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FEDERAL RESERVE BANK OF CLEVELAND

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papers

by Paul W. Bauer and Yoonsoo Lee

P O L I C Y D I S C U S S I O N PA P E R

Estimating GSP and
Labor Productivity by State

NUMBER 160 MARCH 2006

P O L I C Y D I S C U S S I O N PA P E R S

FEDERAL RESERVE BANK OF CLEVELAND

Estimating GSP and Labor Productivity by State

Paul W. Bauer is an
economic advisor at the Federal
Reserve Bank of Cleveland.
Yoonsoo Lee is an economist at
the Bank.

by Paul W. Bauer and Yoonsoo Lee

In gauging the health of state economies, arguably the two most important series to track are employment and output. While employment by state is available about three weeks after the end of a month,
data on output, as measured by Gross State Product (GSP), are only available annually and with a
significant lag. This Policy Discussion Paper details how more current estimates of GSP can be
generated using U.S. Gross Domestic Product and personal income along with individual states’
personal income. A straightforward share approach yields reasonable GSP estimates, but a more
sophisticated econometric approach, at a cost of imposing more structure, yields even better ones.
Both techniques are also applied to estimate nonfarm-business GSP in order to calculate a measure
of labor productivity at the state level that follows as closely as possible the method used by the
Bureau of Labor Statistics to calculate the national measure of labor productivity. We then briefly
examine how labor productivity varies across states.

Materials may be reprinted if the
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P O L I C Y D I S C U S S I O N PA P E R S

Policy Discussion Papers are published by the Research Department of the Federal Reserve
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Policy Discussion Papers are available electronically through the Cleveland Fed’s site on the World
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Views stated in Policy Discussion Papers are those of the authors and not necessarily those of the
Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System.

ISSN 1528-4344

FEDERAL RESERVE BANK OF CLEVELAND

Introduction
Data on the Gross State Product (GSP), the state counterpart of the U.S. Gross Domestic Product
(GDP), for 2001 were released in May of 2003. Data for 2002 and a “prototype” estimate for 2003
were released in December of 2004. Important data required for policymakers? Definitely. But if this
data were more timely, even with some error, they could be even more useful.
In gauging the health of the regional economy, arguably the two most important series to track are
employment and output. Both series are of interest in themselves, but combined they form a measure of productivity that in the long run ultimately drives living standards. While employment by state
is available approximately three weeks after the end of a given month, data on output—as measured
by the Bureau of Economic Analysis’ (BEA) GSP—are only available annually and with a multi-year
lag. Yet GSP is just as important an indicator of state economic performance as GDP is of national.
GSP is the broadest measure of a state’s production of goods and services, and looking at GSP over
time can help identify regional business cycles. Following GSP can also aid states in managing their
finances, as a significant proportion of state tax revenue is tied to output rather than to employment.
Of course, the more timely GSP data are, the more useful they become.
This Policy Discussion Paper details how more current estimates of GSP can be generated using U.S.
GDP and personal income combined with individual states’ personal income. Two approaches are discussed and compared to actual GSP to determine how well they perform. A simple model that
requires no parametric regression estimates provides fairly good GSP estimates for most states; however, a regression model performs even better, particularly for states that have a large share of GSP coming from natural resources, such as oil.
We also use these approaches to estimate nonfarm-business GSP. This series is useful for calculating
estimates of labor productivity for states that follow as closely as possible the method used in calculating
the most widely watched national measure. Explaining the variation in productivity growth across states
has been an important topic among economists; for example, Beeson (1987), Beeson and Husted (1989),
and Hulten and Schwab (1984) look at productivity and efficiency of manufacturing across states.
Measuring labor productivity is important to economists and policymakers because, in the long run,
labor-productivity growth is closely tied to gains in wages and living standards. At the state level, laborproductivity growth provides a measure of a state’s competitive position over time.
In constructing a measure of state-level productivity, we follow as closely as possible the method
used by the Bureau of Labor Statistics to calculate output-per-worker-hour for the private nonfarmbusiness economy, perhaps the most watched measure of productivity at the national level. One
unavoidable problem is that, at the national level, nonfarm-business labor productivity is calculated in
terms of output per hour, but at the state level, only data on the number of workers are available.
Consequently, we are forced to look at output per worker. In order to better understand the properties of this productivity measure, we compare output per hour and output per worker using data at the
national level where both can be calculated to show how these two measures differ over the long run
and over the business cycle. We then briefly examine how labor productivity varies across states.

