Discontinuity of output convergence within the United States: why has the course changed?
Choi, Chi-Young ; Wang, Xiaojun
I. INTRODUCTION
The standard neoclassical growth theory predicts that economies
with similar technologies and preferences should ultimately converge
toward the same standard of living. This convergence prediction is
particularly relevant for subnational economies, such as the states in
the United States, which share nearly identical institutional
environments with a high mobility of technology and production factors.
In fact, ever since the seminal work by Barro (1991) on output
convergence among the U.S. states, a large number of researchers have
documented that the standard of living of residents of the U.S. states
has converged over time (e.g., Barro and Sala-i-Martin 2004; Mitchener
and McLean 1999, 2003). This prevailing view in the literature, however,
has been called into question by more recent studies which claim that
the process of output convergence in the United States stalled in the
1970s (e.g., Bauer, Schweitzer, and Shane 2006; Ganong and Shoag 2012).
(1)
[FIGURE 1 OMITTED]
Inspired by this, we plot in Figure 1 two conventional measures of
output convergence for the log output per worker of the 48 continental
U.S. states since 1929. (2) Our inspection of the top-left panel of
Figure 1 suggests that there has been a convergence in output among the
U.S. states over much of the twentieth century as widely documented in
the literature. The output dispersion across states, measured by the
coefficient of variation (CV), continuously declined until the
mid-1970s. Output convergence, however, does not appear to be a feature
throughout the rest of the period because the dispersion has hitherto
increased gradually. A similar picture is painted in the top-right panel
of Figure 1 which plots the estimated speed of [beta]-convergence in the
spirit of Barro and Sala-i-Martin (1992). (3) The rolling 25-year
estimate of [beta] drops drastically from positive values to near zero
in the late-1970s, indicating that cross-state output evolution switched
from convergence to divergence. This can be viewed from a slightly
different angle in the bottom panels of Figure 1, which present two
scatterplots of the logged values of initial output level (horizontal
axis) against the average annual growth rates (vertical axis) for each
state before and after 1977. A clear inverse association is noted in the
bottom-left panel between the average growth rate between 1929 and 1976
and the log output per worker in 1929, indicating strong evidence of
[beta]-convergence. As shown in the bottom-right panel, however, there
is no evidence of convergence after 1977 when the negative relationship
disappeared completely, in line with our earlier observation. As a
further piece of evidence, Figure 2 displays dynamics of cross-state
output dispersion densities along the lines of Quah (1996). The left
panel of Figure 2 tracks the evolution of the density distributions
since 1963. Notice that the distribution appears to have undergone a
notable shift from nearly unimodality to multimodality around the 1970s,
thereafter the distribution collates into several clubs or subgroups.
This change in output distribution is also reflected in its contour
pattern exhibited in the right panel of Figure 2, where the single
distribution mass has clearly split into a multitude during the latter
sample period. Combined together, our visual inspection of Figures 1 and
2 convincingly suggests that the process of output convergence in the
United States stopped in the 1970s and hence output convergence may no
longer be a viable hypothesis for the U.S. states in the ensuing period.
[FIGURE 2 OMITTED]
It is natural to wonder, then, what happened to the development of
output convergence in the United States after the 1970s and what factors
are behind it. The primary objective of this study is to shed light on
these questions by making several improvements over the previous
literature. To begin, this study focuses on the past five decades when
the output convergence process stalled in the United States, in lieu of
the century-long period that has been popularly studied in the previous
literature. The reason for this is twofold. First, while a near
consensus has been formed in the literature on the convergence
experience in the United States prior to the 1970s, there has been
relatively little formal effort to explore the period after that. In
light of our visual impression of the discontinuity of output
convergence among U.S. states, it would be illuminating to analyze how
the cross-state output differences have proceeded in the following
period. Second, focusing on a more recent time period permits us to
utilize an arguably more appropriate measure of state-level output.
While it has been customary in the literature to construct state-level
real output data by deflating state personal income (SPI) data using a
common national price index, deflating in this way, as emphasized by
Barro and Sala-i-Martin (1992) and Mitchener and McLean (1999), leads to
mismeasurement of real per capita state income when price dynamics
differ considerably across states. (4) Since nominal output series
comprise both real output and price, it is hard to tell whether
empirical evidence on convergence in nominal output is driven by
convergence in real output or by convergence in price level. With a few
notable exceptions (e.g., Mitchener and McLean, 1999; Turner et al.
2006), the extant literature has largely remained silent on this
critical issue mainly due to the paucity of proper state-level price
data for a sufficiently long period. In the current study, we tackle
this issue by using gross state product (GSP) data in which both nominal
and real output series are available. Since the real GSP data are
currently available only after 1977, we extend the series back to 1963
using the state consumer price index (CPI) data borrowed from Berry and
Fording (2000) as in Turner et al. (2006). Consequently, our sample
period for real output per worker spans for almost five decades from
1963 to 2011.
Another distinctive feature of our study rests on the
methodological approach. Although the pattern of output convergence
remains an unsettled issue, it is now widely documented that nonlinear
specifications provide a superior characterization of the dynamics of
output convergence processes (e.g., Durlauf et al. 2006; Henderson et
al. 2012; Phillips and Sul 2009). Much of the previous studies on output
convergence among U.S. states have resorted to conventional and popular
approaches based on linear models, such as the cross-section methods of
[beta]- and [sigma]- convergences or the time-series method of
stochastic convergence (e.g., Carlino and Mills 1993; Evans and Karras
1996; Heckelman 2013; Young et al. 2008), but they may be of reduced
merit for capturing the transitional dynamics of state-level output
observed in the 1970s. In fact, our analysis based on nonparametric
techniques uncovers the nonlinear and time-varying behavior of the U.S.
output process. One of the main challenges in this regard is to select a
specific form of nonlinearity in the absence of any guidance from
theoretical models. Durlauf et al. (2006) stressed the usefulness of the
econometric tools proposed by Phillips and Sul (2007, 2009; hereafter
referred to as PS) in capturing the transitional dynamics of output
processes toward steady states. Based on a nonlinear time-varying
dynamic factor model, the PS technique enables us to test the
convergence hypothesis across a wide spectrum of nonlinear dynamics by
allowing for heterogeneity in parameters over time as well as across
states.
By applying the PS methods to the real output per worker of the 48
continental U.S. states, we find that states had not fully converged
over the last five decades, as evidenced by the significant difference
in output that has persisted across states. A clustering algorithm
reveals the presence of four distinctive subgroups of convergence, or
convergence clubs, each of which comprises states with similar dynamic
patterns of output. To identify the potential factors that are conducive
to the formation and specific compositions of convergence clubs, we
carry out a further regression analysis and find a few key state-level
characteristics that are shared in common among states in the same
clubs. Among them, variables related to knowledge accumulation, such as
patents and educational attainment, turn out to play an important role
in determining states' club membership. States with higher levels
of these variables are likely to fall into the club of a higher
productivity, consistent with the finding of Glaeser and Saiz (2004)
that knowledge stock is meaningfully correlated with the living standard
of states.
Our empirical findings are compatible with the prediction of
recently developed growth theories. In a multistate endogenous growth
model, for instance, Aghion et al. (2009) show that cross-state
differences in economic growth within the United States are mainly
determined by states' proximities to the technological frontier,
which are often proxied by patents. Gennaioli et al. (2013a and 2013b)
also present a modified version of the neoclassical growth model in
which they attribute the highly persistent disparities in regional
incomes and the consequent multiple growth regimes to a wide
cross-regional variation in educational attainment resulting from
barriers to factor mobility. The authors raise a serious question on the
empirical validity of the common view that diffusion of knowledge and
technology across state borders is frictionless. In fact, Allen and
Arkolakis (forthcoming) recently claim that a substantial fraction of
the spatial variation in incomes across the United States can be
explained by geographic location alone. Provided that technology and
production factors do not move freely due to spatial frictions, the
distribution of technology and knowledge would give rise to a
considerable variation in the regional standard of living. This point is
vindicated by our further analysis based on a nonparametric
deterministic frontier approach which reveals significant cross-state
differences in the level of technology. While states belonging to the
high-income club are either on the frontier or very close to it, states
in the low-income club are far below the frontier. The discontinuity of
the output convergence process is conjectured to have been driven to a
great extent by these factors as they played larger roles after the
1980s due to the technology- and human capital-intensive feature of the
information era (e.g., Oliner and Sichel 2000).
The remainder of the paper is organized as follows. Section II
begins with a brief discussion of the data and its preliminary analysis.
Section III is devoted to an explanation of the econometric analysis
focusing on the methodology developed by PS. The results of the
convergence test and the clustering algorithm are also discussed in this
section, together with theoretical implications of our empirical
findings. Section IV conducts regression analysis based on discrete
dependent models to identify the state-level characteristics responsible
for the formation and composition of convergence clubs. In this section,
we also check the robustness of our empirical findings against the
well-known issue of endogeneity. Section V concludes the paper.
II. DATA AND PRELIMINARY ANALYSIS
A. The Data
To compare the economic performance of different states, we use
annual GSP per worker (henceforth, output per worker), published by the
Bureau of Economic Analysis (BEA: http://www.bea.gov/regional), for the
48 continental U.S. states over the period 1963-2011. As a comprehensive
measure of state-level output, GSP is defined as the sum of output
produced within a given state by all factors used in the state
regardless of their owners' residence, and hence is different from
another popular measure of state-level output, SPI, which is based on
income generated by state residents. (5)
An attractive feature of the GSP data, relative to the alternative
measures of state-level output including SPI, must be the availability
of state price deflator data, which allows us to distinguish real output
from nominal output. As is widely recognized, this distinction is
intuitively important because the two measures of output are known to
have very different time-series properties especially when price
dynamics differ greatly across states. Unfortunately, the GSP deflator
data are available for a relatively short time period (i.e., only after
1977). To deal with this issue, we utilize the state cost of living
index data constructed by Berry and Fording (2000) and provided on
William Berry's web page (http://pubadm.fsu.edu/archives) to
deflate nominal GSP series prior to 1977. We extend the sample back as
far as possible so that we can study the long-run evolution of state
real output per worker. Specifically, all nominal GSP values are
converted into real 2000 dollars after extending the GSP deflator index
back to 1963. (6) As a result, our sample spans from 1963 to 2011,
resulting in 49 annual observations of real GSP per worker for each of
the 48 continental U.S. states.
