Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 120
Firearms and Violence: A Critical Review 6 Right-to-Carry Laws This chapter is concerned with the question of whether violent crime is reduced through the enactment of right-to-carry-laws, which allow individuals to carry concealed weapons.1 In all, 34 states have right-to-carry laws that allow qualified adults to carry concealed handguns. Proponents of these laws argue that criminals are deterred by the knowledge that potential victims may be carrying weapons and therefore that the laws reduce crime. However, it is not clear a priori that such deterrence occurs. Even if it does, there may be offsetting adverse consequences. For example, increased possession of firearms by potential victims may motivate more criminals to carry firearms and thereby increase the amount of violence that is associated with crime. Moreover, allowing individuals to carry concealed weapons may increase accidental injuries or deaths or increase shootings during arguments. Ultimately, it is an empirical question whether allowing individuals to carry concealed weapons generates net social benefits or net social costs. The statistical analysis of the effects of these laws was initiated by John Lott and David Mustard (1997) and expanded by Lott (2000) and Bronars and Lott (1998) (hereinafter referred to simply as Lott). Lott concludes that the adoption of right-to-carry laws substantially reduces the prevalence of violent crime. Many other researchers have carried out their own statistical analyses using Lott’s data, modified versions of Lott’s data, or expanded 1 The laws are sometimes called shall-issue laws because they require local authorities to issue a concealed-weapons permit to any qualified adult who requests one. A qualified adult is one who does not have a significant criminal record or history of mental illness. The definition of a nonqualified adult varies among states but includes adults with prior felony convictions, drug charges, or commitments to mental hospitals.
OCR for page 121
Firearms and Violence: A Critical Review data sets that cover the more recent time period not included in the original analysis.2 Because the right-to-carry issue is highly controversial, has received much public attention, and has generated a large volume of research, the committee has given it special attention in its deliberations. This chapter reviews the existing empirical evidence on the issue. We also report the results of our own analyses of the data. We conclude that, in light of (a) the sensitivity of the empirical results to seemingly minor changes in model specification, (b) a lack of robustness of the results to the inclusion of more recent years of data (during which there are many more law changes than in the earlier period), and (c) the imprecision of some results, it is impossible to draw strong conclusions from the existing literature on the causal impact of these laws. Committee member James Q. Wilson has written a dissent that applies to Chapter 6 only (Appendix A), and the committee has written a response (Appendix B). DESCRIPTION OF THE DATA AND METHODS Researchers studying the effects of right-to-carry laws have used many different models. However, all of the analyses rely on similar data and methodologies. Accordingly, we do not attempt to review and evaluate each of the models used in this literature. Instead, we describe the common data used and 2 Two other general responses to Lott’s analysis deserve brief mention. First, some critics have attempted to discredit Lott’s findings on grounds of the source of some of his funding (the Olin Foundation), the methods by which some of his results were disseminated (e.g., some critics have claimed, erroneously, that Lott and Mustard, 1997, was published in a student-edited journal that is not peer reviewed), and positions that he has taken on other public policy issues related to crime control. Much of this criticism is summarized and responded to in Chapter 7 of Lott (2000). The committee’s view is that these criticisms are not helpful for evaluating Lott’s data, methods, or conclusions. Lott provides his data and computer programs to all who request them, so it is possible to evaluate his methods and results directly. In the committee’s view, Lott’s funding sources, methods of disseminating his results, and opinions on other issues do not provide further information about the quality of his research on right-to-carry laws. A second group of critics have argued that Lott’s results lack credibility because they are inconsistent with various strongly held a priori beliefs or expectations. For example, Zimring and Hawkins (1997:59) argue that “large reductions in violence [due to right-to-carry laws] are quite unlikely because they would be out of proportion to the small scale of the change in carrying firearms that the legislation produced.” The committee agrees that it is important for statistical evidence to be consistent with established facts, but there are no such facts about whether right-to-carry laws can have effects of the magnitudes that Lott claims. The beliefs or expectations of Lott’s second group of critics are, at best, hypotheses whose truth or falsehood can only be determined empirically. Moreover, Lott (2000) has argued that there are ways to reconcile his results with the beliefs and expectations of the critics. This does not necessarily imply that Lott is correct and his critics are wrong. The correctness of Lott’s arguments is also an empirical question about which there is little evidence. Rather, it shows that little can be decided through argumentation over a priori beliefs and expectations.
