Ann Reg Sci (2005) 39:1–20
DOI: 10.1007/s00168-004-0209-6
A prerequisite for meaningful state economic
performance comparisons: adjusting for population
density
H.J. Smoluk1, Bruce Andrews1
1Center for Business and Economic Research, University of Southern Maine, 96 Falmouth Street, Portland, ME 04104-­‐9300, USA (e-­‐mail: [email protected]) Received: May 2003/Accepted: April 2004 Abstract. This paper examines labor productivity across the lower 48 states from 1993 to 2000, a period that coincides considerably with the longest economic expansion, as chronicled by the National Bureau of Economic Research to date. Our results suggest that states with high education levels, high population density, and low tax burden tend to have high labor productivity. Further analysis shows that diơerences in population density ac-­‐ count for the largest share of the diơerences in labor productivity across states. Since population density is not generally considered a policy variable for most states, more meaningful state economic performance comparisons can be made by taking into consideration diơerences in state population densities. These Ƥndings should be of interest to economic development organizations and policy makers because labor productivity is the primary source of wages in the long run. JEL classification: O47, O18, P52 1. Introduction
Long-­‐term economic prosperity, as measured by per capita income, depends largely on labor productivity and its growth rate. Economic policies de-­‐ signed to promote labor productivity growth, if successful, ultimately result in higher wages and higher living standards.1 Per capita income is known to vary markedly from state to state in America, and the source of this dis-­‐ parity is widely considered to be due to diơerences in labor productivity. The goal of this paper is to examine the elements that ‹ƪ—‡…‡ labor productivity among the lower 48 states and provide insight into the variables that support long-­‐term economic prosperity. ’‡…‹Ƥ…ƒlly, we measure the impact on labor productivity of several commonly-­‐known determinants of production (i.e., education level, population density, and state/local taxes) within the Both co-­‐authors are Senior Research Associates in the University of Southern Maine’s Center for Business and Economic Research, Maine’s EDA University Center serving the public and private sectors. 1 See Steindel and Stiroh (2001) for a discussion of the labor productivity growth and its eơect on per capita income growth and, hence, living standards. 1 6 8 0 0 2 0 9
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J. Smoluk and Brace Andrews
context of a production function. Our focus is on private-industry labor
productivity, excluding agriculture and mining, from 1993 to 2000.2 We find
that, while education and density are positively related to labor productivity,
taxes are negatively related.
An important element of this paper is that it examines labor productivity
from 1993 to 2000, a period that significantly overlaps with the longest economic expansion in U.S. history. According to the National Bureau of
Economic Research, the longest U.S. expansion started in March 1991 and
ended in March 2001. Our sample was chosen to start in 1993, a full
21 months after the beginning of this expansion, since it is widely known that
labor productivity decreases during recessions and increases during booms.3
The procyclical nature of labor productivity challenges economic theory because, in a competitive market environment where prices (including wages)
can change freely, firms should be able to adjust to changing supply and
demand conditions leaving output per employee relatively unchanged
throughout the business cycle. Empirical evidence, however, suggests that
firms do have difficulty making these necessary adjustments, especially during
recessions and soon thereafter. Therefore, we exclude the early part of the
economic expansion from our sample to focus on a period when firms are
better able to optimize the utilization of their resources.
There is a substantial body of literature that explores the factors affecting
productivity and the reasons for differences among regional economies. A
wide variety of variables ranging from the number of railroad miles to
industry mix are hypothesized to impact productivity and, at least conceptually, can account for differences in productivity among regional economies.
The goal of this paper is not to find additional variables that influence labor
productivity, but to uniquely integrate within one analysis some of the more
important variables found in existing literature.
The contribution of this paper to the economic literature is threefold. First,
for each variable examined (education, density, and taxes) it provides parameter estimates, often in the form of elasticities, that show the relative impact that
a given percentage change in the variable will have on labor productivity. This is
important to know because it identifies those variables that have greater
influence on labor productivity. Such knowledge has important policy implications for manipulating labor productivity and, ultimately, for a state’s economic health. For example, the results show that a significant variable in
explaining differences in state labor productivity is density. States with a low
population per square mile are predisposed to below average economic prosperity. This implies that less dense states, all else being equal, are less likely to
have success in their policy actions that are designed to ‘‘catch-up’’ with national economic averages than a more densely populated state.4 As the second
2
Private industry for the purposes of this paper includes seven industries at the one-digit SIC
level: manufacturing, construction, retail, wholesale, services, transportation and utilities, and
financial, insurance and real estate.
3
See Baily et al. (1996).
4
We chose a state as our spatial unit of measure for several reasons. First, states have clearly
defined permanent boundaries, unlike the concepts urban vs. rural, which change periodically and
depend on subjective definitions. Second, a state may also be considered a political unit, so that its
economy and labor productivity reflect the political environment of the state. Lastly, since states
are considered political units as well as economic units, policy actions are often implemented at
the state level with the intentions of positively influencing state economic growth.
Adjusting for population density
168/0209/3
contribution, this paper demonstrates that diagnosing the relative economic
health of a state’s economy can be performed using wage data. Labor productivity is closely associated with wages since labor productivity measures the
value of output of goods and services produced per employee. The more productive an employee, the more valuable the individual is to an employer, and the
employee’s wages should reflect the value of his or her output. Since wages make
up a significant portion of personal income, a commonly-used measure of
economic well-being, low labor productivity is likely to be associated with low
living standards. Lastly, this paper shows that differences in state population
density are one of the largest drivers of differences in labor productivity among
states. Since population density is generally not considered a economic policy
variable for states, the paper demonstrates that by adjusting a state’s labor
productivity for density, more meaningful state comparisons of economic
performance can be made.
Population density may be considered a proxy for the degree of external
agglomeration economies in a state. The literature on agglomeration economies details the sources for the reduction in production costs that are often
associated with increased labor productivity. According to Alonso-Villar
(2002), reduced production costs are found in spatially dense areas with many
independent firms spanning a variety industries, as well as, many independent
firms concentrating in a particular industry. Using a general equilibrium
model, they find that firms located in large industry-diverse cities can experience knowledge spillovers and lower production costs. Parr (2004), on the
other hand, discusses external agglomeration economies that reflect the
advantages of shared inputs, such as labor and technology. Such advantages
can be obtained by independent firms in specialized industries and/or unrelated industries that merge spatially. These papers, as well as other agglomeration studies, support the idea that labor productivity is higher in more
densely populated areas.