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NUMBER 16, MARCH 2006

Estimation Techniques
In this section we describe two techniques for estimating a given state’s GSP. One approach, first used
by the Federal Reserve Bank of San Francisco, involves no econometric estimation and can be obtained
as follows:
(1) GSPit = GDPt*PIitPIt,
where GSPit is the estimate of GSP for state i in period t, GDPt is U.S. GDP in period t, PIit is the
personal income of state i in period t, and PIt is U.S. personal income in period t. This approach
assumes that personal income’s share of output is roughly constant over time and similar across all
states. As we will see in the next section, this approach does a fairly good job for most states and has
the advantage of having no econometric parameters that have to be re-estimated as time goes by.
Unfortunately, we will also see that the assumption that personal income’s share of output is constant
across states does not hold very well, particularly for natural-resource-rich states.
Our other approach uses these same series but employs an econometric model with lags to develop
a potentially better fit. We estimate the following equation for each state and the District of Columbia:
(2) ∆ ln GSPit = αi + βli ln GDPt + β2i ln GDPt–1
+ η1i lnPIit + η2i lnPIi,t–1 + λ1i In PIt + λ2i lnPIt–1 + εit .
We use the growth rate of a state’s GSP as the dependent variable because we want to fit growth rates
as well as possible. Toward that end we also include lagged values of personal income and GDP.
Assuming that these parameter estimates are relatively stable over a one- to two-year horizon going
forward, we can obtain estimates of a state’s GSP for time periods in which the BEA has not yet released
the official GSP figures, but for which GDP and personal income are available. In addition to comparing how well these techniques perform in sample, we also calculate GSP estimates for 2003 and 2004.
But first it is useful to briefly review the definition and characteristics of the data we will be using.

Data
In both estimation techniques, we use the annual estimates of nominal GDP published by the BEA as
the measure of national output. GDP measures total value of all goods and services produced by labor
and property located in the United States.
As defined by the BEA, GSP is a value-added concept that is consistent with the nation’s GDP.1
For a given state, overall GSP is the sum of the GSP originating in all industries in the state.
Specifically, an industry’s GSP is equal to its gross output (defined as sales or receipts and other operating income, commodity taxes, and inventory change) minus its intermediate inputs (consumption
of goods and services purchased).
Although GSP is related to GDP, the sum of states’ GSP for a given year is not precisely equal to
U.S. GDP for several reasons. First, GSP is measured as the sum of the distributions by industry of
the components of gross domestic income, which differs from GDP by the statistical discrepancy;
insufficient information is available to allocate the statistical discrepancy across states. Second, unlike
GDP, GSP does not include the compensation and other expenses related to federal civilian and

4

1. For full details see, Bureau of
Economic Analysis, “State
Personal Income Methodology,
1998–2003,”
http://www.bea.gov/bea/
regional/articles/spi2003/.

FEDERAL RESERVE BANK OF CLEVELAND

military personnel stationed abroad. Lastly, the sum of states’ GSP and GDP can differ because they
have different revision schedules.
In addition to GSP, the BEA also publishes personal income for the U.S. and for individual states.
State personal income, published quarterly, is loosely defined as the income received by all the residents of the state from all sources. Personal income includes the sum of wages and salaries, proprietors’ income, personal dividend, and interest income. Here, persons consist of nonprofit institutions
that serve individuals, private non-insured welfare funds, private trust funds, and individuals. The
state-level estimates of personal income are designed to be conceptually and statistically consistent with
the national estimates of personal income.2
Our main goal is to obtain more current estimates of GSP, so we want to extend the data as far forward as can reasonably be done.3 When we collected the data for this paper, data for U.S. personal
income and GDP were available through 2004 (in contrast to GSP data, which were only available for
the years 1977–2002, although a “prototype” estimate for 2003 was first released in December 2004).

How Well Do These Approaches Perform?
Econometric results from equation 2 for each state are presented in table 1. For all but a handful of
states, the R-square is fairly high, with a median of 0.831. This suggests that the model fits the data
fairly well, but does it outperform equation 1, the personal-income-share approach? One way to compare the performance of these two techniques is to look at the mean absolute percentage deviations for
each technique from the actual published data (see table 2).4 For every state except Tennessee, equation 2’s estimates (the regression approach) outperformed equation 1’s (the personal-income-share
approach), so it is not surprising that both the mean and the median of the absolute percentage
deviations are lower for the estimates from the regression approach than for those from the personalincome-share approach. The means for equation 1 and 2 are 0.0732 and 0.0140, while the medians
are 0.0449 and 0.0109, respectively.
A closer look at these figures reveals that for most states, both techniques work fairly well; yet for
states that have a large share of their GSP coming from mining (such as Alaska, Texas, Louisiana, and
West Virginia), the regression approach (equation 2) performs far better than the personal-incomeshare approach (equation 1). This latter approach also appears to have trouble forecasting the GSP
level for small states and the District of Columbia. For example, the mean absolute percentage deviation of heavily oil-dependant Alaska is 0.3242 for equation 1, yet only 0.0565 for equation 2.
Sometimes economic observers are more interested in growth rates than levels. This is a more challenging test because to get a good estimate of a growth rate, implicity one needs to obtain good estimates
of two levels. The results of looking at mean absolute deviations in growth rates are presented in table 3.
Here, although the regression approach still outperforms the personal-income-share approach for every
state but Washington, the advantage of the regression approach is much smaller. The means are 0.0156
and 0.0130, while the medians are 0.0114 and 0.0103, respectively.
A few figures can graphically illustrate the findings above. For some large diversified states such as
California, New York, and even Kentucky, it is visually hard to discern much of a difference. Although

