peer reviewed article

map of the U.S.A.


by William L. Seyfried

William L. Seyfried is an associate professor in the Department of Humanities and Social Sciences at Rose-Hulman Institute of Technology.


Much anecdotal evidence exists regarding the success of regional economies with several studies having attempted to compare the performance of regional economies to that of the overall economy in terms of economic growth and job creation. (For example, see Eberts and Montgomery, 1994; Smith, 1995.) In order to distinguish between cyclical factors and underlying sectoral trends, this study borrows concepts well known in the finance literature, alpha (a) and beta (B).

This technique has been applied to employment trends by Berry, House and McGreary (1981) and Chotigeat (1987). The former used the result to help provide information on how to promote employment stability in a particular region, while the latter took a similar approach for the Puerto Rican economy. Estimates of a and B can be found in the following manner: monthly employment growth in a particular sector is regressed on overall employment growth. The Bs are thus a measure of sectoral-employment elasticity or the volatility of a particular sector. The a coefficients reveal whether a sector is growing or declining, in terms of employment, relative to the overall employment once the role of B is taken into account.

Monthly employment data from 1991 to 1996 are used to estimate employment as and Bs in major sectors of the economy. These are then statistically tested to assess whether the employment trends in particular regions of the country are similar to those of the nation.



Beta analysis has been used in financial portfolio theory to assess the volatility of particular stocks over time. (For example, see Elton and Gruber 1991.) This can be done in a bivariate regression involving the stock return and the market return in which beta (B) represents the coefficient on the market return and alpha (a) represents the constant term. High values of B -- those greater than one -- indicate that the stock fluctuates more than the market, while values of B less than one indicate that the stock is more stable than the market as a whole. The constant term, a, in the regression also has significance. A stock with a positive a is growing more than the overall market, once its volatility (as measured by its beta) is taken into account, while a negative a indicates a relatively poor performing stock.

Several studies in the literature on sectoral shifts employ similar approaches. Abraham and Katz (1986) regressed the natural log of sectoral employment on a time trend and the difference between the natural logs of real GNP and potential real GNP. They interpreted the coefficient on the latter term as a measure of the cyclical sensitivity of the particular sector. Palley (1992) regressed sectoral employment growth on current and lagged total employment growth to obtain the part due to aggregate factors or aggregate demand shocks and that due to sectoral factors. Brainard and Cutler (1993) estimated the relationship between the natural log of sectoral employment and the natural log of total employment, describing the noncyclical component as the excess employment change (comparing it to the excess stock return in finance theory, i.e., alpha). With regard to regional analysis, the slope of the time-series regression of a regional unemployment rate on the national unemployment rate has been recognized as a measure of the cyclical sensitivity of regional unemployment to fluctuations in overall economic activity. This approach "decomposes regional unemployment into a secular component and a cyclical component" (Byers, 1990). Regressing regional sectoral employment growth on total employment growth can be viewed in a similar manner. The coefficient on total employment growth can be seen as a measure of the cyclical sensitivity of sectoral employment in a particular region, while alpha is a measure of the sectoral or secular trend.

One would expect construction to be more volatile than the economy as a whole, since generally during downturns less building takes place, while during upturns pent-up demand is released, resulting in significant activity. Likewise, manufacturing (particularly that of durable goods) is expected to display above-average volatility, as the sale of durable goods is known to experience considerable fluctuations. Service-oriented industries including services, transportation and public utilities (TPU) and finance, insurance and real estate (FIRE) are expected to be relatively more stable. Employment trends in wholesale and retail trade (WRT) should be quite similar to the overall economy. Palley (1992) regressed sectoral employment growth on current and lagged values of total employment growth using quarterly data from 1948 to 1988. His results were in line with expectations: high coefficients on current total employment growth for construction and both durable and nondurable manufacturing; coefficients on both wholesale and retail trade were not statistically different from one, while TPU, FIRE and services had coefficients significantly less than one.


