Weak Identification of Forward‐looking Models in Monetary Economics*

Recently, single‐equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward‐looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Galí and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward‐looking Taylor rules of Clarida, Galí and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual ‘weak instruments’ problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control.     

Nonparametric transformation to white noise

We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao et al. [2003. More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980–992]. In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is nonstandard in the unit root case. We also investigate its finite sample performance through simulation experiments.     

Semiparametric three‐step estimation methods for simultaneous equation systems

This paper proposes a new method for estimating a structural model of labour supply in which hours of work depend on (log) wages and the wage rate is considered endogenous. The main innovation with respect to other related estimation procedures is that a nonparametric additive structure in the hours of work equation is permitted. Though the focus of the paper is on this particular application, a three‐step methodology for estimating models in the presence of the above econometric problems is described. In the first step the reduced form parameters of the participation equation are estimated by a maximum likelihood procedure adapted for estimation of an additive nonparametric function. In the second step the structural parameters of the wage equation are estimated after obtaining the selection‐corrected conditional mean function. Finally, in the third step the structural parameters of the labour supply equation are estimated using local maximum likelihood estimation techniques. The paper concludes with an application to illustrate the feasibility, performance and possible gain of using this method. Copyright © 2005 John Wiley & Sons, Ltd.     

Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors

We consider the problem of estimating and testing for multiple breaks in a single‐equation framework with regressors that are endogenous, i.e. correlated with the errors. We show that even in the presence of endogenous regressors it is still preferable, in most cases, to simply estimate the break dates and test for structural change using the usual ordinary least squares (OLS) framework. Except for some knife‐edge cases, it delivers estimates of the break dates with higher precision and tests with higher power compared to those obtained using an instrumental variable (IV) method. Also, the OLS method avoids potential weak identification problems caused by weak instruments. To illustrate the relevance of our theoretical results, we consider the stability of the New Keynesian hybrid Phillips curve. IV‐based methods only provide weak evidence of instability. On the other hand, OLS‐based ones strongly indicate a change in 1991:Q1 and that after this date the model loses all explanatory power. Copyright © 2013 John Wiley & Sons, Ltd.     

A flexible parametric approach for estimating switching regime models and treatment effect parameters

In this paper, we propose a flexible, parametric class of switching regime models allowing for both skewed and fat-tailed outcome and selection errors. Specifically, we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean–variance mixture distributions. We extend Heckman’s two-step estimation procedure for the Gaussian switching regime model to the new class of models. When the distributions of the outcome errors are asymmetric, we show that an additional correction term accounting for skewness in the outcome error distribution (besides the analogue of the well known inverse mill’s ratio) needs to be included in the second step regression. We use the two-step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties. Simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated.     

Private demands for public capital: evidence from school bond referenda

This paper develops a framework for estimating demand for school infrastructure investment that is financed through local bond referenda. Our framework takes explicit account of the irregular and discrete nature of local capital investment and the objective functions of local school boards. Our empirical model consists of a three-equation system composed of a proposed spending equation, a vote equation, and a selection equation. Estimated income and price elasticities of demand for school infrastructure are similar to those found in studies of current school spending. We also find that school boards act like risk-averse, budget-maximizing agenda-setters.     

Bayesian Inference in Spatial Sample Selection Models

In this study, we consider Bayesian methods for the estimation of a sample selection model with spatially correlated disturbance terms. We design a set of Markov chain Monte Carlo algorithms based on the method of data augmentation. The natural parameterization for the covariance structure of our model involves an unidentified parameter that complicates posterior analysis. The unidentified parameter – the variance of the disturbance term in the selection equation – is handled in different ways in these algorithms to achieve identification for other parameters. The Bayesian estimator based on these algorithms can account for the selection bias and the full covariance structure implied by the spatial correlation. We illustrate the implementation of these algorithms through a simulation study and an empirical application.     

Generalized smooth finite mixtures

We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model’s parameterization and variable selection prior are chosen to prevent overfitting. We use simulated and real data sets to illustrate the methodology.     

Gender wage gap: A semi-parametric approach with sample selection correction

Sizeable gender differences in employment rates are observed in many countries. Sample selection into the workforce might therefore be a relevant issue when estimating gender wage gaps. We propose a semi-parametric estimator of densities in the presence of covariates which incorporates sample selection. We describe a simulation algorithm to implement counterfactual comparisons of densities. The proposed methodology is used to investigate the gender wage gap in Italy. We find that, when sample selection is taken into account, the gender wage gap widens, especially at the bottom of the wage distribution.     