2. See BEA, “State Personal Income
Methodology, 1997–2002” for
details about the estimates and
differences between state and
national estimates.
3. For researchers interested in past
economic performance, our
techniques could also be applied
to obtain GSP estimates prior to
1977. Although annual estimates
of personal income extend back to
1929, it would not be reasonable
to extend the estimates that far
back because the parameter
estimates are unlikely to be stable
over very long periods of time.
As we will see, the parameter
estimates of state-level-GSP
regression show large variation
across states that seems to
originate from differences in
industry composition across
states. In particular, these
differences are most noticeable
among states with a relatively
large share of industries that have
low shares of labor shares or
volatile output over time, such as
mining. Given that the U.S.
economy has experienced
significant restructuring across
industries since 1929, while our
estimates could reasonably be
used to extend the GSP series
back a few years, we certainly
do not believe the parameter
estimates obtained for the period
from 1977 to 2001 should be
employed to estimate the GSP
back to 1929.
4. While the personal-income-share
approach directly estimates GSP
levels, the regression approach
estimates percentage growth rates
of GSP. GSP levels are calculated
from the BEA estimates of 1977
GSP and estimated growth rates
from the regression approach.

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NUMBER 16, MARCH 2006

both approaches work well for fitting the level of GSP for certain states, the regression approach
outperforms the personal-income-share approach for Ohio and Pennsylvania (see figure 1a–e).
Similarly, for changes in GSP, it is easy to see that the fit is not quite as good when looking at growth
rates (figure 2a–e).
For states such as Alaska, Texas, Louisiana, and West Virginia (see figure 3a–d for levels and
figure 4a–d for growth rates) that have a significant share of GSP coming from mining, the personalincome-share approach clearly does not perform as well as the regression approach, visually confirming the results reported in table 2.
In summary, the regression approach (equation 1) fits the data better than the personal-incomeshare approach (equation 2). For most states, the actual and estimated levels and growth rates are very
close using the latter approach. While we do not have enough observations to perform meaningful
out-of-sample analysis of these two approaches, it appears that useful, more-timely estimates of GSP
can be obtained for most states. We now demonstrate how estimates of state-level labor-productivity
estimates can be obtained.

Constructing State Labor-Productivity Indices
To construct a measure of state productivity comparable to the most widely watched national productivity measure (output per hour for nonfarm business), an estimate of nonfarm business GSP is needed
in addition to the more-timely estimates of overall GSP. To obtain this measure of state output, we
follow the major sectors and subsectors of the U.S. economy included in the Bureau of Labor Statistics
(BLS) measure for nonfarm business. Due to the differences in classification of sectors, some compo5

nents of the data used in the BLS measures are not available at the state level. Real GSP in the nonfarmbusiness sector is constructed from the private-industry GSP from the BEA, excluding the outputs of
private households and agricultural sectors (Agriculture Services, forestry and fishing as well as farms).6
For the years we are forced to estimate GSP, we estimate nonfarm-business GSP using equation 2, but
instead of using all state personal income, we use state personal income in the nonfarm-business sector
only. We then divide these GSP estimates by the BEA’s GDP deflator to obtain real output estimates.7
For the denominator of our labor-productivity index, a measure of the quantity of labor inputs is
required. At the national level, the BLS publishes series for both the number of workers and the hours
worked, but unfortunately data on the number of hours are not available by state. As an alternative,
we use the number of workers as our labor input measures. The BLS Current Employment Statistics
program provides employment in non-agricultural establishments for states. Since the payroll
employment does not include employees of private households, we just have to exclude government
employment to get nonfarm-business-industry employment.
This difference in the measures calls for caution when comparing the state labor-productivity
measures to the national labor-productivity measures. If all employees worked a standard 40-hour
work week, then the two series would contain identical information, but this is not the case. Salaried
workers, part timers, overtime workers, and workers with multiple jobs all loosen the link between
hours and number of workers.

6

5. See Beemiller and Downey (2001)
for more details on GSP estimates
by industry.
6. The BEA has not published GSP
for private households since 1998,
when it switched from SIC to
NAICS. Our nonfarm private GSP
measures for years after 1998
thus include private households,
which account for only less than
1 percent of total GSP.

7. Real business-sector output in the
BLS measures excludes the
following outputs from the gross
domestic product: general
government, nonprofit institutions,
paid employees of private households, and the rental value of
owner-occupied dwellings. The
rental value of owner-occupied
dwellings is not available at the
state level and thus not subtracted
from the output.

FEDERAL RESERVE BANK OF CLEVELAND

At the national level, where both measures of labor input are available, we can explore the differences in the labor-productivity measures based on hours and those based on workers. In figure 5a, we
plot the standard measure of nonfarm private business-labor productivity (output per hour) with an
alternative measure (output per worker). While the two series are clearly similar, they do differ in two
significant ways. The most obvious way is how they move over the business cycle. In a downturn,
employers tend to retain workers but reduce hours, thus lowering output per worker relative to output per hour. In a recovery, employers tend to be cautious in hiring as demand rebounds, and they
tend to increase workers’ hours more quickly than the number of workers, thus raising output per
worker relative to output per hour.