OCR for page 122
Firearms and Violence: A Critical Review focus on the common methodological basis for all of them. In particular, we use the results presented in Tables 4.1 and 4.8 of Lott (2000) to illustrate the discussion. We refer to these as the “dummy variable” and “trend” model estimates, respectively. Arguably, these tables, which are reproduced in Table 6-1 and Table 6-2, contain the most important results in this literature. Data The basic data set used in the literature is a county-level panel on annual crime rates, along with the values of potentially relevant explanatory variables. Early studies estimated models on data for 1977-1992, while more recent studies (as well as our replication exercise below) use data up to 2000. Between 1977 and 1992, 10 states adopted right-to-carry laws.3 A total of 8 other states adopted right-to-carry laws before 1977. Between 1992 and 1999, 16 additional states adopted such laws. The data on crime rates were obtained from the FBI’s Uniform Crime Reports (UCR). Explanatory variables employed in studies include the arrest rate for the crime category in question, population density in the county, real per capita income variables, county population, and variables for the percent of population that is in each of many race-by-age-by-gender categories. The data on explanatory variables were obtained from a variety of sources (Lott, 2000: Appendix 3). Although most studies use county-level panels on crime rates and demographic variables, the actual data files used differ across studies in ways that sometimes affect the estimates. The data set used in the original Lott study has been lost, although Lott reconstructed a version of the data, which he made available to other researchers as well as the committee. This data set, which we term the “revised original data set,” covers the period 1977-1992.4 More recently, Lott has made available a data set covering the 3 There is some disagreement over when and whether particular states have adopted right-to-carry laws. Lott and Mustard, for example, classify North Dakota and South Dakota as having adopted such laws prior to 1977, but Vernick and Hepburn (2003) code these states as having adopted them in 1985. Likewise, Lott and Mustard classify Alabama and Connecticut as right-to-carry states adopting prior to 1977, yet Vernick codes these states as not having right-to-carry laws. See Ayres and Donohue (2003a:1300) for a summary of the coding conventions on the adoption dates of right-to-carry laws. 4 There are 3,054 counties observed over 16 years in the revised original data. In the basic specifications, there are a number of sample restrictions, the most notable of which is to drop all counties with no reported arrest rate (i.e., counties with no reported crime). This restricts the sample to approximately 1,650 counties per year (or approximately 26,000 county-year observations). In specifications that do not involve the arrest rate, Lott treats zero crime as 0.1 so as not to take the log of 0. Black and Nagin (1998) further restrict the sample to counties with populations of at least 100,000, which limits the sample to 393 counties per year. In some regressions, Duggan (2001) and Plassmann and Tideman (2001) estimate models that include data on the over 2,900 counties per year with nonmissing crime data.
OCR for page 123
Firearms and Violence: A Critical Review period 1977-2000 that corrects acknowledged errors in data files used by Plassmann and Whitley (2003). We term this file the “revised new data set.”5 We make use of both of these data sets in our replication exercises. Dummy Variable Model For expository purposes it is helpful to begin by discussing the dummy variable model without “control” variables.6 The model (in Lott, 2000: Table 4.1) allows each county to have its own crime level in each category. Moreover, the crime rate is allowed to vary over time in a pattern that is common across all counties in the United States. The effect of a right-to-carry law is measured as a change in the level of the crime rate in a jurisdic-tion following the jurisdiction’s adoption of the law. Any estimate of a policy effect requires an assumption about the “counterfactual,” in this case what would have happened to crime rates in the absence of the change in the law. The implicit assumption underlying this simple illustrative dummy variable model is that, in the absence of the change in the law, the crime rate in each county would, on average, have been the county mean plus a time-period adjustment reflecting the common trend in crime rates across all counties. Dummy variable models estimated in the literature are slightly more complicated than the above-described model. First, they typically include control variables that attempt to construct a more realistic counterfactual. For example, if crime rates vary over time with county economic condi-tions, then one can construct a more credible estimate of what would have happened in the absence of the law change by including the control vari-ables as a determinant of the crime rate. Most estimates in the literature use a large number of control variables, including local economic condi-tions, age-gender population composition, as well as arrest rates. Second, some estimates in the literature model the time pattern of crime differently. In particular, some studies allow each region of the country to have its own time pattern, thereby assuming that in the ab-sence of the law change, counties in nearby states would have the same time pattern of crime rates in a crime category. We term this the “region-interacted time pattern model,” in contrast to the “common time pattern” dummy variable model above. 5 These data were downloaded by the committee from www.johnlott.org on August 22, 2003. 6 This no-control model is often used as a way to assess whether there is an association between the outcome (crime) and the law change in the data. The committee estimates and evaluates this model below (see Tables 6-5 and 6-6, rows 2 and 3).
OCR for page 124
Firearms and Violence: A Critical Review Mathematically, the common time pattern dummy variable model takes the form where Yit is the natural logarithm of the number of crimes per 100,000 population in county i and year t, YEARt = 1 if the year is t and YEARt = 0 otherwise, Xit is a set of control variables that potentially influence crime rates, LAWit = 1 if a right-to-carry law was in effect in county i and year t and LAWit = 0 otherwise, γi is a constant that is specific to county i, and εit is an unobserved random variable. The quantities αt, βb, and δ are coefficients that are estimated by fitting the model to data. The coefficient δ measures the percentage change in crime rates due to the adoption of right-to-carry laws. For example, if δ = –0.05 then the implied estimate of the adoption of a right-to-carry law is to reduce the crime rate by 5 percent. The coefficients αt measure common time patterns across counties in crime rates that are distinct from the enactment of right-to-carry laws or other variables of the model. The vector Xit includes the control variables that may influence crime rates, such as indicators of income and poverty levels; the density, age distribution, and racial composition of a county’s population; arrest rates; and indicators of the size of the police force. The county fixed effect γi captures systematic differences across counties that are not accounted for by the other variables of the model and do not vary over time. The values of the parameters αt, β, and δ are estimated separately for each of several different types of crimes. Thus, the model accounts for the possibility that right-to-carry laws may affect different crimes differently. Trend Model While the dummy variable model measures the effect of the adoption of a right-to-carry law as a one-time shift in crime rates, one can alternatively estimate the effect as the change in time trends. The following trend model, which generated the results in Lott’s Table 4.8, allows right-to-carry laws to affect trends in crime: In this model, YRBEFit is a variable equal to 0 if year t is after the adoption of a right-to-carry law and the number of years until adoption if year t precedes adoption. YRAFTit is 0 if year t precedes adoption of a right-to-carry law and is the number of years since adoption of the law otherwise. The other variables are defined as in Model 6.1. The effect of adoption on the trend in crime is measured by δA – δB.
