Empirical Properties of Crime Rate Trends

• Published date: 01 February 2024
• DOI: http://doi.org/10.1177/10439862231189979
• Author: David McDowall
• Date: 01 February 2024

https://doi.org/10.1177/10439862231189979

Journal of Contemporary Criminal Justice

2024, Vol. 40(1) 7 –25

© The Author(s) 2023

Article reuse guidelines:

sagepub.com/journals-permissions

DOI: 10.1177/10439862231189979

journals.sagepub.com/home/ccj

Article

Empirical Properties of Crime

Rate Trends

David McDowall1

Abstract

This article considers the operation of the time series processes that underlie U.S.

crime rate trends. These processes are important because they carry the influence

of the variables that generate the rates. They limit the forms that explanations of

crime trends can take, and they open avenues for new theoretical development.

Using data from the nation and a panel of large cities, analysis finds that crime trends

operate much like random walks or their smoothed cousins; that they rarely deviate

from a constant pattern; and that they show little evidence of nonlinearity. The

article discusses the substantive implications of these features for understanding

crime trends, and it considers directions for expanding the study of their empirical

properties.

Keywords

time series processes, equilibria, nonstationarity, nonlinearity, stylized facts

Introduction

The goal of this article is to consider several empirical regularities in crime rate trends.

The typical way of studying crime trends is to propose a theory and then test its fit to

the data. A less explored approach begins with the trends and tries to discover the

structures that underlie them. If successful, the second approach can yield a set of

properties that apply broadly to fluctuations in crime and that offer a foundation for

theorizing. The article applies this second approach.

An obvious feature of a time series is that it connects values from the past to values

in the present. In popular usage, a “trend” is exactly that: a set of observations arranged

1University at Albany—State University of New York, USA

Corresponding Author:

David McDowall, School of Criminal Justice, University at Albany—State University of New York, 135

Western Avenue, 223B Draper Hall, Albany, NY 12222, USA.

Email: dmcdowall@albany.edu

1189979CCJXXX10.1177/10439862231189979Journal of Contemporary Criminal JusticeMcDowall

research-article2023

8Journal of Contemporary Criminal Justice 40(1)

in temporal order. Using Uniform Crime Report (UCR) data, Figure 1 graphs U.S.

homicide, rape, robbery, assault, burglary, and auto theft rates since 1933, and U.S.

larceny rates since 1960. The accuracy of the data is always open to question, and the

series even now are relatively short. Still, the graphs clearly display significant varia-

tions, such as the increases in the 1960s and the drops in the 1990s.

The trends are the outcomes of probability processes that underlie the rates. Many

processes are possible, differing in how they work. At one extreme, a process may

produce a white noise series, where observations have only chance relationships to the

ones before and after them. At the other extreme, a process may follow an exacting

equation, such as one that produces a linear trend.

Time series processes are not simply abstractions, and instead, they have important

practical uses. They allow conventional statistical analyses, for example, by supplying

a basis for inference. The process that underlies a time series is the equivalent of the

population that underlies a cross-sectional sample, and it justifies the standard statisti-

cal procedures and tests.

Equally important, processes constrain and focus theoretical explanations of how a

series can vary. Only some forms of change are possible, and the behavior that a theory

requires might be incompatible with the process. Some processes do not have constant

means, for example, and for them explanations that assume average rates cannot be

correct. The same is true of theories that assume rates follow cycles, or are contagious,

or shift in their causal structure. A process can support or help rule out large classes of

theories because it sets conditions that they must meet.

Knowledge of the generating process can also be helpful in developing theories. A

process carries the influence of the causal variables that are ultimately of interest to

researchers. It cannot identify these variables individually, especially if they are

numerous. Still, it can offer insight into their collective dynamics and into the behav-

iors of which they are capable. It can address questions such as: What general forms

must explanations of crime trends take? What features of the trends are theoretically

meaningful? What empirical conditions must a trend theory satisfy?

The current article will investigate some features of the processes that underlie the

trends in the major U.S. rates. Researchers have commented on a few of these features

in the past, but they have largely ignored others. Even when they have been a topic of

earlier study, the substantive implications of the features have not received much

discussion.

In the remaining sections, the article first describes the data that form its empirical

basis. The following section then goes on to consider the structure of crime trends,

separating theory from empirics. The next two sections examine deviations from the

temporal structure, especially involving outliers and nonlinearity. The final section

discusses the implications of the results for understanding crime trends and for devel-

oping a catalog of their empirical properties.

Data

The article relies on two sets of data to illustrate the characteristics that it considers.

One set consists of national crime rate series from the UCR. These cover homicide,