In order to obtain the employment as and Bs for the nation and its regions, OLS was used to estimate the model with monthly sectoral employment growth as the dependent variable and total US private employment growth as the independent variable. (Growth rates were used as opposed to levels to ensure stationarity; Augmented Dickey-Fuller tests run on the respective variables indicated that each was stationary in the form of growth rates but not levels.) Employment data from April 1991 to December 1996 were collected from Employment and Earnings. The specific period was chosen, as it represents the period of the most recent economic recovery as defined by the National Bureau of Economic Research. It has been noted in previous studies that there is asymmetric behavior of employment over a business cycle; thus the period chosen was limited to an expansion. (For example, see Franses 1995.) After obtaining the employment a and B coefficients for the national economy and different regions, the equivalence of the regional as and Bs to those economy-wide was examined by using a dummy variable variant of the Chow test.

OLS was used to estimate the model for the pooled data with a dummy variable, zero for the first sample (economy-wide) and one for the second (region), in order to allow for differing values of alpha (If one is testing for the equivalence of the B coefficients; likewise, allow for different values of B when considering the equivalence of the a coefficients.) for each sample. The coefficients on the respective dummy variables were then tested for their significance to assess whether regional economies display different behavior than that of the nation.


Estimates of B

The results of the estimation for the nation and regions are displayed in Tables 1 through 5. For the United States as a whole, construction had a B significantly greater than one, while the values for FIRE, Service, TPU and manufacturing were less than one; the B for WRT was statistically equivalent to one. The result for manufacturing differed from that of Palley and from what was expected. This may be due to the different periods covered. Also, manufacturers undertook significant restructuring and implemented new managerial strategies (e.g., just-in-time inventories, etc.) in the 1980s that may have helped stabilize production and employment.

Go to Table 1

Construction Bs were significantly greater than one in New England, the Mid-Atlantic and South-Atlantic, while the manufacturing Bs were less than one in the West North Central and East South Central. All other regions had values close to one for the two sectors. Coefficients for service were statistically equal to one only in the Mid- and South-Atlantic, with the same two regions having Bs for FIRE no different from one (along with the Mountain region). Other regions displayed values less than one for both sectors. Coefficients for TPU were less than one other than in New England, the West North Central and East and West South Central. All regional Bs for WRT were not statistically different from one.

Go to Tables 2 - 5.

Analysis of the national and regional Bs indicated that employment volatility differed in some cases regionally from the nation. The most differences were found for FIRE -- five of the nine regions with three statistically different at the 5% level (East and West North Central and Pacific; the Mid- and South-Atlantic were significant at the 10% level). Both manufacturing and service Bs differed from the nation in three regions: the Mid-Atlantic and East South Central in both cases along with the Mountain region for manufacturing and South-Atlantic for services. Both the Mid- and South-Atlantic exhibited different volatility from the nation in the construction sector. Only the West North Central was different for WRT, while the West South Central was the only one different for TPU. From a regional perspective, no sector was statistically different from the nation in New England, while the Mid-Atlantic had the most that were significantly different at the 10% level (four sectors).

Estimates of a

Three sectors nationally had negative as (indicating that they were relatively poor performing sectors once volatility was taken into account), while the service a was positive, and WRT and construction were not statistically different from zero. Manufacturing, construction, FIRE and WRT as were negative in New England and the Mid-Atlantic, while those of service were positive. (Others were not different from zero.) In the East and West North Central, both FIRE and service had positive as. (WRT had a positive a in the West North Central.) All as were significantly positive in the Mountain region. Service and WRT displayed positive as in the East and West South Central. Negative as for manufacturing and WRT were found in the Pacific, where only service exhibited a positive a. In the South Atlantic the as for both construction and manufacturing were negative, while the service a was positive.

Analysis of the as revealed that manufacturing and WRT differed statistically in seven regions from that of the nation. Differences were found in six regions for FIRE, four regions each for construction and services, and two for TPU. Every sector grew significantly faster in the Mountain region as well as five of the sectors in the East South Central (all but TPU), three sectors in the West North Central and West South Central, and two sectors in the East North Central. Five of the sectors had lower as in the Mid-Atlantic (all but TPU), four in New England and one in the Pacific region (WRT). This is in accordance with the anecdotal evidence regarding the relative weakness of the current economic recovery in the Northeast. Similarly, most accounts indicate that the Midwest, Mountain region and South have experienced strong growth in recent years.


In this paper, I wanted to develop a quantifiable measure of the volatility of sectoral employment trends relative to overall employment trends. Furthermore, I wanted to investigate the hypothesis whether these trends were similar regionally and nationally. Beta analysis provides such a measure. Estimates for all sectors considered were obtained for the United States and its regions. To address the second objective, the appropriate statistical tests were performed. The findings indicated that for some sectors the underlying growth trends and volatilities differed in particular regions from those of the nation.

