Accounting for differences in aggregate state productivity

Regional Science and Urban Economics 22 (1992) 597-617. North-Holland

Accounting for differences in aggregate state productivity

Gerald A. Carlino and Richard Voith*

Federal Reserve Bank of Philadelphia, Philadelphia PA, USA

Received November 1989. final version received November 1990

The purpose of this paper is to analyze the determinants of aggregate productivity at the state level by utilizing the new GSP data. State differences in aggregate productivity are modeled as a Hicks-neutral shifter term in an aggregate production function framework. The model attempts to account for variations in aggregate productivity resulting from state-to-state differences in industry mix, human capital characteristics, public investment in infrastructure, and metropolitan structure. In addition, a random-effects extension of the model is employed to capture the effects on state productivity of other important localized factors that are not directly entered into the empirical model. The findings indicates that a state’s industrial mix, infrastructure, education level, and metropolitan structure all effect productivity. Relative state productivity rankings that allow cross-state comparisons of overall productivity and identify the sources of productivity differences are developed. For comparison, the model is re-estimated using manufacturing data. An important tinding is that the productivity rankings based on the aggregate state output differ markedly from rankings based solely on data for the manufacturing sector. This raises questions about making inferences about overall productivity based solely on manufacturing data.

1. Introduction

There has been a proliferation of studies investigating differences in regional productivity in the U.S. as well as a number of other countries. The majority of these papers have examined differences in urban manufacturing productivity [see Moomaw (1983) for a survey of this literature]. Recently, Beeson (1987) and Beeson and Husted (1989) compare the productive efficiency in manufacturing at the state level, and Hulten and Schwab (1984) have considered these differences at the regional level (defined as the nine census divisions). These studies have been limited to considering productivity in manufacturing because value added at the metropolitan, state or regional

Correspondence to: Jerry Carlino, Federal Reserve Bank of Philadelphia, Ten Independence Mall, Philadelphia, PA 19106-1574, USA.

*We thank an anonymous referee who provided very useful suggestions. Sherry Kuczynski and Jim McAnany provided excellent research assistance. The views expressed here do not necessarily represent those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

01660462/92/SO5.00 &? 1992-Elsevier Science Publishers B.V. All rights reserved

598 G.A. Carlino and R. Voith, LXjjerences in aggregate state productivity

level was generally not available for other industries.’ While these studies have added to our understanding of regional productivity differences in manufacturing, they provide little evidence on overall regional productivity differences and the factors underlying those differences.

The present paper attempts to fill this void by using a new Commerce Department data set. In May 1988, the U.S. Commerce Department’s Bureau of Economic Analysis (BEA) introduced an annual gross state product (GSP) series by industry, analogous to that of gross domestic product for the nation, for each state for the years 1963-1986.2 Although these data are estimates, they are the most comprehensive measures of aggregate state production available, and allow investigation of overall state productivity, not just manufacturing productivity.

The purpose of this paper is to analyze the determinants of aggregate productivity at the state level by utilizing the new GSP data. State differences in aggregate productivity are modeled as a Hicks-neutral shifter term in an aggregate production function framework. The model attempts to account for variation in aggregate productivity resulting from state-to-state differences in industry mix, labor force characteristics, public investment in infrastructure, and metropolitan structure. In addition, a random-effects extension of the model is employed to capture the effects on state productivity of other important localized factors that are not directly entered into the empirical model. The findings indicate that a state’s industrial structure, infrastructure, education level, and metropolitan structure all significantly affect productivity. Relative state productivity rankings that allow cross-state comparisons of overall productivity and identify the sources of productivity differences are developed. Since prior studies on productivity differences are based on manufacturing data, we also estimated the model for the manufacturing sector. An important tinding is that the productivity rankings based on the overall state economies differ markedly from rankings based solely on data for the manufacturing sector. This raises important reservations about making inferences on aggregate productivity at the regional level based on manufacturing data.

2. The model

Aggregate output in state i at time t is assumed to be represented by a homogeneous of degree h production function:

Qit = Aitf(Kit, Lit)Ah, ‘The studies on manufacturing productivity are generally based on pre-1979 data since the

Annual Census of Manufactures was not published for the years 1979, 1980, and 1981. ‘The data are developed in Renshaw et al. (1988). For a critical discussion of these data see

Giese (1989).

