## Violent-Crime Rates and Racial Composition: Covergence Over Time

by
Allen E. Liska, Paul E. Bellair

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Title:

Violent-Crime Rates and Racial Composition: Covergence Over Time

Author:

Allen E. Liska, Paul E. Bellair

Year:

1995

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The American Journal of Sociology

Volume:

101

Issue:

3

Start Page:

578

End Page:

610

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Language:

English

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**Updated:**January 30th, 2013

Abstract:

### Violent-Crime Rates and Racial Composition: Convergence over ~irne'

Allen E. Liska and Paul E. Bellair

State University of New York at Albany

Considerable research reports that racial composition strongly af- fects violent-crime rates. Unfortunately, most research ignores the possibility that violent-crime rates may affect racial composition. Using a sample of U.S. cities, the authors examine the reciprocal effects of racial composition and violent-crime rates over the last 40 years. While racial composition strongly affects the change in violent-crime rates from 1980 to 1990, it only minimally affects changes in rates for the previous three decades; but violent-crime rates (especially robbery) substantially affect the change in racial composition for all four decades. Indeed, robbery rates appear to play a significant role in the white flight from central cities.

The link between race and criminal violence is a major issue throughout the social sciences. It is examined at both micro and macro levels of analyses. Does an individual's race influence his or her level of violence? Does an area's racial composition influence its rate of violence? This article focuses on the latter question.

This question has a long history. Within the social sciences it can be traced back to the classic works of Shaw and McKay (1931) who linked the rate of crime and delinquency in urban areas to social disorganization. This theoretical and research tradition continued in various forms through the 1950s (Lander 1954) and early 1960s (Chilton 1964), stag- nated during the late 1960s and 1970s, and has been revitalized since the 1980s (Bursik and Grasmick 1993; Sampson and Groves 1989; Land, McCall, and Cohen 1990). Specifically, crime and delinquency are viewed as the outcome of low social control, which in turn is affected by social disorganization. Racial minorities are linked to crime and delin- quency (violence) because they reside in socially disorganized areas.

' We would like to thank Glenn Deane, Richard Felson, John Logan, Steven Messner, Scott South, and Stewart Tolnay for their thoughtful suggestions on this project. Please direct all correspondence to Allen Liska, Department of Sociology, State Uni- versity of New York, Social Science 340, Albany, New York 12222.

O 1995 by The University of Chicago. All rights reserved.

0002-9602196110103-0002$01.50

578 AJS Volume 101 Number 3 (November 1995): 578-610

The relationship between race and violence has also been explained using variants of economic strain theory (Merton 1938). According to economic strain theory, the high rate of violence among racial minorities and in areas with a high proportion of racial minorities results from the economic deprivation associated with race in the United States (Braithe- waite 1979; Blau and Blau 1982; Messner 1983). Specifically, economic deprivation (defined absolutely or relatively) leads to frustration, which in turn leads to aggression. Blau and Blau (1982), for example, report that inequality based on ascribed statuses (race) is particularly frustrat- ing, leading to diffuse forms of aggression.

Finally, the issue of race and violence has been conceptualized in terms of subcultural theories. Some subcultures are thought to be more prone to violence than are others, either because they are more tolerant of violence as a mode of addressing personal grievances or because they encourage or value it. These subcultures are associated with country (United States), region (South), gender (masculine), community type (ur- ban), occupation (hockey), and ethnicity or race (nonwhite; see Corzine and Huff-Corzine 1989; Gastil 1971; Reed 1971; Wolfgang and Ferracuti 1967; Messner 1983, 1988; Huff-Corzine, Corzine, and Moore 1986; Luckenbill and Doyle 1989).

Though empirical research on the relationship between racial composi- tion and violence has mushroomed, approaching that of a research spe- cialty, just about all of the work ignores the very real possibility that crime, especially violent crime, influences people's decisions of where to play, work, and live and thus may influence the social, economic, and racial composition of areas (neighborhoods and cities) as much as they influence crime. Hence, in explaining the relationship between racial composition and violent crime both processes should be taken into ac- count.

Consequences of Crime

In Rules of the Sociological Method Durkheim (1938, p. 97) points out that "to explain a social fact it is not enough to show the cause on which it depends; we must also, . . . show its function in the establishment of social order." Crime is certainly a social fact-a patterned, ecologically distributed, and stable social phenomenon. Thus, it seems reasonable to assume that it influences people and their social lives; yet, sociologists have rarely examined its effects on the social milieu. Studies have gener- ally examined crime as something to be explained, not as the explanation of something.

Over the last 25 years some such studies have appeared, mainly orga- nized around the issue of persons' fear of crime. Surveys (Harris, NORC, and NCS) report that a high percentage of the U.S. population fears crime and that this percentage increased substantially during the 1970s and 1980s (Garafalo 1979; Yin 1985; Skogan 1990). Many studies exam- ine the consequences of crime for individuals, especially victims. They generally link fear to various deleterious psychological states, such as anxiety, mistrust, alienation, dissatisfaction, and even mental illness, and to various patterns of social behavior, such as social isolation and forms of self-protection (Yin 1985; Liska and Warner 1991; Liska, Sanchirico, and Reed 1988; Gordon and Riger 1979; Skogan 1990). Only a few studies examine the consequences of crime for social areas. We focus on those that bear specifically on the issue of racial composition.

Wilson (1987) has recently drawn attention to this issue. He argues that people who can afford to do so leave high-crime areas, especially inner-city neighborhoods, that the resources and opportunities to leave are related to race, and, therefore, that crime rates, by differentially affecting white and nonwhite migration, affect the racial composition of areas. We doubt that violent crime substantially affects long-distance migration, such as between geographical regions and states. Much re- search (Frey and Speare 1988) suggests that such migration is strongly affected by economic conditions (e.g., opportunities and tax burdens) and climate. However, it seems reasonable to hypothesize that violent crime affects short-distance migration, such as from one neighborhood to an- other, from one city to another, and from central cities to suburbs, thereby altering the racial composition of neighborhoods, cities, and suburbs.

Although the findings are mixed, there are now a few studies sug- gesting that crime rates influence the social characteristics of areas (e.g., neighborhoods and cities). Many of these studies deal directly or indi- rectly with migration. In a study of 40 neighborhoods in eight cities, Skogan (1990) reports that crime rates affect persons' dissatisfaction with a neighborhood and their intention to move. Yet, using a panel survey (1966-69), Droettboom et al. (1971) found that, although crime rates affect the motive to move, they do not affect moving itself; and based on another panel survey (1979-80), South and Deane (1993) recently reported that perceiving crime as a problem in one's neighborhood does not affect moving. On the other hand, some studies report that crime rates affect some migration patterns but not others. Based on 44 census tracts in Dallas, Katzman (1980) reports that, though crime rates show little effect on migration generally, they strongly affect the in-migration of upper-income families and families with children. In a study of popula- tion change from 1965 to 1970, Frey (1979) reports that, though crime rates do not affect the rate of migration, they do affect the destination of migration (suburbs); however, the effect is substantially reduced when the percentage of blacks is included in the equation. Marshall (19791, based on a sample of 112 standard metropolitan statistical areas (SMSAs), reports that crime rates affect out-migration but not in-migration. And, in a study of the 55 largest U.S. cities, Sampson and Wooldredge (1986) report that crime rates affect population change generally from 1970 to 1980.

Fewer studies extend this logic to racial composition. Yet, if the re- sources needed to migrate are differentially distributed by race, then we should expect that whatever affects the impetus to migrate (such as crime rates) also affects racial composition. In panel studies of Chicago neigh- borhoods and Los Angeles census tracts, Bursik (1986) and Schuerman and Kobrin (1986), respectively, found that delinquency rates affect neighborhood social characteristics conceptualized as multivariable social factors. This work is clearly important, but it only indirectly bears on the issue of this article. While the social factors in both studies include racial composition, they include so many other social variables that it is difficult to know exactly what is being affected by delinquency rates. For example, Bursik includes percentage black, percentage of homes that are owner occupied, and percentage unemployed as one social factor, and Schuerman and Kobrin include five variables as one social factor.