This technique opens up several new lines of research. As financial planners use Beta Analysis to develop optimal portfolios, local development planners can use employment alphas and betas to formulate strategies for local economic development, seeking to attract firms with high alphas (i.e., superior growth) and low betas (less volatility). Future research can examine the optimality of current strategies. Also, the factors that affect alpha and beta can be analyzed, attempting to determine why they differ across regions.


Abraham, Katherine G. and Lawrence F. Katz, "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?" Journal of Political Economy 94 (1986): 507-522.

Berry, S.G., M. House and F.M. McGreary, "Optimizing Local Area Employment Stability: Utilizing the Employment Data," Paper Presented at the Southern Economic Association meetings (1981).

Brainard, S. Lael and David M. Cutler, "Sectoral Shifts and Cyclical Unemployment Reconsidered," Quarterly Journal of Economics (1993): 219-243.

Byers, J.D., "The Cyclical Sensitivity of Regional Unemployment: An Assessment," Regional Studies 24 (1990): 447-453.

Chotigeat, Tosporn, "Measurement of Industrial Employment Volatility in an Open Economy," Social and Economic Studies 36 (1987): 113-125.

Cox, W. Michael, "Help Wanted: A Look at America's Changing Job Market," The Southwest Economy, Federal Reserve Bank of Dallas (1994): 5-8.

Eberts, Randall W. and Edward R. Montgomery, "Employment Creation and Destruction: An Analytical Review," Economic Review Federal Reserve Bank of Cleveland (Third Quarter 1994): 14-26.

Elton, Edwin J. and Martin J. Gruber, Modern Portfolio Theory and Investment Analysis, John Wiley and Sons: New York, 1991.

Franses, Philip Hans, "Quarterly US Unemployment: Cycles, Seasons and Asymmetries," Empirical Economics 20 (1995): 717-725.

Kahn, George A., "Sluggish Job Growth: Is Rising Productivity or an Anemic Recovery to Blame?" Federal Reserve Bank of Kansas City Economic Review (Third Quarter 1993): 5-26.

Palley, Thomas I., "Sectoral Shifts and Cyclical Unemployment: A Reconsideration," Economic Inquiry 30 (January 1992): 117-133.

Smith, Tim R., "A Healthy Tenth District Economy," Economic Review Federal Reserve Bank of Kansas City (First Quarter 1995): 49-61.

US Department of Labor, Employment and Earnings, 1984-97.

Table 1

Sectoral Employment Estimates for the United States

  a B R2
Manufacturing -0.14* 0.55^ 0.20
Construction -0.15 2.27^ 0.29
FIRE -0.02 0.45^ 0.18
Service 0.22* 0.49^ 0.19
Transport. & Pub. Utilities -0.02* 0.55^ 0.22
Wholesale & Retail Trade 0.00 1.01 0.67

Note: two -sided test of whether B = 1 where ^ indicates 5% level of significance; two-sided test of whether a = 0 where * indicates 5% level of significance

Table 2

Sectoral Employment Estimates for the Northeast

New England a B R2 ta tB
Manufacturing -0.28* 0.82 0.33 3.36x 1.35
Construction -0.42* 3.23^ 0.25 1.63 1.18
FIRE -0.11* 0.60^ 0.20 2.45 x 0.79
Service 0.11* 0.56^ 0.17 2.72 x 0.37
Transport. & Pub. Utilities -0.03 0.47 0.04 0.21 0.24
Wholesale & Retail Trade -0.11* 1.15 0.38 2.73 x 0.71
Manufacturing -0.29* 0.89 0.44 4.11x 1.82'
Construction -0.62* 3.80^ 0.33 2.87 x 1.92'
FIRE -0.12* 0.75 0.30 2.81 x 1.65'
Service 0.04 0.90 0.34 4.45x 2.05 x
Transport. & Pub. Utilities -0.04 0.30^ 0.02 0.35 0.83
Wholesale & Retail Trade -0.13* 1.18 0.43 3.32x 0.88

Note: two -sided test of whether B = 1 where ^ indicates 5% level of significance; two-sided test of whether a = 0 where * indicates 5% level of significance. ta and tB are the t-statistics from the respective tests where x indicates 5% level of significance, ' indicates 10% level.

