International Tax and Public Finance, 10, 435–452, 2003 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Inequality, Crime and Economic Growth. A Classical Argument for Distributional Equality STEFAN DIETRICH JOSTEN
[email protected] Institute of Public Finance, University of the Federal Armed Forces Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany
Abstract This paper studies the dynamic general-equilibrium interactions between inequality, crime and economic growth by embedding the rational choice-theoretical approach to criminal behavior in a heterogeneous-agents endogenous-growth OLG model. Based on their respective opportunity costs, individuals choose to specialize in either legal or criminal activities. While legal households contribute to aggregate goods supply over time by either working or building human capital, criminals make a living by expropriating legal citizens of part of the latter’s income. An increase in inequality lowers the economy’s growth rate and possesses negative welfare effects for all agents with endowments equal to or above average and for agents with endowment below average that are born sufficiently far in the future. Keywords: distribution, inequality, crime, economic growth, human capital JEL Code: D3, K42, Z13, O41
1. Introduction “Poverty is the parent of revolution and crime” (Aristotle, as cited by Spiegel (1991), p. 29) Up to recent years, one of the most commonly held prejudices among (mainstream) economists was that of an inherent and unavoidable trade-off between distributional equality and the supply of goods: You cannot divide the economic pie more equally and, at the same time, have more of it. This view appears to be theoretically well founded. In savings-driven growth models, such as the ones implicit in classical economists’ writings, a more egalitarian pattern of (functional) income distribution involves a trade-off in terms of slower economic growth acting through a decline in national savings. In more recent neoclassical growth models of the Solow–Swan or optimal-capital-accumulation type, income distribution does not directly affect economic growth. Rather, feasible policy instruments of redistribution are seen as distortionary and detrimental to savings and growth; or as a famous quote of Okun (1975, p. 91) puts it: “the money must be carried from the rich to the poor in a leaky bucket. Some of it will simply disappear in transit”. However, while apparently well founded in economic theory, this conventional wisdom has been fundamentally challenged by a—large and still increasing—number of recent empirical studies (surveyed, e.g., by Perotti (1996)) which, all in all, deliver a consistent
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message: (initial) inequality is detrimental to long-run economic growth. Stimulated by this evidence, as well as theoretical developments in intertemporal macroeconomics and public choice, the last decade has witnessed a resurgence of academic work on income distribution and economic growth. This literature has worked out three transmission channels through which inequality in income and/or wealth distribution actually slows down economic growth. The first channel is an economic one. It works through capital market imperfections due to which the poor are denied an efficient amount of investment. With decreasing returns at the individual level, redistribution to the less endowed will be growth enhancing since their marginal product is higher.1 Secondly, there exists a politicoeconomic channel. In models endogenizing both economic growth and public policy, income inequality influences the balance of power in the political system in such a way as to generate pressure on the government to increase income redistribution that, in turn, reduces incentives and, thereby, slows down economic growth.2 This paper aims at highlighting the third, socio-economic transmission channel that has received much less attention in the set of theories linking inequality and growth.3 It is based on the general idea that deviant behavior and non-compliance to social norms reduces the security of property rights, thereby discouraging accumulation and impeding economic growth; an idea that can be traced back to classical economists such as Smith, Malthus, Bentham and J. St. Mill or even (as shown by the introductory quote) classical Greek philosophers. To illustrate that general idea, the present paper embeds Becker’s (1968) partialequilibrium rational-choice approach to criminal behavior in a dynamic general-equilibrium model.4 In doing so, it adds to the existing literature in two significant ways. The first one is of mainly expository nature. This paper modifies the heterogeneous-agents endogenous-growth OLG model first used by Persson and Tabellini (1994) and, subsequently, popularized by Bénabou (1996) as well as Aghion and Howitt (1998) by making explicit both the individual household’s human capital accumulation and the economy’s firms and production sector. Second and more importantly, the present paper supplements this model’s legal sector by an endogenous rational-choice derivation of criminal behavior: Based on their respective opportunity costs, individuals choose to specialize in either a legal or a criminal career. While legal households contribute to aggregate goods supply and factor accumulation by either working or building human capital, criminals make a living by expropriating legal citizens of part of the latter’s income. Using this integrated analytical framework, the present paper shows that when the gap between rich and poor widens in a society, the opportunity costs of criminal activities are decreased for those poorly endowed with productive abilities. The resulting increase in crime makes property rights less secure which, in turn, discourages investment, thereby, impeding economic growth. An increase in inequality, thus, possesses negative welfare effects for all agents with endowments equal to or above average, and for agents with endowment below average that are born sufficiently far in the future. The rest of the paper proceeds as follows. Section 2 develops the formal framework of analysis, starting with decentral optimizing decisions of both legal and criminal individual agents and moving to aggregate variables describing macroeconomic behavior. Section 3 solves for the economy’s equilibrium growth path and explores the effects of increased
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inequality on the economy’s growth rate and on the economic agents’ welfare. Section 4 discusses some of the empirical and public policy implications the model analysis may have and Section 5 concludes by providing a summary of results.
