Estimating Loss Function Parameters

In situations where a sequence of forecasts is observed, a common strategy is to examine ‘rationality’ conditional on a given loss function. We examine this from a different perspective - supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.

[1]  Stephen Figlewski,et al.  The Formation of Inflationary Expectations , 1981 .

[2]  Eric Ghysels,et al.  Federal budget projections: a nonparametric assessment of bias and efficiency , 1995 .

[3]  E. Fama,et al.  Short-Term Interest Rates as Predictors of Inflation , 1975 .

[4]  L. Hansen,et al.  Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis , 1980, Journal of Political Economy.

[5]  C. Granger,et al.  Forecasting Economic Time Series. , 1988 .

[6]  K. West,et al.  A Utility Based Comparison of Some Models of Exchange Rate Volatility , 1992 .

[7]  Donald W. K. Andrews,et al.  Empirical Process Methods in Econometrics , 1993 .

[8]  Roy Batchelor,et al.  Rationality testing under asymmetric loss , 1998 .

[9]  Victor Zarnowitz,et al.  Rational Expectations and Macroeconomic Forecasts , 1985 .

[10]  Clive W. J. Granger,et al.  Outline of forecast theory using generalized cost functions , 1999 .

[11]  N. B. Gultekin,et al.  Stock Market Returns and Inflation Forecasts , 1983 .

[12]  Norman R. Swanson,et al.  A Consistent Test for Nonlinear Out of Sample Predictive Accuracy , 2002 .

[13]  A. Zellner.  Bayesian Estimation and Prediction Using Asymmetric Loss Functions , 1986 .

[14]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[15]  Josef Lakonishok.  Stock Market Return Expectations: Some General Properties , 1980 .

[16]  F. Diebold,et al.  Optimal Prediction Under Asymmetric Loss , 1994, Econometric Theory.

[17]  David E. Runkle,et al.  Testing the Rationality of Price Forecasts: New Evidence from Panel Data , 1990 .

[18]  F. Diebold,et al.  Forecast Evaluation and Combination , 1996 .

[19]  Kenneth A. Froot,et al.  Using Survey Data to Test Some Standard Propositions Regarding Exchange Rate Expectations , 1985 .

[20]  Andrew J. Patton,et al.  Properties of Optimal Forecasts , 2003 .

[21]  Scott L. Smith,et al.  A Reexamination of the Rationality of the Livingston Price Expectations , 1986 .

[22]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[23]  Allan Timmermann,et al.  Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss? , 2008 .

[24]  Scott E. Hein,et al.  On the Accuracy of Time-Series, Interest Rate, and Survey Forecasts of Inflation , 1984 .

[25]  Richard Cohen,et al.  Testing the Rationality of Price Forecasts: Comment , 1995 .

[26]  Calyampudi R. Rao.  Handbook of statistics , 1980 .

[27]  W. D. Bondt,et al.  Inflation Forecast Errors and Time Variation in Term Premia , 1992, Journal of Financial and Quantitative Analysis.

[28]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

[29]  Victor Zarnowitz,et al.  An Analysis of Annual and Multiperiod Quarterly Forecasts of Aggregate Income, Output, and the Price Level , 1979 .

[30]  L. Hansen,et al.  Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models , 1982 .

[31]  Shlomo Maital,et al.  What Do Economists Know? An Empirical Study of Experts' Expectations , 1981 .

[32]  David I. Harvey.  The evaluation of economic forecasts , 1997 .

[33]  F. Diebold,et al.  Further results on forecasting and model selection under asymmetric loss , 1996 .

[34]  Robert H. Edelstein,et al.  How Well Do Economists Forecast Stock Market Prices? A Study of the Livingston Surveys , 1988 .

[35]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[36]  Michael W. McCracken.  Robust out-of-sample inference , 2000 .

[37]  D. Peel,et al.  Optimal Monetary Policy in a Model of Asymmetric Central Bank Preferences , 1998 .

[38]  Frederic S. Mishkin.  Are Market Forecasts Rational? , 1980 .

[39]  C. Granger,et al.  Economic and Statistical Measures of Forecast Accuracy , 1999 .

[40]  Judea Pearl,et al.  Generalized Instrumental Variables , 2002, UAI.

[41]  W. Newey,et al.  Asymmetric Least Squares Estimation and Testing , 1987 .

[42]  Massimiliano Marcellino,et al.  Fiscal forecasting: The track record of the IMF, OECD and EC , 2001 .

[43]  Clive W. J. Granger,et al.  A Decision_Theoretic Approach to Forecast Evaluation , 2000 .

[44]  H. White.  Asymptotic theory for econometricians , 1985 .

[45]  J. Stiglitz,et al.  Economic Forecasts and Expectations. , 1971 .

[46]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[47]  J. E. Pesando,et al.  A Note on the Rationality of the Livingston Price Expectations , 1975, Journal of Political Economy.

[48]  R. A. Meyer,et al.  The Term Structure of Inflationary Expectations and Market Efficiency , 1980 .