G.A. Carlino and R. Voith, Dijerences in aggregate state productivity 599

where Qi, is output in state i at time t, Ki, is the stock of capital in state i during time period t, and L, is labor input in state i for year t. Following Sveilkauskas (1975) f(.);l” is taken to be the same across states, and differences in productivity from state to state are ‘captured’ by the Hicks- neutral production function shifter (A,). Ai, differs from state to state due to state differences in a variety of factors such as industry mix, public infrastructure, human capital characteristics and metropolitan structure. Assuming that f(.),Jh has the CES from (1) becomes

Qir=Ai,[GK;hp+(l -S)L;hp]-(l’p). (2)

Because capital stock data are not generally available, most regional productivity studies have estimated a labor demand equation that is derived from eq. (2). It is assumed that labor is hired until the marginal product of labor equals the wage rate (IV) in each state. Differentiating (2) with respect to labor and setting the resulting expression equal to W yields an aggregate demand curve for labor in state i during t:

The literature that has used this approach to analyze the productivity of a metropolitan area tends to make Ai, simply a function of metropolitan statistical area (MSA) population size. These studies consistently find evidence for the proposition that productivity increases with MSA population size [Moomaw (1983)]. While this approach is interesting, it seems possible to employ a more generalized approach incorporating many of the factors that affect productivity through Ai,. It is hypothesized that Ai, is an exponential function of a number of other variables such as a state’s industrial mix, a state’s labor force characteristics (e.g., educational attainment, degree of unionization), state infrastructure investment (e.g., ports, highways, bridges), as well as metropolitan structure. Denoting these factors as Xkit, where k indexes the production function shifter terms:

A,=exp dI0 + c akxkit 1 . k=l J

(4)

Substituting (4) into (3) and taking the logarithmic transformation yields

600 G.A. Carlino and R. Voith, Differences in aggregate state productivity

B kXkit +eln Q;t +Y In Lit> k=l

where Po=ln((1-6)h)-pcr,,Bk=-pak(k=1,2,...,K),e=1+p,

y= -(l +hp).

Most of the production function parameters are identified:

p=8-1,

h=-C(y+l)lpl=(y+l)/(l-8)

a0 = Cln 0 1 - W) -Bolls.

The parameter y is, however, not identified.

3. The empirical model

The stochastic version of labor demand eq. (5) can be written as

(6) k=l

where vit = In vi, and vi= In Ui. Let i index states and t index time periods. The two-part error term in eq. (6) reflects both the random error term, vit, and a time-invariant state-specific effect, vi. The so-called within estimator treats vi as fixed effects and estimates a separate intercept for each state. This is accomplished by suppressing the constant term and adding a dummy variable for each of the N states. This is referred to as the least-squares dummy variable model (LSDV).3 Alternatively, we can treat vi as random effects and make the (testable) assumption that these state-specific effects are uncorrelated with the regressors. The main advantage of the GLS estimator relative to the LSDV estimator, for our purposes, is its ability to include time-invariant variables.4

The stochastic labor demand eq. (6) forms the basis of the empirical model. The dependent variable, W, the average wage bill, is in real terms;

‘The main advantage of LSDV model is that its consistency does not depend on the uncorrelatedness of the regressors and ri.

“Provided that ui and the regressors are uncorrelated, the GLS estimator is consistent. Further, for small samples, the GLS estimator is effkient relative to the LSDV estimator. Hausman (1978) has developed a test for the null hypothesis that u, and the regressors are uncorrelated. The proposed test is based on the significance of the difference between the LSDV estimator and the GLS estimator.

G.A. Carlino and R. Voith, Differences in aggregate state productivity 601

nominal wages are converted to real terms by utilizing the national producer price index (PPI).5 Unfortunately, data for many of the variables that are thought to influence the production function shifter term are not available. As a result, a number of proxy variables for Xkir are developed to capture the effects of these forces on aggregate production. Educational attainment in 1980, Ei, and percent unionization in 1970, Ui, are used as proxies for labor force characteristics. To capture the effects of state infrastructure on labor productivity, a highway density in 1980, Ii, is used. A time index, denoted 7;, is employed to capture the effects of Hicks-neutral technical progress on productivity, which is assumed to be identical for each state. A dummy variable, denoted Z,, is utilized to capture the effects of the energy shock years (1973-1978) on state productivity. To capture the effects of agglomeration economies on state productivity, the percent of the state’s population living in metropolitan areas, Pit, is used. This variable is also squared, pt, and employed to capture agglomeration diseconomies associated with congestion. For observations in 1975 and prior years, 1970 values for Pi, and Pi: are used. For observations after 1975, Pi, and Pi”, assume the values for 1980. A state’s industrial structure is measured as the percent share of total GSP accounted for by the jth one-digit industry in state i at time t, denoted Sjil. Qi, and Li, are measured by real GSP and employment in the ith state for time t, respectively.6 Given this notation, eq. (6) becomes

+ P,P,” + 1 fij+ 7Sjit + 0 In Qi, + Y In Lit + Vi + Vit. j=l

(7)

4. Findings

The results are based on estimations of a pooled cross-section time-series model for the 48 contiguous states for the period 1967-1986 (providing 960 observations). Table 1 gives the definitions of the variables used in this study. Table 2 reports the findings for three versions of eq. (7). Column 1 of table 2

5According to the theory, W in eq. (6) should reflect marginal rather than average wages. Data on wage rates exist, however, only for the manufacturing industries. Due to this data limitation, average wage rates are employed.

