Trend Model
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
102 103 104 105 106 107 108 109 110 111 112 113 114 115
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:
(6.2)
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-tocarry
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 dA – dB.
Y YEAR X LAW it t t
t
it it i it
= + + + +
=
Σα β δ γ ε
1977
1992
Y YEAR X YRBEF YRA it t t
t
it B it A
= + + +
=
Σα β δ δ
1977
1992
FTit i it
+γ +ε
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.