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JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY RICE UNIVERSITY

TURING ROBOTS: INCOME INEQUALITY AND SOCIAL MOBILITY

BY

DAGOBERT L. BRITO

RICE FACULTY SCHOLAR, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY PETERKIN PROFESSOR OF POLITICAL ECONOMY, RICE UNIVERSITY

AND

ROBERT F. CURL

RICE FACULTY SCHOLAR, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY PITZER–SCHLUMBERGER PROFESSOR OF NATURAL SCIENCES EMERITUS,

UNIVERSITY PROFESSOR EMERITUS AND PROFESSOR OF CHEMISTRY EMERITUS, RICE UNIVERSITY

Turing Robots: Income Inequality and Social Mobility

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JUNE 3, 2015

THESE PAPERS WERE WRITTEN BY A RESEARCHER (OR RESEARCHERS) WHO PARTICIPATED IN A BAKER

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THOSE OF THE INDIVIDUAL RESEARCHER(S), AND DO NOT NECESSARILY REPRESENT THE VIEWS OF THE

JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY.


3

© 2015 BY THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY OF RICE UNIVERSITY

THIS MATERIAL MAY BE QUOTED OR REPRODUCED WITHOUT PRIOR PERMISSION, PROVIDED APPROPRIATE CREDIT IS GIVEN TO THE AUTHOR AND

THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY. Abstract

In 1970, the top 10 percent of the population earned about 32 percent of labor income; by 2012

the share of the top 10 percent increased to 47 percent. We explain this change in the

distribution of income by increased automation, which has directly replaced human labor in

tasks that can be reduced to algorithms. If this process continues, we can expect a society where

material goods are plentiful, but a substantial faction of the population has no economic

function. Such a society would require substantial redistribution. The paper then explores some

of the social and political implications of such development, and possible solutions. The

problems arising from increasing automation must be addressed now.


4

Introduction

In the period from 1970 to 2007, the U.S. economy grew at an average rate of about 3 percent a

year (2.8 percent for the period from 1970 to 2012). The distribution of labor income was stable

until about 1980 (see Figure 1 below). Then something happened. The economy’s real growth

rate remained on the same trend, but the distribution of income started to become less equal. In

1970, the top 10 percent of the population earned about 32 percent of labor income; by 2012 the

share of the top 10 percent has increased to 47 percent.

Figure1.1Top10PercentShareDividedbyBottom90PercentSharevs.Year

Source: Data from Paris School of Economics, “Capital in the 21st Century,” Table 8.2, piketty.pse.ens.fr/en/capital21c2.

We begin our discussion of Figure 1 by asserting that computer technology is taking over tasks,

displacing the workers who previously did them. The reaction of many people is that this is

1 A substantial part of the data we use in this paper is from Thomas Piketty’s Capital in the Twenty-First Century (Belknap Press of Harvard University Press: Cambridge, Mass., 2014). The book and the accompanying online data sets are sufficient for most of our purposes and are easily accessed by interested parties. Our results and conclusions do not necessarily differ from Piketty’s, but the focus of our paper is on the scarcity and distribution of human talent rather than the distribution of the ownership of capital.

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creative destruction, and the jobs will come back just as the machine age created new jobs to

replace the ones it destroyed. This time there is a huge difference.

The machine age replaced muscle power with machines. However, until 1980 machines still

needed human brains to operate and guide them, and the total number of jobs increased with

growing production. The second machine age is replacing human brains in tasks that can be

reduced to an algorithm. It will be difficult to replace the jobs lost to computers. It will be very

difficult to replace the jobs lost to computers with high-paying jobs.

High-paying jobs for humans must have two characteristics. First, they must require a skill set

that cannot be reduced into an algorithm and thus subject to automation. Second, the skill set

must be scarce in the human population and be in demand. If the first condition is not met, then

the job will be automated. If the second conditions do not hold, then the law of supply and

demand will apply and these will not be high-paying jobs.

It may well be that investment in human capital can mitigate the problem and humans can will

the race between education and technology. However, this will involve teaching skills that do not

compete with automation. We believe that increasing the literacy and numeracy of the general

population will probably not solve the problem.

In addition to the mechanical devices used in industrial production, automation also takes the

form of developments in computer software, hardware, and communications that have displaced

many clerical workers. When you purchase something from Amazon, human work is no longer

used in recording the order, directing that it be shipped, and in the payment process. Because of

our focus on the impact of technology upon the displaced human workers, we will write of the

displacing technology in terms of “Turing robots,” defining such a robot as an automation

technology that displaces one human worker.

What does this have to do with the growing inequality shown in Figure 1? Our explanation is

that the highly paid 10 percent does not face competition with computers because these

individuals have scarce skills demanded by the market that cannot be performed by computers


6

with current technology. They are not competing with computers. This explains the growing

inequality.

If the skills of the highly paid group could be taught to the other workers, the market would erase

the skill premium. Goldin and Katz (2008) believed the failure to be in the education process,

describing the issue as a race between education and technology in which education started to lag

behind technological development.

In our view, the concept of a race between education and technology does not address the

essence of the problem. We assume that the population is heterogeneous in their initial

endowments of talents. Not all individuals can be taught the skills that the market demands, i.e.,

most workers in competition with computers usually cannot be trained to be competitive with the

highly paid group. We believe that the highly paid group has attributes that cannot generally be

taught. This assumption seems elitist and thus very controversial. Later we will discuss in detail

our reasons for believing this assumption valid.

We begin this paper by considering the status of computer technology.

TheImpactofComputerTechnology

The seminal book The Second Machine Age by Brynjolfsson and McAfee (2014) brings to the

fore the profound implications to the economy and society of the latest developments in

computers, connectivity, and robots. Their work makes it clear that the full impact of the

computer revolution lies ahead. This second machine age will result in even greater production

of material goods. We may well be entering an era where scarcity of material goods ceases to be

an issue in the developed world.

The new technologies may be displacing the labor of a very large fraction of the population from

the labor force. A recent paper by Carl Frey and Michael Osborne (2013) estimates that 47

percent of total U.S. jobs are at high risk of being automated in the next decade. The second

machine age may eliminate the scarcity of material goods, but it will also increase


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unemployment and inequality. We believe this, in turn, may result in increased redistribution

and a substantial increase in the role of government.

Changes in the U.S. Labor Market

The U.S. labor market has undergone an enormous transformation that started about 35 years

ago. In the past, the assembly line provided good jobs for less educated Americans. This no

longer is the case. Since 1992 the number of high school dropouts employed in manufacturing

has decreased by 47 percent while the number of people with advanced degrees in the area has

increased by 44 percent. Employment of production and non-supervisory workers in

manufacturing fell from 10 million to 8.4 million in the same period (U.S. Department of Labor

2015).

In contrast, highly educated, highly intelligent workers have not been displaced; in fact, their

employment prospects and income have improved over the same time period. The share of labor

income of the top 10 percent of the population went from about 33 percent in 1980 to 47 percent

in 2012. Figure 1 above plots the total income of the top 10 percent, excluding capital gains,

divided by the total income of the bottom 90 percent (Piketty 2014a). This ratio was stable from

1950 to 1979, but around 1980 it began to rise. The increasing share of income going to the top

10 percent is believed to be caused by two developments: free international trade and

technological change (Baldwin and Cain 2000). Lower wage low-skilled workers from

developing countries and computer technology and robots have displaced American labor.

The income of the American middle class has been stalled for the past 30 years (“Income

Inequality in America” 2011). The initial phase of this stagnation in middle class income can be

attributed to the opening of world markets. American workers had to compete with low-wage

workers in China and Mexico. However, most of the recent stagnation in the income of the

middle class can be blamed on technical change and automation rather than free trade (Sherk

2010). As the cost of computer-controlled manufacturing drops, production that was offshore is

beginning to return to the United States and computer-controlled manufacturing is beginning to


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replace humans even in places where wages are low, such as China (“Robots Don’t Complain or

Die” 2011; Yee and Jim 2011; Markoff 2012; and Larson 2014).

We believe that the effect of international trade has run its course, but the effect of computers

and robots is growing. Employment in manufacturing has dropped from 14.3 million in 2004 to

12 million in 2013; most losses were of workers actually on the assembly line.

