the current context is Shapiro (1986), who used structural

estimation. Our paper di¤ers along several dimensions:(i) labor adjustment costs here pertain to gross costs and

therefore are a function of gross worker ‡ows into employment; in Shapiro (and other work) they pertain to net costs

and relate to changes in the employment stock, which are considerably smaller; (ii) the current paper uses the asset

values of …rms in estimation while no such information is used in Shapiro; (iii) the latter paper uses linear-quadratic

adjustment costs, a formulation found to be too restrictive here; (iv) Shapiro’s uses data on manufacturing while here

non-…nancial corporate business data are used; (v) the discount rate in Shapiro is a T-bill rate plus a risk premium,

while here alternative time-varying rates are used.

6

underlying estimation. The literature has typically used less information, i.e., employed special

cases of the formulations studied here.

2.3. Production-Based Asset Pricing

Cochrane (1991,1996) has shown that the Q model can be used as a production-based asset pricing

model. The earlier contribution [Cochrane (1991)] shows that investment returns equal stock

returns according to the model and provides empirical support via correlation analysis, regressions

at various frequencies and, mostly, forecasting regressions. The correlation analysis, for example,

shows a 0.24 correlation at the quarterly frequency and 0.45 at the annual frequency between

aggregate investment returns and stock returns. The later contribution [Cochrane (1996)] examines

an investment-based asset pricing model whereby physical (capital) investment returns are factors

in the stochastic discount factor. The empirical work uses returns for non-residential investment and

residential investment as components of the stochastic discount factor that “prices” 10 portfolios

of NYSE stocks:The results indicate that the model performs well, as well as two standard …nance

models and better than a consumption-based model.

The current paper lends stronger support to this view. It estimates the adjustment costs

function, incorporates labor market frictions (hitherto unexamined), and explicitly shows how stock

prices are determined by hiring and investment in a model which is structurally estimated.

3. The Model

We delineate the model which serves as the basis for estimation. The parts concerned with the

labor market follow the prototypical search and matching model within a stochastic framework.3

3 See the details in Pissarides (2000).

7

3.1. The Economic Environment

The economy is populated by identical workers and …rms who live forever. All agents have rational

expectations. Workers and …rms interact in the markets for goods, labor, and …nancial assets. This

setup deviates from the standard neoclassical framework. That is, it takes time and resources for

…rms to adjust capital and for workers and …rms to create a new job-match. A job-match is created

each time a job-vacancy and an unemployed worker randomly meet. A matching function captures

this matching process in a highly stylized fashion:

Mt = M(¹t; Ut; Vt); Mt · min(Ut; Vt) ; (3.1)

The function states that in period t new matches M are produced using job-vacancies V and the

total number of unemployed workers, U , as inputs, and ¹ a stochastic shock. When M is CRS,

the matching probability for a given vacancy, q, depends on the degree of labor market tightness

µ—the ratio of job-vacancies to total unemployment:

qt =MtVt

= q(µt):

In what follows, capital letters denote aggregate variables, and small letters denote per-capita

variables. All variables are expressed in terms of the output price level.

3.2. Hiring and Investment

Firms make investment and hiring decisions. They own the physical capital stock k and decide each

period how much to invest in capital, i. They hire labor services from workers n, posting vacancies

v in an e¤ort to create new job-matches qv. Once a match is created, the …rm pays the worker

a per-period gross compensation wage rate w. Firms use physical capital and labor as inputs in

order to produce output goods y according to a constant-returns-to-scale production function f

with productivity shock z:

yt = f(zt;nt; kt); (3.3)

8

Hiring and investment involve costs. Hiring costs include advertising, screening, and train-

ing. In addition to the purchase costs, investment involves capital installation costs, learning the

use of new equipment, re-assignment of old capital lowering e¢ciency, etc. Both involve disruptions

to production. All of these costs are captured by an adjustment cost function g[it; kt; qtvt; nt] and

are assumed to reduce the …rm’s pro…ts. We assume the adjustment cost function to have constant

returns-to-scale and we allow for the interaction of hiring and capital adjustment costs. We specify

its functional form in the empirical work below.

The capital stock depreciates at the rate ± and is augmented by new investment i. The

capital stock’s law of motion equals:

kt+1 = (1 ¡ ±t)kt+ it; 0 · ±t · 1: (3.4)

Similarly, the number of matches employed by a …rm decreases at the rate Ã. It is augmented by

newly created job-matches qv:

nt+1 = (1 ¡ Ãt)nt + qtvt; 0 · Ãt · 1: (3.5)

Firms’ pro…ts before tax, ¼, equal the di¤erence between revenues net of adjustment costs

and total labor compensation, wn:

¼t = [f(zt;nt; kt) ¡ g (it; kt; qtvt;nt)] ¡wtnt : (3.6)

Every period, …rms make after-tax cash ‡ow payments cf to the owners of the …rm. These cash

‡ow payments equal pro…ts after tax minus purchases of investment goods plus investment tax

credits and depreciation allowances for new investment goods:

cft = (1 ¡ ¿ t)¼t ¡ (1 ¡Ât ¡ ¿ tDt) epIt it ; (3.7)

where ¿ t is the corporate income tax rate, Ât the investment tax credit, Dt the present discounted

value of capital depreciation allowances, and eptI the real pre-tax price of investment goods.

9

The representative …rm’s ex dividend market value in period t, st, is de…ned as follows:

st = Et£¯t+1 (st+1 + cft+1)

¤; (3.8)

where Et denotes the expectational operator conditional on information available in period t. The

discount factor between periods t + j ¡ 1 and t + j for j 2 f1; 2; :::g is given by:

¯t+j =1

1 + rt+j¡1;t+j

where rt+j¡1;t+j denotes the time-varying discount rate between periods t+j¡1 and t+j. Appendix

B contains a detailed description of how alternative values of discount rate r are computed in the

empirical work. Using the time-varying discount rates, we can alternatively de…ne the …rm’s market

value in period t as the present discounted value of future cash ‡ows4 .

st = Et

8<:

1X

j=1

à jY

i=1

¯t+i

!cft+j

9=; (3.9)

Wages are set as the Nash solution to the …rm-worker bargaining problem. The surplus

shared is the job-worker match rent, which is equal to the sum of the expected search costs of the

…rm and the worker (including foregone wages and pro…ts). This wage is …xed by the …rm and the4 In case of debt …nance in addition to equity …nance, the …rm’s value is given by:

st = est + (1 + rbt¡1)bt¡1

= Et

( 1X

j=1

ÃjY

i=1

¯t+i

!cft+j

)

est = Et

( 1X

j=1

ÃjY

i=1

¯t+i

!(cft+j ¡ rt+j¡1bt+j¡1)

)

¡rbt¡1bt¡1

where est is the equity value, rbt¡1 is the interest rate on bonds (adjusted for taxes), and bt¡1 is the existing stock of

bonds. See Bond and Meghir (1994, in particular the appendix) for the full derivation in a similar model. We do not

pursue here issues such as bankruptcy risk, di¤erential capital income taxation, and tax advantages of debt …nance.

10

worker after they meet. Because all jobs are equally productive and all workers place the same

value on leisure, the wage …xed for each job is the same everywhere. An individual …rm or worker is

too small to in‡uence the market, so they take behavior in the rest of the market as given. Formally

the wage is given by:

wt = arg max(JNt ¡JUt )Á(JFt ¡JVt )1¡Á (3.10)

where J i is the present value of state i (= N employment, U unemployment, F …lled job, V vacant

job), and the parameter Á 2 (0; 1) is the worker’s bargaining weight.

The solution is given by:

wt = Áffnt ¡ gnt + ptEt¡¯tJ

Ft+1

¢g + (1 ¡ Á)zt (3.11)

where pt = MtUt and zt is the ‡ow value of unemployment.

The representative …rm chooses sequences of it and vt in order to maximize its cum dividend

market value cft+ st :

maxfit+j;vt+jg

Et

8<:

1X

j=0

à jY

i=0¯t+i

!cft+j

9=; (3.12)

subject to the de…nition of cft+j in equation (3.7) and the following constraints:

kt+1+j = (1 ¡ ± t+j)kt+j + it+j

nt+1+j =¡1 ¡ Ãt+j

¢nt+j + qt+jvt+j

wt = Áffnt ¡ gnt + ptEt¡¯tJFt+1

¢g + (1 ¡Á)zt

The Lagrange multipliers associated with these two constraints are QKt+j and QNt+j , respectively.

These Lagrange multipliers can be interpreted as Tobin’s marginal q for physical capital, and a

Tobin’s marginal q equivalent for employment, respectively.