Another notable feature of our data is that we focus on output per
worker or labor productivity, instead of output per capita, as our
measure of states' standard of living. This is because we view it
more compatible with theoretical models, such as growth accounting. The
difference between the two measures largely reflects the labor force
participation rate difference across states. While output per capita can
provide a general picture of a state's prosperity, output per
worker can be viewed as an approximate indicator of a state's
productivity. As noted by Bauer and Lee (2006), productivity measures
are important to economists and policymakers partly because they provide
a measure of a state's competitive position over time at the state
level, and more because their growth is closely related to gains in the
standard of living. (7)
In order to estimate the U.S. technology frontier in Section IV.D,
we also utilize a dataset employed in Turner et al. (2006) for the
state-level physical and human capital for the period 1963-2000.
B. Preliminary Analysis
Table 1 presents the summary statistics for three variables of
interest at the state level: nominal output per worker, real output per
worker (using 2000 as the base year), and inflation rates. Two
interesting results emerge from Table 1. First, a broad-based difference
exists in the behavior between nominal and real output per worker,
especially in terms of annual growth rates. Virginia (VA), for instance,
has experienced a relatively high growth rate of nominal output per
worker (5.2%), ranking 9th in the nation; however, this rapid growth was
largely driven by a high inflation rate (4.4%) rather than by real
output growth. When the nominal output was adjusted for state price
level, the annual growth rate of real output per worker in VA was just
0.7%, ranking 27th in the nation. Second, a considerable variation is
noted across states in all of the three variables. Cross-state
dispersion is particularly noticeable in real output per worker, judging
from the large magnitudes of SD and CV shown at the bottom of Table 1.
In terms of CV, the dispersion of real output growth is almost seven
times as large as that of nominal output growth. Since cross-sectional
variation is conceptually related to o-convergence that looks at dynamic
evolution of the cross-state output dispersion, this implies that
inference drawn from nominal output data is likely to overstate the true
underlying output convergence.
A similar story is told from Figure 3 which displays the estimated
speed of [beta]-convergence for real and nominal output per worker.
Convergence speed is estimated from the conventional cross-sectional
growth regression model (e.g., Barro and Sala-i-Martin 1992),
(1) [t.sup.-1] log ([y.sub.it]/[y.sub.i0]) = [alpha] - [(1 -
[e.sup.-[beta]t])/t] x log ([y.sub.i0]) + [u.sub.it],
where [y.sub.i0] is the initial level of output per worker in state
i, [t.sup.-1] log ([y.sub.it]/[y.sub.i0]) denotes the growth rate of
output per worker between time 0 and t, and t is the length of the
sample. In this exposition, positive values of [beta] estimate are
interpreted as evidence of [beta]-convergence, while negative values or
zero indicate divergence or lack of convergence. To capture potential
time-varying behavior of the convergence speed, we use a rolling
regression approach with a rolling window of 25 years.
[FIGURE 3 OMITTED]
Figure 3 plots the corresponding rolling estimates of [beta]: the
solid line is for nominal output, while the dashed line is for real
output. The numbers on the horizontal axis represent the beginning year
of each 25-year window, so that 1973 captures the subsample period of
1973-1997, and so on. As can be seen from the plots, the [beta] estimate
for real output data is consistently smaller than that of nominal output
data over the entire sample period. This implies that using nominal
output may overstate the true speed of convergence by failing to take
into account the impact of price changes, which facilitates the
convergence process of nominal output. (8) Moreover, the [beta]
estimates for both nominal and real output drop near to zero in the late
1970s, indicative of the discontinuity of convergence process. This
echoes what we have seen in the previous section regarding the halted
convergence process. Taken together, the significant difference observed
in the behavior between nominal and real output data stresses the
importance of drawing inference from real output data.
Another crucial data-related issue in the convergence literature is
uncertainty regarding model specifications. While previous research has
predominantly focused on linear models for characterizing convergence
process, there is no solid justification for linearity especially in the
absence of any theoretical guidance on the functional form. In view of
the extensive empirical evidence of nonlinearities in output convergence
(e.g., Durlauf et al. 2006; Henderson et al. 2012), it would be
instructive to identify the functional form of the underlying
convergence processes prior to drawing inference from the data. To this
end, we follow Shintani (2006) and adopt a nonparametric approach that
allows for flexibility in identifying functional forms of underlying
series. The basic idea of this nonparametric approach is to estimate an
unknown nonlinear autoregressive model of [y.sup.d.sub.i,t] =
m([y.sup.d.sub.i,t-1]) + [[epsilon].sub.i,t], where [y.sup.d.sub.i,t] =
[y.sub.i,t] - (1/N) [[summation].sup.N.sub.i=1] denotes the
ith-state's output deviation from the cross-sectional average. The
conditional mean function m([y.sub.t-1]) captures the average local
speed of convergence and the underlying functional form of m(*) is
identified without imposing any specific parametric restriction on the
structure. The first derivatives of m([y.sub.t-1]) are then estimated
using local quadratic regression with the Gaussian kernel. (9) The
estimated local speed of adjustment would be constant if the true
underlying process is linear, while it changes with the level of real
output per worker if the underlying process is not linear. Figure 4
illustrates the estimated local speed of adjustment for real output per
worker for a couple of selected states, NJ and TX. Since none of them
looks flat, the adjustment process of real output per worker is likely
to be nonlinear. (10) The nonmonotonic shapes, however, indicate that no
single specific nonlinear model can capture all of the various dynamics.
For this reason, most tools popularly adopted in the convergence
literature are of limited appeal due to their linearity assumption. As
emphasized by PS (2009), conventional cross-sectional tools for
convergence testing, such as [beta]- and [sigma]-convergence, are
susceptible to inconsistency and bias problems in the presence of
nonlinear and heterogeneous transitions in growth patterns. Inference on
stochastic convergence also becomes fragile since standard techniques
based on unit-root and cointegration tests are known to suffer from a
poor power problem in distinguishing a nonlinear but stationary process
from a nonstationary process (e.g., Choi and Moh 2007).
[FIGURE 4 OMITTED]
III. TESTING FOR CONVERGENCE AND THEORETICAL UNDERPINNINGS
Our discussion in the previous section highlights the importance of
accounting for underlying nonlinear dynamics in the study of output
convergence. Here we employ the technique developed by PS (2007) which
is known to be suitable for accommodating a wide spectrum of nonlinear
models, including transitional dynamics (e.g., Durlauf et al. 2006).
Based on a nonlinear time-varying dynamic factor model, the intuition
behind the PS technique is to test for long-run convergence by examining
whether the cross-sectional dispersion of real output decreases over
time. The PS method consists of two parts. The first part concerns
testing for convergence using the so-called log-t test and the second
part is a clustering algorithm that applies the log-t test to subsets of
data when the null hypothesis of convergence is rejected for the full
sample. The reader is referred to their original work for a more
detailed description of the PS method.
A. The Log-t Convergence Test
Let [y.sub.it] denote the real output per worker of state i at time
t which is assumed to follow a nonlinear factor model
(2) log [y.sub.it] = [b.sub.it][[mu].sub.t],
where [[mu].sub.t] represents a common steady-state growth path and
[b.sub.it] denotes a time-varying idiosyncratic element measuring the
heterogeneous transition path of state i to [[mu].sub.t]. Notice that
this model embraces the time-series and cross-sectional heterogeneity of
technological progress that is endogenously determined. The transition
coefficient [b.sub.it] is further modeled as
(3) [h.sub.it] = log [y.sub.it]/([N.sup.-1] [N.summation over
(i=1)] log [y.sub.it]) = [b.sub.it]/([N.sup.-1] [N.summaion over (i=1)]
[b.sub.it].
where [h.sub.it] is called the relative transition path (RTP)
measuring economy Ts relative departure from [[mu].sub.t]. Under the
null hypothesis of growth convergence, the following log-t regression
model can be formulated:
log ([H.sub.1][H.sub.t]) - 2 log (log t) = [alpha] + [gamma] log t
+ [u.sub.t], for t = [T.sub.0], ..., T,
where [H.sub.t] is the quadratic distance measure of [H.sub.t] =
[N.sup.-1] [[summation].sup.N.sub.i=1] [([h.sub.it] - 1).sup.2] and
[T.sub.0] and T respectively, denote the initial and last observations
in the regression. A one-sided r-test is then constructed such that
output converges over time if [gamma] [greater than or equal to] 0 and
diverges if [gamma] is negative. If [gamma] [greater than or equal to]
2, there exists an absolute convergence of output, whereas 2 >
[gamma] [greater than or equal to] 0 implies a conditional convergence
of output.
Before applying the log-? convergence test to state output data, it
would be informative to track the behavior of the relative transition
curves in Equation (3) that captures the transitional and convergence
behavior of real output over time relative to the common factor
([[mu].sub.t]). (11) Relative convergence takes place if those
transition curves converge toward unity over time. The top panel of
Figure 5 shows the relative transition curves for the entire 48 states.
The transitional pattern looks quite heterogeneous across states due to
cross-sectional and time-series heterogeneity in state output per
worker, and it shows no pattern of convergence toward unity over time,
indicating a lack of convergence in the full sample.
Turning to the results of the log-t test, the first row of Table 2
shows that the log-t test strongly rejects the null hypothesis of
convergence for the full sample, confirming the visual evidence shown in
the top panel of Figure 5. Since the point estimate of [gamma] is
significantly negative, [??] = -0.545, the null hypothesis of
convergence can be rejected even at the 1% level. This result runs
counter to the findings of earlier studies, including that of PS, which
are typically based on nominal output deflated by a common national
price for a longer sample period. (12) But, it is consistent with the
recent evidence on the end of output convergence in the United States.
This can be viewed as saying that the impact of the conventional driving
forces of output convergence has diminished since the 1970s.
B. Clustering Algorithm and Convergence Clubs
The lack of overall convergence motivates us to probe the
possibility of convergence in its subgroups, or convergence clubs. Given
that the log-? convergence test would reject the null of convergence in
the presence of as few as only one divergent series, the rejection could
be compatible with many different scenarios, including convergence among
some subgroups of states. To check whether convergence takes place in
any subsets of states, we exploit the clustering mechanism procedure
proposed by PS, which involves a stepwise and recursive application of
log-t regression tests to subsamples. As described in detail in their
original work (e.g., Phillips and Sul 2009, p. 1170), the basic idea of
the clustering mechanism is to split the full sample, which was rejected
by the log-t test, into a multitude of subsamples in a stepwise manner
on the basis of a recursive application of log-t regression tests. The
mechanism consists of several steps: (1) order the entire sample based
on the final period output per worker; (2) select a core primary group
based on the log-t regression test; (3) add new series to the core group
in a sequential manner and run the log-t test until a subgroup is found
within which the log-t test does not reject the null of convergence; (4)
repeat this procedure until the remaining series do not contain any
convergence subgroup.