This job loss has been accompanied by accelerating productivity growth. Between 1990 and

2000, productivity in manufacturing went up by 4.1 percent and employment dropped by 0.2

percent; between 2000 and 2007, productivity in manufacturing went up by 3.9 percent and

employment dropped by 4.0 percent (Helper, Krueger, and Wial 2012). The nature of

manufacturing has changed, but wages have not kept pace. Since 1992, real output per hour has

grown twice as fast as real compensation per hour for production and non-supervisory workers

(Krueger 2013). What we are now witnessing is the displacement of labor by capital through

information technology.2

Advances in computer and robotics technology are making it possible for capital to replace labor

with machines in ever increasing ways, not just in manufacturing. In one example of many

possible, a Walmart warehouse has been pictured filled with autonomous machines picking up

things to be shipped (Peterson 2013).

Societal Impact

The exponential increase in the power of computers and their constantly decreasing cost mean

that an increasing fraction of human workers will be displaced or replaced by a machine.

Consequently, those vulnerable to displacement will experience decreasing wages as the price of

computers drops. That said, many workers who are not in direct competition with machines will

nonetheless see their wages also decrease. Unless they have a special skill or scarce attribute,

workers in non-robot areas will have to compete for jobs with workers who have been displaced

2 It can be argued that information technology is capital. However, we wish to maintain a distinction between the two.


9

by robots. If there is no redistribution policy, the income of these workers probably will continue

to decrease until it falls below the subsistence level. The unregulated market would lead to

“starving in the streets.”

The societal impact of this revolution is qualitatively different from previous revolutions, which

have been marked by ultimate job recovery when new sectors of the economy developed and

employed the displaced workers. It is hard to see why they will be employed once a substantial

fraction of the workforce is in direct competition with computers and robots. The increased

employment expected in an expanding economy will be undercut as the price of computers

continues to fall.

Increasing the number of jobs for humans will mitigate the problem of inequality in the

distribution of income only if these new jobs have three properties: (1) they must be jobs that a

computer cannot perform; (2) they must require skills that are scarce in the human population;

and (3) these new jobs must include a substantial fraction of the population. Increasing the

number of jobs such as supermarket checkers that do not have a scarce skill requirement will not

solve the problem. Creating an increased demand for a rare skill such as unicycle jugglers will

also not solve the problem. The problem may be that a large fraction of the population may have

skills that a computer cannot perform, but these skills are common to a large fraction of the

population. Wages are set at the margin, and if at the margin humans are competing with robots,

the resulting distribution of income will be extremely unequal. This technological revolution is

likely to create enough permanent displacements to require a major restructuring of economic

and governmental policy.

It is not difficult to make an argument against “starving in the streets” without calling for

altruism from the rich. Social stability may require either the use of force or substantial

redistribution. If goods are not scarce, the elites should favor redistribution because it is cheaper

to maintain social order by the transfer of non-scarce goods than by resorting to force to maintain

order. Similarly, assuming that democracy is allowed to function, transfer payments should be

accepted as preferable to defeat at the ballot box. If a substantial fraction of the labor force is


10

unemployed, the result is a “bread and circuses” society or, in the modern context, a “food

stamps and television” society (Schroeder 2011).

Objections to such transfer payments will be raised. Most Americans believe in the “free

market.” Adam Smith is cited by many, few of whom have read The Wealth of Nations. There

are many who deeply believe that the free market and factor endowments determine the

“legitimate” distribution of income. The marginal product of a factor determines its value in the

market. The intuition behind this belief is powerful. In an economy where factors are paid their

marginal product, workers’ wages reflect the value of their labor and the capitalists’ income

reflects the value of time and the return for delayed gratification. The neoclassical paradigm,

shared in some degree by a majority of American economists, gives theoretical support to this

argument.

It takes a very small leap in logic to argue that this implies that the free market endows

individuals with the just fruits of their labor. Deviations from the market allocation by way of

government redistribution require strong justification or rationalization. Social Security and

Medicare are provided in consideration for a lifetime of contributions; Medicaid and child

support payments are the result of the unfortunate necessity of caring for the very poor and

children. Taxes to provide for the national defense and the institutions that define and protect

property rights are an unfortunate necessity in a market economy. Transfers will be strongly

opposed because they increase the role and power of government in the economy.

Despite these objections, we believe that transfer payments will be necessary for social stability.

Although we can find no alternative to transfer payments for avoiding a humanitarian crisis and

support this approach, we believe that a “bread and circuses” society is unhealthy. This judgment

is reinforced by the 1997 book3 by Wilson, When Work Disappears, which provides a bleak

description of the effects of high unemployment on human and societal capital in the slums of

South Chicago. We recognize that our judgment of a “bread and circuses” society reflects our

background and personal set of values. Saying that learning to play the piano and eating home

cooked meals are better than watching television and eating junk food is a value judgment.

3 This book wrestles with the issue of what policy issues might address job loss, as we also will below.


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The motivation for our work is to develop arguments against a “bread and circuses” society that

do not depend on value judgments.4 We summarize them here to be fleshed out later.

1. The need to maintain competent elites. Successful societies need competent elites for

governance, innovation, creativity, the transmission of values, and as protection for

unforeseen external threats. We believe there is a strong genetic component in the

transmission of the qualities needed in such elites. However, individuals in the top tail of

distribution of such qualities will have children who are on average less able than their

parents because of the phenomenon of reversion to the mean. Thus in each new

generation, many members of the elite will need to be replaced by individuals coming

from the outside. We believe that such necessary class mobility will be impaired if there

exists an underclass that is not part of the recruiting pool. If talent is scarce, it is

necessary to recruit from as wide a pool as possible.

2. The need to avoid loss of social capital. Without the possibility of work, there are few

incentives to acquire an education and the other forms of human and social capital needed

for employment. These are the same attributes needed to be a functioning member of a

civil society. There are positive externalities to work and education, and without

education many elements of a dysfunctional society follow.

3. The need to maintain a civil society. There is evidence that employment is an important

factor in the maintenance of a civil society. Males tend to be more reckless and prone to

violence between the ages of 16 to 26. Employed young males are one-third as violent as

unemployed young males (Wilson 1997, 22). Of course, the direction of causation is

unclear: either employment reduces recklessness or responsible behavior results in

employment.

4. Unhealthy shifts in the economic system. In a democracy with a large unemployed

population, governmental redistribution appears inevitable, with the result that the role of

government increases. New technologies create economies of scale and economies of

scope leading to natural monopolies. Income is concentrated in the productive elite. The

role of the free market as an institution of decentralized power is diminished. Finally, 4 We recognize that the goal of a stable democratic society is a value judgment.


12

there is the macroeconomic problem of insufficient demand if the distribution of income

is very unequal. The poor may not be able to purchase the goods being produced

primarily by robots, and perhaps half of the population is impoverished if there is no

redistribution.

Can we avoid these problems by creating more jobs? There are several schools of thought on

how to address our persistently high unemployment. One school believes that we can educate our

labor force for the new high tech jobs of the new economy. This was reflected in the 2014 State

of the Union Address.5 A second school, looking to past experience while ignoring the pain

involved, believes that the market and free enterprise economics will develop new products and

services that will employ the redundant labor (Goldin and Katz 2008). Brynjolfsson and McAfee

seem to base their hope on the realization that computers and humans can be synergistic. Their

example: the best computer can beat the best human at chess, but a good human chess player

using his laptop can beat the best computer. This suggests that humans must have capabilities

that computers lack and could only develop if they become self-aware.6 There are some tasks

that only humans, capable of self-awareness and thus able to recognize a completely unexpected

issue and address it, can perform.

All three schools are optimistic. They believe that the huge increase in productivity will

overwhelm the distributional implications of the new technology. We are pessimistic.

Technology that increases productivity does not necessarily lead to higher wages. An example is

the introduction of scanners in supermarkets. Scanners substantially increased the productivity of

supermarket checkers by checking out customers faster while simultaneously generating valuable

data for inventory control. The productivity of supermarket checkers has increased, but scanner

technology also made it possible for a larger pool of unskilled workers to do the job, and wages

have not increased.

5 E.g.,“Of course, it’s not enough to train today’s workforce. We also have to prepare tomorrow’s workforce, by guaranteeing every child access to a world-class education.” See “President Barack Obama's State of the Union Address,” January 28, 2014, http://www.whitehouse.gov/the-press-office/2014/01/28/president-barack-obamas-state-union-address. 6 The raison d'être of the human race after a singularity that results from self-aware computers is not a question we wish to address.


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The aim of the present work is to search for new options that would keep our society healthy and

to explore the consequences of choosing among these options.

UnderstandingtheEffectofExpandingTechnologyUponLabor

Figure2.DefiningTypeALabor

Figure 2: The classification of tasks. Type A people belong in the highlighted region.