The remainder of this paper is organized in four sections. Section 2 provides a literature review of labor productivity and the variables that influence
it. Section 3 describes the production function and the data employed in this
paper, and Sect. 4 discusses the empirical findings. Section V decomposes
differences in state labor productivity into its various components, including
population density, and illustrates how more meaningful economic comparisons can be made across states. Lastly, Sect. 6 concludes the paper.
2. Literature review
The United States serves as an excellent subject for state labor productivity
analysis due to its sizable number of states, common monetary system and
federal government, and significant across-state variation. This has given rise
to a large body of literature on state labor productivity and the many variables that influence it. The literature review that follows focuses on studies
that employ commonly-known determinants of production.
The findings presented in this paper update and enhance those of
Carlino and Voith (1992). Carlino and Voith consider differences in state
labor productivity by examining education, population density, public
infrastructure density, unionized labor, while controlling for industry mix.
168/0209/4
J. Smoluk and Brace Andrews
They bypass the lack of state private capital stock data by using a constant elasticity of substitution (CES) production function that assumes that
labor is paid according to its productivity. When labor is paid according
to its productivity, wage data that are produced by the Bureau of Labor
Statistics can be substituted in place of labor productivity data.5 Population density is measured as the percentage of a state’s population in
urbanized areas. While they bypass the problem of lack of private capital
stock data by state, they nevertheless use federal-aid highway miles (a
component of public capital stock) per square mile of state by arguing that
highway density contributes to increases in labor productivity like any
other factor of production available to workers. Their sample period is
1963–1986, and their results indicate that education, percentage of
urbanized population, and public infrastructure, among other variables,
have a statistically significant positive influence in explaining differences in
labor productivity across states.
While Carlino and Voith’s work shows how education, highway density,
population, and other variables account for differences in labor productivity
across states, there are some intriguing, yet unexplored, questions that need to
be addressed. For example, they do not consider differences in state and local
tax burden as a factor in explaining differences in labor productivity across
states. Tax burdens from state to state vary dramatically and influence not
only individuals’ incentives to work, but also business’s desire to locate in a
state.6 Furthermore, their sample period spans several business cycles,
including several severe recessions, oil price shocks, extraordinarily high
interest rates, and high inflation. These are awkward times for firms that are
often associated with negative or slow economic growth. Firms’ reactions to
recessions, especially in terms of labor productivity, are puzzling to economists, as Baily et al. (1996) point out.
The idea that high density states experience economies of scale is examined
extensively by Ciccone and Hall (1996). They suggest that increased density
results in positive externalities by promoting a greater variety of intermediate
products that enhance the productivity of final goods and services. This is
supported by the observation that large cities pay higher wages than less
densely-populated areas. Ciccone and Hall estimate county density and
aggregate it to a state level while controlling for differences in county-level
education and state-level public capital.
An interesting aspect of their paper surrounds the question of equilibrium.
If higher wages are found in high density areas, then why does a substantial
portion of individuals live outside of metropolitan areas? Ciccone and Hall
offer two explanations. First, some individuals prefer less dense areas and are
willing to accept a lower salary to avoid some of the negative externalities
associated with cities. Second, real estate prices are substantially lower in less
dense areas, partially offsetting lower wages.
Ciccone and Hall find that density accounts for more than one
half (R2>0.50) of the differences in average labor productivity across
states and that doubling employment density results in a 6% increase in
average labor productivity. While their paper also examines the role of
5
6
Labor productivity data by state are generally not available.
See, for example, Mullen and Williams (1994).
Adjusting for population density
168/0209/5
education in labor productivity, other factors such as tax burden are not
addressed.
The link between education and economic growth is explored in Krueger
and Lindahl (2001). While some researchers, such as Topel (1999), claim that
the effect that education has on economic growth is so large that it is difficult
to misinterpret, the arguments set forth in Krueger and Lindhal suggest
otherwise. While the main focus in Krueger and Lindahl is on education
growth differences across countries, they bring forward two important issues
that are also relevant to state-by-state comparisons within the United States.
First, substantial measurement error in education makes analyzing the effects
that changes in education have on subsequent economic growth difficult to
assess. Since the education level in countries can be dramatically different, the
relationship between average level of schooling and economic growth is more
reliable. Second, there is an unresolved question of causality in the link between changes in education and economic growth. Increases in economic
growth through technological advances may cause the return on the investment in education to increase dramatically, thereby driving the increase in
education. Thus, the extent to which high growth in education in a particular
state drives labor productivity growth in that state is a knotty issue.
Bils and Klenow (1998) investigate the causal link between economic
growth and education. They develop several empirical tests that consider the
return on education by examining variables that reflect the opportunity cost
of schooling such as life span, discount rates, and lost wages while in school.
Work experience, the quality of schooling, and higher wages are among some
of the other variables Bils and Klenow consider. They conclude that economic growth drives the return on schooling, rather than ‘‘the other way
around’’. The work of both Krueger and Lindahl (2001) and Bils and Klenow
(1998) suggest that the indiscriminate use of changes in education in growth
research is perilous, while the use of the level of education is more reliable.
There is a voluminous literature addressing the effects that taxes have on
labor productivity and wages. A significant body of empirical literature,
spanning either across-country or across-state comparisons, finds that higher
marginal tax rates lead to reduced pre-tax real wages.7 Many researchers
suggest that higher marginal tax rates tend to reduce labor productivity
through reduced work effort. More specifically, high marginal tax rates
diminish the reward to work and induce a substitution effect toward leisure.
Sorenson (1999) addresses these issues, including the complex issue of
changing tax progressivity relative to average tax rates, in determining an
optimal tax structure in light of labor productivity.