[FIGURE 5 OMITTED]
Table 2 reports the results of the clustering algorithm which
detects four different clubs of convergence. The point estimates of
[gamma] in each club are positive and statistically significant,
pointing toward convergence at the subgroup level. The clubs appear to
be formed in the order of average level of real output per worker, with
the highest for Club 1 and the lowest for Club 4. (13) Table 2 also
lists the names of states belonging to each club. Club 1 includes six
states that form a core primary group that passed the clustering test
before others. Except for CA, all the states in Club 1 are located in
the east and are recognized as traditionally rich states. Since these
relatively richer states constitute the first club, our result here
lends credence to the view that economic growth in the past several
decades might have favored those states that were already relatively
rich and hence increased inequality among states. Club 2 is the largest
subgroup encompassing 23 states that accounts for the largest share of
the nation's population and production. Compared to the first club,
however, this club is quite heterogeneous not only in terms of
geographical location, from NH in the Northeast to WA in the West, but
also in terms of average output level. Club 3 is the second largest
subgroup with 15 states that are geographically scattered as well. Club
4 comprises only four states that are conventionally recognized as
low-income states. Overall, it is hard to relate the composition of
clubs to the geographical location as there is little systematic pattern
of geographical distribution of states within a convergence club as
displayed in Figure 6.
To ensure that the formation of clubs is well grounded, we run a
couple of robustness checks. A quick robustness check would be to look
at the RTP of state output in each club. As displayed in the four lower
panels of Figure 5, the transition curves in each club are clearly
converging toward unity, reflecting convergence of output toward its own
cross-sectional average. This is in stark contrast to the case of the
full sample we have seen earlier. Figure 7 provides another piece of
evidence on the robustness of our club formation. We apply two popular
methods of testing convergence, [beta]- and [sigma]-convergence, to the
real output of states in each club. If the clustering mechanism works
properly within the conventional framework, one may expect to see the
evidence of convergence within clubs but not across clubs. The left-hand
panel in Figure 7 displays strong evidence of [beta]-convergence in each
club as the fitted line of the scatterplot clearly shows an inverse
relationship between initial output level (on the horizontal axis) and
average output growth rates (on the vertical axis). Note that states in
Club 1 are clustered in the upper-right corner, while states belonging
to Club 4 are in the lower-left corner. This implies that the states in
Club 1 not only had higher initial output levels, but also experienced
faster output growth compared to those in Club 4, leading to divergence
between the two clubs. A similar story is told from the right-hand panel
of Figure 7 which shows compelling evidence of [beta]-convergence at the
club level. Output dispersion appears to have declined over time in each
club, whereas it has risen substantially for the full sample around the
mid-1970s. As such, both popular measures of output convergence reach an
agreement that output convergence in the United States has proceeded
among the subsets of states for the last several decades. It seems
natural to ask, then, what characteristics do the member states in the
same club share which are distinctive from those of the other clubs. We
will pursue this issue in Section IV.
C. Theoretical Underpinnings on Club Convergence
Our finding on the club convergence among U.S. states is compatible
with the prediction of many theoretical models. Although originally
emerging from empirical evidence, (14) the notion of club convergence
has its theoretical underpinnings in both neoclassical and endogenous
growth models. Galor (2010), for example, illustrates that club
convergence is viable in the standard neoclassical growth models once
they are augmented with empirically significant variables, such as human
capital and capital market imperfections. (15) Club convergence is also
accommodated within the framework of endogenous growth theories by
differences in human capital or frictions in the diffusion of
technological innovations across economies. (16)
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Theoretical exploration at the subnational level, however, has been
rather limited. This is in large part due to the common perception that
a much faster convergence can be achieved among regions within a nation
with more homogeneous economic and institutional environments and lower
barriers to factor mobility. As an important contribution along this
line, Aghion et al. (2009) develop a multistate endogenous growth model
which postulates that cross-state variation of economic growth in the
United States is largely determined by a state's proximity to the
technological frontier, which in turn depends on investments in
education. The authors emphasize patenting and migration as important
"intermediating variables" for the relationship between
education and economic growth. More recently, Gennaioli et al. (2013b)
present a modified version of the neoclassical model of regional growth
in which highly persistent disparities in regional incomes and the
consequent multiple growth regimes are attributed to a wide variation in
barriers to factor mobility. As for the sources of limited factor
mobility, they suggest (a) the intrinsic nontradeability of some factors
or goods, such as land and housing; and (b) the presence of man-made
barriers to factor mobility, such as policy and regulation. In their
model, they have argued compellingly that human capital, using
educational attainment as a proxy, is especially important in accounting
for regional differences in both income and productivity. In fact, the
related literature witnesses a growing body of empirical evidence
suggesting that the presence of spatial frictions in knowledge transfer
gives rise to a significant variation in the creation and diffusion of
knowledge across regions within a nation (e.g., Hillberry and Hummels
2003; Glaeser and Kohlhose 2004). (17) Provided that production factors
and knowledge do not move freely due to spatial frictions, technology
creation and spillovers would be geographically localized and thus
regional economies may evolve toward multiple steady states depending on
the degree to which technology spillovers are locally appropriated.
As such, more recent theories of growth and development tend to
focus on technology spillovers and human capital as the main driving
forces behind regional output differences. Since the notion of club
convergence is borne out by a variety of theoretical models, however, it
seems improbable to pin down a single growth theory that can
sufficiently explain why convergence clubs emerge among similarly
situated subnational economies. Besides, there seems no clear consensus
on which growth determinants ought to be included in such a growth
model. As noted by Acemoglu (2009), for example, technology and human
capital themselves could be influenced in some way by deeper variables,
such as geography and institutions. Indeed, the fact that U.S. states,
which are far more homogeneous than countries in terms of technological
and productivity developments, have gone through different paths of
output growth may lend credence to the view that institutional and
policy differences play a crucial role in the observed club convergence
patterns. (18) In a similar context, Mitchener and McLean (2003) have
stressed institutional and geographical features as key determinants of
differences in productivity levels across U.S. states. We therefore view
that focusing on a specific theoretical model may not provide a full
account of the formation of convergence clubs, although theoretical
models provide useful guidance to the potential determinants of club
formation. This renders us to resort to data-driven analysis in
identifying the factors behind the formation of club convergence in the
next section.
IV. FACTORS RESPONSIBLE FOR THE CLUB CONVERGENCE
In this section, we implement a couple of regression analyses in
searching for the potential factors that account for the formation and
composition of convergence clubs observed in the data. Our first
regression analysis is based on a discrete response model in which we
link the estimated club membership of states to a host of state-level
characteristics that have appeared relevant in the growth literature
(e.g., Durlauf et al. 2006; Reed 2009). Due to the well-known
endogeneity issue, however, the identified potential determinants are
not much informative about the direction of causality. To address this
issue, we carry out robust regression analysis using dynamic panel data
estimation techniques.
A. Candidate Explanatory Variables
The literature is replete with candidate explanations for the
composition of club convergence. Although there is no simple mapping
between the factors that enhance output growth and the factors conducive
to the formation of convergence clubs, the determinants of output growth
could be relevant factors for club convergence so long as they vary
systematically across clubs in such a way that they favor a specific
group of states compared to others. Among the large number of potential
determinants that were offered by many previous applications of growth
regression to the presence of multiple growth regimes, we consider over
50 explanatory variables as candidates to investigate whether and how
they account for the formation of convergence clubs. (19) The sources
and descriptions of these candidate determinants are presented in Table
Al. Following the guidance from theoretical work, we group them into
several major categories: (1) technology; (2) education and human
capital; (3) physical capital; (4) geographic and climatic
characteristics; (5) institutional and policy characteristics; and (6)
other characteristics including demography and industry structure. Most
of these variables are available for the entire sample period of
1963-2011, but with different frequencies. While many of them have
annual observations, some variables based on decennial census data
(e.g., demographic variables) have at most five observations over the
sample period.
B. Ordered Logit Model
The ordered logit model permits us to assess the relative
importance of potential explanatory variables by regressing them on the
ordered structure of a state's club membership. (20) We consider
the following ordered regression model
[[y].sub.i] = [X.sub.i][beta] + [[epsilon].sub.i]
where [y.sub.i] denotes state i's membership in a certain club
which is categorically coded as 1 for Club 1, 2 for Club 2, and so on.
It should be noted that the numerical category is assigned in the
opposite order of the corresponding average output level of clubs.
Moreover, the numerical value of dependent variable bears no
quantitative meaning and thus the magnitudes of the corresponding
coefficients are not straightforward to interpret. [X.sub.i], contains
explanatory variables with a constant term. Because of the limited
cross-sectional dimension (A = 48), we set the maximum number of
explanatory variables to seven in each regression exercise.
Table 3 summarizes the ordered regression results for coefficient
estimates and standard errors in seven different model specifications
which are selected based on the values of log-likelihood. In each
specification, all of the included explanatory variables are
statistically significant in combination and separately. Among a set of
potential factors suggested in the literature (e.g., Durlauf et al 2006;
Reed 2009), our econometric analysis identifies 12 strong explanatory
variables on states' club memberships: PATENTS, COLLEGE, FINANCE,
EDUPROD, EDUEXP, HEALTH, MIGRATION, INEQUALITY, DENSITY, INFLATION, EFI,
and FDIGSP, whose detailed descriptions are relegated to Table A1.
Among them, the strongest evidence is found for three variables,
PATENTS, COLLEGE and FINANCE, as they appear significant in each model
specification. The significance of PATENTS and COLLEGE is consistent
with the prevailing view established in the theoretical literature that
economic growth has been predominantly driven by technology and human
capital. As an indicator of state's ability to innovate new
products and production techniques, PATENTS is significant in
determining state's club membership probably through diverging
effects of the creation and exploitation of knowledge exerted on the
interstate output distribution. Negative signs of the coefficient
estimates imply that states with higher level of innovative activities
are likely to join Club 1, which on average experience higher levels of
output per worker. Also known as a proxy measure of distance to the
technological frontier, PATENTS reflects the level of technology to
which states have access. States producing more (per capita) patents are
likely to be closer to the technological frontier and hence have more
innovation-driven industries that lead to higher relative output per
worker. Aghion et al. (2009), for instance, maintain that cross-state
variation of economic growth in the United States is largely determined
by a state's proximity to the technological frontier, proxied by
patents. To the extent that frontier technologies are constantly
improving through patents, states with a larger stock of patents are
presumed to be more innovative in creating new products and production
techniques and thus achieve a higher productivity.