Clearly, there is some evidence, although mixed, that crime is not only an important personal event, having consequences for both offenders and victims, but that the crime rate is an important social fact, having consequences for social areas. It seems reasonable to hypothesize that people avoid working, playing, and living in high-crime areas. If they can afford to do so, they do not move there, and if they live there, they move out. These social processes help shape the economic and racial makeup of communities. Hence, when studying the impact of racial com- position on crime rates, we simply cannot ignore the impact of crime rates on racial composition.

Although these studies lay the groundwork for posing this hypothesis and the general issue, they are problematic in many respects that may account for some of the inconsistencies among them. First, none of the studies focus on violent crime, especially by strangers, even though that is the crime most identified in the literature as affecting fear (Garafalo 1979; Liska, Lawrence, and Sanchirico 1982) and thus the crime most likely to affect racial and economic characteristics of areas. Second, many of the studies (e.g., Skogan 1990; Frey 1979) do not consider time lags; yet it seems reasonable that the social effects of crime rates operate through processes that take considerable time. Increases in crime rates may take five or 10 years to affect some social characteristics of areas, such as economic and racial composition. The reputation of a high-crime area, for example, may take years to develop and may take additional years to affect the migration decisions of enough people to affect its social composition. Third, most studies examine only one point in time or one interval of change; yet, the effects of crime rates may vary over time, in part reflecting temporal variation in the extent to which crime is per- ceived as threatening. Fourth, most studies do not examine the reciprocal effects of crime rates and racial composition on each other. The few that do examine reciprocal effects include racial composition as part of a general social factor, making it difficult to isolate the effect of crime rates on racial composition, and some of these few studies use problematic analytical techniques. For example, Schuerman and Kobrin (1986) use cross-lag correlation, which has long been criticized as yielding biased estimates of causal effects.

Building on this extant research, our work examines the reciprocal effects of racial composition and crime rates. We extend prior research in the following ways: (1) We disaggregate general crime rates into nonvi- olent- and violent-crime rates. Relying on fear research, we assume that violent crime, especially violent crime by strangers (epitomized in rob- bery), has the most impact on where people live. (2) We disaggregate change in racial composition into change in the white and nonwhite populations. We assume that violent-crime rates affect the migration of whites, who have the resources to act on their fears and intentions, more than that of nonwhites, who have fewer resources and are more con- strained by housing discrimination (Alba, Logan, and Bellair 1994). (3) We examine these reciprocal effects over a 40-year period from 1950 to 1990. Again relying on fear research, we assume that the fear associated with violent crime changes over time and thus that the effects of violent- crime rates may change over time. (4) We examine time-lag structures. We expect that the time lag of the crime rate's effect on racial composition may be relatively long, operating through slow-moving processes. Though some people may leave high-crime areas immediately upon expe- riencing victimization, others may not leave until crime rates affect job opportunities, the quality of education, and the general reputation of an area. (5) If violent-crime rates and racial composition affect each other over each decade from 1950 to 1990, these effects, however modest, would yield a pattern of escalating cross-sectional correlations over these decades. We attempt to model this long-term process.

METHODS

Sample

Studies have examined dimensions of this issue at varying levels of analy- sis, including neighborhoods, cities, SMSAs, and states. It is not clear that this issue is better addressed at one level than another. Migration between neighborhoods, cities, states, and certainly from cities to sub- urbs, are all significant social processes; crime rates may affect all of them, especially short distance ones, such as between neighborhoods within a city and from cities to suburbs. Our work focuses on cities because we wish to study the relationship between racial composition and violent-crime rate over a relatively long period of time, and such data are not available for neighborhoods. The sample consists of between 104 and 107 cities over 50,000 population. Because of population changes over the decades, a few cities fall slightly under 50,000 for some decades. And because of some missing data and a few outliers, the sample varies slightly over the 40-year period. Although these cities were selected be- cause their segregation levels had been calculated since 1940 (making historical comparisons possible),' they are a reasonably representative sample of large U.S. cities. For the decade 1980-90 the sample contains approximately 60% of U.S. cities over 100,000 population and 82% of the 50 largest cities. It is well distributed geographically: 25 cities are located in the East, 27 in the Midwest, 23 in the West, and 34 in the South (including the Mid-Atlantic).

Measures

The two primary variables, violent-crime rates (homicide, assault, rape, and robbery) and percentage nonwhite, are measured with data available in the Uniform Crime Reports and the U.S. census, respectively. In deciding what other variables to include, it should be remembered that our major concern is to examine the relationship between violent-crime rates and racial composition, not to explain either. While the latter sug- gests including all other variables that may affect either in order to in- crease the explained variance, the former suggests focusing on the other variables that affect both. The exclusion of these common variables could bias estimates of the effects of violent-crime rates and racial composition on each other. To identify common variables, we have reviewed and drawn on the migration and violent-crime literatures. While both litera- tures are extensive, including dozens of variables, four common general categories can be identified (see Frey and Speare 1988; Land et al. 1990): economic, racial, population, and family structures.

Perhaps economic structure or composition is the major category of variables identified in both literatures. Hard economic times in an area may increase violent-crime rates (Blau and Blau 1982; Messner 1983)

The sample was originally selected during the 1960s, and segregation levels for the 1940s and 1950s were calculated at that time.

and may drive out those who can afford to leave (whites more than nonwhites), thus increasing the percentage nonwhite (Frey and Speare 1988; South and Deane 1993) and yielding a positive relationship between it and violent-crime rates. We therefore include three dimensions of eco- nomic structure (median income, percentage below poverty, and percent- age unemployed) in the analysis.

As to racial structure, the literature identifies residential segregation, in addition to percentage nonwhite, as affecting migration patterns of whites and nonwhites (Frey and Speare 1988) and violent-crime rates (Wilson 1987; Peterson and Krivo 1993). Thus, we include residential segregation in the analysis.

Of the many dimensions of family structure, percentage divorced as a source of family disruption is most clearly identified in the violent-crime literature as increasing frustration and reducing social control (Sampson 1986; Blau and Blau 1982). It is also clearly identified in the migration literature as producing a mobile population (South and Deane 1993).

Of the dimensions of population structure, age distribution is identified in both literatures. The migration literature frequently identifies the pop- ulation between 20 and 29 years old as a mobile population (Frey 1979), and the violent-crime literature identifies the population between 15 and 20 years old as being crime prone, especially for violent crime (Hirschi and Gottfredson 1983). Because the migration literature identifies the 20-29-year-old age category as most mobile and the violent-crime litera- ture identifies the 15-20-year-old age category as the most violence prone, we use the category 15-24 years old as including populations prone to both moving and violence.

We include two additional variables that are clearly identified in one literature but not the other. The violent-crime literature identifies popula- tion size, another dimension of population structure, as a general source of frustration and weak social control and thus as general cause of violent crime, but size is only marginally noted in the migration literature (e.g., Marshall 1979). On the other hand, revenue per capita (as a measure of the tax burden and the availability of social services) is identified in the migration literature (Frey and Speare 1988) but not at all noted in the violent-crime literature. Hence, we include population size in the crime- rate equations and revenue per capita in the racial composition equa- tion~.~

To empirically test this theoretical assumption, population size was also included in the racial composition equations and revenue rate was also included in the crime-rate equation. They show no effects. We initially selected these variables as instruments to identify the equations in a simultaneous equation analysis. As the results turn out, lag models provide better fits to the data than do simultaneous models; thus, the simultaneous equation analyses are not discussed here (results available upon request).

