A Matched Pairs Analysis of State Growth Differences*
Brian Goff
Alex Lebedinsky
Stephen Lile
Department of Economics/Ford College of Business
Western Kentucky University
Bowling Green, KY 42101
Contact: brian.goff@wku.edu
*The authors thank Bob Tollison, Dennis Wilson, and participants on the panel at the Academy of
Economics and Finance Meetings for useful comments and suggestions.
Abstract
The American states have provided a rich laboratory in which to examine influences on economic
growth, including convergence, physical capital, human capital, and a variety of policy variables.
Existing studies have typically used broad cross-sections of all states or particular regional subsamples. Pairwise matching has been used in many observational studies to better control for
omitted variables. We estimate a growth model for U.S. states for 1997-2005 before and after
applying different pairwise matching techniques. Our results indicate that a sample based on
pairwise matching substantially improves the overall explanatory capability of the model and
provides much more support for particular hypotheses, such as convergence and the growthenhancing effects of lower individual income-tax rates.
I. Introduction
The American states have been and continue to be a useful laboratory for testing influences
on economic growth, including convergence, physical capital, human capital, and a variety of
policy variables. Routinely, all 50 states or regional subsets of them are grouped together and
regression analysis is performed to estimate parameters of the models. Implicitly, this practice
generates coefficients by comparing states with widely divergent populations such as California
and Wyoming, widely divergent incomes such as Connecticut and Mississippi, widely divergent
historical and cultural backgrounds such as Pennsylvania and Utah, and with other extreme
differences. Although these regressions take into account a variety of "control" variables, they
omit or use proxy measures of important, long-run differences between the states. Regional subsamples or regional dummy variables are used as a means to "soak up" some of the variability due
to these omitted factors.
In this paper, we offer an alternative methodology to estimate state growth models by using
matched pairs based on common geographical characteristics. The intuition behind matching is
straightforward. Matching of birth twins, for example, can eliminate or reduce genetic differences
as a source of variation so that other factors can be isolated and estimated with greater accuracy.
Although matching can be used, and may be most frequently considered, as a pre-treatment
experimental design method, it has also been developed as a post-treatment method.1 Although the
method is not a panacea to cure all observational study problems, under certain conditions, the
post-treatment matching imitates the results of randomizing treatments among observations.
Statistical investigators in a variety of disciplines -- including economics, finance,
statistics, psychology, and biomedicine -- have made use of post-treatment matched pairs to
improve estimates. In economics, the methods have been used where the observational units have
ranged from individual employees or borrowers to financial institutions, and the subjects studied
have ranged from bank problems, to risk, wage rates, and firm size.2 Although the theoretical links
have not been worked out, creating sub-samples of data based on common socio-demographic
characteristics is a closely related method that has been shown to improve estimates. For example,
Barro and Sala-i-Martin (1991) show that while the Solow growth model's prediction of
convergence in growth rates does not hold for a large sample of countries, it does hold for a
reduced sample containing only OECD countries. The practice of reducing samples based on
Chow tests rejecting coefficient equality is closely related to ex post matching methods because
the objective, as in pairwise matching, is to better align the sample to the underlying process
generating outcomes.
In spite of the growing use of matching methods in statistical studies in economics, their
use at a state level of analysis has largely been limited to time series studies of a particular pair of
states or small groupings of states.3 The U.S. states provide an attractive basis for matching.
State-based, pairwise matches compare observational units generated, at least in part, by similar
underlying processes, doing so on the front end of the estimation process using similar
characteristics of the data rather than on the back end of the estimation process (as with a Chowtype sample partitioning method). State matching pairs states that share important similarities
and, therefore, can implicitly eliminate differences that are difficult to measure. In particular, we
pair states by location, and these pairs also capture historical, political, climatic, topographic, and
transportation similarities. Many states share similar geographic and historical backgrounds and
traits. For example, Kentucky and Tennessee or Arizona and New Mexico provide specific
examples of states that are near "twins" when viewed from a long-run historical, political, and
geographic perspective. Kentucky and Tennessee are not only contiguous, and therefore share
similar continental locations, but also share a 350-mile border, are within 95 percent of the same
land area, and are both landlocked. In terms of historical similarities, they entered the Union
within four years of each other (Kentucky in 1792 and Tennessee in 1796). Arizona and New
Mexico, as another example, entered the Union one month apart, are about 94 percent of the same
land area, are landlocked, share similar topography, and share a 300-plus mile border.