2. The Model This section presents an endogenous growth model incorporating a rational-choice derivation of criminal activity. The modelled economy consists of a sector of heterogeneous households of overlapping generations and a sector of firms producing the single good. Economic agents interact on a goods, a labor and a frictionless credit market.
2.1. Firms and Goods Production Production is carried out by firms. They operate with a constant-returns-to-scale production function which transforms human capital, measured in efficiency units of labor, into a homogenous good: Yt = AY Ht .5
(1)
Yt denotes output of goods, AY a productivity parameter and Ht efficiency units of labor employed in goods production. Firms choose the optimal employment of effective labor as to maximize the firm value, taking prices as given. This leads to an inverse demand function for effective labor according to which human capital is paid its marginal product which, in turn, implies wage rates to be constant over time: ∀t
wt = w = AY .
(2)
2.2. Legal Households and Human Capital Accumulation In every period t = 0, 1, 2, . . . there exist two generations of economic agents: an old generation, born in the previous period and a young generation, born in t. All individuals possess a life-expectancy of two periods and their number is constant over time. Each generation consists of a continuum of heterogeneous agents, indexed by i ∈ [0, 1], that differ in their human capital endowment. 2.2.1. Preferences Preferences of all individuals are defined over their respective consumption vector and will be represented by a Cobb–Douglas utility function. Accordingly, the utility of an individual i born at date t is given by i i Uti = ln c1t + β ln c2t +1 ,
(3)
i and c i where c1t 2t +1 denote consumption in agent i’s youth and old age, respectively, and β is a non-negative subjective discount factor.
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2.2.2. Youth Individuals differ in their initial endowments of human capital. Person i of generation t is born endowed with hi1t = εti h1t units of human capital, where εti is an identically and independently distributed random shock with mean normalized to one that measures individual i’s access to general knowledge, h1t ≡ E[hi1t ]. Each individual can either engage in criminal or in legal activities. When they choose a legal career, young households divide their total disposable time, normalized to unity, between time spent by using their effective labor in goods production (“working”), vti , and time spent to enhance their stock of knowledge, skills or health capital (in short, “learning”). All individuals are assumed to have access to the same technology of human capital accumulation. This technology converts time investment when young to improved labor quality, thereby permitting a higher flow of labor services when workers are old. In more concrete terms, in t + 1 the flow of efficiency units of labor from individual i of generation t will equal α (1−α) (4) hi2t +1 = AH eti h1t , where AH is a constant technological parameter, 0 < α ≤ 1 and eti = (1 − vti )hi1t denotes the amount of human capital invested by agent i of generation t in her youth period.6 With education technology (4) individual returns are decreasing, but the aggregate technology is linear due to intragenerational knowledge spillovers: Agent i can supplement his initial level of effective labor only through private investment but the higher the general level of human capital, h1t , the easier it is for each individual agent to acquire new skills and knowledge. Additionally, let us assume intergenerational spillovers (as in Persson and Tabellini (1994)) through which the average level of knowledge achieved by generation t − 1 becomes embodied into the basic human capital endowment of generation t: 1 hi2t di = h2t .7 (5) h1t = 0
With the fraction of human capital she does not invest into her further training the young household earns a labor income. In addition, she can make use of a frictionless credit market where agents in each generation borrow from and lend to each other at the endogenous interest rate r. Let the amount borrowed by individual i of generation t be denoted by bti . i Then, individual i’s young-age consumption, c1t , is restricted by the following budget constraint: i ≤ wt hi1t − eti + bti . (6) c1t 2.2.3. Old Age When old, a household born in t inelastically supplies all of her efficiency units of labor to goods production. However, in their old age legal individuals are subject to property crimes committed by the illegal fraction of population. Due to these criminal activities, we assume every legal household of generation t to lose a fraction κt +1
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of her old-age labor income. Society has (cost-free) access to some technology to capture and prosecute old-age criminals with a given probability, denoted by (1 − π). However, after a crime is committed the community is not able to reconstruct the original property rights. Therefore, out of the revenue collected from the income stolen by convicted criminals, the community of citizens transfers an equal per-capita amount 1 i y˜2t +1 = (1 − π)κt +1 y2t +1 di 0
to each of its legal members as financial compensation for committed crimes. Her resulting i income, yˆ2t +1 ,—net of principal and interest payments to creditors or from debtors—is spent on consumption by household i born in t: i i i i i c2t +1 ≤ yˆ2t +1 − (1 + rt +1 )bt = (1 − κt +1 )h2t +1 wt +1 + y˜2t +1 − (1 + rt +1 )bt . (7)
2.2.4. Individual Optimization Since training provides no non-pecuniary benefits, legal individuals’ educational choices are made to maximize wealth. Thus, the individual problem of lifetime-utility maximization can be solved as a two-step procedure. As a first step, household i of generation t chooses her optimal amount of human capital invested in further education, eti , simply to maximize her discounted lifetime income: (1 − κt +1 )hi2t +1 wt +1 + y˜2t +1 Max yLi t = wt hi1t − eti + 1 + rt +1 eti i i s.t.: 0 ≤ et ≤ h1t , α hi2t +1 = AH eti h1−α 1t .
