Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Testing the exogeneity specification in the complete dynamic simultaneous equation model

It is shown that in the complete dynamic simultaneous equation model exogenous variables cause endogenous variables in the sense of Granger (1969) and satisfy the criterion of econometric exogeneity discussed by Sims (1977a), but that the stationarity assumptions invoked by Granger and Sims are not necessary for this implication. Inference procedures for testing each implication are presented and a new joint test of both implications isderived. Detailed attention is given to estimation and testing when the error vector of the final form of the complete dynamic simultaneous equation model is both singular and serially correlated. The theoretical points of the paper are illustrated by testing the exogeneity specification in a small macroeconometric model.     

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.     

When is an aggregate of a time series efficiently forecast by its past?

The paper gives necessary and sufficient conditions for a linear combination of the elements of a vector time series to be efficiently forecast by its own past values, where by past we mean both the infinite and also the finite past. We observe that the problem is equivalent to testing a single element of a vector for exogeneity, this observation also suggesting a method for empirically testing the derived conditions.     

Cointegration and joint efficiency of international commodity markets

This paper investigates the semi-strong efficiency hypothesis in the international commodity markets of four industrialized countries, using vector autoregression (VAR) and cointegration techniques. Efficiency in these markets requires the corresponding real exchange rates to be martingales with respect to any information set available in the public domain. In the context of a VAR consisting only of real exchange rates, we show that necessary and sufficient conditions for joint efficiency of all the markets under consideration amount to the VAR being of order one (Markovness) and non-cointegrated. On the contrary, in a VAR extended by other potentially “relevant” variables, such as the corresponding real interest rates, non-cointegration and Markovness are only sufficient conditions for the same commodity markets to be characterized as jointly efficient. We also suggest methods for efficiency testing in each individual market within a cointegrated VAR and, finally, we discuss possible long-run linkages among the real exchange rates and real interest rates in association with efficiency in the commodity markets. JEL Classification Number: F31     

Testing the nominal-to-real transformation

This paper establishes the necessary and sufficient condition for nominal-to-real data transformations routinely used in empirical work to reduce the order of integration of an I(2) vector process while retaining the cointegrating relations among the variables. The condition potentially fails in a direction which is often dealt with by assumption in applied work. In this case, the transformed process satisfies a well-specified vector equilibrium model, yet I(1) inference and interpretation based on the real transformed system are invalidated. An easy-to-implement sequential test of the transformation based on I(1) cointegration methods demonstrates good size and power properties. An empirical example illustrates the need to test the nominal-to-real transformation.     

Exogeneity in structural equation models

The practical relevance of several concepts of exogeneity of treatments for the estimation of causal parameters based on observational data are discussed. We show that the traditional concepts, such as strong ignorability and weak and super-exogeneity, are too restrictive if interest lies in average effects (i.e. not on distributional effects of the treatment). We suggest a new definition of exogeneity, KL-exogeneity. It does not rely on distributional assumptions and is not based on counterfactual random variables. As a consequence it can be empirically tested using a proposed test that is simple to implement and is distribution-free.     

GMM redundancy results for general missing data problems

We consider questions of efficiency and redundancy in the GMM estimation problem in which we have two sets of moment conditions, where two sets of parameters enter into one set of moment conditions, while only one set of parameters enters into the other. We then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest, and the second set of moment conditions is for the selection process. We use these results to explain the counterintuitive result in the literature that, under an ignorability assumption that justifies GMM with weighted moment conditions, weighting using estimated probabilities of selection is better than weighting using the true probabilities. We also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid, and we show that when weighting is not needed for consistency, it is also not useful for efficiency.     

Tighter bounds in triangular systems

We study a nonparametric triangular system with (potentially discrete) endogenous regressors and nonseparable errors. Like in other work in this area, the parameter of interest is the structural function evaluated at particular values. We impose a global exclusion and exogeneity condition, in contrast to Chesher (2005), but develop a rank condition which is weaker than Chesher’s. The alternative rank condition can be satisfied for binary endogenous regressors, and it often leads to an identified interval tighter than Chesher (2005)’s minimum length interval. We illustrate the potential of the new rank condition using the Angrist and Krueger (1991) data.     

Inference in a synchronization game with social interactions

This paper studies inference in a continuous time game where an agent’s decision to quit an activity depends on the participation of other players. In equilibrium, similar actions can be explained not only by direct influences but also by correlated factors. Our model can be seen as a simultaneous duration model with multiple decision makers and interdependent durations. We study the problem of determining the existence and uniqueness of equilibrium stopping strategies in this setting. This paper provides results and conditions for the detection of these endogenous effects. First, we show that the presence of such effects is a necessary and sufficient condition for simultaneous exits. This allows us to set up a nonparametric test for the presence of such influences, which is robust to multiple equilibria. Second, we provide conditions under which parameters in the game are identified. Finally, we apply the model to data on desertion in the Union Army during the American Civil War, and find evidence of endogenous influences.     

Goodness-of-fit tests based on series estimators in nonparametric instrumental regression

This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors. The tests’ asymptotic distributions under correct specification are derived and their consistency against any alternative model is shown. Under a sequence of local alternative hypotheses, the asymptotic distributions of the tests are derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases. A Monte Carlo study examines finite sample performance of the test statistics.     