The significance of COLLEGE is not surprising in view of the fact
that innovative activities are contingent on the stock and quality of
human capital as more educated population can enhance the ability of
learning and adoption of new innovations in technologies. (21) The
negative sign for COLLEGE implies that states with a higher proportion
of the population with a college degree are more likely to belong to
Club 1, probably because innovative activities require a higher level of
knowledge stock accumulation. Typically measured by the fraction of
people that has attained a certain schooling level, human capital has
been central to the theories of endogenous growth (e.g., Lucas 1988) and
is empirically found to have a significant and positive effect on the
long-run growth path of technology. More recent studies (Gennaioli et
al. 2013a) tend to stress the importance of differences in human capital
quality in accounting for intranational variation in output per worker.
Vandenbussche et al. (2004) document that the growth effects of primary
and secondary education are insignificant while that for higher
education is significantly positive. Our result lends credence to this
view as we fail to find any significance for another measure of
educational attainment, HIGHSCHOOL, which is the fraction of the
population that has graduated from at least high schools. That is, the
contribution of human capital to the growth of output and productivity
depends critically on the types and levels of human capital. While human
capital affects both innovation and imitation, output growth is mainly
driven by innovations by highly educated people rather than by
imitations by unskilled human capital. In this vein, interstate
differences in higher educational attainment may have exerted a
diverging effect on output distribution across states. The impact of
educational attainment on economic growth could have strengthened after
the 1980s with the inception of the information era and the rise of the
IT industry due to their more human capital-intensive character (e.g.,
Oliner and Sichel 2000).
Another variable that is significantly related to the composition
of convergence clubs is FINANCE which measures the share of the finance
industry in a state's output. The negative coefficient of this
variable implies that states with an industrial base that is more
concentrated in the finance industry are more likely to belong to Club
1, consistent with the well-established positive impact of financial
development on economic growth (e.g., Levine 2005). A more developed
financial system tends to spur economic growth by promoting efficient
allocation of resources and a rapid accumulation of capital through
diversification of risks. At the regional level, Gennaioli et al.
(2013b) argue that financial development can account for cross-state
patterns of regional income disparities.
For the other nine variables, their estimated coefficients have the
expected signs except for EDUEXP (i.e., negative for INFLATION and
positive for the remaining eight variables). It is reassuring to note
that a negative sign indicates that states belonging to Club 1 have a
higher level in terms of the corresponding characteristic compared to
those in Clubs 2-4. Consequently, states with higher labor productivity
in education sector, higher diversified industrial structure, a more per
capita spending on health by government, a higher level of income
inequality, a higher density of population, a greater level of economic
freedom (or less government intervention and regulation), and a higher
FDI-GSP ratio, are more likely to be a member of Club 1, whereas states
in Club 4 are likely to have higher inflation rates. The negative sign
of INEQUALITY corroborates the finding by Partridge (2005) on the
positive relationship between income inequality and economic growth.
This suggests that income inequality in the United States might have
proceeded across states as well as within each state. The significance
of variable FDIGSP confirms the general view on the positive role of FDI
in economic growth. The industrial structure (DIVERSITY) also enters
with the expected negative signs, in accordance with the widely agreed
positive effect of diversified industry structure on economic growth.
The public finance variables, however, have mixed results on
explanatory power. While state and local governments' spending on
health (HEALTH) appears to have an influence on states' club
membership, state governments' expenditures on public
infrastructure, such as highway capital, do not. Another public finance
variable, EDUEXP, is statistically significant but enters with an
unexpected positive sign. Since the positive sign of the variable
suggests that states with a larger government spending on education (or
investment in education) are more likely to join Club 4 than Club 1, it
is counter-intuitive and contradicts the well-established empirical
regularity on the positive correlation between education spending and
economic growth. A plausible explanation for this, however, can be found
from the negative sign of the MIGRATION variable. To the extent that
highly educated workforce in poorer states with more spending on
education migrate into richer states with a lower investment in
education (out-migration from poorer states and in-migration to richer
states), education spending in the poor states is enhancing economic
growth not in the poorer states but in the richer states.
When it comes to the significance of the so-called deeper
explanatory variables, some policy-related institution variables, such
as government expenditure on health and education, and economic freedom,
have explanatory power on the club membership of states, but no strong
evidence is found for geographic or climatic characteristics of states.
C. Endogeneity and Dynamic Panel Data Analysis
While our regression analysis in the previous section identified a
handful of state-level characteristics as potential determinants of club
formation, the results do not necessarily establish the direction of
causality due to the well-known problem of endogeneity. Put differently,
the correlation found in the regression analysis may simply reflect
associative links or even reverse causation if both dependent variable
and explanatory variables are jointly determined by a third variable or
if explanatory variables are themselves functions of the dependent
variable. Since the four convergence clubs are formed in such a way that
is roughly related to the level of output per worker, this issue is
particularly relevant to some of our regressors such as COLLEGE and
FINANCE that are likely affected by states' economic conditions and
hence output level (e.g., Bils and Klenow 2000; Durlauf et al. 2006).
(22) In empirical growth research, a popular approach to dealing with
the endogeneity problem has been to implement difference- and
system-generalized method of moments (GMM) estimators (e.g., Arellano
and Bond 1991; Arellano and Bover 1995) which involve using instruments
to control for unobserved heterogeneity and simultaneity. The basic idea
of GMM estimators is to exploit the dynamic nature of growth models by
utilizing lagged variables as instruments. As documented in more recent
studies (e.g., Bazzi and Clemens 2013; Durlauf et al. 2006), however,
use of the GMM estimators is not desirable if instrumental variables are
either invalid or weak, or both, as often is the case in the growth
literature. An alternative strategy we consider here is the recursive
mean adjustment (RMA) method proposed by Choi et al. (2010) who show
that the RMA strategy is useful in reducing bias in the estimation of
linear dynamic panel data models. As highlighted by Choi et al. (2010),
the RMA estimator is straightforward to implement and is more
practically appealing than GMM/IV estimators in the presence of weak
moment conditions. Moreover, it is shown that the RMA estimator performs
well in terms of reducing bias even when error terms are
cross-sectionally dependent.
In this section, we adopt both the dynamic panel GMM estimators and
the RMA estimator to probe the causal links between output per worker
and the key determinants identified in the previous section, after
accounting for the endogeneity issue. Specifically, we consider the
following prototypical dynamic panel data model, (4)
[y.sub.it] = [p.summation over (j=1)][[alpha].sub.j][y.sub.i,t-j] +
[X.sub.it][beta] + [W.sub.it][gamma] + [[tau].sub.t] + [v.sub.i] +
[[epsilon].sub.it],
which can be rewritten as
(5) [DELTA][y.sub.it] = ([[alpha].sub.1] - 1) [y.sub.i,t-1] +
[p.summation over (j=2)][[alpha].sub.j][y.sub.i,t-j] + [X.sub.it][beta]
+ [W.sub.it][gamma] + [[tau].sub.t] + [v.sub.i] + [[epsilon].sub.it],
where [y.sub.i]t is log output per worker at state i in year 7,
[X.sub.i]t is a set of exogenous regressors, [W.sub.i]t is a vector of
endogenous regressors, [[tau].sub.t], represents time-specific effects,
[v.sub.i], denotes state-specific effects, and [[epsilon].sub.it] is an
error term. This specification allows us to address the question of
whether endogenous variables (VT) have an economically and statistically
significant causal effect on y, while holding X constant. Beware that by
design the lagged dependent variables ([y.sub.i,t-j]) are correlated
with the unobserved fixed effects ([v.sub.i]), giving rise to bias and
inconsistency of estimators. The inclusion of time dummies
([[tau].sub.t]) is to capture unobserved cross-sectional dependence
across state output which is correlated through common national shocks.
In our regression exercise, this term is removed by using
cross-sectionally demeaned data for all variables. Since our purpose
here is to examine the direction of causality, we focus on the three
most significant explanatory variables that were found in our ordered
logit model analysis, PATENTS, FINANCE and EDUPROD, in which annual
observations are available for the entire sample period. (23)
Table 4 presents the regression results. In the GMM estimation, all
three explanatory variables are treated as potentially endogenous
variables. Nonetheless, the estimation results are qualitatively very
similar in both GMM and RMA estimators as the coefficient estimates
enter the regressions with the same signs. The variable PATENTS enters
the regressions significantly in all specifications with an expected
positive sign. That is, PATENTS exerts a positive impact on output per
worker, leading states with higher level of patents to Club 1, even
after controlling for the potential endogeneity of regressors. By
contrast, the evidence for the other two regressors is not much
compelling. While the point estimate is unexpectedly negative for
FINANCE, it is positive but insignificant for EDUPROD, (24) To sum, our
dynamic panel data analysis suggests PATENTS as the most consistently
significant causal factor affecting club formation.
D. Technology Progress and Club Convergence
Our result on the strong significance of PATENTS in explaining the
formation of convergence clubs poses a challenge for the conventional
assumption that technology and human capital have virtually unlimited
mobility across state borders. (25) In the absence of barriers to the
mobility of technology and human capital, diffusion of technology, and
knowledge should facilitate convergence among states, because states
that are further behind the technology frontier experience a more rapid
growth due to lower costs of adopting new technology as stipulated in
the "advantage of backwardness." If the mobility of technology
and factors is spatially limited or localized, however, cross-state
differences in the technology level may generate diverging patterns of
output per worker across states. Cross-state variation in human capital
composition can further promote economic clustering of states with
persistently different levels of output because off-frontier states do
not have sufficient levels of human capital to take advantage of new
technology developed on the frontier. In fact, in addition to earlier
evidence on localized technology spillovers (e.g., Jaffe et al. 1993),
more recent studies (e.g., Belenzon and Schankermanz 2013; Ganong and
Shoag 2012; Smith 1999) have found compelling evidence that the mobility
of human capital and technology spillovers within the United States are
far from frictionless. Analyzing knowledge spillovers at the state level
using state patent grants as a proxy, for example, Smith (1999) finds
that the interstate knowledge spillovers within the United States are
geographically localized and exert a diverging effect on cross-state
standards of living. Belenzon and Schankermanz (2013) also document the
relevance of state borders in the diffusion of knowledge from
universities as citations to patents are strongly constrained by state
borders.
To elucidate how frictions in technology spillovers could lead to
the clustering of states with different levels of output per worker, we
estimate the U.S. production frontier using a nonparametric
deterministic frontier approach called data envelopment analysis (DEA).
The basic idea of the DEA approach is to construct an efficient
production frontier taking physical capital (AT) and human capital (H)
as inputs without assuming any specific functional form. The associated
efficiency levels of individual states are then measured by distances
from the frontier.
Figure 8 plots the estimated technology frontier and the actual
output per worker of 48 states given factor combination (K/H) for the
year 1963 and 2000 using the dataset constructed by Turner et al.
