Research Publications and Papers

[1.] The Dynamic Factor Analysis of Economic Time Series Models

in D. Aigner and A. Goldberger (eds.), Latent Variables in Socioeconomic Models, 365-383.
Amsterdam: North-Holland, 1977.

[2.] Wage and Price Dynamics in U.S. Manufacturing

in New Methods in Business Cycle Research, 111-158.
Minneapolis: Federal Reserve Bank of Minneapolis, 1977.

[3.] Testing the Exogeneity Specification in the Complete Dynamic Simultaneous Equation Model

in Journal of Econometrics, 1978, 7, 163-185.

Abstract: It is shown that in the complete dynamic simultaneous equation model exogenous variables cause endogenous variables in the sense of Granger (1969) and satisfy the criterion of econometric exogeneity discussed by Sims (1977a), but that the stationarity assumptions invoked by Granger and Sims are not necessary for this implication. Inference procedures for testing each implication are presented and a new joint test of both implications is derived. Detailed attention is given to estimation and testing when the error vector of the final form of the complete dynamic simultaneous equation model is both singular and serially correlated. The theoretical points of the paper are illustrated by testing the exogeneity specification in a small macroeconometric model.

[4.] Temporal Aggregation in the Multiple Regression Model

in Econometrica, 1978, 46, 643-661.

Abstract: The regression relation between regularly sampled Y(t) and X"1(t),..., X"N(t) implied by an underlying model in which time enters more generally is studied. The underlying model includes continuous distributed lags, discrete models, and stochastic differential equations as special cases. The relation between parameters identified by regular samplings of Y and X"j and those of the underlying model is characterized. Sufficient conditions for identification of the underlying model in the limit as disaggregation over time proceeds are set forth. Empirical evidence presented suggests that important gains can be realized from temporal disaggregation in the range of conventional measurement frequencies for macroeconomic data.

[5.] The Temporal and Sectoral Aggregation of Seasonally Adjusted Time Series

in A. Zellner (ed.), Seasonal Analysis of Economic Time Series, 411-432.
Washington: U.S. Government Printing Office, 1978.

Abstract: Procedures for the optimal seasonal adjustment of economic time series and their aggregation are derived, given a criterion suitable for the adjustment of the data used in political or journalistic contexts. It is shown that data should be adjusted jointly and then temporally or sectorally aggregated, as desired, a procedure that preserves linear aggregation identities. Examination of actual economic time series indicates that the optimal seasonal adjustment and aggregation of data provide a substantial improvement in the quality of sectorally disaggregated, adjusted data and considerably reduces the required subsequent revision of current adjusted series.

[6.] The Revision of Seasonally Adjusted Time Series

in 1978 Proceedings of the Business and Economic Statistics Section - American Statistical Association, 320-325.

[7.] Some Joint Tests of the Efficiency of Markets for Forward Foreign Exchange

in Review of Economics and Statistics, 1979, 61, 334-341. (E. Feige, coauthor)

[8.] On Specification in Simultaneous Equation Models

in J. Kmenta and J. Ramsey (eds.), Evaluation of Econometric Models, 169-196.
New York: Academic Press, 1980. (W. Dent, coauthor)

[9.] Interpreting the Likelihood Ratio Statistic in Factor Models When Sample Size is Small

in Journal of the American Statistical Association, 1980, 75, 133-137. (K. Singleton, coauthor)

Keywords: Asymptotic distribution; Exploratory factor analysis; Maximum likelihood estimation; Monte Carlo experiments; Finite samples

[10.] Some Economic Consequences of Technological Advance in Medical Care: The Case of a New Drug

in R. Helms (ed.), Drugs and Health, 235-271.
Washington: American Enterprise Institute, 1980. (B. Weisbrod, coauthor)

[11.] Maximum Likelihood 'Confirmatory' Factor Analysis of Economic Time Series

in International Economic Review, 1981, 22, 37-54. (K. Singleton, coauthor).

[12.] Estimating Regression Models of Finite but Unknown Order

in International Economic Review, 1981, 22, 54-70. (R. Meese, second author).

[13.] Latent Variable Models for Time Series: A Frequency Domain Approach with an Application to the Permanent Income Hypothesis

in Journal of Econometrics, 1981, 17, 287-304. (K. Singleton, coauthor).

Abstract: The theory of estimation and inference in a very general class of latent variable models for time series is developed by showing that the distribution theory for the finite Fourier transform of the observable variables in latent variable models for time series is isomorphic to that for the observable variables themselves in classical latent variable models. This implies that analytic work on classical latent variable models can be adapted to latent variable models for time series, an implication which is illustrated here in the context of a general canonical form. To provide an empirical example a latent variable model for permanent income is developed, its parameters are shown to be identified, and a variety of restrictions on these parameters implied by the permanent income hypothesis are tested.

[14.] A Comparison of Tests of the Independence of Two Covariance Stationary Time Series

in Journal of the American Statistical Association, 1981, 76, 363-373

Keywords: Independence; Time series; Tests; Approximate slopes; Monte Carlo

[15.] The Approximate Slopes of Econometric Tests

in Econometrica, 1981, 49,1427-1442.