Consider the set of all possible tasks humans can do. The set can be partitioned into two sets two

ways: (1) those skills that are scarce and those skills that are not scarce; and (2) tasks that only

humans can do and those that either humans or robots can do. The market defines the degree of

scarcity. The previously mentioned set of people that can ride a unicycle and juggle at the same

time may be small, but the demand is also small. We will ignore such cases. In Figure 2, these

divisions are shown. We will define the set of tasks that computers or robots can do as Turing

tasks, and the set of tasks that computers or robots cannot do as non-Turing tasks. A Turing task

is one that can be defined by an algorithm. A Turing robot is a machine that can do what a

human can do if programmed (Luk 2014).

Computers are spectacularly better at numerical computing than people. Examples of tasks that

are easy for many humans, but computers cannot do, are taking care of children and cutting hair.

But we must be careful about stating tasks that computers cannot do; the pace of technical


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development is astonishing. A few years ago, it was impossible to imagine a driverless car in city

traffic. Now Google cars are zipping around the Bay Area. The locations of the partitioning walls

in Figure 2 can move. Scarcity is a function of demand and thus of price. The tasks that

computers or robots can do economically are also a function of cost and technology.

Which tasks that can be done by computers often seem to be unrelated to the perceived

intellectual ability required for a task or the amount of skilled knowledge required for the task.

Chess programs using only moderately large computer systems reliably beat the very best of the

grandmasters. Some kinds of medical expertise such as microscopic examination of biopsies and

their interpretation or the interpretation of X-ray images can now be replaced by computer

measurement.

Thus the vertical partition in Fig. 2 above will continue to move to the left as technologies

develop, and the tasks lost by humans will depend not on how hard the required thinking is or

how much knowledge is required. Instead the need for the brains of human will depend upon

whether the ability to deal with unexpected events is needed, or if creative thought is required, or

if a sympathetic human touch matters. However, rush hour traffic to the contrary, a sympathetic

human touch is not scarce.

The bottom 90 percent of the population in terms of income have skills and talents that

computers and automation cannot match; it will be very expensive to develop automation that

can replace humans in these jobs. However, as automation increasingly displaces workers, the

displaced can be trained to compete for the remaining jobs lowering wages at the low end of the

economy. Any increased productivity of these workers resulting from technological advances

will probably not be reflected in their income. Recall the example of the introduction of scanning

in supermarket checkout.

If we accept the assumptions that (1) there is a segment of the workforce whose skills are scarce

and who perform tasks that cannot the performed by robots, and (2) a segment of the population

has skills that are not scarce, then our arguments follow logically. In a later section, we will


15

describe a mathematical model that we have developed to estimate the impact of automation

upon the labor market, but first we must look for a way out.

Can we educate our way out of the falling wages at the low end?

David Autor has a very nice analysis of this issue in his paper “Polanyi’s Paradox and the Shape

of Employment Growth” (2014). Autor argues that humans can do complex tasks that cannot be

described and thus cannot be performed by a computer. We agree.

Autor believes that any scarcity of high-skilled workers is a failure of education. He argues that

many of these “professions require both college and graduate degrees (MBAs, JDs, MDs, PhDs),

meaning that the production pipeline for new entrants is five to ten years in length and, hence,

supply almost necessarily responds slowly.” We believe is that what is scarce is not education,

but talent. Considering that the divergence between the incomes of the top 10 percent from the

bottom 90 percent started around 1979, the market has had time to adjust.7 It seems more likely

to us that for many people their education is limited by their ability.

Figure 3. Wage Behavior of Top 10% and Top 1% Compared

7 The exception may be medicine, where there are institutional supply constraints such as medical school positions and constraints at teaching hospitals.

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Fig. 3 This compares the natural logarithms of the fraction of wages of the top 10% and top 1%. During the 1960’s, the top 1% were actually getting a decreasing share, but this changed. (In order to start the curves at zero, the ln’s at 1950 were subtracted.)

This viewpoint implies that inequality would be seen as a large rise of the very top incomes

simply because the most challenging jobs require the most talent. Figure 3 above shows that this

is the case.

A few of these high incomes may be due to non-market forces such as over lapping boards that

set CEO pay. However there are 1.6 million people in the top one percent. For a group that large,

it is most likely that their pay is set by market forces and they are worth their pay. It seems likely

that they have some qualities that make them valuable. We believe that it is important to society

to recognize and advance the most able, and that we must try to avoid losing them through a

childhood blighted by poverty and social decay. We now describe our inadequate efforts to

understand the trajectories of some of the most able.

Talent and Leadership

We label these particularly talented people with scarce skills as Type A+. It seems obvious to us

that education and training play a vital role in developing these people, but to what extent?

Given a disciplined, intelligent person, can education alone make her into a Type A+ person?

Can great talent be discerned in the educational process? The answers to these questions are

vital to one of our central concerns: keeping the pathway to elite status for the children of non-

elites open is essential in maintaining a viable elite. If talent is scarce, the generational renewal

of top leaders may be endangered by the indirect effect of automation upon a large fraction of the

population. Later we explore this; for now we pursue the question of what is talent and how

important is it?

We believe that some people have qualities that make them very successful These qualities are

very hard to measure and quantify. It is easy to talk of intelligence, self-discipline, and hard work

as leading to success. We agree that these constitute necessary conditions for success, but at the

highest level these qualities do not seem to be sufficient for success. We do not know what these

extra factors are, and there is ample proof that no one can predict success at the top levels.


17

In the top, the nature of the talents can vary enormously. Some individuals are capable of holding

in their minds extremely complex systems, knowing the relations between their parts. Such a

person might be a master of the negotiation of complex legal contracts. Other individuals might

be gifted mathematicians or scientists. Yet others might be skilled at analyzing difficult choices,

envisioning the consequences of each course of action. Such a person could be a great judge

through recognizing the effect on the whole legal system of her decision in a particular case. Still

others might be gifted with the ability to discern and nurture talent, while others can plan and

execute complex operations.

It is useful to examine two processes involving educational sorting in order to consider how

successful it is. There are data on lawyers and economists that suggest that well-paid lawyers and

successful research economists have a set of skills that are hard to measure in advance.

Susan Athey et al. (2007) did a study of the relationship between admissions ranking, grades,

completion, and job placement for economics Ph.D. students at the five top schools in an effort

to measure the success of the admissions process. They found:

“Admissions rank is not a significant predictor of job placement, even if it is the

only variable in the model.

Diligence, perseverance, and creativity—factors that surely matter for successful

research careers and job placements—are difficult to define and measure. Our

results suggest that there is not an easily recognizable star profile or single path to

success for an economics graduate student” (Athey et al. 2007, 518).

This work makes clear that the information available to the admission committees at the five top

schools in economics cannot predict job placement. It also cannot predict productivity after the

completion of the Ph.D. In Appendix II, we explore this case in detail using the results of a

recent paper by John Conley and Ali Önder (2014). We summarize this with the following.

Conley and Önder sum up the problem well:

“Students put tremendous effort into acquiring the credentials that allow them to

gain admission to graduate school. Graduate schools, in turn, put tremendous


18

effort into figuring which of these applicants are worthy of admission and then

spend countless hours in their training and supervision. The hiring process takes

weeks of thought and attention as recommendations are written, papers are read,

candidates to be interviewed are identified, fly-outs are scheduled, and seemingly

endless job talks are attended. These data suggest, but by no means prove, that our

long-standing and expensive process may not be very effective. It may in fact be

that many students and graduates have the potential for success, but realizing it is

a matter of luck, position, or a having random but hard-to-measure endowment of

something special.” (Italics added.)

Figure 4. Distribution of Starting Salaries of Law School Graduates in 2011

Source: Data extracted from the National Association of Law Placement website, http://www.nalp.org/.

Consider now the legal market, where there is good data. If we examine the starting salaries for

law graduates of the class of 2011 (“The NALP Salary Curve for the Class of 2011” 2012), we

see that there are really two markets, as shown in Figure 4 above. There are two groups of law

students: one group has an average salary below $60,000 and the other has an average salary of

around $160,000. Legal training is reasonably uniform and all lawyers have to pass a bar exam.

The bimodal distribution of starting legal salaries requires some explanation. The top salaries are

usually offered to people hired by the top firms.

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Here one can see to some extent the interaction between educational sorting and hiring. Most of

the graduates of the top schools get jobs at the top firms. Graduates at the top of their class from

middle-ranked schools can usually get jobs in the top firms. However, there are schools where

the top firms do not recruit. Thus the margin of this market is in the second-rank schools. From a

middle-level school, top firms could have hired two middle-ranked students for the cost of one

highly ranked student. The sorting at the top level is far from complete at the hiring stage,

because students hired by top firms are beginning a further sorting process. Some will make

partner and some will not.8

Although the data on law students is very suggestive, it represents the perception of the market

before the law graduates start practice and reflects the prestige of the law schools. The somewhat

strange sorting process emerging from legal education shown in Figure 4 gives one pause. Why

are the select few worth up to three times as much as some of their fellow graduates? Clearly the

big firms think so (Baker and Parkin 2006).