Mullen and Williams (1994) examine state economic growth and its
relationship to both marginal tax rates and average tax rates. The average
tax rate is defined as total state and local taxes collected as a percentage of
total gross state product (GSP). They estimate the impact of these tax
rates on total (all sectors, including government) GSP growth and productivity growth, net of the effects of capital and labor growth. Interestingly, they find that marginal tax rates are negatively related to growth in
total GSP and productivity growth, yet average tax rates were positively
7
See, for example, Tyrvainen (1995), Aronsson and Brannland (1997), Mullen and Williams
(1994). These papers find that either wages or economic growth are negatively affected by higher
marginal tax rates.
168/0209/6
J. Smoluk and Brace Andrews
related. The authors, however, caution against putting too much weight on
the average tax rate estimates since they are using total GSP (including
government) and total productivity growth. High average tax rates are
likely to result in high government expenditures tainting the analysis.
The puzzling procyclical nature of labor productivity is addressed by Baily
et al. (1996). In their analysis, they examine a number of hypotheses found in
the literature that support procyclical labor productivity. We focus on the
hypotheses that relate to the awkwardness that firms in aggregate may face
during recessions and use this reasoning as support for our examination of
labor productivity over an economic boom, rather than the entire business
cycle. There are four hypotheses supporting procyclical labor productivity :
1) labor hoarding, 2) large adjustment costs, 3) measurement error, and
4) increasing returns to scale. Labor hoarding, the first hypothesis, results
when firms retain more employees than needed during a perceived temporary
economic slowdown. Employees represent human capital and to the extent
that this human capital takes time to develop, particularly in specialized
industries, firms are reluctant to let go of employees. Furthermore, in competitive markets, workers may be lost to industry competitors making
rehiring difficult. If the adjustment costs associated with downsizing an
organization during a recession are too high, firms will retain employees
according to the second hypothesis. The measurement error, the third
hypothesis, states that during recessionary periods, when production slows,
labor hours are redirected towards maintenance of facilities, equipment, and
human capital. The shift in maintenance costs to recessionary periods,
without a corresponding increase in output, gives an illusion of low productivity. Labor productivity, however, actually remains high during these
periods, but the use of gross state product (output) to measure labor productivity results in a measurement error. Lastly, according to the fourth
hypothesis, firms that have attained increasing returns to scale will naturally
see a reduction in labor productivity as output shrinks during a recession.
3. The Production function and data
In this section, we describe the constant elasticity of substitution (CES)
production function with the ambition of performing a cross-sectional analysis using state data. In Subsect 3.1. A, we review the production function,
and, in Subsecti 3.2, we define the variables.
3.1 Production Function
Based on the our literature review, we employ the following CES production
function for state i during time t:8
8
This production function was developed by Arrow et al. (1961). The CES can be applied using
time series or cross-sectional data. The CES is often employed within a time series framework
where the elasticity of substitution between labor and capital (% change in labor to capital
divided by the % change in the technical rate of substitution between labor and capital, keeping
output fixed) is constant through time. With cross-sectional data by state, the function may be
more appropriately titled ‘‘equal elasticity of substitution’’ since it implies an equal elasticity of
substitution across states. Regardless of its title, this production function is more flexible than the
Cobb-Douglas production function, which assumes that the elasticity of substitution is constant
(or equal across states) and constrained to equal one.
Adjusting for population density
h
i"ðd=qÞ
"q
Qi;t ¼ Ai aL"q
i;t þ ð1 " aÞKi;t
168/0209/7
ð1Þ
The term Qi,t represents real GSP for state i during time t, Ai is a neutral
technical progress parameter for state i, Li,t is the number of state i employees
(labor) at time t, Ki,t is the amount of state i’s capital available to workers at
time t, a is the distribution parameter that determines the relative importance
of labor and capital, e is the returns to scale parameter, q is the substitution
parameter that determines the elasticity of substitution between labor and
capital.
By taking its first partial derivative with respect to labor, we arrive at a
wage equation that excludes capital (subscripts are removed for notational
simplicity),
@Q
¼ aeL"ð1þqÞ A½aL"q þ ð1 " aÞK "q '"ðe=qÞ"1
@L
We can rewrite Eq. 2a as
ð2aÞ
@Q
¼ aeL"ð1þqÞ A"ðe=qÞ A"ð1þq=eÞ ½aL"q þ ð1 " aÞK "q '"ðe=qÞ"ðeq=qeÞ
@L
Then, by regrouping terms, Eq. 2b can be reduced to
ð2bÞ
@Q
¼ aeL"ð1þqÞ A"ðe=qÞ Q"ð1þq=eÞ
ð2cÞ
@L
The term Q/L represents the marginal product of labor, and since marginal
wages are not available at the state level, we use average wages, W. 9 The term
A incorporates the variables hypothesized to impact labor productivity and is
particular to a state: education, density, and tax burden. The specification for
A is
!
"
ð3Þ
A ¼ EDa DEN b TAX "c :
Substituting (3) into (2c) and taking the natural log of both sides results in
aq
lnðW Þ ¼ lnðaÞ þ lnðeÞ " ðl þ qÞ lnðLÞ " ED
e
ð4Þ
#
bq
Cq
q$
" DEN þ
TAX þ 1 þ
lnðQÞ:
e
e
e
Equation (4) is easily transformed into a OLS equation of the form
lnðW Þ ¼ b0 þ b1 lnðLÞ þ b2 lnðEDÞ þ b3 lnðDEN Þ
þ b4 lnðTAX Þ þ b5 lnðQÞ þ e
ð5Þ
The parameters of interest in (5) are defined as follows,
b1 ¼ "ð1 þ qÞ; b2 ¼ "aq=!; b3 ¼ "b=rho=e; b4 ¼ cq=e; b5 ¼ ð1 þ q=eÞ. From
9
The substitution of wages for marginal product of labor, is also done in Carlino and Voith
(1992). They also use the CES production function in their analysis. The marginal product of
labor, however, should be proxied with wages plus other labor income. Other labor income
includes contributions by employers for pension and health-benefit plans. Other labor income is
estimated at the federal level and then proportionately allocated to the states based on non-farm
private industry wages, since the state data on other labor income are not available from the
sources used to prepare the national estimates. Thus, the other labor income account prepared by
the Bureau of Economic Analysis does not provide any additional information beyond the wages
account. Wages represent approximately 90 % of total non-farm private labor income.
