NON‐LINEAR DSGE MODELS AND THE CENTRAL DIFFERENCE KALMAN FILTER

This paper introduces a quasi maximum likelihood approach based on the central difference Kalman filter to estimate non‐linear dynamic stochastic general equilibrium (DSGE) models with potentially non‐Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models solved up to third order. These properties are verified in a Monte Carlo study for a DSGE model solved to second and third order with structural shocks that are Gaussian, Laplace distributed, or display stochastic volatility. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model. To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric estimation framework with parametric copula and nonparametric marginal distributions. We establish asymptotic theory, including root‐n normality, for the sieve maximum likelihood estimators that can be used to conduct inference on the individual structural parameters and the average treatment effect (ATE). In order to show the practical relevance of the proposed framework, we conduct a sensitivity analysis via extensive Monte Carlo simulation exercises. The results suggest that estimates of the parameters, especially the ATE, are sensitive to parametric specification, while semiparametric estimation exhibits robustness to underlying data‐generating processes. We then provide an empirical illustration where we estimate the effect of health insurance on doctor visits. In this paper, we also show that the absence of excluded instruments may result in identification failure, in contrast to what some practitioners believe.     

Estimation of linear dynamic panel data models with time‐invariant regressors

We present a sequential approach to estimating a dynamic Hausman–Taylor model. We first estimate the coefficients of the time‐varying regressors and subsequently regress the first‐stage residuals on the time‐invariant regressors. In comparison to estimating all coefficients simultaneously, this two‐stage procedure is more robust against model misspecification, allows for a flexible choice of the first‐stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite‐sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment.     

On Maximum Likelihood Estimation of Dynamic Panel Data Models

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.     

Ordinal-response GARCH models for transaction data: A forecasting exercise

We use numerous high-frequency transaction data sets to evaluate the forecasting performances of several dynamic ordinal-response time series models with generalized autoregressive conditional heteroscedasticity (GARCH). The specifications account for three components: leverage effects, in-mean effects and moving average error terms. We estimate the model parameters by developing Markov chain Monte Carlo algorithms. Our empirical analysis shows that the proposed ordinal-response GARCH models achieve better point and density forecasts than standard benchmarks.     

Structural estimation of jump-diffusion processes in macroeconomics

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data.     

Estimating dynamic equilibrium economies: linear versus nonlinear likelihood

This paper compares two methods for undertaking likelihood‐based inference in dynamic equilibrium economies: a sequential Monte Carlo filter and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. We report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, although relatively small in absolute values, have important effects on the moments of the model. We conclude that the nonlinear filter is a superior procedure for taking models to the data. Copyright © 2005 John Wiley & Sons, Ltd.     

THE PREDICTABILITY OF AGGREGATE CONSUMPTION GROWTH IN OECD COUNTRIES: A PANEL DATA ANALYSIS

We examine aggregate consumption growth predictability. We derive a dynamic consumption equation which encompasses relevant predictability factors: habit formation, intertemporal substitution, current income consumption and non‐separabilities between private consumption and both hours worked and government consumption. We estimate this equation for a panel of 15 OECD countries over the period 1972–2007, taking into account parameter heterogeneity, endogeneity and error cross‐sectional dependence using a GMM version of the common correlated effects mean group estimator. Small‐sample properties are demonstrated using Monte Carlo simulations. The estimation results support income growth as the only variable with significant predictive power for aggregate consumption growth. Copyright © 2013 John Wiley & Sons, Ltd.     

The dynamic Laurent flexible form and the demand for money

I derive the dynamic full Laurent model to estimate economic models that assume a dynamic process. The application in this paper is to use the dynamic full Laurent to estimate a system of dynamic asset demand equations. The main results are that the dynamic full Laurent rejects its static version and the estimated elasticities are variable over time. Results from a Monte Carlo analysis, using a dynamic data-generating process, show that the prediction errors from the dynamic full Laurent are much smaller than those from the static version. Thus when the data are generated by a dynamic process, inferences from the static full Laurent model can be severely biased. © 1997 John Wiley & Sons, Ltd.     

Dynamic spatial autoregressive models with autoregressive and heteroskedastic disturbances

We propose a new class of models specifically tailored for spatiotemporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, that is, SARAR(1, 1), by exploiting the recent advancements in score‐driven (SD) models typically used in time series econometrics. In particular, we allow for time‐varying spatial autoregressive coefficients as well as time‐varying regressor coefficients and cross‐sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite‐sample properties of the maximum likelihood estimator for the new class of models as well as its flexibility in explaining a misspecified dynamic spatial dependence process. The new proposed class of models is found to be economically preferred by rational investors through an application to portfolio optimization.     

Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods

Abstract

This article considers autoregressive (SAR) models. We method to estimate the parameters of likelihood (ML) method. Our Bayesian by the Monte Carlo studies. We found the efficient as the ML estimators.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

MULTI-STEP ESTIMATION FOR FORECASTING

We delineate conditions which favour multi-step, or dynamic, estimation for multi-step forecasting. An analytical example shows how dynamic estimation (DE) may accommodate incorrectly-specified models as the forecast lead alters, improving forecast performance for some misspecifications. However, in correctly-specified models, reducing finite-sample biases does not justify DE. In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favour DE, though other solutions exist to that scenario. A second Monte Carlo study obtains the estimator biases and explains these using asymptotic approximations.     

Dynamic specification tests for dynamic factor models

We derive computationally simple expressions for score tests of misspecification in parametric dynamic factor models using frequency domain techniques. We interpret those diagnostics as time domain moment tests which assess whether certain autocovariances of the smoothed latent variables match their theoretical values under the null of correct model specification. We also reinterpret reduced‐form residual tests as checking specific restrictions on structural parameters. Our Gaussian tests are robust to nonnormal, independent innovations. Monte Carlo exercises confirm the finite‐sample reliability and power of our proposals. Finally, we illustrate their empirical usefulness in an application that constructs a US coincident indicator.     

Estimating nonlinear time-series models using simulated vector autoregressions

This paper develops two new methods for conducting formal statistical inference in nonlinear dynamic economic models. The two methods require very little analytical tractability, relying instead on numerical simulation of the model's dynamic behaviour. Although one of the estimators is asymptotically more efficient than the other, a Monte Carlo study shows that, for a specific application, the less efficient estimator has smaller mean squared error in samples of the size typically encountered in macroeconomics. The estimator with superior small sample performance is used to estimate the parameters of a real business cycle model using observed US time-series data.     

The stochastic volatility in mean model: empirical evidence from international stock markets

In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is developed elsewhere for Autoregressive Conditional Heteroscedastic (ARCH) models, known as the ARCH in Mean (ARCH‐M) model. The estimation of ARCH models is relatively easy compared with that of the Stochastic Volatility (SV) model. However, efficient Monte Carlo simulation methods for SV models have been developed to overcome some of these problems. The details of modifications required for estimating the volatility‐in‐mean effect are presented in this paper together with a Monte Carlo study to investigate the finite sample properties of the SVM estimators. Taking these developments of estimation methods into account, we regard SV and SVM models as practical alternatives to their ARCH counterparts and therefore it is of interest to study and compare the two classes of volatility models. We present an empirical study of the intertemporal relationship between stock index returns and their volatility for the United Kingdom, the United States and Japan. This phenomenon has been discussed in the financial economic literature but has proved hard to find empirically. We provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process. Copyright © 2002 John Wiley & Sons, Ltd.     

Semiparametric Bayesian inference for dynamic Tobit panel data models with unobserved heterogeneity

This paper develops semiparametric Bayesian methods for inference of dynamic Tobit panel data models. Our approach requires that the conditional mean dependence of the unobserved heterogeneity on the initial conditions and the strictly exogenous variables be specified. Important quantities of economic interest such as the average partial effect and average transition probabilities can be readily obtained as a by‐product of the Markov chain Monte Carlo run. We apply our method to study female labor supply using a panel data set from the National Longitudinal Survey of Youth 1979. Copyright © 2008 John Wiley & Sons, Ltd.     

Issue Information

Much research studies US inflation history with a trend‐cycle model with unobserved components, where the trend may be viewed as the Fed's evolving inflation target or long‐horizon expected inflation. We provide a novel way to measure the slowly evolving trend and the cycle (or inflation gap), by combining inflation predictions from the Survey of Professional Forecasters (SPF) with realized inflation. The SPF forecasts may be treated either as rational expectations (RE) or updating according to a sticky information (SI) law of motion. We estimate RE and SI state‐space models with stochastic volatility on samples of consumer price index and gross national product/gross domestic product deflator inflation and the associated SPF inflation predictions using a particle Metropolis–Markov chain Monte Carlo sampler. The trend converges to 2% and its volatility declines over time—two tendencies largely complete by the late 1990s.     

Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation

Motivated by the need for a positive‐semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra‐high‐frequency asset prices in a state‐space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and expectation maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive‐semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations that mimic the liquidity and market microstructure characteristics of the S&P 500 universe as well as in a high‐dimensional application on US stocks. KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Hidden group patterns in democracy developments: Bayesian inference for grouped heterogeneity

We propose a nonparametric Bayesian approach to estimate time‐varying grouped patterns of heterogeneity in linear panel data models. Unlike the classical approach in Bonhomme and Manresa (Econometrica, 2015, 83, 1147–1184), our approach can accommodate selection of the optimal number of groups and model estimation jointly, and also be readily extended to quantify uncertainties in the estimated group structure. Our proposed approach performs well in Monte Carlo simulations. Using our approach, we successfully replicate the estimated relationship between income and democracy in Bonhomme and Manresa and the group characteristics when we use the same number of groups. Furthermore, we find that the optimal number of groups could depend on model specifications on heteroskedasticity and discuss ways to choose models in practice.