In the next section, we discuss our specific matching methodology and the model of
economic growth that we employ. Section III provides estimates of the growth model, comparing
results using a typical cross-section of all 50 states for 1997-2005 with pairwise matched samples.
Section IV offers concluding remarks.
II. State Matching Theory and Methods
Matching has been used most frequently to compare means (or another simple
distributional parameter) where the matching is intended to take into account all (or as many as
possible) of the influences on the dependent variable other than the variable of primary interest. In
these studies, a simple t-test of mean differences is sufficient to estimate the effect of that (binary)
variable of interest. To a lesser extent, matching has also been employed in conjunction with
regression modeling as a method to control for some or most of the non-treatment differences.4
The regression model extends this effort to control for other effects that the matching may have
missed. It is this matching-regression combination that we employ. Our purpose is to use
matching to eliminate many of the differences in natural endowments, as well as long-run
historical and cultural differences, between states, and then estimate a regression for a basic
empirical growth model.
The potential advantages of matching can be illustrated by starting with a cross-sectional
equation for growth (Y) of state i that is a function of an observed variable Xi and an omitted
variable Zi as shown below:
(1)
Yi = β0 + β 1Xi + β 2Zi + ui .
When this equation is estimated using only data on Yi and Xi, the expected value of b1, the OLS
estimator of β 1, is
(2)
E[b1] = β 1 + β 2[Cov(Xi, Zi)/Var(Xi)].
The second term on the right hand is the bias that results from omitting Zi: Whenever Xi and Zi are
correlated, b1 will be biased. With pairwise matching between states i and j, the underlying model
changes to
(3)
Yi - Yj = β 1(Xi - Xj) + β 2(Zi - Zj) + (ui - uj).
The bias for β 1 from omitting (Zi - Zj) is
(4)
E[b1] = β 1 + β 2(Cov[(Xi - Xj),(Zi - Zj)])/Var(Xi - Xj)) .
The benefit of matching states with similar unobserved characteristics is quickly apparent. If these
unobserved characteristics between states i and j are equal, then
Zi - Zj = 0, Cov[(Xi - Xj),(Zi - Zj)] = 0, and E[b1] = β 1. Of course, if the matching does not equate
Zi and Zj, then bias will be present. However, the bias in the matched sample will be less than the
bias in the unmatched cross-section as long as
(5)
Cov[(Xi - Xj),(Zi - Zj)]/Var[Xi - Xj] < Cov[Xi, Zi]/Var[Xi].
Simply put, if correlations between the omitted growth equation variables and the included
variables are lower in the matched pair sample of states, then matching will produce lower bias.
By comparing cross-section and matched pairs estimates, we will be able to see if crosssection estimates are affected by omitted variable bias: If Zi is not correlated with Xi, both methods
should produce similar estimates of β1. On the other hand, a big difference in estimates obtained
using these two methods would indicate that cross-section estimates are biased.
Two common matching methods exist. The first method matches directly on covariate
values. The second method matches on equivalence or similarity of likelihood of a treatment
conditioned on the covariate values. This method, known as "propensity scoring,” has the
advantage of using information across a wide variety of covariates but condensing this multidimensional information into a scalar on which to base matches. Comparisons of matching based
on covariate values versus propensity matching has not yielded results indicating that one method
dominates the other in terms of reducing bias of estimated parameters in all situations.5
Most important to our purposes, the statistical and econometric literature on propensity
matching has concentrated primarily on pairing observations based on a binary, treatment/notreatment variable. The method has been extended to multi-valued discrete treatment variables,
but not to continuous variables. Our interest does not lie in matching based on whether a single,
binary policy variable has been adopted. Instead, we seek to estimate a model of state economic
growth that takes into account not only continuous policy variables as well as binary ones, but also
non-policy growth model variables.