(P1)
From first-order conditions, it follows that α(1 − κt +1 )
hi2t +1 wt +1 eti
wt
= 1 + rt +1 .
(8)
The return to an additional unit of human capital consists of its marginal product plus the gains that are connected with a change in the wage rate. Thus, condition (8), that governs optimal allocation of time, rules out any arbitrage between the returns to an investment into financial capital (right-hand side) and human capital (left-hand side). It also implies that every legal individual invests the same amount of efficient labor, et ; hence, we have for all legal households: i α 1−α 8 y2t +1 = AH et h1t wt +1 = y2t +1 .
(9)
In the second step of her lifetime-utility maximization problem, the household now intertemporally allocates her consumption by choosing her young-age net borrowing (or lending), bti , while taking as given her optimal time allocation (8). Regardless of their human capital endowments, all agents choose the slope of the consumption path according to the usual Euler equation which under our assumption of a logarithmic utility function implies
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= β(1 + rt +1 ).
(10)
Utilizing individual budget constraints (6) and (7) as well as the no-arbitrage condition (8), this becomes i c2t +1 i c1t
=
i (1 − κt +1 )AH etα h1−α 1t wt +1 + y˜ 2t +1 − (1 + rt +1 )bt
(hi1t − et )wt + bti h1t 1−α = βαAH (1 − κt +1 ) . et
Since all legal households have identical second-period incomes, the community’s financial compensation to the victims of property crimes is given by y˜2t +1 = (1 − π)κt +1 y2t +1 .
(11)
Taking (11) into account, summing over all agents and using the loan-market clearing condition: 1 bti di = 0, 0
yields et =
βα(1 − κt +1 ) h1t =: ut h1t . 1 + βα(1 − κt +1 ) − πκt +1
(12)
Thus, each legal household invests the same fraction ut of her generation’s average human capital endowment into her further education. Since (π − 1)βα ∂ut = < 0, ∂κt +1 [1 + βα(1 − κt +1 ) − πκt +1 ]2
(13)
criminal activity can be seen to pose a threat of expropriation of part of the returns to investment into human capital. Due to the distortionary character of insecure property rights, it thus reduces the fraction of a generation’s human capital endowment invested into further education. 2.3. Criminal Behavior The model of criminal behavior used here is in the choice-theoretical vein of Becker (1968) and Ehrlich (1973). An individual household will engage in criminal activities whenever his expected utility exceeds the utility he could get by using his time for legal activities. To keep matters simple, we shall assume that any individual has to decide whether to become criminal or not at the beginning of his life, and that if he opts for crime, he will have to spend his entire non-leisure time in both his periods of life on criminal activities. In addition, it is assumed that the only purpose of crime is to obtain the monetary reward. Unlike in Becker (1968), agents in this model do not engage in criminal activities simply
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because they like crime. Assuming, furthermore, that criminals may use the loan market in just the same way as legal households,9 it follows that an individual household will decide to become criminal if his expected maximized lifetime-income from criminal activity is larger than his maximized legal lifetime-income. The latter one amounts to yLi ∗ t
i y2t i 1 − πκt +1 +1 i i −1 . = wt h1t − et + = wt h1t + ut h1t 1 + rt +1 α(1 − κt +1 )
(14)
It has already been assumed that only old individuals are victims of crime and that every household of the old generation is robbed. The reward for engaging in criminal activity in one’s youth is, therefore, given by the average income of the old generation, wt h2t , whereas the reward to criminals in their old age is given by the average income of the legal members of their own generation, AH uαt h1t wt +1 . However, society has (cost-free) access to some technology to capture and convict criminals in the latter’s old age.10 Let the probability of not being caught and convicted in old age be represented by the constant π.11 If convicted, an individual is forced to return the income he has stolen in the current period.12 Accordingly, the expected discounted lifetime-income of a criminal member of generation t amounts to c πy2t +1 π = wt h1t + ut h1t E yLt = wt h1t + . (15) 1 + rt +1 α(1 − κt +1 ) According to our choice-theoretic framework, all those members of generation t will become criminal for whom 1 − π(1 + κt +1 ) j∗ =: h1t . −1 (16) E yLc t > yLi ∗ or hi1t < h1t 1 − ut t α(1 − κt +1 ) j∗
Thus, all individuals with human capital endowment above h1t will specialize in legal activity. While young they will invest a fraction of their time to build additional human capital, and they will work for the rest of their young-age time endowment and for their j∗ entire non-leisure time while old. On the other hand, individuals with ability below h1t will specialize in property crime. They will not acquire any education since for them it is optimal to live on their rewards for engaging in criminal activity. This, of course, implies that only poor people with little human capital endowment will become criminals. However, one should stress that this does not mean that poor people are inherently worse in any sense. It is assumed that everybody has the same preferences toward crime and, therefore, that everybody is equally inclined to follow the law. The implication of the model comes from the opportunity costs faced by rich and poor, respectively. It is simply more profitable for the highly endowed agents to be legal and for the poorly endowed to be criminal. We have assumed above that every legal member of generation t in his old age loses a fraction κt +1 of his income to criminals of both his own and the young generation. In addition, we have just seen that the fraction jt∗ of the poorest endowed members of generation t will become criminals. The economy’s overall resource restriction then requires
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the old legal agents’ income losses to criminals to equal the sum of the incomes received by old-age and young-age criminals: 1 jt∗ j∗ t+1 i κt +1 y2t di = y di + wt h2t +1 di 2t +1 +1 jt∗
0
0
which, in turn, implies: κt +1 = jt∗ + jt∗+1.
