Estimating linear functionals in nonlinear regression with responses missing at random

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate expectations of functions of covariate and response we use a fully imputed estimator, namely an empirical estimator based on estimators of conditional expectations given the covariate. We exploit the independence of covariates and errors by writing the conditional expectations as unconditional expectations, which can now be estimated by empirical plug-in estimators. The mean zero constraint on the error distribution is exploited by adding suitable residual-based weights. We prove that the estimator is efficient (in the sense of H\'{a}jek and Le Cam) if an efficient estimator of the parameter is used. Our results give rise to new efficient estimators of smooth transformations of expectations. Estimation of the mean response is discussed as a special (degenerate) case.Comment: Published in at http://dx.doi.org/10.1214/08-AOS642 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comparing Expectations and Outcomes: Application to UK Data

The validity of the rational expectations hypothesis is explored using 12 years direct individual expectations data derived from the BHPS. The usage of micro data drives off the possibility of spurious rejections caused by the existence of micro-heterogeneity. And the 12 years BHPS micro panel data can release the average-out problem in a comparatively short term micro panel data. In short, I test if the individual expectations are unbiased and efficient in a comparatively long term in this paper. As a result, expectations errors are found to be biased and inefficient. Furthermore, the hypothesis that expectations errors are random is investigated by exploring the existence of systematic components in expectations errors. There exists the micro-heterogeneity among different types of respondents. Also, the factors that significantly affect individual’s expectations are identified.rational expectations; systematic heterogeneity; forecast errors; rational expectations hypothesis; subjective

Physician Income Prediction Errors: Sources and Implications for Behavior

Although income expectations play a central role in many economic decisions, little is known about the sources of income prediction errors and how agents respond to income shocks. This paper uses a unique panel data set to examine the accuracy of physicians' income expectations, the sources of income prediction errors, and the effect of income prediction errors on physician behavior. The data set contains direct survey measures of income expectations for medical students who graduated between 1970 and 1998, their corresponding income realizations, and a rich summary of the shocks hitting their medical practices. We find that income prediction errors were positive on average over the sample period, but varied significantly over time and cross-sectionally. We trace these results to persistent specialty-specific shocks, such as the growth of health maintenance organizations (HMOs) and other changes across health care markets. Physicians who experienced negative income shocks were more likely to respond by increasing their hours worked, allocating fewer of their work hours to teaching/research and more to patient care, and were more likely to switch specialties.

Forecasting Errors: Yet More Problems for Identification?

Forecasting errors pose a serious problem of identification, often neglected in empirical applications. Any attempt of estimating choice models under uncertainty may lead to severely biased results in the presence of forecasting errors even when individual expectations on future events are observed together with the standard outcome variables.identification, forecasting errors, subjective probabilities

Estimating a small DSGE model under rational and measured expectations: some comparisons

Using European panel data and GMM system estimation, we explore the empirical performance of the standard three-equation New Keynesian macro model under different informational assumptions. As a benchmark, we consider the performance of the model under rational expectations and revised (final) data. Alternatively, instead of imposing rational expectations hypothesis we use real- time information, ie Consensus Economics survey data, to generate empirical proxies for expectations in the model and the current output gap in the Taylor rule. We demonstrate that, contrary to the assumption of rational expectations, the errors in measured expectations and real-time current output gaps are positively autocorrelated. We produce evidence that the use of real-time variables (including measured expectations) improves the empirical performance of the New Keynesian model. Relaxation of the rational expectations hypothesis makes a noticeable difference for the parameters of the New Keynesian model, especially in the Taylor rule.DSGE model; survey expectations; GMM system estimation; expectations; estimation

Price expectations and price dynamics: the case of the rice sector in developing Asia

Uncertainty is a crucial issue for producers who must make input decisions without knowing prices and without perfect knowledge of realized output. In this context, price expectations strongly determine the production choices and market prices that result from market-clearing conditions. This study analyzed the role that price expectations play in price dynamics, developing a theoretical model of trade in varieties following Armington (1969) and augmented with yield and price uncertainty to highlight several main determinants of domestic producer prices, including exchange rates, proximity to world markets, input prices, natural disasters, and producers' expectations. An econometric estimation of the rice sector, using a panel of 13 developing Asian countries during 1965-2003, confirmed that expectations count, with a 1% increase in the expected price resulting in a 1.18% decrease in the market price. A simulation exercise based on these empirical results demonstrated that forecasting errors are large. Specifically, Asian rice farmers have a 50% chance of making prediction errors of 10% or more on the final market price. This high error rate suggests the need for developing ways of sharing information, such as radio programs dedicated to agricultural producers or the introduction of futures markets, to stabilize agricultural incomes.Rice ; Asia ; price dynamics ; price expectations ;

Expectations and the effects of monetary policy

This paper examines the predictive power of shifts in monetary policy, as measured by changes in the real federal funds rate, for output, inflation, and survey expectations of these variables. The authors find that policy shifts have larger effects on actual output than on expected output; thus policy predicts errors in output expectations, a violation of rational expectations. Policy shifts do not predict errors in inflation expectations. The authors explain these results with a model in which agents systematically underestimate the effects of policy on aggregate demand. This model helps to explain the real effects of policy.Monetary policy

The decline of activist stabilization policy : natural rate misperceptions, learning, and expectations

We develop an estimated model of the U.S. economy in which agents form expectations by continually updating their beliefs regarding the behavior of the economy and monetary policy. We explore the effects of policymakers' misperceptions of the natural rate of unemployment during the late 1960s and 1970s on the formation of expectations and macroeconomic outcomes. We find that the combination of monetary policy directed at tight stabilization of unemployment near its perceived natural rate and large real-time errors in estimates of the natural rate uprooted heretofore quiescent in inflation expectations and destabilized the economy. Had monetary policy reacted less aggressively to perceived unemployment gaps, in inflation expectations would have remained anchored and the stag inflation of the 1970s would have been avoided. Indeed, we find that less activist policies would have been more effective at stabilizing both in inflation and unemployment. We argue that policymakers, learning from the experience of the 1970s, eschewed activist policies in favor of policies that concentrated on the achievement of price stability, contributing to the subsequent improvements in macroeconomic performance of the U.S. economy