Abstract: In this paper the concept of approximate slope, introduced by R. R. Bahadur, is used to make asymptotic global power comparisons of econometric tests. The approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases, under a given alternative. A test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope. Two theorems, which facilitate the computation and interpretation of the approximate slopes of most econometric tests, are established. These results are used to undertake some illustrative comparisons. Sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis

[16.] The Measurement of Linear Dependence and Feedback Between Multiple Time Series

in Journal of the American Statistical Association, 1982, 77, 304-324. (With comments by E. Parzen, D. A. Pierce, W. Wei, and A. Zellner, and rejoinder)

Abstract: Measures of linear dependence and feedback for multiple time series are defined. The measure of linear dependence is the sum of the measure of linear feedback from the first series to the second, linear feedback from the second to the first, and instantaneous linear feedback. The measures are nonnegative, and zero only when feedback (causality) of the relevant type is absent. The measures of linear feedback from one series to another can be additively decomposed by frequency. A readily usable theory of inference for all of these measures and their decompositions is described; the computations involved are modest.

Keywords: Multiple time series; Feedback; Dependence; Causality

[17.] Feedback Between Monetary Policy, Labor Market Activity, and Wage Inflation in the United States, 1955-1978

in M. Baily (ed.), Workers, Jobs and Inflation, 159-198.
Washington: The Brookings Institution, 1982.

[18.] Clinical Evaluation vs. Economic Evaluation: The Case of a New Drug

in Medical Care, 1982, 20, 821-830. (B. Weisbrod, coauthor)

Abstract: To economically evaluate a new. drug or other medical innovation one must assess both the changes in costs and in benefits. Safety and efficacy matter, but so do resource costs and social benefits. This paper evaluates the effects on expenditures of the recent introduction of cimetidine, a drug used in the prevention and treatment of duodenal ulcers. This evaluation is of interest in its own right and also as a "guide" for studying similar effects of other innovations. State Medicaid records are used to test the effects on hospitalization and aggregate medical care expenditures of this new medical innovation. After controlling to the extent possible for potential selection bias, we find that: 1) usage of cimetidine is associated with a lower level of medical care expenditures and fewer days of hospitalization per patient for those duodenal ulcer patients who had zero health care expenditures and zero days of hospitalization during the presample period; an annual cost saving of some $320.00 (20 per cent) per patient is indicated. Further analysis disclosed, however, that this saving was lower for patients with somewhat higher levels of health care expenditures and hospitalization in the presample period, and to some extent was reversed for the patients whose prior year's medical care expenditures and hospitalization were highest.

[19.] Inference and Causality in Economic Time Series Models

in Z. Grilliches and M. Intriligator (eds.), Handbook of Econometrics, 1101-1144.
Amsterdam: North-Holland, 1984.

[20.] Comparing Alternative Tests of Causality in Temporal Systems: Analytic Results and Experimental Evidence

in Journal of Econometrics, 1983, 21, 161-194. (R. Meese and W. Dent, second authors)

Abstract: This paper discusses eight alternative tests of the absence of casual ordering, all of which are asymptotically valid under the null hypothesis in the sense that their limiting size is known. Their behavior under alternatives is compared analytically using the concept of approximate slope, and these results are supported by the outcomes of Monte Carlo experiments. The implications of these comparisons for applied work are unambiguous: Wald variants of a test attributed to Granger, and a lagged dependent variable version of Sim's test introduced in this paper, are equivalent in all relevant respects and are preferred to the other tests discussed.
 

[21.] Causality, Exogeneity, and Inference

invited paper, Fourth World Congress of the Econometric Society, in D. Hildenbrand (ed.), Advances in Econometrics, 209-236.
Cambridge: Cambridge University Press, 1983.

[22.] How does Technological Change Affect Health Care Expenditures? The Case of a New Drug

in Evaluation Review, 1984, 8, 75-91. (B. Weisbrod, coauthor)

Abstract: The expenditure consequences of the drug cimetidine for the period 1977-1979 are investigated. Using Medicaid data for the State of Michigan, it is found that expenditures for the first year of treatment of duodenal ulcers are reduced between 26% and 70% The methodology employed can be applied to the assessment of other medical technologies.

[23.] Measures of Conditional Linear Dependence and Feedback

in Journal of the American Statistical Association, 1984, 79, 907-915.

Keywords: Bootstrap; Resampling; Macroeconomics; Spectral density

[24.] The Estimation and Application of Long Memory Time Series Models

in Journal of Time Series Analysis 4, 1984, 221-238. (S. Porter-Hudak, coauthor) Reprinted in A. Harvey (ed.), Time Series, Edward Elgar Publishing, 1994.

Abstract: The definitions of fractional Gaussian noise and integrated (or fractionally differenced) series are generalized, and it is shown that the two concepts are equivalent. A new estimator of the long memory parameter in these models is proposed, based on the simple linear regression of the log periodogram on a deterministic regressor. The estimator is the ordinary least squares estimator of the slope parameter in this regression, formed using only the lowest frequency ordinates of the log periodogram. Its asymptotic distribution is derived, from which it is evident that the conventional interpretation of these least squares statistics is justified in large samples. Using synthetic data the asymptotic theory proves to be reliable in samples of 50 observations or more. For three postwar monthly economic time series, the estimated integrated series model provides more reliable out-of-sample forecasts than do more conventional procedures.