Data for most of these variables are readily available. Population size, age distribution, revenue, median income, percentage below poverty, percentage unemployed, and percentage divorced are all available in the

U.S. census and the City and County Databook or can be computed from data available in these sources. Segregation is measured by a dissimilarity index, which describes the extent to which the racial composition of city blocks reflects the racial composition of the city as a whole. It can be computed from information available in the U.S. census, and it is avail- able in various publications (Sgrensen, Taeuber, and Hollingsworth 1975).

The analysis is divided into five parts: (1) We examine the simple cross-sectional effects of the population, family, racial, and economic structure variables on violent-crime rates to establish the comparability of our data to that reported in the literature. (2) We examine a simple (no controls) reciprocal effects model to establish which violent crime, if any, affects racial composition and to identify the proper causal lag underlying that effect and the effect of racial composition on violent crime. (3) Drawing on these analyses, we specify a more complex model (including controls) to examine the relative effects of percentage nonwhite and violent-crime rates on changes in both over four decades from 1950 to 1990. (4) We disaggregate change in percentage nonwhite into change in the white and nonwhite populations to compare the effect of violent- crime rates on changes in both populations. (5) Drawing on the above findings, we model the pattern of escalating cross-sectional correlations between violent-crime rates and racial composition over the 40-year period.

RESULTS

Preliminary Cross-Sectional Analysis

Before beginning the analysis it may be useful to compare briefly the violent-crime rates of our sample of medium and large cities (over 50,000 population) to those of all cities and all large cities (over 250,000 popula- tion). As might be expected of a reasonably random sample, over each decade from 1950 to 1990 the mean rate for our cities falls directly be- tween the mean rates for all cities and all large cities.

To further examine how our data compare with extant research, we begin by regressing violent-crime rates on the racial, population, family, and economic characteristics used in the literature for the years most reported in the literature (1960, 1970, and 1980). Because of the high correlation between the three economic characteristics, we follow Land et al. (1990) and calculate an economic deprivation factor scored as the weighted sum of these economic variables with weights equal to their factor loadings. We score it so that a high value equals high deprivation. For each of the years (1960, 1970, and 1980) percentage nonwhite shows a consistent effect on violent-crime rates (table 1). Indeed, of all the independent variables, it shows the strongest and most consistent effect. We also estimate the equation separately for each of the crimes that compose the violent-crime index (homicide, assault, robbery, and rape). The results for each crime are generally similar to those reported in table 1, which are also consistent with the extensive review done by Land et al. (1990) of the homicide literature over three units of analysis (state, SMSA, and city) over the same three decade^.^

While the percentage nonwhite effect is consistently substantial and statistically significant, we must be cautious in interpreting this finding, because the percentage nonwhite and the economic deprivation factor are substantially correlated in each decade (.57 in 1960, .54 in 1970, and .67 in 1980). Indeed, the strength of these correlations led Land et al. (1990) to combine percentage nonwhite and various economic dimensions into one factor. While we appreciate the logic underlying this approach, for our purposes it is important to separate the effects of racial composi- tion from those of economic structure. To gauge the possible effects of collinearity, we estimate the percentage nonwhite effect with and without the economic factor in the equation. The percentage nonwhite effect is similar in both specifications of the equation (betas range from .5 1to .64) and statistically significant.' We also calculate variance inflation factors (VIFs). They never exceed 2.6, suggesting that collinearity is not a prob- lem. Finally, we estimate the equations using ridge regression, which provides more efficient, although somewhat biased, estimates. By pro- gressively increasing the ridge constant over a range of values, we obtain estimates of the model parameters over a range of linear transformations of the variance-covariance matrix that balance efficiency and bias. Again, the percentage nonwhite effect remains strong and statistically signifi- cant. In sum, while we remain sensitive to the problems of collinearity

We also estimate these equations including revenue per capita and region (dummy coded "South" and "non-South"). As expected, the former shows no effect, and region shows a statistically significant effect only in 1980 (P = -.16). Even in that year, including region does not change the estimates of the other variables. The beta for percentage nonwhite is .45 including region and .40 excluding it, and the beta for economic deprivation is .29 including it and .36 excluding it. 'We are also interested in whether the inconsistent effect of economic deprivation over the decades reflects collinearity; thus we also estimate the equation deleting percentage nonwhite. While dropping percentage nonwhite increases the size of the economic deprivation coefficients, the pattern of coefficients remains the same. Be- cause economic deprivation is not the focus of this article, we reserve further analysis for another article.

###### TABLE I

CROSS-SECTIONALOLS ESTIMATES OF THE EFFECTS OF CITY CHARACTERISTICS

ON VIOLENT CRIME RATES OVER THREE DECADES

1960 | 1970 | 1980 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

b | P | t-ratio | b | P | t-ratio | b | P | t-ratio | ||||||

% divorced ............................. | 54.78* | .31 | 3.80 | 88.90* | .25 | 3.57 | 61.707 | .13 | 1.94 | |||||

% age 15-24 | ........................... | -6.02 | -.07 | -.92 | -3.14 | -.02 | -.36 | -9.84 | -.03 | -.55 | ||||

Population size$ | ...................... | 4.00* | .2 2 | 2.69 | 10.00* | .2 7 | 3.89 | lO.OOt | .12 | 1.71 | ||||

Economic deprivation | ............... | -3.70 | -.02 | -.20 | -30.49 | -.07 | -.87 | 254.36* | .36 | 3.84 | ||||

Segregation | ............................ | -1.50 | -.07 | -.79 | -4.46 | -.lo | -1.40 | -6.40 | -.07 | -1.08 | ||||

% nonwhite ............................ | 7.91* | .55 | 5.54 | 18.03* | .65 | 7.70 | 16.26* | .40 | 4.24 | |||||

R | ........................................ | .39 | .5 1 | .52 | ||||||||||

* b > 2.0 SE. | ||||||||||||||

7 b > 1.5 SE. |

t Population is expressed in 100,000s.

in separating the effects of racial composition from those of economic structure, our consistent results over a range of methods suggest that the racial composition effect found in this and numerous other cross-sectional analyses is not just a product of collinearity. It is significant and substan- tial and thus warrants our attention.

Yet, if the causal structure underlying the relationship between racial composition and violent-crime rates is reciprocal, as we suggest, then the cross-sectional OLS findings, reported here and in the literature, are biased. They most likely overestimate the racial composition effect. To address this issue, we develop and estimate change models.

Change Models

A major issue in studying change is the procedure for measuring it (see Allison 1990; Kessler and Greenberg 1981; Plewis 1985). At least three methods are advocated: difference-score method, in which the time 1 score (t,) is subtracted from the time 2 score (t,); cross-lag regression method, in which the t, score is included on the right side of the equation; and residual score method, in which the t, score is first regressed on the t, score, yielding a residual t, score (variance in t, not predicted by t,h6 To a large extent, the differences among these methods depend on how the stable component is modeled.' For some time, sociologists have advo- cated the cross-lag method (Bohrnstedt 1969). More recently some have

Recently Firebaugh and Beck (1994) further distinguish the difference method into two subtypes: semi-difference and full difference. The former only differences the dependent variable, regressing this difference on the levels of the independent vari- ables, while the latter method differences both the dependent and independent vari- ables, regressing the differences of the dependent variable on the differences of the independent variables. Firebaugh and Beck argue that the full-difference method provides a better control for the effects of stable unmeasured variables than does the semi-difference method. We are not so sure and thus elect to compare the more traditional semi-difference method to the other methods. 'In the difference-score method the change from time 1 to time 2 is regressed on the independent variables, including the time 1 level of the dependent variable. By includ- ing the lag level of the change variable as a regressor, we both control for and observe the relationship between the level of the dependent variable and the change in that variable. In the residual score method the time 2 score is first regressed on the time 1 score. Then, using this equation, a predicted score is generated and subtracted from the time 2 score, yielding a residual score (that part of the time 2 score not predicted by time 1). Finally, the residual score is regressed on the independent variables. In the cross-lag regression method, the level of the dependent variable is regressed on the lag levels of itself and the other variables at time 1. Because the lag level of the dependent variable is included in the cross-lag equation, the regression coefficients of the other variables are interpreted as effects on the change in the dependent variable. While these three methods differ, much of the difference concerns the method for modeling the stable component of the dependent variable.

questioned the mathematical differences among these methods (Kessler and Greenberg 1981). And some have questioned the rationale for using the cross-lag method over the difference-score method, arguing that in many circumstances the latter yields more meaningful results (Allison 1990).

