Trends And Empirical Econometric Limits

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An important issue that bears on all practical economic analysis is the extent to whichwe 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 iswhether there are limits on how well we can predict future observations using empiricalmodels that are obtained by such processes. Finding quantitative expression for theselimits is the main subject of the project.A primary limitation on empirical knowledge is that the true model for any given datais unknown and, in all practical cases, unknowable. This is because even if the formulatedmodel were correct it would still depend on parameters that need to be estimated fromdata. Often, the data is scarce relative to the number of parameters that need to beestimated, and this is especially so in models that have some functional representationthat necessitates the use of nonparametric or semiparametric methods. In such situationsone might expect that the empirical limitations on modeling are greater than in finiteparameter models. Using reasoning that was pioneered by Jorma Rissanen in 1987, theauthor has shown in collaborative work with Werner Ploberger in 1999 that there is aquantitative bound on how close an empirical model can get (in terms of its log likelihoodratio) to the true model. This bound depends on the data itself as well as the model thatis being used. A discovery that seems important in applications to economic data is thatthe 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 arestationary. This result gives quantitative expresssion to the intuitively appealing notionthat trending data is harder to predict than data that does not trend. The project developsand extends limitation results of this type to models where there are local and grosserrors of specification, to nonparametric situations where the dimension of the parameterspace is infinite or where it may grow with the sample size, that is, in situations wheremodeling becomes more ambitious as more data becomes available. The project also seeksto develop explicit representations of the forecast error divergence so that the limits onempirical forecasting capability are quantifed. The intent of this project is to developthe theory to a stage where the limits will be useful to empirical researchers, especially interms of the implementation of model determination criteria that are designed to achievethe empirical bounds.In subsidiary wings of research that relate to this main theme, the project studiesmore explicit issues of trend regression, where the order of magnitude of the trend isnot specifed but has to be estimated, where there is long memory in the data which ispossibly 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 andTreasury. Thus, monetary policy intervention is a binary decision (intervene or not), yetthe explanatory variables that determine it involve a host of economic data, much of whichhas nonstationary features, like the growth characteristics of industrial production and therandom wandering behavior of stock prices. We seek to learn how various characteristics inthe explanatory data translate into the probability law for the binary variable and, hence,market intervention. Can these probability laws explain, for instance, the tendency ofmarket intervention to lapse into long periods of little intervention broken by periods ofregular intervention?