(2006). We first note that there are nonuniform technological frontiers
across U.S. states as some states are on the efficient frontier, while
many others are below it. More importantly, states in different
convergence clubs tend to have significantly different levels of
technology. Take the frontier in year 2000 for instance, states
belonging to Club 1 (represented in diamonds) are either on the frontier
or very close to it, whereas states in Club 4 (represented in triangles)
remain far below the frontier, implying that technology differences
could be an important source of club convergence. The nonuniform
technological frontiers suggest that although the United States as a
whole has always been on the world technology frontier (WTF) (e.g.,
Jerzmanowski 2007), this is less likely the case at the state level in
light of the considerable cross-state heterogeneity in technology level.
The cross-state heterogeneity can also be seen in the evolution of the
technology frontier over time. The upper-leftward shift of the frontier
line indicates a nonneutral technological progress during the period
1963-2000, with a smaller physical-human capital (K/H) ratio accompanied
by a faster human capital accumulation. Notice that technological
progress has slightly different implications for different clubs.
Whereas states in Clubs 2-4 have made human capital-intensive
technological progress judging from the upper-leftward shift, states in
Club 1 have made factor-neutral technological progress between 1963 and
2000 in view of the upward shift, or stable K/H ratios. This is perhaps
because states in Club 1 concentrate more on innovating new technology
than adopting it, as evidenced by larger average per capita patents, and
hence operate effectively with less human capital relative to other
states. Our results, therefore, can be interpreted as saying that the
club convergence found in the U.S. state output data is driven by this
nonneutral technological progress that may have been relatively more
beneficial for the originally wealthy and physical-capital-rich states.
[FIGURE 8 OMITTED]
To further probe this issue, we estimate average TFP growth and
decompose it into technological progress and changes in technological
efficiency by convergence clubs. The results are presented in Table 5.
Contrary to our prior expectations, it is not Club 1 but Club 3 which
experienced the fastest growth in TFP. While Club 3 states experienced
an annual TFP growth of 0.12% on average, TFP has grown in Club 1 at the
rate of just 0.02% per year. (26) Not surprisingly, Club 4 had the
slowest TFP growth in the sample period. The story changes somewhat
dramatically when we look at the TFP growth decomposed into
technological progress and technological catch-up (or efficiency change)
for a given set of inputs. As reported in Column 2, Club 1 states had
the fastest technological progress at the rate of 0.09% per year but
with the slowest speed of improvement in efficiency, whereas states in
Club 3 experienced the fastest rate of efficiency gain (i.e., catching
up). Combined together, the faster overall TFP growth of states in Clubs
2 and 3 relative to those in Club 1 was mainly driven by improvements in
efficiency rather than in technological progress. In other words, the
TFP growth comes largely from technological change in high-income states
(i.e., by pushing the technological frontier outward), but from catching
up to the frontier in lower income states. It is worth noting that
states in Club 4 experienced comparable improvements in efficiency to
those in Club 3, but the contribution of efficiency gain was outpaced by
the decline in technological progress. As a result, the technological
gap between states in Club 1 and states in Club 4 has further widened
during the sample period under study. Given that the formation of club
convergence is more closely related to the speed of technological
progress than efficiency improvements, we reckon that what matters for a
state's standard of living is its ability to develop technological
innovations rather than its capacity to adopt technologies already
developed in other states.
V. CONCLUDING REMARKS
The progress of output convergence among the continental U.S.
states has been very different since the 1970s. After a century-long
process, output convergence is no longer an adequate description of the
growth pattern for the U.S. states since the mid-1970s when the overall
convergence process came to a halt. From a welfare point of view, this
discontinuity of the output convergence process may have an important
implication, particularly in relation to the ample empirical evidence on
the income-consumption inequality nexus. (27) Furthermore, whether or
not output converges over time bears a crucial policy implication in
that policy measures are often justified by their ability to reduce
output differences across subeconomies within a nation.
This paper reexamined the process of output convergence in the
United States for the last five decades by taking a novel approach to
investigating this long-standing issue. We first utilized real output
per worker data that was generated using state-specific price levels
instead of a national price level, which most studies in the literature
so far have failed to do because of the lack of a proper measure of
state-level price data. In addition, we employed the convergence test
developed by PS that is designed to capture the observed nonlinear and
time-varying dynamics of output data. We found no evidence of overall
convergence among the 48 continental U.S. states. But our clustering
mechanism unveils that output convergence has proceeded among states
within certain subgroups into which states are grouped by dynamic
behaviors of real output per worker.
Using a regression analysis based on discrete dependent models, we
identified a set of state-level characteristics that account for the
formation of convergence clubs. Among them, variables related to
technology and knowledge, such as per capita patents and educational
attainment, stand out. States with larger stocks of patents or higher
portions of college graduates have achieved higher levels of
productivity, possibly because they are closer to the technological
frontiers and hence are more innovative in creating new products and
production techniques. On one hand, our empirical finding supports the
prediction of recent theories of growth and development that technology
and human capital are the key determinants of regional output
differences. On the other hand, our result suggests that states in
different convergence clubs are sufficiently disparate in terms of
technology level and technological changes, casting doubt on the
empirical relevance of the common view that the interstate flow of
knowledge and factors is frictionless in the United States. The
persistent cross-state differences in output per worker is driven by the
fact that a productivity-enhancing technological innovation in one state
does not flow quickly enough to other states, possibly due to the
factors that limit relocation of resources. In fact, our analysis of
frontier approach suggests nonuniform technological frontiers across
U.S. states, which may have different implications for different states.
We posit that the impact of technological progress on output growth
became stronger after 1980 with the inception of the information era and
the rise of the IT industry due to their more knowledge- and
human-capital-intensive nature.
There are some potential policy lessons to draw from our study. If
intranational inequality across individuals is due in large part to
cross-state difference as in the case of the international counterpart
(e.g., Schultz 1998), policy efforts to reduce individual output
inequality within countries could be effective by mitigating cross-state
output differences. The analysis here emphasizes the importance of
specific policies toward technology and human capital improvements.
State-level policies to promote knowledge accumulation may exert a
crucial impact on economic growth mainly through productivity-enhancing
technological innovations. At the national level, policies to improve
the diffusion of knowledge and human capital will help reduce the
cross-state output inequalities. Our results also provide some useful
insights on the future progress of output convergence in an existing
monetary or fiscal union, such as the European Monetary Union. Although
it is widely believed that membership in such a union would promote
convergence across member countries, the debate is far from settled on
its long-term effect. In view of the experience of the U.S. states that
have long been consolidated fiscally as well as monetarily, the
discontinuity of output convergence among its subeconomies hints that a
centralized federal authority with a well-integrated market may not
necessarily achieve a long-run convergence in output among its member
economies, particularly in the presence of frictions in the flow of
knowledge and production factors.
ABBREVIATIONS
BEA: Bureau of Economic Analysis
CPI: Consumer Price Index
CV: Coefficient of Variation
DEA: Data Envelopment Analysis
GMM: Generalized Method of Moments
GSP: Gross State Product
PS: Phillips and Sul
RMA: Recursive Mean Adjustment
RSC: Residual Squares Criterion
RTP: Relative Transition Path
SPI: State Personal Income
WTF: World Technology Frontier
doi: 10.1111/ecin.12129
APPENDIX: DESCRIPTION OF EXPLANATORY VARIABLES
TABLE A1
List of Explanatory Variables Considered in Regression Analysis
Variable Description Source
AVGTAX Average state income Crain (2003)
tax rate [1969-1998]
CAPSTOCK Per capita capital Turner et al. (2006)
in millions of
dollars [1963-2000]
CLIMATE Average annual NOAA website
number of cooling
degree days
[1992-2010]
COLLEGE Average percent of Census Bureau
persons 25 years and
above who have
attained a
bachelor's degree
DECENTRAL Share of total state Census Bureau
and local government
expenditure made by
local government
DENSITY Average population Census Bureau
per square miles
DEPENDENCY Average ratio of the Census Bureau
combined under 18
and 65 and above
populations to the
18 to 64 population
DIVERSITY Industry diversity Census Bureau
measured by
[[summation
of].sup.i]
((Earnings in
industry //Total
Earnings)2
EDUEXP Per capita Census Bureau
expenditure on
education as a share
of total local and
state government
expenditures
EDUPROD Labor productivity Census Bureau
in education
industry
EFI State-level economic Heckelman (2013)
freedom index [1981
-2008]
FDIGSP Foreign direct BEA
investment (the
gross book value in
current dollars of
property, plant, and
equipment of
affiliates in all
industries) as a
percent of GSP
[1977-2008]
FEDEMP Share of total Census Bureau
employee by Federal
employee
FEDGOVT Share of total Census Bureau
earnings by Federal
government
FINANCE Share of F.I.R.E. Census Bureau
industry in terms of
the number of
establishments
HEALTH Per capita Census Bureau
expenditure on
health and hospitals
as a share of total
state and local
government
expenditures
HIGHINST Number of higher Census Bureau
education
institutions per
million people
HIGHSCHOOL Average percent of Census Bureau
persons 25 years and
over who have
graduated from high
school
HIGHWAY Per capita Census Bureau
expenditure on
highways as a share
of total state and
local government
expenditures
INEQUALITY Average top-decile Frank (2009)
income share (in %)
INFLATION State inflation rate BEA
based on GSP
deflator
LATITUDE Latitude for the
centroid of each
state
MARTAX Marginal state Crain (2003)
income tax rate
[1969-1998]
MIGRATION Total net migration Census Bureau
rate (%)
MIGRCOL Net migration rate Census Bureau
(%) of young college
graduates
NORTHEAST Regional dummy for
states in Northeast
PATENTS Average patents Patent and
granted per million Trademark Office
residents
PRODUCTIVITY Labor productivity Census Bureau
in each industry for
nine large
industrial
classifications
SOUTH Regional dummy for
states in South
STATEGOVT Share of total Census Bureau
earnings by state
and local government
STRUCTURE1 Share of each Census Bureau
industry in terms of
the number of
establishments: (1)
Agriculture; (2)
Mining; (3)
Construction; (4)
Manufacturing; (5)
Transportation,
Communication,
Utilities; (6)
Wholesale; (7)
Retail; (8)
F.I.R.E.; (9)
Service
STRUCTURE2 Share of each Census Bureau
industry in terms of
total earnings in
nine large
industrial
classifications
TAXBUR Total state and Census Bureau
local tax revenues
as a share of
personal income
URBANIZATION Percentage of urban Census Bureau
population
REFERENCES
Acemoglu, D. Introduction to Modern Economic Growth. Princeton, NJ;
Oxford: Princeton University Press, 2009.
Aghion, P., L. Boustan, C. Hoxby, and J. Vandenbussche. "The
Causal Impact of Education on Economic Growth: Evidence from US."
Harvard University, Mimeo, 2009.