11

The accompanying …rst-order necessary conditions for dynamic optimality are the same for

any two consecutive periods t+j and t+j+1, j 2 f0; 1; 2; :::g. For the sake of notational simplicity,

we drop the subscript j from the respective equations to follow:

QKt = Et£¯t+1

©(1 ¡ ¿ t+1)

£fkt+1 ¡ gkt+1 ¡ nt+1wkt+1

¤+QKt+1 (1 ¡ ±t+1)

ª¤(3.13)

QKt = (1 ¡ ¿ t)¡git + pIt + ntwit

¢(3.14)

QNt = Et£¯t+1

©(1 ¡ ¿ t+1)

£fnt+1 ¡ gnt+1 ¡ wt+1 ¡nt+1wnt+1

¤+

¡1 ¡Ãt+1

¢QNt+1

ª¤(3.15)

QNt = (1 ¡ ¿ t)(gvt + ntwvt)

qt(3.16)

where we use the real after-tax price of investment goods, given by:

pIt+j =1 ¡Ât+j ¡ ¿ t+jDt+j

1 ¡ ¿ t+jepIt+j : (3.17)

Dynamic optimality requires the following two transversality conditions to be ful…lled

limT!1

ET¡¯T QKT kT+1

¢= 0 (3.18)

limT!1

ET¡¯T QNT nT+1

¢= 0:

We can summarize the …rm’s …rst-order necessary conditions from equations (3.13)-(3.16) by the

following two expressions:

F1 : (1 ¡ ¿ t)¡git + pIt +ntwit

¢= Et

8<:¯t+1 (1 ¡ ¿ t+1)

24 fkt+1 ¡ gkt+1 ¡ nt+1wkt+1

+(1 ¡ ±t+1)(git+1 + pIt+1 + nt+1wit+1)

359=;

F2 : (1 ¡ ¿ t)(gvt + ntwvt)

qt= Et

8<:¯t+1 (1 ¡ ¿ t+1)

24 fnt+1 ¡ gnt+1 ¡wt+1 ¡nt+1wnt+1

+(1 ¡Ãt+1)(gvt+1+nt+1wvt+1)

qt+1

359=; :

Solving equation (3.13) forward and using the law of iterated expectations expresses QKt as

the expected present value of future net marginal products of physical capital:

QKt = Et

8<:

1X

j=0

à jY

i=0

¯t+1+i

!Ã jY

i=0

(1 ¡ ±t+1+i)

!(1 ¡ ¿ t+1+j)

¡fkt+1+j ¡ gkt+1+j ¡ nt+1wkt+1+j

¢9=; :

(3.19)

12

It is straightforward to show that in the special case of time-invariant discount factors, no adjust-

ment costs, no taxes, and a perfectly competitive market for capital, QKt equals one. Similarly,

solving equation (3.15) forward and using the law of iterated expectations expresses QNt as the

expected present value of the future stream of surpluses arising to the …rm from an additional

job-match.:

QNt = Et

8<:

1X

j=0

à jY

i=0¯t+1+i

!Ã jY

i=0

¡1 ¡ Ãt+1+i

¢!

(1 ¡ ¿ t+1+j)¡fnt+1+j ¡ gnt+1+j ¡ wt+1+j ¡ nt+1wnt+1

¢9=; :

(3.20)

In the special case of time-invariant discount factors, no adjustment costs, no taxes, and a perfectly

competitive labor market, QNt equals zero.

3.3. Q Interpretation: Investment and Hiring Equations

Given that investment and hiring are costly, our analytical setup implicitly contains an invest-

ment function and a hiring function. In particular, the …rm’s …rst-order necessary condition for

investment establishes a link between the investment-to-capital ratio and QK, marginal Q for cap-

ital. Similarly, the optimality condition for new hires links the hiring-to-employment ratio to QN ,

marginal Q for employment.

In order to illustrate the presence of an investment function, we focus on the non-stochastic

steady state version of equation (F1) and make the following simplifying assumptions: gi is a

function of the investment-to-capital ratio only, the derivatives of w are small and are therefore

approximated to be zero, and the corporate income tax rate ¿ is zero. We can then rewrite equation

(F 1) as

giµ

ik

¶(r + ±) = fk ¡ gk ¡ pI (r + ±) : (3.21)

A simple rearrangement yields

ik

= (gi)¡1µ

fk ¡ gk ¡ pI (r + ±)r + ±

¶´ I

¡QK ¡ 1

¢; (3.22)

where QK =£fk ¡ gk +

¡1 ¡ pI

¢(r + ±)

¤= (r + ±), and I0

¡QK ¡ 1

¢> 0.

13

Equation (3.22) states that the investment-to-capital ratio increases with QK. The latter

equals one if the marginal adjustment costs of capital are zero and pI equals one.

We can derive a hiring function in an analogous manner. To illustrate this function, we

assume that gv is a function of the hiring-to-employment ratio, and the corporate income tax rate

¿ is zero. Then we can express the steady-state version of equation (F2) as follows:

gv¡qvn

¢

q(r +Ã) = fn ¡ gn¡ w: (3.23)

Rearranging this equation yields

qvn

= (gv)¡1·fn ¡ gn¡ w

r +Ãq¸

´ H£QNq

¤; (3.24)

where QN = [fn ¡ gn¡ w]= (r +Ã), and H0 £QNq¤

> 0.

According to equation (3.24), hiring rates increase with QN: The hiring rate also rises

with the probability of a vacancy leading to a new job-match, q. QN equals zero if the marginal

adjustment costs of employment are zero and labor is paid its marginal product.

It should be emphasized that the above is but a simple illustration. In fact it turns out

that the interaction between investment and hiring rates is essential, and therefore gi and gv are

functions of both investment and hiring rates.

3.4. Implications For Asset Values

We use standard asset-pricing theory to derive the implications of the model for the links between

the asset value of the …rm and the asset value of the job-worker match. As stated in equation (3.8),

the …rm’s period t market value is de…ned as the expected discounted pre-dividend market value

of the following period:

st = Et£¯t+1 (st+1 + cft+1)

¤: (3.25)

The …rm’s market value can be decomposed into the sum of the value due to physical capital, #kt ,

and the value due to the stock of employment, #nt . We label the latter fraction of the …rm’s asset

14

value the asset value of the job-worker match and express st as

st = #kt + #nt = Eth¯t+1

³#kt+1 + cfkt+1

´i+ Et

£¯t+1

¡#nt+1 + cfnt+1

¢¤; (3.26)

where

cft = (1 ¡ ¿ t)£f(nt; kt) ¡ g [it; kt; qtvt; nt] ¡wtnt ¡ pIt it

¤(3.27)

Using the constant returns-to-scale properties of the production function f and of the adjustment

cost function, g, this stream of maximized cash ‡ow payments can be rewritten as

cft = (1 ¡ ¿ t)¡fktkt + fntnt ¡wtnt ¡ pIt it ¡ gktkt ¡ gitit ¡ gntnt ¡ gvtvt

¢

= (1 ¡ ¿ t)£¡

fktkt ¡ pIt it ¡ gktkt ¡ gitit¢

+ (fntnt ¡ wtnt ¡ gntnt ¡ gvtvt)¤

´ cfkt + cfnt :

In order to establish a link between the …rm’s value and its stock of capital and employment

using the …rst-order necessary condition (FONC) we manipulate the latter equation to obtain (see

Appendix A for the full derivation):

st = #kt +#nt = kt+1QKt + nt+1QNt : (3.28)

where QKt and QNt are de…ned in equations (3.19) and (3.20), respectively.

Alternatively, we can express the …rm’s market value in period t as follows:

st = kt+1Et©¯t+1 (1 ¡ ¿ t+1)

£fkt+1 ¡ gkt+1 ¡nt+1wkt+1 +(1 ¡ ±t+1)(git+1 + pIt+1 + nt+1wit+1 )

¤ª(3.29)

+nt+1Et½

¯t+1 (1 ¡ ¿ t+1)·fnt+1 ¡ gnt+1 ¡ wt+1 ¡ nt+1wnt+1 +(1 ¡ Ãt+1)

(gvt+1 + nt+1wvt+1)qt+1

¸¾

We turn now to explore the empirical implications of the model.

4. Data and Methodology

The main idea underlying the empirical work is to explain …rms’ joint hiring and investment be-

havior and to relate it to their asset value. We present the methodology and the key relations to

be studied empirically, including a discussion of the data and the alternative speci…cations used.

15

4.1. Parameterization

To quantify the model we need to parameterize the relevant functions. For the production function

we use a standard Cobb-Douglas:

f(zt;nt; kt) = eztnt®k1¡®t ; 0 < ® < 1: (4.1)

We parameterize the adjustment cost function g as follows:

g(¢) =·

g1´1

( itkt

)´1 + g2´2

(qtvtnt

)´2 + g3´3

( itkt

qtvtnt

)´3¸

f(zt;nt; kt): (4.2)

This generalized convex function is linearly homogenous in i;k; v and n. It postulates that costs

are proportional to output, and that they increase in investment and hiring rates: The third term

in square brackets expresses interaction of capital and labor adjustment costs. The parameters gi,

i = 1; 2;3 express scale, and ´i express the elasticity of costs with respect to the di¤erent arguments.