Our method is similar to covariate matching. Instead of using a large set of covariates on
which to match, we rely heavily on location as a variable that condenses many dimensions of a
state into a single observation. In particular, location tends to incorporate information about date
of statehood, migration history, ethnic and religious backgrounds and migration, climate,
topography, neighboring states, and so on. Our matching approach looks for other states that share
a common geographic relationship rather than matching based on current values for a set of
variables or current likelihood of adoption of a particular policy. We compute different match pair
samples for the 48 contiguous states based on the following criteria:
Criterion 1-- All Contiguous Pairs;
Criterion 2 -- All Contiguous Pairs + within the interquartile range for the ratio of land area
OR
All Contiguous States + within interquartile range for the ratio of population.
Table 1 displays the pairwise matched samples based on the matching procedures discussed
above. The sample includes the 48 contiguous states with 102 unique paired observations. The
most frequently matched states are Missouri, with eight matches, followed by Kentucky and
Tennessee, with seven. Five states have six matches. All states, with the exception of Maine, have
at least two matches. Limiting the sample to the interquartile ranges for the land area and
population ratios reduces the total pairs of observations to 51 and 52. The land area-restricted
sample includes 37 different states, while the population-based restricted sample includes 41
states. The sample of common states appearing in both the land and population interquartile range
includes 28 pairs.
III. State Growth Model and Regression Estimates
Growth theory looks to capital, both human and physical, as the primary source of
economic growth. While measures of tangible capital exist, capital in a broader sense may include
a variety of natural geographical features, such as climate, ports, or arable land. The measurement
of human capital typically requires the use of some kind of proxy variable, such as educational
attainment levels of the population. Standard theoretical growth models, such as the Solow Model,
predict convergence of growth rates. Given the comparatively free movement of labor and capital
across state boundaries, one would expect greater convergence among U.S. states than among
nations.6 However, the existing evidence on convergence of state growth rates is mixed. Not only
has convergence been incomplete, but also Bauer, Schweitzer and Shane (2006) provide evidence
that it has stalled since the mid-1970s.7
Public policies that alter incentives to utilize labor and capital are potential influences on
growth. High taxes, unless associated with improved infrastructure that makes for higher
productivity, can be expected to discourage work and possibly saving and investment. Laws
governing the employer-employee relationship, such as policies that encourage collective
bargaining, are likely to increase wages and, unless associated with higher labor productivity, can
be expected to increase production costs and decrease expected profit and business investment.
Empirical studies of the effects of taxes have produced mixed results. An early study
(Helms, 1985) found that higher taxes reduce growth when used to finance transfer payments but
do not reduce growth when used to finance infrastructure. Another study from this time period
(Genetski and Ludlow, 1982), using 1970-1977 data, found that states that decreased their tax
burdens relative to the national average tended to experience above-average growth. States that
increased their tax burden, relative to the national average, tended to suffer below-average
economic growth. In a time series study of a single matched pair (New Hampshire and Vermont),
Campbell (1994) observed greater economic vitality in New Hampshire and attributed the higher
growth rate to lower taxes. Drawing from analogies to portfolio theory, Crain (2003) finds that tax
rates are much more important determinants of state growth than convergence. In contrast, Bauer,
Schweitzer, and Shane (2006) included a measure of “knowledge stock” and found that tax burden
is statistically insignificant.
Our base regression model estimates changes in Gross State Product (GSP) across the 48
contiguous states as a function of a set of standard growth-model variables, including the initial
level of income, physical capital, human capital, and state public policy variables. The model is
(6)
GSPPCi = a0 + a1GSPPCi0 + a2PhysicalPCi + a3Coastline Per Sq. Mi.i +
a4PCT Collegei + akPolicy Variableik +ui;
where
GSPPCti = percent change in GSP per capital from 1997 to 2005 for state i;
GSPPCi0 = level of GSP per capital in 1997 for state i;
Physical PCi = tangible physical capital per capita for state i8;
Coastline Per Sq. Mi.i = miles of coastline per square mile of land area for state i;
Policy Variablesi = vector of k state policy variables for state i;
Labor Lawti = 1 if state i has a right to work law and 0 if not;
Tax Burdenti = total tax burden as percent of per capita income for state i;
Income Taxti = individual income tax as percent of GSP for state i;
Corp Taxti = corporate tax as percent of GSP for state i;
Reg Indexti = index of regulatory burden for state i.
