Following the seminal theoretical work of Gary Becker (1968), a large body of empirical literature has revealed that preventive and punitive measures do in fact have a significant impact on criminal activities. The key question now at the frontier of the economics of crime and law enforcement is how to make police deployment strategies more efficient. In a new paper, we aim to help answer this question by developing the first general equilibrium model to study how the geographic distribution of police protection affects the decision to become a criminal, the intensity and location of crime, residential choices, housing prices, and the welfare of different socioeconomic groups (Galiani et al. 2016). The goal is to study the positive and normative effects of different ways of spatially allocating police forces in a city.
Our building block is a model of a city populated by agents of different socioeconomic groups and made up of several residential areas, which are denoted as neighbourhoods. Socioeconomic groups are distinguished by their factor endowments. In particular, there is one homogenous group of skilled agents that includes skilled labour, and several homogenous groups of unskilled agents, each of them with a different per capita endowment of unskilled labour. The city is treated as a small and open economy, that is, the prices of tradable goods and inputs are exogenously given. Agents select:
- Their occupation (i.e. to work in firms that produce goods or to become a criminal);
- Their residence (i.e. in which neighborhood to reside); and
- Consumption and housing.
Firms demand unskilled and skilled labour and supply tradable goods using a constant returns to scale technology. Criminals use their labour endowments to extract income from other citizens. The supply of housing in each neighborhood is chosen by profit-maximising developers, who use capital and land to build houses. Capital is a tradable input – that is, it is elastically supplied at a given price – while land is a non-tradable input in fixed supply in each neighbourhood. The government provides public protection by deploying police forces in the city, which reduces the amount that criminals can otherwise extract from their victims. Given the prices of tradable goods and inputs and the allocation of public protection, the model determines:
- Occupational and residential choices;
- The geographic distribution of crime; and
- Housing and land prices in each neighborhood.
In order to determine these endogenous variables, we employ a combination of a standard small and open-economy competitive equilibria, and a spatial notion of equilibrium. In equilibrium, no agent can obtain a rent changing his or her occupation and/or location. Thus, we adopt a long-run perspective that allows agents enough time to change their occupation and residence.
The central object of the analysis is public protection regimes. We consider two extreme strategies to allocate the police across the city, which we assume are both feasible and have the same cost. Under concentrated public protection, the police only protect some neighborhoods and leave the rest of the city completely unprotected. Under dispersed public protection, the police are evenly deployed across the entire city, inducing an equal level of public protection in all neighbourhoods. With these two protection regimes, we try to capture – albeit in stylised fashion – the basic trade-off faced by the police with regard to the geographic allocation of protection. With the same resources, the police can either extensively protect a smaller area (concentrated protection) or partially protect a larger area (dispersed protection).
Relying on our model, we show that, under proper conditions, concentrated public protection leads to a spatially segregated city. Only rich agents are willing to pay the high housing prices in protected neighbourhoods, while poor workers and criminals reside in unprotected neighbourhoods. When the police force is evenly dispersed across all neighbourhoods, the city becomes fully integrated. All neighbourhoods are inhabited by citizens of all income levels. Indeed, income per capita and crime levels are equalised across the city.
There are two mechanisms operating in the model presented here that produce these results. Regarding occupational choices, the payoff from crime does not vary with a citizen’s labour endowment, while the payoff from working obviously increases a citizen’s labour endowment. This makes relatively poor citizens more prone to become criminals. Indeed, both under concentrated and dispersed public protection, we focus on a region of the parameter space for which, in equilibrium, only agents in the poorest socioeconomic group decide to become criminals. Regarding residential choices, the wealthier the agents, the more harmful criminal activities are for them and, as a consequence, the more they are willing to sacrifice in order to avoid high-crime areas. Under concentrated public protection, these differences in the willingness to pay for a safe neighbourhood produce a concentration of rich agents in protected neighbourhoods and poor agents in unprotected neighbourhoods. Under dispersed public protection, there is no essential difference among neighbourhoods, crime distributes evenly in the city, and agents only take into account housing prices in their residential choices. As a consequence, there is housing price equalisation across the city and all neighbourhoods have the same income per capita.