The function encompasses the widely used quadratic case for which ´1 = ´2 = 2. This generalized

functional form proved useful in structural estimation of the search and matching model presented

in Yashiv (2000a). The estimates of these parameters will allow the quanti…cation of the derivatives

git and gvt that appear in the …rms’ FONC.5

4.2. The Data

Our data sample is quarterly, corporate sector data for the U.S. economy in the period 1976:1-

1997:4.6 In what follows we brie‡y describe the data set and emphasize its distinctive features; for

full de…nitions and sources see Appendix B.5 We also try the slightly more general formulation:

g(¢) =·g1´1

( itkt

)´1 + g2´2

(qtvtnt

)´2 + g3µitkt

¶´3 µqtvtnt

¶´4¸f(zt;nt; kt):

as discussed below.6 The sample period is constrained by the availability of consistent gross worker ‡ow data.

16

For output f, capital k and investment i we use a relatively new data set on the non-…nancial

corporate business (NFCB) sector recently published by the BEA.7 We use a series for depreciation

± from the same source. This data set leaves out variables that are sometimes used but that are

not consistent with the above model, such as residential or government investment.

For gross hiring ‡ows qv we use adjusted CPS data as computed by Bleakely et al (1999).

Two aspects of the data merit attention: (i) We use ‡ows into employment from both unemployment

and out of the labor force; the latter ‡ow is sizeable, and in terms of the model is no di¤erent from

unemployment to employment ‡ows. (ii) The data ‡ows are adjusted to cater for misclassi…cation

and measurement error; see Bleakely et al (1999) for an extensive discussion of the adjustment

methodology. Note that the gross hiring ‡ows are substantially bigger than net ‡ows: the former

has a mean of 8.9% per quarter, while the latter averages 0.5% per quarter: We derive the separation

rate à by solving it out of the dynamic equation of labor (equation 3.5 above). For employment n

we use two alternative BLS employment measures. For the labor share of income wnf we use the

compensation of employees (the sum of wage and salary accruals and supplements to wages and

salaries) as a fraction of the gross product of the non…nancial corporate sector (from NIPA).

For the asset value s we use the market value of non-farm, non-…nancial business. This

value is the sum of …nancial liabilities and equity less …nancial assets. The data are taken from Hall

(2001) based on the Fed Flow of Funds accounts. For the discount rate r we use a weighted average

of the returns to debt (using a commercial paper rate) and to equity (using CRSP returns). We also

test two alternatives: the SP500 rate of change, and the rate of non-durable consumption growth,

which serves as the discount rate in a DSGE model with log utility. Table 1 presents summary

statistics.

Table 17 See www.bea.doc.gov/bea/ARTICLES/NATIONAL/NIPAREL/2000/0400fxacdg.pdf

17

4.3. Methodology

We structurally estimate the …rms’ …rst-order necessary conditions (F1) and (F2), and the as-

set pricing equation (3.29) using Hansen’s (1982) generalized method of moments (GMM). The

moment conditions estimated are those obtained under rational expectations. That is, the …rms’

expectational errors are orthogonal to any variable in their information set at the time of the in-

vestment and hiring decisions. The moment conditions are derived by replacing expected values

with actual values plus expectational errors (j) and specifying that the errors are orthogonal to the

instruments Z i.e. E(jt ­ Zt) = 0: We formulate the equations in stationary terms.8

We explore a number of alternative speci…cations:

1) Functional form of the g function and its degree of convexity. A major issue proves to

be the functional form and degree of convexity of the g function. The literature has for the most

part assumed the quadratic form. We examine more general convex functions, either by estimating

the power parameters (´1;´2;´3) or by constraining them to take di¤erent values. We also allow for

an asymmetric formulation for the interaction term, i.e. g3( itkt )´3(qtvtnt )´4 rather than g3´3 (

itktqtvtnt

)´3.

2) Instrument sets. We use alternative instrument sets in terms of variables and number of

lags. The instrument sets di¤er across the three equations and include lags of variables appearing

in the corresponding equation.

3) Variables’ formulation. We check the e¤ect of using alternative time series for some of

the variables, which have multiple representations. These include ±;Ã and ¯:

We use two criteria to judge the results. After verifying that the estimates of the g function

satisfy the conditions for convexity with respect to the decision variables i and v; we apply two

major GMM test statistics (see the discussion in Ogaki and Jang (2002), in particular chapters

3.2.3, 9 and 10): the J-statistic test of the overidentifying restrictions proposed by Hansen (1982)

and the Noise Ratio statistic proposed by Durlauf and Hall (1990). The latter is based on the8 In order to induce stationarity we divide the FONC for capital by ft+1

kt+1and the FONC for labor by ft+1

nt+1. We

divide the asset pricing equation throughout by the level of output, f:

18

following rationale: under the null hypothesis, the error described above is a white noise forecast

error. Under any alternative, the error is the sum of white noise and a variable (St) that represents

the deviation of the error from white noise, and is called “the model noise” i.e. jt+1 = et+1 + St

where et+1 is the white noise “new information.” An estimate of St - to be denoted^St - may be

obtained by projecting jt+1 on the information set at time t. We compute it by running an OLS

regression of jt+1 on the variables included in the instrument set. Durlauf and Hall show that

var(^St) < var(St). The Noise Ratio statistic is then de…ned as: N:R: = var(

^St)

var(jt+1)which is a lower

bound on the percentage of var (jt+1) attributable to model noise.

5. Results

The focal point of the empirical work is estimation of the parameters of the adjustment costs

function g. These estimates allow us to generate time series for the costs of hiring and investing,

and for asset values. The literature has typically used the quadratic formulation and ignored the

interaction between hiring and investment costs. It turns out that modifying this speci…cation can

substantially improve the results. We report alternative speci…cations, including unconstrained

powers and alternative forms of constrained parameters.

Table 2 reports in four panels the results of the joint GMM estimation of equations F1;

F2 and (3.29). We present the point estimates of the power parameters ´1, ´2; and ´3; the scale

parameters g1; g2; and g3; and the production function parameter ®; the standard errors of the

estimates (except where constrained) and the test statistics discussed above.

Table 2

We start o¤ in panel (a) with estimation of the power parameters. In column 1 all power

parameters are freely estimated, using the more general formulation of the interaction term dis-

cussed above, i.e. g3( itkt )´3(qtvtnt )´4: The estimates of the scale parameters exhibit large standard

errors. The other columns show that constraining the power parameters yields estimates with much

19

lower standard errors and better test statistics. Following the point estimates of column 1 and some

experimentation, we use the following constraints in columns 2-3: ´2 is freely estimated, ´1 is con-

strained to be ´2 +1; while ´3 and ´4 are constrained to be ´2 ¡K where K 2 (0:7; 0:8; 0:9): The

estimates point to ´2 = 2 with a low standard error. There does not seem to be much importance

for the di¤erentiation of ´3 and ´4: The point estimates of the scale parameters are similar across

the two columns, and the test statistics are relatively good. The production function labor para-

meter ® is estimated at values around 0.67, which is a reasonable point estimate. Thus panel (a)

points to a cubic formulation for gross investment costs (´1 = 3), quadratic formulation for gross

hiring costs (´2 = 2), and an approximately linear interaction term (´3 = ´4 = 1:2).

Panel (b) reports variations on this basic speci…cation. Here we go back to the symmetric

speci…cation of the interaction term, i.e. g3´3 (itktqtvtnt )´3 : Columns 1-4 report alternative instrument

sets, outlined in the notes to the table. The point estimates (and thus the implied cost function)

are very similar across these columns. The major di¤erence is that with additional instruments,

the standard errors drop and the p-values improve. The noise ratios however tend to worsen.9

Columns 5-7 report three power speci…cations where the powers are …xed at di¤erent values

in the neighbourhood of the ones freely estimated. This yields lower point estimates (in absolute

value) for the scale parameters, lower standard errors for all estimated parameters, but the test

statistics worsen. Because of the latter feature the freely estimated ´2 speci…cations are to be

preferred. We explore below the implications of the two columns with the best test statistics –

column 1, which has the lowest noise ratios, and column 3, which has the highest p-value.

Panel (c) looks at other formulations of the variables, using the speci…cation of column

(1) of panel (b). Column 1 in this panel uses …xed values for the depreciation rate (±) and the

separation rate (Ã) employing sample averages. Column 2 uses a discount factor based on the rate

of growth of non-durable consumption while column 3 uses a discount factor based on the SP500

rate of change (see Appendix B). Finally, column 4 uses a …xed discount factor ¯ = 0:985: The

…xed ± and à do not change the results but the alternative discount factor speci…cations produce9 The noise ratio does not employ corrections of the type used in adjusted R2 computations, hence these results.

20

bad results: columns 2 and 3 yield g functions that do not satisfy the convexity conditions as well

as high ® estimates. In these columns and in column 4, the standard errors increase, and the

p-values indicate rejection. Thus the speci…cation of the discount factor seems to be important for

the results.