61deally, Li, should be in terms of man-hours rather than number of employees. While data on man-hours exist for manufacturing, it is not generally available for other industries. As a result of this data limitation, total employment is used in the estimation of eq. (6).


_ “All variables designated ‘real’ are transformed to real terms by using the appropriate national

product price index (PPI).

Table 1

Variable definitions.”

Average annual aggregate real wage bill divided by number of employees in state i for time t (Country Business Patterns) Educational Attainment (percent with 12 or more years) in i in 1980 (State and Metropolitam Area Data Book, 1986) Union membership as a percent of employees in non-agricultural establishments in i for 1970 (Directory of National Unions and Employee Associations) Total primary Federal-Aid Highway System miles per square mile of land area in state i for 1980 (Statistical Abstract) Technical progress is represented by incorporating a time index in the regressions Dummy variable to capture the effects of the energy shock years; Z, = 1 if t = 1973-1978; and 0 otherwise Percent of state i’s population living in metroolitan areas in 1970 and 1980, based on 1983 metropolitan area definition (Provided by the Census Bureau) Real gross state product (GSP) in state i at time t (Survey of Current Business) The real output (GSP) share of jth one-digit industry: agriculture; mining; construction; and public utilities; wholesale and retail trade; FIRE; services; and government (Survey of Current Business) Aggregate employment in state i at time t (Country Business Patterns) A vector of state dummy variables (I = 2,3,. ,48; Alabama is the base case)

reports the results for an OLS regression. Column 2 of table 2 reports the findings for a least-squares dummy variable or fixed-effects regression (LSDV); and column 3 reports the results for a random-effects model, which is the generalized least-squares estimator (GLS).

In the OLS regression, with the exception of the time variable, which is not statistically significant, all of the estimated coefficients of the labor- demand equation have the anticipated sign and are highly significant. The LSVD version produces results that are somewhat different than those from the OLS regression.’ The major difference between the OLS and the LSDV regressions is with the industrial structure variables. To begin with, not all of the industrial structure variables have positive and significant coefficients in the LSDV regression, as is found in the OLS regression. In the LSDV regression the coefficient on Mining is negative but insignificant. More importantly, three industries (Mining, FIRE, and Government) have estimated coefficients that become insignificant and the magnitudes of the remaining coeffkients change in the LSDV version.8

‘To avoid perfect collinearity it is necessary to drop the percentage share of one industry; agriculture is the excluded industry. The estimated coefficients, therefore, give the marginal increase in average state productivity when one industry increases its share at the expense of the agriculture share.

sTo conserve space, the estimated coefficients for the 47 state dummy variables are not reported. They are available upon request.


Variable

Constant

Education

Union

Highway density

Time

Energy shock

Percent urban

Percent urban sq

Mining

Construction

Manufacturing

Transportation

Trade

Fire

Services

Government

log Q

log L

RI

Table 2

Labor demand estimations.a*b

OLS LSDV

2.43 (0.34)*** -

0.003 (0.0004)*** -

0.002 (0.0003)*** -

0.124 (0.04)***

-0.0005 -0.002 (O.Ot305) (o.OOl)*

-0.016 - 0.02 (0.004)*** (0.003)***

0.22 1.68 (0.05)*** (0.52)***

- 0.08 - 1.74 (0.05)* (0.45)***

0.615 -0.21 (0.081)*** (0.15)

1.67 1.12 (0.15)*** (0.19)***

1.53 0.44 (o.lo)*** (0.18)**

1.74 1.43 (0.20)*** (0.29)***

1.22 1.41 (0.23)*** (0.29)***

1.22 0.28 (0.17)*** (0.22)

1.23 0.65 (0.12)*** (0.34)*

0.36 0.09 (o.lo)*** (0.23)

0.43 0.38 (0.030)*** (0.044)***

-0.42 -0.29 (0.03)*** (0.03)***

0.779 0.894

GLS

2.19 (0.79)***

0.007 (0.004)*

0.004 (0.003)

0.637 (0.38)*

-0.001 (0.001)

-0.019 (0.003)***

1.08 (0.39)***

- 1.07 (0.35)***

-0.12 (0.15)

1.24 (0.18)***

0.51 (0.17)***

1.44 (0.28)***

1.35 (0.28)***

0.31 (0.21)

0.70 (0.32)**

0.16 (0.22)

0.37 (0.04)***

-0.30 (0.03)***

0.898

“Numbers in parentheses are estimated standard errors. b*Signiticant at the 10% level; **significant at the 5% level;

***significant at the 1% level.


The discrepancy between the OLS and the LSDV regressions most likely results from variables that are absent from the OLS regression but influence industry level productivity. Various factors that could differ from state-to- state, such as resource endowments and regulatory attitudes, may make some industries more productive in some states than in other states. If these excluded variables are correlated in the long run with industrial structure, their effects will be captured by the industrial structure variable. But in the LSDV, the effects of these omitted variables will tend to be captured by the state specific dummy variable rather than the industrial structure variable. An F-test of the null hypothesis that the state specific dummy variables are equal is strongly rejected by the data, suggesting that state effects are important.