Keywords: Fractional differencing, Long-memory, Integrated models

[25.] A Comparison of Autoregressive Univariate Forecasting Procedures for Macroeconomic Time Series

in Journal of Business and Economic Statistics, 1984, 2, 187-202. (R. Meese, first author)

Abstract: The actual performance of several automated univariate autoregressive forecasting procedures, applied to 150 macroeconomic time series, are compared. The procedures are the random walk model as a basis for comparison; long autoregressions, with three alternative rules for lag length selection; and a long autoregression estimated by minimizing the sum of absolute deviations. The sensitivity of each procedure to preliminary transformations, data, periodicity, forecast horizon, loss function employed in parameter estimation, and seasonal adjustment procedures is examined. The more important conclusions are that Akaike's lag-length selection criterion works well in a wide variety of situations, the modeling of long memory components becomes important for forecast horizons of three or more periods, and linear combinations of forecasts do not improve forecast quality appreciably.

Keywords: Akaike criterion; Autoregression; ARIMA; ARARMA; Forecasting; Macroeconomic time series

[26.] Macroeconomic Modeling and the Theory of the Representative Agent

in American Economic Review, 1985, 75, 206-210.

[27.] Inferring Household Demand for Durable Goods, with Heterogeneous Preferences; A Case Study

Duke University manuscript and report to Research Triangle Institute, 1985

[28.] The Superneutrality of Money in the United States: An Interpretation of the Evidence

in Econometrica, 1986, 54, 1-22.

Abstract: Structural and stochastic neutrality have refutable implications for aggregate economic time series only in conjunction with other maintained hypotheses. Simple and commonly employed maintained hypotheses lead to restrictions on measures of feedback and their decomposition by frequency. These restrictions also suggest an empirical interpretation of the notional long and short runs. It is found that a century of annual U.S. data, and postwar monthly data, consistently support structural superneutrality of money with respect to output and the real rate of return and consistently reject its superneutrality with respect to velocity. A quantitative characterization of the long run is suggested.

[29.] Exact Inference in the Inequality Constrained Normal Linear Regression Model

in Journal of Applied Econometrics, 1986, 1, 127-141.

[30.] Exact Inference for Continuous Time Markov Chains

in Review of Economic Studies, 1986, 53, 653-669. (R. C. Marshall and G. Zarkin, second authors)

[31.] Mobility Indices in Continuous Time Markov Chains

in Econometrica, 1986, 54, 1407-1423. (R. C. Marshall and G. Zarkin, second authors)

Keywords: Mobility indices, Markov chains, embeddability

[32.] Endogeneity and Exogeneity

in J. Eatwell, M. Milgate, and P. Newman (eds.), The New Palgrave: A Dictionary of Economic Theory and Doctrine.
London: The Macmillan Press.

[33.] Long Run Competition in the U.S. Aluminum Industry

in International Journal of  Industrial Organization, 5, 67-78. (L. Froeb, coauthor)

Abstract: A methodology for examining dynamic structure-performance relationships in a single industry is proposed and illustrated. Implications of long run competitive behavior for a simple simultaneous equations model of structure and performance are derived and tested using recently developed methods for the interpretation of economic time series. It is concluded that the structure and performance in the U.S. aluminum industry in the postwar period conform well with the hypothesis that the primary aluminum market was competitive in the long run.

[34.] Exact Inference in Models with Autoregressive Conditional Heteroskedasticity

in E. Berndt, H. White, and W. Barnett (eds.), Dynamic Econometric Modeling, 73-103.
Cambridge: Cambridge University Press, 1988.

[35.] The Secular and Cyclical Behavior of Real GDP in Nineteen OECD Countries, 1957-1983

in Journal of Business and Economic Statistics, October 1988, 6, 479-486.

Abstract: Log per capita real gross domestic product is modeled as a third-order autoregression with a pair of complex roots whose amplitude is smaller than the amplitude of the real root. The behavior of this time series is interpreted in terms of these two amplitudes, the periodicity of the complex roots, and the standard deviation of the disturbance. Restrictions are evaluated and inference is conducted using the likelihood principle, applying Monte Carlo integration with importance sampling. These Bayesian procedures efficiently cope with restrictions that are awkward taking a classical approach. We find very little difference in the amplitudes of real roots between countries and of complex roots relative to within-country uncertainty. There are some substantial differences in the periodicities of complex roots, and the greatest differences between countries are found in the standard deviation of the disturbance.

Keywords: Bayesian inference; Business cycles; International comparisons; Monte Carlo integration.

[36.] Antithetic Acceleration of Monte Carlo Integration in Bayesian Inference

in Journal of Econometrics, 1988, 38, 73-90.

Abstract: It is proposed to sample antithetically rather than randomly from the posterior density in Bayesian inference using Monte Carlo integration. Conditions are established under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size, as sample size increases. The result is illustrated in an experiment using a bivariate vector autoregression.

[37.] Exact Predictive Densities in Linear Models with ARCH Disturbances

in Journal of Econometrics, 1989, 40, 63-86.

Abstract: It is shown how exact predictive densities may be formed in the ARCH linear model by means of Monte Carlo integration with importance sampling. Several improvements in computational efficiency over earlier implementations of this procedure are developed, including use of the exact likelihood function rather than an asymptotic approximation to construct the importance sampling distribution, and antithetic acceleration of convergence. A numerical approach to the formulation of posterior odds ratios and the combination of non-nested models is also introduced. These methods are applied to daily quotations of closing stock prices. Forecasts are formulated using linear models, ARCH linear models and an integrated model constructed from the posterior probabilities of the respective models. The use of the exact predictive density in a decision-theoretic context is illustrated by deriving the optimal day-to-day portfolio adjustments of a trader with constant relative risk aversion.
 

