Abstract
This paper analyzes the role of social safety nets in the form of redistributional transfers and wage subsidies. It argues that public welfare programs can be viewed as devices to prevent crime or disruption because they tend to increase the opportunity cost of engaging in crime or disruptive activities. It is shown that, in the presence of a leisure choice, wage subsidies may be better than pure transfers. Using a simple growth model, the optimal size of the public welfare program is found, and it is argued that public welfare should be financed with income (not lump-sum) taxes, despite the fact that income taxes are distortionary. The intuition for this result is that income ta.xes act as a user fee on congested public goods and transfers can be thought of as productive public goods subject to congestion. [JEL H53, H55, H56, 040,015]
Transfers, Social Safety Nets, and Economic Growth
In the last quarter of the nineteenth century, as the leading nations of Europe and North America emerged from the throes of the Industrial Revolution, the introduction of social safety nets was increasingly regarded as a social necessity. The sight of poverty in the midst of plenty, of need amid unused resources, made societies feel that the government should take on the role of helping the destitute. Traditionally, the job of protecting the poor was held by religious foundations, extended families, or good-hearted criminals like Robin Hood or Curro Jimenez. But. following the lead of the first Chancellor of the German Empire, Otto von Bismarck (1871-90), public welfare programs were instituted in virtually all countries. For nearly a century, it was almost an unquestioned reality that the public sector had the moral and actual obligation to provide social protection. And so, social security programs grew larger and larger all over the world. Today, public transfers in the United States account for almost one-half of all federal spending and involve three times as much money as public investment and more than twice as much as national defense. International institutions like the World Bank and the International Monetary Fund spend a great deal of time and effort worrying about the effects of their programs on the very poor and wonder about how to introduce social safety nets in the countries experiencing economic transitions (IMF, 1993: and Chu and Gupta, 1993).
A century after the introduction of social security in Imperial Germany, the conservative movement led by Ronald Reagan in the United States and Margaret Thatcher in Europe introduced doubts in the minds of many citizens as to the desirability of public welfare programs. Questions like. What are the benefits of social security? and How large should public welfare programs be? have replaced the widely held beliefs that “society” (and. on its behalf, the government) should protect the destitute and that more security is always better.
Whether to have a social security program and, if so, how big it should be are important questions. These questions, however, cannot be answered until we understand why such programs exist in the first place. Several stories have been provided as probable explanations of the existence of public welfare programs. The simplest one is that of social altruism: human societies dislike the sight of poverty in the midst of wealth (Stark, 1995). Alternative explanations are based on median voter behavior: the median voter is poor and votes himself a big transfer, or the median voter gives a transfer to the poor in order to buy his vote. (Persson and Tabellini, 1994; and Tabellini, 1993.) Although these are potentially interesting Nicotics, they will not be explored here.
But the important explanation is that the economic growth literature has uncovered a puzzling positive association between the size of transfer programs and the growth rate of the economy. One example of such a relationship is the following:
where R2 = 0.37 and the number of countries in the regression is 75. In the above regression, γ is the growth rate between 1970 and 1985 for a cross section of 75 countries. In (y) is the log of the initial level of GDP per capita, τ is a measure of the size of taxes in each economy, s is the savings rate, and TR is the size of public transfers as a fraction of GDP. The coefficients on all the variables are the ones expected by reasonable theories, except for the one on transfers:1 transfers appear to be a productive public input.2 If transfers are devices that satisfy social altruism or if they are gifts the median voter votes for himself, they should not have any effect on growth. Furthermore, if. as they are in the real world, transfers are financed through distortionary taxes, they should have a negative effect on growth.
This paper provides an alternative rationale for the existence of public welfare programs and their relationship to economic growth.3 Its main point is that transfers and other social safely net mechanisms are a means to buy social peace, a way to reduce social unrest. They are a way to bribe poor people out of activities that are socially harmful, such as crimes, revolutions, riots, and other forms of social disruption.4
This idea is not new. In fact, von Bismarck himself has been quoted as saying that his main reason for introducing the social security program was to keep the socialist movement out of Imperial Germany.5 Nevertheless, this paper makes some contributions to the literature on social security. First, it shows that public welfare programs may reduce social disruptions. Second, these programs may actually increase the growth rate of the economy, even if they are financed with distortionary taxes. Third, public welfare spending may look like public productive spending subject to congestion. And fourth, as a result of the third finding, financing social security through income taxes is superior to financing it through nondistortionary taxes.