(17)
According to this, the fraction of income that legal agents loose to criminals equals the sum of the population shares of their own and the succeeding generation that become criminal. Taking another look at (16) and taking into account that the continuum of individuals in every generation was defined over the interval [0,1], it can be seen that the fraction of generation t that becomes criminal, jt∗ , is implicitly defined by the value of the cumulative j∗ distribution function of the variable hi1t , denoted by Fh (·), at h1t : j∗ jt∗ − Fh h1t = 0. Moreover, the distribution of relative endowments, hi1t /h1t = εti , is stationary which via (16) will result in both a time-invariant fraction of legal income lost to criminals, i.e. ∀t; κt = κ, and a constant share of criminals in the population.13 For analytical simplicity, let us restrict our attention to the case that ln h1t is normally distributed with mean µt and variance σt2 , i.e. ln hi1t ∼ N (µ, σ 2 ). Then j ∗ is implicitly given by the value of the cumulative standard normal distribution function at j∗ ln h1t − µ 1 − π(1 + κt +1 ) −1 1 2 =: x, =σ σ + ln 1 − ut −1 σ 2 α(1 − κt +1 ) i.e. j ∗ − $(x) = 0.
(18)
This expression now allows us to analyze the effects of an increase in income inequality on a generation’s crime-rate: Lemma 1. A more unequal distribution, in the usual sense of a mean-preserving spread in hi , leads to an increase in the share of the population that engages in criminal activity and, thus, reduces the security of individual property rights. Proof: See Appendix 6.1.
3. Crime, Inequality and Intertemporal Allocation 3.1. Growth Effects of Inequality The average growth rate of individual human capital within each generation is given by
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1 γth
0
hi2t +1 di
:= 1
i 0 h1t
di
1 =
j∗
AH (uh1t )α h1−α 1t di h1t
= 1 − j ∗ A H uα .
(19)
For the labor market to clear in any given period, the input of efficiency units of labor into goods production must equal the sum of the young and old generations’ effective labor supply: 1 1 i Ht = h1t − eti di hi2t di + 0
0
= 2−
j∗ 0
εti
di − u 1 − j AH uαt h1t −1 1 − j ∗ .
∗
Thus, it can readily be seen that the average individual and the aggregate growth rates of human capital coincide: γtH :=
Ht +1 h1t +1 = = γth . Ht h1t
Since human capital is the ultimate driving-force of the economy, its common rate of accumulation also determines the growth rates of the model’s other level variables: Proposition 1 (Long-term growth). In the modelled economy, aggregate output as well as economy-wide human capital and consumption all grow at the average growth rate of individual human capital: γ ∗ = γ Y = γ C = γ H = γ h = 1 − j ∗ A H uα . Proof: See Appendix 6.2.
As shown by Lemma 1, the respective generations’ share of criminal agents depends on the extent of the economy’s inequality. Therefore, a mean-preserving spread in the distribution of human capital endowment can influence the economy’s growth rate both directly and indirectly by its distortionary effects due to less secure property rights: Proposition 2. An increase in inequality reduces the economy’s growth rate. Proof: As shown by Lemma 1, a mean-preserving spread in the distribution of human capital endowment increases the criminals’ population share. Furthermore −1 ∂u ∂κ ∂γ ∗ α ∗ 1 − j αu = A u − 1 < 0. H ∂j ∗ ∂κ ∂j ∗ Thus ∂γ h ∂j ∗ ∂γ ∗ = ∗ < 0. 2 ∂σ ∂j ∂σ 2
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The growth rate of both aggregate human capital and output is reduced by higher inequality for two reasons. First, an increase in the inequality of first period human capital endowment induces a higher fraction of economic agents to become engaged in criminal activity. Since criminals have no incentive to spend their time on further education, this directly reduces the number of investors and, thus, the amount invested in further human capital accumulation. Secondly, the inequality induced increase in criminality leads to a decline in the security of property rights of those agents that remain legal. Expecting (with subjective certainty) to be expropriated of part of the returns to investment into human capital in their old age, young legal households spend less time on further educating themselves, and the resulting decline in economy-wide investments slows down economic growth.
