Extending the Baseline Specification to 2000

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Extending the sample to cover the period 1977-2000 provides an important

test of the robustness of the estimates for two reasons. First, the

number of observations from states with right-to-carry laws in effect more

than triples when the additional years are included. Second, 16 additional

states enacted right-to-carry laws during the period 1993-1999, thereby

providing additional data on the effects of these laws.

Another reason for the importance of the extended data is that aggregate

crime trends differ greatly between the periods 1977-1992 and 1993-

1997. The first period was one of rising crime, especially in large urban

areas, which tend to be in states that did not adopt right-to-carry laws

during 1977-1992. The period 1993-1997 was one of declining crime. Any

differences in estimation results between the 1977-1992 and 1977-1997

TABLE 6-5 Dummy Variable Model with Common Time Pattern, 2000

Data

Violent

Years Controlsa Crime Murder Rape

0. Committee

replication 1992b Yes –1.76 –9.01 –5.38

SE (1.07) (1.70)** (1.33)**

1. Comm estimate

w/ covariates 2000 Yes 4.12 –8.33 –0.16

SE (0.71)** (1.05)** (0.83)

2. Comm estimate

w/o covariates 1992b No –0.12 –1.22 1.39

SE (1.29) (2.65) (2.24)

3. Comm estimate

w/o covariates 2000 No 12.92 –1.95 17.91

SE (0.78)** (1.48) (1.39)**

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). The “no

Aggravated Property

Assault Robbery Crimes Auto Theft Burglary Larceny

–5.60 1.17 5.84 10.28 4.12 6.82

(1.25)** (1.45) (0.76)** (1.24)** (0.83)** (0.82)**

3.05 3.59 11.48 12.74 6.19 12.40

(0.80)** (0.90)** (0.52)** (0.78)** (0.57)** (0.55)**

–4.17 9.18 8.47 11.98 8.53 8.56

(1.54)** (2.17)** (0.79)** (1.48)** (0.94)** (0.93)**

12.34 19.99 21.24 23.33 19.06 22.58

(0.90)** (1.21)** (0.53)** (0.85)** (0.61)** (0.59)**

controls” specification includes county fixed effects, year dummies, and the dummy for

whether the state has a right-to-carry law.

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-tocarry

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

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-

TABLE 6-6 Trend Model with Common Time Pattern, 2000 Data

Violent

Years Controlsa Crime Murder Rape

0. Committee

replication 1992b Yes –2.15 –3.41 –3.37

SE (0.39)** (0.62)** (0.48)**

1. Comm estimate

w/ covariates 2000 Yes –0.95 –2.03 –2.81

SE (0.18)** (0.26)** (0.20)**

2. Comm estimate

w/o covariates 1992b No –1.41 –1.52 –3.45

SE (0.47)** (0.97) (0.82)**

3. Comm estimate

w/o covariates 2000 No –0.62 0.12 –2.17

SE (0.17)** (0.32) (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,

12In 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).

Aggravated Property

Assault Robbery Crimes Auto Theft Burglary Larceny

–2.63 –3.02 –1.13 0.25 –1.80 –0.84

(0.45)** (0.53)** (0.27)** (0.45) (0.30)** (0.30)**

–1.92 –2.58 –0.01 –0.49 –2.13 –0.73

(0.20)** (0.22)** (0.13) (0.19)* (0.14)** (0.13)**

–2.02 –0.44 –1.33 1.62 –2.50 –1.27

(0.57)** (0.79) (0.29)** (0.54)** (0.34)** (0.34)**

–0.65 –0.88 –0.81 0.57 –1.99 –0.71

(0.20)** (0.26)** (0.11)** (0.19)** (0.13)** (0.13)**

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.

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.

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

13That is, we subtract the year 0 coefficient from each year’s coefficient.

-20

-10

0

10

20

-10 -5 0 5 10

Years Relative to Law Passage

Peercentage Change

Violent Crime

-20

-10

0

10

20

-10 -5 0 5 10

Years Relative to Law Passage

Percentage Change

Property Crime

sensibly attribute the estimates from trend models in the literature to the

adoption of right-to-carry laws.