Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.     

Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.     

Recursive residuals for linear mixed models

Quality & Quantity - This paper presents and extends the concept of recursive residuals and their estimation to an important class of statistical models, Linear Mixed Models (LMM). Recurrence...     

Quantile regression methods for recursive structural equation models

Two classes of quantile regression estimation methods for the recursive structural equation models of Chesher [2003. Identification in nonseparable models. Econometrica 71, 1405–1441.] are investigated. A class of weighted average derivative estimators based directly on the identification strategy of Chesher is contrasted with a new control variate estimation method. The latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class. An application of the methods to the study of the effect of class size on the performance of Dutch primary school students shows that (i) reductions in class size are beneficial for good students in language and for weaker students in mathematics, (ii) larger classes appear beneficial for weaker language students, and (iii) the impact of class size on both mean and median performance is negligible.     

Inference in some disaggregated models with special covariance structure

This paper is concerned with parameter identification and estimation in linear structural equation models. We consider a special class of models which arises naturally when we disaggregate economic relations. We show that substantial gains in identification and estimation efficiency for ‘macro’ economic parameters can arise from disaggregation and analysis of the resulting ‘micro’ model.     

Nonparametric IV estimation of local average treatment effects with covariates

In this paper nonparametric instrumental variable estimation of local average treatment effects (LATE) is extended to incorporate covariates. Estimation of LATE is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models. Including covariates in the estimation of LATE is necessary when the instrumental variable itself is confounded, such that the IV assumptions are valid only conditional on covariates. Previous approaches to handle covariates in the estimation of LATE relied on parametric or semiparametric methods. In this paper, a nonparametric estimator for the estimation of LATE with covariates is suggested that is root-n asymptotically normal and efficient.     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

A simulation estimation analysis of the external debt crises of developing countries

In this paper we develop models of the incidence and extent of external financing crises of developing countries, which lead to multiperiod multinomial discrete choice and discrete/continuous econometric specifications with flexible correlation structures in the unobservables. We show that estimation of these models based on simulation methods has attractive statistical properties and is computationally tractable. Three such simulation estimation methods are exposited, analysed theoretically, and used in practice: a method of smoothly simulated maximum likelihood (SSML) based on a smooth recursive conditioning simulator (SRC), a method of simulated scores (MSS) based on a Gibbs sampling simulator (GSS), and an MSS estimator based on the SRC simulator. The data set used in this study comprises 93 developing countries observed through the 1970–88 period and contains information on external financing responses that was not available to investigators in the past. Moreover, previous studies of external debt problems had to rely on restrictive correlation structures in the unobservables to overcome otherwise intractable computational difficulties. The findings show that being able for the first time to allow for flexible correlation patterns in the unobservables through estimation by simulation has a substantial impact on the parameter estimates obtained from such models. This suggests that past empirical results in this literature require a substantial re-evaluation.     

Robustness and the general dynamic factor model with infinite-dimensional space: Identification,estimation, and forecasting

General dynamic factor models have demonstrated their capacity to circumvent the curse of dimensionality in the analysis of high-dimensional time series and have been successfully considered in many economic and financial applications. As second-order models, however, they are sensitive to the presence of outliers—an issue that has not been analyzed so far in the general case of dynamic factors with possibly infinite-dimensional factor spaces (Forni et al. 2000, 2015, 2017). In this paper, we consider this robustness issue and study the impact of additive outliers on the identification, estimation, and forecasting performance of general dynamic factor models. Based on our findings, we propose robust versions of identification, estimation, and forecasting procedures. The finite-sample performance of our methods is evaluated via Monte Carlo experiments and successfully applied to a classical data set of 115 US macroeconomic and financial time series.     

Robust and consistent estimation of nonlinear errors-in-variables models

This paper considers the consistent estimation of nonlinear errors-in-variables models. It adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn. This paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors-in-variables model. The identification is established through characteristic functions. The estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage, and at the second stage, a semiparametric nonlinear least-squares estimator is proposed. The consistency of the proposed estimator is also established. Finite sample performance of the estimator is investigated through a Monte Carlo study.     

A note on Model Reference Adaptive System (MRAS) estimate with infinite variance

This paper discusses the estimation of a parameter in an autoregressive model with infinite variance. A recursive estimation procedure based on minimizing the prediction errors is provided. It is also shown that the model reference adaptive system estimate for an AR (1) model given in Aase (1983) is a special case.     

Efficient learning via simulation: A marginalized resample-move approach

In state–space models, parameter learning is practically difficult and is still an open issue. This paper proposes an efficient simulation-based parameter learning method. First, the approach breaks up the interdependence of the hidden states and the static parameters by marginalizing out the states using a particle filter. Second, it applies a Bayesian resample-move approach to this marginalized system. The methodology is generic and needs little design effort. Different from batch estimation methods, it provides posterior quantities necessary for full sequential inference and recursive model monitoring. The algorithm is implemented both on simulated data in a linear Gaussian model for illustration and comparison and on real data in a Lévy jump stochastic volatility model and a structural credit risk model.     