168/0209/8
J. Smoluk and Brace Andrews
the OLS parameter estimates, we will be able to solve for the production
function parameters a; e; q, a, b, c and the elasticity of substitution,
r ¼ 1=ð1 þ qÞ. The elasticity of substitution coefficient can range from zero to
positive infinity. An estimate between zero and one would imply that labor
and capital are complements in the production process, while an infinite
estimate would indicate that labor and capital are perfect substitutes. Estimates greater than, but close to 1.0, indicate that labor and capital are not
very substitutable. A priori, q is negative but greater than "1.0, e is greater
than 1.0 implying increasing returns to scale for a state, a and b (and hence, b2
and b3 ) are positive since education and density should be positively correlated to labor productivity, and c (and, hence, b4 ) is negative as a higher tax
burden is likely to reduce labor productivity.
3.2 Defining the variables10
The term W in (5) is defined as a state’s average annual real wages for private
industry for 1993 to 2000.11 L is the average number of state private industry
employees over the sample period. DEN represents the average annual state
density and is proxied using two different variables to check the robustness of
our model. The first definition of density is average annual total state population per square mile, which captures the overall density of a state. States
with more population per square mile are likely to realize reduced transportation costs, deeper and more specialized product markets, and more
specialized employees.12 The second measure of state density is the average
annual urban population per square mile. This measure of density complements the first, by taking into consideration states that may be largely
unpopulated except for a few highly urbanized areas. The bulk of the a state’s
output, in such a case, may reflect economies of urbanization. ED represents
human capital and is proxied by the average annual percentage of the state’s
population with a bachelor’s degree or higher. The term Q represents average
annual real private-industry GSP. The term TAX represents average annual
total state and local tax burden on the state’s private sector.13 The tax burden,
a priori, is a negative factor in the production process. The state tax burden is
10
Refer to Appendix A: Data Sources for data details.
As is common in the state productivity literature, mining and agriculture are excluded from the
sample. See, for example, Ciccone and Hall (1996) and Carlino and Voith (1992).
12
As mentioned in Ciccone and Hall (1996), a higher degree of specialization is possible in more
dense areas. More dense areas are associated with an increase in the variety of intermediate goods
locally available making the production of final goods more economical. Belleflamme, Picard,
and Thisse (2000) discuss how higher production localization results not only in lower
transportation costs, but also tough price competition that can be relaxed through product
differentiation. Rosenthal and Strange (2001) show how spatial concentration (density) relates to
labor market pooling, higher productivity, and knowledge spillovers. Each of these papers
suggest that highly dense areas can support highly specialized labor. Highly specialized labor
generally commands a higher wage and, thus, are considered to exhibit higher labor productivity.
13
These amounts exclude federal government transfers to states.
11
Adjusting for population density
168/0209/9
estimated three ways to check the robustness of our model with respect to
taxes.14 First, we use average annual total state and local tax collections as a
percentage of total private GSP.15 Second, following Mullen and Williams
(1994), we compute (average) marginal tax rates for each state by regressing
state and local tax collections onto private GSP for the years 1993 to 2000.
That is,
ð6Þ
Tax Collection st ¼ a0 GSPt þ et :
The slope coefficient represents the (average) marginal tax rate for the period.16 Third, we use state and local GSP as a percentage of total private
GSP.17
Our goal here is to estimate (5) empirically to account for differences in
state labor productivity using wages on the left-hand side of the regression.
There are two important issues that must also be addressed. First, since labor
unions are likely to drive a wedge between wages and labor productivity, we
account for this effect using a union variable (U), the percentage of employees
in a state who are members of unions. Second, labor productivity varies from
sector to sector in the economy, as do wages, so that differences in state
industry mix must be accounted for in the estimation process. Consequently,
we add to (5) two variables that capture differences across states yielding the
following regression equation:
lnðW Þ ¼ b0 þ b1 lnðLÞ þ b2 lnðEDÞ þ b3 lnðDEN Þ þ b4 lnðTAX Þ
þ b5 lnðQÞ þ b6 U þ b7 MIX þ e
ð7Þ
State i’s industry mix, MIXi, is computed as the sum of each industry j labor
productivity in a state, LPij, times the difference between the proportion of
employees in the state’s industry, Lij/Li, and the proportion of the nation’s
employees in industry j for the nation, Lnj/Ln.18 That is,
"
%
&#
7
X
Lij Lnj
LPij
"
MIXi ¼
:
ð8Þ
Li
Ln
j¼1
For each state, Table 1 shows the variables most central to our discussion,
sorted by wages.
14
The economics literature uses a variety of measures to estimate the impact that taxes have on
an economy, depending on the form of the analysis and the type of taxes examined. See Mullens
and Williams (1994) for a discussion on this subject in terms of measuring total tax burden.
15
This definition is consistent with Mullens and Williams (1994), except that we use private sector
GSP, while they use total (all sectors, including government) GSP.
16
Mullen and Williams (1994) employ an intercept in their regressions, while we do not. We
computed the marginal tax rates with an intercept and found extreme variation in marginal tax
rates across states as Mullen and Williams point out. The rates computed were often well above
or below the other tax rates we used in this paper and were not deemed reasonable.
17
We actually estimated tax burden a fourth way, and obtained nearly the same results as shown
in Tables 2 and 4. We computed average annual state and local GSP per capita to across-state
average annual per capita private GSP. This derivation of tax burden takes into consideration the
fact that if state GSP is high, for example, it may reduce the tax burden variable (since it is the
denominator of the fraction) and cause a negative relationship with wages, the dependent
variable. By using a constant across-state average per capita GSP for each state in the
denominator, we effectively eliminate any spurious relationship that might exist.
18
Keep in mind that when summing labor productivity over industries for a state, each industry’s
labor productivity is implicitly weighted by the percentage of employees in that industry.
168/0209/10
J. Smoluk and Brace Andrews
4. Empirical results
Equation (7) is estimated using OLS, and the results are shown in Table 2.