OCR for page 125
Firearms and Violence: A Critical Review The interpretation of the “trend” model is slightly complicated, since the model already includes year effects to accommodate the time pattern of crime common across all counties. To see what this model does, consider a more flexible model with a series of separate dummy variables, for each number of years prior to—and following—the law change for adopting states (see the figures illustrating the section later in the chapter called “Extending the Baseline Specification to 2000”). Thus, for example, a variable called shall_issue_minus_1 is 1 if the observation corresponds to a county in a state that adopts the law in the following year, 0 otherwise. Similarly, shall_issue_plus_5 is 1 if the observation corresponds to a county in a state that adopted five years ago, 0 otherwise. And so on. The coefficient on each of these variables shows how adopting states’ time patterns of crime rates move, relative to the national time pattern, surrounding the respective states’ law adoption. Note that the time pattern in question is not calendar time but rather time relative to local law adoption, which occurs in different calendar years in different places. The trend model in equation 6.2 constrains the adopting states’ deviations to fall on two trend lines, one for years before and one for years after adoption. Thus, the model restricts the yearly movements in the deviations to fall on trend lines with break points at the time of law adoption. STATISTICAL ANALYSES OF RIGHT-TO-CARRY LAWS In this section, we review the basic empirical findings on the effects of right-to-carry laws. We begin with a discussion of Lott’s original estimates of Models 6.1 and 6.2 and the committee’s efforts to replicate these findings. We then discuss results from other studies that estimate the effects of right-to-carry laws on crime. Lott’s Results Table 6-1 (first row) displays Lott’s estimates from Model 6.1. Lott finds that where they have been adopted, right-to-carry laws have reduced homicide by about 8 percent, rapes by about 5 percent, and aggravated assaults by about 7 percent (Lott, 2000:51). Lott also finds that adoption of right-to-carry laws may increase the rates of nonviolent property crimes (burglary, larceny, auto theft). In theory, this is possible, as criminals substitute away from crimes that involve contact with victims toward crimes that do not involve encounters with victims. Rows 2 and 3 of Table 6-1 report the results of the committee’s replication of these estimates. In row 2, we use the revised original data set and Lott’s computer programs. The committee was unable to replicate Lott’s estimate of the reduction in the murder rate, although the estimates are
OCR for page 126
Firearms and Violence: A Critical Review TABLE 6-1 Dummy Variable Model with Common Time Pattern, Original and Revised Dataa Sample Years Violent Crime Murder Rape 1. Lott (2000) Original 1992 1992 –4.9% –7.7% –5.3% 2. Committee replication SE Revised 1992b 1992 –4.91 (0.98)** –7.30 (1.57)** –5.27 (1.22)** 3. Committee replication SE Revised 2000c 1992 –1.76 (1.07) –9.01 (1.70)** –5.38 (1.33)** aThe regressions use the covariates and specification from the original Lott and Mustard (1997) models that do not control for state poverty, unemployment, death penalty execution rates, or regional time trends. The controls include the arrest rate for the crime category in question (AOVIOICP), population density in the county, real per capita income variables (RPCPI RPCUI RPCIM RPCRPO), county population (POPC), and variables for the percentage of the population that is in each of many race x age x gender categories (e.g., PBM1019 is the percentage of the population that is black, male, and between ages 10 and 19). The “no controls” specification” includes county fixed effects, year dummies, and the dummy for whether the state has a right-to-carry law. close and consistent with the conclusion that right-to-carry laws reduce the incidence of murder. Through communication with Lott, the committee learned that the data used to construct Table 4.1 of Lott (2000) were lost and that the data supplied to the committee are a reconstruction and not necessarily identical to the original data. Row 3 displays estimates using the revised new data set restricted to period 1977-1992. The estimates from these revised data are substantially different from those originally reported by Lott (2000). In the dummy variable model, the magnitude of the estimated reduction in the rates of violent crime and aggravated assault was reduced, the estimated reduction in the murder rate increased, and the sign of the estimated effects of right-to-carry laws on robbery reversed. Moreover, the effects of right-to-carry laws on violent crime are no longer statistically significantly different from zero at the 5 percent significance level. Finally, the estimated increase in the rates of all property crimes increased substantially. Table 6-2 presents estimates of the trend model. The first row displays Lott’s estimates. Lott finds the passage of right-to-carry laws to be associated with changes in the crime trend. He finds a 0.9 percent reduction in the annual rate of growth of violent crime overall, and a 0.6 percent reduction in the rate of growth of property crimes. Row 2 of Table 6-2 shows the committee’s attempt to replicate Lott’s results using the revised original data set. The committee was unable to replicate most of the results in Lott’s Table 4.8. Through communication with Lott, the committee learned that