[38.] Modeling with Normal Polynomial Expansions

in J. Geweke, K. Shell, and W. Barnett (eds.), Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, 337-360.
Cambridge: Cambridge University Press, 1989.

Abstract: Polynomial expansions of the normal probability density function are proposed as a class of models for unobserved components. Operational procedures for Bayesian inference in these models are developed, as are methods for combining a sequence of such models and evaluation of the hypotheses of normality and symmetry. The contributions of this chapter are illustrated with an application to daily rates of change in stock price.

[39.] Acceleration Methods for Monte Carlo Integration in Bayesian Inference

in E. J. Wegman, D. T. Gantz, and J. J. Miller (eds.), Proceedings of the 20th Symposium on the Interface: Computationally Intensive Methods in Computing Science and Statistics, 587-592. Alexandria: American Statistical Association, 1989.

Abstract: Methods for the acceleration of Monte Carlo integration with n replications in a sample of size T are investigated. A general procedure for combining antithetic variation and grid methods with Monte Carlo methods is proposed, and it is shown that the numerical accuracy of these hybrid methods can be evaluated routinely. The derivation indicates the characteristics of applications in which acceleration is likely to be most beneficial. This is confirmed in a worked example, In which these acceleration methods reduce the computation time required to achieve a given degree of numerical Accuracy by several orders of magnitude.

[40.] Semiparametric Bayesian Estimation of the Asymptotically Ideal Model: The AIM Demand System

in W. Barnett, J. Powell, and G. Tauchen (eds.), Nonparametric and Seminonparametric Methods in Econometrics and Statistics, 127-174. Cambridge: Cambridge University Press, 1991. (W. Barnett and P. Yue, coauthors)

[41.] Bayesian Inference in Econometric Models Using Monte Carlo Integration

in Econometrica, 1989, 57,1317-1339. Reprinted in G. C. Box and N. Polson (eds.), Bayesian inference, Edward Elgar Publishing, 1994

Abstract: Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference in econometric models are developed. Conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of Monte Carlo replications increases, and the numerical accuracy of this approximation may be assessed reliably, are set forth. Methods for the analytical verification of these conditions are discussed. Importance sampling densities are derived from multivariate normal of Student t approximations to local behavior of the posterior density at its mode. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. The practical procedures based on these innovations are illustrated in two different models

[42.] The Posterior Distribution of Roots in Multivariate Autoregressions

in American Statistical Association 1989 Proceedings of the Business and Economic Statistics Section.

[43.] A Bayesian Method for Evaluating Medical Test Operating Characteristics When Some Patients Fail to be Diagnosed by the Reference Standard

in Medical Decision Making, 1990, 10, 102-115. (D. B. Matchar, D. C. Simel, and J. R. Feussner, coauthors)  (With Commentary by F R. Nease, Jr., and D. K. Owens, and Response)

Abstract: The evaluation of a diagnostic test when the reference standard fails to establish a diagnosis in some patients is a common and difficult analytical problem. Conventional operating characteristics, derived from a 2 x 2 matrix, require that tests have only positive or negative results, and that disease status be designated definitively as present or absent. Results can be displayed in a 2 x 3 matrix, with an additional column for undiagnosed patients, when it is not possible always to ascertain the disease status definitively. The authors approach this problem using a Bayesian method for evaluating the 2 x 3 matrix in which test operating characteristics are described by a joint probability density function. They show that one can derive this joint probability density function of sensitivity and specificity empirically by applying a sampling algorithm. The three-dimensional histogram resulting from this sampling procedure approximates the true joint probability density function for sensitivity and specificity. Using a clinical example, the authors illustrate the method and demonstrate that the joint probability density function for sensitivity and specificity can be influenced by assumptions used to interpret test results in undiagnosed patients. This Bayesian method represents a flexible and practical solution to the problem of evaluating test sensitivity and specificity when the study group includes patients whose disease could not be diagnosed by the reference standard. Keywords: Bayesian analysis; test operating characteristics; probability density functions. (Med Decis Making 1990;10:102-111)

[44.] Generic, Algorithmic Approaches to Monte Carlo Integration in Bayesian Inference

in Contemporary Mathematics, 1991, 115, 117-135.

Abstract: Program of research in generic, algorithmic approaches to Monte Carlo integration in Bayesian inference is summarized. The goal of this program is the development of a widely applicable family of solutions of Bayesian multiple integration problems, that obviate the need for case-by-case treatment of arcane problems in numerical analysis. The essentials of the Bayesian inference problem, with some reference to econometric applications, are set forth. Fundamental results in Monte Carlo integration are derived and their current implementation in software is described. Potential directions for fruitful new research are outlined.

[45.] Seminonparametric Bayesian Estimation of Consumer Demand and Factor Demand Functions

in W. Barnett, B. Cornet, C. d'Aspremont, J. Gabszewicz, and A. Mas-Colell (eds.), Equilibrium Theory and Applications, 425-480. Cambridge: Cambridge University Press, 1991. (W. Barnett and M. Wolfe, coauthors)

[46.] Seminonparametric Bayesian Estimation of the Asymptotically Ideal Production Model

in Journal of Econometrics, 1991, 49, 5-50. (W. Barnett and M. Wolfe, coauthors)

Abstract: Recently it has been shown that seminonparametric methods can be used to produced high-quality approximations to a firm's technology. Unlike the local approximations provided by the conventional class of `flexible functional forms', seminonparametric methods generate global spans within large classes of functions. However, that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling. An exception is the asymptotically ideal model (AIM) generated from the Müntz-Szatz series expansion. Since every basis function in that expansion is within the neoclassical function space, a straightforward method exists for imposing neoclassical regularity, when all factors are substitutes. Since the relevant constraints are inequality restrictions, we implement the approach using Bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods. We further discuss the relevant extensions that would permit complementary factors, nonconstant returns to scale, and technological change.
 