Rather than enter this debate, we use all three methods. We regress the differences in violent-crime rates and percentage nonwhite over vary- ing time intervals on lag levels of themselves and the other variables (difference-score method); we regress residuals of violent-crime rates and percentage nonwhite over varying time intervals on lag levels of them- selves and the other variables (residual score method); and we regress violent-crime rates and percentage nonwhite levels on varying time lags of themselves and the other variables (cross-lag method). As expected (Kessler and Greenberg 1981; Allison 1990), all three methods yield the same pattern of metric coefficients and statistical significance over the four decades. There are two differences, which are more technical than substantive. In the cross-lag regression the b (autoregression coefficient) for the lag-dependent variable (e.g., violent crime 1980 regressed on vio- lent crime 1970) reflects both its stability and its effect on the change in itself (structured change), whereas in the difference-score and residual score methods the b reflects just its effect on the change in itself. Hence, the b's for the lag-dependent variable yielded by the cross-lag regression are always larger than those yielded by the difference-score and residual score methods (Kessler and Greenberg 1981).' On the other hand, the standardized coefficients (betas) of the other variables yielded by the cross-lag regression are generally smaller than those yielded by the other methods, because the full variance of violent-crime rates and percentage nonwhite, not just the part that changes, is regressed on them. Because our focus is on the effect of violent-crime rates and percentage nonwhite on the change in each other, we report the coefficients estimated by the most intuitive method for studying change (Allison 1990): the difference- score method. (Estimates of the other two methods are available upon request.)

Simple change models.-To establish the effects of different violent- crime rates on the change in racial composition, we first estimate a simple

Because the autoregression b's in the cross-lag method reflect both stability and the change in a variable that is related to its prior level, the autoregression coefficients obscure observing either the former or the latter. This is particularly problematic when change in a variable is negatively related to its prior level (as is the case for our data in some eras). For example, if a variable changes by only a small amount (10%) that is negatively affected by its prior level, then the autoregression coefficient would still be strongly positive, reflecting the large positive stability effect (90%), thereby obscuring the small but significant negative causal effect of prior level on change.

model in which change in racial composition is regressed on just its own level and each of the violent-crime rates. To examine the extent to which the results are sensitive to the length of the time interval and the period, we estimate this simple model from 1950 to 1990 for intervals of 5, 10, 15, 20, 25, 30, 35, and 40 years. For example, controlling for the effects of percentage nonwhite in 1950, we estimate the effects of violent-crime rates in 1950 on changes in percentage nonwhite over time intervals of 5-40 years.9 Varying the length of the time interval is important, because the effects of violent-crime rates may operate through long-term social processes.

Consistent with the literature, the robbery rate (violent crime by strangers) by far shows the strongest effect whether the analysis uses all four violent crimes simultaneously or independently. Most of the effect occurs within an interval of 10-15 years; that is, the strength of the effect increases with the length of the change interval but at a decreasing rate. An interval of 10-15 years appears optimal; longer intervals yield insig- nificant increases in the regression coefficients. This pattern is particu- larly informative because it is not evident in the effect of racial composi- tion on violent-crime rates. For example, the effect of percentage nonwhite on change in robbery rates increases slightly from 5 to 10 year intervals and then decreases progressively from 15 to 40 year intervals. In sum, the analysis suggests that, of the four violent crimes, robbery rates (violent crimes by strangers) affect the change in racial composition and that most of the effect occurs within 15 years, whereas the effect of percentage nonwhite on changes in robbery rates occurs more quickly.

Complex change models.-Given these preliminary findings, we now focus our attention on the effect of percentage nonwhite and robbery rates on 10-year changes in each other by period, controlling for the other theoretically significant variables. We use 10-year changes by decennial year because they are the optimal interval in our preliminary analysis and because most studies use them based on the availability of census data. We also use 20-year changes, but the results are generally weaker;

Accordingly, we estimate the effect of violent-crime rates in 1960 on change in racial composition from 5 to 30 years, the effect of violent-crime rates in 1970 on change in racial composition from 5 to 20 years, and the effect of violent-crime rates in 1980 on change in racial composition from 5 to 10 years. In examining the lag issue, we are not concerned with the structure of the lag, that is, in estimating a model that distrib- utes the causal effect over various time intervals (a distributive lag model). Estimating such a model requires making assumptions about the structure of the lag distribution that we are unprepared to make. Our goals are more modest. We only wish to estimate the length of the lag over which most of the causal effect occurs. Thus, we approach this question by estimating the effect of crime rates and percentage nonwhite on the change in both over varying intervals of time ranging from 5 to 40 years.

and we use 5-year changes for robbery (where data are available annu-

ally), and the pattern of results is similar.

We regress 10-year robbery rate and percentage nonwhite changes on the base levels of each variable and the control variables. For example, we regress change in robbery rates and percentage nonwhite from 1980 to 1990 on the 1980 levels of robbery rates, percentage nonwhite, and the control variables. We treat changes from 1970 to 1980, from 1960 to 1970, and from 1950 to 1960 similarly. The lag level of the dependent variable is included as a causal variable because it often relates both to the degree of change in it and to the other causal variables. Table 2 presents the results for the robbery change equations, and table 3 presents the results for the percentage nonwhite change equations. Because of our concern about collinearity, we have dropped from the final equations all variables that are not statistically significant in at least two of the four decades. Hence, while included in the initial estimates of these equations, age distribution is not included in the final tables of the robbery and percentage nonwhite change equations (tables 2 and 3). In both equations it achieves statistical significance in only one of the four decades (1960- 70). (Even in that decade its effect is not in the predicted direction.) Percentage divorced is not included in the final estimates of percentage nonwhite change equations (table 3), because it is not statistically signifi- cant in any of the decades.

We examine the data for collinearity and influential outliers. As noted before, the moderate correlations between percentage nonwhite and the economic deprivation factor suggest possible problems. To reiterate, we calculate the VIFs for the equations in each decade. They never exceed 2.6, indicating modest levels of collinearity. Nonetheless, to adjust for whatever collinearity may exist, we also estimate the equations for all four decades using ridge regression. These estimates are similar to (in most cases, the same as) those in table 2, further indicating that collinear- ity is not a problem. Because the correlations among the independent variables are the strongest for percentage nonwhite, economic depriva- tion, and robbery rate, we also estimate each of the equations dropping each of these variables one at a time and again dropping all combinations of two (one combination at a time). While the estimated effects of the remaining variables increase as other variables are dropped from the equations (as should be expected), the pattern of coefficients and the significance level of all the coefficients remain generally the same.'' We

'O The few exceptions occur in the 1980-90 decade for the economic deprivation effect. As described in table 2, economic deprivation does not affect change in the robbery rate, but when percentage nonwhite is dropped from the equation it shows a statisti- cally significant effect. Also, as described in table 3, economic deprivation does not

also examine partial regression plots and Cook's D for influential outliers. We find only a few for any decade, which are dropped from the analysis."