This phenomenon is clearly seen in the last peak as

output per worker plunged in 2000 and 2001 only to sharply rebound in subsequent years. The other
way the two measures of labor productivity differ is that there is a long-run trend toward fewer hours
per worker, mainly because of the growth in the number of part-time workers. This phenomenon is
only subtly manifest in figure 5a by the growth rate in output per worker tending to be below that of
output per hour; it is more clearly seen in figure 5b, which directly plots hours per worker.
The bottom line is that when making longer-term comparisons, the two series will tend to yield
similar results, especially if one adjusts for the trend toward fewer hours per worker. However, when
considering year-to-year movements in productivity, this differing behavior over the business cycle
must be kept in mind.
In comparing the state-level measures to the national labor-productivity measures, it is also important to remember that the definition of GSP is not the same as GDP. Figure 5c shows, at the national level, the relationship between the GDP per worker and GSP (nonfarm business summed over all
of the states) per worker. Note that in the national comparisons, using GSP rather than GDP makes
about the same amount of difference in the productivity figures as does using the number of workers
rather than the number of hours.

A First Look at Labor Productivity across States
In figure 6a, we plot each state’s average annual labor-productivity growth rate from 1977 to 2000.
The first thing to notice is how remarkably wide the variation is across states. States averaged 1.1 percent growth over this period, from a low of –0.4 percent in Alaska to Connecticut’s comparatively blistering 2.8 percent. In the Fourth District, Pennsylvania led with 1.3 percent, followed by Ohio (0.8
percent), Kentucky (0.4 percent), and West Virginia (–0.3 percent).
During the period since the last business-cycle peak (2000–04), states’ average annual labor productivity grew 2.3 percent—an increase of 1.2 percentage points over the previous period—but again
this gain was far from evenly distributed (see figure 6b). This is not entirely surprising, considering the
differential impact of the economic downturn on the states and their industries during these years.
Delaware led the nation with average annual labor-productivity growth that soared to 8.6 percent;
eight states experienced declines, led by Alaska at –4.5 percent.
In the Fourth District, state labor-productivity growth exceeded that of the nation from 2000 to
2004. In particular, West Virginia rose from the second-slowest-growing state from 1977 to 2000 to
the sixth-fastest-growing, at 4.4 percent. Kentucky, at 2.4 percent, went from sixth-slowest to midpack

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NUMBER 16, MARCH 2006

performer. Ohio and Pennsylvania, at 3.7 percent and 3.2 percent respectively, also turned in solid
numbers. Given that the current expansion has not been kind to the Fourth District, particularly
Ohio, the region’s strong relative labor-productivity growth comes as a bit of a surprise.
In figure 7a we plot the level of labor productivity for selected large states along with the national
average of GSP per worker. The level of labor productivity for California and New York remain well
above the national average over the whole period. Texas, buoyed by high real prices for petroleum
products, performed as well or better in the late 1970s to mid-1980s but has since fallen off toward
the national average. Florida’s labor productivity, despite its rapid growth in GSP over this period,
remains well below the national average. Figure 7b plots the growth rate of labor productivity for this
group. The growth rates are quite volatile at the state level. The oil-price collapse in 1986 is clearly
visible in Texas’s series, as is the dot-com boom and bust around 2000 in California’s.
Figure 8a plots the Fourth District states’ levels of labor productivity along with the nation’s. Note
that all of the states trail the nation over this period. High real prices for coal helped Kentucky and
West Virginia in the late 1970s but hurt them as its real price fell later. First Kentucky and then West
Virginia have managed to boost their labor productivity. Ohio and Pennsylvania have largely moved
together, although they have swapped places: in the late 1970s, Ohio’s labor productivity was closer to
the nation’s, but in 1990, Pennsylvania’s was closer. Looking at the growth rates in figure 8b, a great
deal of volatility is again seen, particularly for Kentucky and West Virginia around 2000. Coal prices
did slump for 1998 through 2000, but further investigation is required to explore what else may have
contributed to the extremely sharp decline in those states’ labor-productivity growth rates. Since 2002,
all the Fourth District states have outperformed the nation, particularly Ohio.

Summary
Two approaches to speeding up the availability of GSP data are discussed and compared to actual
GSP to determine how well each approach performs. The first model requires no estimation and
provides fair estimates for most states. However, our regression model performs much better, particularly for states that have a large share of GSP coming from mining.
We also construct estimates of private nonfarm-labor productivity for states in as similar a way as
possible to the way U.S. estimates are constructed. After discussing how the state measure differs conceptually from the national one, we provide a brief look at how labor productivity has varied across
states, focusing on large states and Fourth District states. Perhaps the most interesting finding is how
much variation there is across states; looking for the sources of this variation is an important project
left to future research.

8

FEDERAL RESERVE BANK OF CLEVELAND

.

References
Richard M. Beemiller and George K. Downey. 2001. “Gross State Product by Industry, 1992–99,” Survey
of Current Business, vol. 81 (August): 159–72.
Patricia Beeson. 1987. “Total Factor Productivity Growth and Agglomeration Economies in
Manufacturing, 1959–73,” Journal of Regional Science, vol. 27, no. 2.
Patricia E. Beeson and Steven Husted. 1989. “Patterns and Determinants of Productive Efficiency in State
Manufacturing,” Journal of Regional Science, vol. 29, no. 1: 15–28.
Bureau

of

Economic

Analysis,

“State

Personal

Income

Methodology,

1998–2003,”

http://www.bea.gov/bea/regional/articles/spi2003/.
Charles R. Hulten and Robert M. Schwab. 1984. “Regional Productivity Growth in U.S. Manufacturing:
1951–1978,” American Economic Review, vol. 71, no. 1 (March): 152–62.

