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Econometrics, Volume 5, Issue 1 (March 2017)

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Editorial

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Open AccessEditorial Acknowledgement to Reviewers of Econometrics in 2016
Econometrics 2017, 5(1), 7; doi:10.3390/econometrics5010007
Received: 11 January 2017 / Revised: 11 January 2017 / Accepted: 11 January 2017 / Published: 11 January 2017
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Abstract The editors of Econometrics would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...] Full article

Research

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Open AccessArticle Fixed-b Inference for Testing Structural Change in a Time Series Regression
Econometrics 2017, 5(1), 2; doi:10.3390/econometrics5010002
Received: 19 August 2016 / Revised: 13 December 2016 / Accepted: 14 December 2016 / Published: 30 December 2016
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Abstract
This paper addresses tests for structural change in a weakly dependent time series regression. The cases of full structural change and partial structural change are considered. Heteroskedasticity-autocorrelation (HAC) robust Wald tests based on nonparametric covariance matrix estimators are explored. Fixed-b theory is
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This paper addresses tests for structural change in a weakly dependent time series regression. The cases of full structural change and partial structural change are considered. Heteroskedasticity-autocorrelation (HAC) robust Wald tests based on nonparametric covariance matrix estimators are explored. Fixed-b theory is developed for the HAC estimators which allows fixed-b approximations for the test statistics. For the case of the break date being known, the fixed-b limits of the statistics depend on the break fraction and the bandwidth tuning parameter as well as on the kernel. When the break date is unknown, supremum, mean and exponential Wald statistics are commonly used for testing the presence of the structural break. Fixed-b limits of these statistics are obtained and critical values are tabulated. A simulation study compares the finite sample properties of existing tests and proposed tests. Full article
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
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Open AccessArticle Regime Switching Vine Copula Models for Global Equity and Volatility Indices
Econometrics 2017, 5(1), 3; doi:10.3390/econometrics5010003
Received: 30 June 2016 / Revised: 19 December 2016 / Accepted: 20 December 2016 / Published: 4 January 2017
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Abstract
For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic
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For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature that correlations and higher moments between different indices tend to vary in time. However, to the best of our knowledge, no one has yet considered a global setup including both equity and implied volatility indices of various continents, and allowing for a changing dependence structure. We aim to close this gap by applying Markov-switching R-vine models to investigate the existence of different, global dependence regimes. In particular, we identify times of “normal” and “abnormal” states within a data set consisting of North-American, European and Asian indices. Our results confirm the existence of joint points in a time at which global regime switching between two different R-vine structures takes place. Full article
(This article belongs to the Special Issue Recent Developments in Copula Models)
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Open AccessArticle Between Institutions and Global Forces: Norwegian Wage Formation Since Industrialisation
Econometrics 2017, 5(1), 6; doi:10.3390/econometrics5010006
Received: 31 August 2016 / Revised: 9 December 2016 / Accepted: 13 December 2016 / Published: 12 January 2017
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Abstract
This paper reviews the development of labour market institutions in Norway, shows how labour market regulation has been related to the macroeconomic development, and presents dynamic econometric models of nominal and real wages. Single equation and multi-equation models are reported. The econometric modelling
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This paper reviews the development of labour market institutions in Norway, shows how labour market regulation has been related to the macroeconomic development, and presents dynamic econometric models of nominal and real wages. Single equation and multi-equation models are reported. The econometric modelling uses a new data set with historical time series of wages and prices, unemployment and labour productivity. Impulse indicator saturation is used to achieve robust estimation of focus parameters, and the breaks are interpreted in the light of the historical overview. A relatively high degree of constancy of the key parameters of the wage setting equation is documented, over a considerably longer historical time period than earlier studies have done. The evidence is consistent with the view that the evolving system of collective labour market regulation over long periods has delivered a certain necessary level of coordination of wage and price setting. Nevertheless, there is also evidence that global forces have been at work for a long time, in a way that links real wages to productivity trends in the same way as in countries with very different institutions and macroeconomic development. Full article
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Open AccessArticle A Fast Algorithm for the Computation of HAC Covariance Matrix Estimators
Econometrics 2017, 5(1), 9; doi:10.3390/econometrics5010009
Received: 10 August 2016 / Revised: 5 January 2017 / Accepted: 9 January 2017 / Published: 25 January 2017
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Abstract
This paper considers the algorithmic implementation of the heteroskedasticity and autocorrelation consistent (HAC) estimation problem for covariance matrices of parameter estimators. We introduce a new algorithm, mainly based on the fast Fourier transform, and show via computer simulation that our algorithm is up
