Measurement Error. and Latent Variables
Traditionally, an assumption underlying econometric models is that the regressors are observed without measurement error. In practice, however, economic observations, micro and macro, are often imprecise (Griliches, 1986). This may be due to clearly identifiable factors. If these are known, we may apply a better measurement procedure on a later occasion. However, it may also be the case that no better procedure is possible, not even in a perfect world. The variable concerned may be a purely mental construct that does not correspond to a variable that can, at least in principle, be observed in practice. In fact, quite often economic theorizing involves such latent variables.
Typical examples of latent variables appearing in economic models are utility, the productivity of a worker, permanent income, consumer satisfaction, financial health of a firm, the weather condition in a season, socioeconomic status, or the state of the business cycle. Although we use the epithet "latent" for these variables, we can, for each of these examples, think of related observable variables, so some kind of indirect measurement is possible. In this sense the latency of variables is a generalization of measurement error, where the relation between the observed variable and its true or latent counterpart is just of the simple kind: observed = true + measurement error.
Clearly, many variables economists work with are latent, due to measurement error or intrinsically so. In this chapter, we will discuss the problems that are invoked by the presence of measurement error and latent variables in econometric models, possible solutions to these problems, and the opportunities offered by latent variable models. Related references are Aigner, Hsiao, Kapteyn, and Wansbeek (1984), who give an extensive overview of latent variable models, and Fuller (1987) and Cheng and Van Ness (1999), which are book-length treatments of measurement error models.