All of the parameter estimates are significant at the 5% level, much like
the OLS estimates in Carlino and Voith (1992). Heteroskedasticity-consistent standard errors are in parenthesis. All of the R2s are around 0.94
indicating that we have accounted for approximately 94% of the variation
in the differences in labor productivity among the lower 48 states.19
Interestingly, since we are using wages as a proxy for labor productivity,
the union variable is positive and significant at the 5% level. Differences in
industry mix also appear to play a statistically significant role in
accounting for differences in labor productivity across states. Overall, the
results in Table 2 are robust and very consistent under all six combinations
of density and tax burden definitions. Given that the most important
independent variables and the dependent variable are in natural log form,
the coefficient estimates are elasticities, which are readily interpreted. For
example, the education coefficient estimate of 0.1280 in the first column
indicates that a one% increase in the proportion of individuals in a state
that have a bachelor’s degree or higher, translates (on average) into a
0.1280% increase in labor productivity for a state. On a state level, this
represents the return on an investment in education. An interpretation of
the population per square mile density coefficient estimate of 0.0212 in
column 1 of Table 2 is that for every one percent increase in the population per square mile, productivity increases by 0.0212%. The tax burden
coefficient estimate of "0.1734 in column 1 implies that a one percent
increase in the proportion of state and local tax collections relative to
private state GSP translates (on average) into a decrease of 0.1734% in
labor productivity.
The bottom of Table 2 provides some diagnostics in terms of the production function used. The estimates for the substitution parameter, q, are
negative and greater than 1.0, and the estimates for the economies of scale
parameter, e, indicate increasing returns to scale since they are greater than
1.0. Intuitively, this makes sense and is consistent with underpinnings of the
model. States that expand their inputs in the production process, and likely
increase their density, are expected on average to see an even greater proportional increase in output. The elasticity of substitution estimates are between 2.4372 and 2.5307 and are consistent with estimates by Willman (2002)
who also employs a CES production function, but with Euro area data. In
addition, the parameter estimates for a, b, and c are of the correct sign. In
each case, the regression residuals are well behaved. The p-values associated
with the Kolmogorov-Smirnov test, under the null hypothesis of normality,
are all relatively high.
19
For comparative purposes, the R2’s are slightly higher than Carlino and Voith’s (1992)
estimates which range from 0.779 to 0.898. In addition, Carlino and Voith’s OLS parameter
estimates for ln L and ln Q, which are "0.42 and 0.43 respectively, are very close to our estimates.
The big difference between our model and theirs is that they control for industry mix using a
separate variable for each private industry sector in their model, rather than our one mix variable,
making the number of variables on the right-hand side of Carlino’s and Voith’s regression 18.
Further, Carlino and Voith do not consider differences in tax burden across states.
Real
wages $
35,035
34,804
34,106
32,581
30,996
30,729
30,544
28,911
27,843
27,244
27,171
27,036
26,979
26,691
26,657
25,706
25,694
25,681
25,596
25,556
25,321
25,191
25,070
24,398
24,368
24,297
24,279
24,062
State
New York
Connecticut
New Jersey
Massachusetts
Michigan
Delaware
Illinois
California
Washington
Minnesota
Pennsylvania
Maryland
Georgia
Ohio
Virginia
Indiana
Nevada
Texas
Colorado
New Hampshire
Rhode Island
Missouri
Wisconsin
Arizona
North Carolina
Tennessee
Oregon
Florida
26.18
30.86
28.93
31.66
20.93
24.28
24.78
26.15
27.06
28.11
21.78
30.25
22.29
21.80
28.29
16.70
18.86
22.60
32.33
27.11
25.44
22.79
22.20
21.50
21.51
17.76
24.90
21.49
Education
%
395.89
691.36
1,103.73
791.60
171.82
381.95
218.33
207.95
84.34
59.54
272.57
525.68
131.22
274.69
171.61
165.12
15.63
74.69
38.29
131.88
982.79
79.07
96.44
40.85
155.43
131.99
33.98
278.26
Density:
population
sq.mile
Table 1. Average production factors sorted by real wages 1993–2000
333.73
546.87
986.73
667.32
121.13
278.83
184.71
192.56
64.44
41.62
187.80
427.38
82.93
203.54
119.10
107.16
13.80
59.98
31.55
67.26
845.20
54.32
63.36
35.75
78.34
80.38
23.95
235.96
Density:
urban pop.
sq. mile
19.39
13.72
15.38
13.88
16.91
13.36
13.89
16.59
18.85
18.41
16.20
15.69
13.72
17.45
13.92
14.02
14.57
13.44
14.58
12.68
16.65
13.84
19.30
15.60
14.68
14.84
17.92
17.14
Tax burden:
tax collections
GSP %
19.70
13.95
15.67
14.20
17.19
13.62
14.11
17.06
19.27
18.85
16.44
16.00
14.07
17.66
14.30
14.22
15.08
13.80
15.01
12.99
17.06
14.10
19.66
16.01
15.19
15.07
18.30
17.55
Marginal
tax rate %
8.96
7.06
8.40
7.59
9.23
6.80
7.68
8.52
9.59
8.54
7.82
8.64
8.03
8.69
8.22
8.02
7.83
8.30
8.42
6.91
8.49
7.92
9.12
9.05
8.74
7.97
9.51
9.29
Tax burden state &
local GSP/GSP %
5.23
8.76
"5.03
"4.62
2.89
14.62
7.74
"1.83
"1.80
4.31
0.01
"11.17
3.27
2.88
"5.45
6.16
"19.16
"1.09
"2.28
"5.03
"3.27
2.20
7.28
"4.24
6.32
4.29
"0.91
"11.60
Industry
mix
Adjusting for population density
168/0209/11
Real
wages $
23,186
23,140
23,101
22,882
22,777
22,015
21,964
21,776
21,050
20,989
20,870
20,569
20,406
20,251
20,147
19,950
18,476
18,126
17,186
16,807
24,754
State
Alabama
Kansas
Kentucky
South Carolina
Louisiana
Utah
Nebraska
Iowa
Vermont
West Virginia
Maine
Arkansas
Mississippi
Oklahoma
Idaho
New Mexico
North Dakota
South Dakota
Wyoming
Montana
Average
Table 1. Continued
18.40
26.11
18.60
18.93
19.20
25.46
21.83
20.99
27.01
14.34
21.13
15.44
18.76
20.90
20.48
22.91
21.04
21.20
20.69
23.39
23.06
Education
%
85.62
32.11
99.02
127.41
101.10
25.37
21.78
51.63
64.27
75.47
40.65
49.49
58.82
48.88
14.64
14.41
9.36
9.77
5.01
6.06
180.16
Density:
population
sq.mile
51.71
22.19
51.29
69.57
68.85
22.07
14.40
31.29
20.70
27.25
18.13
26.48
27.71
33.09
8.40
10.52
4.99
4.88
3.26
3.18
138.66
Density:
urban op.