The rest of the paper is organized as follows. Section I presents a partial equilibrium model where people choose the amount of time they want to devote to criminal activities. The model is in the spirit of Becker (1968) and Ehrlich (1973), but, unlike them, this paper does not try to determine what policies are optimal for combating illegal behavior (such as the optimal severity of punishment or the optimal size of penalties for different types of crimes). The goal of this section is to show that transfers and other forms of social safety nets act as devices that reduce the incentive to commit crimes because they increase the amount of income one can legally receive outside jail. These results are shown to be robust to the inclusion of leisure, even though economic intuition says that transfers unrelated to work effort could have a perverse effect on criminal intensity.
One of the key results of the first section is that the decision to commit crimes is based on the size of transfers relative to the average level of income of the economy. Hence, in the aggregate economy, transfers look very much like a public good subject to congestion: when a person increases his income, the average income of the economy also rises. This increases the reward for criminal behavior and, concomitantly, the protective role of transfers is congested.
Section II incorporates the analysis into an aggregate model of growth, revealing the growth-maximizing amount of public welfare in the economy as the government balances the beneficial, protective effects of transfers and wage subsidies with the adverse effects of the distortionary taxes needed to finance such programs. It also shows that the government can replicate the planner’s solution by using income taxes and not lumpsum taxes. The intuition is that income taxes act like “user fees” on the protective role of the public welfare policies.
Section III concludes.
I. A Partial Equilibrium Model of Criminal Behavior
The model used here to analyze transfers extends Becker (1968) and Ehrlich (1973), Let ti, be the fraction of time an individual devotes to illegal, criminal, or disruptive activities, such as thefts, robberies, strikes, or revolutions. After normalizing total nonleisure disposable time to one. the time devoted to legal activities is 1 - ti. The reward for devoting one unit of time to a legal activity (work) is the wage rate w. The reward for engaging in criminal activity is βy per unit of time, where y is the average income of the economy and β is a number between zero and one. If we argue that criminal activity is akin to mugging people on the street and that the average person carries a fraction β of his income in his pocket,6 then βy is the reward per unit of time devoted to crime and βyti is the reward for criminals who choose to devote ti, units of their time to this activity. 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 because they like crime.7 Utility is solely a function of consumption.
Society, through its government, has access to some technology to capture and prosecute criminals. The probability of a criminal being caught and convicted is represented by π. This probability should be an increasing function of the effort the government puts into enforcing laws. It can also be thought to be an increasing function of the amount of crime committed by any given person. In this first, simple model, however, π is assumed to be independent of the number of crimes people choose to commit.8 This assumption will be relaxed later on. Stigler (1970) shows that, if law enforcement is costly, there is an optimal amount of enforcement that may be lower than the maximum allowed by the current technology. Hence, the probability of capture need not be one. even though achieving such probability may be technologically feasible. We can simply think of π as the probability of capture and conviction given by the existing technology and the optimal level of public effort.
An individual’s preferences can be represented by the following expected utility function:
where cp is the level of consumption if he is caught and convicted (p stands for “penalized”) and cnp is the level of consumption if he is not penalized.
The level of income if the individual is not convicted is equal to legal work income. w(1-ti), plus the income he gets from his criminal activities, βyti. It is further assumed that there is a public welfare system in the economy. Public welfare could take the form of either a lump-sum transfer T or a subsidy on the wage w.9 Given that the model is static, all income is consumed, so that the level of consumption if the individual is not convicted is
If convicted, an individual must pay a monetary fee F. which is related to the level of income.10 This relationship could reflect the wages forgone while the individual is serving time in jail, or the reduction in lifetime income attributable to the stigma attached to convicted criminals: conviction may stigmatize offenders by demonstrating that they are untrustworthy. To the extent that jobs that require trust have better wages, the loss of such jobs will be an additional reason why the fee is related to the level of income. Waldfogel (1992) quantifies the importance of this effect empirically. It is assumed here that the fee is homogeneous of degree one in the amount of income one earns if not convicted:
where the fraction of income lost if convicted is λf(ti). and f´(ti) > 0, f(0) = 0, and f″(ti) > 0. In the above. λ indicates the severity of the fee per unit of crime, and f(ti) relates the amount of crime to the severity of the penalty. The assumption on the concavity of the penalty is made to ensure that the second-order conditions are satisfied.11 Consumption if convicted is therefore
One feature of this analysis is that, since the probability of the individual’s being caught is independent of whether he actually commits crimes or not, he will have to pay the fee with probability π, even if ti= 0 (in other words, people could be erroneously prosecuted and convicted). Assuming that the fee people pay when they commit no crimes is zero (as f(0) = 0) and, in addition, that they do not suffer any disutility from being penalized, then whether innocent people are penalized or not is irrelevant (that is. cp(ti = 0) =cnp(ti = 0)). Another way to think about the constant probability model is the following: every person faces a probability π of being investigated or searched by the police. If the police search an individual and discover that he has committed a crime, he must pay a fee. If he did not commit a crime, he pays nothing.
