Trends And Empirical Econometric Limits

Yale University, New Haven CT

Investigators

Abstract

An important issue that bears on all practical economic analysis is the extent to which we can expect to understand economic phenomena by the process of developing a theory, taking observations and fitting a model. An especially relevant question in practice is whether there are limits on how well we can predict future observations using empirical models that are obtained by such processes. Finding quantitative expression for these limits is the main subject of the project. A primary limitation on empirical knowledge is that the true model for any given data is unknown and, in all practical cases, unknowable. This is because even if the formulated model were correct it would still depend on parameters that need to be estimated from data. Often, the data is scarce relative to the number of parameters that need to be estimated, and this is especially so in models that have some functional representation that necessitates the use of nonparametric or semiparametric methods. In such situations one might expect that the empirical limitations on modeling are greater than in finite parameter models. Using reasoning that was pioneered by Jorma Rissanen in 1987, the author has shown in collaborative work with Werner Ploberger in 1999 that there is a quantitative bound on how close an empirical model can get (in terms of its log likelihood ratio) to the true model. This bound depends on the data itself as well as the model that is being used. A discovery that seems important in applications to economic data is that the magnitude of the bound depends on the presence and nature of trends in the data. In particular, the achievable distance is greater for trending data than when the data are stationary. This result gives quantitative expresssion to the intuitively appealing notion that trending data is harder to predict than data that does not trend. The project develops and extends limitation results of this type to models where there are local and gross errors of specification, to nonparametric situations where the dimension of the parameter space is infinite or where it may grow with the sample size, that is, in situations where modeling becomes more ambitious as more data becomes available. The project also seeks to develop explicit representations of the forecast error divergence so that the limits on empirical forecasting capability are quantifed. The intent of this project is to develop the theory to a stage where the limits will be useful to empirical researchers, especially in terms of the implementation of model determination criteria that are designed to achieve the empirical bounds. In subsidiary wings of research that relate to this main theme, the project studies more explicit issues of trend regression, where the order of magnitude of the trend is not specifed but has to be estimated, where there is long memory in the data which is possibly nonstationary and the memory parameter must be estimated semiparametrically, and where there is nonstationary explanatory data but a limited dependent variable. The latter study is relevant to market intervention policy by the Federal Reserve and Treasury. Thus, monetary policy intervention is a binary decision (intervene or not), yet the explanatory variables that determine it involve a host of economic data, much of which has nonstationary features, like the growth characteristics of industrial production and the random wandering behavior of stock prices. We seek to learn how various characteristics in the explanatory data translate into the probability law for the binary variable and, hence, market intervention. Can these probability laws explain, for instance, the tendency of market intervention to lapse into long periods of little intervention broken by periods of regular intervention?