3.2. Welfare Effects of Inequality Welfare effects of a change in inequality differ according to the respective individual’s human capital endowment relative to the average one. Any agent i’s optimal consumption path entails a net borrowing of bti =
β wt h1t − hi1t . 1+β
(20)
This implies that an agent with human capital endowment equal to the average one, h1t , does not make use of the loan market. Her indirect intertemporal utility is thus given by Vt∅ = (1 + β) ln h1t + ln(1 − u) + β ln (1 − κ)AH uα . (21) The indirect utility function for any other individual i can now be expressed as the sum of the intertemporal utility of the individual with human wealth equal to the average and an individual specific term: Vti = Vt∅ + (ti , where the latter one is given by hi1t /h1t − 1 i (t = (1 + β) ln 1 + . (1 + β)(1 − u)
(22a)
(22b)
These expressions allow for the analysis of the welfare effects of a change in distribution: Proposition 3. An increase in inequality reduces the welfare of all individuals with human capital endowment equal to or above average. In general, the welfare effects for agents with human capital endowment below average are ambiguous. However, at least for those poorly endowed individuals who belong to generations born sufficiently far after an increase in inequality, the overall welfare effects of that increase will be negative as well.
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Proof: Differentiating (21) with respect to the variance of the distribution of human capital endowments gives ∂j ∗ 1 + β ∂h1t (π − 1)2 βακ ∂Vt∅ 2 = − − ∂σ 2 ∂σ 2 h1t ∂j ∗ (1 − κ)(1 + βα (1 − κ) − πκ)(1 − πκ) 1 − κ < 0. The individual specific utility term (22b) is such that: < 0 for hi1t > h1t , ∂(ti ∂j ∗ ∂(ti = = 0 for hi1t = h1t , ∂σ 2 ∂σ 2 ∂j ∗ > 0 for hi1t < h1t . Accordingly, welfare effects for individuals with human capital endowment equal to or above average are unambiguously negative. Welfare effects for poorly endowed individuals are, in general, more ambiguous. On the one hand, as measured by ∂Vt∅ /∂σ 2 < 0, their welfare is reduced as a result of both the negative incentive effect of less secure property rights and the resulting negative growth effect which leads to a decrease in their inherited stock of human capital. On the other hand, as captured by the positive sign of ∂( i /∂σ 2 , the welfare of those with a human capital endowment below average is raised due to the redistributional effects implicit in the community’s compensation scheme from convicted criminals to lawful agents. However, let us assume that the inequality of endowments increases in period T to remain at that higher value in all future periods. Then the positive partial welfare effect for poorly endowed individuals, as expressed by the first derivative of the individual specific term (22b), remains constant for any t > T . On the other hand, human capital endowment of a young household born in t is given by h1t = h1T (1 + γ ∗ )t −T . Thus, the negative partial welfare effect: ∂h1t ∂γ ∗ = (t − T )h <0 1T −1 ∂j ∗ ∂j ∗ increases with t, due to the negative growth effects of increased criminality. Therefore, at least for poorly endowed individuals in generations born sufficiently far after the increase in inequality, the overall welfare effects of that increase will be negative as well. 4. Empirical and Public Policy Implications 4.1. Empirical Assessment The main results derived from the above dynamic general equilibrium model and their respective empirical implications are consistent with key features of the U.S. and international data. As mentioned in the introduction, the positive reduced-form relationship
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between equality and growth that the above model implies, is confirmed by a large number of recent empirical studies (see Perotti (1996) for a nice survey). However, a reducedform estimate cannot shed light on the underlying mechanisms and the positive equalitygrowth correlation is consistent with alternative (economic or politico-economic) transmission channels as well. To evaluate the specific socio-economic channel of operation of income distribution proposed in the present paper, one has to look at empirical support of its two logical components: (1) greater inequality is associated with higher crime-rates; and (2) an increase in criminal activities reduces an economy’s growth rate. First, the above model predicts greater inequality to be associated with higher rates of crime. This relationship has general empirical support, even though a causal link is not as well documented. Several authors have used income inequality measures in their statistical models, but they disagree on whether inequality captures costs or benefits to crime. Mathur (1978) uses the Gini coefficient to measure the benefits to crime and finds its effect on crime to be ambiguous. On the other hand, Ehrlich (1996) uses an income distribution variable to capture opportunity costs of crime and finds it to be statistically significant. Based on his own, as well as related, empirical studies, Freeman (1996, p. 33f.) concludes that higher inequality is associated with higher rates of crime. Finally, Imrohoroglu, Merlo and Rupert (2000) also find the standard deviation of income and the poverty crime rate in 1990 to be positively correlated at the U.S. state level. Secondly, criminal activity should have some bearing on an economy’s goods supply or—in intertemporal terms—growth. In the real world there are two indicators of the aggregate cost of crime to society. On the one hand, there are opportunity costs of crime control, i.e. the resources used for police, prisons, private spending on security, etc. that could be spent on other activities. On the other hand, the costs of crime control lead to some “accepted” level of crime and, thus, there are losses from those remaining criminal activities. Based on data from the U.S. National Crime Survey and various criminological studies, Freeman (1996) estimates