We do not like to call upon some mysterious quality that we cannot completely describe to

explain the observed data, especially because we are keenly aware that luck can often be an

important factor in achieving success. However, from the above discussion, we hope it is clear to

the reader that while the attributes that define the top one percent, the A+ people, still remains

somewhat unclear to us, the hypothetical Type A+ person seems very necessary to a healthy

society. Implicit in this paper is the assumption that people who do not have certain scarce skills,

that something special, cannot be taught these scarce skills. If this assumption is wrong, then the

problem we are addressing can be solved by education and everybody can live happily ever after.

Otherwise we need to be seriously concerned if automation results in losing many of these Type

A+ people because they are not born to parents who are in the labor market and do not enter the

search process for talent. As we will discuss below, we fear that one of the major costs of a 8 We can get an estimate of the probability that an associate hired at a top firm will be promoted to partner. At present, the ratio of partners to associates is one. The partner track is about 10 years and partners remain in rank about 35 years. In a steady state, 2.86 percent of the partners will retire. If there is no attrition in the associate ranks, then these partners are replaced from the senior decile of the associate ranks, making an associate have a 28.6 probability of making partner. This is an upper bound because there is attrition in the ranks of the associates so the number of associates hired must be greater than 10 percent of the number of associates to maintain the partner/associate ratio.


20

“Bread and Circuses” is the lost for talent from that fraction of the population that is nor

participating in the market economy.

AnEconomicModelAimedAtMeasuringtheExtentofAutomation

There has been an increase in the income inequality between Type A and Type B workers in the

years since 1980. Type A income grew while Type B income remained flat and actually lost

ground when inflation was included. We believe that increased income inequality resulted from

the loss of Type B jobs to foreign workers and from competition from computer technology.

Computer and communication advances have impacted white-collar workers. Both cheaper

foreign workers and advances in robot manufacturing have impacted manufacturing workers.

The increase in the demand for their services has benefited Type A workers.

Assuming these causes, we use the an economic model (see Appendices I and II) and the data of

Figure 1 to understand what has happened to the U.S. labor market and calculate the number of

robots competing with Type B labor. Our economic model assumes that there are two sectors in

the economy. Sector 1 uses capital, Type A labor, and Type B labor. Sector 2 uses capital, Type

A labor, and Turing robots. Overall since 1980, Type B workers have had to compete with free

trade, outsourcing, and technological change. Recent work suggests that technological change

has become the most important component, and we expect that technological change will

continue to be the most important factor in the future. Therefore, for simplicity, we will refer to

the factor that competes with Type B workers as Turing robots. Turing robots are a metaphor. In

reality, robots are specialized as to function. Technical change will occur with advancements in

both robot hardware and software.

One way to visualize a Turing robot is as a robot that can do any task a human can do if

programmed to do so. Technical change can be viewed as the development of programs that

enable the Turing robot to perform more tasks. There are probably some tasks that a robot could

do, but a higher cost. Thus, at the margin, the cost of a robot performing a task is equal to the

cost of a human performing the same task. As technological change enables robots to perform

more tasks at less expense, robots compete with human workers for more jobs.


21

We assume that Type A labor is 10 percent of the labor force and Type B labor is 90 percent of

the labor force. As robots enter the labor force, they displace Type B labor. This results in a

decrease in wages of Type B workers for two reasons. First, the robot-displaced workers

compete for the remaining Type B jobs. And second, the supply of Type A workers is fixed and

some are allocated to work with robots, which decreases the productivity of Type B workers.

How much Type B wages drop depends on the elasticity of substitution between Type A and

Type B labor.

Recall that in Figure 1 at the beginning of this paper, we plotted the income distribution

calculated by Piketty. Making the assumptions above and using the economics model developed

in Appendix I, we can determine (see Figures 5 and 6) from this Piketty data the fraction of Type

A workers employed in each sector and the ratio of robots to Type B labor. In the model we use

a constant elasticity of substitution function. (Technical details are in Appendix I.) This function

has two parameters. We can use the data from 1950 to 1979 to calculate a relationship between

the two parameters. We chose as the free parameter the parameter associated with the elasticity

of substitution, ρ. ρ determines the extent to which Type B labor can substitute for Type A labor.

The function has the property that if ρ = 1, Type B labor can be freely substituted for Type A

labor, implying that there would be no point in paying Type A labor more than Type B. If

ρ=-∞, neither type of labor can substitute for the other. In practice, we have examined

calculations for ρ values between -1 and +0.5. Our examples here are for ρ=0.

Robots increase the demand for Type A labor and thus Type A wages. Type B wages drop

because robots are a substitute for Type B labor and because the introduction of robots reduces

the amount of Type A labor in Sector 1, thus reducing the marginal product of Type B workers.

This is illustrated in Figure 5 below.


22

Figure 5. The Fraction of Type A Workers Left in Sector 1

The fraction of Type A workers left in the Sector 1, which contains all U.S. Type B human workers, assuming ρ=0 (see Appendix I for explanation).

In Figure 5, almost half of Type A workers have moved from Sector 1 to Sector 2. This result is

derived from the assumption that the Sector 1 labor market is in equilibrium, the relative shares

of Type A and Type B workers of Figure 1, and our assumption of CES technology (ρ=0 ) for

labor services.

Figure 6. The Ratio of Robot to Type B Workers for ρ=0

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23

Robots must be lower in cost than U.S. Type B workers; otherwise, U.S. companies would not

use them. If we assume that the cost of robots is equal to the cost of Type B workers, then we

can calculate the number of robots. If this assumption is not correct then we can only calculate

the lower bounds of the number of robots. Figure 6 shows these lower bounds. Note that by

2010, the lower bound number of robots was more than 80 percent of the total number of U.S.

Type B workers.

In order to give the reader an opportunity to observe the effect of the parameter ρ that we

introduced, we show calculations as a function of ρ for the last year (2010) in Figure 1. Figure 7

shows these 2010 calculations as a function of ρ. Clearly, the choice of ρ makes a big difference.

We have chosen to illustrate with ρ =0 because this corresponds to the often used Cobb-Douglas

production function. A positive ρ implies great substitution of Type B labor and robots for Type

A labor. Then Type A labor constraint is less binding. This can be inverted to indicate that a

labor market with a large negative ρ implies that a small change in the supply of a factor can

give rise to a large change in the price for another factor. The surprisingly high number of robots

shown in Figure 6 suggests that a negative value of ρ is likely. Figure 7 shows that at ρ=-0.5, the

number of robots (equivalent to a human Type B worker) drops by about 40 percent.


24

Figure7.Dependenceon ρ ofNumbersofTypeAin1andRobotLimitin2

Year 2010 dependence upon ρ of the fraction of Type A workers in Sector 1 and the number of

equivalent Type B “workers” in Sector 2 expressed as the ratio of effective Type B human workers, i.e., R/Lb where R is the total of robots expressed in units of the work of a U.S. Type B worker. The thin vertical line corresponds to the choice for Figures 5 and 6.

Societal Problems Arising from a “Bread and Circuses” Approach to Unemployment

The problems with a “bread and circuses” society seem as intuitively obvious and as hard to

articulate as the definition of pornography: “I know it when I see it.”9 To argue that people

should not sit in an easy chair all day watching television and eating junk food is a value

judgment. It may be a value judgment that many are willing to make, but nevertheless it is a

value judgment. Our instinct is to believe that this development will corrupt and weaken our

society, but in addition to this gut reaction we need to have an intellectual understanding of why.

What are our reasons for not wanting an economy where a substantial fraction of the population

is not in the labor force?

Maintaining a Healthy Elite

Education and employment have served as a mechanism to supply labor to the economy—an

important factor of production and thus valuable to society. Education and employment have also

9 Justice Potter Stewart in Jacobellis v. Ohio 378 U.S. 184 (1964).

Type A Sector 1

Type B Limit Sector 2

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25

served as sorting mechanisms that allow society to identify talent. Identifying talent is important

because our society needs a competent elite to perform those necessary tasks that cannot be

performed by computers. There is no guarantee that the elite of today will replicate themselves

and produce the elite needed for tomorrow without recruitment.