Panel (d) attempts to gauge the added value of di¤erent components of the afore-going

speci…cations. Column 1 reports the “traditional” equation estimated in the Q literature: quadratic

adjustment costs of capital only. The results imply a reasonable cost function: a sample average of

1% of output for total costs and a sample mean of 0.84 of average output (fk ) for marginal costs.

However its test statistics indicate strong rejection. Column 2 merits special attention. It takes

the same power speci…cation for ´1 and ´2 as used in the preceding panels but does not allow

for interaction between capital adjustment costs and hiring costs (i.e. g3 = 0 is imposed). This

yields a negative g2 estimate, i.e. negative costs of hiring, and both the p-value and the noise

ratios indicate again strong rejection. In column 3 we replicate the basic speci…cation of panels (a)

and (b) but estimate only F1 and the asset pricing equation, i.e. we drop the F 2 equation. Here

too we get a negative g2 estimate as well as a huge standard error for the interaction parameter

g3. In column (4) we estimate F1 and F2 only, dropping the asset pricing equation. We addsf and ¯ to the instrument sets to allow for stock market information to be taken into account.

Here the point estimates do not display the aberrations of columns 2 and 3 but the noise ratio of

F2 is relatively high, and the implied g function has extremely low marginal costs of hiring and

extremely high marginal costs of investment in capital. We thus draw the following conclusions:

using speci…cations that fail to take into account hiring costs, the hiring optimality condition, or

the interaction between capital adjustment costs and hiring costs, perform poorly. Not taking into

account the asset pricing equation yields unreasonable estimates.

We turn now to examine the implications of the preferred estimates (columns 1 and 3

of panel b) for the adjustment costs function, for hiring and investment, and for the time series

behavior of asset values. The results of panels (a) and (b) indicate that not only do these have

good test statistics, but also that they are not very di¤erent from the other speci…cations, with

21

di¤erent instrument sets or instrument lags.

6. Hiring, Investment and Asset Values

In this section we look at the implications of the results, using the preferred speci…cations – the

point estimates reported in columns 1 and 3 of Table 2b. We begin by looking at the implied

adjustment costs function (6.1). We then study the joint behavior of hiring and investment (6.2)

and the behavior of asset values (6.3).

6.1. Adjustment Costs

The results of Table 2 allow us to construct time series for total and marginal adjustment costs by

using the point estimates of the parameters of the g function. As can be seen from equations (F 1)

and (F 2), it is these costs that are key for the determination of hiring and investment behavior.

The two …rst moments for these series in the sample, using the preferred speci…cations, are reported

in Table 3.

Table 3

Panels (a) and (b) of the table report the LHS of each Euler equation (without taxes) and

its decomposition. This represents the cost for the …rm of hiring or investing at the margin. In

panel (c) total costs are reported.

Consider hiring …rst, as reported in the …rst panel. The …rst row reports net costs on the

marginal gross hire. This is basically QN before taxes, set in terms of average output per worker

(fn): The two speci…cations yield results of 0.6 and 0.8. This is roughly equivalent to one quarter of

wage payments (as wages are 0.648 of output per worker on average, see Table 1). We are aware of

no study on the aggregate U.S. economy to which these numbers can be compared, but it seems a

plausible estimate, i.e., that marginal costs are in the order of a quarter worth of work. Note that

gross marginal costs (reported in row 2) are much higher than net marginal costs, as gross costs are

22

reduced by the interaction between hiring and investment costs, with the interaction term having

a negative sign (reported in row 3). The volatility of marginal costs, as reported in the standard

deviation statistics, is higher for net costs than for each component (gross costs and the interaction

term).

Consider now the costs on the marginal unit of capital, as reported in the second panel.

Here we note that the …rm pays a purchase price (pI ) and incurs adjustment costs. We present

the data on both in terms relative to output per unit of capital (fk ). The …rst row reports the

total capital expenditure on the marginal unit. Looking at its decomposition in rows 2, 3 and 4,

it is clear that it is dominated by the purchase price – comparing rows 1 and 2 we see that the

purchase price is almost 99% of the total marginal expenditure. This is so because, as in the hiring

case, gross adjustment costs are greatly reduced by the interaction term, leaving much smaller net

adjustment costs (reported in the next to last row). The adjustment costs terms exhibit higher

volatility than the purchase price. The table also reports Tobin’s QK (before-tax); the estimates

are around 1.3.

How reasonable are these magnitudes of capital adjustment costs? There exists a vast

literature on the quantitative importance of adjustment costs for investment in physical capital.

This literature builds upon the traditional Q-theory of investment discussed above and encompasses

time series as well as panel data analyses. Chirinko (1993) provides a comprehensive survey. In

what follows, we brie‡y review the main …ndings in order to compare to the results of panel b in

Table 3. The studies examined typically assume the following quadratic formulation:

gµ

itkt

¶= g1

2

µitkt

¶2kt: (6.1)

This functional form implies marginal costs of adjusting investment, gi, which are linear in the

investment rate:

gi = g1µ

itkt

¶: (6.2)

With this marginal adjustment cost function, there is a linear relationship between the investment-

to-capital ratio itkt and marginal Q for capital, QK; as implied by equation (3.22). The results

23

reported below are based on regression estimation of this linear relationship or, alternatively, on

Euler equation estimation of equation F1 (omitting the other terms, i.e. without the terms involvingqvn ): Table 4 o¤ers a summary of some key studies.

Table 4

The cited studies, relating to di¤erent data sets and time periods, indicate that the average

investment rate ( ik ) per annum di¤ers for aggregate data, where it is typically around 0:10; and

the widely-used Compustat …rm panel data, where it is around 0:20: The estimates of gi exhibit

large variation within and across studies. This variation may be described as follows: the early

studies [Summers (1981) and Hayashi (1982)] tended to show large values of adjustment costs,

implying very slow adjustment of capital. This …nding led researchers to re…ne the data used and

the econometric speci…cation and so later studies typically yield estimates of gi in a lower range,

typically between 0:1 and 1:1: This variation is found both across and within studies and re‡ects

di¤erences in the sample of …rms, in the speci…cation (variables included, measurement issues) and

econometric methodology. Note that even for the …ve papers dealing with Compustat data the

estimates vary widely in the cited range.10

How do these results compare to those reported in panel b of Table 3? First, note that

the estimates reported in Table 4 do not refer to purchase costs and that the cited studies do not

consider an interaction between capital adjustment costs and hiring costs. Next, note that our

speci…cation has ´1 = 3 based on estimation, while the reported literature assumes ´1 = 2: These

di¤erences notwithstanding, the net estimates reported in the next to last row of panel b in Table 3

are consistent with the cited range: the mean estimate (0.11 or 0.13) is at the low end of this range.

More importantly, the results of Table 3 shed light on two issues with respect to this literature:

…rst, judging marginal costs as high or low requires consideration of the purchase price, which is10 The study of Abel and Eberly (2002), using Compustat data and both OLS and IV estimation, suggests a

di¤erent, higher range: 1:2¡ 22:9: These high estimates are described by the authors as excessive and lead them to

adopt a di¤erent speci…cation with …xed costs and capital heterogeneity. The latter yields much lower estimates.

24

clearly dominant in our results, and the interaction with hiring costs, that greatly reduces gross

costs. Second, it is clear from Table 3 that omitting the hiring-investment interaction, one obtains

very high estimates – around 21 or 22. This …nding can explain the tendency of studies with such

omission to yield high estimates.

The last panel of Table 3 shows total adjustment costs, with estimates of 3-4% of output.

These appear to be reasonable. Their decomposition into components shows that gross costs of

hiring are almost twice as big as gross costs of investment and, once more, the importance of the

interaction term is straightforward.

6.2. Hiring and Investment

Across all speci…cations, the estimate of g3; the coe¢cient of the interaction term, is negative. To

understand the signi…cance of this result, it is useful to see how hiring is a¤ected by the value of

investment and how investment is a¤ected by the value of hiring. First, consider the former. The

FONC may be re-written as follows (ignoring the derivatives of w; re-introducing them does not

change the argument):

F1 :µ

egit(itkt

; qtvtnt

) + pIt

¶= Qkt (6.3)

F2 :1qt

egvt(itkt

;qtvtnt

) = QNt :

Di¤erentiate with respect to QK :

@egit@ itkt

@ itkt@Qk

+ @egit@ qtvtnt

@ qtvtnt@Qk

= 1

1qt

"@egvt@ itkt

@ itkt@Qk

+@egvt@ qtvtnt

@ qtvtnt@Qk

#= 0

where we use the following notation:

25

gii = @egit@ itkt

giv =@egit@ qtvtnt

gvi =1q

@egvt@ itkt

gvv =1q

@egvt@ qtvtnt

Then:

gii@ itkt@Qk

+ giv@ qtvtnt@Qk

= 1

gvi@ itkt@Qk

+ gvv@ qtvtnt@Qk

= 0

Solving for the marginal e¤ect of QK on investment and on hiring:

@ itkt@Qk

=gvv

giigvv ¡ givgvi> 0

@ qtvtnt@Qk

= ¡ gvigiigvv ¡ givgvi

With a convex g function, the denominator is positive. Evidently investment rates rise with

QK; its e¤ect on hiring (@ qtvtnt@Qk ) depends on the sign of gvi: A negative point estimate of g3 implies

gvi < 0 and so@ qtvtnt@Qk > 0: Hence, when QK rises both i

k and qvn rise. A similar argument shows that

when QN rises both ik and qvn rise.

