Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes, and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes, and are directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.Comment: Accepted by the Journal of Education and Behavioral Statistic

Does State Growth Management Change the Pattern of Urban Growth? Evidence From Florida.

This paper evaluates growth management in Florida by using a land use based regional adjustment model to project adjustments toward equilibrium densities of population and employment at the county level. The analysis utilizes a unique data set that contains detailed information on initial outcomes of the 1992 plan review in the State of Florida. These plan review outcomes are interacted with adjustment variables to test the hypothesis that Growth Management-specific policies have affected equilibrium adjustments in the following time period. The analysis is motivated by three specific research questions: Has Florida’s (1985) Growth Management Act increased changes in density during any of the three year time periods? Does plan compliance affect the growth trajectories of approved counties? And, finally, does the inclusion of optional plan elements further affect these growth trajectories? The findings suggest that compliance with state growth management mandates in Florida may push the adjustment process toward higher population densities in the1992-1997 time period. Additionally, the inclusion of an optional educational plan element may also push adjustments toward higher density. The results indicate that growth management efforts to address the technical planning process, as well as human capital needs, can increase the desirability, and thus the density, of sprawling counties in the Atlantic Southeast. Finally, because population and employment growth are jointly determined in the Atlantic Southeast, the long-term sustainability of economic development in Florida may depend on policies that preserve its desirability as a place to live. This paper elaborates upon work by Carruthers, McLaughlin, and Boarnet (2006) that shows Florida’s growth trajectory during the early 1990’s was significantly different than the Atlantic Southeast region.

Identifying Effects of Multivalued Treatments

Multivalued treatment models have only been studied so far under restrictive assumptions: ordered choice, or more recently unordered monotonicity. We show how marginal treatment effects can be identified in a more general class of models. Our results rely on two main assumptions: treatment assignment must be a measurable function of threshold-crossing rules; and enough continuous instruments must be available. On the other hand, we do not require any kind of monotonicity condition. We illustrate our approach on several commonly used models; and we also discuss the identification power of discrete instruments

Margins of discrete Bayesian networks

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.Comment: 41 page

Don't (fully) exclude me, it's not necessary! Identification with semi-IVs

This paper proposes a novel tool to nonparametrically identify models with a discrete endogenous variable or treatment: semi-instrumental variables (semi-IVs). A semi-IV is a variable that is relevant but only partially excluded from the potential outcomes, i.e., excluded from at least one, but not necessarily all, potential outcome equations. It follows that standard instrumental variables (IVs), which are fully excluded from all the potential outcomes, are a special (extreme) case of semi-IVs. I show that full exclusion is stronger than necessary because the same objects that are usually identified with an IV (Imbens and Angrist, 1994; Heckman and Vytlacil, 2005; Chernozhukov and Hansen, 2005) can be identified with several semi-IVs instead, provided there is (at least) one semi-IV excluded from each potential outcome. For applied work, tackling endogeneity with semi-IVs instead of IVs should be an attractive alternative, since semi-IVs are easier to find: most selection-specific costs or benefits can be valid semi-IVs, for example. The paper also provides a simple semi-IV GMM estimator for models with homogenous treatment effects and uses it to estimate the returns to education