Suppose we have a population where a large fraction of the population does not participate in the

sorting from education and employment. This may affect the supply of members of the elite if

talent results from a combination of genetics and nurture, which we believe is the case. If

genetics is determinant, then there is a 100 percent correlation between parents and children. The

children of the elite, providing they produce enough of them, would be sufficient to staff the elite

of the next generation. If talent is produced entirely by nurturing and investment in human

capital, elite members will have the resources to invest in their children. Again, the children of

the elite would be sufficient to staff the elite of the next generation with the same proviso that the

elite produce enough offspring (which currently does not seem to be the case).

If, however, the mechanism that produces talent is some mixture of genetics and nurture, then

there will be problems. Elites typically have some intrinsic endowments such as high intelligence

and self-discipline. There is strong evidence of the inheritability of intelligence and significant

evidence for the inheritability of impulsivity—the opposite of self-discipline. Their children are

likely to be less well endowed with high intelligence and self-discipline because of the well-

known effect of reversion toward the mean. An elite must recruit from non-elites or produce

more children to maintain it. Without social mobility and sorting, such recruiting is difficult.

We now develop a simple mathematical method for quantifying how much recruitment will be

required from the non-elite segment. Suppose a population consisting of N individuals can be

classified by some objective criterion of ability into two groups. Let group 1 of size N1 be the

more able and group 2 of size N2 be the less able, with N1 + N2 = N . Further suppose the

probability that an individual born into group 1 will be less able is p1 and that the probability that

an individual born into group 2 will rise to group 1 is p2. Then at equilibrium the number leaving

group 1 and the number rising to group 1 in the next generation will be equal. p1N1 = p2N2 . This

tells us that at equilibrium


26

N1N2

= p2p1

= R

using N1 + N2 = N

N1 =p2

p1 + p2N

Clearly p2 is the social mobility indicator. Any decrease in p2 lowers the equilibrium fraction of

the elite.

Without some estimate of p1, these equations are meaningless. Fortunately, the recent book The

Son Also Rises: Surnames and the History of Social Mobility by Gregory Clark (2014) provides

useful information. Clark’s intergenerational correlation coefficient b is approximately our 1− p1. Many believe that social mobility is still relatively high. For example, the correlation of the

income of the son to the father in the United States is as low as about 0.48, but the thesis of

Clark’s book, however, is that this is a false measure of social status. He argues that across

nations and cultures the actual correlation if calculated using an aggregate measure of ability is

about 0.7. Thus, roughly one-third of the elite must be replaced each generation, i.e., p1 is about

0.3. If we are considering the elite as the top 10 percent, this implies that a child of the bottom 90

percent has about one chance in 33 of moving into the top 10 percent. Clearly there is a

gradation: a child with a parent near the top of the bottom 90 percent has a much higher chance

of moving up. This calculation may give a clue as to how unlikely it now is to become a member

of the elite in any society, including the U.S. today—especially if you start off poor. If your

parents belong to the lowest 10 percent, your chance of rising to elite status appears very slim.

Our concern is that in an economy where a substantial fraction of the population is receiving

transfer payments, the lack of incentives to acquire an education will eliminate a substantial

fraction of the population from the talent pool necessary to maintain a viable society. History

provides many examples of bad leadership and incompetent elites. The tragic start of the First

World War leaps to mind, followed closely by the idiocy of the Treaty of Versailles.


27

Social Capital

It can be argued that education and employment produce social capital. We recognize that many

economists are skeptical of the concept of social capital including two of the best living

economists, Kenneth Arrow and Robert Solow (Arrow 1999; Solow 1999). Arrow urged “the

abandonment of the metaphor of capital and the term ‘social capital.’” Solow (1999) concurred

in being “critical of the concept of social capital and the way it is used.” Solow argued that

various things normally referred to as social capital, such as “trust, the willingness to cooperate

and coordinate, [and] the habit of contributing to a common effort even if no one is watching,”

may be referred to as “behavior patterns.” Nevertheless, while the concept of capital for behavior

patterns may not be appropriate (Aoki 2010), society prospers when the behavior patterns listed

above are widespread and fails when they are not. What Brynjolfsson and McAfee call “The

Second Machine Age” is going to create problems with respect to the maintenance and creation

of social capital.

We have already mentioned the book When Jobs Disappear describing desperate conditions in a

predominantly black area. The deleterious effects of chronic high unemployment are not

confined to black ghettos. Charles Murray, in Coming Apart, describes the decline of social

capital in a statistical construct he calls “fishtown.” The essence of Coming Apart is that by

many measures over the last 40 years, there has been a serious loss of “social capital” in

predominately white lower-income communities. This loss is indicated by standards such as high

school completion, criminal convictions, marriages, divorce rates, the percentage of single parent

(mother) households with mothers who never were married, and adult male fecklessness arising

from persistent unemployment. This alarming book suggests a decline in the social capital of a

significant fraction of society has already taken place. It covers a time period during which a

substantial job loss for the unskilled took place.

The lack of opportunities in the labor force has two effects. First, it eliminates the role of work in

creating the habits and disciplines required to hold a job. The military recognized this. In the

past, when the value of draftee time was cheap, the army put soldiers to work white-washing

rocks (the white-wash will come off after a rain and the work would have to be done over again)

rather than allowing conscripts to be idle in the barracks. Now the military finds more productive


28

uses of idle time. Second, lack of opportunity for employment reduces the incentives for

education. Even if school attendance is compulsory, a lack of work opportunities reduces the

incentive to work in school and can create bad behavior in the classroom.

Distinguishing between human capital and social capital may be difficult, but doing so is not

necessary to address the problem. It may be more productive to argue that some of the benefits of

human capital are private and are captured by the individual and some may create societal

externalities (both positive and negative; the Turnverein was a prime place for Nazi party

recruiting). Education increases an individual’s direct productivity and also has positive social

externalities. An example is reading. Being able to read has obvious private benefits. Illiteracy

has public negative externalities. It is much easier to train an army if the population is literate.10

Even if individuals are no longer needed in the production process, the need to sort for talent and

the need to develop social capital for a stable society require that institutions be created to

motivate the population to acquire an education.

Possible Solutions

We have not been able to find any solutions based on the free market. All our proposals involve

government intervention. Governmental activities are often less efficient than the market, as

bureaucracies are not subject to market discipline and government expansion leads to a further

concentration of its power. States and local governments cannot accomplish the needed actions

simply because of the huge inequality in the geographical distribution of wealth. Thus, the

federal government must be involved.

Transfer payments to the large fraction of the population who lose jobs or income as a result of

the introduction of robots are inevitable. The question is how should transfer payment schemes

be structured to minimize damage to our society?

10 Illiteracy is a big problem in trying to train the Afghanistan army. See Emma Graham-Harrison, “Illiteracy persists among Afghan troops despite U.S. education drive,” The Guardian, January 28, 2014, http://www.theguardian.com/world/2014/jan/28/illiteracy-afghan-troops-us-education. In early England, literacy was considered so valuable that a literate person was allowed one murder. Literate persons were considered to be members of a lower order of the clergy and under the jurisdiction of ecclesiastical courts. The penalty for murder was expulsion from the clergy. A second murder was tried by a civil court.


29

Work provides positive societal benefits by providing structure and discipline to people’s lives. It

also provides sorting. Through his work life a person can demonstrate outstanding ability and

rise. Thus transfer payments that encourage work are an important concern. A way to provide

jobs for the displaced is to reduce the supply of labor by shortening the work week. This was

suggested by Keynes. However, some people are not able to work. Friedman suggested a

negative income tax. The policies aimed at taking care of those not able to work should be

structured to provide incentives for working. The details of such policies are beyond the scope of

this paper.

Whatever the plan, it would involve the transfer of large amounts of money constituting a

significant portion of the GDP, perhaps as much as 20 percent. Virtually all the additional return

from new technology and robots will accrue to Type A workers (perhaps 10 percent of the

population). The adjusted gross income including capital gains of the top 10 percent of tax filers

is currently almost equal to that of the bottom 90 percent and soon will be more than half of total

income. It is no longer true that taxes have to be raised on the middle class in order to raise any

significant amount of money.

Shortening the workweek for jobs not exempt from overtime would provide work for more

individuals—provided a scheme for discouraging working multiple jobs is created. This would

have to be coupled to a very substantial increase in the minimum wage— perhaps doubling it.

Such doubling of the minimum wage would likely fall heavily on small businesses ill able to

afford it.

A bureaucratic way to effect transfer payments that reduce the working of two jobs and reduce

the load on small businesses could be as outlined below.

1. A shortened workweek is adapted. Any excess work time for a single employer is

overtime for employees who are not exempt and is paid as double-time.

2. Each employer pays half the new minimum wage to the employee.


30

3. Each employer adds hours worked by each employee to his quarterly payroll tax report to

the IRS. Adding together the number of reported hours from all employers for the

quarter, the IRS subtracts from the reported hours any excess hours. The IRS then

computes the resulting additional minimum wage payment, and transfers this sum to the

employee’s bank account or debit card.