Aghion, P., and P. Howitt. Endogenous Growth Theory. Cambridge, MA:
MIT Press, 1998.
Allen. T., and C. Arkolakis. "Trade and the Topography of the
Spatial Economy." Quarterly Journal of Economics, forthcoming.
Arellano, M., and S. Bond. "Some Tests of Specification for
Panel Data: Monte Carlo Evidence and an Application to Employment
Equations." Review of Economic Studies, 58(2), 1991,277-97.
Arellano, M., and O. Bover. "Another Look at the Instrumental
Variable Estimation of Error Components Models." Journal of
Econometrics, 68, 1995, 29-51.
Attanasio, O., E. Hurst, and L. Pistaferri. "The Evolution of
Income, Consumption, and Leisure Inequality in the U.S.,
1980-2010." National Bureau of Economic Research Working Papers No.
17982, 2012.
Barro, R. J. "Economic Growth in a Cross-Section of
Countries." Quarterly Journal of Economics. 106, 1991, 407-43.
Barro, R. J., and X. Sala-i-Martin. "Convergence."
Journal of Political Economy, 100, 1992, 223-51.
--. Economic Growth. 2nd ed. Cambridge, MA: MIT Press, 2004.
Bauer, P. W., and Y. Lee. "Estimating GSP and Labor
Productivity by State." Federal Reserve Bank of Cleveland Policy
Discussion Papers 16, 2006.
Bauer, P. W., M. E. Schweitzer, and S. Shane. "State Growth
Empirics: The Long-Run Determinants of State Income Growth."
Federal Reserve Bank of Cleveland Working Paper Series No. 06-06, 2006.
Baumol, W. "Productivity Growth, Convergence and
Welfare." American Economic Review, 76, 1986, 1072-85.
Bazzi, S., and M. A. Clemens. "Blunt Instruments: Avoiding
Common Pitfalls in Identifying the Causes of Economic Growth."
American Economic Journal: Macroeconomics, 5(2), 2013, 152-86.
Belenzon, S., and M. Schankermanz. "Spreading the Word:
Geography, Policy and Knowledge Spillovers." Review of Economics
and Statistics, 95, 2013. 884-903.
Berry. W. D., and R. C. Fording. "An Annual Cost of Living
Index for the American States, 1960-95." Journal of Politics, 60,
2000, 550-67.
Bils, M., and P. Klenow. "Does Schooling Cause Growth?"
American Economic Review, 90, 2000, 1160-83.
Carlino, G. A., and L. Mills. "Are U.S. Regional Incomes
Converging? A Time Series Analysis." Journal of Monetary Economics,
32, 1993, 335-46.
Chen. L.-L., S. Choi, and J. Devereux. "Have Absolute Price
Levels Converged for Developed Economies? The Evidence since 1870."
Review of Economics and Statistics, 90(1), 2008, 29-36.
Choi, C. Y. "A Reexamination of Output Convergence in the U.S.
States: Toward Which Level(s) Are They Converging?" Journal of
Regional Science, 44(4), 2004, 713-41.
Choi, C. Y., N. C. Mark, and D. Sul. "Bias Reduction in
Dynamic Panel Data Models by Common Recursive Mean Adjustment."
Oxford Bulletin of Economics and Statistics, 72(5), 2010, 567-99.
Choi, C. Y., and Y.-K. Moh. "How Useful Are Tests for
Unit-Root in Distinguishing Unit-Root Processes from Stationary but
Nonlinear Processes?" Econometrics Journal, 10, 2007,82-112.
Crain, W. M. Volatile States: Institutions, Policy, and Performance
of the American States. Ann Arbor, MI: University of Michigan Press,
2003.
Del Negro, M. "Asymmetric Shocks among U.S. States."
Journal of International Economics, 56, 2002, 273-97.
Dowrick, S., and J. B. DeLong "Globalization and
Convergence," in Globalization in Historical Perspective, edited by
M. D. Bordo, A. M. Taylor, and J. G. Williamson. Chicago: University of
Chicago Press, 2003, 191-220.
Durlauf, S., and P. A. Johnson. "Multiple Regimes and Cross
Country Growth Behaviour." Journal of Applied Econometrics, 10(4),
1995, 365-84.
Durlauf. S., P. A. Johnson, and J. R. Temple "Growth
Econometrics," in Handbook of Economic Growth, Vol. 1 A, edited by
P. Aghion and S. Durlauf. Amsterdam: Elsevier Science, 2006, 555-677.
Evans, P, and G. Karras. "Do Economies Converge? Evidence from
a Panel of U.S. States." Review of Economics and Statistics, 78,
1996, 384-8.
Fan. J., and I. Gijbels Local Polynomial Modelling and Its
Applications. London: Chapman and Hall, 1996.
Frank, M. W. "Inequality and Growth in the United States:
Evidence from a New State-level Panel of Income Inequality
Measures." Economic Inquiry, 47(1), 2009, 55-68.
Galor, O. "The 2008 Lawrence R. Klein Lecture-Comparative
Economic Development: Insights from Unified Growth Theory."
International Economic Review, 51(1), 2010, 1-44.
Ganong, R, and D. Shoag. "Why Has Regional Convergence in the
U.S. Stopped?" Harvard Kennedy School, Mimeo, 2012.
Gennaioli, N., R. La Porta, F. Lopez-de-Silanes, and A. Shleifer.
"Human Capital and Regional Development." Quarterly Journal of
Economics, 128(1). 2013,105-64.
--. "Growth in Regions." National Bureau of Economic
Research Working Paper No. 18937, 2013.
Glaeser, E. L., and A. Saiz. "The Rise of the Skilled
City." Brookings-Wharton Papers on Urban Affairs, 2004, 2004.
47-105.
Glaeser, E. L., and J. E. Kohlhose. "Cities, Regions and the
Decline of Transport Costs." Papers in Regional Science, 83, 2004,
197-228.
Heckelman, J. C. "Income Convergence among U.S. States:
Cross-Section and Time Series Evidence." Canadian Journal of
Economics, 46(3), 2013, 791-1155.
Henderson, D. J., C. Papageorgiou, and C. F. Parameter.
"Growth Empirics without Parameters." Economic Journal, 122,
2012, 125-54.
Henriksen, E., F. E. Kydland, and R. Sustek. "Globally
Correlated Nominal Fluctuations." National Bureau of Economic
Research Working Papers No. 15123, 2009.
Hillberry, R., and D. Hummels. "Intranational Home Bias: Some
Explanations." Review of Economics and Statistics, 85(4), 2003,
1089-92.
Jaffe, A. B., M. Trajtenberg, and R. Henderson. "Geographic
Localization of Knowledge Spillovers as Evidenced by Patent
Citations." Quarterly Journal of Economics, 108(3), 1993, 577-98.
Jerzmanowski, M. "TFP Differences: Appropriate Technology vs.
Efficiency." European Economic Review, 51 (8), 2007.2080-110.
Jones, C. I. "Time Series Tests of Endogenous Growth
Models." Quarterly Journal of Economics. 110(2), 1996. 495-525.
Kalemi-Ozcan, S., A. Reshef, B. E. Sprensen, and O. Yosha.
"Why Does Capital Flow to Rich States?" Review of Economics
and Statistics, 92(4), 2010, 769-83.
Levine, R. "Finance and Growth: Theory and Evidence," in
Handbook of Economic Growth, Vol. 1, edited by P.
Aghion, and S. Durlauf. Amsterdam: Elsevier Science, 2005, 865-934.
Lucas, R. "On the Mechanics of Economic Development."
Journal of Monetary Economics, 22(1), 1988, 3-42.
Mitchener, K. J., and I. W. McLean. "U.S. Regional Growth and
Convergence, 1880-1980." Journal of Economic History, 59(4), 1999,
1016-42.
--. "The Productivity of U.S. States since 1880." Journal
of Economic Growth, 8(1), 2003, 73-114.
Oliner, S. D., and D. E. Sichel. "The Resurgence of Growth in
the Late 1990s: Is Information Technology the Story?" Journal of
Economic Perspectives, 14(4), 2000, 3-22.
Partridge, M. D. "Does Income Distribution Affect U.S. State
Economic Growth?" Journal of Regional Science, 45(2), 2005, 363-94.
Phillips, P. C. B., and D. Sul. "Transition Modelling and
Econometric Convergence Tests." Econometrica, 75, 2007, 1771-855.
--. "Economic Transition and Growth." Journal of Applied
Econometrics, 24, 2009, 1153-85.
Quah, D. "Empirics for Economic Growth and Convergence."
European Economic Review, 40(6), 1996, 1353-75.
Reed, W. R. "The Determinants of U.S. State Economic Growth: A
Less Extreme Bounds Analysis." Economic Inquiry, 47(4), 2009,
685-700.
Romer, P. "Human Capital and Growth: Theory and
Evidence." Carnegie-Rochester Series on Public Policy, 32, 1990,
251-86.
Schultz, T. P. "Inequality in the Distribution of Personal
Income in the World: How It Is Changing and Why." Economic Growth
Center, Yale University, Discussion Paper No. 784, 1998.
Shintani, M. "A Nonparametric Measure of Convergence towards
Purchasing Power Parity." Journal of Applied Econometrics, 21,
2006, 589-604.
Smith. P. J. "Do Knowledge Spillovers Contribute to U.S. State
Output and Growth?" Journal of Urban Economics, 45, 1999, 331-53.
Tamura, R. "Development Accounting and Convergence for US
States." Clemson University, Mimeo, 2012.
Turner, C., R. Tamura, S. E. Mulholland, and S. Baier.
"Education and Income of the States of the United States:
1840-2000." Journal of Economic Growth, 12, 2006, 101-58.
Vandenbussche, J., P. Aghion, and C. Meghir. "Growth and the
Composition of Human Capital." Journal of Economic Growth, 11(2),
2004, 97-127.
Young, A. T., M. J. Higgins, and D. Levy. "Sigma Convergence
versus Beta Convergence: Evidence from U.S. County-Level Data."
Journal of Money, Credit and Banking, 40(5), 2008, 1083-93.
(1.) Bauer, Schweitzer, and Shane (2006) document that the
dispersion of state per capita incomes has risen from 1976, in large
part stemming from the departure of some relatively high-income states
relative to the national average. Ganong and Shoag (2012) claim that
tight regulations on land use weakened convergence in per capita income
among U.S. states after 1980.
(2.) The data used here, generously supplied by Robert Tamura for
1929-2000, are extended by us to 2011. We are grateful to Robert Tamura
for sharing the data with us.