Consider first the robbery equations (table 2). We focus only on the percentage nonwhite effect. Note that the metric coefficient increases from the 1950-60 equation to the 1960-70 equation, decreases in the 1970-80 equation, and finally increases substantially in the 1980-90 equation. To increase the efficiency of the estimates, we estimate the equations simultaneously for the four decades, allowing the error terms to correlate for adjacent decades. It seems reasonable that conditions that cause the robbery rate to change during one decade (e.g., 1950-60) may correlate with those that cause robbery rates to change in adjacent de- cades (e.g., 1960-70). The parameters and standard errors of these equa- tions are similar to those in table 2. To test the statistical significance of the differential percentage nonwhite effect, we estimate the equations across the decades simultaneously as one multiyear model and compare the fits (x21df) for a nested set of models: when all percentage nonwhite parameters are free to vary, when they are constrained for the 1980-90 and 1970-80 equations to be equal, when they are constrained for the 1980-90, 1970-80, and 1960-70 equations to be equal, and when they are constrained for all equations to be equal. The constraints do not yield statistically significant increases in x2 until the 1950-60 equation is added, suggesting that the effects of percentage nonwhite on 10-year changes in the robbery rate from 1960 to 1990 are equal and statistically significant (t-ratio = 2.4). l2

The other variables show effects similar to those reported in the litera- ture. Population size shows a positive statistically significant effect in two decades, the economic deprivation factor shows a positive statistically

affect change in the white population, but when both percentage nonwhite and rob- bery rates are dropped from the equation, it shows a statistically significant effect. The results suggest that the observed effect of economic deprivation on change in robbery and percentage nonwhite is spurious, depending on the correlation between economic deprivation and both percentage nonwhite and robbery rates.

" Over the course of the article we estimate four change equations (robbery rates, percentage nonwhite, nonwhite population, and white population) over four decades (16 equations). Influential outliers are evident in 10 of them. In two equations only one city appears as an outlier, in six equations two cities appear, and in two equations three cities appear. These cities tend to be the same across the equations. For example, Miami appears as an outlier in eight of the 10 equations. We used two deletion procedures. (1) An outlier in any one year is deleted in all years to maintain a uniform sample size. (2) An outlier for any one year is deleted only for that year to maximize sample size in all years. As the results are insensitive to the deletion procedure, we report only the results yielded by the latter procedure.

l2 This test is facilitated by using a structural equation program, such as LISREL or EQS.

TABLE 2

OLS ESTIMATES OF THE EFFECTSOF CITY CHARACTERISTICS ON 10-YEARCHANGESIN ROBBERYRATES

1950-60 | 1960-70 | 1970-80 | 1980-90 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

b | p | t-ratio | b | p | t-ratio | b | p | t-ratio | b | p | t-ratio | |

%divorced .................... Populationsize$ .............. Economic deprivation ....... Segregation .................... % nonwhite .................... Robbery rates ................. R ................................ | 16.02* 3.19* -1.71 1.55t 1.24t -.09 | .34 .48 -.03 .15 .25 -.06 .27 | 2.79 4.47 -.25 -1.63 1.79 -.46 | -8.05 6.97* -10.76 -5.72* 3.39t 1.09* | -.03 .27 .05 -.20 .18 .37 .36 | -.37 3.08 .46 -2.16 1.70 3.60 | 38.69t -05.78 53.11t 8.80* 1.94 .09 | -.I6 -.01 .20 -.30 .10 .09 .16 | -1.66 -.I6 1.73 -3.02 .82 .70 | 4.09* 5.12t 35.46 .56 5.50* -.31* | -.03 .18 .16 .02 .43 .56 .23 | -.324 1.93 1.24 .23 3.41 -4.66 |

* b > 2.0 SE. t b > 1.5 SE. |

f Population is expressed in 100,000s.

8 Robbery rate is expressed as the number of robberies per 1,000 population

significant effect in one decade, and segregation shows a negative statisti- cally significant effect in three decades. Finally, the robbery rate itself shows a positive statistically significant effect on the rate of change for one decade, an insignificant effect in two decades, and a negative effect in the 1980-90 decade, suggesting that when the robbery rate reaches a very high level, processes may be set into motion that reduce further increases. (In part, the robbery rate is included in the equation to control for these effects.) While these processes and those underlying the effects of all the control variables may be interesting to study, they are not the focus of this article and thus will not be further discussed here.

Consider now the percentage nonwhite equations (table 3).13 The robbery effect is moderately substantial and statistically significant for each decade. First, consider its absolute strength (metric coefficients). It decreases substantially with each decade. As expressed in table 3, an increase of one robbery per 1,000 population (or 100 robberies per 100,000 population) yields an increase of 2.98 in the percentage non- white from 1950 to 1960, 1.72 from 1960 to 1970, 0.51 from 1970 to 1980, and 0.18 from 1980 to 1990. Note that from 1950-60 to 1980-90 the absolute effect of the robbery rate decreases by a factor of more than

15. Again, to increase the efficiency of our estimate, we estimate the four equations over the four decades simultaneously, allowing the error terms to correlate for adjacent years. Estimates of the causal parameters and the standard errors are similar to those in table 3. To test the statistical significance of these differential effects, we again compare the fits of a nested set of models: allowing all robbery parameters to be free; con- straining them to be equal for the 1980-90 and 1970-80 equations; con- straining them to be equal for the 1980-90, 1970-80, and 1960-70 equa- tions; and constraining them to be equal for all four decades. Constraining just the 1980-90 and 1970-80 robbery rate parameters does not yield a significant increase in the x2;however, adding the 1960-70 robbery rate parameter to the constraints yields a statistically significant increase (P < .lo), and adding the 1950-60 equation to the constraints yields a further statistically significant increase (P < .05). Hence, the robbery rate effects are not only statistically significant for each decade, they also show a statistically significant pattern of declining effects over the decades.

Now consider the strength of the robbery effect relative to that of the other variables (the standardized coefficients). The pattern of effects is quite different. Relative to other variables, the effects of robbery rates

l3 We realize that as percentage nonwhite approaches 100, large changes are not possible. Yet, few of our cities have a nonwhite population over 60% for any decade and few are even close to this percentage.

on percentage nonwhite change are constant over the four decades (P = .2 1). The standardized and unstandardized effects diverge because over the decades not only do robbery rates increase substantially in most cities but the robbery rate variance increases dramatically. A 1-SD difference among cities in robbery rates constitutes a difference of 36 robberies per 100,000 population in 1950, 75 per 100,000 population in 1960, 282 in 1970, 424 in 1980, and 442 in 1990. If the metric effect of each robbery (per 100,000 population) remained at the 1950 level, then, given the dramatic increase in the robbery rate variance, we would expect an equally dramatic increase in the standardized coefficients. However, as we observe, the effect of each robbery (per unit of population) decreases as dramatically as the robbery variance increases over the decades, yield- ing a stable standardized effect relative to that of other variables. Thus, even though the metric coefficients decrease over the decades, the effect of the robbery rates relative to other variables (as expressed in the stan- dardized coefficients) remains constant over the four decades. The de- crease in the sensitivity to each robbery, reflected in decreasing metric coefficients, is compensated for by the tremendous increase in the robbery rate variance, reflected in stable betas.

Disaggregating the change in percentage nonwhite.-Increases in the percentage nonwhite can occur either because whites move out and/ or do not move in or because nonwhites move in and/or do not move out. Numerous demographic analyses (e.g., Frey and Speare 1988; Frey 1980) clearly show that the change in percentage nonwhite experi- enced by American cities from 1950 to 1990 occurred because whites migrated from cities to suburbs and nonwhites migrated from rural areas to cities. Our hypothesis suggests that robbery rates in cities played a significant role in only the former process. To test this, we disaggregate the change in the percentage nonwhite over each decade into change in the white population and change in the nonwhite population. To be

cautious we calculate both absolute change (e.g., population 1960 population 1950) and relative change (e.g., [population 1960 -population 19501 / population 1950) for both racial populations. We regress both measures of change for both populations on the lag levels of the robbery rate, the specific racial (white and nonwhite) population, and the other variables. Generally, the absolute and relative measures of change yield similar patterns of statistically significant coefficients. Those for the rela- tive change measure are reported in tables 4 and 5, and the few discrep- ancies between them and those for the absolute change measures are noted. For change in the nonwhite population (table 4) robbery rates show no clear pattern of effects over the four decades and are not statistically significant except for the 1980-90 decade, where the effect is marginally

