CONSTRUCTING INSTRUMENTS FOR REGRESSIONS WITH MEASUREMENT ERROR WHEN NO ADDITIONAL DATA ARE AVAILABLE, WITH AN APPLICATION TO PATENTS AND R&D

摘要

Given a linear regression model with measurement errors in variables, this paper shows how simple functions of the model data can be used as instruments for two staged least squares (TSLS) estimation, exploiting third moments of the data. These instruments can be used when no other data are available, or they can supplement outside instru-ments to improve efficiency. The distribution of the errors is not required to be normal (or known), and the method readily extends to regressions containing more than one mismeasured regressor. These results build on earlier work proposing functions of mismeasured variables as instruments, e.g., Wald (1940), Madansky (1959), and Durbin (1954) (problems with these earlier methods are documented by Pakes (1982) and Aigner, Hsiao, Kapteyn, and Wansbeek (1984)); see also Fuller (1987). There is a separate long literature on the use of higher order moments of observed data to estimate the coefficients in linear regression models with measurement error. See, e.g., Geary (1943), Scott (1950), Reiers0l (1950), Drion (1951), Durbin (1954), Kendall and Stuart (1979), Pal (1980), Kapteyn and Wansbeek (1983), and Aim and Schmidt (1995). Recent work that combines these two approaches includes Dagenais and Dagenais (1994, 1995), and Cragg (1995). The present paper extends these results and provides an empirical application. The empirical model concerns estimation of the elasticity of patent applications with respect to Research and Development (R&D) expenditures. Simple OLS estimates indicate substantial decreasing returns to scale, but are subject to the usual attenuation bias toward zero in the presence of measurement error. Using a variety of more structural models, most empirical research points to constant returns, i.e., an elasticity close to one (see Griliches (1990) for a survey). The simple moment based TSLS estimator proposed here also yields estimates very close to one, and so seems to work as intended to mitigate the effects of measurement error.