Bayesian Treatments for Panel Data Stochastic Frontier Models with Time Varying Heterogeneity*Econometrics* **2017**, *5*(3), 33; doi:10.3390/econometrics5030033 - 28 July 2017**Abstract **

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This paper considers a linear panel data model with time varying heterogeneity. Bayesian inference techniques organized around Markov chain Monte Carlo (MCMC) are applied to implement new estimators that combine smoothness priors on unobserved heterogeneity and priors on the factor structure of unobserved

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This paper considers a linear panel data model with time varying heterogeneity. Bayesian inference techniques organized around Markov chain Monte Carlo (MCMC) are applied to implement new estimators that combine smoothness priors on unobserved heterogeneity and priors on the factor structure of unobserved effects. The latter have been addressed in a non-Bayesian framework by Bai (2009) and Kneip et al. (2012), among others. Monte Carlo experiments are used to examine the finite-sample performance of our estimators. An empirical study of efficiency trends in the largest banks operating in the U.S. from 1990 to 2009 illustrates our new estimators. The study concludes that scale economies in intermediation services have been largely exploited by these large U.S. banks.
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Recent Developments in Copula Models*Econometrics* **2017**, *5*(3), 34; doi:10.3390/econometrics5030034 - 24 July 2017**Abstract **

Copula models have become very popular and well studied among the scientific community.[...]
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On the Interpretation of Instrumental Variables in the Presence of Specification Errors: A Reply*Econometrics* **2017**, *5*(3), 32; doi:10.3390/econometrics5030032 - 19 July 2017**Abstract **

We appreciate the effort and thoughtfulness of Raunig’s (2017) attempted critique of Swamy et al. (2015).[...]
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On The Interpretation of Instrumental Variables in the Presence of Specification Errors: A Causal Comment*Econometrics* **2017**, *5*(3), 31; doi:10.3390/econometrics5030031 - 18 July 2017**Abstract **

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Swamy et al. (2015) argue that valid instruments cannot exist when a structural model is misspecified. This note shows that this is not true in general. In simple examples valid instruments can exist and can help to estimate parameters of interest.
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Using a Theory-Consistent CVAR Scenario to Test an Exchange Rate Model Based on Imperfect Knowledge*Econometrics* **2017**, *5*(3), 30; doi:10.3390/econometrics5030030 - 7 July 2017**Abstract **

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A theory-consistent CVAR scenario describes a set of testable regularieties one should expect to see in the data if the basic assumptions of the theoretical model are empirically valid. Using this method, the paper demonstrates that all basic assumptions about the shock structure

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A theory-consistent CVAR scenario describes a set of testable regularieties one should expect to see in the data if the basic assumptions of the theoretical model are empirically valid. Using this method, the paper demonstrates that all basic assumptions about the shock structure and steady-state behavior of an an imperfect knowledge based model for exchange rate determination can be formulated as testable hypotheses on common stochastic trends and cointegration. This model obtaines remarkable support for almost every testable hypothesis and is able to adequately account for the long persistent swings in the real exchange rate.
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Modeling Real Exchange Rate Persistence in Chile*Econometrics* **2017**, *5*(3), 29; doi:10.3390/econometrics5030029 - 7 July 2017**Abstract **

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The long and persistent swings in the real exchange rate have for a long time puzzled economists. Recent models built on imperfect knowledge economics seem to provide a theoretical explanation for this persistence. Empirical results, based on a cointegrated vector autoregressive (CVAR) model,

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The long and persistent swings in the real exchange rate have for a long time puzzled economists. Recent models built on imperfect knowledge economics seem to provide a theoretical explanation for this persistence. Empirical results, based on a cointegrated vector autoregressive (CVAR) model, provide evidence of error-increasing behavior in prices and interest rates, which is consistent with the persistence observed in the data. The movements in the real exchange rate are compensated by movements in the interest rate spread, which restores the equilibrium in the product market when the real exchange rate moves away from its long-run benchmark value. Fluctuations in the copper price also explain the deviations of the real exchange rate from its long-run equilibrium value.
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Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems*Econometrics* **2017**, *5*(3), 28; doi:10.3390/econometrics5030028 - 29 June 2017**Abstract **