As table 2 shows, there is a close similarity of results between the LSDV and the GLS regressions except for the inclusion of the time-invariant variables.g In addition, the education and highway density variables are positive and significant, while the union variable is not significant, in the GLS regression. lo Because the GLS and LSDV estimators are similar and the more efficient GLS estimation allows the inclusion of time-invariant variables, we focus the remainder of the discussion on the GLS results.

The estimated coefficients reported in table 2, Bj, must be transformed to obtain the estimates of the parameters of the production function shifter term. The desired coefficients, Bj, are equal to bj/fi where fi is equal to (1 - 8), and e^ is the parameter on the In Q variable.

Table 3 shows the estimated parameters of the production function shifter terms as well as estimates of the economies of scale parameter, h. We find that state productivity is associated with a more educated labor force but it is not significantly affected by the degree of unionization. Infrastructure, as proxied by highway density is positively related to productivity.

The time, or technical progress, variable does not seem to affect state productivity in that the estimated coefficient, while negative, is insignificant.” The estimated coefficients on the energy shock variable are, however, negative and significantly different from zero in both versions of the model. Although the expected sign on the coefficient of the shock variable is obtained, the magnitude seems rather large. The estimated parameters

9We tested for possible correlation among the state-specific error component and the regressors using a procedure described in Hausman (1978). The data did not reject the null hypothesis of zero correlation among the state-specific error component and the included variables.

“Moulton (1986, 1987) demonstrates that when group effects exist in the data, the standard errors for the OLS regression coefficients for the variables that have no within group variation are biased downward. This could account for why the unionization variable is significant in the OLS regression, but insignificant in the GLS regression.

“Since all states have equal weight in the regression, the coefficient on the technical progress does not necessarily equal the average productivity change nationwide.

Sources of state productivity differentials, 1967-1986.a.b

OLS LSDV GLS Variable

Education

Union

Highway density

Time

Energy shock

Percent urban

Percent urban sq.

Mining

Construction

Manufacturing

Transportation

Trade

Fire

Services

Government

P

Economy of scale

0.005 (o.OOl)***

0.004 (o.OOl)***

0.219 (0.075)***

-0.001 (0.001)

- 0.028 (0.007)***

0.38 (0.078)***

-0.141 (0.085)*

1.084 (0.162)

2.935 (0.347)***

2.692 (0.282)***

3.067 (0.434)***

2.142 (0.361)***

2.157 (0.352)***

2.162 (0.293)***

0.633 (0.187)***

-0.567 (0.03)***

1.029 (0.017)***

- 0.003 (0.002)*

- 0.032 (0.006)***

2.686 (0.867)***

- 2.78 (0.767)***

-0.332 (0.251)

1.792 (0.346)***

0.702 (0.293)**

2.294 (0.504)***

2.253 (0.489)***

0.445 (0.365)

1.035 (0.590)*

0.147 (0.378)

-0.625 (0.044)***

1.144 (0.026)***

0.012 (0.007)*

0.006 (0.005)

01.008 (0.604)*

- 0.002 (0.002)

- 0.030 (o.OOs)***

1.713 (0.63)***

- 1.692 (0.573)***

-0.193 (0.232)

1.963 (0.333)***

0.803 (0.273)***

2.273 (0.481)***

2.125 (0.465)***

0.484 (0.347)

1.111 (0.539)**

0.258 (0.354)

- 0.633 (o&to)***

1.113 (0.020)***


Table 3

“Numbers in parentheses are estimated standard errors. b*Significant at the 10% level; **significant at the 5% level;

***significant at the 1% level.


indicate that state productivity fell at a 3.2% annual rate during the middle to late 1970s (all other things held constant).

The variables percent urban and percent urban squared attempt to relate spatial distribution of a state’s population to productivity. As expected, states where a large portion of the population is concentrated in metropolitan areas tend to be more productive (agglomeration economies). Similarly, congestion, measured by percent urban squared, reduces state productivity (agglomeration diseconomies). The coefficients on these two variables imply that the ‘optimal’ percentage of a state’s population in metropolitan areas is 51%.

State productivity varies depending on its industrial mix. The industrial grouping Transportation (transportation, communications, and utilities) con- tributed the most to overall state productivity during the period 1967-1986. This is followed by: Trade (wholesale and retail combined), Construction, Other Services, Manufacturing, FIRE (finance, insurance, and real estate), Government, and Mining. i2 However, the coefficients on the Mining, FIRE and Government groupings are not statistically significant.

Finally, the results indicate increasing returns to scale in aggregate state production. The estimated value for h is 1.11, which is significantly different from unity at the one percent level.

