The limit distribution of the estimates in cointegrated regression models with multiple structural changes

We study estimation and inference in cointegrated regression models with multiple structural changes allowing both stationary and integrated regressors. Both pure and partial structural change models are analyzed. We derive the consistency, rate of convergence and the limit distribution of the estimated break fractions. Our technical conditions are considerably less restrictive than those in Bai et al. [Bai, J., Lumsdaine, R.L., Stock, J.H., 1998. Testing for and dating breaks in multivariate time series. Review of Economic Studies 65, 395–432] who considered the single break case in a multi-equations system, and permit a wide class of practically relevant models. Our analysis is, however, restricted to a single equation framework. We show that if the coefficients of the integrated regressors are allowed to change, the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly. If, however, only the intercept and/or the coefficients of the stationary regressors are allowed to change, the estimates of the break dates are asymptotically independent as in the stationary case analyzed by Bai and Perron [Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78]. We also show that our results remain valid, under very weak conditions, when the potential endogeneity of the non-stationary regressors is accounted for via an increasing sequence of leads and lags of their first-differences as additional regressors. Simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples.     

Estimating structural changes in regression quantiles

This paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions. The analysis covers time series models as well as models with repeated cross-sections. We estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates. The limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations. A procedure to determine the number of breaks is also discussed. Empirical applications to the quarterly US real GDP growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone.     

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.     

Block recursion and structural vector autoregressions

In applications of structural VAR modeling, finite-sample properties may be difficult to obtain when certain identifying restrictions are imposed on lagged relationships. As a result, even though imposing some lagged restrictions makes economic sense, lagged relationships are often left unrestricted to make statistical inference more convenient. This paper develops block Monte Carlo methods to obtain both maximum likelihood estimates and exact Bayesian inference when certain types of restrictions are imposed on the lag structure. These methods are applied to two examples to illustrate the importance of imposing restrictions on lagged relationships.     

Greek sovereign bond index,volatility, and structural breaks

This article investigates volatility changes in the 10-year Greek sovereign bond index returns using the multiple structural break test developed by Bai and Perron (Econometrica 66:47–78, 1998, J Appl Econ 18:1–22, 2003), which allows for endogenous identification of break dates. We find that there exists one break date in volatility, April 2010, when the European debt crisis worsened and the Greek sovereign bond was downgraded to junk status. We also obtain evidence of performance improvement in our modeling by including structural break dummies into the variance equation. We observe sharp drops in a measure of volatility persistence after incorporating the structural change. Our findings are important for not only investors who assess the volatility of sovereign bonds for portfolio risk management, but also for policy makers who wish to understand and minimize the impacts of excess volatility on the financial system in government bond markets.     

MULTIVARIATE METHODS FOR MONITORING STRUCTURAL CHANGE

Detection of structural change is a critical empirical activity, but continuous ‘monitoring’ for changes in real time raises well‐known econometric issues that have been explored in a single series context. If multiple series co‐break then it is possible that simultaneous examination of a set of series helps identify changes with higher probability or more rapidly than when series are examined on a case‐by‐case basis. Some asymptotic theory is developed for maximum and average CUSUM detection tests. Monte Carlo experiments suggest that these both provide an improvement in detection relative to a univariate detector over a wide range of experimental parameters, given a sufficiently large number of co‐breaking series. This is robust to a cross‐sectional correlation in the errors (a factor structure) and heterogeneity in the break dates. We apply the test to a panel of UK price indices. Copyright © 2011 John Wiley & Sons, Ltd.     

Computation and analysis of multiple structural change models

In a recent paper, Bai and Perron ( 1998 ) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least‐squares operations of order O(T²) for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program. Copyright © 2002 John Wiley & Sons, Ltd.     