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NUMBER 16, MARCH 2006

Table 1: Regression Approach Estimates
State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
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

lnpi
0.643 [0.368]
0.633 [0.881]
1.099** [0.277]
0.924** [0.192]
1.268** [0.430]
0.914** [0.147]
0.811** [0.259]
0.612 [0.466]
0.614** [0.199]
0.196 [0.176]
1.625** [0.261]
0.903** [0.130]
1.102** [0.176]
1.208** [0.286]
1.548** [0.330]
0.504** [0.128]
1.004** [0.142]
0.597 [0.355]
1.287** [0.381]
1.115** [0.171]
1.329** [0.203]
1.339** [0.096]
1.194* [0.484]
1.006** [0.263]
0.973** [0.196]
1.412** [0.437]
0.895** [0.145]
0.602** [0.165]
0.665** [0.119]
0.992** [0.216]
0.932** [0.243]
1.034 [0.552]
0.972** [0.233]
0.897** [0.313]
0.561** [0.139]
1.781** [0.445]
1.372** [0.230]
0.883* [0.349]
0.167 [0.395]
0.912** [0.199]
1.117 [0.652]
0.633** [0.137]
1.438** [0.296]
1.326** [0.259]
0.846** [0.223]
1.435** [0.229]
0.863** [0.228]
1.033** [0.245]
0.730** [0.239]
0.641 [0.322]
1.469** [0.275]

Standard errors in brackets
All regressions use 26 observations.
*significant at 5%; **significant at 1%

10

lnpi_lag
-0.525 [0.345]
-1.497* [0.698]
-1.311** [0.295]
-1.005** [0.192]
-1.361** [0.430]
-0.897** [0.152]
-0.915** [0.266]
-0.826 [0.452]
-0.640* [0.228]
-0.390* [0.162]
-1.744** [0.284]
-1.014** [0.128]
-1.151** [0.176]
-1.217** [0.224]
-1.613** [0.263]
-0.837** [0.114]
-1.026** [0.137]
-0.705 [0.357]
-1.168** [0.368]
-1.184** [0.166]
-1.428** [0.196]
-1.415** [0.095]
-1.215** [0.366]
-0.953** [0.232]
-0.941** [0.196]
-0.798 [0.432]
-0.809** [0.149]
-1.039** [0.164]
-0.707** [0.112]
-1.046** [0.206]
-1.048** [0.254]
-1.312* [0.532]
-1.093** [0.243]
-0.537 [0.400]
-0.853** [0.131]
-1.165* [0.422]
-1.360** [0.223]
-1.030** [0.321]
-0.318 [0.370]
-0.995** [0.194]
-0.973 [0.702]
-0.586** [0.135]
-1.241** [0.291]
-1.432** [0.263]
-0.888** [0.236]
-1.375** [0.221]
-0.915** [0.201]
-1.057** [0.244]
-0.666* [0.245]
-0.754* [0.307]
-1.351** [0.305]

lnus_pi
-0.798* [0.302]
-1.797 [2.984]
-0.658 [0.398]
-0.983** [0.273]
-0.762 [0.738]
-0.584 [0.365]
-0.842 [0.561]
0.133 [0.749]
-0.848 [0.598]
0.028 [0.242]
-1.513** [0.330]
-0.789* [0.311]
-1.682** [0.369]
-1.212** [0.357]
-0.960** [0.306]
-0.713* [0.264]
-0.938** [0.241]
-1.114 [0.536]
-1.024 [1.069]
-0.706* [0.292]
-1.473** [0.290]
-1.536** [0.210]
-0.691 [0.480]
-0.852* [0.383]
-1.015** [0.255]
-0.944* [0.399]
-1.038* [0.405]
-0.586 [0.345]
-0.929** [0.155]
-1.469** [0.494]
-1.121* [0.433]
-1.897 [1.011]
-0.891* [0.410]
-0.414 [0.384]
-0.452 [0.752]
-1.053** [0.327]
-1.393 [0.776]
-1.004* [0.460]
-0.369 [0.380]
-0.931* [0.366]
-0.883 [0.535]
-0.879* [0.384]
-1.156** [0.268]
-1.012 [0.663]
-0.384 [0.424]
-1.370** [0.328]
-0.283 [0.266]
-0.828* [0.380]
-0.749 [0.402]
-0.509 [0.310]
-0.974 [1.136]

lnus_pi_lag
0.671* [0.281]
0.87 [2.886]
0.824 [0.418]
0.683* [0.247]
1.291 [0.704]
0.054 [0.373]
0.929 [0.489]
0.208 [0.644]
0.737 [0.359]
0.398 [0.226]
1.275** [0.268]
0.736* [0.273]
1.291** [0.347]
1.271** [0.343]
1.323** [0.359]
0.132 [0.245]
0.684** [0.232]
0.861 [0.540]
-0.745 [1.062]
0.873** [0.253]
1.459** [0.211]
1.376** [0.168]
1.602* [0.599]
0.774* [0.357]
0.817** [0.257]
0.444 [0.388]
0.213 [0.385]
0.636 [0.310]
0.441 [0.237]
1.329** [0.454]
1.649** [0.381]
0.937 [0.987]
1.071** [0.334]
0.836* [0.312]
-0.527 [0.760]
1.223** [0.340]
0.545 [0.800]
0.516 [0.580]
0.409 [0.396]
0.961** [0.312]
0.946 [0.499]
0.485 [0.346]
1.448** [0.279]
0.828 [0.662]
0.015 [0.442]
1.393** [0.312]
0.808** [0.211]
1.080* [0.451]
0.071 [0.433]
0.7 [0.412]
0.594 [1.281]