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood

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Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are presented, and asymptotic properties sketched. The techniques are illustrated using the analysis of the PPP and UIP between Switzerland and the US.
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Sustainable Financial Obligations and Crisis Cycles*Econometrics* **2017**, *5*(2), 27; doi:10.3390/econometrics5020027 - 22 June 2017**Abstract **

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The ability to distinguish between sustainable and excessive debt developments is crucial for securing economic stability. By studying US private sector credit loss dynamics, we show that this distinction can be made based on a measure of the incipient aggregate liquidity constraint, the

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The ability to distinguish between sustainable and excessive debt developments is crucial for securing economic stability. By studying US private sector credit loss dynamics, we show that this distinction can be made based on a measure of the incipient aggregate liquidity constraint, the financial obligations ratio. Specifically, as this variable rises, the interaction between credit losses and the business cycle increases, albeit with different intensity depending on whether the problems originate in the household or the business sector. This occurs 1–2 years before each recession in the sample. Our results have implications for macroprudential policy and countercyclical capital-buffers.
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A Spatial Econometric Analysis of the Calls to the Portuguese National Health Line *Econometrics* **2017**, *5*(2), 24; doi:10.3390/econometrics5020024 - 16 June 2017**Abstract **

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The Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health

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The Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health services. This study aims to describe and evaluate the use of LS24. Since for LS24 data, the location attribute is an important source of information to describe its use, this study analyses the number of calls received, at a municipal level, under two different spatial econometric approaches. This analysis is important for future development of decision support indicators in a hospital context, based on the economic impact of the use of this health line. Considering the discrete nature of data, the number of calls to LS24 in each municipality is better modelled by a Poisson model, with some possible covariates: demographic, socio-economic information, characteristics of the Portuguese health system and development indicators. In order to explain model spatial variability, the data autocorrelation can be explained in a Bayesian setting through different hierarchical log-Poisson regression models. A different approach uses an autoregressive methodology, also for count data. A log-Poisson model with a spatial lag autocorrelation component is further considered, better framed under a Bayesian paradigm. With this empirical study we find strong evidence for a spatial structure in the data and obtain similar conclusions with both perspectives of the analysis. This supports the view that the addition of a spatial structure to the model improves estimation, even in the case where some relevant covariates have been included.
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The Realized Hierarchical Archimedean Copula in Risk Modelling*Econometrics* **2017**, *5*(2), 26; doi:10.3390/econometrics5020026 - 15 June 2017**Abstract **

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This paper introduces the concept of the realized hierarchical Archimedean copula (rHAC). The proposed approach inherits the ability of the copula to capture the dependencies among financial time series, and combines it with additional information contained in high-frequency data. The considered model does

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This paper introduces the concept of the realized hierarchical Archimedean copula (rHAC). The proposed approach inherits the ability of the copula to capture the dependencies among financial time series, and combines it with additional information contained in high-frequency data. The considered model does not suffer from the curse of dimensionality, and is able to accurately predict high-dimensional distributions. This flexibility is obtained by using a hierarchical structure in the copula. The time variability of the model is provided by daily forecasts of the realized correlation matrix, which is used to estimate the structure and the parameters of the rHAC. Extensive simulation studies show the validity of the estimator based on this realized correlation matrix, and its performance, in comparison to the benchmark models. The application of the estimator to one-day-ahead Value at Risk (VaR) prediction using high-frequency data exhibits good forecasting properties for a multivariate portfolio.
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Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles*Econometrics* **2017**, *5*(2), 25; doi:10.3390/econometrics5020025 - 14 June 2017**Abstract **

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It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the

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It is well known that inference on the cointegrating relations in a vector autoregression (CVAR) is difficult in the presence of a near unit root. The test for a given cointegration vector can have rejection probabilities under the null, which vary from the nominal size to more than 90%. This paper formulates a CVAR model allowing for multiple near unit roots and analyses the asymptotic properties of the Gaussian maximum likelihood estimator. Then two critical value adjustments suggested by McCloskey (2017) for the test on the cointegrating relations are implemented for the model with a single near unit root, and it is found by simulation that they eliminate the serious size distortions, with a reasonable power for moderate values of the near unit root parameter. The findings are illustrated with an analysis of a number of different bivariate DGPs.
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Dependence between Stock Returns of Italian Banks and the Sovereign Risk*Econometrics* **2017**, *5*(2), 23; doi:10.3390/econometrics5020023 - 8 June 2017**Abstract **

