A Simple Test for Cointegration in Dependent Panels with Structural Breaks*

This paper develops a very simple test for the null hypothesis of no cointegration in panel data. The test is general enough to allow for heteroskedastic and serially correlated errors, unit‐specific time trends, cross‐sectional dependence and unknown structural breaks in both the intercept and slope of the cointegrated regression, which may be located at different dates for different units. The limiting distribution of the test is derived, and is found to be normal and free of nuisance parameters under the null. A small simulation study is also conducted to investigate the small‐sample properties of the test. In our empirical application, we provide new evidence concerning the purchasing power parity hypothesis.     

General‐to‐Specific Model Selection Procedures for Structural Vector Autoregressions*

Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper, we propose general‐to‐specific (Gets) model selection procedures to overcome these limitations. It is shown that single‐equation procedures are generally efficient for the reduction of recursive SVAR models. The small‐sample properties of the proposed reduction procedure (as implemented using PcGets) are evaluated in a realistic Monte Carlo experiment. The impulse responses generated by the selected SVAR are found to be more precise and accurate than those of the unrestricted VAR. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (Review of Economics and Statistics, Vol. 78, pp. 16–34, 1996) . The results are consistent with the Monte Carlo and question the validity of the impulse responses generated by the full system.     

Simplified Implementation of the Heckman Estimator of the Dynamic Probit Model and a Comparison with Alternative Estimators*

This paper presents a convenient shortcut method for implementing the Heckman estimator of the dynamic random effects probit model and other dynamic nonlinear panel data models using standard software. It then compares the estimators proposed by Heckman, Orme and Wooldridge, based on three alternative approximations, first in an empirical model for the probability of unemployment and then in a set of simulation experiments. The results indicate that none of the three estimators dominates the other two in all cases. In most cases, all three estimators display satisfactory performance, except when the number of time periods is very small.     

Cointegration Testing in Panels with Common Factors*

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.     

Testing for Panel Cointegration with Multiple Structural Breaks*

This paper proposes a Lagrange multiplier (LM) test for the null hypothesis of cointegration that allows for the possibility of multiple structural breaks in both the level and trend of a cointegrated panel regression. The test is general enough to allow for endogenous regressors, serial correlation and an unknown number of breaks that may be located at different dates for different individuals. We derive the limiting distribution of the test and conduct a small Monte Carlo study to investigate its finite sample properties. In our empirical application to the solvency of the current account, we find evidence of cointegration between saving and investment once a level break is accommodated.     

Automated Model Selection in Finance: General‐to‐Specific Modelling of the Mean and Volatility Specifications*

General‐to‐Specific (GETS) modelling has witnessed major advances thanks to the automation of multi‐path GETS specification search. However, the estimation complexity associated with financial models constitutes an obstacle to automated multi‐path GETS modelling in finance. Making use of a recent result we provide and study simple but general and flexible methods that automate financial multi‐path GETS modelling. Starting from a general model where the mean specification can contain autoregressive terms and explanatory variables, and where the exponential volatility specification can include log‐ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications.     

The Likelihood Ratio Test for the Rank of a Cointegration Submatrix*

This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent–transitory decompositions and of subhypotheses related to neutrality and long‐run Granger noncausality. The proposed test has a chi‐squared limit distribution and indicates the validity of the normalization with probability one in the limit, for valid normalizations. The asymptotic properties of several derived estimators of the rank are also discussed. It is found that a testing procedure that starts from the hypothesis of minimal rank is preferable.     

A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression*

Graph‐theoretic methods of causal search based on the ideas of Pearl (2000), Spirtes et al. (2000), and others have been applied by a number of researchers to economic data, particularly by Swanson and Granger (1997) to the problem of finding a data‐based contemporaneous causal order for the structural vector autoregression, rather than, as is typically done, assuming a weakly justified Choleski order. Demiralp and Hoover (2003) provided Monte Carlo evidence that such methods were effective, provided that signal strengths were sufficiently high. Unfortunately, in applications to actual data, such Monte Carlo simulations are of limited value, as the causal structure of the true data‐generating process is necessarily unknown. In this paper, we present a bootstrap procedure that can be applied to actual data (i.e. without knowledge of the true causal structure). We show with an applied example and a simulation study that the procedure is an effective tool for assessing our confidence in causal orders identified by graph‐theoretic search algorithms.     

Searching for the Causal Structure of a Vector Autoregression*

We provide an accessible introduction to graph‐theoretic methods for causal analysis. Building on the work of Swanson and Granger (Journal of the American Statistical Association, Vol. 92, pp. 357–367, 1997), and generalizing to a larger class of models, we show how to apply graph‐theoretic methods to selecting the causal order for a structural vector autoregression (SVAR). We evaluate the PC (causal search) algorithm in a Monte Carlo study. The PC algorithm uses tests of conditional independence to select among the possible causal orders – or at least to reduce the admissible causal orders to a narrow equivalence class. Our findings suggest that graph‐theoretic methods may prove to be a useful tool in the analysis of SVARs.     

Cointegration,long-run structural modelling and weak exogeneity: Two models of the UK economy

Cointegration ideas as introduced by Granger in 1981 are commonly embodied in empirical macroeconomic modelling through the vector error correction model (VECM). It has become common practice in these models to treat some variables as weakly exogenous, resulting in conditional VECMs. This paper studies the consequences of different approaches to weak exogeneity for the dynamic properties of such models, in the context of two models of the UK economy, one a national-economy model, the other the UK submodel of a global model. Impulse response and common trend analyses are shown to be sensitive to these assumptions and other specification choices.     

