in smoking as the treatment state before the intervention. In selecting controls, we look at the 24 months before the conception of pregnancies that were at some stage when the
tax was enacted. For Michigan, the tax hike occurred in May 1994, so we look at women who conceived between September 1991 and August 1993 to pick controls.
Our procedure to choose controls is as follows. Each treatment state has a unique set of potential controls that had no nominal change in state cigarette excise tax levels
during the 56-month window.
6
Potential controls for each state are listed in Table 2. From this set, we ran regressions including data from only the treatment state and one
potential control for the 24-month pretreatment period. The model for each treatment state is of the form:
+ D
S X
2
ism ism
s m
s ism
2
= +
+ +
b n
y m
m
This equation is similar to Equation 1 above. In these regressions, we add the same set of covariates listed for Equation 1 and u and v are state and month of conception effects
respectively. Since data from after the tax-hike treatment period is excluded, the equa- tion does not include the DPART TAX or DFULL TAX terms. The key terms in this
regression are the coefficients on
λ
m
, which allow the monthly dummy variables to dif- fer between the state with a tax hike and a potential control. If we cannot reject the
hypothesis that λ
1
= λ
2
= . . . . λ
23
= 0, then conditional on differences in the level of use and X, the treatment state and the potential control have statistically the same
monthly pattern in maternal smoking and we include this state as a control. The states in bold in Table 2 are those where we cannot reject the null the
λ’s are jointly zero.
IV. Results
A. The Impact of Large Tax Hikes on Smoking
Before we present the results for Equation 1, we first graphically illustrate the impact of the tax hike on smoking rates. For each state experiment, we calculate monthly mean
smoking rates for the treatment and control states and graph the difference over the 56-month samples. For the 24 pretreatment months, the eight transition months, and 24
post-treatment months we also provide a smoothed linear time trend that best fits the dif- ference. The results for Arizona, Illinois, Massachusetts, and Michigan are presented in
Figures 1A–1D, respectively. First, note that for each state, there is little time trend in the pretreatment differences in smoking rates, which we would expect given our statis-
tical procedure to pick control groups. Second, in all states except Illinois, there is a noticeable drop in smoking rates in the 24 post-treatment months. In Arizona and
Michigan, these differences drop somewhat over time and in Massachusetts, there is lit- tle change over the initial drop in smoking. In contrast, the temporary drop in smoking
experienced in Illinois during the transition period is eliminated by a slow steady increase in smoking in the post-treatment period. These figures suggest we should find
little impact of the tax change in Illinois but noticeable changes for the other states.
Table 3 shows the treatment effects of the partial-tax and full-tax effects in the four states we consider and the results line up closely with the simple graphical analysis in
6. Indiana and South Dakota were excluded as potential controls due to a lack of maternal smoking infor- mation in the birth certificate data.
Lien and Evans 379
The Journal of Human Resources 380
Table 2 All Potential Control States, with Control States Matched on Smoking in Bold
Arizona Illinois
Massachusetts Massachusetts without Worcester
Michigan Alabama
Alabama Alabama
Alabama Alabama
Alaska Alaska
Alaska Alaska
Alaska Colorado
Colorado Colorado
Colorado Colorado
Delaware Delaware
Florida Florida
Florida Georgia
Georgia Georgia
Georgia Georgia
Iowa Iowa
Kansas Kansas
Kansas Kansas
Kansas Kentucky
Kentucky Kentucky
Kentucky Kentucky
Louisiana Louisiana
Louisiana Maine
Mississippi
Mississippi Mississippi
Mississippi Mississippi
Nevada Nevada
Nevada Nevada
Nevada New Hampshire
New Hampshire New Hampshire
New Hampshire New Hampshire
New Jersey New Jersey
New Jersey
North Carolina North Carolina
Oklahoma Oklahoma
Oklahoma Pennsylvania
Pennsylvania South Carolina
South Carolina South Carolina
South Carolina South Carolina
Tennessee Tennessee
Tennessee Tennessee
Tennessee
Texas Texas
Texas
Utah Utah
Virginia Virginia
Virginia Virginia
Virginia West Virginia
West Virginia West Virginia
West Virginia West Virginia
Wyoming Wyoming
Wyoming Wyoming
Wyoming
States in bold are those that had statistically matched monthly smoking effects with the specified treatment state prior to the excise tax hike.
Lien and Evans 381
Figure 1. We use as controls those states chosen systematically by the procedure out- lined for Equation 2.
7
For each regression, we present three sets of standard errors. The first set is simply the OLS standard errors. In our case, the intervention is at the state level but the unit
of observation is the individual so there is concern that errors within a stateyear-cell may be correlated, reducing the effective number of observations. This problem is
typically referred to as a “design effect” in the theoretical literature on random assign- ment trials and the problem arises when treatment randomization is done at the group
rather than at the individual level. A standard solution for this problem is to use a pro- cedure similar to that in Huber 1967 that allows for arbitrary correlation in errors for
7. For each state, the results are similar regardless of whether we use the matched set of control states or the broader control group; therefore, we focus on the results from the matched model.
-0.060 −0.050
−0.040 −0.030
−0.020 −0.010
1 5
9 13
17 21
25 29
33 37
41 45
49 53
M onth D
iffe re
n ce
i n
s m
o k
in g
ra te
s
−0.035 −0.030
−0.025 −0.020
−0.015 −0.010
1 5
9 13
17 21
25 29
33 37
41 45
49 53
M onth D
iffe re
n ce
i n
s m
o k
in g
ra te
s
Figure 1A Differences in Smoking Rates, Arizona—Controls
Figure 1B Differences in Smoking Rates, Illinois—Controls
a stateyear cluster. We have adopted this convention and standard errors generated by this procedure are reported in square brackets.