5. Productivity indices

The estimates of the parameters of eq. (4) can be used to sources of productivity variation across states. First, define average productivity shift, A,, as

r

compare the the national

8 1

A,=exp 1

~,+hlE+h21+~3T+B,Z+B,U+~,P+B,P2+ C Lij+,Sj , j=l J

(8)

where 8,-B, 5 are the estimated parameters of the random-effects regression reported in table 3; .I?, 0, I, 7; Z, P and Sj represent the grand means for educational attainment, for unionization, for highway density. for the time index, for the energy shock dummy variable, for percent metropolitan and

‘*Included in the other services category are business, health, and legal services, private education, hotels and motels, domestic help, non-profit institutions, and numerous smaller subcategories.


for industry mix variables averaged across the 48 states and across time; go is the average of the estimated ‘random effects’ for the 48 states.

Similarly, define the average productivity shifter term for each state, Ai, as

+ 2 6j+Tsji 3

j=l 1 (9)

-- - - where Ei, Ui, Ii, T, Zi, Pi and Sji represent the average values during the sample period for educational attainment, for unionization, for highway density, for the time index, for the energy shock dummy variables, for percent metropolitan and for industry mix in state i, respectively.13 The constant term koi is the estimated random effect for the ith state (&,, + Ci).

The contribution of educational attainment and highway density alone to a state’s productivity, setting all other variables at the national average is14

+ ~ ~j+,Sj .

j=l 1 (10)

Note that educational attainment and highway density assume the average value for these variables in the ith state, while the remaining variables in (10) assume their 48-state average values.

Analogous calculations can be made for the net agglomeration economies alone, Ai,P, for industrial structure alone, Ai,s, and for random-effects alone,

Ai.R:

13The mean values of the time and energy shock variables are the same for each state as well as for the nation.

14The A,& index is constructed to measure the effects of variables under government influence. Since the degree of unionization is not easily influenced by state governments, other than through right-to-work legislation, unionization did not take on its state specific mean value in computing the A,, index.


+ ~ ~j+7Sji

1 ) (12)

j=l

+ $ kj+TSj j=l 1 (13)

Given the above definitions, it is possible to create the following indices:

PI = AJAn, p~=Ai,dAn, P~=Ai,plAn, P,=Ai,s/An,

PS =A:. R/An,

PI is an index expressing total productivity in the ith state relative to the nation (defined as the 48 state average). P, expresses the shift in productivity in the ith state from national average productivity that results from state i’s educational attainment and highway density. Similarly, P, captures the shift in productivity in state i from the national average that is due to net agglomeration economies. P, measures the shift in productivity in the ith state from the national average productivity that results from state i’s industrial structure. Finally, P, captures the productivity effects relative to the national average resulting from state specific random-effect. As P,, q=l , . . . ,5, for the ith state is greater, equal, or less than unity, it implies that productivity in the ith state is greater, equal, or less than the national average.’ 5

Tables 4a-4c present the results of the calculations for PI-P, based on the estimated parameters of the random-effects regression. The states in table 4a are ranked according to the P, (total productivity) index. Two sets of rankings are given in table 4b. One set is ranked according to the P, (education and highway) index and another set is ranked according to the P, (net agglomeration economies) index. Similarly, two sets of rankings are

“PI is not a weighted average of P,, P,, P, and P, due to the way the latter indices are constructed. The indexes P,-P, do sum to P, in logs. It is therefore possible to compute the percentage contribution to the log of the shift from the national average shift of each component index. For example, the productivity index for Delaware is 1.5002, 11% of the log of the shift term is a result of education and infrastructure, 49% from industrial mix, and 24% from agglomeration economies, and 15% from unexplained random effects. Note the percentages do not sum to 100 because of rounding.


Table 4a

Ranking of states by productivity levels.

Total productivity Total productivity

State PI

1 Delaware 1.5002 25 2 Rhode Island 1.2282 26 3 S. Carolina 1.2081 21 4 Georgia 1.1833 28 5 Connecticut 1.1685 29 6 New Hampshire 1.1456 30 I Tennessee 1.1230 31 8 Vermont 1.1156 32 9 Indiana 1.1061 33

10 W. Virginia 1.1007 34 11 Missouri 1.0949 35 12 N. Carolina 1.0913 36 13 Alabama 1.0868 37 14 Massachusetts 1.0864 38 15 Michigan 1.0832 39 16 Maine 1.0830 40 17 Illinois 1.0788 41 18 Ohio 1.0662 42 19 Wisconsin 1.0515 43 20 New York 1.0450 44 21 Pennsylvania 1.0386 45 22 New Jersey 1.0381 46 23 Minnesota 1.0337 41 24 Kentucky 1.0274 48

State

Nevada 1.0210 Arkansas 1.0178 Maryland 1.0177 Arizona 0.9953 Oregon 0.9867 Virginia 0.9751 Iowa 0.9687 Mississippi 0.9653 Colorado 0.9364 Florida 0.9343 Washington 0.9289 Kansas 0.9274 Nebraska 0.9250 Idaho 0.9138 Oklahoma 0.9061 Utah 0.9022 Texas 0.8433 N. Dakota 0.8409 California 0.8285 Louisiana 0.8236 S. Dakota 0.8143 New Mexico 0.7989 Montana 0.7744 Wyoming 0.6457

PI

given in table 4c, one set for P, (industry-mix), and another set for P, (random-effects).