Individuals choose tt so as to maximize utility (2) subject to equations (3), (4), and (5). The first-order condition entails the equalization of the marginal utility of tt to zero. This condition can be rewritten as
If we assume that the maximum possible fee is all income (λf(ti) < 1), then the term inside the square brackets is positive. Since the right-hand side of equation (6) is positive, people will devote positive amounts of effort to criminal activities only if β> w/y. In other words, only if the reward for committing crimes is higher than the reward for spending the same time in a legal activity will people commit crimes. This, of course, implies that only poor, low-wage people will become criminals (rich people can earn more money by working).12 The second-order condition that ensures that this is a maximum is
Figure 1 plots the marginal benefit MB (which corresponds to the left-hand side of equation (6)) and the marginal cost MC (which corresponds to the right-hand side of equation (6)) of criminal behavior. Because the fee is convex, the marginal cost is upward sloping. The marginal benefit is downward sloping. The optimal amount of criminal activity is determined by the crossing of MB and MC. If they cross at a point where ti is between zero and one, the solution will be interior. If they cross to the right off ti = 1. individuals will become full-time criminals. If they cross to the left of ti = 0, individuals will devote all their time to legal activities.
Optimal Criminal Behavior
Citation: IMF Staff Papers 1997, 001; 10.5089/9781451957112.024.A004
The Effects of Growth on Crime
Imagine that the average income, the transfer received by potential criminals, and the wage rate all increase in the same proportion. The first-order condition says that the amount of crime remains unchanged. In other words, in an economy where the fines, wages, and transfers are fully indexed, the amount of crime is invariant to the level of income. The reason is that the rewards and costs of engaging in criminal behavior increase in the same proportion, and. therefore, there is no additional incentive or disincentive to perform such activities.
Penalty systems that are not fully indexed, in contrast, will tend to generate more crime as the economy grows since the rewards for committing crimes grow faster than the penalties. In terms of the analysis, this would correspond to a steady decline of λ, holding everything else constant (this case will be analyzed later on). The model, therefore, does not directly predict the relationship between the amount of crime and the level of income of the economy.
Increase in Income Inequality
Economic development is not always homogeneous across people: income inequality may increase or decrease as the economy develops. Some people argue that income inequality rises in economies in transition. In fact, this is what leads institutions like the World Bank and the IMF to worry about the introduction of social safety nets.
We can now analyze the effects of an increase in income inequality on the optimal amount of crime. In the present setup, this can be thought of as a reduction in the wage rate w, holding constant the average level of income y, or a reduction in w/y. The MB schedule in Figure 1 shifts up while MC shifts down. The result is an increase in the optimal amount of crime. This can also be seen by applying the implicit function theorem to the first-order condition:
The intuition is that an increase in income inequality reduces the benefits of working in the legal sector while keeping the gains from crime constant. The obvious optimal reaction is an increase in crime. Hence, models that predict that economic growth is associated with larger income inequality will also predict an increase in disruptive activities. Ehrlich (1973) provides evidence supporting this proposition.
Better Law Enforcement
Consider now an increase in the probability of conviction. This could be the result of higher investment in police protection or an improvement in the technology used by the police force. In terms of Figure 1, the MC line shifts upward while MB remains unchanged. The total amount of crime goes down. The exact change is given by
Again, the intuition is straightforward: a higher probability of being caught and convicted lowers the expected rewards of criminal activity and, therefore, lowers the number of crimes committed.
Larger Fees
Imagine now that the authorities decide to increase the fees paid for every level of crime. This corresponds to an increase in λ in the model. The MB schedule shifts down and MC shifts up. The result is a reduction in the amount of crime. The quantitative change is given by
When penalties for being convicted are high, crime is low.