TABLE 4 OLS ESTIMATESOF THE EFFECTSOF CITY CHARACTERISTICS ON 10-YEAR CHANGES IN THE NONWHITE POPULATION

b | p | t-ratio | b | p | t-ratio | b | p | t-ratio | b | p | t-ratio | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Revenuerate? ................. | 19.15? | .14 | 1.68 | 8.61* | .21 | 2.42 | -1.29 | .05 | -.9 | -.37 | -.09 | .89 | ||

Economic deprivation ....... | -11.54* | -.26 | -2.44 | -10.99* | -.43 | -4.26 | .18 | .004 | .04 | ~7.47~-.39 | -3.32 | |||

Segregation | .................... | -.22 | .03 | .33 | .68* | .20 | -2.19 | 1.32* | .31 | -3.24 | -.71* | -.32 | -3.85 | |

%nonwhite .................... | 1.13* | -.31 | -2.75 | -.07 | -.03 | -.33 | -1.10* | -.40 | -3.51 | .31* | .29 | -2.47 | ||

Robbery rate8 ................. | -1.14 | .01 | -.I1 | 2.61 | .08 | .93 | -.75 | .05 | .47 | 1.05? | .22 | 1.80 | ||

R | ................................ | .32 | .40 | .32 | .35 | |||||||||

* b > 2.0 SE. | ||||||||||||||

t b > 1.5 SE. |

t Revenue rate is expressed in dollars per person; to reduce places to the right of the decimal, the b is multiplied by 100

6 Robbery rate is expressed as the number of robberies per 1,000 population.

TABLE 5 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

OLS ESTIMATES OF THE EFFECTSOF CITY CHARACTERISTICS ON 10-YEAR CHANGES IN THE WHITE POPULATION | ||||||||||||

b | p | t-ratio | 6 | p | t-ratio | 6 | p | t-ratio | b | p | t-ratio | |

Revenue rate* ................. .......Economic deprivation Segregation .................... % nonwhite .................... Robbeyrates ................. RZ................................ | -24.02* 3.19 1.06* -.018 -7.20 | -.30 .12 .22 -.01 -.lo .19 | -3.19 1.02 2.39 -.6 -1.07 | -5.70 2.17 .55? -.30 3.74 | -.I5 .10 .19 .I6 .I2 .12 | -1.49 .78 1.64 1.29 -1.23 | 1.61 .51 .76* -.47* -2.57* | .13 .03 .38 -.37 -.36 .43 | 1.48 .29 4.38 -3.53 -3.83 | -.04 -4.14* .18 -.15t -1.23* | -.01 -.29 .11 -.I8 -.22 .36 | .I4 -2.57 1.33 -1.57 2.06 |

* b > 2.0 SE. t b > 1.5 SE. t Revenue rate is expressed in dollars per person; to reduce places to the right of the decimal, the b is multiplied by 100. § Robbery rate is expressed as the number of robberies per 1,000 population. |

significant but positive.14 Similar to past research (Frey and Speare 1988; Frey 1979, 1980; Massey and Denton 1993; Denton and Massey 1991), our research shows that change in the nonwhite population is affected by economic structure (measured here by economic deprivation and city revenue), by racial tolerance (measured here by segregation), and by the racial composition.15 Generally, nonwhites migrate to those cities where both the percentage nonwhite and segregation are low and economic conditions are good.

For the white population, however, robbery rates are much more im- portant (table 5). The effects are consistently negative over the four de- cades and are statistically significant for the last two.16 While each indi- vidual robbery has more impact on the change in the white population from 1950 to 1970 than from 1970 to 1990, the variation of the robbery rate during the first two decades is too small to produce much variation in the change in the white population among cities; but while each indi- vidual robbery has less impact on the change in the white population from 1970 to 1990 than from 1950 to 1970, the dramatic increase in the variation in robbery rates during the last two decades is more than enough to produce substantial and statistically significant variation in the change in the white population. Again, to increase the efficiency of our estimates, we estimate the four equations over the four decades simultaneously, allowing the error terms to correlate for adjacent years. Estimates for the causal parameters and standard errors are similar to those in table 5. To test the statistical significance of the differential robbery rate effects on the white population over the decades, we again compare the fits of a nested set of models: (1) freeing the robbery parame- ters for all equations, (2) constraining them to be equal in the 1980-90 and 1970-80 equations, (3) constraining them to be equal in the 1980-90, 1970-80, and 1960-70 equations, and (4) constraining them to be equal in all equations. The first set of constraints does not yield a statistically significant increase in the x2,the second set does yield a statistically significant increase, and the third set does not yield a further statistically significant increase. These results suggest that the robbery effect is similar within the periods from 1950 to 1970 and from 1970 to 1990 but different between these periods.

The 1970-80 decade is particularly important, because it is the decade

l4 For the absolute measure of change, robbery rates also show no statistically signifi-

cant effects.

l5 Neither using ridge regression nor allowing the error terms of the equations for

adjacent years to correlate alters the findings.

l6 For the absolute measure of change, the robbery rate effect is statistically significant for the last three decades.

when the racial composition of cities changed the most (e.g., a mean decrease of 18% in the white population, compared to decreases of 5% in 1960-70 and 8% in 1980-90). During that decade the equation ex- plains 43% of the variance in white population change, and the robbery effect is strong. If the robbery rate is not included in the equation, the R2drops from .43 to .35 and the effects of the other variables, particularly percentage nonwhite, are overestimated. Including the robbery rate in the equation yields a percentage nonwhite beta of -.37 compared to -.52 when robbery is not included. It seems that past research, by not including robbery rates in the analysis, attributes too much causal significance to percentage nonwhite in explaining change in the urban white population. Percentage nonwhite and robbery rates appear to be equally important in explaining change in the urban white population during that era.

The 1980-90 decade is also important and interesting. It is the only decade where a 20-year lag robbery effect is stronger than a 10-year lag effect on the change in the white population. While the effect of the 1980 robbery rate is negative (P = -.15), it is not quite statistically significant; the effect of the 1970 robbery rate (20-year lag) is both negative (P = -.22) and statistically significant." Hence, the 1970 robbery rate, which dramatically increased from 1960, seems to substantially affect change in the white population not only over the next decade (1970-80) but over the following decade (1980-90) as well. It may be that the time lag through which robbery rates affect change in the white population may be increasing.

Recovering the Pattern of Escalating Cross-Sectional Coefficients

Perhaps the most important characteristic of the relationship between racial composition (percentage nonwhite) and violent crime by strangers (robbery) is that the relationship has been increasing systematically and dramatically over the last 40 years. The correlation was only .15 in 1950, which by most standards is relatively insignificant. It increased to .29 in 1960, to .48 in 1970, to .58 in 1980, and to .67 in 1990 (see table 6, col. 1). It is important to note not just that the strength of the relationship is a relatively recent phenomenon but that its dramatic increase cannot be accounted for by comparable increases in the causal parameters of the change model, particularly in the causal effect of robbery rates and racial composition on changes in each other. Remember, the standardized coef- ficients of robbery rates on percentage nonwhite remain constant, and

" When robbery rates for both 1970 and 1980 are included in the equation, the robbery rate effect for 1970 is still stronger than that for 1980.

TABLE 6 PREDICTED OF GROWTHIN THE CROSS-SECTIONAL

PATTERNS CORRELATION BETWEEN PERCENTAGE AND ROBBERY

NONWHITE RATE

Observed | ||||||
---|---|---|---|---|---|---|

Year | Correlation | Model 1 | Model 2 | Model 3 | Model 4 | |

1950 | ........... | .15 | .15 | .15 | .15 | .15 |

1960 | ........... | .29 | .26 | .30 | .19 | .17 |

1970 ........... | .48 | .33 | .43 | .24 | .26 | |

1980 | ........... | .58 | .37 | .53 | .41 | .43 |

1990 | ........... | .67 | .40 | .61 | .58 | .60 |

NOTE.-Model 1: stability coefficients = .80, and causal coefficients = .lo; model 2: stability coefficients = .90, and causal coefficients = .lo; model 3: causal and stability coefficients estimated by simple cross-lag model; model 4: causal and stability coefficients estimated from complex cross-lag model (includes all other variables from tables 2 and 3).

while the standardized coefficients of percentage nonwhite on robbery rates do increase, the increases are not nearly enough to account for the dramatic increase in the cross-sectional correlation from 1950 to 1990.