OCR for page 127
Firearms and Violence: A Critical Review Aggravated Assault Robbery Property Crimes Auto Theft Burglary Larceny –7.0% –2.2% 2.7% 7.1% 0.05% 3.3% –7.01 (1.14)** –2.21 (1.33) 2.69 (0.72)** 7.14 (1.14)** 0.05 (0.76) 3.34 (0.89)** –5.60 (1.25)** 1.17 (1.45) 5.84 (0.76)** 10.28 (1.24)** 4.12 (0.83)** 6.82 (0.82)** bUsing Lott’s reconstruction of his original 1977-1992 data. cUsing the revised new data set, which contains observations, 1977-2000, even though the estimates in this row use data only through 1992. NOTE: All samples start in 1977. SE = standard error. Standard errors are in parentheses, where * = significant at 5% and ** = significant at 1%. this is because there are many misprints in Table 4.8. Nonetheless, Lott’s and the committee’s results have the same signs for all crimes except aggravated assault. Row 3 displays estimates using the revised new data set restricted to the period 1977-1992. These new results tend to show larger reductions in the violent crime trends than those found using the revised original data. Other Statistical Evaluations of Right-to-Carry Laws Researchers have estimated the effects of right-to-carry laws using Lott’s or related data and models. Many of these studies have found that the use of plausible alternative data, control variables, specifications, or methods of computing standard errors, weakens or reverses the results. Tables 6-3 and 6-4 display estimates from selected studies that illustrate variability in the findings about the effects of right-to-carry laws. The committee does not endorse particular findings or consider them to provide better estimates of the effects of right-to-carry laws than do Lott’s results. Moreover, the committee recognizes that several independent investigators have used alternative models or data to obtain results that are consistent with Lott’s. These investigators include Bartley and Cohen (1998) and Moody (2001). We focus on the conflicting results in this section because they illustrate a variability of the findings that is central to the committee’s evaluation of their credibility.
OCR for page 128
Firearms and Violence: A Critical Review TABLE 6-2 Trend Model with Common Time Pattern, 1977-1992a Sample Years Violent Crime Murder Rape 1. Lott (2000) Original 1992 1992 –0.9% –3.0% –1.4% 2. Committee replication SE Revised 1992b 1992 –0.50 (0.41) –4.25 (0.65)** –1.37 (0.51)** 3. Committee replication SE Revised 2000c 1992 –2.15 (0.39)** –3.41 (0.62)** –3.37 (0.48)** aThe regressions use the covariates and specification from the original Lott and Mustard (1997) models that do not control for state poverty, unemployment, death penalty execution rates, or regional time trends. The controls include the arrest rate for the crime category in question (AOVIOICP), population density in the county, real per capita income variables (RPCPI RPCUI RPCIM RPCRPO), county population (POPC), and variables for the percentage of the population that is in each of many race × age × gender categories (e.g., PBM1019 is the percentage of the population that is black, male, and between ages 10 and 19). Control Variables and Specification The most common modifications to Lott’s original analyses of right-to-carry laws has been to assess the sensitivity of the findings to variation in the control variables or the specification of the model. Lott’s basic model relies on dozens of controls, but concerns have been raised that some controls may be missing, others may be unnecessary, and still others may be endogenous (that is, related to the unobserved determinates of county crime rates). Duggan (2001), for example, raises concerns that county-level control variables may not be precisely measured on an annual basis and that the arrest rate control variable, which includes the crime rate in the denominator, may bias the estimates. In response to these concerns, Duggan estimated a simple dummy variable model that controls only for year and county fixed effects.7 Duggan drops all other covariates from the model. When estimated on all county-year observations with nonmissing crime 7 Duggan also changed the coding of the dates of adoption of right-to-carry laws, although this had only a minimal effect on the estimates. According to Duggan (2001) and others (see, for example, Ayres and Donohue, 2003a), there is an inconsistency in the coding used by Lott and Mustard. Duggan finds that in 8 of the 10 right-to-carry states, the adoption date is defined as the year the law was passed, but in 2 states, Florida and Georgia, the adoption date is set to the calendar year after the law was passed. Lott, in personal communications, maintains that the dates are coded correctly. The committee does not take a stand on which coding is correct.