Another way of putting this result is that for given levels of investment (hiring) rates, total

and marginal costs of investment (hiring) decline as hiring (investment) increases. One interpreta-

tion of this result is that simultaneous hiring and investment is less costly than sequential hiring

and investment of the same magnitude. This may be due to the fact that simultaneous action by

the …rm is less disruptive to production than sequential action.

26

Note, however, the following distinction: the afore-going argument favors simultaneous

hiring and investment, i.e., positive levels of both. It also indicates that it could be the case that

when investment rises, so does hiring, i.e., a positive correlation. However the latter need not always

be true. Using (6.3) note that if QK rises and QN declines at the same time then the former will

lead to higher investment and higher hiring while the latter will lead to lower investment and lower

hiring. If the e¤ect of QK on investment and the e¤ect of QN on hiring are dominant (respectively),

then investment would rise and hiring would fall. Thus hiring may fall when investment rises even

when g3 < 0. In the data sample, hiring and investment have been generally negatively correlated

– moderately (-0.34) for entire sample or strongly (around -0.8) for the sub-samples 1976-1985 and

1991-1997 – but have also been positively correlated (0.30) in the sub-sample 1985-1990.

6.3. Asset Values

The estimates allow us to generate time series of asset values using the RHS of equation (3.29),

formulared in stationary terms as follows:

stft

=µ

¯t+1(1 ¡ ¿ t+1)ft+1ft

¶ ·kt+1ft+1

£fkt+1 ¡ gkt+1 ¡ nt+1wkt+1 +(1 ¡ ±t+1)(git+1 + pIt+1 + nt+1wit+1)

¤

+·nt+1

ft+1

·fnt+1 ¡ gnt+1 ¡ wt+1 ¡nt+1wnt+1 + (1 ¡Ãt+1)

(gvt+1 +nt+1wvt+1)qt+1

¸¸¸+ j (6.4)

The RHS, without the expectational error j, is decomposed in order to examine the relative

role played by capital and by labor. Table 5 takes up the point estimates from the preferred

speci…cations and presents these implications using the following decomposition:

27

sf

=stft

1a+

stft

1b+

s2tft

+s3tft

stft

1a= ¯t+1(1 ¡ ¿ t+1)

ft+1ft

·kt+1ft+1

£fkt+1 +(1 ¡ ±t+1)pIt+1

¤¸

stft

1b= ¯t+1(1 ¡ ¿ t+1)

ft+1ft

·nt+1ft+1

¡fnt+1 ¡wt+1

¢¸

stft

2= ¯t+1(1 ¡ ¿ t+1)

ft+1

ft

·kt+1

ft+1

£¡gkt+1 ¡ nt+1wkt+1 + (1 ¡ ±t+1)(git+1 +nt+1wit+1)

¤¸

stft

3= ¯t+1(1 ¡ ¿ t+1)

ft+1

ft

·nt+1

ft+1

·¡gnt+1 ¡nt+1wnt+1 + (1 ¡Ãt+1)

(gvt+1 +nt+1wvt+1)qt+1

¸¸

where:

wvt = Áf¡gnvt +ptqt

¯t (1 ¡ ¿ t) (gvvt + ntwvvt)

wit = Áf¡gnit +ptqt

¯t (1 ¡ ¿ t) (gvit +ntwvit)

wnt = Áffnnt ¡ gnnt +ptqt

¯t (1 ¡ ¿ t) (gvnt + ntwvnt +wvt)

wkt = Áffnkt ¡ gnkt +ptqt

¯t (1 ¡ ¿ t) (gvkt + ntwvkt)

The …rst two parts represent the …rm’s rents from capital (stft1a) and from labor (stft

1b).

Consider the former (stft1a) and note that it can be re-written as:

s1atkt+1

= (1 ¡ ¿ t+1)

"(1 ¡ ®) ft+1kt+1 +(1 ¡ ±t+1)pIt+1

1 + rt;t+1

#

This expression can be compared to the user-cost model (see Jorgenson (1996) for a survey and

discussion). In the latter model the …rm’s FONC is

1 + rt;t+1 =(1 ¡ ¿ t+1)(1 ¡ ¿ t)

"(1 ¡®)ft+1

kt+1 + (1 ¡ ±t+1)pIt+1

pIt

#

and so s1atkt+1

becomes: µst

kt+1

¶uc= (1 ¡ ¿ t)pIt

28

With ¿ = 0 and pI = 1, the last equation is the familiar condition st = kt+1:

We can express the last equation in terms relative to output rather than to capital:

µstft

¶uc=

(1 ¡ ¿ t)pItft+1kt+1

ft+1ft

We can thus compare³stft

´ucto

³stft

´1a: Note that departures from the user-cost formulation

are consistent with the current model.

Similarly, for (stft1b) note that in the absence of any labor market frictions, as in the neo-

classical model, the following would hold true:

® ¡ wt+1nt+1

ft+1= 0

and hence:

stft

1b= 0

The other two parts represent the value of capital adjustment (stft2) and of hiring costs (stft

3).

Table 5

We examine the results reported in Table 5:

Panel (a) presents the sample average value of the above decomposition. Comparing thestft

1a term to the value implied by the user cost model (de…ned above as³stft

´uc), the results indicate

that the latter is 99% of the former. Thus the part due to capital is about the same as the value

predicted by the user cost model. However this part (stft1a) is but 86%-89% (and not 100%) of total

…rm value. The labor rent part (stft1b) is less than 0.5% of total …rm value.

The value due to adjustment costs is 11-14% of the total value. Out of the latter the larger

part is due to hiring costs (stft3) at 6%-8% of the total asset value, while adjustment costs of capital

(stft2) account for about 5%.

29

Panel (b) shows the sample variance decomposition of the RHS of the asset pricing equation

(without j3). Each term is divided by the total variance so the elements of the matrix sum to 1.

The two speci…cations are almost identical here. By far the biggest role in explaining the variance

is played by the second term (stft2), i.e. by capital adjustment costs. The “traditional” part (stft

1a)

plays a very small role. This is consistent with the fact noted by Christiano and Fisher (1998) that

pI was negatively correlated with s in the sample period, and the estimates of pI as having much

lower volatility than capital adjustment costs as reported in Table 3b above. Other noteworthy

results are that hiring costs ( stft3) contribute more than the “classic” part of the asset value (stft

1a) to

overall variance and that there is negative co-variance between capital adjustment costs and hiring

costs, that serves to reduce the overall variance.

7. Conclusions

The key message of this paper is that one needs to examine investment and hiring jointly and

that both are essential for the determination of asset values. In particular, the interaction between

their adjustment costs is important. The main …ndings are that adjustment costs play a role

in explaining mean asset values, and in this context hiring costs play an even bigger role than

capital adjustment costs. The latter account for most of asset value volatility. We show that the

conventional speci…cation, with adjustment costs for capital and no hiring costs, performs poorly.

The results also suggest some reasons for the empirical failures of previous models: lack of

consideration of the interaction between capital and labor adjustment costs (or the use of net rather

than gross labor adjustment costs), and insu¢cient convexity of the adjustment cost function.

Possibly the use of aggregate data which is too broad or econometric techniques that did not

su¢ciently cater for non-linearities were pitfalls too.

It would appear that a panel study of …rms or plants may be insightful. Such a study

could allow for heterogeneity and the examination of issues such as …xed costs. However, a serious

empirical di¢culty is likely to be the (non) existence of appropriate gross ‡ows worker data in

30

conjunction with matching data on investment ‡ows and stock prices. Given the results indicating

a key role played by the interaction of hiring and investment rates, this data problem needs to be

resolved before any further exploration is accomplished.

31

References

[1] Abel, Andrew B. and Janice C. Eberly, 2002. “Investment and q With

Fixed Costs: An Empirical Analysis,” working paper available online at

http://www.kellogg.nwu.edu/faculty/eberly/htm/research/research.html

[2] Barnett, Steven A. and Plutarchos Sakellaris, 1999. “A New Look at Firm Market Value,

Investment, and Adjustment Costs,” The Review of Economics and Statistics 81:250-

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[3] Bleakley, Hoyt, Ann E. Ferris, and Je¤rey C. Fuhrer, 1999. “New Data on Worker Flows

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[4] Bond, Stephen, and Costas Meghir, 1994. “Dynamic Investment Models and the Firm’s Fi-

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[5] Caballero, Ricardo J., 1999. “Aggregate Investment,” in: John B. Taylor and Michael Wood-

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[6] Chirinko, Robert S., 1993. “Business Fixed Investment Spending: Modeling Strategies, Empir-

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[8] Cochrane, John H., 1991. “Production-Based Asset Pricing and the Link Between Stock Re-

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[9] Cochrane, John H., 1996. “A Cross-Sectional Test of an Investment-Based Asset Pricing

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[10] Cooper, Russell and John Haltiwanger, 2002. “On the Nature of Capital Adjustment Costs,”

working paper available online at http://www.bu.edu/econ/faculty/cooper/.