lnus_gdp
0.930** [0.303]
4.066 [2.674]
0.546 [0.412]
0.863** [0.294]
0.296 [0.405]
0.651* [0.259]
0.524 [0.352]
0.154 [0.586]
0.844 [0.413]
0.532** [0.166]
0.836** [0.254]
0.434 [0.274]
1.562** [0.346]
1.004** [0.176]
0.682 [0.333]
1.515** [0.238]
0.993** [0.157]
1.290** [0.432]
1.703 [0.906]
0.526* [0.224]
1.108** [0.179]
1.153** [0.138]
0.979 [0.617]
1.049** [0.229]
0.896** [0.253]
0.506 [0.355]
1.306** [0.355]
1.257** [0.296]
1.201** [0.161]
1.018* [0.401]
0.865** [0.251]
1.838 [0.890]
0.772** [0.254]
0.556 [0.296]
1.247 [0.691]
0.61 [0.307]
1.181 [0.584]
1.219* [0.480]
0.901** [0.226]
0.917** [0.269]
0.72 [0.376]
1.089* [0.383]
0.689* [0.285]
0.876 [0.439]
0.799* [0.351]
0.821** [0.244]
0.386* [0.158]
0.765* [0.319]
0.815* [0.333]
0.879** [0.232]
1.455 [0.991]

lnus_gdp_lag
-0.931* [0.352]
-2.366 [2.882]
-0.432 [0.398]
-0.484 [0.325]
-0.746 [0.467]
-0.125 [0.329]
-0.533 [0.387]
-0.266 [0.628]
-0.729 [0.384]
-0.748** [0.195]
-0.44 [0.286]
-0.294 [0.333]
-1.108* [0.391]
-1.055** [0.225]
-0.982** [0.324]
-0.622* [0.265]
-0.706** [0.189]
-0.932 [0.498]
0.041 [1.106]
-0.632* [0.265]
-0.994** [0.207]
-0.915** [0.153]
-1.869* [0.660]
-1.013** [0.271]
-0.736* [0.270]
-0.573 [0.398]
-0.52 [0.426]
-0.886* [0.344]
-0.644** [0.205]
-0.835 [0.472]
-1.304** [0.268]
-0.568 [1.037]
-0.850** [0.263]
-1.407** [0.398]
0 [0.879]
-1.306** [0.370]
-0.316 [0.745]
-0.552 [0.519]
-0.810* [0.289]
-0.868* [0.319]
-0.948 [0.493]
-0.733 [0.438]
-1.206** [0.318]
-0.556 [0.560]
-0.357 [0.436]
-0.923** [0.290]
-0.859** [0.192]
-0.993* [0.405]
-0.166 [0.416]
-0.957** [0.295]
-1.138 [1.285]

Constant
0.735 [2.000]
8.199 [21.068]
-1.647 [3.094]
2.19 [1.723]
-2.885 [3.084]
3.313 [2.052]
0.128 [2.434]
-2.3 [3.657]
1.145 [3.265]
-2.346 [1.264]
1.373 [1.544]
0.92 [1.916]
2.46 [2.273]
-0.325 [1.297]
-2.251 [2.145]
4.940** [1.546]
1.592 [1.361]
2.012 [2.935]
10.097 [6.826]
-0.915 [1.571]
0.357 [1.352]
1.278 [1.015]
-6.095 [5.069]
0.184 [1.654]
1.393 [1.637]
0.938 [2.128]
4.745 [2.511]
0.605 [2.039]
2.923 [1.492]
1.224 [2.947]
-2.702 [1.696]
6.346 [6.238]
-0.403 [1.639]
-2.846 [1.842]
7.107 [4.958]
-4.766 [2.464]
5.201 [5.129]
3.09 [3.713]
0.6 [1.663]
-0.045 [1.946]
-0.398 [2.252]
2.509 [2.426]
-2.051 [1.799]
1.171 [3.922]
2.07 [2.748]
0.115 [1.799]
-3.338* [1.265]
-1.606 [2.605]
3.94 [2.346]
-0.96 [1.913]
1.574 [8.347]

R-squared
0.821
0.518
0.846
0.870
0.788
0.901
0.816
0.410
0.687
0.947
0.900
0.900
0.830
0.900
0.871
0.923
0.947
0.600
0.689
0.892
0.927
0.974
0.705
0.880
0.878
0.744
0.821
0.865
0.964
0.822
0.874
0.498
0.881
0.823
0.826
0.847
0.844
0.742
0.771
0.831
0.817
0.804
0.863
0.852
0.794
0.914
0.924
0.803
0.668
0.787
0.768