A striking feature of table 4a is the broad range in total productivity across states. The differential in state productivity runs from about 50% above the national average (48 state average) in Delaware to almost 35% below the national average in Wyoming. The large productivity differential for Delaware appears to be an outlier. To begin with, there is a 27% differential between Delaware and Rhode Island, the second most productive state. In general, the productivity differentials decline much less rapidly ignoring Delaware. The strong productivity reading for Delaware probably has to do with the fact that Delaware is a small state, in close proximity to both the Philadelphia and New York metropolitan areas. Even with the exclusion of Delaware, there is a 58% differential between Rhode Island and Wyoming, the least productive state.

In terms of regional groupings, states in the northern regions of the country are among the more productive states. Every state in the New England, Middle Atlantic, and the East North Central region of the country


1 2 3 4 5 6 I 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 31 38 39 40 41 42 43 44 45 46 47 48

Table 4b


Education and highways

State p,

Net agglomeration

State

Rhode Island Massachusetts Connecticut Maryland Pennsylvania Delaware New Jersey New York Illinois S. Carolina Georgia Ohio Wisconsin Indiana Iowa Florida Tennessee Virginia Vermont Alabama New Hampshire Mississippi Minnesota Michigan W. Virginia Missouri Kentucky Kansas Arkansas N. Carolina Nebraska Oklahoma N. Dakota California Washington S. Dakota Louisiana Texas Maine Oregon Colorado Montana New Mexico Urah Wyoming Arizona Idaho Nevada

1.3614 1.2320 1.2001 1.1433 1.1170 1.1037 1.0990 1.0664 8 1.0647 9 1.0639 1.0628 1.0627 1.043s 1.0390 1.0298 1.0214 1.0205 1.0172 1.0096 1.0084 1.0078 0.9942 0.9853 0.9808 0.9766 0.9721 0.9676 0.9675 0.9667 0.9609 0.9597 0.949 1 0.9476 0.9459 0.9455 0.9444 0.9419 0.9352 0.9342 39 0.9199 40 0.9 125 41 0.9079 42 0.905 1 43 0.9049 44 0.9032 45 0.903 1 46 0.9018 47 0.8859 48

6

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Kansas 1.1223 N. Carolina 1.1206 Kentucky 1.1201 New Hampshire 1.1194 Oklahoma 1.1167 Nebraska 1.1159 S. Carolina 1.1102 Iowa 1.1072 Georgia 1.1002 New Nexico 1.0964 Arkansas 1.0946 Alabama 1.0942 W. Virginia 1.0922 Minnesota 1.0892 Tennessee 1.0851 Maine 1.0846 Missouri 1.0759 Oregan 1.0726 N. Dakota 1.0708 Wisconsin 1.0705 Louisiana 1.0680 Indiana 1.0674 Delaware 1.0645 Virginia 1.053 1 Mississippi 1.0219 Arizona 1.0207 Montana 0.9972 Utah 0.9972 Texas 0.9841 Vermont 0.9816 Ohio 0.9750 Colorado 0.9699 Washington 0.9662 Nevada 0.9606 Michigan 0.9542 Illinois 0.9522 Idaho 0.9286 Pennsylvania 0.9194 Wyoming 0.9097 S. Dakota 0.9076 Florida 0.8623 New York 0.8554 Massachusetts 0.8436 Rhode Island 0.8403 Connecticut 0.8321 Maryland 0.8289 California 0.8002 New Jersey 0.7450

p3

G.A. Carlino and R. Voith, Differences in aggregate state productivity

Table 4c

611


Industry mix Random effects

State P, State P,

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Nevada Florida Missouri Georgia New Jersey New York Illinois Pennsylvania Massachusetts Oregon Maine New Hampshire Washington Ohio Arizona Tennessee Minnesota Indiana Maryland Vermont Delaware Connecticut Rhode Island Michigan N. Carolina Colorado California Wisconsin S. Carolina Utah Alabama Nebraska Idaho Arkansas Virgina Iowa Kansas Mississippi W. Virginia Kentucky S. Dakota Montana N. Dakota Texas Oklahoma New Mexico Louisiana Wyoming

. .