OCR for page 129
Firearms and Violence: A Critical Review Aggravated Assault Robbery Property Crimes Auto Theft Burglary Larceny –0.5% –2.7% –0.6% –0.1% –0.3% –1.5% 0.46 (0.48) –2.72 (0.56)** –0.69 (0.30)* –0.31 (0.48) –1.58 (0.32)** –0.11 (0.37) –2.63 (0.45)** –3.02 (0.53)** –1.13 (0.27)** 0.25 (0.45) –1.80 (0.30)** –0.84 (0.30)** bUsing Lott’s reconstruction of his original 1977-1992 data. cUsing the revised new data set, which contains observations, 1977-2000, even though the estimates in this row use data only through 1992. NOTE: All samples start in 1977. SE = standard error. Standard errors are in parentheses, where * = significant at 5% and ** = significant at 1%. data, this reduced the magnitude of the estimated reduction in the rates of murder and aggravated assault, and it reversed the signs of the estimated effects of right-to-carry laws on rape, robbery, and all violent crime. That is, according to Duggan’s estimates, adoption of right-to-carry laws increases the frequencies of rape, robbery, and violent crime as a whole. Moreover, Duggan found there is no statistically significant effect of right-to-carry laws on violent crimes (at the 5 percent significance level). Other researchers have varied the specification of the model, allowing for the effects of right-to-carry laws to be more heterogeneous. Black and Nagin (1998), for example, estimated a dummy variable model in which the effects of right-to-carry laws are allowed to vary among states (that is, the coefficient δ is allowed to take different values for different states). Plassmann and Tideman (2001) estimate a nonlinear Poisson regression model with a restricted set of covariates, but otherwise similar to Model 6.1. Ayres and Donohue (2003a) combined Models 6.1 and 6.2, thereby obtaining a hybrid model in which adoption of right-to-carry laws can affect both the level and the trend of crime. The results from these analyses, which vary the way in which right-to-carry laws can effect crime, are highly variable, with some suggesting that the laws increase crime, others suggesting that they decrease crime, and many being statistically insignificant. In Black and Nagin (1998), for example, only Florida has a statistically significant decrease in the murder rate following adoption of a right-to-carry law, and only West Virginia has a statistically significant increase in
OCR for page 130
Firearms and Violence: A Critical Review TABLE 6-3 Summary of Selected Studies: Dummy Variable Model (percentage) (shaded cells indicate a positive coefficient) Source Modification Violent Crime Murder Rape Lott (2000) Original specification and data –5* –8* –5* Moody Unweighted –6* –4* –5* State-level analysis –11 15 –22* Duggana County and time effects only –1 –6 3 All counties 0 –1 6 Black and Nagin Large counties –9* –4 Exclude Florida –1 1 Florida –27.7* –17* Georgia –5.2 –5 Idaho –21 –10 Maine 7.2 4 Mississippi 5.4 32* Montana –36.7 –97* Oregon –5.9 4 Pennsylvania –8.9 4 Virginia 3.9 –8 West Virginia 72* –29* Plassmann and Tideman No control for arrest rate –7* –6* All counties –2 –5 Count model (Poisson) –11* –4* Florida –24* –16* Georgia –8* –16* Idaho –6 10* Maine 1 –2 Mississippi 5 11* Montana –7 –4 Oregon –10* –2 Pennsylvania –5 14* Virginia 8* –3 West Virginia 5 –1 Ayres and Donohue (2003a) State trends 0 –9* –2 1977-1997 data 2 0 3 State level analysis State and time effects only –3 –8 –1 1977-1999 data 9* –2 6* Plassmann and Whitleya,b Regional trend + others 1977-2000 data –3 –6* –7* Ayres and Donohue (2003b)a,b Regional trends + other controls 1977-2000 corrected data 0 –4 –5
OCR for page 141
Firearms and Violence: A Critical Review Aggravated Assault Robbery Property Crimes Auto Theft Burglary Larceny –5.60 (1.25)** 1.17 (1.45) 5.84 (0.76)** 10.28 (1.24)** 4.12 (0.83)** 6.82 (0.82)** 3.05 (0.80)** 3.59 (0.90)** 11.48 (0.52)** 12.74 (0.78)** 6.19 (0.57)** 12.40 (0.55)** –4.17 (1.54)** 9.18 (2.17)** 8.47 (0.79)** 11.98 (1.48)** 8.53 (0.94)** 8.56 (0.93)** 12.34 (0.90)** 19.99 (1.21)** 21.24 (0.53)** 23.33 (0.85)** 19.06 (0.61)** 22.58 (0.59)** bUsing the revised new data set, which contains observations, 1977-2000, even though the estimates in this row use data only through 1992. NOTE: All samples start in 1977. SE = standard error. Standard errors are in parentheses, where * = significant at 5% and ** = significant at 1%. data constitute evidence of model misspecification (e.g., because the model cannot account for the change in the aggregate crime trend) and raise the possibility (although do not prove) that the estimated effects of right-to-carry laws are artifacts of specification errors. This is a particularly important concern because states that pass right-to-carry laws are not representative of the nation as a whole on important dimensions (e.g., percentage rural) that are correlated with rising crime in the 1977-1992 period and falling crime in the years 1993-2000. The first row of Table 6-5 reports the results of extending the dummy variable model (6.1) to the new data covering the period 1977-2000. The specifications estimated are identical to the original model, with the only difference being that the number of years has been expanded. Compared with the model estimated on the original (1977-1992) sample period (see Table 6-5, Row 0), the results have now changed rather substantially. Only the coefficient on murder is negative and significant, while seven coefficients are positive and significant (violent crime overall, aggravated assault, robbery, property crime overall, auto theft, burglary, and larceny). The dummy variable results that were apparent with the earlier data set and