FEDERAL RESERVE BANK OF CLEVELAND

Table 2: Mean Absolute Deviations (levels)

State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
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

average
min
max
median

Share Approach
Regression Approach
Difference
0.0500
0.0089
0.0411
0.3242
0.0565
0.2677
0.0396
0.0111
0.0285
0.0472
0.0080
0.0392
0.0256
0.0135
0.0121
0.0186
0.0081
0.0105
0.0735
0.0165
0.0570
0.1664
0.0206
0.1458
0.5190
0.0170
0.5021
0.1566
0.0056
0.1510
0.0368
0.0135
0.0233
0.0261
0.0140
0.0121
0.0475
0.0096
0.0379
0.0241
0.0067
0.0173
0.0342
0.0112
0.0230
0.0295
0.0081
0.0214
0.0404
0.0068
0.0337
0.0174
0.0133
0.0041
0.1482
0.0265
0.1217
0.1034
0.0090
0.0944
0.1771
0.0085
0.1686
0.0448
0.0056
0.0393
0.0648
0.0196
0.0452
0.0217
0.0052
0.0165
0.0355
0.0078
0.0277
0.0298
0.0161
0.0137
0.0810
0.0179
0.0631
0.0224
0.0097
0.0127
0.0420
0.0054
0.0366
0.1246
0.0145
0.1101
0.0872
0.0099
0.0773
0.0781
0.0367
0.0415
0.0125
0.0068
0.0057
0.0331
0.0109
0.0222
0.0548
0.0468
0.0079
0.0426
0.0100
0.0326
0.0669
0.0181
0.0489
0.0531
0.0150
0.0381
0.1030
0.0093
0.0937
0.1106
0.0102
0.1004
0.0226
0.0110
0.0115
0.0249
0.0162
0.0088
0.0091
0.0103
-0.0012
0.0821
0.0185
0.0636
0.0284
0.0109
0.0175
0.0736
0.0065
0.0670
0.0449
0.0086
0.0363
0.0175
0.0111
0.0064
0.0695
0.0121
0.0573
0.0438
0.0068
0.0370
0.2204
0.0352
0.1852

0.0732
0.0091
0.5190
0.0449

0.0140
0.0052
0.0565
0.0109

11

P O L I C Y D I S C U S S I O N PA P E R S

NUMBER 16, MARCH 2005

Table 3: Mean Absolute Deviations (growth rates)

State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
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
average
min
max
median

12

Share Approach
0.0097
0.0994
0.0128
0.0094
0.0151
0.0106
0.0139
0.0222
0.0141
0.0091
0.0093
0.0124
0.0140
0.0070
0.0101
0.0109
0.0063
0.0133
0.0384
0.0100
0.0083
0.0082
0.0170
0.0094
0.0094
0.0134
0.0169
0.0148
0.0057
0.0170
0.0122
0.0344
0.0082
0.0102
0.0316
0.0095
0.0197
0.0140
0.0094
0.0107
0.0114
0.0185
0.0092
0.0172
0.0150
0.0112
0.0089
0.0109
0.0146
0.0081
0.0408
0.0156
0.0057
0.0994
0.0114

Regression Approach
Difference
0.0091
0.0006
0.0718
0.0276
0.0123
0.0005
0.0083
0.0011
0.0138
0.0013
0.0091
0.0014
0.0120
0.0020
0.0178
0.0044
0.0104
0.0037
0.0057
0.0034
0.0077
0.0016
0.0096
0.0027
0.0123
0.0018
0.0068
0.0002
0.0096
0.0006
0.0076
0.0034
0.0054
0.0010
0.0131
0.0002
0.0310
0.0074
0.0078
0.0021
0.0064
0.0019
0.0049
0.0033
0.0154
0.0016
0.0084
0.0010
0.0085
0.0009
0.0116
0.0017
0.0126
0.0042
0.0109
0.0039
0.0048
0.0008
0.0148
0.0021
0.0088
0.0034
0.0342
0.0001
0.0082
0.0000
0.0089
0.0013
0.0233
0.0083
0.0086
0.0009
0.0193
0.0003
0.0131
0.0008
0.0087
0.0007
0.0103
0.0004
0.0111
0.0002
0.0138
0.0048
0.0082
0.0010
0.0141
0.0031
0.0131
0.0020
0.0092
0.0020
0.0061
0.0028
0.0110
-0.0001
0.0118
0.0029
0.0077
0.0005
0.0345
0.0063
0.0130
0.0048
0.0718
0.0103

FEDERAL RESERVE BANK OF CLEVELAND

FIGURE 1
GSP Actual and Estimates
A: California

B: New York

C: Ohio

1400000

900,000

400,000

1200000

800,000

350,000

1000000

700,000

800,000

600,000

600,000

500,000

400,000

400,000
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

300,000
250,000
200,000
1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year

Actual

Share

Regression

D: Pennsylvania

1989

1992

1995

1998

2001

2004

Year

Actual

Share

Regression

Actual

Share

E: Kentucky

500,000
450,000
400,000
350,000
300,000
250,000
200,000

140,000
120,000
100,000
80,000
60,000
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

2004

Year

Actual

Share

Regression

Actual

Share

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and authorsʼ calculations.