Individual states’ economic growth rates varied markedly in recent years. From 1997 to –
2005, growth in nominal gross state product ranged from a low of 26 percent in Michigan to a high
of more than 85 percent in Nevada. State economic growth, when measured by nonfarm
employment, varied from a low of 3 percent in Michigan to a high of 56 percent in Nevada.
Descriptive statistics for all variables are provided in an Appendix.
Multicollinearity is strong between some of the policy variables. Specifically, Tax Burden
is highly correlated with Income Tax, with a correlation coefficient absolute magnitude above
0.60. Therefore, in the results presented below, Labor Law and Tax Burden are used together
while Income Tax, Corp Tax, and Reg Index are used in separate equations.
Table 2 presents the results of estimating this growth model using the cross-section of the
48 contiguous states without any pairing. These results imitate the common practice in cross-state
estimation and provide a benchmark for comparison with the matched pair results below. The two
sets of results, using different policy variables, explain 36 percent and 31 percent of the cross-state
variation in GSP per capita. Among the specific non-policy variables, the amount of coastline and
PCT College are significant at or below the 5-percent level in the first column. Physical capital
per capita is significant below the 10-percent level. In the second column, coastline and Income
Tax are significant at below the 1-percent level, and PCT College is significant just below the 10percent level. One important result is that there is no indication of convergence of growth rates
based upon the initial level of GSP.
Among the policy variables in the two equations, Labor Law is significant at below the 1percent level with a positive coefficient, indicating that state incomes grew at higher rates where
right-to-work laws existed. Total tax burdens are not significant, but Income Tax in the second
equation is below the 1-percent level. Higher tax rates across the states were associated with lower
rates of growth.
For the matched pair samples, the estimated growth model is
(7)
GSPPCij = b0 + b1GSPPCij0 + b2PhysicalPCij + b3Coastline Per Sq. Mi.ij +
b4PCT Collegeij + bkPolicy Variableijk + wij ,
where all of the variables represent differences between matched state i and state j. Equation (5)
describes the condition necessary for this matching equation to produce lower omitted variable
bias than the cross-sectional sample.
There is no way to directly test whether the condition in (5) holds for the matched samples
for variables that are omitted because they are unobserved or unmeasurable. Table 3 presents
illustrative evidence for the potential gains from matching for three variables not included in our
growth equation. We refer to this as "illustrative" evidence because these variables are, in fact,
measured and could be included in the estimates. They provide indirect evidence for the ability of
matched pair samples to include information from a variety of variables and control for the
correlation between these variables and the included variables. In Table 3 we estimate correlations
between the policy variables from the growth equation and these three variables: percent of
Democratic vote in the 2000 presidential election, year of statehood, and percent of farm acres.
While many variables might be used for this illustration, we used these three because they measure
different characteristics of a state.
The correlations coefficients in Table 3 show that the matched pair samples do reduce the
correlation between these three variables and the policy variables from the growth equation. Nine
of the twelve correlation coefficients between these three variables and the policy variables are not
only significant at the 5-percent level, but also have absolute magnitudes above 0.30. For each
matched pair sample, no more than two coefficients of each set of twelve exceed 0.30 in
magnitude or are statistically significant. Again, this is not proof that the condition described in
equation (5) holds but does illustrate that it may be very likely.
Table 4 and 5 present OLS estimates based on four matched pair samples. The first column
presents data for all contiguous states matched. The second column reduces this sample to include
only contiguous states that are in the interquartile range of land area ratios, the third column
reduces the sample down to only contiguous states in the interquartile range of population ratios,
and the fourth column includes only states in the interquartile ranges for both land and population.
The differences with the unmatched, cross-sectional results are stark. In particular, the
overall explanatory value of these matched pair regressions ranges from 61 percent to 72 percent,
roughly double the explanatory capability of the 48-state unmatched, cross-sectional results. The
specific coefficient estimates are also considerably different in these matched pair samples from
the 48-state cross section. Among the coefficients, differences in the initial level of GSP per capita
between the pairs are negative and significant below the 1-percent level in all eight samples,
lending strong support to the convergence hypothesis, unlike the 48-state cross-sectional samples.
