Abstract—Recently there has been a surge in econometric work focusing on estimating average treatment effects under various sets of assumptions. One strand of this literature has developed methods for estimating average treatment effects for a binary treatment under assumptions variously described as exogeneity, unconfoundedness, or selection on observables. The implication of these assumptions is that systematic (for example, average or distributional) differences in outcomes between treated and control units with the same values for the covariates are attributable to the treatment. Recent analysis has considered estimation and inference for average treatment effects under weaker assumptions than typical of the earlier literature by avoiding distributional and functional-form assumptions. Various methods of semiparametric estimation have been proposed, including estimating the unknown regression functions, matching, methods using the propensity score such as weighting and blocking, and combinations of these approaches. In this paper I review the state of this

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... this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response. To explicate our objective and state assumptions, we use the potential outcomes model. The proposed method makes smooth, parametric assumptions only on quantities directly relevant to the goal of estimating the optimal rules. We illustrate the proposed methodology via a small simulation.

This paper utilizes the Asset and Health Dynamics of the Oldest Old (AHEAD) Panel to test for the absence of causal links from socio-economic status (SES) to health innovations and mortality, and from health conditions to innovations in wealth. We conclude that there is no direct causal link from SES to mortality or to incidence of most sudden onset health conditions (accidents and some acute conditions), but there is an association of SES with incidence of gradual onset health conditions (mental conditions, and some degenerative and chronic conditions), due either to causal links or to persistent unobserved behavioral or genetic factors that have a common influence on both SES and innovations in health. We conclude that there is no direct causal link from health status to innovations in wealth.

ABSTRACT: I describe two new methods for estimating the optimal treatment regime (equivalently, protocol, plan or strategy) from very high dimesional observational and experimental data: (i) g-estimation of an optimal double-regime structural nested mean model (drSNMM) and (ii) g-estimation of a standard single regime SNMM combined with sequential dynamicprogramming (DP) regression. These methods are compared to certain regression methods found in the sequential decision and reinforcement learning literatures and to the regret modelling methods of Murphy (2003). I consider both Bayesian and frequentist inference. In particular, I propose a novel “Bayes-frequentist compromise ” that combines honest subjective non- or semiparametric Bayesian inference with good frequentist behavior, even in cases where the model is so large and the likelihood function so complex that standard (uncompromised) Bayes procedures have poor frequentist performance. 1

This paper (which is mainly expository) sets up graphical models for causation, having a bit less than the usual complement of hypothetical counterfactuals. Assuming the invariance of error distributions may be essential for causal inference, but the errors themselves need not be invariant. Graphs can be interpreted using conditional distributions, so that we can better address connections between the mathematical framework and causality in the world. The identification problem is posed in terms of conditionals. As will be seen, causal relationships cannot be inferred from a data set by running regressions unless there is substantial prior knowledge about the mechanisms that generated the data. There are few successful applications of graphical models, mainly because few causal pathways can be excluded on a priori grounds. The invariance conditions themselves remain to be assessed.

Causality is a very intuitive notion that is difficult to make precise without lapsing into tautology. Two ingredients are central to any definition: (1) a set of possible outcomes (counterfactuals) generated by a function of a set of ‘‘factors’ ’ or ‘‘determinants’ ’ and (2) a manipulation where one (or more) of the ‘‘factors’ ’ or ‘‘determinants’’ is changed. An effect is realized as a change in the argument of a stable function that produces the same change in the outcome for a class of interventions that change the ‘‘factors’ ’ by the same amount. The outcomes are compared at different levels of the factors or generating variables. Holding all factors save one at a constant level, the change in the outcome associated with manipulation of the varied factor is called a causal effect of the manipulated factor. This definition, or some version of it, goes back to Mill (1848) and Marshall (1890). Haavelmo’s (1943) made it more precise within the context of linear equations models. The phrase ‘ceteris paribus’ (everything else held constant) is a mainstay of economic analysis

We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set A of incompatible experiments, and a transformation group G on the cartesian product Π of the parameter spaces of these experiments. The set of possible parameters is constrained to lie in a subspace of Π, an orbit or a set of orbits of G. Each possible model is then connected to a parametric Hilbert space. The spaces of different experiments are linked unitarily, thus defining a common Hilbert space H. A state is equivalent to a question together with an answer: the choice of an experiment a ∈ A plus a value for the corresponding parameter. Finally, probabilities are introduced through Born’s formula, which is derived from a recent version of Gleason’s theorem. This then leads to the usual formalism of elementary quantum mechanics in important special cases. The theory is illustrated by the example of a quantum particle with spin. 1. Introduction. Both

We consider four classes of graphical causal models: the Finest Fully Randomized Causally