[47.] Efficient Simulation from the Multivariate Normal and Student-t DistribuAmerican tions Subject to Linear Constraints

in E. M. Keramidas (ed.), Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface, 571-578. Fairfax: Interface Foundation of North America, Inc., 1991.

• Postscript file containing April 1, 1991 working paper
• PDF file containing April 1, 1991 working paper

The following routines constitute the software for the paper, "Efficient Simulation from the Multivariate normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities," by John Geweke. This paper is to appear in the volume, "Computing Science and Statistics: Proceedings of the Twenty-Third Symposium on the Interface." This work was supported by NSF Grant SES-8908365.

• Fortran code

[48.] Threshold Autoregressive Models for Macroeconomic Time Series: A Bayesian Approach

 in  American Statistical Association 1991 Proceedings of the Business and Economic Statistics Section, 42-50. (N. Terui, coauthor)

[49.] Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments

in J.O. Berger, J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (eds.), Bayesian Statistics 4, 169-194. Oxford: Oxford University Press, 1992.

Abstract: Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods from spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model with informative priors, and in the Tobit-censored regression model.

Keywords: Data augmentation, Gibbs sampling, Mixed estimation, Monte Carlo integration, Tobit model 

• Postscript file containing December 1, 1991 working paper
• PDF file containing December 1, 1991 working paper

[50.] Bayesian Threshold Autoregressive Models for Nonlinear Time Series

in Journal of Time Series Analysis, 1993, 14, 441-455. (N. Terui, coauthor)

Abstract: This paper provides a Bayesian approach to statistical inference in the threshold autoregressive model for time series. The exact posterior distribution of the delay and threshold parameters is derived, as is the multi-step-ahead predictive density. The proposed methods are applied to the Wolfe's sunspot and Canadian lynx data sets.

[51.] Inference and Forecasting for Chaotic Nonlinear Time Series

in P. Chen and R. Day (eds.), Nonlinear Dynamics and Evolutionary Economics, Oxford: Oxford University Press, 1993.

[52.] Bayesian Treatment of the Independent Student-t Linear Model

in Journal of Applied Econometrics, 1993, 8, S19-S40. Also published in H.K, van Dijk, A. Monfort, and B.W. Brown (eds.), Econometric Inference using Simulation Techniques. Chichester: John Wiley & Sons, 1995, 35-56.

[53.] Priors for Macroeconomic Time Series and Their Application

in Econometric Theory, 1994, 10, 609-632.

Abstract: This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but non-linear in the parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter which can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odds ratios using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson-Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of prior distribution.

Keywords: Difference stationary, Gibbs sampling, Leptokurtic distribution, Student-t distribution, Trend stationary

• Postscript file containing April 1, 1993 working paper
• Postscript file containing May 1, 1992 working paper
• PDF file containing April 1, 1993 working paper
• PDF file containing May 1, 1992 working paper
• Ascii file containg fortran code for both working papers
• Ascii file containing the data used in the study
• Directory containing the simulator output matrices, input files and output files

[54.] Advances in Random Utility Models

in Marketing Letters, 1994, 5, 311-322. (J.L.Horowitz, M. Keane, et al., coauthors)

Abstract: In recent years, major advances have taken place in three areas of random utility modeling: (1) semiparametric estimation, (2) computational methods for multinomial probit models, and (3) computational methods for Bayesian estimation. This paper summarizes these developments and discusses their implications for practice.

[55.] Alternative Computational Approaches to Inference in the Multinomial Probit Model

in Review of Economics and Statistics, 1994, 76, 609-632. (M. Keane and D. Runkle, coauthors)

Abstract: 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.

[56.] Recursively Simulating Multinomial Multiperiod Probit Probabilities

in American Statistical Association 1994 Proceedings of the Business and Economic Statistics Section. (M. Keane and D. Runkle, coauthors)

[57.] A Fine Time for Monetary Policy?

in Federal Reserve Bank of Minneapolis Quarterly Review 19: (1) 18-31. (D. Runkle, coauthor)

[58.] Variable Selection and Model Comparison in Regression

in J.O. Berger, J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (eds.), Bayesian Statistics 5. Oxford: Oxford University Press, 1996, 609-620.

Abstract: In the specification of linear regression models it is common to indicate a list of candidate variables from which a subset enters the model with nonzero coefficients. This paper interprets this specification as a mixed continuous-discrete prior distribution for coefficient values. It then utilizes a Gibbs sampler to construct posterior moments. It is shown how this method can incorporate sign constraints and provide posterior probabilities for all possible subsets of regressors. The methods are illustrated using some standard data sets.

• Postscript file containing November 9, 1994 working paper
• Postscript file containing May 20, 1994 working paper
• PDF file containing November 9, 1994 working paper
• PDF file containing May 20, 1994 working paper

[59.] Monte Carlo Simulation and Numerical Integration

in H. Amman, D. Kendrick and J. Rust (eds.), Handbook of Computational Economics. Amsterdam: North-Holland, 1996, 731-800.