More Transfers and/or Wage Subsidies
Finally, consider the effect of an increase in transfers (while maintaining average income constant). Because of the linear homogeneity of the fee with respect to income, the marginal benefit of committing crimes does not change. The marginal cost, however, increases as people who are convicted forgo a larger amount of income. The result is a reduction in crime:
Transfers in this model act just like fees because they increase the (opportunity) cost of being penalized: when convicted, people lose a fraction λf(ti) of their income. Of course, the more they earn, the more they lose if convicted. In other words, transfers provide an incentive to stay away from criminal activities by increasing the level of income outside jail. Hence, governments may want to use transfers as a mechanism to bribe people out of crime: when transfers are high, crime does not pay.
Note that this result depends on an increase in transfers relative to income. Transfers of a certain amount protect the population against crime, given the amount of income. Income is the prize that criminals obtain by committing crimes. Holding constant the degree of protection (transfers), an increase in the prize (income) induces people to commit more crimes.
Using cross-country data for 40 industrial and developing economies, Tabellini (1993) finds that the level of transfers per unit of GDP is positively related to the pretax level of income inequality, even after he holds constant the initial level of income and the ratio of the elderly to the total population (both variables are significantly positively related to the level of transfers). He provides a political economy explanation for this finding. The theory outlined in this paper, however, is also consistent with these correlations: income inequality leads to high levels of crime and. therefore, to the need for public welfare protection.
A natural question to ask is, Why and when would governments go to the trouble of establishing a tax transfer system instead of just increasing penalties, given that transfers act just like penalties or fees? To answer this question, we must bear in mind that there are limits to the fees that governments can impose on people. In particular, people cannot pay more than everything they own.13 Suppose that the penalty system is such that the fees that someone pays if caught being a full-time criminal (ti = 1) are everything.14 Consider that group of people (desperate people) whose wage rate relative to the average is so low that, despite these enormous fees, they decide to become full-time criminals (so they pay everything if caught). An increase in fees will not induce these desperate people out of criminal behavior because they will already lose everything if convicted. Hence, once people are in such a desperate situation, fees are irrelevant in the sense that higher fees will not decrease criminal behavior. Transfers, on the other hand, will still work as an incentive device to reduce crime because they are not a direct cost, but rather an opportunity cost, of committing crimes: by increasing the amount of income people receive if they stay out of jail, transfers increase the size of “everything” to criminals. Hence, they still increase the penalty and, therefore, they still reduce die optimal amount of crime.
Note that, in this model where there is no leisure choice, wage subsidies work in much the same way that transfers do. A wage subsidy would increase w relative to y. We already established that an increase in w/y reduces crime. Thus, like transfers, wage subsidies work as a crime-reduction device. Note that, also like transfers, what matters is the wage rate relative to the average level of income in the economy. As we saw above, if wages and income increase in the same proportion (along with transfers and fees), the total amount of crime will remain unchanged.
An additional point is that, when people find it optimal to commit crimes under a certain economic environment, it is likely that they will still find it optimal to commit crimes after serving time in jail unless the economic environment has changed. Transfer programs and public subsidies may be a way to change this adverse economic environment.15
Extensions of the Model: Making the Probability of Conviction a Function of Crime
Up to now. every person was assumed to be investigated by the police with the same probability π. This probability was independent of the amount of crime committed. It is natural to assume that the probability of capture and conviction increases as a person commits more crimes: in the real world, the probability of noncriminals being arrested by mistake is not zero, but it is surely smaller than the probability faced by true criminals. Hence, π is now assumed to be an increasing function of ti, where π´(ti) > 0, π″(ti) > 0, and π(0) = 0. Individuals maximize utility (2) subject to equations (3), (4), and (5), taking into account that their actions will affect the probability of being caught:
The first two terms in equation (12) represent what would be optimal if the probability of capture were unaffected by the choice of ti, The third term reflects the marginal losses in utility caused by the increase in the probability of capture when people decide to devote one more unit of time to illegal activities. Note that this first-order condition is still invariant to the level of income if the wage rate and the transfer system are fully indexed (that is, if w/y and T/y are constant). Hence, growth that preserves income inequality still does not affect the level of crime. Using the implicit function theorem, we can see that crime is still increasing in income inequality and decreasing in the size of the penalties. The effect of transfers on crime, however, is now the following:
where
The main lesson is that, if we allow the probability of capture and conviction to be an increasing function of the number of crimes committed, the relevant features of the model do not change. In particular, transfers are still an opportunity cost of being penalized and therefore act as a crime-preventing device.
