Bayesian Analysis of Nested Logit Model by Markov Chain Monte Carlo

We develop a Markov Chain Monte Carlo (MCMC) algorithm for estimating nested logit models in a Bayesian framework. Appropriate "heating target" and reparameterization techniques are adopted for fast mixing. For illustrative purposes, we have implemented the algorithm on two real-life examples involving 3-level structures. The first example involves Social Security's disability determination process, Lahiri et al. (1995). The second one is taken from Amemiya and Shimono's (1989) model of labor supply behavior of the aged. We applied a combination of various convergence criteria to ensure that the chain has converged to its target distribution.Discrete Choice, Random Utility Maximization, MCMC, Mixing Speed.

A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments

We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Chao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imbens and Krueger (1999) and Blomquist and Dahlberg (1999) are also considered. Since the posterior densities and their conditionals in CP and KVD are non-standard, we propose a "Gibbs within Metropolis- Hastings" algorithm, which only requires the availability of the conditional densities from the candidate generating density. Our results show that in cases with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner's MELO does the best. When the endogeneity is not weak and rw > 0, where r is the correlation coefficient between the structural and reduced form errors, and w is the co-variance between the unrestricted reduced form errors, BMOM outperforms all other estimators by a wide margin. When the endogeneity is not weak and brLimited Information Estimation, Metropolis-Hastings Algorithm, Gibbs Sampler, Monte Carlo Method

A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments

We compare the finite sample performance of a number of Bayesian and Classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Ch ao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the Sample theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imben s and Krueger (1999) and Blomquist and Dahlberg (1999) are also considered. Since the posterior densities and their conditionals in CP and KVD are non-standard, we propose a ''Gibbs within Metropolis-Hastings'' algorithm, which only requires the availabi lity of the conditional densities from the candidate generating density. Our results show that in cases with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner's MELO does the best. When the endogeneity is not weak and $\rho$$w_{12}>0$, where $\rho$ is the correlation coefficient between the structural and reduced form errors, and $w_{12}$ is the covariance between the unrestricted reduced form errors, BMOM outp erforms all other estimators by a wide margin. When the endogeneity is not weak and $\beta \rho

Learning and heterogeneity in GDP and inflation forecasts

We estimate a Bayesian learning model with heterogeneity aimed at explaining the evolution of expert disagreement in forecasting real GDP growth and inflation over 24 monthly horizons for G7 countries during 1990-2007. Professional forecasters are found to begin and have relatively more success in predicting inflation than real GDP at significantly longer horizons; forecasts for real GDP contain little information beyond 6 quarters, but forecasts for inflation have predictive value beyond 24 months and even 36 months for some countries. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs of experts, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement.Bayesian learning, Public information, Panel data, Forecast disagreement, Forecast horizon; Content function; Forecast efficiency; GDP; Inflation targeting

Measuring Forecast Uncertainty by Disagreement: The Missing Link

Using a standard decomposition of forecasts errors into common and idiosyncratic shocks, we show that aggregate forecast uncertainty can be expressed as the disagreement among the forecasters plus the perceived variability of future aggregate shocks. Thus, the reliability of disagreement as a proxy for uncertainty will be determined by the stability of the forecasting environment, and the length of the forecast horizon. Using density forecasts from the Survey of Professional Forecasters, we find direct evidence in support of our hypothesis. Our results support the use of GARCH-type models, rather than the ex post squared errors in consensus forecasts, to estimate the ex ante variability of aggregate shocks as a component of aggregate uncertainty.

Estimating International Transmission of Shocks Using GDP Forecasts: India and Its Trading Partners

Using a Factor Structural Vector Autoregressive (FSVAR) model and monthly GDP growth forecasts during 1995-2003, we find that Indian economy responds largely to domestic and Asian common shocks, and much less to shocks the from the West. However, when we exclude the Asian crisis period from our sample, the Western factor comes out as strong as the Asian factor contributing 16% each to the Indian real GDP growth, suggesting that the dynamics of transmission mechanism is time-varying. Our methodology on the use of forecast data can help policy makers of especially developing countries with frequent economic crises and data limitations to adjust their policy targets in real time.

On the Use of Density Forecasts to Identify Asymmetry in Forecasters' Loss Functions

Abstract: We consider how to use information from reported density forecasts from surveys to identify asymmetry in forecasters' loss functions. We show that, for the three common loss functions - Lin-Lin, Linex, and Quad-Quad - we can infer the direction of loss asymmetry by just comparing point forecasts and the central tendency (mean or median) of the underlying density forecasts. If we know the entire distribution of the density forecast, we can calculate the loss function parameters based on the first order condition of forecast optimality. This method is applied to forecasts for annual real output growth and inflation obtained from the Survey of Professional Forecasters (SPF). We find that forecasters treat underprediction of real output growth more dearly than overprediction, reverse is true for inflation.

Determinants of Multi-period Forecast Uncertainty Using a Panel of Density Forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). We show that previous studies based on aggregate data are biased due to heterogeneity of individual forecasts. Instead, we estimate a dynamic heterogeneous panel data model. We find that, although past forecast uncertainty is important, it is not as important as previously thought. In addition, the strong link between past squared forecast errors and the current forecast uncertainty, as often is found in the GARCH literature, is largely lost in the multi-period context with varying forecast horizons. Forecasters are found to pay more attention to recent “news†about inflation than the out-dated past squared forecast errors. We propose a novel way to estimating uncertainty of “news†using Kullback-Leibler Information, and show that it is an important determinant of the current inflation forecast uncertainty. Our results also support Friedman (1977)’s conjecture that higher inflation rate leads to higher inflation uncertaintyForecast uncertainty; Heterogeneity of forecasts; Panel data; Survey of professional forecasters; Dynamic panels

Health Inequality and Its Determinants in New York

Self-assessed health status conditioned by several objective measures of health and socio-demographic characteristics are used to measure health inequality. We compare the quality of health and health inequality among different racial/ethnic groups as well as across 17 regions in New York State. In terms of average health and health inequality, American Indian/Alaskan Natives and Hispanics are found to be the worst, and North Country, Bronx County, and Richmond County lag behind the rest of the State. Three major contributing factors to health inequality are found to be employment status, education, and income. However, the contribution of each of these determinants varies significantly among racial/ethnic groups as well as across regions, suggesting targeted public health initiatives for vulnerable populations to eliminate overall health disparity.

Learning and Heterogeneity in GDP and Inflation Forecasts

Using a Bayesian learning model with heterogeneity across agents, our study aims to identify the relative importance of alternative pathways through which professional forecasters disagree and reach consensus on the term structure of inflation and real GDP forecasts, resulting in different patterns of forecast accuracy. Forecast disagreement arises from two primary sources in our model: differences in the initial prior beliefs, and differences in the interpretation of new public information. Estimated model parameters, together with two separate case studies on (i) the dynamics of forecast disagreement in the aftermath of the 9/11 terrorist attack in the U.S. and (ii) the successful inflation targeting experience in Italy after 1997, firmly establish the importance of these two pathways to expert disagreement, and help to explain the relative forecasting accuracy of these two macroeconomic variables.