Structural break tests and the Greek sovereign debt crisis: revisited

Amidst the lack of consensus from previous academic studies, this paper contributes to existing literature by further examining the commencement date of the Sovereign Debt Crisis for the Greek economy. The contribution of this paper purports that the contentious issue of the start of the Greek crisis was taking place much earlier than reported by previous research. Empirical results from this paper challenge earlier studies that may have underestimated the impact of the degree of persistence in the volatility of bond returns. This analysis uses monthly 10-year Greek government bond data and three independent structural break model tests which allow for the detection of possible endogenous break dates to capture the beginning of the crisis. Each model provides empirically plausible and robust frameworks for examining the volatility of bond returns in an evolving time series behaviour. Ultimate results from a series of autoregressive EGARCH estimations, with and without dummy variables for break dates are compared. The dummy variables are incorporated within the coefficients of the mean and variance equations to validate the structural breaks in each series. Overall results show a significant presence of nonconsistent parameters capturing a structural break in the time series sample. The detection of this break, November 2009, represents a major regime change triggered by the start of the debt crisis for the Greek economy. Crucially, research implications of such excess volatilities in sovereign bond markets have poignant implications for regulators, investors and portfolio risk managers alike.     

Generalized method of moments and inverse control

This paper presents a generalized method of moments algorithm for estimating the structural parameters of a macroeconomic model subject to the restriction that the coefficients of the monetary policy rule minimize the central bank's expected loss function. The algorithm combines least-squares normal equations with moment restrictions derived from the first-order necessary conditions of the auxiliary optimization. We assess the performance of the algorithm with Monte Carlo simulations using three increasingly complex models. We find that imposing the optimizing restrictions when they are true improves estimation accuracy and that imposing those restrictions when they are false biases estimates of some of the structural parameters but not of the policy-rule coefficients.     

Partial Structural Break Identification

We propose an extension of the existing information criterion‐based structural break identification approaches. The extended approach helps identify both pure structural change (break) and partial structural change (break). A pure structural change refers to the case when breaks occur simultaneously in all parameters of regression equation, whereas a partial structural change happens when breaks occur in some parameters only. Our approach consistently outperforms other well‐known approaches. We also extend the simulation studies of Bai and Perron ( 2006 and Hall, Osborn and Sakkas ( 2013 ) by including more general cases. This provides more comprehensive results and reveals the cases where the existing identification approaches lose power, which should be kept in mind when applying them.     

Financial reforms and money demand: Evidence from 20 developing countries

The effects of financial reforms on money demand (M1) are analysed with estimates for two sets of sub-samples and two break dates for twenty developing Asian and African countries. In all cases, the magnitude of income elasticity does not change significantly when compared with sub-samples and whole sample periods. Using CUSUM and CUSUMSQ tests, we find that the demand for money functions in our selected countries are temporally stable and therefore the respective monetary authorities may target money supply as the conduct of monetary policy.     

Asymptotic least-squares estimation efficiency considerations and applications

This paper is concerned with the large sample efficiency of the asymptotic least-squares (ALS) estimators introduced by Gouriéroux, Monfort, and Trognon (1982, 1985) and Chamberlain (1982, 1984). We show how the efficiency of these estimators is affected when additional information is incorporated into the estimation procedure. The relationship between ALS and maximum likelihood is discussed. It is shown that ALS can be used to obtain asymptotically efficient estimates for a large range of econometric models. Many results from the literature on estimation are special cases of the framework adopted in this paper. An application of ALS to a dynamic rational expections factor demand model in the manufacturing sector in The Netherlands demonstrates the potential of the method in the estimation of the parameters in models which are subject to nonlinear cross-equation restrictions.     

Timing structural change: a conditional probabilistic approach

We propose a strategy for assessing structural stability in time‐series frameworks when potential change dates are unknown. Existing stability tests are effective in detecting structural change, but procedures for identifying timing are imprecise, especially in assessing the stability of variance parameters. We present a likelihood‐based procedure for assigning conditional probabilities to the occurrence of structural breaks at alternative dates. The procedure is effective in improving the precision with which inferences regarding timing can be made. We illustrate parametric and non‐parametric implementations of the procedure through Monte Carlo experiments, and an assessment of the volatility reduction in the growth rate of US GDP. Copyright © 2006 John Wiley & Sons, Ltd.     

