where φ is the parameter of interest which models the relationship while U is an error term. Contrary to usual statistical regression models, the error term is correlated with the explanatory variables X, hence E(U |X) 6= 0, preventing direct estimation of φ. To overcome the endogeneity of X, we assume that there exists an observed random variable W , called the instrument, which decorrelates t...

We apply Bayesian methods to a model involving a binary endogenous regressor and an instrumental variable in which the functional forms of some of the covariates in both the treatment assignment and outcome distributions are unknown. Continuous and binary response variables are considered. Under the assumption that the functional form is additive in the covariates, we develop efficient Markov c...

Instrumental variable (IV) estimation methods that allow for certain nonlinear functions of the data as instruments are studied. The context of the discussion is the simple unit root model where certain advantages to the use of nonlinear instruments are revealed. In particular, certain classes of IV estimators and associated t-tests are shown to have simpler (standard) limit theory in contrast ...

Bias due to unobserved confounding can seldom be ruled out with certainty when estimating the causal effect of a nonrandomized treatment. The instrumental variable (IV) design offers, under certain assumptions, the opportunity to tame confounding bias, without directly observing all confounders. The IV approach is very well developed in the context of linear regression and also for certain gene...

Single equation instrumental variable models for discrete outcomes are shown to be set not point identifying for the structural functions that deliver the values of the discrete outcome. Identi…ed sets are derived for a general nonparametric model and sharp set identi…cation is demonstrated. Point identi…cation is typically not achieved by imposing parametric restrictions. The extent of an iden...

Subspace estimation plays an important role in, for example, sensor array signal processing. Recursive methods for subspace tracking, with obvious applications to non-stationary environments, have also drawn considerable interest. In this paper we present an Instrumental Variable (IV) extension of the recently developed Projection Approximation Subspace Tracking (PAST) algorithm. The IV-approac...

We propose a general estimation principle based on the assumption that instrumental variables (IV) do not explain the error term in a structural equation. The estimators based on this principle is independent of the normalization constraint, unlike the standard IV estimators such as the two-stage least squares estimator. Using the new principle, we propose the L1 IV estimator, which is an IV es...