Roberto S. Mariano

Comparing Predictive Accuracy

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss of function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.

New tests of the life cycle and tax discounting hypotheses

Abstract We first test a version of the permanent income consumption function recently suggested by Barro. The results support the theory except that consumption expenditures show sensitivity to transitory income. Next we use the consumption model to test the tax discounting hypothesis, which is strongly supported. This support for tax discounting disagrees with results from some earlier studies using more traditional specifications of the consumption function. However, we show that when certain obviously inadequate estimation procedures are corrected, the traditional models also support tax discounting. This uniform support for tax discounting suggests that the sensitivity of consumption to transitory income is not due to liquidity constraints.

A Coincident Index, Common Factors, and Monthly Real GDP

The Stock–Watson coincident index and its subsequent extensions assume a static linear one‐factor model for the component indicators. This restrictive assumption is unnecessary if one defines a coincident index as an estimate of monthly real gross domestic products (GDP). This paper estimates Gaussian vector autoregression (VAR) and factor models for latent monthly real GDP and other coincident indicators using the observable mixed‐frequency series. For maximum likelihood estimation of a VAR model, the expectation‐maximization (EM) algorithm helps in finding a good starting value for a quasi‐Newton method. The smoothed estimate of latent monthly real GDP is a natural extension of the Stock–Watson coincident index.

Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System

This paper proposes the residual-based stochastic predictor as an alternative procedure for obtaining forecasts with a static nonlinear econometric model. This procedure modifies the usual Monte Carlo approach to stochastic simulations of the model in that calculated residuals over the sample period are used as proxies for disturbances instead of random draws from some assumed parametric distribution. In compar-ison with the Monte Carlo predictor, the residual-based should be less sensitive to distributional assumptions concerning disturbances in the system. It is also less demanding computationally. The large-sample asymptotic moments of the residual-based predictor are derived in this paper and compared with those of the Monte Carlo predictor. Both procedures are asymptotically unbiased. In terms of asymptotic mean squared prediction error (AMSPE), the Monte Carlo is efficient relative to the residual-based when the number of replications in the Monte Carlo simulations is large relative to sample size. This order of relative efficiency is reversed, however, when replication and sample sizes are similar. In any event, the amount by which the AMSPE of either predictor exceeds the lower bound for AMSPE is small as a percentage of the lower bound AMSPE when sample and replication sizes are at least of moderate magnitude. The paper also discusses the extension of the residual-based anld Monte Carlo procedures to the estimation of higher order moments and cumulative distribution functions of endogenous variables in the system.

Simulation-based inference in econometrics : methods and applications

Part I. Simulation-Based Inference in Econometrics, Methods and Applications: Introduction Melvyn Weeks 1. Simulation-based inference in econometrics: motivation and methods Steven Stern Part II. Microeconometric Methods: Introduction Melvyn Weeks 2. Accelerated Monte Carlo integration: an application to dynamic latent variable models Jean-Francois Richard and Wei Zhang 3. Some practical issues in maximum simulated likelihood Vassillis A. Hajivassiliou 4. Bayesian inference for dynamic discrete choice models without the need for dynamic programming John Geweke and Miochael Keane 6. Bayesian analysis of the multinomial probit model Peter E. Rossi and Robert E. McCulloch Part III. Time Series Methods and Models: Introduction Til Schuermann 7. Simulated moment methods for empirical equivalent martingale measures Bent Jesper Christensen and Nicholas M. Kiefer 8. Exact maximum likelihood estimation of observation-driven econometric models Francis X. Diebold and Til Schuermann 9. Simulation-based inference in non-linear state space models: application to testing the permanent income hypothesis Roberto S. Mariano and Hisashi Tanizaki 10. Simulation-based estimation of some factor models in econometrics Vance L. Martin and Adrian R. Pagan 11. Simulation-based Bayesian inference for economic time series John Geweke Part IV. Other Areas of Application and Technical Issues: Introduction Roberto S. Mariano 12. A comparison of computational methods for hierarchical methods in customer survey questionnaire data Eric T. Bradlow 13. Calibration by simulation for small sample bias correction Christian Gourieroux, Eric Renault and Nizar Touzi 14. Simulation-based estimation of a nonlinear, latent factor aggregate production function Lee Ohanian, Giovanni L. Violante, Per Krusell, Jose-Victor Rios-Rull 15. Testing calibrated general equilibrium models Fabio Canova and Eva Ortega 16. Simulation variance reduction for bootstrapping Bryan W. Brown Index.