Table 3

Sectoral Employment Estimates for the Midwest

East North Central a B R2 ta tB
Manufacturing 0.00 0.56 0.07 2.36x 0.02
Construction -0.03 2.01 0.18 0.85 0.37
FIRE 0.09* 0.10^ 0.01 2.86x 1.96 x
Service 0.23* 0.34^ 0.07 0.11 0.79
Transport. & Pub. Utilities 0.08 0.22^ 0.01 1.34 0.93
Wholesale & Retail Trade 0.05 0.71 0.19 1.25 1.52
West North Central          
Manufacturing 0.21 0.58^ 0.13 3.40x 0.14
Construction 0.11 1.57 0.07 1.52 0.85
FIRE 0.15* 0.04^ 0.00 4.09x 2.07 x
Service 0.23* 0.50^ 0.11 0.21 0.05
Transport. & Pub. Utilities 0.06 0.53 0.06 1.42 0.06
Wholesale & Retail Trade 0.11* 0.51^ 0.11 2.74 x 2.61 x

Note: two -sided test of whether B = 1 where ^ indicates 5% level of significance; two-sided test of whether a = 0 where * indicates 5% level of significance. ta and tB are the t-statistics from the respective tests where x indicates 5% level of significance.

Table 4

Sectoral Employment Estimates for the West

Mountain a B R2 ta tB
Manufacturing 0.07* 1.02 0.26 4.10x 1.87'
Construction 0.54* 1.80 0.14 4.82x 0.67
FIRE 0.26* 0.61 0.08 4.81x 0.59
Service 0.36* 0.57^ 0.17 3.29x 0.39
Transport. & Pub. Utilities 0.15* 0.44^ 0.04 2.93x 0.37
Wholesale & Retail Trade 0.23* 0.75 0.20 5.57x 1.26
Manufacturing -0.22* 0.91 0.18 1.49 1.30
Construction -0.16 1.90 0.07 0.08 0.38
FIRE 0.00 -0.03^ 0.00 0.31 2.23*
Service 0.16* 0.54^ 0.09 1.25 0.21
Transport. & Pub. Utilities 0.03 0.17^ 0.01 1.05 1.51
Wholesale & Retail Trade -0.07* 0.82 0.27 1.70' 1.05

Note: two -sided test of whether B = 1 where ^ indicates 5% level of significance; two-sided test of whether a = 0 where * indicates 5% level of significance. ta and tB are the t-statistics from the respective tests where x indicates 5% level of significance, ' indicates 10% level.

Table 5

Sectoral Employment Estimates for the South

East South Central a B R2 ta tB
Manufacturing 0.02 0.10^ 0.00 3.31x 1.89'
Construction 0.12 1.48 0.08 1.76' 1.06
FIRE 0.06 0.44^ 0.08 1.69' 0.04
Service 0.38* 0.05^ 0.00 2.92x 1.71'
Transport. & Pub. Utilities 0.09 0.41 0.02 1.29 0.32
Wholesale & Retail Trade 0.10* 1.01 0.25 2.20 x 0.01
West South Central          
Manufacturing -0.03 0.73 0.29 2.79x 0.92
Construction 0.14 1.35 0.11 2.15x 1.44
FIRE 0.00 0.64^ 0.18 0.48 0.95
Service 0.27* 0.53^ 0.10 1.09 0.16
Transport. & Pub. Utilities 0.03 1.00 0.25 0.92 1.80'
Wholesale & Retail Trade 0.11* 0.78 0.24 2.72 x 1.21
South Atlantic          
Manufacturing -0.11* 0.73 0.29 0.68 0.92
Construction -0.37* 3.76^ 0.43 1.56 2.17 x
FIRE 0.01 0.87 0.25 0.59 1.90'
Service 0.27* 0.87 0.24 0.91 1.65'
Transport. & Pub. Utilities 0.07 0.52^ 0.08 1.73' 0.13
Wholesale & Retail Trade 0.03 1.19 0.49 0.95 1.05

Note: two -sided test of whether B = 1 where ^ indicates 5% level of significance; two-sided test of whether a = 0 where * indicates 5% level of significance. ta and tB are the t-statistics from the respective tests where x indicates 5% level of significance, ' indicates 10% level.

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