The Kuznets criminal curve

By: Paolo Buonanno*, Leopoldo Fergusson**, Juan F. Vargas***

 

Introducing … the CKC

In almost every US state, the relationship between crime and income is strikingly clear.  Since 1970, the data shows a pervasive pattern similar to an inverted U-shape: crime increases with per capita income until it reaches a maximum and then decreases as income keeps rising. Figure 1 shows income measured in the horizontal axis as real per capita GDP (2009) and the crime rate –per 100,000 inhabitants– which aggregates the seven felony offenses recorded in the FBI’s Uniform Crime Reports. The solid line is a flexible non-parametric fit of the data, and the shaded area is the 95% confidence band.

Figure 1: Crime rates and income in the US, 1970-2011

In a recent paper, we document for the first time (as far as we can tell) the existence of this non-monotonic relationship between crime and income. We call it the “Crime Kuznets Curve” (or CKC) inspired by the classic Kuznets Curve (KC). In his seminal 1955 paper, Simon Kuznets noted a similar non-linear association between inequality and economic growth.

The CKC could then simply be a reflection of the traditional KC: Inequality affects crime, and because inequality increases and then falls with income, there is a mechanical (but not truly substantial) inverted U relation between income and crime. Inequality under this interpretation is the culprit of the CKC.

Or is it?

As it turns out this is not the case. One simple way to see this is that, in our sample, there is in fact no KC in the traditional way. Figure 2 shows that inequality has increased monotonically with income in every US state since the 1970s.

 Figure 2: Inequality and income in the US, 1970-2011: Non-parametric fit (solid lines) and 95% confidence bands (shaded area)

What then, explains the CKC? We don’t know yet, but the answer is likely to be important for policy. Let’s look closer at what can’t explain the CKC, and talk about a few first ideas of what could.

What explains the CKC? Ruling out the usual suspects

Table 1 reports the results from estimating a very simple equation with crime as the de- pendent variable and income as the main explanatory variable. We report three different aggregations of crime: total crime in columns 1 and 2, property crimes (burglary, larceny and car theft) in columns 3 and 4, and violent crime (murder, assault, rape and robbery) in columns 5 and 6. The odd columns include linear and quadratic income terms (income and income squared), and the even columns include income cubed as well. Of course, while including only up to a quadratic term is sufficient to model an inverted U pattern, quadratic functions are symmetric, and this may impose a very strong restriction on the data. The cubic function can draw a non-symmetric parabola, which seems to be the case in several states (recall Figure 1).

In any case, the bottom line is that if a CKC exists we should see a negative coefficient for the quadratic income term in Table 1. This is indeed the case in most columns. Focusing on Panel A, the coefficient of income is positive and significant and that of in- come squared is negative and significant. This combination is consistent with an inverted U-shaped relationship between income and crime.

The regressions include state and year fixed effects. This means that we allow each state to have a different average level of crime, and similarly for each year across all states. The implication is that our results are not driven by differences between states (as we know from Figure 1) or by overall trends in crime across the US. This last observation is crucial: it implies that the curve is not driven by a downward trend in overall crime in the US concurrently as income in the whole country was increasing.

Is the income-crime relationship really picking up something else? As noted, it could be inequality, which in the traditional KC story moves non-monotonically with income and could potentially be explaining these patterns. But it could also be other variables that move with income and influence crime rates, like the demographic structure (the fraction of males at different age brackets), population density, or the level of employment. However, in addition to the state and year fixed effects, Panel B of Table 1 also includes all these potential confounders as controls in the regressions. If they are responsible for the income-crime relationship, the coefficients on the polynomial terms should change. But they do not: Results in Panel B are very similar to Panel A (both in terms of the sign and magnitude of coefficients for the polynomial terms).

Table 1: The Crime Kuznets Curve in Aggregate Crime Categories

Summarizing, there are three main messages from these results. First, there is a robust CKC for total crime and for property crime. Second, since the results are very similar with and without the set of controls often highlighted in theories of crime, the CKC is not driven by a correlation between income and such characteristics. Notably, since inequality is included in the set of controls, the comparison between Panel A and Panel B implies that the CKC is not a mere reflection of the traditional KC (where income and inequality have an inverted U relationship). Finally, while the CKC is also apparent in some specifications for violent crime, the two last columns in the table show that this relationship is less robust than in property crime. This is consistent with the idea that property crimes are more likely to depend on economic motivations than violent crimes as in the benchmark economic model of crime of Becker (1968) and Ehrlich (1973).

What lies behind these results? The effect of income on crime is theoretically ambiguous. To name just two important but opposing forces, as incomes rises the opportunity cost of devoting time to criminal activities falls. But at the same time wealthy individuals become more attractive targets of crime. But why would one of these effects dominate when income is below a certain level, and the other prevail above such threshold? This is just one of the key questions that the CKC raises.

So what? And what next?

The CKC is a very robust empirical pattern of the last 40 years in the US. Because it is not explained by obvious determinants of crime, we believe it is necessary to develop and test new theories that can account for it. Thus we conclude this entry by suggesting some possible avenues for future research.

One hypothesis is that the provision of certain public goods with the potential to reduce crime only increases significantly after communities have attained a sufficiently high level of average income. These could be public goods affecting crime directly, like police expenditures or investments in judicial efficiency, or indirectly, like schooling and certain types of public infrastructure and amenities. A demand-side mechanism could create this relationship if households initially focus on consuming some basic “subsistence goods” and only later demand the types of public goods that are key drivers of crime. Conceivably, supply-side mechanisms with the same spirit could also explain these pat- terns, if communities are only able to provide certain public goods once a certain level of development has been achieved.

Other hypotheses could emphasize the opposite direction of causality. For instance, it may be that in early stages of development the types of activities that can enrich societies are not too threatened by environments with relatively high incidence of crime. Perhaps activities like resource extraction or industrial development intensive in physical capital could survive or even thrive in spite of high rates of property and violent crime. However, as the most productive activities in the technological frontier start demanding high levels of human capital, it may be especially important to have an environment that attracts highly-qualified individuals willing to live in these communities. In this hypothesis, only when communities are able to diminish crime rates they may increase their income beyond a certain threshold (which happens to be just above a yearly GDP per capita of US$20,000 in our estimates).

Our findings are also relevant for policy as they suggest that violent conflict cannot be tackled solely by the trickle-down forces of economic growth and both more effective policing as well as preventive strategies are needed. The CKC thus deserves more attention from both theorists and applied social scientists.

 * Paolo Buonanno, University of Bergamo

** Leopoldo Fergusson, Universidad de Los Andes, Twitter: @LeopoldoTweets

*** Juan F. Vargas, Universidad del Rosario, Twitter: @juanf_vargas