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\begin{center}
{\large Development Economics}

{\large Problem Set \#2 Due Week 6}
\end{center}

\begin{enumerate}
\item \textsc{Income-Health Relationship. }\newline
Consider an agent with income $y_{t}.$ The agent maximizes a Cobb-Douglas
function $c_{t}h_{t}$ where $c_{t}$ is the agent's consumption and $h_{t}$
is her level of health. In order to reach the level of health $h_{t},$ the
agent must spend $h_{t}$. The agent must meet a subsistence constraint $%
c_{t}\geq \overline{c}.$ Agent's productivity is the function of his health $%
A_{t}=\sqrt{h_{t}}.$ Agent's income is $y_{t}=wA_{t-1}+\overline{y}$ where $%
w $ is the wage per unit of productivity and $\overline{y}$ \ is a lump sum
welfare benefit.

\begin{enumerate}
\item Draw the graph of agent's productivity as a function of her current
income.

\item Describe dynamics of agent's health and income over time. Find steady
states and the basins of attraction.

\item Describe the comparative statics with regard to $w$ and $\overline{y}.$
\end{enumerate}

\item \textsc{Financial constraints and development. }\newline
In Banerjee-Newman model, the wealth evolves over time as follows:

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Denote $p_{u}(t)$, $p_{m}(t)$, $p_{l}(t)$ shares of upper, middle and lower
class, respectively. Draw a phase diagram in $p_{u}$, $p_{l}$ space. Given
parameters $q\in (0,1)$, $q\prime \in (0,1)$ and $\mu >2$, $\mu >1/q,$ $%
q>q\prime $ find equilibrium (equilibria), check for cycles and determine
basins of attraction.

\newpage

\item \textsc{Incentives to study for Kenyan girls}.

This problem examines the relationship between merit awards and academic
performance, as measured by school exams, among Kenyan schoolgirls. In early
2001, Grade 6 girls in a random subset of \textquotedblleft
treatment\textquotedblright\ schools (variable name \textquotedblleft
treat\textquotedblright ) were offered a large cash award if they scored in
the top 15\% of all treatment school girls. The attached generated dataset
contains test score information from late 2000, the year before the program,
and late 2002, one year after the program had ended. (The test score
outcomes (\textquotedblleft test00\textquotedblright , \textquotedblleft
test02\textquotedblright ).) Attach the STATA code (or code from another
statistical package that you will be using). The goal of this problem set is
to understand medium-term impact of the program.

\begin{enumerate}
\item Estimate ATE (Average Treatment Effect) consistently using bivariate
relationship.

\item Compare standard errors if you do and do not take into account
correlations of program responses within schools. Which empirical strategy
is more reasonable? What does it imply about the resulting bivariate
estimate of ATE?

\item Can one make estimation more precise? How? Do it. Interpret the
results. State the size of the effect on average.

\item Is there a difference in returns for the program depending on the
skill (which can be proxied by the initial test score). Estimate it.

\item Is anyone losing from the program? If yes, who exactly? By how much?
Why this might be?

\item Is there a relationship between age and returns from the program?
\end{enumerate}
\end{enumerate}

\end{document}