[...] Read more.
This paper considers the algorithmic implementation of the heteroskedasticity and autocorrelation consistent (HAC) estimation problem for covariance matrices of parameter estimators. We introduce a new algorithm, mainly based on the fast Fourier transform, and show via computer simulation that our algorithm is up to 20 times faster than well-established alternative algorithms. The cumulative effect is substantial if the HAC estimation problem has to be solved repeatedly. Moreover, the bandwidth parameter has no impact on this performance. We provide a general description of the new algorithm as well as code for a reference implementation in R. Full article
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Open AccessArticle Consistency of Trend Break Point Estimator with Underspecified Break Number
Econometrics 2017, 5(1), 4; doi:10.3390/econometrics5010004
Received: 31 August 2016 / Revised: 19 December 2016 / Accepted: 26 December 2016 / Published: 5 January 2017
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Abstract
This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such
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This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such as allowing a time trend in the model. Despite the consistency of break point estimators of level shifts, there are few papers on the consistency of trend shift break point estimators in the presence of an underspecified break number. The simulation study and asymptotic analysis in this paper show that the trend shift break point estimator does not converge to the true break points when the break number is underspecified. In the case of two trend shifts, the inconsistency problem worsens if the magnitudes of the breaks are similar and the breaks are either both positive or both negative. The limiting distribution for the trend break point estimator is developed and closely approximates the finite sample performance. Full article
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
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Open AccessArticle Business Cycle Estimation with High-Pass and Band-Pass Local Polynomial Regression
Econometrics 2017, 5(1), 1; doi:10.3390/econometrics5010001
Received: 30 June 2016 / Revised: 13 December 2016 / Accepted: 16 December 2016 / Published: 5 January 2017
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Abstract
Filters constructed on the basis of standard local polynomial regression (LPR) methods have been used in the literature to estimate the business cycle. We provide a frequency domain interpretation of the contrast filter obtained by the difference of a series and its long-run
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Filters constructed on the basis of standard local polynomial regression (LPR) methods have been used in the literature to estimate the business cycle. We provide a frequency domain interpretation of the contrast filter obtained by the difference of a series and its long-run LPR component and show that it operates as a kind of high-pass filter, so that it provides a noisy estimate of the cycle. We alternatively propose band-pass local polynomial regression methods aimed at isolating the cyclical component. Results are compared to standard high-pass and band-pass filters. Procedures are illustrated using the US GDP series. Full article
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Open AccessArticle Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses
Econometrics 2017, 5(1), 5; doi:10.3390/econometrics5010005
Received: 17 November 2016 / Revised: 28 December 2016 / Accepted: 3 January 2017 / Published: 8 January 2017
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Abstract
This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999), which are locally
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This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999), which are locally best invariant and uniformly most powerful, to allow for a slope change in trend with or without a concurrent level shift under both the null and alternative hypotheses. We show that the limit distribution of the proposed LM tests is standard normal. Finite sample simulation experiments show that the tests have good size and power. As an empirical analysis, we apply the tests to the Consumer Price Indices of the G7 countries. Full article
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
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Open AccessArticle Endogeneity, Time-Varying Coefficients, and Incorrect vs. Correct Ways of Specifying the Error Terms of Econometric Models
Econometrics 2017, 5(1), 8; doi:10.3390/econometrics5010008
Received: 5 September 2016 / Revised: 5 December 2016 / Accepted: 8 December 2016 / Published: 3 February 2017
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Abstract
Using the net effect of all relevant regressors omitted from a model to form its error term is incorrect because the coefficients and error term of such a model are non-unique. Non-unique coefficients cannot possess consistent estimators. Uniqueness can be achieved if; instead;
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Using the net effect of all relevant regressors omitted from a model to form its error term is incorrect because the coefficients and error term of such a model are non-unique. Non-unique coefficients cannot possess consistent estimators. Uniqueness can be achieved if; instead; one uses certain “sufficient sets” of (relevant) regressors omitted from each model to represent the error term. In this case; the unique coefficient on any non-constant regressor takes the form of the sum of a bias-free component and omitted-regressor biases. Measurement-error bias can also be incorporated into this sum. We show that if our procedures are followed; accurate estimation of bias-free components is possible. Full article
Open AccessArticle A Note on Identification of Bivariate Copulas for Discrete Count Data
Econometrics 2017, 5(1), 10; doi:10.3390/econometrics5010010
Received: 5 August 2016 / Revised: 26 January 2017 / Accepted: 7 February 2017 / Published: 15 February 2017
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Abstract
