Working with the Translog Factor Demand System

"These trends support the notion that, historically, biased technological change has been an important source of increased (relative) demand for skilled labor. They also suggest that we avoid exaggerating the uniqueness of the computer revolution.” Berman, Bound and Griliches (1994).

In this assignment you will employ the translog factor demand system to evaluate labor demand elasticities for manufacturing industries. You will also conduct related tests of hypotheses and consider how labor demand elasticities have varied over time in response to nonneutral technical change.

ü initial steps with data

The data sets for this set of exercises are related to the study by Baltagi and Rich (2005). There are annual observations from 1958-1996 for U.S. manufacturing industries. Data sets are available for downloading in MS Excel workbook format and organized into separate worksheets for selected industry groups: mfg1 (food products, textiles and apparel, chemicals and petroleum, plastics and related), mfg4 (primary and fabricated metals, industrial machinery and equipment, electrical and electronic equipment, transportation equipment, and instruments). Variables include input prices for five inputs, input quantities and output. Choose one of these industry groups (subject to instructor approval) and create an EViews workfile from the spreadsheet as a balanced panel with the detailed industry code (sic4) as the cross-section identifier.

Inspect the data in the context of labor demand for production and nonproduction labor. How does the average annual growth of production and nonproduction employment compare to the average annual growth of output across your group of industries? Construct cost shares for all inputs and present the pattern of change over time. Identify which of your detailed industries appear to experience the largest decline in the cost share of production labor. Also construct relative prices of all inputs relative to production labor and note significant patterns or trends that may induce input substitution.

ü using the translog factor demand system

Construct all of the variables you will need to estimate the translog (TL) system. Use the homogeneity, symmetry and adding up constraints to define four factor share equations (exclude materials). Estimate this system using the SUR-IZEF method in EViews.

Use the Wald coefficient test procedure to evaluate whether production is homothetic across the two labor categories and across all inputs. Discuss the implications of nonhomothetic responses across the two labor categories and across all inputs.

Evaluate goodness-of-fit for your translog factor demand system using either the Wald coefficient test or the likelihood ratio test (see Berndt, pp. 468-469).

Calculate the full set of own-price and cross-price elasticities at sample means for both production and nonproduction labor. Discuss any asymmetric findings across the two labor categories.

ü introducing nonneutral technical change

Observed patterns in the relative employment of production labor may arise from nonhomothetic responses to output changes, price-induced substitution among inputs, or nonneutral responses to technical change. Construct a time trend variable (1958 = 1) and introduce this variable into each of your factor share equations. Reestimate the translog system, present your estimates of technical change bias, and discuss the results for production and nonproduction labor. You may want to explore this issue in more detail using industry-specific trend variables.

If there is nonneutral technical change then we might expect the elasticities to change over time. Split your sample into three equal time periods, construct the appropriate trend variables for each subsample, and reestimate the system for each subsample. Calculate the own-price and cross-price elasticities for production and nonproduction labor. Discuss how the labor demand relationships are changing over time.

ü related references

Berndt, The Practice of Econometrics: Classic and Contemporary, Addison-Wesley, 1991. Christensen, Jorgenson and Lau, "Transcendental Logarithmic Production Frontiers,” Review of Economics and Statistics, 1973. Allen and Liu, “Service Quality and Motor Carrier Costs: An Empirical Analysis,” Review of Economics and Statistics, August 1995. Baltagi and Rich, “Skill-Biased Technical Change in U.S. Manufacturing: A General Index Approach,” Journal of Econometrics, June 2005.

update 10/12/06