This paper tests the rationality of individual price forecasts in a panel of professional forecasters. Here, unlike in most previous studies, rationality is not rejected. The results here differ because (1) using individual forecasts avoids aggregation bias, (2) comparison of forecasts to initial data avoids bias due to data revision, (3) the professional forecasters have economic incentives to state their expectations accurately, (4) a new covariance matrix estimator consistent when forecast errors are correlated across individuals is used.

One of the oldest questions in macroeconomics concerns the correlation between the business cycle and the real wage. We provide new evidence on this question by examining the possible bias that arises when (1) workers have unobserved characteristics that affect their wages and (2) those workers who move in and out of the work force over the cycle have unobserved characteristics systematically different from those who stay in. We distinguish as well between the bias that arises from those unobserved characteristics that are permanent components of wages and those that are transitory. We utilize micro, panel data, and maximum likelihood selectivity bias techniques to estimate both the extent of this selectivity-cum-aggregation bias and the true effect of the cycle on real wages. We find that selectivity bias is present: workers are more likely to lose employment during a recession if they have high wages, especially if they have a high transitory wage component. Overall, the effect of selectivity is to bias ordinary least squares estimates based only on workers in a procyclical direction. Our results show that the true effect of the cycle on wages is still procyclical but much smaller in magnitude than previous estimates using micro data have suggested.

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH‐M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH‐M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

The authors find support for a negative relation between conditional expected monthly return and conditional variance of monthly return using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, they also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility, whereas negative unanticipated returns result in an upward revision of conditional volatility.

This research compares several approaches to inference in the multinomial probit model, based on two Monte Carlo experiments for a seven choice model.The methods compared are the simulated maximum likelihood estimator using the GHK recursive probability,simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm.Overall, the Gibbs sampling algorithm has a slight edge, with the relative performance of MSM and SML based on the GHK simulator being difficult to evaluate.The MSM estimator with the kernel-smoothed frequency simulator is clearly inferior.I. Introduction T HE multinomial probit is an appealing model of choice behavior because it allows a flexible pattern of conditional covariance among the latent utilities of alternatives.Nevertheless, multinomial probit applications have been limited because the required integrations of the multivariate normal density over subsets of Euclidean space are computationally burdensome.The computational simplicity of the multinomial logit has made it the model of choice for applied work.However, because the multinomial probit model relaxes the assumption of independence of irrelevant alternatives, it is generally preferred in principle to the multinomial logit model (McFadden, 1984, pp.1395-1458).Recently the method of simulated moments (McFadden, 1989; Pakes and Pollard, 1989) and Gibbs sampling with data augmentation (Albert and Chib, 1993; McCulloch and Rossi, 1994) have shown promise of making the required computations in the multinomial probit model practical.The development of the highly accurate GHK probability simulator (see Geweke, 1991; Hajivassiliou and McFadden, 1990; and Keane, 1990, 1994a) has also led to renewed interest in simulated maximum likelihood (Albright, Lerman, and Manski, 1977) as a method for estimating multinomial probit models.The objective of the research reported here is to provide a systematic comparison of the numerical properties of different simulation-based methods of inference in the multinomial probit model.Rather than considering the performance of these methods on a single model for a single data set, we attempt to control for a number of features of the inference problem, such as the number and nature of the unknown parameters of interest and the information content of the data on which inference is based.Also, we investigate for the first time how the performance of MSM estimation is affected by the type of probability simulator employed (i.e., GHK vs. kernel smoothing).While some investigators have examined the performance of particular estimators and computational techniques, Borsch-Supan and Hajivassiliou (1993), Hajivassiliou (1992), and Hajivassiliou, McFadden, and Ruud (1992) have made systematic comparison of alternative probability simulators, we are aware of only one systematic comparison of different estimators per se: Keane (1994a) compares method of simulated moments and simulated maximum likelihood estimators for an eight period binomial probit model in a Monte Carlo study.This paper is the first to compare performance of alternative methods of inference for the multinomial probit model and the first to examine how the relative performance of alternative methods differs across model specifications and across different data sets.In addition to addressing this main objective, this work introduces a new factor structure for the disturbances that may help to alleviate the proliferation of covariance matrix parameter problems in MNP models.We also illustrate Bayesian inference in a multinomial probit model with a factor structure for the first time.(See Elrod and Keane (forthcoming) for a discussion of factor structures for probit models.)

Carl Bonham and Richard Cohen (1995) are quite correct in noting the errors in our paper (Keane and Runkle, 1990), which were caused by our ignorance of cointegration. We stand chagrined. However, Bonham and Cohen are overstating their case when they claim that Keane and Runkle's results do not support the empirical validity of the rational-expectations hypothesis (p. 289). Bonham and Cohen focus on our tests of price-forecast rationality conditioned on past oil prices and Ml, which they claim are the core of our paper and provide our most stringent tests of rationality. Those particular tests account for only two paragraphs of our 20-page paper-obviously, these tests do not provide the core results of our paper. Rather, the main result of our paper is that individual price forecasts are unbiased and rational, conditioned on the forecaster's own past errors. No previous researchers had ever found even this limited support for the rational-expectations hypothesis. These core results are unaffected by the cointegration issues noted by Bonham and Cohen. Given that caveat, however, note how few of our results are actually overturned by Bonham and Cohen. Although our test statistics for determining whether forecasters properly condition on Ml growth are incorrect, Bonham and Cohen reach the same conclusion that we do: price forecasts conditioned on Ml growth are rational. Bonham and Cohen do reach different conclusions about forecast rationality than we do when they condition on oil price changes. But they themselves show that forecasters were only irrational in conditioning on oil prices after 1973 (their table 2, rows 5 and 6). To call such forecasting failure irrationality may or may not be correct. We think that Bonham and Cohen's results merely confirm the widespread view that forecasters did not completely understand the effects that oil price shocks would have on the economy because such large oil price shocks had never been seen before. Although Bonham and Cohen overturn only one of our original tests, they do provide additional evidence against forecast rationality with their tests that condition on interest-rate spreads and the unemployment rate. We have no doubt that a search over a large number of conditioning variables will uncover some instances in which forecast rationality is rejected. But conducting such a search will also incorrectly bias tests toward rejecting rationality. Since our original paper, we have also examined the rationality of earnings forecasts made by individual stock analysts-a group that has even more incentive than economic forecasters to make accurate predictions. Although all previous studies in that literature had found individual earnings forecasts to be irrational, we found (Keane and Runkle, 1994) that analysts' forecasts are rational. This additional research provides further support for the paper criticized by Bonham and Cohen.

This paper tests the rationality of individual price forecasts in a panel of professional forecasters. Here, unlike in most previous studies, rationality is not rejected. The results here differ because (1) using individual forecasts avoids aggregation bias, (2) comparison of forecasts to initial data avoids bias due to data revision, (3) the professional forecasters have economic incentives to state their expectations accurately, and (4) a new covariance matrix estimator consistent when forecast errors are correlated across individuals is used.