Sq. mile
16.01
15.44
15.42
16.63
15.02
17.32
17.79
15.93
16.33
18.36
17.79
15.19
17.01
16.56
16.63
17.25
17.56
14.17
17.01
18.85
16.02
Tax Burden:
tax collections
GSP %
9.13
15.64
15.72
16.94
15.27
17.84
18.02
16.08
16.61
18.52
18.17
15.48
17.28
16.85
17.09
17.56
17.81
14.44
17.38
19.05
16.19
Marginal
tax rate %
12.80
9.81
8.76
10.61
9.16
10.03
10.24
9.64
9.36
10.97
9.90
8.98
10.38
10.21
9.63
10.91
9.27
8.27
9.82
10.54
8.95
Tax burden state &
local GSP/GSP %
3.50
"0.15
"0.91
1.87
"9.03
"0.11
0.13
1.28
"8.86
"11.17
"8.76
6.16
4.31
"6.39
"4.75
"18.43
"12.18
"4.21
"13.91
"17.27
"1.88
Industry
mix
168/0209/12
J. Smoluk and Brace Andrews
1.0670
"0.5968
0.2476
0.0476
"0.3140
2.4734
4.6714**
"0.4032**
0.1385**
0.0266**
"0.1756**
0.4407**
0.0070**
0.3309**
0.9380
0.999
Marginal
Tax Rate
(0.0000)
(0.0000)
(0.0001)
(0.0051)
(0.0180)
(0.0000)
(0.0002)
(0.0004)
1.0676
"0.5957
0.2238
0.0475
"0.2875
2.4734
4.5817** (0.0000)
"0.4043** (0.0000)
0.1249** (0.0012)
0.0265** (0.0084)
"0.1604** (0.0306)
0.4420** (0.0000)
0.0054** (0.0001)
0.3114** (0.0022)
0.9369
0.980
State & Local
GSP as a % of GSP
1.0608
"0.6103
0.2314
0.0473
"0.2955
2.5661
4.8908** (0.0000)
"0.3897** (0.0003)
0.1331** (0.0002)
0.0272** (0.0083)
"0.1700** (0.0224)
0.4247** (0.0000)
0.0068** (0.0002)
0.3460** (0.0003)
0.9367
0.981
Tax Collections
as % of GSP
1.0606
"0.6124
0.2260
0.0469
"0.3057
2.5727
4.9391** (0.0000)
"0.3876** (0.0003)
0.1305** (0.0003)
0.0271** (0.0080)
"0.1765** (0.0153)
0.4226** (0.0000)
0.0069** (0.0001)
0.34413** (0.0002)
0.9374
0.981
Marginal
Tax Rate
Density: Urban Population Per Square Mile
1.0613
"0.6113
0.2028
0.0469
"0.2800
2.5800
4.8477** (0.0000)
"0.3887** (0.0003)
0.1168** (0.0026)
0.0270** (0.0128)
"0.1613** (0.0258)
0.4240** (0.0000)
0.0053** (0.0001)
0.3245** (0.0014)
0.9362
0.970
State & Local
GSP as a % of GSP
**
Significant at the 5 % level.
Regression estimate p-values (in parentheses) are based on White (1980) heteroskedasticity-consistent standard errors. Also presented are the p-values for the
Kolmogorov-Smirnov goodness-of-fit test of normality of the regression residuals.
1.0674
"0.5942
0.2536
0.0479
"0.3027
2.4643
4.6166**
"0.4058**
0.1412**
0.0268**
"0.1685**
0.4433**
0.0069**
0.3330**
0.9372
0.965
Constant
Labor, l
Education, ed
Density, den
TaxBurden, tax
GSP,q
Union,U
IndustryMix, MIX
Adjuste R2
KolmogorovSmirnov p-value
e
q
a
b
c
Elasticity of
Substitution
(0.0000)
(0.0000)
(0.0001)
(0.0055)
(0.0268)
(0.0000)
(0.0002)
(0.0004)
Tax Collections
as % of GSP
Regression
Term
Density:Population Per Square Mile
Table 2. Regression estimates of state labor productivity function dependent variable: Log realwages1993–2000
Adjusting for population density
168/0209/13
168/0209/14
J. Smoluk and Brace Andrews
The above empirical results were based on time averaged data.20 As a
result, the dynamic aspects of labor productivity are not captured. Since our
data are both time series and cross sectional, we employ panel data regression
analysis, to check the robustness of our conclusions above. There are two
commonly-employed panel data methods, fixed effects or random effects. In
many cases, there is a large degree of subjectivity as to which method is more
appropriate in a given situation, so we report results under both methods.21
The first four columns of numbers in Table 3 show our estimates. These
parameter estimates, p-values, and adjusted R2s are not very different than
Table 2. The production function estimates at the bottom of the table are
plausible and show a higher degree of economies of scale and lower degree of
elasticity of substitution.
The standard errors associated with the parameter estimates in the first
four columns of Table 3, however, may reflect autocorrelation, heteroskedasity, and spatial dependence. Spatial dependence, in this study, reflects the
correlation among the states (panels) due to macroeconomic influences.
Following Driscoll and Kraay (1998), we estimate the model using a heteroskedasticity, autocorrelation, and spatially-dependent consistent covariance
matrix. According to Driscoll and Kraay, the finite sample performance of
this matrix, even for panels with short time dimensions, dominates methods
that do not consider spatial correlation. The last two columns of Table 3
present these results using instrumental variables estimation. Again, the
p-values indicate that each of the coefficients is statistically significant at the
5% level.
5. Making state economic performance comparisons more meaningful
Many states compare their economic performance, using variables such as
labor productivity or wages, to a select set of other states and also to the
national (state) average for benchmarking purposes. The results shown
above, however, indicate that a significant difference in economic performance is due to differences in density, a factor, which for the most part, is not
an economic policy variable. An interesting application of our findings is to
decompose the differences in state labor productivity into their education,
density, tax burden, union participation, and industry mix components. This
analysis allows us to attach a dollar amount to each component when making
comparisons across states.22 Furthermore, since population density is generally not considered an economic policy variable, meaningful state-by-state
comparisons should be adjusted for density differences.