the average cost of crime, including non-pecuniary costs and losses of production by the incarcerated, for the U.S. to amount to as much as 2 percent of national GDP and reports, in addition, another 2 percent of GDP to be allotted to crime control activities. Therefore, up to 4 percent of U.S. national GDP could be spent on whatever ways and means to make all potential criminals forego crime and social wellbeing would still be improved. This latest figure also provides a way to compare the inequality-growth link proposed in the present paper to alternative explanations, in particular endogenous fiscal policy and rent seeking. Turning to the endogenous fiscal policy approach first, one has to note that the politico-economic mechanism, whereby higher redistribution through well-defined, orderly channels and by legal means (in particular political activity and legislation) reduces growth, receives little or no empirical support. Easterly and Rebelo (1993) include various average and marginal tax rates in growth regression and find the coefficients are almost never significant. Several studies, including Perotti (1992), Perotti (1996), and Sala-iMartin (1997), even find a significant positive relation between redistributive fiscal instruments (tax rates and transfers, respectively) and growth. As Perotti (1996, p. 171) summarizes his findings in empirical tests of the politico-economic theory: “these results are difficult to explain for virtually any of the existing standard economic and political models
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of fiscal policy”. Regarding, secondly, the rent-seeking thesis, one should note both analogies to and differences from the model presented in this paper. On the one hand, defining rent seeking as “the socially costly pursuit of wealth transfers” (Tollison (1997, p. 506)), criminal activity as presented above might well be interpreted as a way of rent seeking taking place in a non-governmental setting: Property crime is an activity of transfer seeking and it embodies a social cost both in terms of the foregone product (or investment) of the criminal fraction of population and the deadweight costs of insecure property rights resulting as a by-product of such activities. Indeed, some of the measures of rent-seeking costs used in empirical estimates (like, e.g., “crime prevention”, “police”, “private spending on locks and insurance” or “property-rights disputes”) are categories which could be equally well understood as costs of crime or crime control. On the other hand, the criminal activities the present paper brings in as explanation for the effect on growth—like, e.g., theft and robbery—are more of the small-criminality type, rather than the type of threat to property rights that derives from corruption, bribery, and the effect of rent seeking in general. There are numerous empirical results on the social cost of rent seeking, varying with the study’s methodology as well as the time-period and economy analyzed (see Tollison (1997) for a survey). Estimates of the costs of rent seeking vary between 3% (Posner (1975) for the U.S.) and 50% (Laband and Sophocleus (1992) also for the U.S.) of GNP. In one sense, these generally large numbers show the absolute as well as the comparative importance of rent seeking. However, their variation is too wide to allow for a definitive assessment of the relative weight of criminality versus corruption, bribery, etc. Also, as mentioned above, several of the empirical measures of rent-seeking costs used in those studies could be equally well understood as costs of crime or crime control. The bottom line on all of this is that criminal behavior appears to be empirically important for explaining the effects of income inequality on economic growth both in absolute terms and in comparison to more orderly defined means of redistribution, in particular fiscal policy and rent seeking.
4.2. Public Policy Implications Given that, as we have seen above, an increase in inequality induces a rise in criminal activity that has detrimental effects on both economic growth and individual welfare, one is naturally led to think of income redistribution through a government tax-and-transfer scheme as an effective way to not only reduce crime, but also exploit the growth and welfare potential which is created by too high a level of inequality.14 However, since individual incentives to become criminal stem from the individuals’ heterogeneity in initial human capital endowments, for such redistributive policies to potentially have any growth benefit, they must take place before investment is completed. By what measures could the original endowments be changed and by whom? Aghion, Caroli and García-Peñalosa (1999) consider an ex-ante redistribution of endowments which consists of taxing highly endowed individuals directly on their endowments, and then using the revenues from this tax to subsidize the less endowed.15 Because this amounts to a lump-sum tax-and-transfer policy, it only affects the incentives to invest in education insofar as it changes the economic agents’
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current wealth. Since, in the above model, any legal household’s investment in human capital accumulation is independent of individual current wealth, while a more equal distribution of endowments lowers the fraction of a generation which specializes in a criminal career, redistribution will have an overall positive effect on aggregate output and growth. In reality, of course, lump-sum taxation is rare (to say the least). If redistribution were financed through distortionary (ex-post) taxation, there would be a negative incentive effect which would conflict with the positive career-choice effect: taxation reduces net returns to education investments and, therefore, individuals’ incentives to build human capital. Then, whether redistribution raises or reduces the rate of growth depends on which of the two conflicting effects dominates.