The long-term increase is much more insidious: it appears to be the accumulative result of small causal effects operating consistently over the last 40 years. Consider the cross-lag model in figure 1. It implies that the cross-sectional correlation at 1960 is equal to the observed correlation at 1950 plus the stability and causal effects as described by equation (I):

Y %NW1960,RR1960= (Y %NW19jo, RR1950 X a1 bi) f (a1 CI)

+ (dl x b,) + (Y %NW19jO, RR19so X CI X dl),

where %NW,,,, is the percentage nonwhite, RR,,,, is the robbery rate, a and b are stability effects, c is the causal effect of robbery rate on percentage nonwhite, and d is the causal effect of percentage nonwhite on robbery rate. Figure 1 also suggests that the cross-sectional correlations at

FIG.1 .-Simple cross-lag reciprocal effects model of robbery rates and percent- age nonwhite.

1970, 1980, and 1990 are equal to the model implied or imputed correla- tion at the previous time plus the stability and causal effects as described by equation (2):

where 7 %NWyear, RR,,,, = model imputed correlation, t = 2 for 1960-70, 3 for 1970-80, and 4 for 1980-90. The cross-sectional correla- tion is attenuated to the extent to which the product of the stability parameters (a x b) is less than 1, and it is increased (or decreased) by the relative strengths of the causal parameters. Various combinations of stability and causal parameters yield consistent increases in the cross- sectional correlation. Indeed, if the stability coefficients are strong (> .75), as they are in most of the 10-year intervals, then only small positive causal parameters are needed to produce consistent and dramatic in- creases in the cross-sectional correlations over time.

To keep matters initially simple, assume constant stability coefficients of .80 for both percentage nonwhite and robbery rates over the 10-year time intervals and cross-lag causal effects of only .lo over the time inter- vals. If we assume an initial correlation of .15 (the actual initial correla- tion between percentage nonwhite and robbery rates in 1950), then the model implies the following growth pattern of the cross-sectional correla- tions over four cycles (40 years): .26, .33, .37, .40 (see table 6, model 1). For example, the model implies that the 1960 cross-sectional correlation is equal to the 1950 cross-sectional correlation times the stability parame- ters (.I5 X .8 X .8), plus the 1950 cross-sectional correlation times the causal parameters (. 15 X .10 X .lo), plus one stability parameter times its corresponding causal parameter (.8 x .lo), plus the other stability parameter times its corresponding causal parameter. In turn the model implied 1970 cross-sectional correlation is equal to the 1960 implied cross- sectional correlation plus the same stability and causal effects over the 1960-70 decade, and so on for the 1980 and 1990 model implied cross- sectional correlations (see fig. 1 and eqq. [I] and [2]). If we increase the stability parameters to .90, the model implies the following pattern: .30, .43, 53, .61 (table 6, model 2). Generally, if the model parameters are relatively stable and positive, the cross-sectional correlation increases at a decreasing rate, eventually reaching an equilibrium.

The real world, however, is not so orderly. Our change analysis sug- gests that both the stability and causal parameters change over the 40 years from 1950 to 1990. To study the implications of the empirically estimated stability and causal parameters for the pattern of cross-sectional correlations, we estimate 10-year cross-lag models from 1950 to 1990, first using only percentage nonwhite and robbery rates (fig. 1).The pattern and size of the metric coefficients and the pattern of standardized coefficients are quite similar to those yielded by the change analysis (see tables 2 and 3).18 Constraining the stability and causal parameters to these values, the simple cross-lag model generates substantial growth in the implied cross-sectional correlation (see table 6, model 3). While the pattern of growth approximates the pattern of growth in the observed correlations, the model underestimates the degree of growth, suggesting that other variables may be involved.

We thus reestimate the cross-lag model, adding all other variables in the previous analyses (see tables 2 and 3). Constraining the causal and stability parameters of the model to equal these values, the expanded model (table 6, model 4) generates a pattern of growth slightly higher than that generated when only robbery rates and percentage nonwhite are included in the model. Further assuming that other variables that affect both racial composition and violent-crime (robbery) rates are miss- ing from the expanded model, we reestimate it allowing the error terms for each decade to correlate. The generated pattern of growth in the cross-sectional correlations is exactly the same as above.19 While the final model closely reproduces the observed pattern of growth (table 6, cf. cols. 1 and 6), it still underestimates the observed degree of growth. In sum, what is important here is not that different model specifications and parameters yield slightly different patterns of growth, but that a reciprocal effect model operating over time with strong stability coeffi- cients implies a growth pattern of cross-sectional correlations over a wide range of model specifications and with relatively modest causal param- eters.

Now, what are the implications of these models for the relationship between racial composition and the robbery rate by the end of the century (the year 2000)? Starting with the 1990 cross-sectional correlation of .67, if the stability and causal parameters of the 1980-90 decade remain con-

'' Of course, the size of the standardized coefficients is smaller than those yielded by the change models, because the variance of both variables at any year is much larger than the variance of the change between years.

l9 Assuming that we may be overestimating the length of the causal lag, we also estimate two simultaneous models: one regresses percentage nonwhite and robbery rates on simultaneous levels of each other and on 10-year lag levels of themselves, and the other includes the above variables plus simultaneous levels of the other vari- ables that prove to be statistically significant in the change analysis (see tables 2 and 3). Identification is achieved by using lags of each dependent variable as instruments. The estimates of the causal parameters of these models are only slightly larger than those in the cross-lag models, and, while they generate slightly more growth in the cross-sectional correlation, the pattern of growth for both the cross-lag and simultane- ous models is exactly the same.

stant over the decade, the simple cross-lag model predicts a cross-sectional correlation of .76 by the year 2000. On the other hand, if, by some miracle, the causal coefficients reduce to zero, the stability effects of the model would still yield a cross-sectional correlation of .44 by that year and a correlation of .28 by the year 2010. Remember, these relatively modest causal effects have taken some 40 years to increase the cross- sectional correlation from .15 in 1950 to .67 in 1990; unless something drastic occurs, we have no reason to presume that the cross-sectional correlation will decrease any faster than it increased or that it will de- crease at all.

DISCUSSION

Numerous studies report that violent-crime rates and racial composition are strongly correlated at most levels of aggregation (neighborhood, city, SMSA, and state). Most of this work is cross-sectional and assumes a recursive causal model whereby the correlation is accounted for by the effect of racial composition on violent-crime rates. Debate centers on the proper sociological explanation. Interestingly, just about all of this work somehow ignores the possibility that violent-crime rates may influence the racial composition of social units through differential racial migration. Demographers have not conceptually organized the scattered work on crime rates and decisions to move, especially where to move, and crimi- nologists have ignored the social consequences of a volume of work on the fear of crime.

While there appears to be some empirical support for the hypothesis that crime rates affect some patterns of migration (in-migration more than out-migration and the migration of upper-income more than lower- income families), the literature on the effects of crime rates on migration is not consistent and the literature on the effects of crime rates on racial composition is close to nonexistent. To some extent, the inconsistency in the literature may reflect the following: different studies examine the effects of crime rates at different periods of time, yet the fear and threat associated with crime may well vary over these periods; most studies use relatively short causal lags, yet the causal process underlying the crime rate effect may operate over a relatively long period; and nearly all studies examine the effect of the general crime rate, yet research strongly suggests that fear of crime is most strongly linked to violence by strangers, most clearly expressed in the robbery rate.