32

[11] Danthine, Jean-Pierre and John B. Donaldson, 2002.“Labour Relations and Asset Returns,”

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on Corporate Investment,” Journal of Finance, LIV:1939-1967.

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investment,” Journal of Monetary Economics 36:541-572.

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NBER Macroeconomics Annual 223-262.

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[20] Hansen, Lars P., 1982. “Large Sample Properties of Generalized Method of Moments Estima-

tors,” Econometrica 50:1029-1054.

[21] Hayashi, Fumio, 1982. “Tobin’s Marginal q and Average q: A Neoclassical Interpretation.”

Econometrica 50:213-224.

33

[22] Herman, Shelby, 2000. “Fixed Assets and Consumer Durable Goods,” Survey of Current Busi-

ness, Bureau of Economic Analysis, Department of Commerce, April, 17-30.

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Survey of the Matching Function,” Journal of Economic Literature 39:390-431.

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34

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Belassa and R.Nelson (eds.) Economic Progress, Private Values and Public Policies:

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[34] Yashiv, Eran, 2000a. “The Determinants of Equilibrium Unemployment,” American Eco-

nomic Review 90:1297-1322.

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3:486-522.

35

A. Derivation of the Firms Asset Value Equation

The following derivations are based on Hayashi (1982). First we multiply throughout the FONC

with respect to investment (3.14) by it; the FONC with respect to capital (3.13) by kt+1; the FONC

with respect to vacancies (3.16) by vt; and the one with respect to employment (3.15) by nt+1 to

get

0 = ¡(1 ¡ ¿ t)¡pIt + git + ntwit

¢it + itQKt (A.1)

0 = ¡(1 ¡ ¿ t) (gvtvt + ntwvt) + vtqtQNt (A.2)

kt+1QKt = kt+1Et©¯t+1[(1 ¡ ¿ t+1)

¡fkt+1 ¡ gkt+1 ¡ nt+1wkt+1

¢+ (1 ¡ ±t+1)QKt+1]

ª(A.3)

nt+1QNt = nt+1Et©¯t+1

£(1 ¡ ¿ t+1)

¡fnt+1 ¡ gnt+1 ¡wt+1 ¡ nt+1wnt+1

¢+ (1 ¡ Ãt+1)QNt+1

¤ª(A.4)

Then we insert the law of motion for capital (3.4) into equation (A.1), roll forward all

expressions one period, multiply both sides by ¯t+1 and take conditional expectations on both

sides:

Et£¯t+1 (1 ¡ ¿ t+1)

¡pIt+1 + git+1 + nt+1wit+1

¢it+1

¤= Et

©¯t+1 [kt+2 ¡ (1 ¡ ±t+1)kt+1]QKt+1

ª:

(A.5)

and so:

Et£¯t+1(1 ¡ ±t+1)

¡kt+1QKt+1

¢¤= Et

©¯t+1

£¡kt+2QKt+1 ¡ (1 ¡ ¿ t+1)

¡pIt+1 + git+1 + nt+1wit+1

¢it+1

¢¤ª

Combining the last expression with equation (A.3) we get

kt+1QKt = Et³¯t+1

³cfkt+1 + kt+2QKt+1

´´(A.6)

or

Et³¯t+1cfkt+1

´= kt+1QKt ¡Et

¡¯t+1kt+2QKt+1

¢: (A.7)

36

It follows from the de…nition of the …rm’s market value in equation (3.26) that

#kt ¡ Et³¯t+1#kt+1

´= Et

³¯t+1cfkt+1

´: (A.8)

Thus,

#kt ¡ Et³¯t+1#

kt+1

´= kt+1QKt ¡Et

¡¯t+1kt+2QKt+1

¢; (A.9)

which implies

#kt = kt+1QKt :

We derive a similar expression for the case of labor. Inserting the law of motion for labor

from equation (3.5) into equation (A.2), multiplying both sides by ¯t, rolling forward all expressions

by one period and taking conditional expectations yields

Et£¯t+1 (1 ¡ ¿ t+1) (gvtvt +ntwvt)vt+1

¤= Et

©¯t+1

£nt+2 ¡ (1 ¡Ãt+1)nt+1

¤QNt+1

ª= 0; (A.11)

and therefore

Et¡¯t+1(1 ¡Ãt+1)nt+1QNt+1

¢= Et

©¯t+1

£nt+2QNt+1 ¡ (1 ¡ ¿ t+1) (gvtvt + ntwvt)

¤ª

When combining the last expression with equation (A.4) we get

nt+1QNt = Et¡¯t+1cfnt+1 + ¯t+1nt+2QNt+1

¢; (A.12)

or

Et¡¯t+1cfnt+1

¢= nt+1QNt ¡ Et

¡¯t+1nt+2QNt+1

¢: (A.13)

The de…nition of the …rm’s value in equation (3.8) implies that

#nt ¡ Et¡¯t+1#

nt+1

¢= Et

¡¯t+1cf

nt+1

¢: (A.14)

Thus,

#nt ¡Et¡¯t+1#

nt+1

¢= nt+1QNt ¡ Et

¡¯t+1nt+2QNt+1

¢: (A.15)

37

This implies the following expression for the asset value of a job-match:

#nt = nt+1QNt :

Hence, the total market value of a …rm, st, equals:

st = #kt +#nt = kt+1QKt + nt+1QNt : (A.17)

where QKt and QNt are de…ned in equations (3.19) and (3.20), respectively.

38

B. Data

The data are quarterly and cover the period 1976:1-1997:4. They pertain to the U.S. non-…nancial

corporate sector unless noted otherwise.

B.1. Output and Price De‡ator

Output, ft and its price de‡ator pft pertain to the non-…nancial corporate business (NFCB) sector.

They originate from the NIPA accounts published by the BEA of the Department of Commerce.11

B.2. Investment, Capital, Depreciation and the Price of Investment

These are new data series on the non-…nancial corporate sector made available in 2001:Q1 by the

BEA of the Department of Commerce. See Herman (2000)12 for de…nitions.

The capital stock kt series is measured as the sum of non-residential equipment, software

and structures of the non-…nancial corporate sector. In 1998, for example, total private k was 18,643

billion dollars; total private non-residential k totalled 9,450 billion dollars; 6,402 billion dollars were

non-…nancial corporate. Thus the latter was 34% of private k and 68% of the non-residential part.

B.2.1. Computations

Both k and i are reported at an annual frequency.

The Capital Stock We construct the quarterly capital stock data by interpolating the annual

series according to the following formula:

ln(kt+1;i) = ln(kt) +i4[ln(kt+1) ¡ ln(kt)]

11 See web page http://www.bea.doc.gov/bea/dn/st-tabs.htm12 See www.bea.doc.gov/bea/ARTICLES/NATIONAL/NIPAREL/2000/0400fxacdg.pdf

39

i = 1;2; 3; 4, kt denotes the capital stock at the end of year t and kt+1;i denotes the capital stock

in the i-th quarter of year t + 1.

The Investment Flow We construct the quarterly investment series using the following three

alternative interpolation schemes:

(i) distributing i according to the weights of the private sector investment series which is

available quarterly.

b) dividing i evenly to 4 quarters.

c) taking the annual growth rate in logs, denoting it by ga, de…ning g = (1 +ga)0:25¡ 1 and

then computing

i1 = i1+g+g2+g3 ; i2 = i1(1 + g); i3 = i2(1 + g); i4 = i3(1 + g)

It turns out that there is little di¤erence between these series. Thus in the tables we focus

on the last measure.

The Rate of Depreciation We have two sets of measures:

(i) ±1 the depreciation series computed by the BEA; this is available in annual frequency13

and we convert it to quarterly using ±t = (1 + ±at )0:25 ¡ 1

(ii) ±2 we solve for ±t using the equation

±t =itkt

+1 ¡ kt+1kt

and the three measures for it computed above

The Price of Investment In order to compute the real price of capital, pI, we determine the

price indices for output and for investment goods. The price index for output, pf , equals the ratio13 See line 28 in Tables 4.1 (Current-Cost Net Stock of Nonresidential, Non…nancial Fixed

Assets) and 4.4 (Current-Cost Depreciation of Nonresidential, Non…nancial Fixed Assets) at

http://www.bea.gov/bea/dn/faweb/AllFATables.asp#S4

40

of nominal to real GDP. Similarly, the price index for a particular type of investment good, PSE

equals the ratio of nominal to real investment. We let ¿ denote the statutory corporate income tax

rate, ITC the investment credit on equipment and public utility structures, ZPDE the present

discounted value of capital depreciation allowances, and  the percentage of the cost of equipment

that cannot be depreciated if the …rm takes the investment tax credit. Furthermore, S denotes

structures, Eq denotes equipment, and sEq denotes the fraction of equipment in business …xed

investment.