Estimation and inference of dynamic structural factor models with over-identifying restrictions

This paper develops a new estimator for the impulse response functions in structural factor models with a fixed number of over-identifying restrictions. The proposed identification scheme nests the conventional just-identified recursive scheme as a special case. We establish the asymptotic distributions of the new estimator and develop test statistics for the over-identifying restrictions. Simulation results show that adding a few more over-identifying restrictions can lead to a substantial improvement in estimation accuracy for impulse response functions at both zero and nonzero horizons. We estimate the effects of a monetary policy shock using a U.S. data set. The results show that our over-identified scheme can help to detect incorrect specifications that lead to spurious impulse responses.     

MIXED‐FREQUENCY STRUCTURAL MODELS: IDENTIFICATION,ESTIMATION, AND POLICY ANALYSIS

The mismatch between the timescale of DSGE (dynamic stochastic general equilibrium) models and the data used in their estimation translates into identification problems, estimation bias, and distortions in policy analysis. We propose an estimation strategy based on mixed‐frequency data to alleviate these shortcomings. The virtues of our approach are explored for two monetary policy models. Copyright © 2014 John Wiley & Sons, Ltd.     

The Multinomial Probit Model Revisited: A Discussion of Parameter Estimability,Identification and Specification Testing

In this paper we examine the multinomial probit model in the light of recent developments in the field of simulation-based inference. We focus upon five broad areas: specification of multinomial choice models; parameter estimability and the use of simulation techniques, parameter identification; specification testing; and practical issues in simulation-based inference. Although the substitution of simulated probabilities for difficult to compute multidimensional integrals represents a significant step, by examining the more tenuous task of identification and in particular the identification of covariance parameters, we show how the specification and estimation of the multinomial probit still represents a formidable task.     

Identification and estimation of Gaussian affine term structure models

This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In some cases, MCSE allows researchers to recognize with certainty whether a given estimate represents a global maximum of the likelihood function and makes feasible the computation of small-sample standard errors.     

Recursive estimation of simultaneous equation models

A recursive instrumental variable estimator is derived. For simultaneous equation estimation, the choice of the instruments is discussed. A computationally simple and asymptotically efficient recursive estimator is proposed in this context.     

ARE EMPIRICAL MEASURES OF MACROECONOMIC UNCERTAINTY ALIKE?

Abstract There is a plethora of time series measures of uncertainty for inflation and real output growth in empirical studies but little is known whether they are comparable to the uncertainty measure reported by individual forecasters in the survey of professional forecasters. Are these two measures of uncertainty inherently distinct? This paper shows that, compared with many uncertainty proxies produced by time series models, the use of real‐time data with fixed‐sample recursive estimation of an asymmetric bivariate generalized autoregressive conditional heteroskedasticity model yields inflation uncertainty estimates which resemble the survey measure. There is, however, overwhelming evidence that many of the time series measures of growth uncertainty exceed the level of uncertainty obtained from survey measure. Our results highlight the relative merits of using different methods in modelling macroeconomic uncertainty which are useful for empirical researchers.     

Models of Quality‐Adjusted Life Years when Health Varies Over Time: Survey and Analysis

Abstract.  Quality‐adjusted life year (QALY) models are widely used for economic evaluation in the health care sector. In the first part of the paper, we establish an overview of QALY models where health varies over time and provide a theoretical analysis of model identification and parameter estimation from time trade‐off (TTO) and standard gamble (SG) scores. We investigate deterministic and probabilistic models and consider five different families of discounting functions in all. The second part of the paper discusses four issues recurrently debated in the literature. This discussion includes questioning the SG method as the gold standard for estimation of the health state index, re‐examining the role of the constant‐proportional trade‐off condition, revisiting the problem of double discounting of QALYs, and suggesting that it is not a matter of choosing between TTO and SG procedures as the combination of these two can be used to disentangle risk aversion from discounting. We find that caution must be taken when drawing conclusions from models with chronic health states to situations where health varies over time. One notable difference is that in the former case, risk aversion may be indistinguishable from discounting.     

Data‐Driven Identification Constraints for DSGE Models

We propose imposing data‐driven identification constraints to alleviate the multimodality problem arising in the estimation of poorly identified dynamic stochastic general equilibrium models under non‐informative prior distributions. We also devise an iterative procedure based on the posterior density of the parameters for finding these constraints. An empirical application to the Smets and Wouters ( 2007 ) model demonstrates the properties of the estimation method, and shows how the problem of multimodal posterior distributions caused by parameter redundancy is eliminated by identification constraints. Out‐of‐sample forecast comparisons as well as Bayes factors lend support to the constrained model.