Extensions of the Model: Introducing Leisure Choice
The simple model used up to now treats wage subsidies and transfers in a symmetrical way. The reason is that agents were not allowed to choose the amount of leisure optimally. One could argue that, if the choice of leisure is allowed, then a transfer induces people to want to buy more leisure. Of course, they do so by spending less time in the activity with the lowest reward: legal work. Wage subsidies (which you can collect only if you work) have an offsetting substitution effect as the relative reward of legal work. Transfers that are not linked to work, however, do not have the substitution effect, although they still have the perverse wealth effect. To investigate whether this perverse effect is possible in the present model, the utility function is amended so as to incorporate a preference for leisure:
where ψ is some discount rate on leisure. lp is the amount of leisure the agent enjoys if penalized, and lnp is the leisure the agent enjoys if not penalized. The time spent working is (1 - ti - l), where ti is still the time devoted to crime (because total time available is still normalized to one). As in the previous section. we define cnp and cp as follows:
and
Assume that a part of the penalty for criminal behavior involves lost utility. If we denote the amount of leisure an individual enjoys when not penalized by l (so that lnp = 1), the leisure he enjoys when penalized is16
Agents choose l and ti so as to maximize utility subject to the constraints above. The first-order conditions entail
where l* is the optimum amount of leisure given by
The derivative of l* with respect to the transfer per unit of income is positive:
Other things being equal, more transfers lead people to enjoy more leisure. Using equation (19), we can now calculate the effect on crime of an increase in transfers per unit of income:
where
The effect of wage subsidies on crime, in contrast, does not involve any potentially perverse effects. The reason is that, unlike transfers, wage subsidies have a negative effect on leisure: public transfers in the form of wages increase the reward for legal activities. The substitution effect induces an increase in work effort and a reduction in crime and leisure. The wealth effect involves an increase in leisure and a reduction in crime and work. The overall effect is a reduction in leisure. The overall effect on crime is given by
where
The lesson from this section is that, even though we could think that transfers that are not linked to work may have a perverse effect on criminal behavior because of a wealth effect on leisure, the overall effect is still negative. However, the quantitative effects of wage subsidies on crime are likely to be much larger than those of transfers. The main result is still that public welfare should have a negative impact on the amount of time people devote to criminal activities and that the relevant variable is the total spending on public welfare as a ratio to the average income of the economy (which is, in turn, related to the average prize for criminal behavior).
II. Public Welfare, Taxes, and Growth
Setup of the Model
In the previous section, we considered the partial equilibrium effects of aggregate public welfare policies on the criminal behavior of people. The natural question to ask is, given that the government can reduce crime by increasing the size of the public welfare system, why doesn’t it get rid of all crime by having an enormous public welfare program? The answer is, of course, that it must finance transfers and subsidies by raising taxes. Taxes, in turn, may distort private choices for savings and investment, which, in turn, affect the consumption path. The government will therefore have to balance the distortionary effects of the implicit “taxes” imposed by criminals with those of the explicit taxes imposed by the government itself. This section uses a simple model of growth to analyze these issues.
Agents maximize a utility function of the form
where c is the average consumption of the population. There are two ways to think about equation (23). First, we could think that the representative agent does not care about the utility of criminals. Under this interpretation, c is the average consumption of the noncriminal population. Alternatively, we could think in terms of the “veil of ignorance” of Harsany and Rawls, which says that, ex ante, people do not know whether they will end up being criminals or not. If we assume that, ex ante, all agents are identical, the choice variable c could be interpreted as the level of consumption of the representative or average agent, and equation (23) then represents his utility.
Because most crimes entail just a transfer from victim to criminal (at least this is true for most property crimes), one might think that no aggregate output is lost as a result. There are several reasons, however, why output losses may result. First, society may not care about the happiness of criminals. If this is the case, any resources that end up in their hands should be considered social losses. Second, victims of crime may be emotionally and physically disrupted. The consequence of disruption will be a reduction in the victim’s ability to perform his job at pre-crime levels. Crime, therefore, lowers labor productivity. Third, private individuals may devote effort, time, and resources to protecting themselves against crime. This is a social waste much in the same manner as rent-seeking activities that use up some output for no particularly useful purpose. Fourth, some output may simply he destroyed as a result of criminal activities: at the very least, robbers are careless and break precious pieces of china when they enter somebody’s house.
