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Ph.D. Econometrics I \linebreak
Heinz School, Carnegie Mellon University \linebreak
90-906, Spring 2005 \linebreak
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Final
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\begin{itemize}
  \item[Instructions] You may use any books, notes, calculators, and
                      other aids you like.  You may not converse, nor
                      may you cooperate.

                      Please complete all questions.

                      Please show all relevant work.

                      Please interpret your results in plain English.

                      Use the backs of pages if you need more space.

                      Each question is worth 33\%.  1\% for putting your name
                      on the paper.


                       
\end{itemize}

\pagebreak
\begin{enumerate}

\item Please consider the SAS program and output you were provided.  In that program,
      I use the ``gallup'' data described on the class website (codebook and 
      description are attached to the SAS output).

      \begin{enumerate}
      \item What is the effect (and 95\% CI) of aging one year on wages?
      \item What are you assuming in the previous part?
      \item Interpret the coefficient on Tech.
      \item Test the hypothesis that neither technical education nor training affect
            wages.
      \item How many years of experience is a training program ``worth'' --- interpreting
            age as the effect of experience?  95\% CI?
      \item What is the difference (95\% CI) in wages between a person with a HS 
            degree and a person with college or more?
      \end{enumerate}

\item Consider a dataset tracking consumer spending.  Let $Y$ be total spending and let
      $E_d$, $E_n$, $E_s$ be spending on durables, non-durables, and services: note
      $Y = E_d + E_n + E_s$.  Consider
      the following three regression models:

      \begin{align*}
      E_d &= \beta_1 + \alpha_1Y + \epsilon_1 \\
      E_n &= \beta_2 + \alpha_2Y + \epsilon_2 \\
      E_s &= \beta_3 + \alpha_3Y + \epsilon_3 \\
      \end{align*}

      Prove that the sum of the $\hat{\beta}_{\text{OLS}}$s is zero and the sum of the 
      $\hat{\alpha}_{\text{OLS}}$s is 1.

\item Consider the following dataset:

      \begin{math}
      Y = \left[
          \begin{array}{r}
          2 \\ -1 \\ -4 \\ 6 \\ -1 \\ -1 \\ -1 
          \end{array}
          \right]
          \qquad \qquad
      X = \left[
          \begin{array}{r}
          0 \\ -1 \\ -3 \\ 3 \\ 2 \\ -2 \\ 1
          \end{array}
          \right]
      \end{math}

      Consider a regression model with $Y$ as a LHS var and $X$ as a RHS var.

      \begin{enumerate}
      \item What are the OLS estimates of the intercept and slope?
      \item Usual estimate of the variance of the slope?
      \item Test for non-linearity.
      \item Use the Goldfeld Quandt test for heteroskedasticity (omit one data point).
      \end{enumerate}

\end{enumerate}

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