Abstract: This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.

Keywords and phrases : Acceptance sampling, Antithetic variates, Control variates, Gibbs sampler, Importance sampling, Laplace approximation, Low discrepancy methods, Markov chain Monte Carlo methods, Metropolis- Hastings algorithm, Quadrature, Pseudorandom numbers, Variance reduction

• Postscript file containing the first part of November 7, 1994 working paper
• Postscript file containing the second part of November 7, 1994 working paper
• PDF file containing the first part of November 7, 1994 working paper
• PDF file containing the second part of November 7, 1994 working paper

[60.] Bayesian Reduced Rank Regression in Econometrics

in Journal of  Econometrics, 1996, 75, 121-146 .

Abstract: The reduced rank regression model arises repeatedly in theoretical and applied econometrics. To date the only general treatment of this model have been frequentist. This paper develops general methods for Bayesian inference with noninformative reference priors in this model, based on a Markov chain sampling algorithm, and procedures for obtaining predictive odds ratios for regression models with different ranks. These methods are used to obtain evidence on the number of factors in a capital asset pricing model

Keywords: Factor model; Predictive odds; Capital asset pricing model

 

[61.] Bayesian Inference for Linear Models Subject to Linear Inequality Constraints

in W.O. Johnson, J.C. Lee and A. Zellner (eds.), Modeling and Prediction: Honoring Seymour Geisser. New York: Springer-Verlag, 1996, 248-263.

Abstract: The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints, Bayesian inference is much simpler than classical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. This paper shows how the Gibbs sampling algorithm can provide an alternative, attractive approach to inference subject to linear inequality constraints in this situation, and how the GHK probability simulator may be used to assess the posterior probability of the constraints.

• Postscript file containing June 1, 1995 working paper
• PDF file containing June 1, 1995 working paper

[62.] Measuring the Pricing Error of the Arbitrage Price Theory

in Review of Financial Studies, 1996, 9, 557-587. (G. Zhou, coauthor)

[63.] Posterior Simulators in Econometrics

 in D. Kreps and K.F Wallis (eds.), Advances in Economics and Econometrics: Theory and Applications, vol. III. Cambridge: Cambridge University Press, 1997, 128-165. (Invited symposium paper, Econometric Society Seventh World Congress)

Abstract: The development of posterior simulators in the last decade has revised beliefs about the foregoing three propositions held by many econometricians who have followed these developments closely. The purpose of this paper is to convey these innovations and their significance for applied econometrics, to econometricians who have not followed the relevant mathematical and applied literature. There are four substantive sections. One section reviews aspects of Bayesian inference essential to understanding the implications of posterior simulators for Bayesian econometrics. Another section describes these simulators and provides the essential convergence results. Implications of these procedures for some selected econometric models are drawn in a third section. This is done to indicate the range of tasks to which posterior simulators are well suited, rather than provide a representative survey of the recent Bayesian econometric literature. Finally, the paper turns to some implications for model comparison, and for communication between those who do applied work and their audiences, that are beginning to emerge from the use of posterior simulators in Bayesian econometrics.

Keywords and phrases: Bayes factor; Bayesian inference; Importance sampling; Markov chain Monte Carlo; Prior distributions

• Postscript file containing the first part of September 17, 1995 working paper
• Postscript file containing the second part of September 17, 1995 working paper
• PDF file containing the first part of September 17, 1995 working paper
• PDF file containing the second part of September 17, 1995 working paper

[64.] Simulation-Based Bayesian Inference for Economic Time Series

in R.S. Mariano, T. Schuermann and M. Weeks (eds.), Simulation-Based Inference in Econometrics: Methods and Applications. Cambridge: Cambridge University Press, 2000, 255-299. 

[65.] Bayesian Inference for Dynamic Discrete Choice Models Without the Need for Dynamic Programming

in R.S. Mariano, T. Schuermann and M. Weeks (eds.), Simulation-Based Inference in Econometrics: Methods and Applications. Cambridge: Cambridge University Press, 2000, 100-131. (M. Keane, coauthor)

[66.] Statistical inference in the Multinomial Multiperiod Probit model

in Journal of  Econometrics,1997, 80, 125-166. (M. Keane and D. Runkle, coauthors)

Abstract: Statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions, posterior distributions, or moment conditions in these models. We describe three alternative estimators, implemented using simulation-based approaches to inference, that circumvent the integration problem: posterior means computed using Gibbs sampling and data augmentation (GIBBS), simulated maximum likelihood (SML) estimation using the GHK probability simulator, and method of simulated moment (MSM) estimation using GHK. We perform a set of Monte-Carlo experiments to compare the sampling distributions of these estimators. Although all three estimators perform reasonably well, some important differences emerge. Our most important finding is that, holding simulation size fixed, the relative and absolute performance of the classical methods, especially SML, gets worse when serial correlation in disturbances is strong. In data sets with an AR(1) parameter of 0.50, the RMSEs for SML and MSM based on GHK with 20 draws exceed those of GIBBS by 9% and 0%, respectively. But when the AR(1) parameter is 0.80, the RMSEs for SML and MSM based on 20 draws exceed those of GIBBS by 79% and 37%, respectively, and the number of draws needed to reduce the RMSEs to within 10% of GIBBS are 160 and 80 respectively. Also, the SML estimates of serial correlation parameters exhibit significant downward bias. Thus, while conventional wisdom suggests that 20 draws of GHK is `enough' to render the bias and noise induced by simulation negligible, our results suggest that much larger simulation sizes are needed when serial correlation in disturbances is strong.