Bertrand, Duflo, and Mullainathan 2004 demonstrate a high Type I error rate in difference-in-difference models such as the one we outline above and attribute this to
autocorrelation. They recommend implementing the Huber-type procedure allowing for arbitrary correlation in errors at the state level, which we adopt here and report in
curly brackets. We should caution however that these Huber-type procedures are only consistent when the number of groups tends to infinity Wooldridge 2003 and in our
case, we have at most 11 states and as few as six.
Although state tax hikes reduced smoking among pregnant women in all four states, the results are quite varied. Both the partial and full tax effects decreased smok-
ing in Illinois, Massachusetts and Michigan. In all states the full tax hike produced a larger reduction in smoking than the partial tax effect. The largest partial and full tax
The Journal of Human Resources 382
−0.080 −0.060
−0.040 −0.020
0.000 0.020
0.040 0.060
1 5
9 13
17 21
25 29
33 37
41 45
49 53
M onth D
iffe re
n ce
i n
s m
o k
in g
ra te
s
−0.050 −0.040
−0.030 −0.020
−0.010
1 5
9 13
17 21
25 29
33 37
41 45
49 53
M onth D
iffe re
n ce
i n
s m
o k
in g
ra te
s
Figure 1C Differences in Smoking Rates, Massachusetts—Controls
Figure 1D Differences in Smoking Rates, Michigan—Controls
Lien and Ev
ans 383
Table 3 First-stage Estimates and Implied Price Elasticity of Smoking Participation State Cigarette Excise Taxes’ Impact on Maternal Smoking
Arizona Illinois
Massachusetts Massachusetts wo Worcester
Michigan OLS Estimates
Partial tax hike 0.0029
−0.0015 −0.0649
−0.0349 −0.010
0.0019 0.0013
0.0023 0.0024
0.00195 [0.0016]
[0.0011] [0.0023]
[0.0022] [0.0021]
{0.0022} {0.0013}
{0.0017} {0.0017}
{0.0028} Full tax hike
−0.0092 −0.0011
−0.0699 −0.0379
−0.0114 0.0013
0.0009 0.0017
0.0017 0.0014
[0.0022] [0.0010]
[0.0018] [0.00195]
[0.0014] {0.0029}
{0.0018} {0.0039}
{0.0039} {0.0010}
Full tax hike −0.34
−0.10 −3.24
−1.83 −0.22
Implied price 0.048
0.090 0.08
0.08 0.026
Elasticity of participation Probit Marginal Effects
Partial tax hike 0.001
−0.002 −0.0672
−0.043 −0.0120
0.002 0.001
0.002 0.002
0.002 Full tax hike
−0.013 −0.002
−0.072 −0.047
−0.014 0.001
0.001 0.002
0.002 0.001
Full tax hike −0.46
−0.17 −3.33
−2.25 −0.26
Implied price 0.046
0.10 0.07
0.08 0.028
Elasticity of participation
Standard errors are in parenthesis. Standard errors in brackets curly brackets are heteroskedastic-consistent that allow for arbitrary correlations across observations within a state-month state group. For each sample, the control states used are listed in Table 2. All models include covariates for age, education, race, and ethnicity of mother, sex
of child, parity of birth, plurality of birth, Kessner index of prenatal care adequacy, month of conception fixed effects, and state fixed effects.
impact was in Massachusetts where the full tax hike resulted in a statistically signifi- cant 7 percentage point drop in smoking among pregnant women. The next largest
drop in maternal smoking was in Arizona and Michigan, where there was a statisti- cally significant 1 percentage point drop in smoking. Illinois, the state with the small-
est tax hike, had a statistically insignificant 0.1 percentage point drop in maternal smoking. For Arizona, Massachusetts, and Michigan we find little difference in the
standard errors when we adjust for correlation within the statemonth groupings or when errors are clustered solely by state.
In the bottom half of Table 3, we report results where we reestimate the basic mod- els using a probit instead of a linear probability specification. The marginal effects
from the probit model, which represents the change in the probability of smoking given exposure to either the partial or full tax hike, are similar to the linear probabil-
ity estimates.
Some have suggested that the impact of the tax hike may grow over time in that more addicted smokers may take longer to quit in response to the tax hike. The graphs
in Figure 1 illustrate that the only state with a pronounced time series pattern in the treatment effect is Arizona. Breaking the final 24 months of the data into half-year
intervals, the treatment effect in Arizona for these four periods is −0.0064, −0.0045,
−0.0115, and −0.0143, respectively. The standard error in each of these cases is 0.0029 and we can reject the null hypothesis that all these coefficients are the same.
In the other three states, we could not reject the null hypothesis that the treatment effect was the same over these four six-month periods.
The results for Massachusetts are of note. First, the drop in smoking is an astound- ing 7 percentage points, roughly 30 percent of the pre-reform smoking rate. This is
an incredibly large drop in smoking for only a 25-cent increase in taxes. We looked at the data for Massachusetts in detail and noticed some abnormalities with the smok-
ing data in Worcester County. Of births in December 1992, 54 percent of Worcester County women giving birth reported smoking during pregnancy, as opposed to
31 percent in February 1993. It would seem something concerning the vital statistics in Worcester County changed over this period and caused the drastic drop in smok-
ing.
8
For this reason, Worcester County is excluded from further analysis. When Worcester County is excluded from the Massachusetts sample, the decrease in smok-
ing from the full tax-hike effect is a 4 percentage point drop.
B. The Implied Price Elasticity of Smoking Participation