Analyzing Three-Dimensional Panel Data of Forecasts
With the proliferation of quality multi-dimensional surveys, it becomes increasingly important for researchers to employ an econometric framework in which these data can be properly analyzed and put to their maximum use. In this chapter we have summarized such a framework developed in Davies and Lahiri (1995, 1999), and illustrated some of the uses of these multi-dimensional panel data. In particular, we have characterized the adaptive expectations mechanism in the context of broader rational and implicit expectations hypotheses, and suggested ways of testing one hypothesis over the others. We find that, under the adaptive expectations model, a forecaster who fully adapts to new information is equivalent to a forecaster whose forecast bias increases linearly with the forecast horizon. A multi-dimensional forecast panel also provides the means to distinguish between anticipated and unanticipated changes in the forecast target as well as volatilities associated with the anticipated and unanticipated changes. We show that a proper identification of anticipated changes and their perceived volatilities are critical to the correct understanding and estimation of forecast uncertainty. In the absence of such rich forecast data, researchers have typically used the variance of forecast errors as proxies for shocks. It is the perceived volatility of the anticipated change and not the (subsequently-observed) volatility of the target variable or the unanticipated change that should condition forecast uncertainty. This is because forecast uncertainty is formed when a forecast is made, and hence anything that was unknown to the forecaster when the forecast was made should not be a factor in determining forecast uncertainty. This finding has important implications on how to estimate forecast uncertainty in real time and how to construct a measure of average historical uncertainty, cf. Lahiri and Sheng (2010a). Finally, we show how the Rational Expectations hypothesis should be tested by constructing an appropriate variance-covariance matrix of the forecast errors when a specific type of multidimensional panel data is available.
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