OCR for page 142
Firearms and Violence: A Critical Review TABLE 6-6 Trend Model with Common Time Pattern, 2000 Data Years Controlsa Violent Crime Murder Rape 0. Committee replication SE 1992b Yes –2.15 (0.39)** –3.41 (0.62)** –3.37 (0.48)** 1. Comm estimate w/ covariates SE 2000 Yes –0.95 (0.18)** –2.03 (0.26)** –2.81 (0.20)** 2. Comm estimate w/o covariates SE 1992b No –1.41 (0.47)** –1.52 (0.97) –3.45 (0.82)** 3. Comm estimate w/o covariates SE 2000 No –0.62 (0.17)** 0.12 (0.32) –2.17 (0.30)** aThe regressions use the covariates and specification from the original Lott and Mustard (1997) models that do not control for state poverty, unemployment, death penalty execution rates, or regional time trends. The controls include the arrest rate for the crime category in question (AOVIOICP), population density in the county, real per capita income variables (RPCPI RPCUI RPCIM RPCRPO), county population (POPC), and variables for the percentage of the population that is in each of many race x age x gender categories (e.g., PBM1019 is the percentage of the population that is black, male, and between ages 10 and 19). The “no controls” specification includes county fixed effects, year dummies, and th dummy for whether the state has a right-to-carry law. earlier sample periods almost completely disappear with the extension of the sample to 2000. The committee views the failure of the original dummy variable model to generate robust predictions outside the original sample as important evidence of fragility of the model’s findings.12 These results are also substantially different from those found when using the expanded set of control variables first adopted by Lott (2000: Table 9.1). As described above, Ayres and Donohue (2003b) estimate a dummy variable model using the revised new data (see Table 6-3). As in Lott (2000, Table 9.1) and Plassmann and Whitley (2003), they modify the original specification to include additional covariates (i.e., state poverty, unemployment, and death penalty execution rates) and region-interacted time patterns, as opposed to a common time trend used in the original Lott models (Lott 2000:170). These seemingly minor adjustments cause sub- 12 In light of the variability in the estimates, statistical tests might aid in determining whether particular specifications can be rejected by the data. It is not possible to test empirically whether a proposed set of explanatory variables is the correct one. It is possible to test for specification, given a set of controls (see Horowitz, Appendix D). None of the models examined by the committee passes a simple specification test (i.e., Ramsey’s 1969 RESET test).
OCR for page 143
Firearms and Violence: A Critical Review Aggravated Assault Robbery Property Crimes Auto Theft Burglary Larceny –2.63 (0.45)** –3.02 (0.53)** –1.13 (0.27)** 0.25 (0.45) –1.80 (0.30)** –0.84 (0.30)** –1.92 (0.20)** –2.58 (0.22)** –0.01 (0.13) –0.49 (0.19)* –2.13 (0.14)** –0.73 (0.13)** –2.02 (0.57)** –0.44 (0.79) –1.33 (0.29)** 1.62 (0.54)** –2.50 (0.34)** –1.27 (0.34)** –0.65 (0.20)** –0.88 (0.26)** –0.81 (0.11)** 0.57 (0.19)** –1.99 (0.13)** –0.71 (0.13)** bUsing the revised new data set, which contains observations, 1977-2000, even though the estimates in this row use data only through 1992. NOTE: All samples start in 1977. SE = standard error. Standard errors are in parentheses, where * = significant at 5% and ** = significant at 1%. stantial changes to the results. For example, right-to-carry laws are estimated to decrease murder by about 4 percent using the revised specification, but about 8 percent using the original specification. The estimated effects for the eight other crime categories decrease between 2 and 6 points when moving from the original to the revised specification. We also estimate the trend model extending the sample to 2000 (row 1, Table 6-6). Relative to the estimates in row 0 (using only data to 1992), the estimates are mostly smaller but remain negative and statistically significant. Thus, the trend specification continues to show reductions in the rate of growth of crime following right-to-carry passage. To explore why the updated dummy variable and trend models give conflicting results, we do two things. First, we estimate a more flexible year-by-year specification, a variant of Model 6.1, the dummy variable model. Second, we reanalyze the trend model (Model 6.2) by varying the number of years after the law’s adoption to estimate its effects on crime. In each of these cases, we use the revised new Lott data through 2000 and we include the original controls used by Lott and Mustard (1997). In each of these cases, except for sampling variability, the changes should not affect the results if the trend model in equation 6.2 is properly specified.