1.1272 1.1214 1.1195 1.1164 1.1103 1.0968 1.0930 1.0894 1.0868 1.0792 1.0749 1.0683 1.0617 1.0657 1.0644 1.0600 1.0586 1.0553 1.0535 1.0533 1.0464 1.0424 1.0333 1.0310 1.0292 1.0288 1.0242 1.0185 1.0167 1.0159 1.0129 1.0073 1.0054 1.0028 0.9841 0.9763 0.9619 0.9532 0.948 1 0.9443 0.9440 0.9335 0.8920 0.8591 0.8095 0.7586 0.707 1 0.6459

2

4 5 6

8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Delaware 1.2204 Wyoming 1.2173 Louisiana 1.1582 New Jersey 1.1415 Connecticut 1.1225 Michigan 1.1217 W. Virginia 1.0872 Idaho - 1.0857 Vermont 1.0692 California 1.0684 Texas 1.0672 Nevada 1.0639 New Mexico 1.0616 Oklahoma 1.0567 New York 1.0438 Rhode Island 1.0389 Colorado 1.0286 Maryland 1.0194 Arizona 1.0147 S. Dakota 1.0070 S. Carolina 1 .OO68 Kentucky 1.0037 Mississippi 0.9973 Maine 0.9946 N. Carolina 0.9855 Utah 0.9843 Illinois 0.9729 Alabama 0.9127 Ohio 0.9649 Massachusetts 0.9618 Arkansas 0.9595 Tennessee 0.9570 Washington 0.9514 New Hampshire 0.9508 Florida 0.9465 Indiana 0.9445 Missouri 0.9345 N. Dakota 0.9294 Pennsylvania 0.9276 Oregon 0.9263 Virgina 0.9253 Wisconsin 0.9238 Montana 0.9 159 Minnesota 0.9096 Georgia 0.9068 Kansas 0.8883 Iowa 0.8703 Nebraska 0.8578


have total productivity indices that are greater than one. Four of the six New England states are among the ten most productive states in the nation. Rhode Island, the most productive of the New England states, was almost 23% more productive than the national average during the sample period. Even the least productive New England state, Maine, is more than 8% more productive than the average state. The industrial-belt states fared rather well in terms of overall productivity. l6 In fact, the least productive industrial belt state, Maryland, is still about 2”/, more productive than the 48 state average.

The southern part of the country did well according to the total productivity index. Six of the eight South Atlantic states have productivity indices above unity, while three of the East South Central states have total productivity indices greater than one.

Alternatively, the West region of the country is generally less productive than the national average. Every state in the Pacific and Mountain regions have overall productivity indices that are less than one in value. In addition, the majority of the West North Central states and West South Central states have total productivity indices below unity in value.

As table 4b shows, there is also a great deal of variation in productivity across states resulting from educational attainment and highway density. This index ranges from 36% above the national average for Rhode Island, to about 21% below the 48 state average in Nevada. In terms of regional effects, with the exception of Iowa, all of the states with an index greater than unity for educational attainment and highway density are east of the Mississippi river.

Table 4b also shows the results of agglomeration and congestion on state productivity. There is somewhat less variation in productivity resulting from a state’s net agglomeration economies. The net agglomeration economies index ranges from 12% above the national average for Kansas, to about 25% below the 48 state average in New Jersey. In terms of regional effects, many of the industrial-belt states have indices below unity as congestion effects tend to dominate.

As table 4c shows, there is also a great deal of variation in productivity resulting from a state’s industrial structure. The industrial structure index ranges from almost 13% above the national average for Nevada, to 35% below the 48 state average in Wyoming. Florida, Missouri, Georgia, and New Jersey, follow Nevada, with industrial structures that contribute 11% more to productivity in this category than the 48 state average.

In terms of broad geographic regions, every state in the New England, Middle Atlantic, East North Central, and Pacific regions have industrial structure indices greater than one in value. In terms of negative findings, the

16The industrial-belt extends from New York in the Northeast, southward to Maryland, east to New Jersey, and west to Illinois.


West South Central region is the only region in which every state has an industrial-mix index below unity.

Finally, the unexplained, state-specific variation is relatively small as is evident in the random-effects index, P,. According to this index, Delaware once again leads the list, being 22% above the national average for this category. Wyoming, in second place, with an index slightly below 22%. Nebraska is at the other end of the distribution being roughly 14% below the national average.

In terms of regional effects, the East North Central and West North Central states have random effects below the national average for 10 of the 12 states in these regions. The South Atlantic and East South Central regions have many states with indices below unity for this category as well.

6. Manufacturing results

Since most of the prior work on productivity differences is based on manufacturing data, the model is also estimated using output, employment and wages for the manufacturing sector. The estimated regression coefficients are shown in column 1 of Table 5 and the production function parameters are shown in column 2. The equation differs from the overall equation only in that the industrial structure variables are not included.17 Manufacturing percent of total GSP is included, however, to capture localization economies.

According to the results reported in Table 5a, only the education, union and time variables have the expected (positive) sign and are significant. The only other significant variable, percent manufacturing, a proxy for localization economies, has a negative coefficient which is most readily interpreted as reflecting disequilibrium in manufacturer’s location during the period. The proxies for urbanization economies, percent urban, and urbanization diseconomies, percent urban squared, are insignificant.