A fraction 1-ϕ(.) of income is lost and a fraction ϕ(.) is still available after a crime is committed. We can also think of ϕ(.) as the instantaneous probability of maintaining one’s property rights on output. According to the analysis above, this fraction or probability will be an increasing function of the overall level of police and legal protection, an increasing function of the size of the penalties for conviction, and a decreasing function of income inequality. Most important, it will be an increasing function of the total amount of aggregate transfers or public welfare. TR, per unit of average income.19 Since the population is assumed to be constant, the stock of people can be normalized to one so that average and aggregate income coincide. To concentrate on the effects of transfers on growth, assume that the fraction tp is solely a function of TR/Yac where Yac is national income after a crime.20 In particular, police protection and public investment in property rights and law enforcement are ignored, despite the fact that these expenditures are relevant to criminal activities. Hence, it is assumed that
where ϕ´(.) > 0, ϕ″(.) < 0, ϕ(0) ≥ 0, ϕ(1) ≤ 1, and ϕ(0) < ϕ´(0). (The assumption on the last inequality is made so as to ensure that the problem of crime is important enough to warrant public intervention.)
Under this specification, redistributional transfers and public welfare resemble productive public goods subject to congestion: the amount of income people get to keep after a crime is committed depends on the level of public welfare relative to the size of criminal threat. This threat, in turn, depends on the prize that criminals get if they decide to commit crimes, which is proportional to national income. When a person increases his economic activity, he raises the economy’s average level of income, which congests the protective power of public welfare. (Thompson (1974) and Barro and Sala-i-Martin (1992) interpret national defense spending along similar lines.)
Imagine that the production function is linear in the capital stock:
where ypc is per capita pre-crime income and k is per capita capital. The linearity of the production function is not essential to the analysis, but it yields closed-form solutions for growth rates. (Using a neoclassical production function, the growth effects of different policies would be temporary and analytically intractable; the direction of the growth effects along the transitional path would, however, be the same.)
The government collects revenue from a constant tax rate on after-crime income τ (we assume that illegal income does not pay taxes) and always runs a balanced budget. All components of public spending other than transfers are excluded from the present analysis. All public revenue is therefore spent on public welfare. The government budget constraint is
where K is the aggregate capital stock, and Yac = ϕ(.)AK is the after-crime aggregate income available to noncriminal. Legal after-tax and after-crime output is devoted to either consumption or investment. The constraint faced by the individual is. therefore,
where k0 > 0 is given, τ is the tax rate on after-crime output, and 5 is the constant rate of capital depreciation.
Legal individuals maximize (24) subject to (27). Given that all agents are small relative to the aggregate, they all think that their actions do not affect the behavior of the government. Hence, when they optimize, they take ϕ(TR/Yac) and τ as given.21 The first-order conditions are
and
where p is the shadow price associated with the constraint (27). Note that, since τ is constant, the government budget constraint says that TR/Yac is also constant. Transfers and output therefore grow at the same rate. It follows that consumption grows at a constant rate at all points in time. From the budget constraint (27), it can be seen that, in the steady state, consumption, physical capital, and, therefore, output grow at the same rate γc = γk = γy =γ ≡ γ. The transversality conditions imply that physical capital grows at that same rate at all points in time. Hence, the model displays no transitional dynamics: all variables grow at the same constant rate all the time. We can use (28) to find the growth rate of the economy:22
The size of the public welfare program has two effects on the growth rate γ on the one hand, higher taxes reduce growth as they distort investment decisions (this is the term (1 - τ) in equation (30)); on the other hand, they increase growth as they reduce the amount of crime and disruption in the economy (this is the term ϕ(τ) in equation (30)). For high levels of τ (large governments), the first, detrimental effect dominates. For low levels of τ, the second, beneficial effect dominates because ϕ(0) < ϕή(0) (see (24)). In other words, if the crime problem when there is no public welfare is serious enough, then an increase in the size of such public programs will increase the growth rate of the economy. If this condition does not hold (that is, the crime problem is not too serious), then it could be the case that ∂γ/∂τ < 0 for all τ, so that the optimal size of the government is τ* = 0. Under these circumstances, there is a size of the government τ* at which the two effects exactly cancel each other out and growth reaches its maximum. The rate τ* is given by the following implicit function:
The maximization of growth is not always equivalent to the maximization of the utility of the representative agent. This is true, however, when ϕ(.) takes a Cobb-Douglas form.