Regression Models with Data‐based Indicator Variables*

Ordinary least squares estimation of an impulse‐indicator coefficient is inconsistent, but its variance can be consistently estimated. Although the ratio of the inconsistent estimator to its standard error has a t‐distribution, that test is inconsistent: one solution is to form an index of indicators. We provide Monte Carlo evidence that including a plethora of indicators need not distort model selection, permitting the use of many dummies in a general‐to‐specific framework. Although White's (1980) heteroskedasticity test is incorrectly sized in that context, we suggest an easy alteration. Finally, a possible modification to impulse ‘intercept corrections’ is considered.     

GMM Estimation with Non‐causal Instruments*

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non‐causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J‐test of overidentifying restrictions that may be inconsistent and has, in general, low finite‐sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non‐causality is quite common among economic variables, making these problems highly relevant.     

A Comparison of Johansen's,Bierens’ and the Subspace Algorithm Method for Cointegration Analysis*

The methods listed in the title are compared by means of a simulation study and a real world application. The aspects compared via simulations are the performance of the tests for the cointegrating rank and the quality of the estimated cointegrating space. The subspace algorithm method, formulated in the state space framework and thus applicable for vector autoregressive moving average (VARMA) processes, performs at least comparably to the Johansen method. Both the Johansen procedure and the subspace algorithm cointegration analysis perform significantly better than Bierens’ method. The real‐world application is an investigation of the long‐run properties of the one‐sector neoclassical growth model for Austria. The results do not fully support the implications of the model with respect to cointegration. Furthermore, the results differ greatly between the different methods. The amount of variability depends strongly upon the number of variables considered and huge differences occur for the full system with six variables. Therefore we conclude that the results of such applications with about five or six variables and 100 observations, which are typical in the applied literature, should possibly be interpreted with more caution than is commonly done.     

GMM Estimation with Non‐causal Instruments under Rational Expectations*

Lanne and Saikkonen [Oxford Bulletin of Economics and Statistics (2011a) Vol. 73, pp. 581–592], show that the generalized method of moments (GMM) estimator is inconsistent, when the instruments are lags of variables that admit a non‐causal autoregressive representation. This article argues that this inconsistency depends on distributional assumptions, that do not always hold. In particular under rational expectations, the GMM estimator is found to be consistent. This result is derived in a linear context and illustrated by simulation of a nonlinear asset pricing model.     

Miller and Modigliani,Predictive Return Regressions and Cointegration*

This paper investigates the use of alternative measures of dividend yields to predict US aggregate stock returns. Following Miller and Modigliani [Journal of Business (1961), Vol. 34, pp. 411–433] we construct a cashflow yield that includes both dividend and non‐dividend cashflows to shareholders. Using a data set covering the course of the 20th century, we show in a cointegrating vector autoregression framework that this measure has strong and stable predictive power for returns. The weak predictive power of standard measures of the dividend yield is explained by the strong rejection of the implied cointegrating and causality restrictions on the impact of non‐dividend cashflows.     

Bayesian Estimation of Willingness‐to‐pay Where Respondents Mis‐report Their Preferences*

We introduce a modified conditional logit model that takes account of uncertainty associated with mis‐reporting in revealed preference experiments estimating willingness‐to‐pay (WTP). Like Hausman et al. [Journal of Econometrics (1988) Vol. 87, pp. 239–269], our model captures the extent and direction of uncertainty by respondents. Using a Bayesian methodology, we apply our model to a choice modelling (CM) data set examining UK consumer preferences for non‐pesticide food. We compare the results of our model with the Hausman model. WTP estimates are produced for different groups of consumers and we find that modified estimates of WTP, that take account of mis‐reporting, are substantially revised downwards. We find a significant proportion of respondents mis‐reporting in favour of the non‐pesticide option. Finally, with this data set, Bayes factors suggest that our model is preferred to the Hausman model.     

Improved likelihood ratio tests for cointegration rank in the VAR model

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.     

A Simple Panel‐CADF Test for Unit Roots*

In this paper, we propose a simple extension to the panel case of the covariate‐augmented Dickey–Fuller (CADF) test for unit roots developed in Hansen (1995) . The panel test we propose is based on a P values combination approach that takes into account cross‐section dependence. We show that the test has good size properties and gives power gains with respect to other popular panel approaches. An empirical application is carried out for illustration purposes on international data to test the purchasing power parity (PPP) hypothesis.     

Modelling Regime‐Specific Stock Price Volatility*

Single‐state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state‐dependent behaviour of volatility nor explain why the equity index skew persists into long‐dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state‐dependent leverage effect to NM‐GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time‐varying volatility risk premia. An empirical study on European equity indices identifies two‐state asymmetric NM‐GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean‐reversion and leverage effects during crash markets are quite different from those in the stable regime.     

Sectoral Survey‐based Confidence Indicators for Europe*

We analyse a novel dataset of Business and Consumer Surveys, using dynamic factor techniques, to produce composite coincident indices (CCIs) at the sectoral level for the European countries and for Europe. Surveys are timely available, not subject to revision, and fully comparable across countries. Moreover, the substantial discrepancies in activity at the sectoral level justify the interest in sectoral disaggregation. Compared with the confidence indicators produced by the European Commission we show that factor‐based CCIs, using survey answers at a more disaggregate level, produce higher correlation with the reference series for the majority of sectors and countries.