5. Conclusion The present paper studied the dynamic general-equilibrium interactions between inequality, crime and economic growth by embedding the rational choice-theoretical approach to criminal behavior in an heterogeneous-agents endogenous-growth OLG model. Based on their respective opportunity costs, individuals rationally chose to specialize in either legal or criminal activities. While legal households contributed to aggregate goods supply either in or over time by either working or building human capital, criminals made a living by expropriating legal citizens of part of the latter’s income. In this model economy, aggregate output as well as economy-wide human capital and consumption all grew at the average rate of individual human capital accumulation. An increase in inequality, as measured by a mean-preserving spread in the young-age human capital endowment, lowered the growth rate of the economy and possessed negative welfare effects for all agents with endowments equal to or above average and for agents with endowment below average that are born sufficiently far in the future. All in all, the above analysis—while in itself fairly restrictive—serves to make a point of more general validity. The disincentive effects of a (partial) expropriation of individuals’ returns to their positive contribution to an economy’s goods supply over time need not come from the political sphere only. In addition to such politico-economic transmission mechanisms as redistributive taxation in a democracy, there obviously also exist socio-economic channels that mediate the relationship between distribution and growth. As an example, it was shown above that when the gap between rich and poor widens, the opportunity costs of criminal activities are decreased for those in a society poorly endowed with productive abilities. The resulting increase in crime makes property rights less secure which, in turn, discourages investment, thereby impeding growth. But, as mentioned before, this should be seen as merely one of several transmission channels through which inequality and social background conditions interact to constrain or foster economic growth—channels remaining to be further elaborated on in future research.
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6. Appendix 6.1. Proof of Lemma 1 Since κ as an element of x depends on j ∗ , equation (18) only implicitly defines j ∗ . Let an increase in inequality be identical with or correlated to a mean-preserving spread in hi , as indicated by an increase in σ 2 . Utilizing the implicit function theorem, we then have ∂j ∗ −(∂$/∂σ 2 ) = − , ∂σ 2 1 − ∂$/∂j ∗ with ∂$ = ∂σ 2
∂$ 1 −3 j 1 − σ ln h1t /h1t >0 4σ 2 ∂x
and ∂$ ∂$ 2β{(π − 1)(π(1 + κ) + α(1 − κ) − 1) + 2π − 1} < 0. = ∂j ∗ ∂x σ (1 − κ){1 + 2βα(1 − κ) − πκ + β(π(1 + κ) − 1)} Thus, we have ∂j ∗ > 0. ∂σ 2 6.2. Proof of Proposition 1 It has already been shown that γtH = γth . From (1), it immediately follows that γtY =
Yt +1 AY Ht +1 = = γtH = γth . Yt AY Ht
Finally, the goods market clearing condition or resource constraint of the modelled economy without physical capital requires Ct = Yt , where Ct is aggregate consumption. Therefore, γtC = γtY = γtH = γth . Acknowledgments This paper has benefited from comments by F. Revelli, S. Voigt, H.-P. Weikard, and Nicolas Marceau, as well as other participants of the Annual Conference of the European Public Choice Society (EPCS) 2002 in Belgirate, the 2002 Annual Congresses of the International Institute of Public Finance (IIPF) in Helsinki and the Verein für Socialpolitik in Innsbruck. For helpful suggestions I am also indebted to three anonymous referees. The usual disclaimer applies.