20
The only exception is the union participation variable, which is a 1996 point estimate for each
state from the U.S. Census Bureau.
21
See Hsiao (1986), Chapt. 3.
22
Our estimates in this section are based on comparisons of fitted values for each state’s labor
productivity equation based on all the independent variables for that state relative to each state’s
fitted equation which systematically substitutes the national average for each state’s time
averaged independent variable. The regressions and equations exclude both the GSP and L
independent variables, thereby allowing us to assign differences to only education, density, tax
burden, union participation, and industry mix. Implicit in our analysis is that differences in
capital employed between states do not account for differences in state labor productivity. See
Appendix B for details.
"0.5710**
0.1002**
0.0219**
"0.0660**
0.6716**
0.1052**
0.9392
1.4290
"0.3063
"0.3051
"0.0667
"0.0928
1.7513
(0.0000)
(0.0000)
(0.0000)
(0.0009)
(0.0000)
(0.0000)
Tax Collections as
% of GSP
"0.5637**
0.0977**
0.0229**
"0.0709**
0.6682**
0.1032**
0.9400
1.3150
"0.4364
0.2945
0.0690
"0.1050
1.7742
(0.0000)
(0.0000)
(0.0000)
(0.0001)
(0.0000)
(0.0000)
State & Local GSP
as a % ofGSP
1.6056**
"0.5818**
0.0998**
0.0212**
"0.0636**
0.6798**
0.1063**
0.9402
1.3061
"0.4182
0.3117
0.0661
"0.0853
1.7188
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.0011)
(0.0000)
(0.0000)
Tax Collections
as % of GSP
Random Effects
1.6245** (0.0000)
"0.5740** (0.0000)
0.0973** (0.0000)
0.0221** (0.0000)
"0.0701** (0.0001)
0.6775** (0.0000)
0.1044** (0.0000)
0.9409
1.3209
"0.4260
0.3018
0.0685
0.0990
1.7422
State & Local GSP
as a % of GSP
"0.6734**
0.0913**
0.0109**
"0.1100**
0.8169**
0.1140**
0.9311
1.7839
"0.3266
0.4985
0.0594
"0.0721
1.4851
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.0000)
Tax Collections
as % of GSP
"0.6678**
0.0850**
0.0120**
"0.1183**
0.8179**
0.1112**
0.9317
1.8247
"0.3323
0.4666
0.0660
"0.0842
1.4976
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.0000)
State & Local GSP
as a % of GSP
Spatially-Dependent
**
Significant at the 5% level.
Regression estimate p"values are in parentheses.
Under the spatially"dependent columns, various lag lengths were employed to capture autocorrelation and the results of each assumption did not change our
conclusions. The above results reflect 3 lags.
Constant
Labor, l
Education, ed
Density, den
Tax Burden, tax
GSP, q
Industry Mix, MIX
Adjusted R2
e
q
a
b
c
Elasticityof
substitution
Regression Term
Fixed Effects
Table 3. Panel Regression Estimates of State Labor Productivity Function Dependent Variable: Log Real Wages 1993–2000
Adjusting for population density
168/0209/15
168/0209/16
J. Smoluk and Brace Andrews
Table 4 accounts for differences in total individual state labor productivity to
the average state labor productivity as well as each of its components. Interpreting Table 4 is best done using an example. According to Table 1, the state
of Maine relative to national averages is characterized by slightly below
average education, low population density, high tax burden, and hence low
labor productivity.23 Table 4 shows that the total difference between Maine’s
labor productivity and the average state is "$3,737. On a per capita basis,
Maine produced $3,737 less goods and services per year on average during the
period 1993 to 2000 than the average state. Approximately "$432 is due to
Maine’s below state average education, "$2,121 to low density, "$661 to high
tax burden, $441 to lower than average union participation, and "$964 to a
less productive industry mix. Since density is not considered by most states to
be an economic policy variable, state economic performance comparisons of
Maine’s labor productivity to the national average need to be adjusted for by
the population density difference variable of $"2,121, or 56.8% of the
shortfall. This suggests that Maine lags the national average in terms of labor
productivity by $3,737"$2,121 = $1,616 rather than $3,737. This suggests a
difference, relative to the national average, of 6.5%, not 15.1%.
Direct comparisons between two states can also be examined using a
similar analysis. For instance, Maine’s labor productivity lags Massachusetts’
productivity by approximately $8,676. Further analysis shows that over half
(51.1%) of the difference is due to Maine’s low population density, which
cannot be easily changed. Specifically, "$2,102 is associated with Maine’s
lower education level, "$4,435 with Maine’s lower density, "$1,586 with
Maine’s higher tax burden, "$101 with Maine’s higher union participation,
and "$452 with Maine’s less productive industry mix.
6. Conclusion
This paper examines labor productivity in the lower 48 states from 1993 to
2000, a period that substantially coincides with the longest economic
expansion in U.S. history. The results show that labor productivity is positively affected by both the percentage of a state’s population with a bachelor’s
degree or higher and the population density of a state. Tax burden, measured
in the form of total state and local tax revenue or expenditures, is negatively
related to labor productivity. The results are robust to a variety of estimation
methods.