The Limiting Distribution of Post-sample Stability Tests for GMM Estimation when the Potential Break Date is Unknown

Recent papers have proposed a split-sample prediction method to test for structural stability in GMM estimation when the potential break date is treated as known. In this note we derive the limiting distribution of the supremum of this test over all possible break dates, thus allowing for endogenous determination of the potential break date.     

Estimating a common deterministic time trend break in large panels with cross sectional dependence

This paper develops an estimation procedure for a common deterministic time trend break in large panels. The dependent variable in each equation consists of a deterministic trend and an error term. The deterministic trend is subject to a change in the intercept, slope or both, and the break date is common for all equations. The estimation method is simply minimizing the sum of squared residuals for all possible break dates. Both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate. The rate of convergence is faster when the errors are stationary than when they have a unit root. When there is no cross sectional dependence among the errors, the rate of convergence depends on the number of equations and thus is faster than the univariate case. When the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters, the rate of convergence does not depend on the number of equations and thus reduces to the univariate case. The limiting distribution of the break date estimate is also provided. Some Monte Carlo experiments are performed to assess the adequacy of the asymptotic results. A brief empirical example using the US GDP price index is offered.     

Indirect inference with time series observed with error

We propose the indirect inference estimator as a consistent method to estimate the parameters of a structural model when the observed series are contaminated by measurement error by considering the noise as a structural feature. We show that the indirect inference estimates are asymptotically biased if the error is neglected. When the condition for identification is satisfied, the structural and measurement error parameters can be consistently estimated. The issues of identification and misspecification of measurement error are discussed in detail. We illustrate the reliability of this procedure in the estimation of stochastic volatility models based on realized volatility measures contaminated by microstructure noise.     

Unit roots and structural breaks in North American unemployment rates

This paper examines the univariate time-series properties of the unemployment rate in Canada, Mexico, and the United States. Tests are employed that allow for endogenously determined break dates and the results are compared to stationarity tests that assume no break in the data. The structural break unit-root tests contradict the findings of the standard tests. We conclude that North American unemployment rates are trend stationary around a breaking trend.     

Unit root testing under a local break in trend

Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in both fixed trend break and no trend break environments, in finite samples pronounced “valleys” in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem, we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without-break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights.     

Identifying restrictions in limited information analysis of the schooling coefficient in a wage equation

Identifying restrictions underlying limited information estimates of the coefficients of a wage equation are considered from a Bayesian point of view. Within this framework ‘exclusion’ restrictions need not be imposed exactly, and it becomes possible to consider the marginal densities of interesting coefficients as functions of the tightness of these restrictions. In the application considered here the posterior mean for the schooling and test-score coefficients in a wage equation are examined as identifying restrictions are relaxed. The paper also serves as an example of the feasibility of Bayesian limited information analysis of a current economic issue.     

Testing for structural change in regression quantiles

Most studies in the structural change literature focus solely on the conditional mean, while under various circumstances, structural change in the conditional distribution or in conditional quantiles is of key importance. This paper proposes several tests for structural change in regression quantiles. Two types of statistics are considered, namely, a fluctuation type statistic based on the subgradient and a Wald type statistic, based on comparing parameter estimates obtained from different subsamples. The former requires estimating the model under the null hypothesis, and the latter involves estimation under the alternative hypothesis. The tests proposed can be used to test for structural change occurring in a pre-specified quantile, or across quantiles, which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function. Both single and multiple structural changes are considered. We derive the limiting distributions under the null hypothesis, and show they are nuisance parameter free and can be easily simulated. A simulation study is conducted to assess the size and power in finite samples.