CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

Economic Development of Urban Areas

In this dissertation I study the development of urban areas. At the aggregate level I investigate how they may be affected by climate change policies and by being designated the seat of governmental power. At the household level I study with coauthors how microfinance could improve the health of urban residents. In Chapter 1, I investigate how local employment may be affected by electricity price increases, which is a likely consequence of climate change policies. I outline how previous studies that find large, negative effects may be biased. To overcome these biases I develop a novel estimation strategy that blends border-pair regressions with the synthetic control methodology. I show the conditions for consistent estimation. Using this estimator, I find no effect of contemporaneous price changes on employment. Consistent with the longer time-frame for manufacturing decisions, I do find evidence for negative effects from perceived permanent price shocks. These estimates are much smaller than previous research has found. National capital cities are often substantially larger than other cities in their countries. In Chapter 2, I investigate whether there is a causal effect from being a capital by studying the 1960 relocation of the Brazilian capital from Rio de Janeiro to Brasília. Using a synthetic controls strategy I find that losing the capital had no significant effects on Rio de Janeiro in terms of population, employment, or gross domestic product (GDP). I find that Brasília experienced large and significant increases in population, employment, and GDP. I find evidence of large spillovers from the public to the private sector. Chapter 3 investigates how microfinance could increase the uptake of costly health goods. We study the effect of time payments (micro-loans or micro-savings) on willingness-to-pay (WTP) for a water filter among households in the slums of Dhaka, Bangladesh. We find that time payments significantly increase WTP: compared to a lump-sum up-front purchase, median WTP increases 83% with a six-month loan and 115% with a 12-month loan. We find that households are quite patient with respect to consumption of health inputs. We find evidence for the presence of credit and savings constraints.