The real price of business …xed capital, pI, then equals

pI = pIEq(1 ¡ ¿ ZPDE)

1 ¡ ¿sEq + pIS

1 ¡ ITC ¡ ¿ZPDE (1 ¡ÂITC)1 ¡ ¿

(1 ¡ sEq) ; (B.1)

where pIEq = PSEEq=pf , and pIS = PSES=pf .

We use two methods of transforming annual values into quarterly values:

method A

ln(PSEt+1;i) = ln(PSEt) + i4[ln(PSEt+1) ¡ ln(PSEt)]

i = 1;2;3; 4, PSEt denotes the price level at the end of year t and PSEt+1;i denotes the

price level in the i-th quarter of year t +1.

method B

1) interpolate the annual i into quarterly using the growth method (method c above)

2) compute the quarterly PSE by dividing the nominal by the real

B.3. Employment, Matches and Separations

Employment We use two alternative measures of employment from Bureau of Labor Statistics.

One measure, covers wage and salary workers in non-agricultural industries less government

workers less workers in private households less self-employed workers less unpaid family workers.

41

We use this series in conjunction with the NFCB GDP f described above. The other measure is

civilian employment used in conjunction with the employment in‡ow qv (see below).

Matches (qv) We use data on worker ‡ows as computed by Bleakely et al (1999). These data

are adjusted CPS data and pertain to ‡ows to employment from unemployment and from out of

the labor force.

The separation rate Solving the employment dynamics equation

nmt+1 = nmt (1 ¡ Ãm) + (qv)m

we get (in monthly terms):

Ãm =(qv)m

nmt+1 ¡ nmt+1

nmtWe then transform to quarterly:

ÃQ = Ã1 + (1 ¡ Ã1)Ã2 + (1 ¡Ã1)(1 ¡ Ã2)Ã3 (B.3)

B.4. The Labor Share

For the labor share of income wnf we use compensation of employees (the sum of wage and salary

accruals and supplements to wages and salaries) as a fraction of the gross product of the non…nancial

corporate business sector.14

14 The data are taken from NIPA Table 1.16, lines 19 and 24 (http://www.bea.gov/bea/dn/nipaweb/TableViewFixed.asp?SelectedTa

42

B.5. Asset Value Data

We use the market value of non-farm, non-…nancial business. The data are taken from Hall (2001)15

based on the Fed Flow of Funds accounts and are de…ned as follows:

Source: Flow of Funds data and interest rate data from www.federalreserve.gov/releases.

The data are for non-farm, non-…nancial business. Stock data were taken from ltabs.zip.16

De…nition: The value of all securities is the sum of …nancial liabilities and equity less …nan-

cial assets, adjusted for the di¤erence between market and book values for bonds. The subcategories

unidenti…ed miscellaneous assets and liabilities were omitted from all of the calculations. These are

residual values that do not correspond to any …nancial assets or liabilities.

B.6. Discount Rate and Discount Factor

We use three alternatives for the …rms’ discount rate rt; which generates the discount factor given

by ¯t = [1= (1 + rt)]:

a. Themain series used, following the weighted average cost of capital approach in corporate

…nance, is a weighted average of the returns to debt, rbt , and equity, ret :

rt = !rbt +(1 ¡ !) ret ;

with

rbt = (1 ¡ ¿ t) iCPt ¡¼t (B.4)

ret =fcf test

+ebst ¡ ¼t (B.5)

where:

(i) ! is the share of debt …nance. We set this share equal to 0.4, consistent with the data

reported in Fama and French (1999).15 See http://www.stanford.edu/~rehall/Procedure.htm for a full description and

http://www.stanford.edu/~rehall/page3.html16 Downloaded at http://www.federalreserve.gov/releases/z1/Current/data.htm.

43

(ii) The de…nition of rbt re‡ects the fact that nominal interest payments on debt are tax

deductible. iCPt is Moody’s seasoned Aaa commercial paper rate. The commercial paper rate for

the …rst month of each quarter represents the entire quarter. The tax rate is ¿ as discussed above.

(iii) ¼t denotes the GDP-de‡ator in‡ation of pf discussed above.

(iv) For equity return we use the CRSP Value Weighted NYSE, Nasdaq and Amex nominal

returns (fcf test +ebst in terms of the model, using tildes to indicate nominal variables) de‡ated by the

same GDP-de‡ator in‡ation ¼:

We experiment with two other series to see their e¤ect:

b. The rate of change of the SP500 index computed as follows:

rQt =

hS3S0S4S1S5S2

i 13

1 +¼¡ 1

where Sj is the level of the stock index at the end of month j; the current quarter has

months 4 and 5; the preceding quarter has months 1;2; 3 and the quarter preceding that has month

0:

c. Non-durable consumption growth, which corresponds to the discount rate in a DSGE

model with log utility. If utility is given by:

U (ct) = ln ct

Then in general equilibrium:

U0(ct) = U 0(ct+1) (1 + rt;t+1)1

1 + rt;t+1=

U0(ct+1)U0(ct)

11 + rt;t+1

=ct

ct+1

Hence:

rt;t+1 =ct+1

ct¡ 1

44

Table 1

Data Summary Statistics

quarterly, 76:1-97:4, n=88

variable mean std.ik 0.025 0.002fk 0.17 0.01

pI 1.29 0.07

¿ 0.41 0.06

± 0.018 0.001

qvn 0.089 0.008wnf 0.648 0.010

à 0.085 0.008

sf 5.3 1.4

r (bonds+equity) 0.023 0.045

r (sp500) 0.013 0.049

r (consumption) 0.006 0.006

Note:

For data de…nitions see Appendix B.

45

Table 2

GMM Estimates of F1, F2 and the Asset Pricing Equation: 1976-1997

a. Alternative Power Speci…cations1 2 3

f´1; ´2; ´3; ´4g free ´0s free ´2 free ´2

´1 3.22 ´2 +1 ´2 + 1

(0.73)

´2 2.17 2.00 2.00

(0.62) (0.07) (0.05)

´3 1.24 ´2 ¡ 0:7 ´2 ¡ 0:9

(0.62)

´4 1.41 ´2 ¡ 0:8 ´2 ¡ 0:7

(1.51)

g1 67,889 36,340 37,729

(264,402) (7,892) (7,287)

g2 103 72 90

(264) (22) (25)

g3 -1,052 -945 -700

(2,248) (452) (260)

® 0.67 0.69 0.66

(0.09) (0.10) (0.11)

J-Statistic 25.8 13.9 14.6

p-Value 0.04 0.08 0.07

N:R: F1 0.20 0.18 0.18

N:R: F2 0.11 0.08 0.08

N:R: 3 0.09 0.02 0.02

46

Notes:

1. The speci…cation used is

g(¢) =·g1´1

(itkt

)´1 +g2´2

(qtvtnt

)´2 + g3µ

itkt

¶´3 µqtvtnt

¶´4¸f(zt; nt; kt):

2. Standard errors are given in parantheses.

3. Instruments used are a constant and two lags of f ik; fkg in F 1; fqvn ; wnf g in F2 and sf in

the asset pricing equation.

47

b. Variations on the Basic Speci…cation1 2 3 4 5 6 7

f´1; ´2; ´3g free ´2 free ´2 free ´2 free ´2 …xed …xed …xed

´1 ´2 +1 ´2 + 1 ´2 + 1 ´2 +1 3 2:85 2

´2 2.00 2.01 2.01 2.00 2 2 2

(0.04) (0.03) (0.02) (0.01)

´3 ´2 ¡ 0:8 ´2 ¡ 0:8 ´2 ¡ 0:8 ´2 ¡ 0:8 1:2 1 1

g1 36,352 36,264 35,363 33,088 27,426 16,939 1,191

(5,371) (4,242) (3,433) (2,542) (2,595) (1,529) (94)

g2 78 76 74 69 54 60 102

(23) (13) (12) (6) (9) (9) (17)

g3 -849 -860 -844 -748 -617 -671 -330

(350) (281) (200) (81) (62) (64) (29)

® 0.67 0.67 0.67 0.66 0.67 0.68 0.70

(0.10) (0.08) (0.06) (0.61) (0.03) (0.03) (0.06)

J-Statistic 14.2 24.1 30.4 65.7 30.9 30.1 29.1

p-Value 0.08 0.15 0.34 0.13 0.04 0.05 0.07

N:R: F1 0.18 0.20 0.26 0.43 0.19 0.19 0.19

N:R: F2 0.07 0.11 0.11 0.26 0.11 0.11 0.11

N:R: 3 0.01 0.09 0.14 0.75 0.16 0.15 0.14

Notes:

1. The speci…cation used is:

g(¢) =·

g1´1

(itkt

)´1 +g2´2

(qtvtnt

)´2 +g3´3

(itkt

qtvtnt

)´3¸

f(zt;nt; kt):

48

2. Standard errors are given in parantheses.

3. Instruments used are a constant and:

a. In column 1 two lags, in column 2 four lags, and in column 3 six lags of f ik ;fkg in F1; fqvn ;

wnf g in F2 and sf in the asset pricing equation.

b. In column 4 four lags of f ik ; fk ; ¿ ; pI ;¯g in F 1;fqvn ; wnf ; ¿ ;¯g in F 2 and f sf ; ik ; fk ; qvn ; wnf gin the asset pricing equation.

c. In column 5, 6,and 7 four lags of f ik; fkg in F1; fqvn ; wnf g in F2 and sf in the asset pricing

equation.