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Notes 1. Seminal papers within this subset of theory include Galor and Zeira (1993), Banerjee and Newman (1993), Bénabou (1996) as well as Aghion and Bolton (1997). 2. Important contributions to this field of study include Bertola (1993), Alesina and Rodrik (1994) as well as Persson and Tabellini (1994). Perotti (1993) as well as Saint-Paul and Verdier (1993) combine asset market incompleteness with the politics of redistribution. 3. A notable exception is given by Benhabib and Rustichini (1996). They focus, however, on social conflicts between groups rather than individual deviate behavior. 4. Imrohoroglu, Merlo and Rupert (2000), Benoit and Osborne (1995), as well as Grossman (1991, 1995) and Grossman and Kim (1996), study inequality and crime in general equilibrium models, but they restrict their analyses to static frameworks. Sala-i-Martin (1997) uses an endogenous growth model incorporating criminal behavior but (in the growth section of his paper) neither derives the amount of crime endogenously nor relates it to inequality in distribution. 5. As in De Gregorio and Kim (2000), it is assumed that no physical capital exists. An introduction of physical capital into the model would significantly increase the analytical effort involved while not changing the main features and results of the model. 6. In general, time-indices indicate the current period (not generation). Variables which relate to both generations co-existing in any given period are double-indexed with the first index indicating young age and the currently born generation (“1”) or old age and, thus, the generation born in the previous period (“2”), respectively. Accordingly, hi1t and hi2t+1 refer to the human capital of individual i born in period t in his young-age period t and his old-age period t + 1, respectively. Since agents invest only in their youth, invested human capital e carries only a single index giving the period of investment. 7. As shown by Bénabou (1996), this dynamic linkage between generations can equivalently be motivated by altruistic parents, which devote some of their second-period resources to their children’s education. 8. It might be well worth noting at this point that the interpersonal equality of both first-period education investments and second-period incomes is not an assumption, but results from the (legal) individuals’ utilitymaximizing choices. Due to the frictionless credit market, opportunity costs of an investment into human capital, namely the interest rate, are the same for all households—regardless of whether they are net borrowers or lenders. When capital markets were assumed to be imperfect, equilibrium investments would differ across heterogeneous agents, being an increasing function of the latter’s initial endowments in human capital. Because of decreasing returns with respect to individual human capital investments greater inequality would then reduce aggregate output and growth even in the absence of criminal activity (see Bénabou (1996) or Aghion, Caroli and García-Peñalosa (1999) for more formal analyses). To be able to separate analytically the crime-induced growth effects from any effects which are due to capital market imperfections, it is, therefore, helpful to consider criminal activities in an environment of perfect credit markets. 9. Initially, this assumption might seem to be particularly counter-intuitive. Upon closer reflection, however, it is not as unrealistic as it might seem at first sight. Note that criminals do not invest—neither in education nor in some “criminal technology”. They thus use the loan market for intertemporal consumption smoothing only, and for this informal loans (perhaps provided within the underground economy itself) seem both realistic and adequate. 10. Why only in old age? One intuitive justification for this assumption are diminishing physical capabilities that, on the one hand, should play a more important role in a criminal career based on robbing other people than in a legal career based on education and that, on the other hand, can plausibly be expected to grow less over a criminal’s life cycle. Analytically, this assumption avoids a bankruptcy problem: When caught twice, i.e. both in their young and in their old age, some criminals might end up with no income and no possible consumption. 11. In general, a criminal’s probability of being caught and convicted should be an increasing function of the level of public and private expenditures devoted to the apprehension of criminals. However, there is no consensus in the literature on what is the most appropriate functional form to describe the apprehension technology, and empirical work to date has failed to provide compelling evidence in favor of any particular specification (see Pyle (1983) for a survey)). Furthermore, Stigler (1970) shows that if law enforcement
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12.
13.
14.
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is costly, there is an optimal amount of enforcement that may be lower than the maximum allowed by the current technology. One could think, for instance, of fixed resources devoted to law enforcement (generating increasing returns to crime), or of endogenizing that level through a vote. Since, however, the focus of the present paper is not on optimal punishment or crime control policy but on intertemporal effects, we chose to trade generality with respect to the apprehension technology for analytical tractability and so specify the probability of apprehension of criminals in the most basal manner. In this perspective, π can best be understood as a criminal’s probability of not being caught and convicted given the existing technology and the optimal level of public effort. Thus, apprehended criminals are subject to partial restitution of what they stole, but not to any additional penalties. Analytically, this assumption again avoids a bankruptcy problem: When forced to pay a monetary fee which is higher than the income stolen in the current period, some criminals might end up with no possible consumption. This analytical problem also indicates that a threat of pecuniary penalties over and above the stolen income could not be credible: with criminals not having any legal sources of income, where should this money come from? Some crimes, of course, are penalized with physical or non-monetary fees (the death penalty being the ultimate example). The present analysis, however, abstracts from these forms of penalties. Strictly speaking, only the first time-invariance follows from (16). A constant κ might well be consistent with a cyclical pattern in j ∗ . For analytical simplicity, however, the following will focus on the case of j ∗ constant over time. Of course, the fact that crime and income inequality are positively correlated has often been used to support the idea that income redistribution can reduce property crime. Smith and Wright (1992), Benoit and Osborne (1995), Grossman (1995) as well as Sala-i-Martin (1997) all advocate the use of government policies that involve redistributing income from rich to poor as an effective way to reduce crime. Supposing that human capital endowments are acquired—with different talents and under diverse social conditions—during an (unmodelled) first period of life with compulsary school attendance, such a policy corresponds, for instance, to a redistribution of education budgets across rich and poor school districts, as is done explicitly in a number of U.S. states and implicitly in countries with a national system of education finance. More detached from the above model’s set-up one can, equivalently, think of a land reform as a means to redistribute original endowments. Alesina and Rodrik (1994), among others, refer to the idea that land reform was an important factor in the growth performance of Japan, Korea, and other Asian countries, in particular when compared to Latin American economies.
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