The Effect of Measurement Errors on Parameter Estimates and Forecasts: A Case Study Based on the Canadian Preliminary National Accounts

Abstract

T HE problem of measurement errors has received rather limited attention in the estimation of econometric models and the application of such models to forecasting. The customary treatment has been to ignore the problem altogether, or else to refer to it and then hastily assume, for purposes of the task at hand, that such errors do not exist.1 There are important exceptions,2 but, on the whole, the generalization seems warranted. A major difficulty, of course, is that in practice one seldom knows much about errors in data. Sometimes estimates will have been generated by a probability sampling process so that confidence intervals can be attached to them, but much more frequently in the world of economic statistics this will not be the case. It is certainly not the case with national accounts from whence come so many of the time series used in the estimation of macroeconomic models. On the other hand, national accounting estimates such as those of Canada and the United States customarily pass through several stages of refinement. The initial estimates for year t may be published in year t + 1, revised estimates in year t + 2, and further revised estimates in year t + 3. Indeed, the process of revision may not be complete for many years. For example, in 1958 the Dominion Bureau of Statistics released historical revisions of the Canadian accounts as far back as 1926. Since the last estimates are presumably more accurate than the first ones, the differences may be looked upon as errors of a sort. It is in this light that the analysis which follows may be regarded as a case study of measurement errors and their effects, as well as an appraisal of the reliability of a particular body of data, namely the Canadian preliminary annual national accounts. We shall study the data from three points of view. First, we shall look at the nature and magnitude of the differences between the preliminary and final (i.e., latest) estimates for the period 1949-1958 3 in a more or less straightforward manner, making use of simple summary measures. Second, we shall examine the degree to which preliminary data distort the relationships between different variables and the consequences of using preliminary or incompletely revised data to estimate the structural equations in a macroeconomic model. Third, we shall inquire into the reliability of the preliminary data as a basis for making short-term forecasts.