Exact tests and confidence sets are obtained for general transformations of the coefficients in linear first-order autoregressive models with exogenous variables and i.i.d. disturbances. The tests proposed have known level and are either similar (constant rejection probability under all...

General characterizations of valid confidence sets and tests in problems involving (locally almost) unidentified (LAU) parameters are presented. In particular, any valid confidence set for an unbounded LAU parameter must be unbounded with positive probability. Consequently, almost surely bounded...

Causality in Granger's sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1 = h = inifinity, providing a rigorous formalization of indirect causal effects and causality chains in (possibly)...

The invariance properties of several asymptotic tests are studied: invariance to hypothesis representation, reparameterization, and rescaling. Noninvariant tests include Wald tests, variants of LM tests, and Neyman's C(" alpha") tests. For all these tests, simply changing measurement units can...

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are...

This article proposes a general method to build exact tests and confidence sets in linear regressions with first-order autoregressive Gaussian disturbances. Because of a nuisance parameter problem, we argue that generalized bounds tests and conservative confidence sets provide natural inference...

It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson-Rubin ((1949), AR) procedure. The latter allows one to build exact tests and...