Keywords: Bayesian inference; Discrete choice; Gibbs sampling; Method of simulated moments; Simulated maximum likelihood; Panel data

 

[67.] Mixture of Normals Probit Models

in C. Hsiao, K. Lahiri, L-F Lee and M. H. Pesaran (eds.), Analysis of Panels and Limited Dependent Variables: A Volume in Honor of G. S. Maddala, 49-78. Cambridge: Cambridge University Press, 1999. (M. Keane, coauthor)

Abstract: This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.

• Postscript file containing August 1997 Staff Working Paper
• PDF file containing August 1997 Staff Working Paper

[68.] Prior Density Ratio Class Robustness in Econometrics

in Journal of Business and Economic Statistics, 1998, 16, 469-478. (L. Petrella, coauthor)

Abstract: This paper provides a general and efficient method for computing density ratio class bounds on posterior moments, given the output of a posterior simulator. It shows how density ratio class bounds for posterior odds ratios may be formed in many situations, also on the basis of posterior simulator output. The computational method is used to provide density ratio class bounds in two economic models. It is found that the exact bounds are approximated poorly by their asymptotic approximation, when the posterior distribution of the function of interest is skewed. It is also found that the posterior odds ratios display substantial variation within the density ratio class, in ways that cannot be anticipated by the asymptotic approximation. 

• Postscript file containing February 1998 working paper
• Postscript file containing July 21, 1995 working paper
• PDF file containing February 1998 working paper
• PDF file containing July 21, 1995 working paper

[69.] Using Simulation Methods for Bayesian Econometric Models: Inference, Development and Communication (with discussion and rejoinder)

in Econometric Reviews, 1999, 18, 1-126.

Abstract: This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models.

Keywords: Bayes factor; diagnostic checking; importance sampling; Markov chain Monte Carlo; model development; model specification; prior distributions

JEL Classification: C15, C11

Postscript Version (Note: This paper is posted in multiple parts)

• Title Page
• Section 1
• Section 2
• Section 3
• Section 4
• Section 5
• Section 6
• Tables
• Tables
• References

PDF Version:

• Title Page
• Section 1
• Section 2
• Section 3
• Section 4
• Section 5
• Section 6
• Tables
• Tables
• References

Comment papers are available in the printed journal:

• Estimating Consumer Surplus Comments on "Using Simulation Methods for Bayesian Econometric Models: Inference, Development, and Communication by W.E. Griffiths
• Some Comments on Model Development and Posterior Existence by C. Fernandez and M.F.J. Steel
• Incomplete Models and Reweighting by G. Koop and D.J. Poirier
• Some Remarks on the Simulation Revolution in Bayesian Econometric Inference by H.K. van Dijk
• Using Simulation Methods for Bayesian Econometric Models: Inference, Development, and Communication: Some Comments by G.M. Martin and C.S. Forbes
• Reply by J. Geweke

[70.] Simulation Methods for Model Criticism and Robustness Analysis

in J.O. Berger, J.M. Bernado, A.P. Dawid, and A.F.M. Smith (eds.), Bayesian Statistics 6, 275-299. Oxford: Oxford University Press, 1999.

Abstract: This paper exposits and develops Bayesian methods of model criticism and robustness analysis. The objectives are to clarify the Bayesian interpretation of non-Bayesian diagnostic tests, and provide explicitly Bayesian procedures accessible to practical investigators. Specific methods for prior density criticism and robustness analysis, and data density criticism, are presented. All are based on the approximation of appropriate Bayes factors, and avoid the need for posterior simulation under alternative model specifications. A general method of data density criticism is developed, that requires neither posterior simulation nor analytical approximations under any model specification. Some of the methods presented here have been implemented in user oriented software. The paper presents a few simple illustrations of the methods.

Keywords: Bayes factor; diagnostic checking; model specification; partial information; posterior simulation; prior density

• Postscript file
• PDF file

[71.] Simulation Based Inference for Dynamic Multinomial Choice Models

 in B.H. Baltagi (ed.), Companion for Theoretical Econometrics, 466-493.  London: Basil Blackwell, 2001.  (D. Houser and M. Keane, coauthors)

[72.] An Empirical Analysis of Income Dynamics among Men in the PSID: 1968-1989

in Journal of Econometrics, 2000, 96, 293-356. (M. Keane, coauthor)

Abstract: This study uses data from the Panel Survey of Income Dynamics (PSID) to address a number of questions about life cycle earnings mobility. It develops a dynamic reduced form model of earnings and marital status that is nonstationary over the life cycle. The study reaches several firm conclusions about life cycle earnings mobility. Incorporating non-Gaussian shocks makes it possible to better account for transitions between low and higher earnings states, a heretofore unresolved problem. The non-Gaussian distribution substantially increases estimates of the lifetime return to post-secondary education, and substantially reduces differences in lifetime earnings attributable to race. In a given year, the majority of variance in earnings not accounted for by race, education and age is due to transitory shocks, but over a lifetime the majority is due to unobserved individual heterogeneity. Consequently, low earnings at early ages are strong predictors of low earnings later in life, even conditioning on observed individual characteristics.

