The research presented in this dissertation focuses on the measurement and
analysis of subjective probability distributions over stochastic outcomes, a
central issue in the study of decision-making under uncertainty. The empirical
setting is rural Tanzania, where the degrees of risk and uncertainty characterizing
both human capital and productive investment decisions are exacerbated
by widespread dependence on rain-fed agriculture, inadequate social
safety nets, and a poorly developed information infrastructure. I present a
sequence of methodological, theoretical and empirical chapters in which I
estimate subjective returns distributions in an existing data set, develop and
explain a new method of collecting subjective distributions data, characterize
the information content of the data collected, and make use of the data to
estimate a structural agricultural production model.
Chapter 1 explores the role of estimated, rather than measured, subjective
returns to education in schooling choice decisions. Using an existing
panel survey from Tanzania, I estimate earnings-education distributions separately
for 1991, 2004 and 2010. I then use individual-level predictions of the
first two moments of the earnings distribution to estimate a random effects
probit model on binary enrollment decisions for school-aged children in the
years 1991-1994. I find that the returns to education have been and remain
high for women, while for men the returns increased over the twenty study
years to nearly match those of women. In addition, the probability of enrollment
is increasing in the subjective conditional expectation of earnings, and
decreasing in the subjective conditional variance of earnings.
Chapter 2 describes the phone-based survey method that I used to gathersubjective probability distributions data from a sample of Tanzanian cotton
farmers. I describe the various technical issues faced in the implementation of
this method, outline the lessons learned and the numerous refinements made
over the course of the study, and speculate on the feasibility of phone-based
data collection in other settings in low income countries.
In Chapter 3, I analyze the information content of subjective distributions
data gathered in the way that has become standard in development
economics, i.e., by having respondents allocate a fixed number of counters
to boxes that represent the intervals of a histogram. I use inference about
the respondents’ choice problem to analyze the partial identification of the
underlying belief. I provide bounds on the density in subsets of intervals,
provide bounds on the underlying CDF, define the joint identification region
for the measure vector, and develop and implement a feasible numerical
method for jointly bounding the moments of the unobserved distribution. I
also provide simulation evidence for the optimal design of survey instruments
and the optimal way to approximate these data with smooth distributions.
Lastly, Chapter 4 makes use of the regularly spaced within-season measures
of subjective yield and price distributions collected from Tanzanian cotton
farmers to study the farmer’s dynamic resource allocation problem. Using
these data, I develop a novel method for estimating a stochastic production
function when error parameters are observed at the plot-level throughout the
cultivation season