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We address the issue of using a set of covariates to categorize or predict a binary outcome. This is a common problem in many disciplines including economics. In the context of a prespecified utility (or cost) function we examine the construction of forecasts suggesting an extension of the Manski (1975, 1985) maximum score approach. We provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on conditional probability models. Large gains over existing methods can be attained when models are misspecified. The results are informative for both forecasting environments as well as program allocation where the value of including the participant in the program depends on how useful the program turns out to be for that participant.
"Pre and Post
Break Parameter Inference" (joint with Ulrich Mueller)
This paper provides a method for conducting inference about the pre and post break value of a scalar parameter in GMM time series models with a single break at an unknown date. We show that treating the break date estimated by least squares as the true break date leads to substantially oversized tests and confidence intervals unless the break is large. We develop an alternative test that controls size uniformly and that is approximately efficient in a well defined sense.
The optimal combination of forecasts, detailed in Bates and Granger (1969), has empirically often been overshadowed in practice by using the simple average instead. Explanations of why averaging might in practice work better than constructing the optimal combination have centered on estimation error and the effects variations of the data generating process have on this error. The flip side of this explanation is that the size of the gains must be small enough to be outweighed by the estimation error. This paper examines the sizes of the theoretical gains to optimal combination, providing bounds for the gains for restricted parameter spaces and also conditions under which averaging and optimal combination are equivalent. The paper also suggests a new method for selecting between models that appears to work well with SPF data.
We show that when outcomes are difficult to forecast in the sense that forecast errors have a large common component that (a) optimal weights are not affected by this common component, and may well be far from equal to each other but (b) the relative MSE loss from averaging over optimal combination is small. Hence researchers could well estimate combining weights that indicate that correlations could be exploited for better forecasts only to find that the difference in terms of loss is negligible. The results then provide another explanation for the commonly encountered practical situation of the averaging of forecasts being difficult to improve upon.
"Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis" (joint with Ulrich Mueller and Mark Watson).
This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish a bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.