(3.) [beta]-convergence occurs when originally poor economies grow
faster than richer ones so that all economies eventually converge in
terms of real per capita output. A positive value of [beta] in Equation
(1) below indicates evidence of [beta]-convergence. [sigma]-convergence
occurs when the dispersion of real per capita output across a group of
economies declines over time.
(4.) Choi (2004) sought to deal with this issue by using
metropolitan area CPIs as a proxy, but the use of metropolitan area CPIs
is of limited merit for answering the question at hand, not just because
they are unavailable for all states, but because they are not good
representatives of state-level prices, especially for those states with
a low urbanization rate. Another important attempt to account for state
price differences has been made by Turner et al. (2006) who constructed
real state output per worker, from 1840 to 2000. They, however, utilized
regional price levels for eight census regions at 20-year intervals from
1840 to 1960 and used Berry and Fording (2000) annual state cost of
living index from 1960 to 1995.
(5.) According to the BEA ("GDP by State Estimation
Methodology," p. 1), GSP consists of three major components: (a)
compensation of employees (wages and salaries and their supplements);
(b) taxes on production and imports; and (c) gross operating surplus
(including noncorporate income). Among them, compensation of employees
is shared by SPI. Because the two measures differ in the subcomponents,
they are expected to take different profiles of convergence. For
example, the wage and salary earned by residents in New Jersey who work
in New York City will be part of SPI in NJ but GSP in NY. If workplaces
are located in richer states than residences, use of SPI as the measure
of state output may exaggerate output convergence because of the
"distribution effect" through employee transfers. Though not
reported here for brevity, we find a faster rate of convergence using
SPI data than using GSP data. The reader is referred to Kalemi-Ozcan et
al. (2010, p. 783) for a further discussion on the difference between
GSP and SPI.
(6.) The real GSP data are not without criticism. Since real GSP is
computed by deflating nominal GSP using the national GDP deflator after
adjusting for states' industry composition, it may not properly
reflect cross-state price variations. Nevertheless, we stick to this
measure of output because there is no other consistent measurement of
prices at the state level. We also considered Del Negro's (2002)
state CPI data which are constructed using American Chamber of Commerce
Association data on Cost of Living by metropolitan areas. But, the CPI
data are available only for the period after 1969.
(7.) Though the number of hours worked is a preferred measure of
labor input in constructing state-level productivity, we compute output
per worker for the private nonfarm business economy as our productivity
measure because data on the number of working hours are unavailable at
the state level.
(8.) The literature is replete with empirical evidence on more
homogeneous dynamics of prices across states than real output. Henriksen
et al. (2009), for instance, documented that the cross-country
correlation of prices is substantially higher than that of (real)
output. For a dissenting view, see Chen et al. (2008) who contended that
the convergence of output took place earlier than that of prices across
11 countries.
(9.) Following Shintani (2006), we choose the smoothing parameter
for the nonparametric estimator by minimizing the residual squares
criterion (RSC) given in Fan and Gijbels (1996). The reader is referred
to Shintani's original work for further details.
(10.) We find similar results for all other states. A complete
version of Figure 4 is available at:
http://wweb.uta.edu/faculty/cychoi/research.htm.
(11.) Since the convergence hypothesis centers on the evolution of
potential output rather than on the deviations from it, we follow PS and
use the HP-filtered output data after removing the cyclical components.
According to PS, the log-r regression test has a decent discriminatory
power against club convergence alternatives.
(12.) PS (2009) have implemented their techniques to find evidence
of convergence in income per capita among the 48 U.S. states over
1929-1998. Their analysis, however, is subject to the aforementioned
limitation of deflating nominal income by national CPIs without
accounting for cross-state price differences.
(13.) One should be cautious in interpreting this as saying that
club membership is purely governed by states' output level. As
presented in Table 1, MA belongs to Club 1 even though its real output
per worker is lower than that of LA which belongs to Club 2. Our
analysis based on real per capita output data yields qualitatively
similar results on the presence of club convergence, but with a
difference in the composition of convergence clubs. Using output per
capita data, we found three convergence clubs with somewhat different
constituents. The results are not reported here, but are available upon
request.
(14.) Since the finding by Baumol (1986) that clustering is an
important feature of world income data, a number of studies (e.g.,
Dowrick and DeLong 2003; Durlauf and Johnson 1995; Quah 1996, to cite a
few) have documented the evidence of club convergence, with different
countries converging towards different steady states depending on their
structural characteristics. A nonexhaustive list of structural
characteristics includes technologies, preferences, population growth,
government policy, factor market structure, and so on.
(15.) Galor (2010) contends that club convergence is more plausible
than a conditional convergence hypothesis if economies that are
identical in their fundamentals converge to the same steady-state level
of output per capita regardless of their initial conditions.
(16.) While human capital has been emphasized in the
first-generation endogenous growth models (e.g., Lucas 1988; Romer 1990)
in which growth is assumed to be primarily driven by the economy-wide
stock of human capital, the second-generation endogenous growth models
(e.g., Aghion and Howitt 1998; Jones 1996; Vandenbussche. Aghion, and
Meghir 2004) focus on the creation and diffusion of knowledge as the
driving force of club convergence.
(17.) In principle, there should be no friction in trade between
U.S. states as it is unconstitutional to impede interstate commerce, but
in practice it is hardly accepted that interstate distribution of goods
and knowledge is totally frictionless. In a recent study, Allen and
Arkolakis (forthcoming) maintain that geographic location alone accounts
for a substantial fraction (about 24%) of the spatial variation in
incomes across the United States.
(18.) Policies are institutional factors that involve the
distribution of resources (e.g., tax rates) which eventually affect
economic agents and their decision making. Differences across states in
the degree of policy and regulation are known to be relevant for
intrinsically nontradeable factors or goods, such as land and housing
(e.g., Ganong and Shoag 2012). Although appealing at the intuitive
level, institutional factors are hard to identify and measure in the
data, especially at the subnational level. Nevertheless, it is often
claimed that the effect of institutional and geographical
characteristics has diluted over time, especially in the role of
resource endowments which has become far less important in production
after 1980 (e.g., Glaeser and Kohlhose 2004).
(19.) Durlauf et al. (2006) list 145 regressors that have been
found to be statistically significant in a number of growth studies
based on conventional standards. Many of them are not relevant for the
analysis of intranational growth. See also Reed (2009. Table 1) for a
long list of variables that were adopted by many previous studies on
U.S. state economic growth.
(20.) This approach is appropriate for our analysis because the
dependent variable, club membership, is ordinal in a couple of senses.
First, the four convergence clubs may have a well-defined ordered
structure because the PS (2007) clustering mechanism is designed to sort
out subgroups in an ordinal manner by its convergence speed. Second, the
identified clubs are roughly in line with the level of output per
worker. States with a relatively high output per capita tend to cluster
to Club 1, while states with a lower output per worker fall into Club 4.
(21). Human capital affects output not only directly as it enters
the production function as an input in growth models, but indirectly as
it contributes to higher technological progress by facilitating
innovation and diffusion of new technologies.
(22.) In their influential work. Bils and Klenow (2000) argue that
the ample correlational evidence between education and economic growth
may represent a reverse causality as higher output growth can lead to
higher levels of education.
(23.) Though COLLEGE is another significant variable, it is not
considered here because the data are available only decennially. For
this reason, we use EDUPROD as a replacement. Asa matter of fact, a
similar problem of data constraint exists in many other variables
identified as being important by the ordered logit model.
(24.) The unexpected negative sign of FINANCE can be explained by
the fact that the dynamic panel techniques look at dynamic, rather than
static, relationship over time. We notice that on average states with a
higher share of finance industry have a higher level of output per
worker, but states with a faster growth in the share of finance industry
do not necessarily experience a faster growth of output per worker.
(25.) Our result also suggests that physical capital has little
explanatory power on the formation of clubs probably due to its
relatively low barriers to mobility (e.g., Gennaioli et al. 2013b;
Tamura 2012).
(26.) The slower TFP growth in Club 1 states relative to those in
Clubs 2 and 3 is somewhat surprising in light of the well-known positive
impact of TFP on output growth. One possible explanation is that the DEA
result is based on data up to 2000, whereas our analysis on convergence
club was conducted using data set covering until 2011. Our DEA analysis
therefore could not account for important changes in the dynamics of
output data occurring in the last 11 years. An alternative explanation
is that in the DEA analysis we measure human capital as average years of
schooling in the labor force for each state. But, it is now widely
agreed that composition of human capital has a vital effect on TFP
growth in the sense that skilled human capital is important for
innovation, while unskilled human capital for imitation. This
composition effect of human capital is not considered in the analysis.
(27.) According to Attanasio et al. (2012), the rise in income
inequality since the 1980s has translated to an increase in actual
well-being inequality by increasing consumption inequality.
CHI-YOUNG CHOI and XIAOJUN WANG *
* The paper has been greatly improved by the constructive comments
and suggestions of Wesley Wilson (editor) and two anonymous referees.
The authors are also grateful to Daniel Allen and Arsalan Nadeem for
research assistance and to Marco Del Negro and Robert Tamura for kindly
sharing their data. We thank Andrew Ching, Yongwan Chun, Paul Evans,
Sumner La Croix, Roger Meiners, Donggyu Sul, Mike Ward, Steve Yamarik,
and Mahmut Yasar for helpful comments and suggestions. Part of the
research was conducted when Choi was visiting the Institute of Economics
at Academia Sinica, Taiwan. Choi gratefully acknowledges the
Institute's support and hospitality during his visit. Any remaining
errors are the authors' own.
