Constructing instruments for regressions with measurement error when no additional data are available, with an application to patents and R & D.

*(English)*Zbl 0898.90044From the introduction: 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 instruments 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.

The present paper extends earlier 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. 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.

The present paper extends earlier 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. 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.

##### MSC:

91B62 | Economic growth models |