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We analyze the interdependence between the government yield spread and stock returns of the banking sector in Italy during the years 2003–2015. In a first step, we find that the Spearman’s rank correlation between the yield spread and the Italian banking system changed

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We analyze the interdependence between the government yield spread and stock returns of the banking sector in Italy during the years 2003–2015. In a first step, we find that the Spearman’s rank correlation between the yield spread and the Italian banking system changed significantly after September 2008. According to this finding, we split the time window in two sub-periods. While we show that the dependence between the banking industry and changes in the yield spread increased significantly in the second time interval, we find no contagion effects from changes in the yield spread to returns of the banking system.
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Unit Roots and Structural Breaks*Econometrics* **2017**, *5*(2), 22; doi:10.3390/econometrics5020022 - 30 May 2017**Abstract **

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Bayesian Inference for Latent Factor Copulas and Application to Financial Risk Forecasting*Econometrics* **2017**, *5*(2), 21; doi:10.3390/econometrics5020021 - 23 May 2017**Abstract **

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Factor modeling is a popular strategy to induce sparsity in multivariate models as they scale to higher dimensions. We develop Bayesian inference for a recently proposed latent factor copula model, which utilizes a pair copula construction to couple the variables with the latent

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Factor modeling is a popular strategy to induce sparsity in multivariate models as they scale to higher dimensions. We develop Bayesian inference for a recently proposed latent factor copula model, which utilizes a pair copula construction to couple the variables with the latent factor. We use adaptive rejection Metropolis sampling (ARMS) within Gibbs sampling for posterior simulation: Gibbs sampling enables application to Bayesian problems, while ARMS is an adaptive strategy that replaces traditional Metropolis-Hastings updates, which typically require careful tuning. Our simulation study shows favorable performance of our proposed approach both in terms of sampling efficiency and accuracy. We provide an extensive application example using historical data on European financial stocks that forecasts portfolio Value at Risk (VaR) and Expected Shortfall (ES).
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Copula-Based Factor Models for Multivariate Asset Returns*Econometrics* **2017**, *5*(2), 20; doi:10.3390/econometrics5020020 - 17 May 2017**Abstract **

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Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to

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Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to model the dependence of unobserved multivariate factors resulting from two dynamic factor models. However, the proposed methodology is general and applicable to several factor models as well as to other copula models for stationary multivariate time series. An empirical study illustrates the forecasting superiority of our approach for constructing an optimal portfolio of U.S. industrial stocks in the mean-variance framework.
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Maximum Likelihood Estimation of the I(2) Model under Linear Restrictions*Econometrics* **2017**, *5*(2), 19; doi:10.3390/econometrics5020019 - 15 May 2017**Abstract **

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Estimation of the I(2) cointegrated vector autoregressive (CVAR) model is considered. Without further restrictions, estimation of the I(1) model is by reduced-rank regression (Anderson (1951)). Maximum likelihood estimation of I(2) models, on the other hand, always requires iteration. This paper presents a new

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Estimation of the I(2) cointegrated vector autoregressive (CVAR) model is considered. Without further restrictions, estimation of the I(1) model is by reduced-rank regression (Anderson (1951)). Maximum likelihood estimation of I(2) models, on the other hand, always requires iteration. This paper presents a new triangular representation of the I(2) model. This is the basis for a new estimation procedure of the unrestricted I(2) model, as well as the I(2) model with linear restrictions imposed.
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The Univariate Collapsing Method for Portfolio Optimization*Econometrics* **2017**, *5*(2), 18; doi:10.3390/econometrics5020018 - 5 May 2017**Abstract **

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The univariate collapsing method (UCM) for portfolio optimization is based on obtaining the predictive mean and a risk measure such as variance or expected shortfall of the univariate pseudo-return series generated from a given set of portfolio weights and multivariate set of assets

