Graham Elliott - US grants

9720675 Elliott The objective of this project is to develop minimum distance methods for inference in cointegrated time series regressions and short panel data models. Cointegrated models have found particular favor among applied researchers because of their direct relationship with economic theory, i.e., distinguishing between long-run and short-run dynamics. Minimum distance methods appear to provide ideal methods for estimating and conducting inference on these models. This is very useful as current methods of estimation of cointegrating models have proven quite difficult to extend in directions that are useful to applied econometricians. Methods are often special to the problems of cointegration per se or result in complicated computational methods. In most situations closed form solutions are available for estimation when minimum distance methods are applied. These methods are very simple and well understood enabling fairly simple extension of methods for estimation of cointegrated models in directions that should prove useful in applied work. The particular extensions envisaged for time series models are estimation when there are restrictions on the cointegrating vectors (linear or nonlinear, within or across equation), the presence of stationary variables, and the presence of heteroskedasticity. In the panel models, the project will be to provide and evaluate estimators and rules for inference in short time dimension panel data sets when observations on many individuals are available. The focus of this model is to incorporate as much heterogeneity across individuals as possible. These methods will be extended also in the same direction as the time series models. ??

Economic time series are often difficult to predict and as a result different forecasters, faced with predicting the same economic variable, often come up with very different answers, reflecting their use of separate forecasting models, information sets and estimation methods. It is very rare for any individual forecast to systematically dominate the others. Many studies have found that a simple equal-weighted combination of forecasts produces better predictions than those generated by individual models. This project develops both theoretical tools and empirical techniques for explaining why simple equal-weighted forecasts do so well in practice and compares these with wider classes of combinations.
The research project develops estimation and forecast combination methods that can compete with the equal-weighted forecast combination. We establish conditions under which our proposed methods can be expected to produce improved forecast. The research project also considers the performance of different forecast combination methods under a host of economic circumstances, including prediction of economic variables in the near, medium and distant future, prediction of the entire probability distribution of an economic variable and prediction with loss functions that are tailored to individual policy makers or economic decision makers. The proposal also investigates the possibility of letting the forecast combination weights vary over time since some models may work better in some situations (e.g. when the economy is in a recession) and others may prove to be better in different circumstances (e.g. an expansion state).
Forecast combination techniques have already been found to be useful in practical situations. This proposal provides further understanding of why this is so and explores various alternative approaches both theoretically and in practice, particularly when many forecasts are involved, and expands the approach in new ways. The interest in developing these methods is in part driven by practical concerns of the Principal Investigators that has come through interaction with the various Federal Reserve banks and other international organizations such as the IMF and through considering their needs and requests. We expect to continue strong relations with these and other organizations through the grant period.

The widespread empirical findings of instabilities in macroeconomic and financial data have attracted a lot of attention recently. As a result, much effort has been devoted to designing new and improved tests for parameter instability, and researchers have paid more attention to such tools in their empirical work. However, methods that allow forecast model evaluation and selection in such unstable environments are still lacking in the literature. It is therefore important to develop such tools, and the investigators' research agenda aims at filling that void. The investigators' propose to investigate new methods for evaluating the forecasting performance of economic models, and for conducting model selection in the presence of structural instability. The novelty of their approach is to allow for unstable environments where the forecasting performance of a model, as well as the relative performance of competing models, could be changing over time.

In the first subproject, Detecting and Predicting Forecast Breakdowns, the investigators propose to investigate a theoretical framework for assessing whether a forecast model estimated over one period can provide good forecasts over a subsequent period. They define a forecast breakdown as a situation in which the out-of-sample performance of the model, judged by some loss function, is significantly worse than its in-sample performance, and propose a method to detect such situations. In a second research project, Non-nested Model Selection in Unstable Environments, the investigators plan to consider non-nested model selection tests in the presence of possible data and parameter instabilities. The novelty of their approach is that it allows the models' relative performance to be varying over time, whereas existing model selection techniques look for an overall best model.

The broader impact of the proposed activity will come from the new methods shared with practitioners within the scientific community and students alike, and the contributions to our understanding the role of instabilities in economics. This project provides mentoring, collaboration opportunity, dissertation motivation and financial support for a graduate student. The proposal will result in papers that will be presented at seminars and professional conferences, and ultimately published in scholarly journals.