Data-based priors for vector error correction models

We propose two data-based priors for vector error correction models. Both priors lead to highly automatic approaches which require only minimal user input. For the first one, we propose a reduced rank prior which encourages shrinkage towards a low-rank, row-sparse, and column-sparse long-run matrix. For the second one, we propose the use of the horseshoe prior, which shrinks all elements of the long-run matrix towards zero. Two empirical investigations reveal that Bayesian vector error correction (BVEC) models equipped with our proposed priors scale well to higher dimensions and forecast well. In comparison to VARs in first differences, they are able to exploit the information in the level variables. This turns out to be relevant to improve the forecasts for some macroeconomic variables. A simulation study shows that the BVEC with data-based priors possesses good frequentist estimation properties.     

Stochastic cointegration: estimation and inference

This paper considers the estimation of a stochastically cointegrating regression within the stochastic cointegration modelling framework introduced in McCabe et al. (Stochastic cointegration: testing, 2001). A stochastic cointegrating regression allows some or all of the variables to be conventionally or heteroscedastically integrated. This generalizes Hansen's (J. Econom. 54 (1992) 139) heteroscedastic cointegrating regression model, where the dependent variable is heteroscedastically integrated, but all the regressor variables are restricted to being conventionally integrated. In contrast to conventional and heteroscedastic cointegrating regression, ordinary least-squares (OLS) estimation is shown to be inconsistent, in general, in a stochastically cointegrating regression. As a solution, a new instrumental variables (IVs) estimator is proposed and is shown to be consistent. Under a suitable exogeneity assumption, standard asymptotic inference on the stochastic cointegrating vector can be carried out based on the IV estimator. The finite sample properties of the test statistics, including their robustness to the exogeneity assumption, are examined by simulation.     

Identifying Structural Breaks in Cointegrated Vector Autoregressive Models*

This article suggests an alternative formulation of the cointegrated vector autoregressive (VAR) model such that the coefficients for the deterministic terms have straightforward interpretations. These coefficients can be interpreted as growth rates and cointegration mean level coefficients and express long‐run properties of the model. For example, the growth rate coefficients tell us how much to expect (unconditionally) the variables in the system to grow from one period to the next, representing the underlying (steady state) growth in the variables. The estimation of the proposed formulation is made operationally in GRaM, which is a program for Ox Professional. GRaM can be used for analysing structural breaks when the deterministic terms include shift dummies and broken trends. By applying a formulation with interpretable deterministic components, different types of structural breaks can be identified. Shifts in both intercepts and growth rates, or combinations of these, can be tested for. The ability to distinguish between different types of structural breaks makes the procedure superior compared with alternative procedures. Furthermore, the procedure utilizes the information more efficiently than alternative procedures. Finally, interpretable coefficients of different types of structural breaks can be identified.     

TESTING PARAMETER CONSTANCY AND SUPER EXOGENEITY IN ECONOMETRIC EQUATIONS

The paper is concerned with testing super exogeneity in a single equation that can either be linear or partially nonlinear. A joint test for testing both weak exogeneity and a form of invariance, which together amount to a form of super exogeneity, is presented and its properties discussed. The considerations also include testing parameter constancy and modelling parameter nonconstancy by an example in which testing super exogeneity in a consumption function for Norway, based on a previously published model is considered. The results are compared with the previous conclusions and found not to disagree with them.     

Testing for the cointegration rank when some cointegrating directions are changing

We develop some tests for characterizing the cointegration space of a cointegrated vector autoregressive model when its long-run parameters are modified by a structural break at a known date. We first consider the case in which the break does not affect the loading factors and second the more general one in which all long-run parameters change. For each configuration, we design procedures to test for the cointegration rank as for the number of directions which are changing between the two regimes. For the simplest case, the cointegration rank test is also extended to the case of an unknown date of shift.     

The validity of instruments revisited

This paper shows how valid inferences can be made when an instrumental variable does not perfectly satisfy the orthogonality condition. When there is a mild violation of the orthogonality condition, the Anderson and Rubin (1949) test is oversized. In order to correct this problem, the fractionally resampled Anderson-Rubin test is derived by modifying Wu’s (1990) resampling technique. We select half of the sample when resampling and obtain valid but conservative critical values. Simulations show that our technique performs well even with moderate to large violation of exogeneity when there is a finite sample correction for the block size choice.     

Testing the Exogeneity of Argentine Devaluation and Default Risks in Retrospect*

This paper studies the relationship between devaluation and default risks during Argentina's convertibility regime. Before default and devaluation occurred, a harder variant of the currency regime was under discussion. An often‐suggested argument among the supporters of dollarization was that the probability of default could have been reduced by removing fears of devaluation. For this to be true, default risk must be dependent on the devaluation risk. Long‐run relationships and ‘exogeneity’ are examined using a ‘cointegrating vector’ system approach. The results show that only devaluation risk can be modelled on default risk. No empirical evidence is found in favour of dollarization. Moreover, these conclusions are maintained when the information set is expanded to include the Latin American risk and Argentine macroeconomic variables.     

Powerful tests for structural changes in volatility

Detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence. We propose modified CUSUM and LM tests that are built on a robust estimator of the long-run variance of squared series. We establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative. The theory allows smooth and abrupt structural changes that can be small. The smoothing parameter is automatically selected such that the proposed test has good finite-sample size and meanwhile achieves decent power gain.     

Generalized method of moments specification testing

This paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions. It shows that any such test may fail against general misspecification that causes estimator inconsistency. The mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived. Applications to testing for exogeneity of a set of instrumental variables are presented.