There are four additional measures we propose to mitigate the negative aspects of the robot

onslaught.

1. There is an enormous quantity of work for the common good that is not being done. An

obvious area is in the improvement of our common infrastructures such as streets, roads,

bridges, water conservation and reuse, sewers, and improving the electrical grid.

Everyone recognizes the importance of these public goods; most want someone else11 to

pay for them. Money spent on these activities is obviously money well spent. It directly

addresses part of the coming employment problem. There are other opportunities for

government to employ people in activities such as providing childcare, helping the

elderly, and organizing community activities.

2. Equalize pre-K through 12 educational opportunities through block grants to the states

based upon the number of pupils—with the proviso that in total, the same amount of

money will be used for each student at a particular grade level. This addresses the need to

find and develop talent.

3. Invest heavily in research and higher education. Regardless of its economic value,

research and education function as a sorting mechanism for talent and serve as

repositories of human knowledge and skills. This would further the sorting needed to

discover talent. Further, the United States has the best university/graduate school system

in the world. It is attracting the best students from all over the world. At this time, about

10 percent of the students at elite schools and a substantial number of graduate students

in many programs are from abroad (Lai 2012). Those students who return to their home

countries are likely to be part of their elites. Those who stay are likely to be those who

have scarce skills.

11 Thomas Picketty reports that Bill Gates is opposed to being taxed more heavily in the belief that he is more effective in helping society than the government. See http://www.huffingtonpost.com/2015/01/04/piketty-bill-gates_n_6413446.html.


31

4. Create a middle class status not linked to economic productivity. This is to say that we

should create a set of ranks or distinctions that people can achieve by passing

examinations, performing public services, or creating works of art. There is much work

such individuals could do in terms of building social cohesion by organizing clubs, sports,

and teaching. Within limits, wages and transfer payments can be a function of rank. This

is a deliberate attempt to create inequalities that will motivate scholarship, public service,

and creativity. Status is a powerful motivator. To quote Napoleon Bonaparte, “A soldier

will fight long and hard for a bit of colored ribbon.” Such a new middle class would have

the potential to organize itself into a political counterweight to the wealthy elite.

5. Take steps to reduce economic segregation of the poor in housing and education. The

incidence of crime is much less in neighborhoods in which both poor and the better off

live. Similarly, lower income students do better in schools that are economically diverse.

The Growing Concentration of Wealth

Inequality will continue to grow as the second machine age develops. Piketty believes that great

inequality of wealth is inherently bad. He also seems to believe that this belief is somehow self-

evident. He remarks that this belief is generally shared in Europe, but not in the United States.

We need to think about whether he is correct.

There is no doubt that money can be used to acquire power. The wealthy have the means to

employ people and institutions to further their agenda. A recent paper demonstrates that

essentially all political and governmental decisions are currently determined by the elites and

special interests (Gilens and Page 2014). How much farther in this direction can the country go if

the distribution of income becomes even more unequal?

We are concerned that if the productive capacity of the economy is concentrated in a few

individuals, democracy as an institution is threatened. Francis Fukuyama in a recent article in

Foreign Affairs titled “Can Liberal Democracy Survive the Decline of the Middle Class?” (2012)

makes the case that a substantial middle class is essential to democracy. Our fourth proposal


32

attempts to create artificial inequalities not based upon wealth to engage the less affluent and the

unemployed in public life. This is a modest effort to build a new middle class participating in the

life of the nation.

Elites in the U.S. have little to fear in the status quo. The rule of law holds; their property is

protected, and they get to control most decisions unless pitted against each other. Elites,

however, must take action in order for the status quo to continue. If the unemployed are

sustained through transfers, they are likely to remain apathetic about politics. On the other hand,

if a large fraction of the population is reduced to poverty, they will eventually use the democratic

process to take over all branches of government in a situation similar to the 1930s.

There is a danger that elites will fail to recognize the seriousness of the situation. Elites live in

growing isolation in rich neighborhoods and gated communities, rarely encountering poverty.

Elites are likely to ignore the fate of their poor fellow citizens because of this isolation. If you do

not see the effects of poverty every day, it is easy to fantasize about lazy takers who could and

should work and be productive, not realizing that technological change has made a substantial

fraction of the population economically redundant. We no longer expect humans to compete with

machines to pick cotton or harvest corn. In the near future, if not now, we will no longer expect

humans to perform many routine tasks on the assembly line or work in warehouses.

Loss of contact with reality is dangerous. The elites may not recognize the loss of social capital

that accompanies unemployment and the dole. Instead of implementing the initiatives proposed

above, elites may argue that only minimum actions are needed to avoid starving in the streets.

Such a course would result in (1) a drastic loss for many of the opportunity for the dignity of

work, (2) the loss of needed investment in the nation’s infrastructure, and (3) the loss of social

mobility and social capital. Loss of social mobility will eventually weaken the elites. Loss of

social capital may finally make Francis Fukuyama a prophet. History may not have ended, but

liberal democracy may not survive.


33

Other Implications of the Second Machine Age

Trade

Efficiency is the justification for free trade. “Comparative advantage” is one of the most

powerful concepts that has come from economics, but the logic behind the concept of

comparative advantage requires scarcity of factors. Trade is important for other reasons. It is a

force for global stability and for helping less developed economies with low labor costs grow. As

machines replace workers and some forms of labor becomes redundant, it will become efficient

for industries that moved to less developed, low-wage countries to return. If comparative

advantage is not the primary reason for trade, then trade becomes a matter of policy.

Here is an example of a likely such development. Carl Frey and Michael Osborne estimate that

there is a 95 percent probability that sewing will be automated within a decade (2013). At

present, thread manufacture and cloth manufacture can and are being done by robots. Robots can

cut fabric into clothing patterns. The sewing of the cut fabric into clothing is the final step in the

complete robotic manufacture of clothing. When this is completed, clothing manufacturing will

return to the United States, destroying the clothing industry of Peru and Bangladesh. As this

process is repeated in other industries, what happens to developing countries?

Robots will start competing with people, even in China. In 2012, Foxconn announced plans to

acquire enough robots to replace one million workers. Foxconn employs about 1.2 million

workers. Foxconn intended to produce the robots in-house, but this plan seems have been

replaced by a collaboration with Google to develop robots. Assuming that the original cost

estimates can be met, the Foxconn robots are expected to cost between $20,000 and $25,000

each. They would replace workers whose yearly earnings are about one-third the total cost of

such a robot (Hillon 2012). Thus, such robots would become economical if they lasted more than

three years. Assuming an interest rate of 10 percent, a robot life of 10 years, and that a robot

works 6,000 hours per year, then the cost per hour of a robot is about $0.65. China is very

dependent on trade based on low-cost labor. If this labor can be replaced by Foxconn-Google

robots, then China may not be able to maintain the growth rates it needs for political stability.


34

Immigration

We have argued that technical change in the form of Turing robots will need substantial

redistribution and the creation of institutions to maintain civil society. If these changes are

properly executed, the United States will be an attractive place to many people in the world. It is

unlikely that the United States will be able to accommodate all who want to immigrate. Limiting

Type B immigration will be imperative; this would require control of the border.

Type A immigrants create a different policy problem. Skilled immigration is certainly in the

short-run interest of the United States. We hope that the United States undergraduate and post-

graduate education system will continue to attract the best students and that some will want to

stay (Wadhwa 2014). This immigration is valuable. Thirty percent of U.S. Nobel laureates are

immigrants (Witte 2013). On the other hand, should we strip other countries of their leaders? Is

bringing in Type A immigrants in the long-run interest of the United States? This is a question

we cannot answer.

Conclusions

The first machine age, ushered by the steam engine, freed mankind’s dependence on muscle

power. It started around 1776 when the population of the world was around 800 million people

(U.S. Census Bureau 2013). By the year 2000, the population of the Earth was over six billion

people. The rate of growth of world GDP (if such a concept is meaningful over such a long

period) increased by a factor of 10, from .22 percent to 2.2 percent (WorldEconomy.org 2001).

Per capita consumption went up by a factor of 20. Brynjolfsson and McAfee argue that the

second machine age, ushered by the computer, will do the same thing for mental power. They

date the start of the new age around 1958 (U.S. Census Bureau 2013). We start in 1978 when the

distribution of income starts to diverge.

We do not know the ultimate implications of the second machine age. Machines are rapidly

progressing in pattern recognition, what was once a human forte. This suggests to us that there is


35

no clear demarcation limiting the abilities of machines. Here we assume the ability of machines

(Turing robots) to be limited by tasks that can be described by algorithms.