[73.] On Markov Chain Monte Carlo Methods for Nonlinear and Non-Gaussian State-Space Models

in Communications in Statistics , 1999, 28, 867-894.  (H. Tanizaki, coauthor)

Abstract: In this paper, a nonlinear and/or non-Gaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the state-space model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random number generation, the Metropolis-Hastings algorithm and the Gibbs sampling technique are utilized. The proposed procedure is very simple and easy for programming, compared with the existing nonlinear and non-Gaussian smoothing techniques. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed estimator.

[74.] Bayesian Econometrics and Forecasting

in Journal of Econometrics, 2001, 100, 11-15.

Abstract: Contemporary Bayesian forecasting methods draw on foundations in subjective probability and preferences laid down in the mid-twentieth century, and utilize numerical methods developed since that time in their implementation. These methods unify the tasks of forecasting and model evaluation. They also provide tractable solutions for problems that prove difficult when approached using non-Bayesian methods. These advantages arise from the fact that the conditioning in Bayesian probability forecasting is the same as the conditioning in the underlying decision problems.

[75.] Bayesian Communication: The BACC System

In 2000 Proceedings of the Section on Bayesian Statistical Sciences - American Statistical Association, 40-49.

[76.] Using Simulation Methods for Bayesian Econometric Models

in D. Giles (ed.), Computer Aided Econometrics. New York: Marcel Dekker, 2003, 209-261. (W. McCausland and J. Stevens, coauthors)

[77.] Computationally Intensive Methods for Integration in Econometrics

in J. Heckman and E.E. Leamer (eds.), Handbook of Econometrics volume 5. Amsterdam: North-Holland, 2001, 3463-3568. (M. Keane, coauthor)

Abstract: Until recently, inference in many interesting models was precluded by the requirement of high dimensional integration. But dramatic increases in computer speed, and the recent development of new algorithms that permit accurate Monte Carlo evaluation of high dimensional integrals, have greatly expanded the range of models that can be considered. This chapter presents the methodology for several of the most important Monte Carlo methods, supplemented by a set of concrete examples that show how the methods are used.
    Some of the examples are new to the econometrics literature. They include inference in multinomial discrete choice models and selection models in which the standard normality assumption is relaxed in favor of a multivariate mixture of normals assumption. Several Monte Carlo experiments indicate that these methods are successful at identifying departures from normality when they are present. Throughout the chapter the focus is on inference in parametric models that permit rich variation in the distribution of disturbances.
    The chapter first discusses Monte Carlo methods for the evaluation of high dimensional integrals, including integral simulators like the GHK method, and Markov Chain Monte Carlo methods like Gibbs sampling and the Metropolis-Hastings algorithm. It then turns to methods for approximating solutions to discrete choice dynamic optimization problems., including the methods developed by Keane and Wolpin, and Rust, as well as methods for circumventing the integration problem entirely, such as the approach of Geweke and Keane. The rest of the chapter deals with specific examples: classical simulation estimation for multinomial probit models, both in the cross sectional and panel data contexts; univariate and multivariate latent linear models; and Bayesian inference in dynamic discrete choice models in which the future component of the value function is replaced by a flexible polynomial.

[78.] A Note on Some Limitations of CRRA Utility

in Economics Letters, 2001, 71, 341-346.

Abstract: In a standard environment for choice under uncertainty with constant relative risk aversion (CRRA), the existence of expected utility is fragile with respect to changes in the distributions of random variables, changes in prior information, or the assumption of rational expectations.

[79.] Embedding Bayesian Tools in Mathematical Software

in E. I. George (ed.), Bayesian Methods with Applications to Science, Policy, and Official Statistics.  Brussels: Eurostat, 2001, 165-174.

The BACC software provides its users with tools for Bayesian Analysis, Computation and Communications. These tools are embedded in mathematical software applications such as Matlab and Gauss. From the user’s perspective, there is a seamless integration of special-purpose BACC commands with the powerful
built-in commands of the application. Several models are currently available, and BACC is designed to be extendible. We give a brief demonstration of the use
of BACC for Matlab, and discuss the implementation of new models for BACC.

[80.] Bayesian Estimation of Nonlinear State-Space Models Using Metropolis-Hastings Algorithm with Gibbs Sampling (2001)

in Computational Statistics and Data Analysis, 2001, 37, 151-170.  (H. Tanizaki, senior author)

Abstract: In this paper, an attempt is made to show a general solution to nonlinear and/or non-Gaussian state-space modeling in a Bayesian framework, which corresponds to an extension of Carlin et al. (J. Amer. Statist. Assoc. 87(418) (1992) 493–500) and Carter and Kohn (Biometrika 81(3) (1994) 541–553; Biometrika 83(3) (1996) 589–601). Using the Gibbs sampler and the Metropolis–Hastings algorithm, an asymptotically exact estimate of the smoothing mean is obtained from any nonlinear and/or non-Gaussian model. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed Bayes estimator.

[81.] Bayesian Specification Analysis in Econometrics

in American Journal of Agricultural Economics,  2001, 83, 1181-1186. (W. McCausland, coauthor)

[82.] Pitfalls in Drawing Policy Conclusions from Retrospective Survey Data: The Case of Advertising and Underage Smoking

in Journal of Risk and Uncertainty, 2002, 25, 111-131. (D. L. Martin, coauthor)

Abstract: This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient's residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model.

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