49

c. Variations in variables1 2 3 4

f´1; ´2; ´3g free ´2 free ´2 free ´2 free ´2

´1 ´2 +1 ´2 +1 ´2 + 1 ´2 +1

´2 2.00 2.00 2.00 2.00

(0.03) (0.05) (0.05) (0.06)

´3 ´2 ¡ 0:8 ´2 ¡ 0:8 ´2 ¡ 0:8 ´2 ¡ 0:8

g1 36,308 36,713 36,590 36,214

(4,285) (4,815) (5,116) (5,691)

g2 76 113 91 80

(13) (34) (22) (25)

g3 -855 -961 -905 -839

(262) (487) (470) (447)

® 0.67 0.81 0.80 0.68

(0.07) (0.30) (0.40) (0.23)

J-Statistic 24.3 36.5 27.9 32.2

p-Value 0.14 0.002 0.02 0.01

N:R: F1 0.21 0.23 0.20 0.23

N:R: F2 0.11 0.12 0.11 0.11

N:R: 3 0.09 0.09 0.12 0.09

Notes:

1. Standard errors are given in parantheses.

2. In column 1, ± = 0:018 and à = 0:08:In column 2, ¯ is based on non-durable consumption

rate of growth and in column 3 on the SP500 rate of change. In column 4 , ¯ = 0:985:

50

d. Other speci…cations1 2 3 4

f´1; ´2; ´3g …xed …xed …xed …xed

´1 2 3 3 3

´2 2 2 2

´3 1.2 1.2

g1 34 1,576 613 7,085

(6) (274) (143) (1,421)

g2 0 -1.6 -1,842 2.9

(0.4) (454) (0.9)

g3 0 0 -2.03 -28

(204) (8)

® 0.66 0.65 0.62 0.67

(0.001) (0.002) (0.09) (0.01)

J-Statistic 43.4 39.9 16.4 23.0

p-value 0.003 0.005 0.09 0.11

N:R: F1 0.09 0.10 0.12 0.09

N:R: F2 0.70 0.45 - 0.20

N:R: 3 0.85 0.85 0.12 -

Notes:

1. In column 1 we set g2 = g3 = 0 and in column 2 we set g3 = 0:

2. In column 3 only F 1 and the asset pricing equation are estimated.

3. In column 4 only F 1 and F 2 are estimated.

51

Table 3

Sample Moments of Marginal Hiring and Investment Costs

and of Total Costs

a. Gross Hiring

speci…cation Table 2b, column 1 Table 2b, column 3

net marginal hiring costs 0.83 0.58

(1) @g=@vf=n =

hg2(qtvtnt )´2¡1 + g3( itkt

qtvtnt )´3¡1 it

kt

i(0.81) (0.75)

(2) gross marginal hiring costs 6.86 6.48

g2(qtvtnt )´2¡1 (0.61) (0.56)

(3) interaction labor-capital -6.04 -5.90

g3( itktqtvtnt )´3¡1 itkt (0.49) (0.48)

b. Investmentspeci…cation Table 2b, column 1 Table 2b, column 3

(1) marginal capital adjustment+purchase costs 7.63 7.62

pIf=k + @g=@i

f=k =

264

pItftkt

+hg1( itkt )

´1¡1 + g3( itktqtvtnt

)´3¡1 qtvtnti

375 (3.76) (3.47)

(2) pItftkt

7.52 7.52

(0.82) (0.82)

(3) gross marginal adjustment costs 21.92 21.22

g1( itkt )´1¡1 (3.12) (3.01)

(4) interaction capital-labor -21.81 -21.09

g3( itktqtvtnt

)´3¡1 qtvtnt (2.27) (2.13)

(3)+ (4) net marginal adjustment costs

24 g1( itkt )

´1¡1

+g3( itktqtvtnt )´3¡1 qtvtnt

35 0.12 0.12

before tax QKt =¡git + pIt

¢1.32 1.32

52

c. Total adjustment costs

speci…cation Table 2b, column 1 Table 2b, column 3

(1) gf =

hg1´1

( itkt )´1 + g2

´2(qtvtnt )´2 + g3

´3( itktqtvtnt )´3

i0.04 0.03

(0.01) (0.01)

(2) g1´1

( itkt )´1 0.18 0.18

(0.04) (0.04)

(3) g2´2

(qtvtnt )´2 0.31 0.29

(0.05) (0.05)

(4) g3( itktqtvtnt )´3 0.45 0.45

(0.05) (0.05)

Notes: The table reports sample means with standard deviations in parantheses.

53

Table 4

Estimates of Marginal Adjustment Costs for Capital

Summary of studies for the U.S. economy

study sample mean ik mean gi

Summers (1981) BEA, 1932-1978 0:13 2:5 ¡ 60: 5

Hayashi (1982) corporate sector, 1953-1976 0:14 3:2

Shapiro (1986) Manufacturing, 1955-1980 0:08 0:43

Hubbard, Kayshap and Whited (1995) Compustat, 1976-1987 0:20 ¡ 0:23 0:15 ¡ 0:45

Gilchrist and Himmelberg (1995) Compustat, 1985-1989 0:17 ¡ 0:18 0:50 ¡ 0:98

Gilchrist and Himmelberg (1998) Compustat, 1980-1993 0:23 0:15 ¡ 0:21

split sample 0:13 ¡ 1:1

Barnett and Sakellaris (1999) Compustat, 1960-1987 0:20 0:27

Cooper and Haltiwanger (2002) LRD panel, 1972-1988 0:12 0:04; 0:26

Hall (2002) 35 industry panel, 1959-1999 0:10(?) 0:15

Abel and Eberly (2002) Compustat 1974-1993 0:15 1:2 ¡ 22:9

Notes:

1. Investment rates ik are expressed in annual terms.

2. All studies pertain to annual data except Shapiro (1986) which is based on quarterly

data.

54

Table 5

Implications of Estimates for Asset Values sf

a. Decomposition of the Mean Predicted Asset Values sf

speci…cation Table 2b, column 1 Table 2b, column 3³sf

´nc

s1atft

0.994 0.996

share of s1atft 0.862 0.892

share of s1btft 0.002 0.003

share of s2tft 0.053 0.047

share of s3tft

0.082 0.059

55

b. Variance Decomposition of the Predicted Asset Values sf

Table 2b, column 1s1atft

s1btft

s2tft

s3tft

s1atft 0.02 -0.0001 -0.09 0.02s1btft -0.0001 0.00001 0.002 -0.0004s2tft

-0.09 0.002 1.69 -0.31s3tft 0.02 -0.0004 -0.31 0.06

Table 2b, column 3s1atft

s1btft

s2tft

s3tft

s1atft

0.03 -0.00014 -0.12 0.02s1btft -0.0001 0.00001 0.00256 -0.00045s2tft -0.12 0.003 1.75 -0.32s3tft

0.02 -0.0005 -0.32 0.06

Notes: The tables use the following de…nitions:

sf

=stft

1a+

stft

1b+

s2tft

+s3tft

stft

1a= ¯t+1(1 ¡ ¿ t+1)

ft+1ft

·kt+1ft+1

£fkt+1 +(1 ¡ ±t+1)pIt+1

¤¸

stft

1b= ¯t+1(1 ¡ ¿ t+1)

ft+1ft

·nt+1ft+1

¡fnt+1 ¡wt+1

¢¸

stft

2= ¯t+1(1 ¡ ¿ t+1)

ft+1

ft

·kt+1

ft+1

£¡gkt+1 ¡ nt+1wkt+1 + (1 ¡ ±t+1)(git+1 +nt+1wit+1)

¤¸

stft

3= ¯t+1(1 ¡ ¿ t+1)

ft+1

ft

·nt+1

ft+1

·¡gnt+1 ¡nt+1wnt+1 + (1 ¡Ãt+1)

(gvt+1 +nt+1wvt+1)qt+1

¸¸

56