Copulas have enjoyed increased usage in many areas of econometrics, including applications with discrete outcomes. However, Genest and Nešlehová (2007) present evidence that copulas for discrete outcomes are not identified, particularly when those discrete outcomes follow count distributions. This paper confirms the Genest
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Copulas have enjoyed increased usage in many areas of econometrics, including applications with discrete outcomes. However, Genest and Nešlehová (2007) present evidence that copulas for discrete outcomes are not identified, particularly when those discrete outcomes follow count distributions. This paper confirms the Genest and Nešlehová result using a series of simulation exercises. The paper then proceeds to show that those identification concerns diminish if the model has a regression structure such that the exogenous variable(s) generates additional variation in the outcomes and thus more completely covers the outcome domain. Full article
Open AccessArticle Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries
Econometrics 2017, 5(1), 11; doi:10.3390/econometrics5010011
Received: 24 August 2016 / Revised: 24 January 2017 / Accepted: 25 January 2017 / Published: 17 February 2017
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Abstract
This study reconsiders the common unit root/co-integration approach to test for the Fisher effect for the economies of the G7 countries. We first show that nominal interest and inflation rates are better represented as I(0) variables. Later, we use the Bai–Perron procedure to
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This study reconsiders the common unit root/co-integration approach to test for the Fisher effect for the economies of the G7 countries. We first show that nominal interest and inflation rates are better represented as I(0) variables. Later, we use the Bai–Perron procedure to show the existence of structural changes in the Fisher equation. After considering these breaks, we find very limited evidence of a total Fisher effect as the transmission coefficient of the expected inflation rates to nominal interest rates is very different than one. Full article
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
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Open AccessArticle Testing for a Structural Break in a Spatial Panel Model
Econometrics 2017, 5(1), 12; doi:10.3390/econometrics5010012
Received: 28 August 2016 / Accepted: 24 February 2017 / Published: 6 March 2017
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Abstract
We consider the problem of testing for a structural break in the spatial lag parameter in a panel model (spatial autoregressive). We propose a likelihood ratio test of the null hypothesis of no break against the alternative hypothesis of a single break. The
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We consider the problem of testing for a structural break in the spatial lag parameter in a panel model (spatial autoregressive). We propose a likelihood ratio test of the null hypothesis of no break against the alternative hypothesis of a single break. The limiting distribution of the test is derived under the null when both the number of individual units N and the number of time periods T is large or N is fixed and T is large. The asymptotic critical values of the test statistic can be obtained analytically. We also propose a break-date estimator that can be employed to determine the location of the break point following evidence against the null hypothesis. We present Monte Carlo evidence to show that the proposed procedure performs well in finite samples. Finally, we consider an empirical application of the test on budget spillovers and interdependence in fiscal policy within the U.S. states. Full article
(This article belongs to the Special Issue Unit Roots and Structural Breaks)
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Open AccessArticle Goodness-of-Fit Tests for Copulas of Multivariate Time Series
Econometrics 2017, 5(1), 13; doi:10.3390/econometrics5010013
Received: 31 December 2016 / Revised: 7 March 2017 / Accepted: 8 March 2017 / Published: 17 March 2017
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Abstract
In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations
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In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.
Full article
(This article belongs to the Special Issue Recent Developments in Copula Models)
Open AccessArticle Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models
Econometrics 2017, 5(1), 14; doi:10.3390/econometrics5010014
Received: 28 December 2016 / Revised: 6 March 2017 / Accepted: 10 March 2017 / Published: 20 March 2017
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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. Full article
(This article belongs to the Special Issue Recent Developments in Panel Data Methods)
Open AccessArticle A Simple Test for Causality in Volatility
Econometrics 2017, 5(1), 15; doi:10.3390/econometrics5010015
Received: 3 January 2017 / Revised: 7 March 2017 / Accepted: 16 March 2017 / Published: 20 March 2017
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Abstract
An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns was the portmanteau statistic for non-causality in the variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test
[...] Read more.
An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns was the portmanteau statistic for non-causality in the variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test of non-causality in the conditional variance by Hafner and Herwartz (2006), who provided simulation results to show that their LM test was more powerful than the portmanteau statistic for sample sizes of 1000 and 4000 observations. While the LM test for causality proposed by Hafner and Herwartz (2006) is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and a test for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the null hypothesis of non-causality. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger’s (1969, 1988) notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test. Full article

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