Executive Compensation,Corporate Governance and Corporate Performance: A Simultaneous Equation Approach

This paper investigates the association between executive compensation and performance. It uniquely utilises a comprehensive set of corporate governance mechanisms within a three‐stage least squares (3SLS) simultaneous equation framework. Results based on estimating a conventional single equation model indicate that the executive pay and performance sensitivity is relatively weak, whereas those based on estimating a 3SLS model generally suggest improved executive pay and performance sensitivity. Our findings highlight the need for future research to control for possible simultaneous interdependencies when estimating the executive pay and performance link. The findings are generally robust across a raft of econometric models that control for different types of endogeneities, executive pay and performance proxies. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

利用GARCH-M类模型和极值理论对上证综指的研究

金融时间序列具有分布的厚尾性、波动的集聚性等特征,传统的方法难以准确的度量其风险。文中运用一种新的估计VaR和ES的方法,即采取两阶段法。首先用GARCH-M类模型(GARCH-M、EGARCH-M和TGARCH-M)拟和原始收益率数据,得到残差序列;第二步用极值分析的方法分析的尾部,最后得到收益率序列的动态VaR和ES。最后对三个模型的计算结果进行比较。     

Improving social harm indices with a modulated Hawkes process

Communities are affected adversely by a range of social harm events, such as crime, traffic crashes, medical emergencies, and drug use. The police, fire, health and social service departments are tasked with mitigating such social harm through various types of interventions. While various different social harm indices have been proposed for allocating resources to spatially fixed hotspots, the risk of social harm events is dynamic, and new algorithms and software systems that are capable of quickly identifying risks and triggering appropriate public safety responses are needed. We propose a novel modulated Hawkes process for this purpose that offers flexible approaches to both (i) the incorporation of spatial covariates and leading indicators for variance reduction in the case of rarer event categories, and (ii) the capture of dynamic hotspot formation through self-excitation. We present an efficient l1-penalized EM algorithm for estimating the model that performs feature selection for the spatial covariates of each incident type simultaneously. We provide simulation results using data from the Indianapolis Metropolitan Police Department in order to illustrate the advantages of the modulated Hawkes process model of social harm over various recently introduced social harm indices and property crime Hawkes processes.     

Asymmetry in first‐price auctions with affiliated private values

Collusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two‐step non‐parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Unemployment and liquidity constraints

We present a dynamic framework for the interaction between borrowing (liquidity) constraints and deviations of actual hours from desired hours, both measured by discrete‐valued indicators, and estimate it as a system of dynamic binary and ordered probit models with panel data from the Panel Study of Income Dynamics. We analyze a household's propensity to be liquidity constrained by means of a dynamic binary probit model. We analyze qualitative aspects of the conditions of employment, namely whether the household head is involuntarily overemployed, voluntarily employed, or involuntarily underemployed or unemployed, by means of a dynamic ordered probit model. We focus on the possible interaction between the two types of constraints. We estimate these models jointly using maximum simulated likelihood, where we allow for individual random effects along with an autoregressive process for the general error term in each equation. A novel feature of our method is that it allows for the random effects to be correlated with regressors in a time‐invariant fashion. Our results provide strong support for the basic theory of constrained behavior and the interaction between liquidity constraints and exogenous constraints on labor supply. Copyright © 2007 John Wiley & Sons, Ltd.     

System‐Equation ADL Test for Threshold Cointegration with an Application to the Term Structure of Interest Rates

This paper proposes a new system‐equation test for threshold cointegration based on a threshold vector autoregressive distributed lag (ADL) model. The new test can be applied when the cointegrating vector is unknown and when weak exogeneity fails. The asymptotic null distribution of the new test is derived, critical values are tabulated and finite‐sample properties are examined. In particular, the new test is shown to have good size, so the bootstrap is not required. The new test is illustrated using the long‐term and short‐term interest rates. We show that the system‐equation model can shed light on both asymmetric adjustment speeds and asymmetric adjustment roles. The latter is unavailable in the single‐equation testing strategy.     

The cross‐Euler equation approach to intertemporal substitution in import demand

This paper addresses the empirical dilemma in identifying and estimating the parameters governing the intertemporal elasticity of substitution (IES) for import demand. We propose a new concept, the cross‐Euler equation, for overcoming this empirical dilemma. IES parameters are estimated by exploiting the cointegrating restriction implied by the cross‐Euler equation. Further, by comparing the IES estimates from the cross‐Euler equation to those from the standard Euler equation, we test the hypothesis whether import demand is affected by nuisance factors. Using the US data, we found imported goods consumption to be robust against nuisance factors, but not for domestic goods. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting With the Standardized Self‐Perturbed Kalman Filter

We propose and study the finite‐sample properties of a modified version of the self‐perturbed Kalman filter of Park and Jun (Electronics Letters 1992; 28 : 558–559) for the online estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is weighted by the estimate of the measurement error variance. This avoids the calibration of a design parameter as the perturbation term is scaled by the amount of uncertainty in the data. It is shown by Monte Carlo simulations that this perturbation method is associated with a good tracking of the dynamics of the parameters compared to other online algorithms and to classical and Bayesian methods. The standardized self‐perturbed Kalman filter is adopted to forecast the equity premium on the S&P 500 index under several model specifications, and determines the extent to which realized variance can be used to predict excess returns. Copyright © 2016 John Wiley & Sons, Ltd.