Superiority of Income Taxes
It is interesting to compare the outcome of this market economy with the outcome of a planner. Given an arbitrary size of the government, s = TR/[AKϕ(TR/AK)], the planner chooses a path of consumption and capital so as to maximize the utility of the representative consumer. The resulting growth rate is
where the effect of s on the rate of growth is given by the following expression:
Note that, if a government using income taxes chooses τ so as to maximize growth (τ = τ* = s*). then the social optimum will be replicated. In other words, if the size of the government is optimal, the proportional income tax is Pareto efficient. It is interesting to see that a shift from income tax to lump-sum tax lowers utility but increases growth. The growth rate under lump-sum taxes is given by
Given the size of the government, the growth rate corresponding to lump-sum taxes is always larger than the one the planner would choose. That is, if taxes are lump sum, there is overinvestment and excessive growth. The intuition for this result is that, when an individual producer decides to increase capital by one unit, he increases the average output of the economy. This, in turn, induces criminals to increase their criminal effort since the rewards for crime have increased. In other words, investors congest the protective role of transfers without really taking this effect into consideration when making investment decisions. Therefore, they lend to overinvest and overcrowd transfers. A lump-sum tax will not help solve this congestion effect. An income tax, however, acts as a fee for the use of transfers as a crime-preventing device: it internalizes the externality and deters people from investing too much. Thus, from a social point of view, an income tax is superior to a lump-sum tax.
III. Conclusions
This paper presented a model that explains the existence of social safety nets in the form of redistributional transfers and wage subsidies. It showed that such transfers are a mechanism to buy poor people out of disruptive activities such us crime, revolutions, and other forms of social disruption. It argued that public welfare is likely to have some effect on crime, especially among those segments of the population that are so poor that the losses of going to jail are very small relative to the potential gains from criminal behavior. It also argued that, in aggregate production functions, transfers and other forms of welfare look like productive public inputs subject to congestion, which increase the productivity of private capital and therefore increase the growth rate of the economy. The growth-maximizing size of the public welfare system was derived. As a result of transfers being “subject to congestion,” an income tax system was shown to be superior to a lump-sum tax system. The reason was that income taxes act as user fees on the use of welfare as a protective device.
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This puzzling positive correlation was first found by Barro (1991b) and has subsequently been documented by Cashin (1995).
A substantial fraction of the recent growth literature deals with the role of government in the process of economic development. Chamley (1981), Lucas (1990), and the subsequent literature deal with the problem of optimal taxation. For example, Barro (1990), Barro and Sala-i-Martin (1992 and 1995, ch. 4), and Cashin (1995), among others, present models where the productive aspects of public spending are offset by distortionary taxes. The literature has devoted little attention to transfers and their role in the process of economic growth. This is surprising given the size of public transfers relative to other forms of public spending, like public investment and infrastructure.
Most of the transfers taking place in rich, industrial nations are not between rich and poor, but between young and old. This paper analyzes transfers between rich and poor. Old-age transfers are analyzed in Sala-i-Martin (1996). In that paper, I argue that old-age transfers appear to be productive because they are used to bribe old, unproductive workers out of their jobs. In the presence of human capital externalities like those proposed by Lucas (1990), the elimination of the elderly from the labor force will increase the level of income of the economy as well as its growth rate.
It can be persuasively argued that, when the World Bank and the IMF worry about social safety nets in transition economies, they do so, at least partly, to ensure the success of the transition process. If too large a fraction of people become impoverished during the transition, riots, revolutions, or military coups may actually end a program that would have been beneficial in the long run.
Encarta’s Encyclopedia, for example, after describing von Bismarck as a ruthless politician who fought any and all who questioned his policies, says that “although he failed to defeat the Socialists, the social security legislation he introduced—national accident and health insurance and old-age pensions—ended whatever revolutionary designs they may have had.”
This fraction β could be thought of as being chosen by the average person according to some money demand model that does not need to be specified here. It should be noted that, when making this choice, this person will take into account the probability of being mugged and will add it to the interest forgone by holding cash. That is, the larger the number of criminals operating in a certain area, the lower is likely to be the reward per unit of time devoted to crime because people living or working in that area will be careful not to carry too much money in their pockets.