Building on this past research, we examine the reciprocal effects of crime rates and racial composition on each other over a 40-year period, examine multiple causal lags, disaggregate violent-crime rates into mur- der, rape, assault, and robbery, and disaggregate change in the percent- age of nonwhites into change in the white and nonwhite populations. Further, we model the accumulative effect of small to modest reciprocal effects on the relationship between crime (robbery) rates and racial com- position over time.

In a preliminary analysis, we first examine the extent to which our data show the strong cross-sectional relationship between racial composi- tion and violent-crime rates, controlling for other variables, that is re- ported in the literature. The findings are consistent with the literature: net of other variables, racial composition and violent-crime rates show a strong cross-sectional relationship for each decade. Yet, if violent-crime rates and racial composition affect each other, as we hypothesize, then cross-sectional relationships provide biased estimates of causal effects. We address this issue via a panel design. Because of the controversy over the optimal method for studying change, we estimate change effects by three different methods.

Disaggregating violent-crime rates into the four specific rates, we first examine the relative effects of each on racial composition and the optimal time lag of the effect. Of the four violent crimes, robbery rates (violence by strangers) by far show the strongest effect on racial composition, and most of this effect occurs within a lag of 5-15 years. It is important to note that this finding is consistent with the fear-of-crime research, which shows that it is violence by strangers, not friends and relatives, that people fear. This form of violence is most clearly expressed in robbery rates. Thus, we should expect that the fear of crime would be highest in communities where the robbery rates are highest, which is reported in the literature (Liska et al. 1982), and we should expect that the social consequences of the fear of crime, such as increased out-migration and decreased in-migration, would also be highest in those communities.

Now, to what extent do these findings hold up when controls, such as economic deprivation, are entered in the analysis? First, while the cross-sectional analysis suggests that racial composition strongly affects violent-crime (including robbery) rates in each decade, the change analy- sis suggests that this effect is more modest. The effect of racial composi- tion on violent-crime rates is moderately evident in two decades (1950- 70) and strongly evident in only one decade (1980-90). The cross-sectional findings reflect the accumulative change of past decades, thus obscuring the causal effect in specific decades. On the other hand, while these other variables also affect racial composition, in no decade do they eliminate the robbery rate effect. It is statistically significant and moderately substantial in every decade. Hence, by failing to take into account the effects of robbery rates on racial composition, previous re- search may have overestimated the effect of racial composition on rob- bery rates and on general indexes of violence, which are heavily weighted by robbery rates.

To more closely approximate our hypothesis that robbery rates affect racial composition by affecting the change in the white population more than the change in the nonwhite population, we disaggregate change in percentage nonwhite into change in the white and nonwhite populations. The findings are supportive. While robbery rates show no predictable statistically significant effects or pattern of effects on change in the non- white population,20 robbery rates show both a general pattern of effects and statistically significant effects on change in the white population. The effects are negative in each decade (as robbery rates increase, the white population decreases) and are statistically significant in the last two decades. Furthermore, robbery rates in 1970 show a stronger effect than robbery rates in 1980 on the white population change from 1980 to 1990, suggesting that the time lag of the robbery rate effect may be increasing or that the causal process itself may be changing. Perhaps, once cities develop a reputation as violent, that reputation persists and influences social processes long after their violent-crime rates have de- creased or have been surpassed by other cities.

Our analysis also shows that the metric coefficients of robbery rates on change in racial composition (percentage nonwhite and the white pop- ulation) progressively decrease from 1950-60 to 1980-90. In other words, while the robbery rate increases over these decades, the effect of each robbery per unit of population decreases. This pattern of effects may reflect two processes. First, many people with the resources and freedom to leave the inner cities had already done so by the 1980-90 decade. Second, as the rate of violence increases those who remain may become less sensitive or more hardened to acts of violence; indeed, as the rate increases, it may take more and more to shock the public conscience (the so-called New York City effect).

Yet, while the shock of each violent crime may have decreased, the variation in violent-crime rates has substantially increased, yielding a stable standardized effect of robbery rates on changes in the percentage of nonwhites from 1950 to 1990 and even an increase in the standardized effect on change in the white population over these years.

Is it possible that we have overestimated the reciprocal effects of robbery rates and racial composition on changes in each other by not including some other variables? We should always be cautious about this issue, because there are always other variables that might be in-

'' The robbery rate does show a small statistically significant effect (b > 1.5 SE) in the 1980-90 decade but not in the predicted direction.

cluded. It should be remembered, however, that our purpose is not to increase the explained variance but to understand the relationship be- tween racial composition and violent-crime rates over time. Hence, our concern is not to focus on all other variables that might increase the explained variance in either racial composition or robbery rates, but to focus on those that affect both and thus may bias estimates of their reciprocal effects on each other. Our review of the literature suggests that economic conditions are the variables most likely to affect both. Thus, we examine three such conditions-median income, percentage unemployed, and percentage below poverty-as one economic factor as well as racial segregation and indicators of population and family struc- ture. Other research on either racial composition or violent crime may include still other variables, yet our review of the violent-crime literature suggests that whatever combination of other variables is included, the relationship between racial composition and violent-crime rates remains statistically significant.

Is it possible that we have misinterpreted the robbery rate effect? We argue that robbery rates affect racial composition through differential racial migration, that. is, through the migration of whites more than nonwhites because whites have more resources and experience fewer con- straints than nonwhites in implementing their fear of crime. We realize the racial composition can also reflect racial differences in fertility and mortality as well as migration, yet there is no theoretical reason to assume or empirical evidence to suggest that crime rates differentially affect the fertility or mortality rates of whites and nonwhites and certainly none to suggest that they differentially affect them enough to significantly alter the racial composition of a city. Moreover, research (e.g., Swicegood and Morgan 1994) shows that the majority of variance in racial composition reflects differential racial migration. Hence, it seems reasonable to as- sume that violent-crime rates affect racial composition mainly by differ- entially affecting the migration patterns of whites and nonwhites.

To what extent do our findings for cities hold for other levels of analysis, such as metro areas and states? We are not sure that we should expect such invariances. Many social processes emerge only at specific levels of analy- sis. Some processes that underlie the effect of crime rates on racial composi- tion may operate at neighborhood and city levels but not at the state level. High crime rates in some cities and neighborhoods may lead to a reputation as crime ridden, which may well affect migration patterns. We are not sure that this process operates for states. If it does not, then crime rates may play a role in the migration from city to city and from cities to suburbs but not from state to state. The only way to empirically isolate the effects by level of analysis is to collect and analyze data at multiple levels of analy- sis-a direction for future research.

Finally, it is important to understand the historical pattern of growth that has led to the strong contemporary link between racial composition and rates of violence among strangers (robbery rate). For our sample of about 100 cities the correlation between racial composition and robbery rates has progressively grown from .15 in 1950 to .67 in 1990. While this could have occurred for many complex reasons, our analysis suggests that such progressive growth is implied in relatively simple reciprocal effect models with high stability coefficients (which is the case in our data) and over a wide range of causal parameters, even modest ones. Given these circumstances, such a strong cross-sectional correlation takes nothing but time to accumulate; once accumulated, however, it takes a dramatic change in the causal process to undo.

In sum, it seems that the strong correlation between rates of violent crime by strangers (robbery rate) and racial composition reflects both the effect of robbery rates on racial composition and the effect of racial composition on these rates. While sociologists have certainly recognized and examined the former, they generally have been reluctant (with some notable exceptions) to examine the effects of crime rates on basic social processes. We are not trying to argue that violent-crime rates are the only cause of racial change. Far from it. Yet violent crime is an important social fact that cannot be ignored. By ignoring the effects of violent-crime rates on racial composition, researchers may have overestimated the ef- fect of racial composition on violent-crime rates. Even relatively small effects of violent-crime rates operating in feedback loops over long pe- riods of time can yield significant social consequences, affecting many aspects of the educational, racial, economic, and political structures of societies.

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