OCR for page 144
Firearms and Violence: A Critical Review In the first exercise, we replace the right-to-carry dummy with a series of dummies for each of the possible numbers of years prior to—and following—adoption. We summarize the estimated coefficients in three figures. These figures show the estimated coefficients normalized on the year of adoption and multiplied by 100 (so the y-axis is a percentage), and the associated 95 percentage confidence intervals.13 The vertical line marks the adoption year, while the horizontal line marks 0. Figure 6-2 shows the time pattern of coefficients from the violent crime model. For years preceding adoption, violent crime is increasing in ultimately adopting states (relative to the national time pattern). Following adoption, the increase relative to trend continues, reverses, then reverses twice again. For property crimes, in Figure 6-2, the upward trend for years prior to adoption continues following adoption. Figure 6-3 and Figure 6-4 show graphs for individual violent and property crime categories, respectively. The obvious striking feature of these figures is that the big reductions in crime occur roughly 9 years after adoption. Otherwise, the postadoption estimates are generally small and sometimes positive and are, in general, both statistically insignificant and statistically indistinguishable from the preadoption estimates. The trend model essentially fits a line with constant slope through the postadoption portions of these graphs, and the line’s slope is affected by years long after adoption. These time patterns raise serious questions about whether the reductions in crime documented in the trend model are reasonably attributed to the change in the law. In the second exercise, to further explore the sensitivity of the trend model estimates, we reestimate the baseline trend model (Model 6.2) using revised new Lott data on the period 1977-2000. Table 6-7, row 1, repeats the estimates from Table 6-6, row 1 which includes all years for all states, regardless of the amount of time elapsed since the law change. Subsequent rows include observations that occur certain numbers of years after the law change. (Row 2, labeled “6 years,” includes the year of the law change and the 5 following years, and so on.) These estimates show that including 5 years or fewer reverses the signs of the estimated effects of right-to-carry laws on murder and property crime (from negative to positive) and reduces the magnitude of the estimated reduction in the rates of rape, aggravated assault, robbery, and violent crime. Moreover, there are fewer statistically significant changes in crime trends. One needs to include at least 6 years following the prelaw-change period to find statistically significant reductions in the violent crime and murder trends. The trend results rely on changes in crime trends occurring long after the law changes, again raising serious questions about whether one can 13 That is, we subtract the year 0 coefficient from each year’s coefficient.
OCR for page 145
Firearms and Violence: A Critical Review FIGURE 6-2 Year-by-year estimates of the percentage change in aggregate crime (normalized to adoption date of right-to-carry law, year 0). ——Estimate,——o——bottom of 95% confidence interval (CI),—|—Top of 95% CI sensibly attribute the estimates from trend models in the literature to the adoption of right-to-carry laws. Are the Results Sensitive to Controls? The final two rows of Table 6-5 present two sets of results obtained by the committee when estimating models identical to those of Model 6.1, but excluding socioeconomic and demographic controls. We include only the
OCR for page 146
Firearms and Violence: A Critical Review FIGURE 6-3 Year-by-year estimates of the percentage change in disaggregate violent crimes (normalized to adoption date of right-to-carry law, year 0). ——Estimate,——o——bottom of 95% confidence interval (CI),—|—Top of 95% CI right-to-carry variable, year dummies, and county fixed effects. These estimates tell us how crime has changed in states that have adopted the right-to-carry laws before and after the law change, relative to national time patterns in crime. It is important to stress that the committee is not arguing that excluding all socioeconomic and demographic covariates is an appropriate method of identifying the effects of right-to-carry laws. Rather, we are simply assessing whether such laws are associated with a decline in the level of crime. If not, then detecting the effect, if any, of right-to-carry laws
OCR for page 147
Firearms and Violence: A Critical Review requires controlling for appropriate confounding variables and thereby reliance on a model such as those used by Lott and others. The results without controls are quite different. Using the earlier sample period and the new data, one finds three negative coefficients, only one of them statistically significant. When the sample is extended to 2000, only one of nine coefficients is negative, and it is insignificantly different from zero. For example, the violent crime coefficient with controls is 4.1 percent, while it is 12.9 percent without controls. These results show that states that
OCR for page 148
Firearms and Violence: A Critical Review FIGURE 6-4 Year-by-year estimates of the percentage change in disaggregate property crimes (normalized to adoption date of right-to-carry law, year 0). ——Estimate,——o——bottom of 95% confidence interval (CI),—|—Top of 95% CI
OCR for page 149
Firearms and Violence: A Critical Review passed right-to-carry laws did not on average experience statistically significant crime declines relative to states that did not pass such laws. There are two points to make about the no-controls results. First, the no-controls results provide a characterization of the data that shows that, if there is any effect, it is not obvious in the dummy variable model. What do estimates from that model mean? The model says that crime rates differ across counties and, moreover, that they change from one year to the next in the same proportionate way across all counties in the United States. Over and above this variation, there is a one-time change in the mean level of crime as states adopt right-to-carry laws. So these estimates indicate that, for the period 1977-1992, states adopting right-to-carry laws saw roughly no change in their violent crime rates and 8.5 percent increases in their property crime rates, relative to national time patterns. Estimating the model using data to 2000 shows that states adopting right-to-carry laws saw 12.9 percent increases in violent crime—and 21.2 percent increases in property crime—relative to national time patterns. The first-blush evidence provided by these no-controls models is thus not supportive of the theory that right-to-carry laws reduce crime. A final lesson to draw from the no-controls dummy variable results is that the results are sensitive to the inclusion of controls. That is, whether one concludes that right-to-carry laws increase or decrease crime based on models of this sort depends on which control variables are included. Such laws have no obvious effect in the model without controls (and therefore no clear level effect in the raw data). Moreover, as demonstrated above, seemingly minor changes to the set of control variables substantially alter the estimated effects. Given that researchers might reasonably argue about which controls belong in the model and that the results are sensitive to the set of covariates, the committee is not sanguine about the prospects for measuring the effect of right-to-carry laws on crime. Note that this is distinct from whether such laws affect crime. Rather, in our view, any effect they have on crime is not likely to be detected in a convincing and robust fashion. Estimates from the trend model are less sensitive to the inclusion of controls. While the no-control point estimates displayed in the third and fourth rows of Table 6-6 are smaller than in the model with controls, most of these estimates are negative and statistically significant. The trend model without controls shows reductions in violent and property crime trends following the passage of right-to-carry laws for both sample endpoints. For murder, however, the results are positive when using the 2000 endpoint, negative when using the 1992 endpoint, and statistically insignificant in both cases.