Becker uses this assumption to explain crimes of passion and other crimes that entail no direct monetary reward to criminals. Another unrealistic assumption is that all persons in the economy have the same attitude or preference for crime. Different people may perceive crime differently, and these differences may be due to educational background or religious beliefs or both.
One could argue that there is learning by doing (or learning by offending): people who commit few crimes are naive and are more likely to be caught. Professional criminals, on the other hand, have more experience and know how to evade the police more easily. Furthermore, full-time criminals may be able to bribe policemen and judges to lower their probability of conviction. The offsetting force is that the more crimes you commit, the more likely the police are to devote their efforts to capturing you, whereas if you are a naive, part-time criminal, the police are likely either to ignore you or to spend little effort in trying to capture you. In this simple model, these forces are assumed to roughly offset one another and the probability of being convicted is taken to be independent of ti.
This wage subsidy could take the form of minimum wage laws or the prohibition of work by children (which entails the elimination of the lowest-wage jobs).
Some crimes are penalized with physical or nonmonetary fees: the death penalty would be an example. The present analysis, however, abstracts from these physical penalties.
In fact, this could be relaxed and the fee could be allowed to be concave as long as it is not too concave. The exact condition is f″> - (β - ω)f ´(1 + π)/(π · cnp).
This does not mean that poor people are inherently worse in any sense. We have assumed that everybody has the same preference toward crime and, therefore, that everybody is equally good. The implication of the model comes from the opportunity set faced by both rich and poor. It is more profitable for the rich to be legal and for the poor to be criminal. The only reward for criminal behavior is assumed to be the average level of income. It is entirely possible that rich people have access to a better, more rewarding set of criminal activities (white-collar crime). If the model is amended to incorporate these factors, the implication would be that, given the size of the criminal reward a particular person faces, he would choose to devote zero time to illegal activities if the wage rate he could earn in legal activities were higher.
Here is where the assumption that governments cannot impose nonmonetary penalties like death or cutting off an offender’s ears becomes relevant. Presumably, the value of lives and ears in terms of income is large enough so that crime can be deterred with the use of these nonmonetary penalties only. Countries that have access to these types of drastic penalties will not need to use transfers to reduce disruptive behavior. This paper does not try to explain why governments do not impose such drastic nonmonetary penalties for seemingly small crimes.
People cannot lose exactly everything when they go to jail: the government must provide some level of consumption while in jail. If it did not, prisoners would starve to death. This would represent a nonmonetary penalty, which we assumed was not allowed in this economy. This sentence should therefore say that they lose almost everything.
This assumes that people do not learn anything new in jail. It is possible that criminals do not really know what jail is all about and that an initial period of incarceration shows them how terrible it is. This would increase the perceived penalty and, therefore, reduce the amount of crime in the future. One argument against this is that a lot of criminals come from families and neighborhoods where crime and criminals are abundant. Hence, it is likely that these people have a pretty good idea of what it is to be in jail, and so their propensity to commit crimes will not change after having been in jail once before. (See Sah (1991) for evidence on this type of social osmosis.)
We could also assume that the fraction of income lost if an individual is convicted is different from the fraction of time lost if he is convicted. The reader can check that the key results remain the same.
This result does not depend on the log utility specification. The overall effect with a utility function of the form c1 - θ/(1 - θ) and l1 - θ(1 - θ) yields
In a general equilibrium model, wage subsidies may have another perverse effect on crime, that is, they tend to generate unemployment. This is not the case for transfers.
We should think of TR as including not only transfers but also wage subsidies and other kinds of public welfare. As we showed in the previous section, all of them affect crime negatively. In the rest of the paper, the terms “transfers” and “public welfare” are used interchangeably.
Alternatively, it could be assumed that ϕ() is a function of TR per unit of pre-crime income. This alternative specification docs not change any of the substantive results.
It is assumed that individuals, who own the firms, produce output at home. The results would be the same if there were competitive markets for goods and capital.
If we assume that ϕ() is a function of TR/Y rather than TR/Y, the growth rate is not a function of ϕ(τ) but, instead, a function of η(τ) with ηή(τ), where η() can be derived as follows: define ϕ2() as the function that satisfies the public budget constraint ϕ2(TR/AK) ≡ τ, where ϕ2!() > 0 (this follows from the assumptions ϕ″< 0 and ϕ(0) ≥ 0). Invert it and plug in ϕ(TR/AK) to find the growth rate as a function of τ only where η(τ) =
