﻿

# Trend Model

К оглавлению

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.