OCR for page 150
Firearms and Violence: A Critical Review TABLE 6-7 Trend Model with Varying Postlaw Change Durations Years Controlsa Violent Crime Murder Rape 1. Baseline comm estimateb from row 1 of Table 6-6 SE 2000 Yes –0.95 (0.18)** –2.03 (0.26)** –2.81 (0.20)** 2. 6 years SE 2000 Yes –0.97 (0.29)** –1.11 (0.42)** –2.90 (0.33)** 3. 5 years SE 2000 Yes –0.65 (0.35) 0.05 (0.50) –2.45 (0.40)** 4. 4 years SE 2000 Yes –0.27 (0.44) 0.48 (0.63) –0.74 (0.50) aThe regressions use the covariates and specification from the original Lott and Mustard (1997) models that do not control for state poverty, unemployment, death penalty execution rates, or regional time trends. The controls include the arrest rate for the crime category in question (AOVIOICP), population density in the county, real per capita income variables (RPCPI RPCUI RPCIM RPCRPO), county population (POPC), and variables for the percentage of the population that is in each of many race × age × gender categories (e.g., PBM1019 is the percentage of the population that is black, male, and between ages 10 and 19). CONCLUSIONS The literature on right-to-carry laws summarized in this chapter has obtained conflicting estimates of their effects on crime. Estimation results have proven to be very sensitive to the precise specification used and time period examined. The initial model specification, when extended to new data, does not show evidence that passage of right-to-carry laws reduces crime. The estimated effects are highly sensitive to seemingly minor changes in the model specification and control variables. No link between right-to-carry laws and changes in crime is apparent in the raw data, even in the initial sample; it is only once numerous covariates are included that the negative results in the early data emerge. While the trend models show a reduction in the crime growth rate following the adoption of right-to-carry laws, these trend reductions occur long after law adoption, casting serious doubt on the proposition that the trend models estimated in the literature reflect effects of the law change. Finally, some of the point estimates are imprecise. Thus, the committee concludes that with the current evidence it is not possible to determine that there is a causal link between the passage of right-to-carry laws and crime rates.
OCR for page 151
Firearms and Violence: A Critical Review Aggravated Assault Robbery Property Crimes Auto Theft Burglary Larceny –1.92 (0.20)** –2.58 (0.22)** –0.01 (0.13) –0.49 (0.19)* –2.13 (0.14)** –0.73 (0.13)** –1.06 (0.32)** –1.88 (0.36)** 0.11 (0.21) 1.40 (0.31)** –1.13 (0.23)** 0.33 (0.22) –0.83 (0.39)* –1.63 (0.43)** 0.28 (0.25) 1.83 (0.37)** –0.77 (0.27)** 0.36 (0.26) –0.34 (0.49) –1.36 (0.55)* 0.44 (0.32) 2.03 (0.47)** –0.47 (0.35) 0.31 (0.33) bUsing the revised new data set, for the full available time period (1977-2000). NOTES: All samples start in 1977. All estimates use the trend model. Rows 2 through 4 of this table restrict the sample to include only years falling fixed numbers of years past the law change. For example, row 2 includes all the prelaw-change years, the year of the law change (year 0), plus 5 additional years, for a total of 6 years after the prelaw-change period. SE = standard error. Standard errors are in parentheses, where * = significant at 5% and ** = significant at 1%. It is also the committee’s view that additional analysis along the lines of the current literature is unlikely to yield results that will persuasively demonstrate a causal link between right-to-carry laws and crime rates (unless substantial numbers of states were to adopt or repeal right-to-carry laws), because of the sensitivity of the results to model specification. Furthermore, the usefulness of future crime data for studying the effects of right-to-carry laws will decrease as the time elapsed since enactment of the laws increases. If further headway is to be made on this question, new analytical approaches and data sets will need to be used. For example, studies that more carefully analyze changes in actual gun-carrying behavior at the county or even the local level in response to these laws may have greater power in identifying the impact of such laws. Surveys of criminals or quantitative measures of criminal behavior might also shed light on the extent to which crime is affected by such laws.
Representative terms from entire chapter: