Estimating parameters of real business cycle models

The calibration technique is the most common procedure to match the data generated from an equilibrium business cycle model with actual macroeconomic time series. This paper goes a step further and tests and applies a maximum likelihood procedure, in combination with the simulated annealing, to estimate the parameters of a baseline RBC model from U.S. macroeconomic time series data. The procedure is tested on a simulated data set where the parameters are known and then applied to U.S. time series data. This permits us to evaluate the efficiency of the procedure and the extent to which the RBC model is a good representation of macroeconomic data.     

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.     

Mixed-frequency VAR models with Markov-switching dynamics

This paper extends the Markov-switching vector autoregressive models to accommodate both the typical lack of synchronicity that characterizes the real-time daily flow of macroeconomic information and economic indicators sampled at different frequencies. The results of the empirical application suggest that the model is able to capture the features of the NBER business cycle chronology very accurately.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Markov-switching models and the unit root hypothesis in real US GDP

I find that real US GDP is better characterized as a trend stationary Markov-switching process than as having a (regime-dependent) unit root. I examine the effects of both assumptions on the analysis of business cycle features and their implications for the persistence of the dynamic response of output to a random disturbance.     

A new energy model to capture the behavior of energy price processes

Owing to the vague fluctuation of energy prices from time to time, a new energy model, which considers both the mean-reverting behavior and the long memory property, is proposed in this paper. Since the problem of estimating parameters, in discrete time for this model, plays a central role in forecast inference, the problem of estimating the unknown parameters has been dealt with for the fractional Ornstein–Uhlenbeck process observed discretely. The asymptotic properties of these estimates are also provided. The numerical simulation results confirm the theoretical analysis and show that our method is effective. To show how to apply our approach in realistic contexts, an empirical study of energy in China, namely Daqing crude oil, is presented. The empirical results seem reasonable when compared to the real data.     

Evaluating the carbon-macroeconomy relationship: Evidence from threshold vector error-correction and Markov-switching VAR models

This paper studies the nonlinear adjustment between industrial production and carbon prices – coined as ‘the carbon-macroeconomy relationship’ – in the EU 27. We model carbon price returns and industrial production as nonlinear and state-dependent, with dynamics depending on the sign and magnitude of past realization of returns and the growth of industrial production. Our findings show that (i) macroeconomic activity is likely to affect carbon prices with a lag, due to the specific institutional constraints of this environmental market; (ii) the joint dynamics of industrial production and carbon prices seem adequately captured by two-regime threshold vector error-correction and two-regime Markov-switching VAR models compared to linear models as main competitors. The regime-switching models proposed are profoundly checked for their economic content and statistical congruency, and are found to provide a sound statistical framework for a comprehensive analysis of the carbon-macroeconomy relationship.     

A comparison of empirical models used to infer the willingness to pay in contingent valuation

The essence of the contingent valuation method consists of creating a hypothetical market where respondents are asked about their willingness to pay (WTP) for a non-market good. Different empirical models can be formulated to estimate the expected WTP of a sample of respondents and, then, through aggregation, the social valuation of the good is inferred.This paper outlines the relevance of the distributional assumptions when estimating mean WTP. Several parametric and non-parametric methods are discussed and applied to calculate the existence value of a natural space. Results show that WTP is extremely sensitive to the empirical model used.First version received: November 2002 / Final version received: January 2004     

Maximum likelihood estimation of sum-constrained linear models with insufficient observations

A maximum likelihood procedure for estimating sum-constrained linear models is presented, which seems to provide a good balance between excessive observational requirements on the one hand and an unduly restrictive specification of the contemporaneous covariance matrix on the other.     

Errors in variables and spatial effects in hedonic house price models of ambient air quality

In the valuation of the effect of improved air quality through the estimation of hedonic models of house prices, the potential “errors in variables” aspect of the interpolated air pollution measures is often ignored. In this paper, we assess the extent to which this may affect the resulting empirical estimates for marginal willingness to pay (MWTP), using an extensive sample of over 100,000 individual house sales for 1999 in the South Coast Air Quality Management District of Southern California. We take an explicit spatial econometric perspective and account for spatial dependence and endogeneity using recently developed Spatial 2SLS estimation methods. We also account for both spatial autocorrelation and heteroskedasticity in the error terms, using the Kelejian–Prucha HAC estimator. Our results are consistent across different spatial weights matrices and different kernel functions and suggest that the bias from ignoring the endogeneity in interpolated values may be substantial. This paper is part of a joint research effort with James Murdoch (University of Texas, Dallas) and Mark Thayer (San Diego State University). Their valuable input is gratefully acknowledged. The research was supported in part by NSF Grant BCS-9978058 to the Center for Spatially Integrated Social Science (CSISS), and by NSF/EPA Grant SES-0084213. Earlier versions were presented at the 5th International Workshop on Spatial Econometrics and Statistics, Rome, Italy, May 2006, the 53th North American Meetings of the Regional Science Association International, Toronto, ON, Nov. 2006, the 2007 Meetings of the Allied Social Science Assocations, Chicago, IL, Jan 2007, and at departmental seminars at the University of Illinois. Comments by discussants and participants are greatly appreciated. A special thanks to Harry Kelejian for his detailed and patient clarification of the HAC estimator. The usual disclaimer holds.     

Maximum-likelihood estimation of misspecified models

Misspecified models occur frequently in econometric practice. It is therefore important to study the sampling distribution of maximum-likelihood estimators of parameters of misspecified models. This note exhibits the asymptotic covariance matrix of the ML estimator of a misspecified model. It points out that the expression for this matrix given by White is incorrect except for the very special case, rarely occuring in econometrics, that each observation is independent and identically distributed. An illustration using the standard linear regression model is provided.     

Average Derivative Estimation of Hedonic Price Models

Conventional parametric techniques for estimatinghedonic price models require a correct functionalform. In this paper, we side-step this parametricshortcoming by estimating a hedonic price model usingaverage derivative estimation (ADE). Thissemiparametric approach produces robust estimates ofthe marginal effects without assuming a specificfunctional form a priori. In our application ofthe model to a unique data set on Korean home prices,ADE produced estimates consistent with priorexpectations, providing initial evidence that themodel may represent a viable alternative when usingthe hedonic approach.     

股市中行业联动效应的实证分析——基于CAPM的空间计量模型的应用

本文基于CAPM模型,通过使用空间权重矩阵将同行业其他股票收益率的影响因素纳入了解释变量之中构建了一个收益率交互影响模型,并通过FF三因素模型从股票市场中找出公司规模和账面市值比的相关变量作为联动效应变量的工具变量,克服了联动效应变量的内生性问题。然后在此基础上分别对上证50、上证180、沪深300这三种股指所包含的股票样本进行了回归分析,证实了我国的证券市场中确实存在收益率之间的行业联动效应,并且联动反应系数大约为0.7到0.8之间。     

The effects of small sample bias in Threshold Autoregressive models

This paper investigates Threshold Autoregressive (TAR) models that contain a limited number of observations in some regimes. Simulations show that within the context of the real exchange rate literature, parameter estimates exhibit significant small sample bias even with long time series data. These distortions create substantial power losses in attempting to identify values of coefficients from data.     

Semi-parametric models for satisfaction with income

An overview is presented of some parametric and semi-parametric models, estimators, and specification tests that can be used to analyze ordered response variables. In particular, limited dependent variable models that generalize ordered probit are compared to regression models that generalize the linear model. These techniques are then applied to analyze how self-reported satisfaction with household income relates to household income, family composition, and other background variables. Data are drawn from the 1998 wave of the German Socio-Economic Panel. The results are used to estimate equivalence scales and the cost of children. We find that the standard ordered probit model is rejected, while some semi-parametric specifications survive specification tests against nonparametric alternatives. The estimated equivalence scales, however, are often similar for the parametric and semi-parametric specifications.JEL Classification: C14, C35, D12Correspondence to: Charles BellemareWe are grateful to an anonymous referee and to participants of a CeMMAP/ESG workshop at University College London and seminars at CentER (Tilburg University) and Humboldt University Berlin for useful comments.     

Nonlinear models with panel data

Panel data play an important role in empirical economics. With panel data one can answer questions about microeconomic dynamic behavior that could not be answered with cross sectional data. Panel data techniques are also useful for analyzing cross sectional data with grouping. This paper discusses some issues related to specification and estimation of nonlinear models using panel data.JEL Classification: C230The research behind this paper was supported by the National Science Foundation, the Gregory C. Chow Econometric Research Program at Princeton University, and Danish National Research Foundation (through CAM at the University of Copenhagen). The author thanks Ekaterini Kyriazidou, Hong Li, Marina Sallustro, and the editors for helpful suggestions.     

A Poisson ridge regression estimator

The standard statistical method for analyzing count data is the Poisson regression model, which is usually estimated using maximum likelihood (ML) method. The ML method is very sensitive to multicollinearity. Therefore, we present a new Poisson ridge regression estimator (PRR) as a remedy to the problem of instability of the traditional ML method. To investigate the performance of the PRR and the traditional ML approaches for estimating the parameters of the Poisson regression model, we calculate the mean squared error (MSE) using Monte Carlo simulations. The result from the simulation study shows that the PRR method outperforms the traditional ML estimator in all of the different situations evaluated in this paper.