We use data from Piketty’s book and a relatively simple economic model to calculate robot

penetration. We find that the implications of robots replacing humans in routine work require

serious attention. Since 1978 the ratio of labor income of the top 10 percent to the bottom 90

percent has increased from .48 to .89. If we extrapolate this growth in Turing robots in a linear

fashion, this ratio will be around 1.3 in 2040, implying an income disparity larger than any

previous era. Substantial redistribution will be required. On a happy note, the demographic

problem of too few young workers to support the elderly will be solved.

This brings up the central question of the paper: What is wrong with “bread and circuses”? Our

answer is twofold. First, work and education are necessary to maintain social capital. Without the

prospect of work, the incentive to acquire an education is reduced. Second, work and education

are necessary for the sorting process required to maintain an elite. Institutions will have to be

developed to motivate education and employ people in a fashion that may not be economically

necessary. Education may become an important sector because it employs people and it is an

excellent sorting mechanism.

Immigration issues will become even more important. There are two immigration issues: one at

the bottom end of the labor market, the other at the top. A society with substantial transfers will

attract immigrants at the bottom end of the labor market where there is a labor surplus. At the

other extreme, the educational sector attracts students from other countries. Top talent, so far, has

tended to stay in the United States, replenishing the supply of elites. This may be good for the

United States, but robs other countries of their sorely needed supply of elites.

International trade may be reduced. Comparative advantage is one of the most powerful concepts

that has come from economics, but the logic behind the concept of comparative advantage

requires scarcity of factors. The economies of many countries depend on exports produced by

relatively cheap labor. As robots replace workers, manufacturing is returning to the United


36

States. This is already happening and if it continues, it could lead to political instability. Political

instability in either China or Mexico would be a serious problem for the United States.

There is also the question of the viability of democracy without a large middle class. As

mentioned earlier, Francis Fukuyama argues that a substantial middle class is essential to

democracy.

Our key assumption is that there is a segment of the workforce whose skills are scarce and who

perform tasks that cannot the performed by robots and a segment of the population whose skills

are not scarce. Data from the legal and economics profession suggest that this assumption is

plausible with current technology. Future developments in computer technology may invalidate

the assumptions upon which this paper is based, leading to large changes in the economy and

consequently in society. While we have no idea what such high-impact developments might be,

we are confident that work and education are essential to maintaining a healthy society, and this

will not change.


37

Appendix I: Calculations

Overview Our purpose here is to show how Figures 5 and 6 are calculated from the data of Fig. 1 and how Fig. 7 is calculated. We will assume that there are two types of labor; La , skilled labor which we assume to be the top ten percent of the labor force and unskilled labor, Lb , which we assume to be the bottom 90 percent of the population. We assume a nested production function with the overall function being Cobb-Douglas and the nested function for the labor being CES. Recall that all Type B workers are in Sector 1 The production functions for Sector 1 are: (I-1) Y1 = A 1− x( )K1⎡⎣ ⎤⎦

αZ La1,Lb( )1−α

and

(I-2) Z La1,Lb( ) = aLa1ρ + 1− a( )Lbρ( )1/ρ

Z La1 ,Lb( ) is a linearly homogeneous function with two parameters, a and ρ and x is the fraction of the capital stock that is in the human robot sector. We can obtain a useful equation by maximizing profit in sector 1 defining this as (I-3) π1 =Y1(K1,La1,Lb1)−waLa1 −wbLb1 Differentiating this with respect to La1 and setting the derivative to zero to maximize profit, we obtain

(I-4) A 1− x( )K1⎡⎣ ⎤⎦

α1/ ρ aLa1

ρ + 1− a( )Lbρ( )1/ρ−1

aρLa1ρ−1 −wa = 0

Differeniating with respect to Lb , we obtain

(I-5) A 1− x( )K1⎡⎣ ⎤⎦

α1/ ρ aLa1

ρ + 1− a( )Lbρ( )1/ρ−1

1− a( )ρLbρ−1 −wb = 0

Moving the wages over to the right hand side and dividing resulting version of I-4 by that of I-5 and canceling we obtain

(I-6) wa

wb

= a1− a

⎛⎝⎜

⎞⎠⎟

La1Lb

⎛⎝⎜

⎞⎠⎟

ρ−1

Note that the variables and parameters A, K , x, and α have been eliminated. It is useful to

define r = a1− a

⎛⎝⎜

⎞⎠⎟ and write (I-6) as


38

(I-7) wa

wb

= r La1Lb

⎛⎝⎜

⎞⎠⎟

ρ−1

and

(I-8) waLa1wbLb

= r La1Lb

⎛⎝⎜

⎞⎠⎟

ρ

In the 1950 to 1980 time period, the income of the top 10 percent, waLa , divided by the income of the bottom 90 percent, wbLb , is essentially constant. We assume therefore that over this time there was negligible influence of either foreign trade or automation upon the labor market and

that La2 = 0 . Thus in that period waLa1wbLb

= waLawbLb

. This data cannot be used to estimate both

parameters of Z La ,Lb( ) , but they do provide one constraint upon the two-parameters of the

function Z La ,Lb( ) . Define S as the average value of waLawbLb

in the 1950 to 1980 time period.

Then because r 0( ) = S LbLa

⎛⎝⎜

⎞⎠⎟

0

(I-9) r ρ( ) = S LbLa

⎛⎝⎜

⎞⎠⎟

ρ

We will compare several values of ρ.


39

Figure I-1.History of Top 10 Percent Divided by Bottom 90 Percent Income

Figure I-1, which is merely a duplicate of Figure 1 of the main text introduced here for the

convenience of the reader. It clearly shows that something started to happen in 1980 that

continued to increase in effect until the last year available from Piketty 2010. This has to be to

the result of a factor affecting wages in the labor market. We will assume that this new factor is a

combination of automation and foreign competition from trade and the offshoring of production.

The exact magnitude of these forces is not clear (see Baldwin and Cain 2002.) We will call the

sector employing only U.S. human workers Sector 1 and the sector that employs robots or

foreign workers through trade and offshoring production, Sector 2 The emergence of Sector 2

displaced middle to low wage workers, whom we call Type B, leading to wage stagnation.

Simultaneously, the new cheaper foreign workers and robots are creating more jobs for the high-

wage managerial class, whom we call Type A, and increasing their wage.

It is possible to use r and the labor function Z1 to calculate, for a given ρ, the fraction of Type A

workers employed in Sector 1.

Piteketty has published (2014b) the series

(I-10) s t( ) = waLawbLb

!"#$ !"%$ !"&$ !"'$ !""$ ($$$ ($!$

$)#

$)%

$)&

$)'

!"#$

%&'()"*#+,(


40

upon which Fig. 1 is based and the ratio of the average values wA / wB can be calculated for

any year between 1980 and 2011. Using (II-8), one has

(I-11) La1Lb

= r ρ( ) wA

wB

⎛

⎝⎜⎞

⎠⎟

1/ ρ−1( )

Using Piketty’s data, one can calculate the ratio. Then remembering that all Type B labor is

employed in Sector 1

(I-12) La1Lb

⎛⎝⎜

⎞⎠⎟

LbLa

⎛⎝⎜

⎞⎠⎟= La1

La

⎛⎝⎜

⎞⎠⎟

Since the ratio La / Lb = 1/ 9 .

(I-13) La1La

⎛⎝⎜

⎞⎠⎟= 9 La1

Lb

⎛⎝⎜

⎞⎠⎟

and

(I-14) La2La

⎛⎝⎜

⎞⎠⎟= 1− La1

La

⎛⎝⎜

⎞⎠⎟= 1− 9 La1

Lb

⎛⎝⎜

⎞⎠⎟

.

Figure I-2 displays the resulting fraction of Type A labor employed in each sector for several

values of ρ. This figure shows that for values of ρ between -1 and 0 the results are not very

sensitive to ρ. However, as ρ becomes larger than zero, the plots show increasing sensitivity to ρ.

This behavior is to be expected because more positive ρ provides easier substitution of cheap

Type B labor for expensive Type A labor.


41

Figure I-2. Fraction of Total Type A Labor in U.S. Human Sector 2 for Various Values of ρ .