These findings have several important implications for economic
development organizations and policy makers of states wishing to increase
their labor productivity (and wage levels) to the national average. First,
state-by-state comparisons of economic variables, especially labor productivity, need to be adjusted for density. Since it is unlikely that population density is a policy variable for states, adjusting for density allows
for more meaningful comparisons. Second, states with below average
density will tend to have a more difficult time reaching the national
average labor productivity level, ceteris paribus, than low density. The
23
Table 1 indicates an approximately $3,884 per capita difference between Maine’s labor
productivity and the national average, whereas, Table 4 shows $3,737. The $147 difference is due
to the use of a fitted value used in the development of Table 4, not an actual labor productivity
value
Adjusting for population density
168/0209/17
Table 4. Decomposition of 48 state differentials in real labor productivity state labor
productivity less the national average 1993–2000
State
Total
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
"$2,367
"4,543
"4,323
1,679
"1,501
8,866
5,423
"2,867
"853
"5,527
5,801
181
"1,903
"2,388
"2,003
"3,466
"3,737
3,053
6,300
2,593
267
"4,113
716
"6,475
"4,417
"3,945
868
10,787
"6,269
5,860
"2,047
"6,613
1,976
"3,777
"1,935
1,812
4,606
"4,021
"5,334
"1,843
"2,232
"3,865
"2,745
"545
101
"4,712
"297
"7,099
Education
Density
Tax Burden
Union
Industry
"$1,219
"328
"2,019
780
1,811
2,170
367
"361
"186
"534
513
"1,970
"508
659
"1,178
"932
"432
1,729
2,208
"624
1,160
"1,019
"63
66
"258
"1,023
972
1,784
"21
902
"371
"381
"347
"484
421
"352
675
"981
"383
"1,452
"100
491
817
1,156
937
"2,356
"213
"440
"$1,106
"2,023
"1,780
244
"2,473
2,709
1,410
609
"498
"3,344
371
"142
"1,931
"2,654
"900
"810
"2,121
1,857
2,787
"84
"1,869
"1,545
"1,395
"4,422
"2,967
"3,628
"523
3,775
"3,204
1,506
"220
"3,714
719
"1,840
"2,620
701
3,029
"470
"4,019
"468
"1,328
"2,826
"1,521
"77
"1,259
"1,155
"1,014
"4,459
$52
44
421
"389
540
1,563
1,712
"489
1,073
"263
1,363
1,067
87
259
325
500
"661
191
1,249
"430
"1,188
"327
1,226
"930
"657
564
1,723
421
"398
"1,926
608
"480
"702
"189
"942
"51
"460
"237
799
567
1,196
"615
"115
1,082
"1,417
"795
"1,462
"294
"$500
"1,796
"1,588
1,288
"1,107
985
"227
"1,283
"1,649
"920
2,376
437
292
"641
"147
"1,217
441
905
782
3,325
1,914
"1,679
655
486
"552
2,333
"635
3,518
"853
4,568
"2,804
"900
1,907
"569
1,309
1,506
1,849
"2,537
"1,309
"998
"1,878
"908
"902
"2,019
2,068
768
1,482
"637
$407
"439
644
"244
"272
1,439
2,161
"1,343
407
"466
1,178
788
156
"12
"102
"1,007
"964
"1,631
"726
407
250
456
293
"1,675
18
"2,191
"668
1,289
"1,793
811
739
"1,138
399
"695
"103
8
"487
203
"422
508
"123
"7
"1,024
"688
"227
"1,175
911
"1,269
Notes:
1) Differences due to rounding.
2) The ‘‘Total’’ column represents the difference between each individual state’s estimated labor
productivity and the estimated national (state) average labor productivity. See Appendix B for
details.
168/0209/18
J. Smoluk and Brace Andrews
results of this study suggest that low density states wishing to promote
economic growth and development must focus on their tax codes and
higher education. An examination of education, density, and tax-burden
during recessionary periods provides for an interesting avenue of future
research.
Appendix A: Data Sources
All dollar denominated amounts are deflated based on the Producers Price
Index (All Commodities, Not Seasonally Adjusted) from the Federal Reserve
Bank of St. Louis. Private industry wages and employment data are from the
Bureau of Labor Statistics (BLS).
The wage variable is from the Bureau of Economic Analysis (BEA), State
and Local Area data, and represents private, non-farm wage and salary
distributions. It includes renumeration of employees, corporate officer compensation, bonuses, and pay-in-kind. Amounts are before social security and
union dues payments. See the publication, ‘‘State Personal Income 1929–97,’’
produced by the BEA, May 1999.
The education variable is from the U.S. Census Bureau and is defined as
the percentage of the noninstitutional population, 25 years and over, who
have completed a Bachelor’s degree or more.
State density is estimated by dividing the state population, from the
BEA, by the number of square miles in a state from the U.S. Census. State
urban density is based on urban population estimates from the 1990 U.S.
Census Bureau (the latest available urban population estimates by state)
and is computed by dividing state urban population by the number of
square miles in the state.
The taxes collected as a percentage of GSP represents total state and local
taxes collected from the U.S. Census of Governments divided by private state
GSP. State and local government GSP as a percent of private state GSP is
computed by dividing the state and local expenditure components of state
GSP by total state GSP. GSP and its components are from the Bureau of
Economic Analysis (BEA.)
Data on labor union membership as a percentage of the labor force are
from U.S. Census Bureau, 1996 Economic Census.
Appendix B: Decomposition of state labor productivity differences, computations supporting Table 4
To estimate state i’s labor productivity, we employ state i’s time averaged
values for all five independent variables in Eq. B.1 below:
^ i ¼ b^0 þ b^1 lnðEDi Þ þ b^2 lnðDENi Þ
LP
ðB:1Þ
þ b^3 lnðTAXi Þ þ b^4 ðUi Þ þ b^5 ðMIXi Þ þ e:
Diagnostic tests on B.1 indicate that the regression results are well-behaved.
The adjusted R2 is 0.843 and the p-values for each parameter, using White
(1980) heteroskedasticity-consistent standard errors, are less than 0.02 in all
Adjusting for population density
168/0209/19
cases. The p-value for the Kolmogorov-Smirnov goodness-of-fit test of normality of the regression residuals is 0.998. Additional details on the regression
coefficient estimates are not provided due to space constraints.
To estimate state i’s labor productivity under the assumption that state
i has the national (state) average education level, we replace EDi with EDavg
for the first independent variable in Eq B.1:
^ i;EDavg ¼ b^0 þ b^1 lnðEDavg Þ þ b^2 lnðDENi Þ þ b^3 lnðTAXi Þ þ b^4 ðUi Þ
LP
ðB:2Þ
þ b^5 ðMIXi Þ þ e:
The difference between the two estimated labor productivity values,
^ i;EDavg , represents the difference in labor productivity between state
^ i " LP
LP
i and the national average due to education differences. One at a time, this
process is repeated systematically for each independent variable in order to
produce the results shown in Table 4.
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