The results obtained from the manufacturing version differ broadly from those obtained from overall GSP. Educational attainment is the only productivity variable producing similar significant results in both sets of data. The inconsistency in the findings between the GSP and manufacturing versions has important implications for the work that has been done on regional productivity. Due to a lack of data on aggregate output at local levels, researchers have had to focus on the manufacturing sector, where data are available, and make inferences about aggregate local productivity based on the manufacturing results. Our findings suggest that such an approach could lead to quite misleading conclusions about aggregate productivity of an area, since the results for manufacturing are broadly inconsistent with those for GSP.

“Also there are fewer observations because of missing data on manufacturing wages.

614 G.A. Carlino and R. Voith, Dgferences in aggregate state productivity

Table 5a

Manufacturing regressions.“sb

Constant

Education

Union

Highway density

Time

Energy shock

Percent urban

Percent urban sq.

Manufacturing

108 Q

log L

P

Economy of scale

RZ 0.957 Obs. 803

GLS Transformed estimates estimates

0.990 1.161 (0.238)*** (0.261)***

0.004 0.005 (0.002)* (0.003)*

0.005 0.006 (0.002)*** (0.002)***

0.151 0.178 (0.202) (0.238)

0.001 0.001 (0.0002)*** (0.0002)***

0.001 0.001 (0.001) (0.001)

-0.196 - 0.230 (0.167) (0.196)

-0.0004 -0.001 (0.150) (0.176)

- 0.097 -0.114 (0.056)* (0.067)*

0.148 (0.021)***

- 0.097 (0.020)***

-0.852 (0.021)***

1.060 (0.002)***

“Numbers in parentheses are estimated standard errors.

“*Significant at the 10% level; **Significant at the 5% level; ***Significant at the 1% level.

Table 5b reports the overall productivity index for manufacturing. One interesting finding is that there appears to be much less variation across states in manufacturing productivity than in GSP productivity. The differential in state manufacturing productivity runs from 10% above the 48 state average in Lousiana to about 10% below in New York. In comparison, the GSP productivity index ranged from about 50% above the average in Delaware to almost 35% below in Wyoming. In terms of broad regional groupings, the more productive manufacturing states are found in the West North Central, the West South Central and the Mountain states. With the

G.A. Carlino and R. Voith, DSfferences in aggregate state productivity 615

Table 5b

Ranking of states by manufacturing productivity level.

1 2 3 4 5 6 I 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Manufacturing productivity

Manufacturing productivity

State

Louisiana S. Dakota Montana Iowa Wyoming N. Dakota Oklahoma Delaware Idaho S. Carolina Nebreaska Kansas Vermont Texas Arizona Kentucky Maryland Alabama Michigan Mississippi New Mexico W. Virginia Georgia Arkansas

P.5 1.1002 1.0898 1.0777 1.0603 1.0541 1.0533 1.0482 1.0468 1.0455 1.0407 1.0344 1.0338 1.0326 1.0294 1.0269 1.0239 1.0225 1.0192 1.0165 1.0115 1.0105 1.0020 0.9992 0.9948

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

State P6 Nevada 0.9945 N. Carolina 0.9899 Connecticut 0.9880 Maine 0.9878 Tennessee 0.9874 Indiana 0.9871 Colorado 0.9849 Oregon 0.9837 Wisconsin 0.9825 Florida 0.9823 Ohio 0.9787 Virginia 0.9787 Minnesota 0.9739 New Hampshire 0.9705 Utah 0.963 1 New Jersey 0.9604 Illinois 0.9570 Rhode Island 0.9545 Missouri 0.9498 Washington 0.9492 Massachusetts 0.9277 Pennsylvania 0.9250 California 0.9231 New York 0.9049

exception of Maryland and Michigan, the manufacturing belf states have productivity indices below the national average. This finding is consistent with movement of manufacturing activity to smaller cities and non- metropolitan places found by Carlino (1985).

Finally, a Spearman rank correlation coefficient is computed to see what correlation, if any, exists between the GSP state rankings, P, and the manufacturing state rankings, P,. The null hypothesis tested is that there is no correlation between P, and P, against the alternative that they are correlated. The test suggests rejection of the null hypothesis in favor of the alternative hypothesis that P, and P, are negatively correlated at the 5% level of significance. This finding underscores the need to be cautious in making inferences about aggregate state productivity from manufacturing based data.

7. Conclusion

This paper shows that the GSP series published by the BEA can be quite


useful in analyzing state level productivity. Specifically, the study finds considerable variation in total productivity across states. Aggregate state productivity differentials can be attributed to a state’s industrial structure, its human capital characteristics, its investment in infrastructure, its metropolitan structure, and other state-specific effects. Moreover, we find that state productivity based on aggregate GSP differs widely from similar measures based solely on manufacturing data. Our findings suggest caution should be taken in making inferences about state productivity based solely on manufacturing data.

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Accounting for differences in aggregate state productivity

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