FIGURE 2
Changes in Real GSP and GSP Estimates
A: California

B: New York

0.12
0.10
0.08
0.06
0.04
0.02
0.00
−0.02
−0.04

C: Ohio

0.10
0.08
0.06
0.04
0.02
0.00
−0.02
−0.04
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

0.10
0.08
0.06
0.04
0.02
0.00
−0.02
−0.04
−0.06
1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year

Actual

Share

Regression

D: Pennsylvania

1989

1992

1995

1998

2001

2004

Year

Actual

Share

Regression

Actual

Share

E: Kentucky

0.08
0.06
0.04
0.02
0.00
−0.02
−0.04

0.10
0.08
0.06
0.04
0.02
0.00
−0.02
−0.04
−0.06
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

Actual

1989

1992

1995

1998

2001

2004

Year
Share

Regression

Actual

Share

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and authorsʼ calculations.

13

P O L I C Y D I S C U S S I O N PA P E R S

NUMBER 16, MARCH 2006

FIGURE 3
GSP Actual and Estimates
A: Alaska

B: Texas

40,000
35,000
30,000
25,000
20,000
15,000
10,000

900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

2004

Year

Actual

Share

Regression

C: Louisiana

Actual

Share

D: West Virginia
60,000

140,000
120,000
100,000
80,000
60,000

50,000
40,000
30,000
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

2004

Year

Actual

Share

Regression

Actual

Share

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and authorsʼ calculations.

FIGURE 4
Changes in Real GSP and GSP Estimates
A: Alaska

B: Texas

0.40
0.30
0.20
0.10
0.00
−0.10
−0.20
−0.30
−0.40

0.12
0.08
0.04
0.00
−0.04
−0.08
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

1989

1992

1995

1998

2001

Actual

Share

Regression

C: Louisiana

Actual

Share

D: West Virginia

0.15
0.10
0.05
0.00
−0.05
−0.10
−0.15

0.08
0.06
0.04
0.02
0.00
−0.02
−0.04
−0.06
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Regression

Actual

1989

1992

1995

1998

2001

2004

Year
Share

Regression

Actual

Share

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis; and authorsʼ calculations.

14

2004

Year

FEDERAL RESERVE BANK OF CLEVELAND

FIGURE 5
A

B
Hours Per worker

Annual Growth Rate (%)

Measures of Labor Productivity
6
5
4
3
2
1
0
−1
−2
1977

1982

1987

1992

1997

2002

Year

1.01
1.00
0.99
0.98
0.97
0.96
1977

Annual Growth Rate (%)

Output per Hour

1982

1987

Output per worker

1992

1997

2002

Year

C
0.06
0.04
0.02
0.00
−0.02
−0.04
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

Year
GDP per worker

GSP per worker

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis;
U.S. Department of Labor, Bureau of Labor Statistics; and authorsʼ calculations.

15

P O L I C Y D I S C U S S I O N PA P E R S

0.03

NUMBER 16, MARCH 2006

FIGURE 6a. LABOR-PRODUCTIVITY GROWTH, 1977–2000

CT
MA
NJ

0.02

DE

GA
DC

UT

0.01

VA

TN

VT

HI

PA

NE

OH

KS

WI

NV

ID

FL

AZ

WA

LA

ND
WY
0

AK MT
KY

OK

IA

MI

AR

IN

MS NM MO

TX

SD

AL

OR

ME

IL

MN MD

CO

SC

CA

NC

NY

RI

NH

WV

–0.01

0.10

FIGURE 6b. LABOR-PRODUCTIVITY GROWTH, 2000–2004
DE

NC
SC

0.05

0

AK NM

HI

NH
WY

OR
LA
–0.05

16

ID

VT

NJ

TX

MS

GA

MO

FL

UT

AL

IL

NE

KS

IN

OH

OK

MT

PA

RI
NY CA

CT

DC

ND

MA

ME

NV

KY

MD WA MN

TN

VA

AR

SD

AZ

WI

CO

WV

IA

MI

FEDERAL RESERVE BANK OF CLEVELAND

FIGURE 7
Labor Productivity in Large States
A

B
0.06

90

0.04

Percent

0.08

100

Index

110

80
70

0.02
0.00

60

−0.02

50

−0.04

40

−0.06
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year

1989

1992

1995

1998

2001

2004

Year

California

Florida

New York

United States

Texas

California

Florida

New York

United States

Texas

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis;
U.S. Department of Labor, Bureau of Labor Statistics; and authorsʼ calculations.

FIGURE 8
Labor Productivity in Fourth District States
A

B

90

0.08
0.06

80

0.04

Percent

Index

0.02
70

0.00
−0.02

60

−0.04
−0.06

50

−0.08
1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

1977

1980

1983

1986

Year
Kentucky

Ohio

West Virginia

United States

1989

1992

1995

1998

2001

2004

Year
Pennsylvania

Kentucky

Ohio

West Virginia

United States

Pennsylvania

SOURCES: U.S. Department of Commerce, Bureau of Economic Analysis;
U.S. Department of Labor, Bureau of Labor Statistics; and authorsʼ calculations.

17

P O L I C Y D I S C U S S I O N PA P E R S

Notes

18

NUMBER 16, MARCH 2006

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