The number R of robots/foreign workers employed by U.S. capital is given by

(I-15) La2R

= r ρ( ) wA

wR

⎛

⎝⎜⎞

⎠⎟

1/ ρ−1( )

Reliable information about the average cost of robots is not readily available. Both foreign labor

and automation have been substituted for U.S. Type B labor because both are cheaper. At the

margin, a firm will switch to robots if the marginal revenue product (price of product times

marginal cost of factor) of robots is greater that or equal to the marginal revenue product of Type

B labor. Thus at the margin, we can expect that wR = wb . The assumption that robots will be

employed at the margin may not hold. However robots will not be introduced if they are more

expensive than humans so the condition,wR ≤ wb , must hold. Therefore if the condition wR = wb

holds, we can calculate the number of robots and if the condition wR ≤ wb holds, we calculate a

lower bound the number of robots, and the number of robots in human equivalent units thus

calculated is displayed in Figure I-3 for several values of ρ.

��

��

��

��

��

��

��

��

��

�

��

� -1.0� -0.5

� 0.0

� 0.5

1950 1960 1970 1980 1990 2000 20100.0

0.2

0.4

0.6

0.8

1.0

Year

AFraction


42

Figure I-3.

Lower limit to the amount of foreign/automaton labor employed by U.S. companies expressed in Type B workers equivalents as the fraction of all U.S. workers, i.e. as R/Lb

Note that these calculations use only the data of Fig. I-1 and do not need to use either the

quantity of capital nor the absolute quantities of labor.

��

��

��

��

��

��

��

��

�

��

��

��

��

��

��

��

�

��

��

��

� -1.0� -0.5

� 0.0

� 0.5

1950 1960 1970 1980 1990 2000 2010

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Year

BFraction


43

Appendix II Research Productivity of Ph.D. Economists

A recent paper by John Conley and Ali Önder (2014) studies the productivity of the graduates of

the top economic departments in the United States. The results of this research are summarized

in Table 1 below.

Table 1. Number of AER-equivalent* Papers Produced at Various Levels

Publishing rates (Percentile)# 99th 95th 90th 85th 80th 75th 70th 60th 50th Average

cohort size Publishing rate (%)

Harvard 4.31 2.36 1.47 1.04 0.71 0.41 0.30 0.12 0.04 30.5 66.3

Chicago 2.88 1.71 1.04 0.72 0.51 0.33 0.19 0.06 0.01 27.3 59.4

U Penn. 3.17 1.52 1.01 0.60 0.40 0.27 0.22 0.06 0.02 19.3 59.5

Stanford 3.43 1.58 1.02 0.67 0.50 0.33 0.23 0.08 0.03 24.7 67.9

MIT 4.73 2.87 1.66 1.24 0.83 0.64 0.48 0.20 0.07 25.5 70.0

UC Berkeley 2.37 1.08 0.55 0.35 0.20 0.13 0.08 0.04 0.02 28.0 62.4

Northwestern 2.96 1.92 1.15 0.93 0.61 0.47 0.30 0.14 0.06 10.1 65.8

Yale 3.78 2.15 1.22 0.83 0.57 0.39 0.19 0.08 0.03 15.7 64.8

UMI Ann Arbor 1.85 0.77 0.48 0.29 0.17 0.09 0.05 0.02 0.01 19.1 54.0

Columbia 2.90 1.15 0.62 0.34 0.17 0.10 0.06 0.01 0.01 17.4 54.8

Princeton 4.10 2.17 1.79 1.23 1.01 0.82 0.60 0.36 0.19 16.2 76.1

UCLA 2.59 0.89 0.49 0.26 0.14 0.06 0.04 0.02 0 17.9 48.5

NYU 2.05 0.89 0.34 0.20 0.07 0.03 0.02 0.01 0 11.7 46.0

Cornell 1.74 0.65 0.40 0.23 0.12 0.07 0.05 0.02 0.01 17.3 57.9

UWI Madison 2.39 0.89 0.51 0.31 0.20 0.11 0.06 0.03 0.01 25.0 60.3

Duke 1.37 1.03 0.59 0.49 0.23 0.19 0.11 0.05 0.02 7.8 59.8

Ohio State U 0.69 0.41 0.13 0.07 0.04 0.02 0.02 0.01 0 15.9 47.9

U Maryland 1.12 0.37 0.23 0.10 0.07 0.05 0.03 0.01 0.01 13.5 56.2

Rochester 2.93 1.94 1.56 1.21 1.14 0.98 0.70 0.34 0.17 8.7 78.5

U TX Austin 0.92 0.53 0.21 0.06 0.05 0.02 0.01 0 0 10.3 38.3

Minnesota 2.76 1.20 0.68 0.46 0.29 0.21 0.12 0.04 0.01 22.2 59.5

U IL Urbana-Ch 1.00 0.38 0.21 0.10 0.06 0.04 0.03 0.01 0.01 26.4 54.8

U C Davis 1.90 0.66 0.42 0.27 0.12 0.08 0.05 0.02 0.01 6.2 53.8

Toronto 3.13 1.85 0.80 0.61 0.29 0.19 0.15 0.07 0.03 6.4 64.6

British Columbia 1.51 1.05 0.71 0.60 0.52 0.45 0.26 0.22 0.11 4.5 73.1

UC San Diego 2.29 1.69 1.17 0.88 0.74 0.60 0.46 0.30 0.18 6.1 78.3

U Southern CA 3.44 0.34 0.14 0.09 0.03 0.02 0.02 0.01 0 4.9 43.8


44

Boston U 1.59 0.49 0.21 0.08 0.05 0.02 0.02 0 0 12.5 41.0

Penn State U 0.93 0.59 0.25 0.12 0.08 0.06 0.02 0.01 0.01 7.1 51.4

Carnegie Mellon 2.50 1.27 1.00 0.86 0.71 0.57 0.52 0.21 0.09 2.0 66.7

Non-Top-30 1.05 0.31 0.12 0.06 0.04 0.02 0.01 0 0 16.8 40.1

* AER stands for American Economic Review. A fairly elaborate scheme exists for making papers in other journals equivalent, e.g., four papers in Economic Theory equals one AER paper. One AER paper is expected to win tenureatamiddle-rankuniversity.#Startingfromtheleftnumbersmeanthatthetop1%ofgraduatesintermsoftotalpublicationsofthisprogramproducedthismanyAERequivalentpublications.Thenextnumberisthetotalpublicationsbetweenthe99thand95th,etc.

On student motivation, Conley and Önder say: “Our experience suggests that most students,

especially at the better programs, enter graduate school planning to seek academic jobs, or at any

rate, jobs that require research.” This appears to be a desire shared by these universities, which

do their best to offer admission to the very best students. The purpose of these programs is to

train research economists.

To be admitted to one of these programs requires almost perfect grades, very high GRE scores,

and strong recommendations. After all this effort in selection, Conley and Önder find that only

the top 10-15 percent of the students will have a research record that will lead to tenure at a

middle-ranked research university. Considering the aim of the programs and the rigor of the

selection process, the scale of the failure of both schools and students to get close to their goal

seems enormous. (Do not weep. Economics Ph.D.s without a strong research publication record

seem to prosper anyway, so all is not lost.) The strangeness of this misfiring of selection is made

even more mystifying in that graduates from lesser-ranked schools publish almost as much as the

graduates of the top schools.

The data in Table 1 can be illustrated12 in Lorenz Curves (Figure 4). For each of the three curves

the percentile value at the level 1 crossing was calculated. This was used to calculate the average

12 The curves in Figure 4 were obtained by empirically fitting (quite well) the appropriate data from Table 1 with the formula

(1) y = aexp b x − x0( )1.2⎡⎣

⎤⎦ + c x − x0( )

where y is the number of high quality research publications produced in the six years after receiving the Ph.D. and x is their percentile obtained by averaging 15 years of output from each school. x0 is 50 for Harvard and top 30


45

number of economics researchers produced by each using the cohort sizes of Table 1. Harvard

admits about 31 students per year; of these, between 4 and 5 can be as classified productive

researchers. The top 30, including Harvard, admit about 460 students each year; of these, about

33 can be classified as productive researchers. The 134 non-top 30 programs admit about 2,250

students into their economics Ph.D. programs; of these, about 26 become productive researchers.

Figure III-1. Lorenz Curves for Ph.D. Economics Programs

The blue mostly highest curve is for Harvard, which was rated number 1 in Table 1. The orange intermediated curve is the average of the top 30 of Table 1, and the green bottom curve is the average for the economics programs not in the top 30. The horizontal line at 1 is the publication level estimated as needed for tenure at a mid-level university. Records above this line succeed by this criterion.

schools and x0 is 70 for the non-top 30. The numbers of potential researchers below the x0 level are completely negligible.

!"#$"#%

&'( )*

+',,'- .).

* /* 0* 1* 2* .***

.

/

)

0

3

!"#$"%&'("

!)*('$+&',%-


46

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turing robots ncome nequality and ocial obility d l. b … · in 1970, the top 10 percent of the...

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