Differences in levels of tangible physical capital between pairs show positive coefficients
significant below the 5-percent level in all eight regressions. Again, in the earlier results, physical
capital was not significant below this level. Human capital, as measured by differences between
states in the percent of college graduates, is positive and significant at the 5-percent level for the
all-contiguous sample but not for the reduced samples. A big difference between the 48-state
cross-sectional results and the pairwise estimates appears in the case of the extent of coastline. It
was nowhere near significant levels in the earlier results, but in the pairwise samples, the
coefficients are all positive and significant below the 1-percent level.
The pairwise estimates also exhibit large differences for the policy variable coefficients. In
particular, Tax Burden, which was not significant in the earlier results, is now negative and
significant below the 5-percent level in all four samples in which it is estimated. The results for
Labor Law are mixed. Its coefficient is positive in all four samples but significant in only the land
IQR and the most-restricted sample. The impact of income-tax and corporate tax rates is relatively
consistent, whether using the 48-state cross-section or the pairwise estimates. In these later results,
individual income tax coefficients are negative and significant at the 5-percent level or below in
every sample. Corporate income-tax rate coefficients are not significant in any of the samples.
The regulatory index is not significant in any of the samples, either.
Another feature of the matched pair estimates is the robustness of several of the
coefficients across the samples. The coefficient on difference in the initial GSP level ranges
narrowly between -1.74 and 1.97 in all eight sets of results. The physical capital coefficients range
between 0.28 and 0.40. The other significant variables -- coastline, tax burden, and income tax
rates -- exhibit similar consistency. The one variable with wider variability in coefficient values is
Labor Law. The correlation coefficients presented in Table 3 suggest that there may unresolved
omitted variable issues influencing its value.
IV. Concluding Remarks
While important for providing more accurate estimates of influences such as physical
capital on growth or regarding the convergence hypothesis, the matching methodology presented
here helps to refine our understanding of the effects of policy on growth. A persistent problem of
policy analysis with data is the likelihood of omitted variables influencing estimates. This problem
is accentuated in long-run growth studies where many variables not included in the models are
changing. Rather than trying to supplant typical regression estimates, the matching method
provides an explicit way of reducing this omitted-variables problem and augmenting the use of
regression for policy analysis.
Taken as a unit, our results provide strong support for the idea that lower tax burdens tend
to lead to higher levels of economic growth. Among tax variables, individual income taxes matter
most. While the evidence on labor law is mixed, there is some evidence that right-to-work laws
promote growth also. In this regard, the coefficient values for the fourth columns in Tables 4 and
5, where the sample is reduced to the IQR for both land and population among contiguous states,
are of special interest. In terms of the matching exercise, this restrictive sample comes the closest
to producing a comparison of "twin" states, such as Kentucky and Tennessee and New Hampshire
and Vermont. Policy analysis based on these states would indicate that higher tax burdens and, in
particular, higher individual income-tax rates, along with right-to-work laws, promote higher
growth -- even when controlling for a broad array of other influences whether through the
matching procedure or through the other growth model variables included in the regressions.
Interestingly, although individual tax rates and work laws appear to matter, corporate tax
rates and regulatory differences do not in our estimates. This may indicate that such policies are
not linked to growth or, alternatively, that businesses are accomplished at finding effective ways of
reducing the burden of these policies.
