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Intro to Econometric Theory \linebreak
Heinz School, Carnegie Mellon University \linebreak
90-906, Spring 2003-4 \linebreak
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Homework \#4
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The Medical Expenditure Panel Survey is an annual survey
      which collects information about medical expenditures, income,
      employment, demographics, health information, \&c for a 
      representative sample of Americans.

      I have prepared an extract of these data for 1996, and it is available
      on the course website.  The following are the columns in the data, in
      order:\vspace{2\baselineskip}

      \begin{tabular}{r r}
      Variable & Meaning \\ \hline\hline
      age      & age of person in years\\
      sex      & sex of person, 1=male \& 0=female\\
      income   & income in 1996 \$\\
      employed & 1=employed, 0=not employed\\
      insured  & 1=had health insurance, 0=not\\
      health   & perceived health status, higher is sicker\\
      spending & spending on health care, 1996 \$
      \end{tabular}\vspace{2\baselineskip}

To begin with, let's consider a model like the one we used on the
midterm:

\begin{eqnarray}
\mathrm{spending}_i &=& \beta_1 + \beta_2 \mathrm{income} 
                     +  \beta_3 \mathrm{age} + \beta_4 \mathrm{sex}
                    \nonumber\\
                    &+& \beta_4 \mathrm{employed} + \beta_5 \mathrm{insured}
                     +  \beta_6 \mathrm{health}
                    \label{eqn:model}
\end{eqnarray}


\begin{enumerate}
\item What do you think of the claim that income and sex do not belong
      in this model?
\item Consider the health status variable.  Respondents were asked to
      rate their health status; their choices were excellent, 
      very good, good, fair, or poor.  These were assigned the numerical
      values 1-5.  Does it make sense to enter health status as a 
      single continuous variable as in equation~\ref{eqn:model}?

      Enter health status into the model as a set of dummies, and then
      test whether they belong.
\item How much more do people in very good health status spend than
      do people in excellent health status (estimate and CI).
\item Test whether it was correct to enter health status linearly.
\item Test whether insurance affects spending for people of different
      health statuses differently and discuss.
\end{enumerate}

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