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We propose a method to explore the causal transmission of an intervention through two endogenous variables of interest. We refer to the intervention as a catalyst variable. The method is based on the reduced-form system formed from the conditional distribution of the two endogenous variables given the catalyst. The method combines elements from instrumental variable analysis and Cholesky decomposition of structural vector autoregressions. We give conditions for uniqueness of the causal transmission.

The classical Chow test for structural instability requires strictly exogenousregressors and a break-point specified in advance. In this paper, we consider twogeneralisations, the one-step recursive Chow test (based on the sequence of studentisedrecursive residuals) and its supremum counterpart, which relaxes these requirements. We useresults on the strong consistency of regression estimators to show that the one-step test isappropriate for stationary, unit root or explosive processes modelled in the autoregressivedistributed lags (ADL) framework. We then use the results in extreme value theory to developa new supremum version of the test, suitable for formal testing of structural instability withan unknown break-point. The test assumes the normality of errors and is intended to be usedin situations where this can be either assumed nor established empirically. Simulations showthat the supremum test has desirable power properties, in particular against level shifts latein the sample and against outliers. An application to U.K. GDP data is given.

This paper proposes a class of partial cointegrated models allowing for structural breaks in the deterministic terms. Moving-average representations of the models are given. It is then shown that, under the assumption of martingale difference innovations, the limit distributions of partial quasi-likelihood ratio tests for cointegrating rank have a close connection to those for standard full models. This connection facilitates a response surface analysis that is required to extract critical information about moments from large-scale simulation studies. An empirical illustration of the proposed methodology is also provided.

In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip.

We consider cointegration tests in the situation where the cointegration rank is deficient. This situation is of interest in finite sample analysis and in relation to recent work on identification robust cointegration inference. We derive asymptotic theory for tests for cointegration rank and for hypotheses on the cointegrating vectors. The limiting distributions are tabulated. An application to US treasury yields series is given.