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Table 1. State Matched Pair Samples
All Contiguous
Matches
AL: FL, GA, MS, TN
AR: LA, MO, MS, OK, TN, TX
AZ: CA, NM, NV, UT
CA: NV, OR
CO: KS, NE, NM, UT, WY
CT: MA, NY, RI
DE: MD, NJ
FL: GA
GA: NC, SC, TN
IA: IL, MN, MO, NE, SD, WI
ID: MT, NV, OR, UT, WA, WY
IL: IN, KY, MO, WI
IN: KY, MI, OH
KS: MO, NE
KY: MO, OH, TN, VA, WV
LA: MS, TX
MA: NH, NY, RI, VT
MD: PA, VA, WV
ME: NH
MI: OH, WI
MN: ND, SD, WI
MO: NE, OK, TN
MS: TN
MT: ND, SD, WY
NC: SC, TN, VA
ND: SD
NE: SD, WY
NH: VT
NJ: NY, PA
NM: OK, TX
NV: OR
NV: UT
NY: PA, VT
OH: PA, WV
OK: TX
OR: WA
PA: WV
SD: WY
TN: VA
UT: WY
VA: WV
n = 102
Contiguous Plus
Land Area IQR
Contiguous Plus
Pop Ratio IQR
AL: FL, GA, MS, TN
AR: MS, OK, TN
AZ: NM, NV
AL: MS, TN
AR: LA, MS, OK
CO: KS, NM, UT, WY
CO: KS, UT
CT: MA
FL: GA
GA: NC
IA: IL, MO, WI
ID: OR, UT, WA, WY
IL: MO, WI
IN: KY, OH
KS: MO, NE, OK
KY: OH, TN, VA
LA: MS
MA: NH, VT
FL: GA
GA: NC, SC, TN
IA: MN, NE
ID: MT, NV, UT
IL: IN, MO, WI
IN: KY, MI
KS: NE, OK
KY: MO, TN, VA, WV
LA: MS
MI: WI
MN: ND, SD
MO: NE, OK
MS: TN
MD: VA
ME: NH
MI: OH, WI
MN: WI
MO: OK, TN
NC: TN, VA
ND: SD
NE: SD
NH: VT
MT: ND, SD, WY
NC: SC, TN, VA
ND: SD
NE: SD
NH: VT
NJ: PA
NV: OR, UT
NV: OR, UT
NY: PA
OH: PA
NY: PA
OH: PA
OR: WA
SD: WY
TN: VA
TN: VA
UT: WY
n = 51
n = 52
Table 2. Percent Growth in GSP 1997-2005, Cross-Sectional Data
Variable
GSP97(i-j)
Physical Capital(i-j)
Coastline(i-j)
PCT College(i-j)
Tax Burden(i-j)
Labor Law(i-j)
Coefficient
(p-value)
-8.5e-7
(0.91)a
0.13
(0.07)
0.002
(0.47)
(0.71)
(0.05)
-1.43
(0.36)
11.19
(<0.01)
30.28
(0.14)
0.36
-0.79
(0.01)
-2.05
(0.23)
-0.32
(0.68)
42.18
(0.02)
0.31
3.92
(<0.01)
48
2.65
(0.02)
48
Income Tax(i-j)
Corporate Tax(i-j)
Regulation Index(i-j)
Intercept
R2
F
N
2.47e-6
(0.80)
0.12
(0.10)
0.001
(0.63)
0.67
(0.09)
Table 3. Correlation Coefficients for Policy Variables and Three
Examples of Omitted Variables
Policy Variable
Sample
Labor Law
Tax
Burden
Income
Tax
Corp Tax
Reg Index
48 State
Cross Section
-0.66*
0.27
0.25
0.30*
0.02
-0.18
0.36*
-0.36*
-0.32*
0.33*
-0.33*
-0.36*
0.30
-0.17
-0.02
Matched Pairs
All Contiguous
-0.51*
0.14
-0.17
-0.03
0.14
-0.15
0.05
-0.18
-0.14
-0.09
0.06
-0.08
0.17
0.14
-0.03
Matched Pairs
IQR Land
-0.60
0.45*
0.15
-0.09
0.17
-0.07
0.09
-0.14
-0.15
-0.21
0.11
-0.05
0.22
-0.11
0.17
Matched Pairs
IQR Pop
-0.33
0.05
-0.44*
-0.18
0.16
-0.05
-0.18
-0.06
0.21
-0.12
-0.08
-0.02
-0.07
-0.23
0.02
Matched Pairs
IQR Land, Pop
-0.32
0.27
-0.18
-0.22
0.05
-0.03
0.01
-0.09
0.14
-0.27
0.09
0.10
-0.11
-0.07
0.15
* Indicates significance at 0.05 level.
The cells report correlation coefficients between the policy variable and Percent Democratic
Presidential Vote in the state in 2000, Year of Statehood, and Percent Farm Acres. For the 48 state
cross section, all variables are in levels. For the matched pair samples, all variables are in
difference between state i and state j.