Predictors in Dynamic Nonlinear Models: Large-Sample Behavior

The large-sample behavior of one-period-ahead and multiperiod-ahead predictors for a dynamic nonlinear simultaneous system is examined in this paper. Conditional on final values of the endogenous variables, the asymptotic moments of the deterministic, closed-form, Monte Carlo stochastic, and several variations of the residual-based stochastic predictor are analyzed. For one-period-ahead prediction, the results closely parallel our previous findings for static nonlinear systems. For multiperiod-ahead prediction similar results hold, except that the effective number of sample-period residuals available for use with the residual-based predictor is T/m , where T denotes sample size. In an attempt to avoid the problems associated with sample splitting, the complete enumeration predictor is proposed which is a multiperiod-ahead generalization of the one-period-ahead residual-based predictor. A bootstrap predictor is also introduced which is similar to the multiperiod-ahead Monte Carlo except disturbance proxies are drawn from the empirical distribution of the residuals. The bootstrap predictor is found to be asymptotically inefficient relative to both the complete enumeration and Monte Carlo predictors.

Prediction of Currency Crises: Case of Turkey

This paper explores the issue of constructing an economic predictive model of financial vulnerability through an alternative econometric methodology that addresses drawbacks in existing approaches. The methodology entails estimating a Markov regime switching model of exchange rate movements, with time-varying transition probabilities. Experiments with monthly and weekly models indicate that real exchange rate, foreign exchange reserves and domestic credit/deposit ratio are the most important determinants of financial vulnerability. These variables should be observed very closely by researchers and policy makers in order to determine if the country is heading for financially difficult times.

Finite Sample Analysis of Misspecification in Simultaneous Equation Models

Abstract This article examines the effects of misspecification on the exact sampling distributions of the k-class estimators of a single equation in a simultaneous equations model. The analysis focuses on the effects of excluding relevant exogenous variables. The misspecification may occur in either the estimated equation itself or in the other equations in the system. Exact expressions and large-concentration parameter asymptotic expansions are stated and analyzed for the bias and mean squared error (MSE) of the k-class estimators in the case of two included endogenous variables. The results in the article suggest that ordinary least squares (OLS) will often be preferable to two-stage least squares (2SLS) when misspecification is a serious possibility; the relative insensitivity of OLS to specification error outweighs its disadvantage in terms of bias and MSE in the correctly specified case. Further, when relevant exogenous variables are omitted from the estimated equation but not from the system, the en...

Nonlinear filters based on taylor series expansions

The nonlinear filters based on Taylor series approximation are broadly used for computational simplicity, even though their filtering estimates are clearly biased. In this paper, first, we analyze what is approximated when we apply the expanded nonlinear functions to the standard linear recursive Kalman filter algorithm. Next, since the state variable αt and αt-t are approximated as a conditional normal distribution given information up to time t - 1 (i.e., It-1) in approximation of the Taylor series expansion, it might be appropriate to evaluate each expectation by generating normal random numbers of αt and αt-1 given It-1 and those of the error terms θ and ηt. Thus, we propose the Monte-Carlo simulation filter using normal random draws. Finally we perform two Monte-Carlo experiments, where we obtain the result that the Monte-Carlo simulation filter has a superior performance over the nonlinear filters such as the extended Kalman filter and the second-order nonlinear filter.

Approximations to the Distribution Functions of the Ordinary Least-Squares and Two-Stage Least-Squares Estimators in the Case of Two Included Endogenous Variables

This paper deals with single-equation estimators in a simultaneous system of linear stochastic equations and approximates the distribution function of the two-stage least-squares estimators up to terms whose order of magnitude is 1//N_, where N is the sample size. For fixed N, an approximation to the OLS distribution function is also obtained up to terms whose order of magnitude 1/li, where p2 is what is referred to in the literature as the concentration parameter.