System Estimation and Labor Demand Elasticities

"He may have a great production function but he sure has a strange utility function." attributed to Arnold Harberger (relating to W. Erwin Diewert's preference for Vancouver over Chicago)

In this assignment you will use single equation and system estimation methods to obtain elasticities of substitution for labor. You will also evaluate price elasticities of labor demand and perform statistical tests relating to functional form and the conditions most conducive to efficiency gains from system estimation.

ü initial steps with data

The data for this exercise is available for downloading as KLEM in MS Excel workbook format. The data set is from a study by Berndt and Wood (1975) and organized in a single worksheet. There are 25 annual observations for U.S. manufacturing. Variables include input prices (Pk, Pl, Pe, Pm), input quantities (Qk, Ql, Qe, Qm), gross output (Qy), value-added output (Qv), corresponding output prices (Py, Pv) and a number of other time series variables (Z1 through Z10). Create an EViews workfile from the spreadsheet as a dated time series.

A valuable preliminary exercise would be to inspect the data in the context of labor demand. What does the time series for manufacturing employment (Ql) look like and what has been the average annual growth in labor input? How does this compare to the time series and average annual growth for manufacturing output (Qy)? What does this imply for labor productivity (Qy/Ql), labor input requirement and labor cost share? With respect to input substitution, does there appear to be a relationship between the relative utilization of inputs and the price of labor relative to other input prices?

ü elasticities of substitution, single equation estimates

The CES specification of the production function yields several alternative means of estimating the elasticity of substitution between two inputs. In particular, equation 9.11 in Berndt (1991, p. 454) is an estimable equation with relative factor demand as a function of relative input prices. Use this specification and OLS to obtain elasticities of substitution between labor-capital, labor-energy, and labor-materials.

The GL specification of the cost function yields a set of cost-minimizing factor demand equations. In particular, equation 9.25 in Berndt (p. 461) gives the input requirement for labor (Ql/Qy) as a function of the square root of relative input prices. Corresponding elasticities of substitution are defined in 9.29 and 9.30 (Berndt, p. 464). Estimate the GL single equation for labor demand and evaluate the elasticities of substitution at sample mean values.

How do the substitution elasticities from these two alternatives (CES and GL) compare? What concerns do you have regarding these estimates?

ü elasticities of substitution, a system estimation approach

What do we hope to gain by using a system estimation approach in this case? Under what conditions would we expect SUR to provide more efficient estimates than equation-by-equation OLS?

Construct a system of equations for GL factor demand based on 9.24 through 9.27 in Berndt (p. 461). Apply the appropriate symmetry conditions through cross-equation parameter restrictions and estimate the system using the seemingly unrelated regressions (SUR) method. Confirm that you are implementing SUR-IZEF with the iteration options set to iterate to convergence. Refer to EViews Help topics on System Estimation for guidance.

Calculate the elasticities of substitution between labor-capital, labor-energy, and labor-materials at sample mean values and compare to those obtained earlier.

There are two ways to evaluate the validity of the primary condition for SUR (you are free to choose either one). The standard approach relies on the Breusch-Pagan test described in the Baltagi reading (2002, pp. 257-258). View the residual correlation matrix in EViews for your OLS estimates to form the chi-squared test statistic. A less formal alternative approach is to compare the standard errors from SUR parameter estimates (for the labor equation alone) to the standard errors from OLS parameter estimates. For this exercise you will need to reestimate using SUR without the symmetry constraints to assure comparability with the OLS estimates.

ü price elasticities and statistical inference in system estimation

In many applications we are interested in the price elasticities of labor demand. Berndt (p. 464) provides the necessary calculations for the own-price (equation 9.32) and cross-price (equation 9.31) elasticities. Use your SUR-IZEF estimates with symmetry conditions imposed and sample mean values to evaluate the price elasticities for labor. How does the own-price elasticity at sample means compare to the results for 1971 reported in Berndt? Discuss which inputs are substitutes and complements for labor.

The GL specification nests the fixed-proportions Leontief form as a special case. EViews provides for statistical inference on the validity of parameter restrictions in systems using the Wald coefficient test procedure. Evaluate the hypothesis of fixed-proportions for U.S. manufacturing production.

Wooldridge (2002) argues that system estimation may have practical advantages even when the appropriate conditions for SUR are not present. What are the advantages of system estimation in the empirical exercises that you have just completed?

ü related references

Berndt, The Practice of Econometrics: Classic and Contemporary, Addison-Wesley, 1991. Diewert, "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, 1971. Baltagi, Econometrics, third edition, Springer-Verlag, 2002. Wooldridge, Econometric Analysis of Cross Section and Panel Data, MIT Press, 2002. Nakamura, “A Nonhomothetic Generalized Leontief Cost Function Based on Pooled Data,” Review of Economics and Statistics, November 1990.

update 9/28/06