Table 4. Percent Growth in GSP 1997-2005, Matched Pair Data
Matching Basis
Initial GSP(i-j)
Physical Capital(ij)
Coastline(i-j)
PCT College(i-j)
Tax Burden(i-j)
Labor Law(i-j)
Intercept
R2
F
N
a
All
Contiguous
-1.90
(<0.01)a
0.40
(<0.01)
0.005
(<0.01)
0.57
(<0.01)
-1.78
(<0.01)
2.00
(0.12)
-0.06
(0.93)
0.67
Cont +
IQR Land
Area Ratio
-1.74
(<0.01)
0.38
(<0.01)
0.006
(<0.01)
0.40
(0.12)
-1.81
(0.02)
4.04
(0.04)
-0.76
(0.41)
0.72
Cont +
IQR
Pop Ratio
-1.97
(<0.01)
0.37
(<0.01)
0.007
(<0.01)
0.38
(0.15)
-2.27
(<0.01)
2.43
(0.23)
0.23
(0.82)
0.61
Cont +
IQR Land and
Pop Ratio
-1.76
(0.02)
0.28
(0.04)
0.009
(<0.01)
0.43
(0.28)
-2.29
(0.04)
6.35
(0.04)
1.03
(0.50)
0.65
32.5
(<0.01)
102
19.2
(<0.01)
51
11.7
(<0.01)
52
6.8
(<0.01)
28
Values in parentheses are p-values.
Table 5. Percent Growth in GSP, Matched Pair Data with Alternative Policy Variables
Matching Basis
GSP97(i-j)
Physical
Capital(i-j)
Coastline(i-j)
PCT College(i-j)
Income Tax(i-j)
Corporate Tax(ij)
Regulation
Index(i-j)
Intercept
R2
F
N
a
All
Contiguous
Contiguous +
IQR Pop Ratio
-1.87
(<0.01)a
0.40
(<0.01)
0.004
(<0.01)
0.72
(<0.01)
-0.29
(<0.01)
-0.66
(0.26)
-0.004
(0.98)
0.45
(0.56)
0.65
Contiguous +
IQR Land Area
Ratio
-1.90
(<0.01)
0.40
(<0.01)
0.005
(<0.01)
0.56
(0.08)
-0.37
(<0.01)
-0.22
(0.81)
-0.11
(0.75)
-0.46
(0.61)
0.71
-1.84
(<0.01)
0.35
(<0.01)
0.005
(<0.01)
0.53
(0.09)
-0.29
(0.04)
-0.69
(0.48)
0.09
(0.72)
-0.19
(0.86)
0.65
Cont +
IQR Land and
Pop Ratio
-1.85
(0.02)
0.32
(0.03)
0.008
(<0.01)
0.45
(0.30)
-0.49
(0.01)
-0.74
(0.61)
-0.26
(0.27)
0.20
(0.91)
0.64
25.3
(<0.01)
102
15.0
(<0.01)
51
7.66
(<0.01)
52
5.18
(<0.01)
28
Values in parentheses are p-values.
1
Among econometricians Heckman and associated coauthors have been at the leading edge of this literature. See, for
example, Heckman, Ichimura, and Todd (1997, 1998). In the statistical literature Rosenbaum and coauthors have led
the way. See Rosenbaum (1989) and Rosenbaum and Rubin (1983, 1985a, 1985b).
2
Some of these studies include Heckman, Ichimura, and Todd (1997), Bharath (2002), Yeager (2004), Pozzolo (2002),
and Kimball (1997).
3
On a limited scale, matching has been used to compare states. For example, Campbell (1994) compares New
Hampshire's tax policies and outcomes with that of three neighboring states.
4
Rosenbaum and Rubin (1985a) is one example of matching coupled with regression analysis.
5
Heckman, Ichimura, and Todd (1998).
6
Caselli and Coleman (2001) develop this point.
7
Crain (2003, Chapter 2) provides a broad-based review of convergence results that calls into question its overall
importance in explaining state growth differences. Barro and Sala-i-Martin (1992) consider convergence using crosscountry evidence with similar results as their state study.
8
This measure of tangible physical capital is computed by taking estimates of capital to income ratios from Garofalo
and Yamarik(2002). The ratio is then converted to capital per capita by multiplying by state income and dividing by
population.