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The univariate collapsing method (UCM) for portfolio optimization is based on obtaining the predictive mean and a risk measure such as variance or expected shortfall of the univariate pseudo-return series generated from a given set of portfolio weights and multivariate set of assets under interest and, via simulation or optimization, repeating this process until the desired portfolio weight vector is obtained. The UCM is well-known conceptually, straightforward to implement, and possesses several advantages over use of multivariate models, but, among other things, has been criticized for being too slow. As such, it does not play prominently in asset allocation and receives little attention in the academic literature. This paper proposes use of fast model estimation methods combined with new heuristics for sampling, based on easily-determined characteristics of the data, to accelerate and optimize the simulation search. An extensive empirical analysis confirms the viability of the method.
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Selecting the Lag Length for the *M*^{GLS} Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations*Econometrics* **2017**, *5*(2), 17; doi:10.3390/econometrics5020017 - 16 April 2017**Abstract **

This is a simulation-based warning note for practitioners who use the ${M}^{GLS}$ unit root tests in the context of structural change using different selection lag length criteria. With $T=100$ , we find severe oversize problems when using some

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This is a simulation-based warning note for practitioners who use the ${M}^{GLS}$ unit root tests in the context of structural change using different selection lag length criteria. With $T=100$ , we find severe oversize problems when using some criteria, while other criteria produce an undersizing behavior. In view of this dilemma, we do not recommend using these tests. While such behavior tends to disappear when $T=250$ , it is important to note that most empirical applications use smaller sample sizes such as $T=100$ or $T=150$ . The $AD{F}^{GLS}$ test does not present an oversizing or undersizing problem. The only disadvantage of the $AD{F}^{GLS}$ test arises in the presence of $MA(1)$ negative correlation, in which case the ${M}^{GLS}$ tests are preferable, but in all other cases they are very undersized. When there is a break in the series, selecting the breakpoint using the Supremum method greatly improves the results relative to the Infimum method.
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Copula–Based vMEM Specifications versus Alternatives: The Case of Trading Activity*Econometrics* **2017**, *5*(2), 16; doi:10.3390/econometrics5020016 - 12 April 2017**Abstract **

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We discuss several multivariate extensions of the Multiplicative Error Model to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional

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We discuss several multivariate extensions of the Multiplicative Error Model to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional expectations of the variables can be simultaneously estimated. Results with realized volatility, volumes and number of trades of the JNJ stock show that significantly superior realized volatility forecasts are delivered with a fully interdependent vMEM relative to a single equation. Alternatives involving log–Normal or semiparametric formulations produce substantially equivalent results.
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Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models*Econometrics* **2017**, *5*(1), 14; doi:10.3390/econometrics5010014 - 20 March 2017**Abstract **

Studies employing Arellano-Bond and Blundell-Bond generalized method of moments (GMM) estimation for linear dynamic panel data models are growing exponentially in number. However, for researchers it is hard to make a reasoned choice between many different possible implementations of these estimators and associated

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Studies employing Arellano-Bond and Blundell-Bond generalized method of moments (GMM) estimation for linear dynamic panel data models are growing exponentially in number. However, for researchers it is hard to make a reasoned choice between many different possible implementations of these estimators and associated tests. By simulation, the effects are examined in terms of many options regarding: (i) reducing, extending or modifying the set of instruments; (ii) specifying the weighting matrix in relation to the type of heteroskedasticity; (iii) using (robustified) 1-step or (corrected) 2-step variance estimators; (iv) employing 1-step or 2-step residuals in Sargan-Hansen overall or incremental overidentification restrictions tests. This is all done for models in which some regressors may be either strictly exogenous, predetermined or endogenous. Surprisingly, particular asymptotically optimal and relatively robust weighting matrices are found to be superior in finite samples to ostensibly more appropriate versions. Most of the variants of tests for overidentification and coefficient restrictions show serious deficiencies. The variance of the individual effects is shown to be a major determinant of the poor quality of most asymptotic approximations; therefore, the accurate estimation of this nuisance parameter is investigated. A modification of GMM is found to have some potential when the cross-sectional heteroskedasticity is pronounced and the time-series dimension of the sample is not too small. Finally, all techniques are employed to actual data and lead to insights which differ considerably from those published earlier.
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