We compare crime – measured as the total income of criminals – aggregate income, and housing prices. With respect to crime, there is likely to be more of it under dispersed protection than under concentrated protection. When the wage-income share of skilled agents is high, dispersing the police force significantly reduces its effectiveness, the proportion of income that criminals can extract from rich agents is high, and the proportion of income that criminals can extract from the poor is low. Aggregate income is more likely to be higher under concentrated protection, the higher the wage-income share of skilled agents, the more intense the reduction in police effectiveness when the force is dispersed, the more criminals can extract from skilled workers, and the less criminals can extract from unskilled workers. We also find conditions under which housing prices under dispersed protection range between housing prices in unprotected and protected neighbourhoods under concentrated protection. We also show that the condition is more likely to be satisfied the higher the wage-income share of skilled agents.
We examine the welfare and distributive effects associated with a change in the public protection regime. First, employing a simple utilitarian welfare function, we show that concentrated protection may induce higher aggregate welfare than dispersed protection. Moreover, income inequality matters. We prove that aggregate welfare is higher under concentrated protection for a society with a high wage-income share of skilled agents, while aggregate welfare is higher under dispersed protection for a society with a low wage-income share of skilled agents.
Second, regarding distributive effects, we prove that, with regard to a utilitarian welfare function, unskilled agents as a whole are better off under dispersed protection. Thus, societies with high levels of income inequality may face a very difficult dilemma. Concentrated protection may maximise aggregate welfare but exacerbate social disparities. In contrast, in more equalitarian societies, dispersed protection simultaneously maximises aggregate welfare and reduces social disparities. One solution to the regressive distributive consequences of concentrated protection is to supplement the regime with a set of taxes and transfers. We deduce a set of equations for the compensation that must be provided in order to make each unskilled agent equally well off between concentrated and dispersed protection.
Third, we explore some interesting political economy implications related to the distributive effects of a change in the public protection regime. In particular, there is room for the formation of atypical political coalitions with respect to public safety. Although at least one group of unskilled agents will be better off under dispersed than under concentrated protection, it is not necessarily the case that all unskilled agents unanimously prefer dispersed protection. Dispersing police forces could induce an increase in the housing prices paid by unskilled workers that consumes most of their gains in income. Thus, skilled and some unskilled agents may have an incentive to form a coalition that supports concentrated protection.
In many countries, different forms of private security are intensively employed by households and businesses. In principle, our baseline model can handle pure private security such us alarm systems and security doors. More interesting are closed neighbourhoods protected by fences and security guards or patrols collectively financed by the neighbours – that is, when private security works as a club good. Thus, we extend our base model to allow for this possibility. In this case, we show that dispersed public protection does not necessarily lead to an integrated city equilibrium in which crime, income per capita, and housing prices are spatially equalised. The reason is that skilled agents may use private protection to endogenously isolate themselves in fully protected areas, while high housing prices exclude unskilled workers from these areas.
Our model suggests that when we consider changes in the geographic distribution of police forces, we need to take into account the effects on housing prices and on reallocation of the population, as well as the overall effect on crime in the entire city (see Jaitman and Ajzenman 2016 for evidence of these effects in Montevideo, Uruguay). It also suggests new paths for empirical work on the economics of crime and law enforcement. For example, we have a very limited understanding of the effectiveness of more concentrated versus more dispersed allocations of police forces. Some work on this issue has been done related to the literature on hot spots (Weisburd et al. 2012). The next empirical step would be a consistent estimation of the parameters of the production function of security across locations. Our model provides a theoretical framework for such an estimation.
Becker, G S (1968) “Crime and punishment: An economic approach”, Journal of Political Economy, 76(2): 169–217.
Galiani, S, I Lopez Cruz and G Torrens (2016) “Stirring up a hornets’ nest: Geographic distribution of crime”, National Bureau of Economic Research Working Paper 22166.
Jaitman, L and N Ajzenman (2016) “Crime concentration and hotspot dynamics in Latin America”, Inter-American Development Bank, Unpublished.
Weisburd, D, E Groff and S Yang (2012) The criminology of place: Street segments and our understanding of the crime problem, Oxford: Oxford University Press.