Choi: Associate Professor, Department of Economics, University of
Texas at Arlington, Arlington, TX 76019. Phone 1-817-272-3860, Fax
1-817-272-3145, E-mail cychoi@uta.edu
Wang: Associate Professor, Department of Economics, University of
Hawaii at Manoa, Honululu, HI 96822 and CEFMS, Hunan University,
Changsha, Hunan, China. Phone 1-808-956-7721, Fax 1-808-956-4347, E-mail
xiaojun@hawaii.edu
TABLE 1
Descriptive Statistics of Labor Productivity for the
48 States (1963-2011)
Nominal Output per Worker Real Output per Worker
State Average Growth Average Growth
AL 33,634 [41] 4.9 [24] 44,766 [37] 0.6 [34]
AZ 39,735 [17] 4.8 [28] 51,504 [21] 0.9 [17]
AR 33,405 [42] 4.9 [21] 43,862 [41] 0.8 [26]
CA 49,656 [4] 5.1 [13] 64,054 [5] 1.1 [7]
CO 41,696 [14] 5.2 |7] 54,320 [14] 1.1 [6]
CT 52,430 [2] 5.4 [2] 67,207 [2] 1.3 [4]
DE 53,101 [1] 5.4 [1] 72,212 [1] 1.0 [10]
FL 38,538 [24] 5.0 [19] 52,219 [18] 0.7 [31]
GA 39,058 [20] 5.3 [5] 50,634 [23] 1.1 [8]
ID 33,953 [37] 4.6 [40] 43,243 [43] 0.9 [13]
IL 45,218 [9] 4.9 [23] 58,741 [9] 0.9 [14]
IN 38,175 [26] 4.6 [41] 49,956 [24] 0.6 [32]
IA 35,828 [35] 4.6 [39] 45,610 [35] 0.8 [22]
KS 35,852 [34] 4.7 [34] 47,958 [30] 0.6 [33]
KY 36,536 [30] 4.1 [47] 49,493 [27] 0.1 [46]
LA 46,001 [7] 4.8 [29] 64,156 [4] 0.1 [48]
ME 33,073 [43] 5.0 [20] 45,083 [36] 0.7 [30]
MD 39,788 [15] 5.1 [14] 53,703 [15] 0.8 [24]
MA 45,309 [8] 5.4 [3] 57,592 [13] 1.5 [3]
Ml 41,784 [13] 4.1 (48| 58,291 [10] 0.0 [47]
MN 39,530 [18] 4.8 [27] 51,661 [20] 0.8 [21]
MS 31,671 [471 4.7 [36] 42,074 [46] 0.3 [44]
MO 36,909 [28] 4.7 [37] 49,726 [26] 0.6 [37]
MT 31,727 [46] 4.5 [44] 42,640 [44] 0.4 [43]
NE 33,776 [40] 4.8 [31] 43,462 [42] 0.8 [19]
NV 42,822 [12] 4.7 [38] 59,578 [8] 0.5 [40]
NH 38,973 [22] 5.4 [4] 47,734 [31] 1.6 [11]
NJ 48,629 [5] 5.0 [18] 63,614 [6] 0.9 [12]
NM 36,293 [31] 4.3 [45] 44,586 [38] 0.5 [38]
NY 50,584 [3] 5.1 [17] 66,602 [3] 1.0 [11]
NC 37,837 [27] 5.1 [10] 49,485 [28] 0.8 [20]
ND 30,753 [48] 4.8 [30] 39,451 [48] 0.8 [23]
OH 39,103 [19] 4.5 [43] 52,237 [17] 0.4 [42]
OK 35,903 [33] 4.8 [26] 47,594 [33] 0.4 [411
OR 38,836 [23] 5.1 115] 49,885 [25] 1.5 [2]
PA 39,746 [16] 4.9 [22] 52,646 [16] 0.7 [28]
RI 38,981 [211 5.3 [6] 51,365 [22] 1.1 [9]
SC 32,628 [44] 5.2 [8] 42,222 [45] 0.9 [16]
SD 32,336 [45] 5.1 [16] 40,143 [47] 1.2 [5]
TN 36,826 [29] 5.1 [12] 48,567 [29] 0.9 [18]
TX 44,444 [10] 5.1 [111 57,886 [12] 0.7 [29]
UT 34,932 [36] 4.8 [25] 46,142 [34] 0.8 [25]
VT 33,847 [38] 4.7 [33] 44,193 [40] 0.9 [15]
VA 38,320 [25] 5.2 [91] 51,716 [19] 0.7 [27]
WA 44,041 [11] 4.7 [32] 60,235 [7] 0.6 [35]
WV 33,826 [39] 4.3 [46] 44,223 [39] 0.2 [45]
Wl 36,176 [32] 4.5 [42] 47,642 [32] 0.6 [36]
WY 47,244 [6] 4.7 [35] 58,007 [11] 0.5 [39]
Average 39,155 4.9 51.457 0.8
SD 5726 0.33 7786 0.36
CV 0.15 0.07 0.15 0.47
Inflation
State Rate Club
AL 4.3 [11] 3
AZ 3.9 [41] 2
AR 4.1 [19] 3
CA 4.0 [33] 1
CO 4.1 [27] 2
CT 4.1 [25] 1
DE 4.4 [5] 1
FL 4.3 [6] 2
GA 4.2 [13] 2
ID 3.6 [47] 3
IL 4.0 [35] 2
IN 3.9 [39] 2
IA 3.8 [45] 3
KS 4.0 [30] 3
KY 4.1 [23] 3
LA 4.9 [1] 2
ME 4.2 [12] 3
MD 4.3 [10] 2
MA 3.9 [40] 1
Ml 4.0 [29] 2
MN 4.0 [34] 2
MS 4.4 [41 4
MO 4.1 [24] 3
MT 4.1 [22] 4
NE 3.9 [37] 3
NV 4.2 [15] 2
NH 3.7 [46] 2
NJ 4.1 [26] 1
NM 3.8 [43] 3
NY 4.0 [28] 1
NC 4.3 [8] 2
ND 3.9 [36] 4
OH 4.0 [31] 3
OK 4.3 [7] 3
OR 3.5 [48] 2
PA 4.2 [16] 2
RI 4.2 [17] 2
SC 4.3 [9] 2
SD 3.8 [42] 2
TN 4.2 [14] 2
TX 4.4 [3] 2
UT 4.0 [32] 3
VT 3.8 [44] 3
VA 4.4 [2] 2
WA 4.1 [20] 2
WV 4.1 [21] 4
Wl 3.9 [38] 3
WY 4.2 [18] 2
Average 4.1
SD 0.23
CV 0.06
Note: Real output data are constructed using 2000
as the base year. Entries inside the square brackets
denote the ranking among 48 states.
TABLE 2
Log-t Convergence Test and Convergence Clubs
Average
Productivity
Constituent
Log-t Test States Nominal Real
Full -0.545 * ALL 38,158 50,201
sample [48] (0.039)
Club 1 [61 0.312 * CA, CT, DE, MA, 49.952 65.214
(0.081) NJ, NY
Club 2 [23] 0.547 * AZ, CO, FL, GA, 40,111 52,811
(0.092) IL, IN, LA, MD,
MI, MN, NV, NH,
NC, OR, PA, RI,
SC, SD, TN, TX,
VA, WA, WY
Club 3 [15] 0.173 * AL. AR, ID. IA, 35.281 46,373
(0.085) KS, KY, ME, MO,
NE, NM, OH, OK,
UT. VT. WI
Club 4 [4] 0.581 * MS, MT, ND, WV 31.994 42,097
(0.068)
Note: Figures in the parentheses and the square brackets,
respectively, represent standard errors and the number
of states in a group.
* denotes statistical significance at 5% level.
TABLE 3
Ordered Logit Estimation Results
Regressors Model 1 Model 2 Model 3 Model 4
patents -0.02 * -0.03 * -0.02 * -0.02 *
(0.01) (0.01) (0.01) (0.01)
college -0.38 * -0.32 * -0.30 ** -0.33 *
(0.16) (0.14) (0.16) (0.16)
finance -0.90 * -0.87 * -1.17 * -1.56 *
(0.44) (0.44) (0.56) (0.70)
eduprod -0.49 * -0.46 *
(0.20) (0.20)
eduexp 0.01 * 0.01 *
(0.00) (0.00)
diversity -21.12 **
(12.20)
health -0.01 **
(0.01)
migration -0.44 *
(0.16)
inequality -103.83 *
(43.01)
density -2.28 * -2.78 *
(0.72) (0.80)
inflation 4.58 * 3.95 *
(2.04) (1.81)
EFI
fdi/gsp
Log-likelihood -26.14 -26.16 -20.94 -20.21
[chi square]
(d.f.) 65.97 65.94 76.38 77.84
Prob > [chi
square] 0.0000 0.0000 0.0000 0.0000
Pseudo [R.sup.2] .5578 .5575 .6458 .6582
Regressors Model 5 Model 6 Model 7
patents -0.02 * -0.02 * -0.02 *
(0.01) (0.01) (0.01)
college -0.31 * -0.77 * -0.46 *
(0.15) (0.29) (0.21)
finance -2.31 * -1.69 ** -2.07 *
(0.79) (0.80) (0.44)
eduprod
eduexp
diversity
health -0.01 *
(0.00)
migration -0.32 **
(0.18)
inequality -327.57 * -199.76 *
(111.16) (60.25)
density -2.40 * -3.81 *
(0.81) (1.23)
inflation
EFI -3.81 * -2.71 *
(1.31) (1.31)
fdi/gsp -0.59 * -0.65 *
(0.27) (0.22)
Log-likelihood -20.19 -17.52 -16.44
[chi square]
(d.f.) 77.89 78.52 80.70
Prob > [chi
square] 0.0000 0.0000 0.0000
Pseudo [R.sup.2] .6586 .6914 .7105
Notes: See Table A1 for the definitions of each
explanatory variable.
* (**) denotes statistical significance at 5% (10%) level.
Standard errors are reported in parentheses.
TABLE 4
Dynamic Panel Estimation
Regressors DIFF-GMM SYS-GMM
[y.sub.t-1] -0.0993 ([double dagger]) -0.04951 ([double dagger])
(0.0106) (0.0071)
PATENT 0.0005 ([double dagger]) 0.00041 ([double dagger])
(0.0002) (0.0002)
FINANCE -0.77361 ([double dagger]) -0.67811 ([double dagger])
(0.1871) (0.1727)
EDUPROD 0.0010 0.0012
(0.0010) (0.0011)
Sargan test .4235 .3568
(p value)
Regressors RMA
[y.sub.t-1] -0.0077 ([double dagger])
(0.0031)
PATENT 0.00041 ([double dagger])
(0.0002)
FINANCE -0.93651 ([double dagger])
(0.1903)
EDUPROD 0.0005
(0.0010)
Sargan test
(p value)
Note: The regression equation is
[DELTA] [y.sub.it] = [p.summation over (j=1)] [[alpha].sub.j]
[y.sub.i,t-j] + [W.sub.it][gamma] + [v.sub.i] + [[epsilon].sub.it],
where [y.sub.it] denotes output per worker in state i in year t and
[W.sub.it] is a vector of explanatory variables that are treated as
endogenous. The Stata commands, xtabond and xtabond2, are
used for the GMM estimation. Both [y.sub.it]: and [W.sub.it]
are cross-sectionally demeaned to remove unobserved fixed effects.
The Sargan test has the null hypothesis that the instruments used
are not correlated with the residuals.
([double dagger]) denotes statistical significance at 1% level.
Entries in parentheses represent robust standard errors.
TABLE 5
Malmquist Index of TFP Growth and Its
Components by Clubs
TFP Growth Efficiency Technical
Change Progress
Club 1 1.0002 0.9993 1.0009
Club 2 1.0010 1.0007 1.0004
Club 3 1.0012 1.0010 1.0002
Club 4 0.9965 1.0008 0.9958
