Measurement Error and Choice of Econometric Estimation Method: Some Empirical Findings

Abstract

The question of what procedure to choose for estimating a given simultaneous-equation model is a basic one in applied econometrics. Considerations of computing cost, small-sample properties of estimators, and the sensitivity of different estimators to specification error are all relevant. Also relevant is the sensitivity of estimators to errors of observation or measurement. Do measurement errors in the data tend to distort some estimators more than others? How important in practice is the problem of measurement error in relation to the more widely discussed problem of choosing among alternative estimators ? The purpose of this paper is to present some results bearing on both of these questions. There are two ways of approaching the questions. One is to carry out Monte Carlo experiments with artificial data.' The other and this is the one followed here is to seek and make use of real-world data for which there is some information about actual errors of measurement.2 Both approaches have advantages and disadvantages. The particular advantage of the second approach is obvious: it produces results based on actual errors rather than artificial ones for which distributions must be assumed. On the other hand, a major disadvantage is the scarcity of data for which anything is known about errors. The presence of measurement error in economic statistics is widely recognized, of course, but specific information is seldom available. One case for which some information is available is the case of preliminary national accounting data. The United Nations Statistical Office compiles and publishes, in standardized form, annual national accounts estimates for a large number of countries. Each year the estimates for previous years may be modified by the national statistical agencies reporting to the U.N. as new or improved information becomes available. Undoubtedly, even the most thoroughly revised figures are still less than perfect but presumably they are better than the preliminary ones. In this sense, the differences between preliminary and revised data may be viewed as measurement errors of a kind. What we have done in this study is to specify a small model, estimate this model using preliminary national accounting data for each of 21 countries, and then re-estimate the same model for the same time period using revised data. The characteristics of the data revisions themselves and their effects on parameter estimates obtained by two-stage least squares have been reported in detail in Denton and Oksanen [4]. In the present study, we have estimated the model by ordinary least squares (OLS) and three-stage least squares (3SLS), as well as two-stage least squares (2SLS). The focus here is on (a) the relative sensitivity to