Estimation of Poorly-Measured Service-Industry Output

The extent of output growth, hence, productivity growth in service industries has been controversial. Although official data indicate productivity growth slowdowns in 1948-60 and 1979- 98, some economists suggest the official figures are inaccurate due to mismeasured output, inputs, or both. The purpose of this paper is to develop, implement, and evaluate an econometric method for jointly estimating quality-adjusted prices and quantities of output in industries with poorly measured or unavailable output data. The method is applied to selected 2-digit S.I.C. service industries whose output is considered to be poorly measured. The application contributes an alternate approach for studying the growth of output of service industries. The method is based on an estimated dynamic adjustment cost model of a representative firm of the industry being studied. The firm in the model maximizes expected present value of profits subject to a production function and laws of motion of endogenous and exogenous state variables. Industry output price and quantity are determined by a competitive demand-supply equilibrium. Industry output demand is a simple static demand function. Industry output supply is determined by explicitly derived decision rules of the representative firm. The firm's decision rules, production constraints, and laws of motion, and the industry's output demand form a dynamic simultaneous-equations system. The firm's dynamic optimization problem is specified as a linear-quadratic (LQ) control problem. In the LQ problem, the production function is approximated in terms of an LQ dual cost function. The equilibrium equations of the model are estimated by the method of maximum likelihood. In the estimation, the prices and quantities of output are treated as unobserved or latent variables. The structural parameters are identified, hence, are estimatable, because the solution of the firm's optimization problem imposes many identifying cross-equation restrictions. The missing-data Kalman filter is used to handle the unobserved variables in the estimation. Then, the Kalman smoother is applied to the estimated model and the data to compute estimates and standard errors of the missing output price and quantity data. Before being applied to service industries, the method is tested with manufacturing industry data. Manufacturing output prices and quantities are treated as missing, are estimated using the method, and the estimates are compared with the actual observations.