Economics 170Spring 1992Final Exam
Answer each of the following equally weighted questions. Remember that the process by which you arrive at an answer earns most of the credit. A correct answer with no explanation or work showing does not receive full credit.
1. We assume that the error term in an econometric equation is uncorrelated with the independent or explanatory variables in the equation. State the consequences of violating this assumption and describe a method of resolving it.
2. Propose a method of estimating the following distributed lag model:
Y(t)=a + b1X(t) + b2X(t-1) + b3X(t-2)+...bkX(t-k-1) + u
where (t) indicates the time period of the observation. For example, X(t-2) is the value of X two periods prior to the current period. Be sure to explain any assumptions which you make and describe the
advantages or disadvantages of your approach. Note that K may, but
need not, be infinity.
3. List the types of specification errors. These errors often show up as either autocorrelation or heteroskedasticity. Explain how this is so.
4. Consider the following model:
Y=a + b1X1 + b2X2 + u Suppose Y is measured as number of cartons of eggs purchased and the X's are the dollar price of a carton of eggs and the consumers income, also measured in dollars. Interpret the coefficients. Second, suppose each of the variables is measured as the natural logarithm of the number of cartons, dollar price, or dollar income, respectively. Now how are the coefficients interpreted? What are the advantages and disadvantages of measuring the variables in one way as opposed to the other?
5. Suppose you are given the two equation model:
Y1=a0 + a1X1 + a2X2 + a3Y2 + ua
Y2=b0 + b1X1 + b2X3 + ub
where ua is the error in the equation with a coefficients and ub the error from the equation with b coefficients and
where Y's are endogenous variables and X's are predetermined or
exogenous variables. Find the reduced form equations and, if
possible, the structural parameters. Describe how you would
estimate the first equation via two stage least squares.
6. You are interested in estimating a consumption function for the years 1920 through 1950. You believe that the years of the Great Depression and of World War II are likely to be different than the other years. Explain how you would test your hypothesis using dummy variables:
a) if only the intercept is thought to be different, and
b) if both the intercept and the slope are thought to be different.
7. You have data for each of 25 neighborhoods on the proportion of individuals within a given neighborhood who voted for a local school bond. You also know the average income of households in each neighborhood, the proportion of the households in each neighborhood which own their own home, and the number of school age children in each neighborhood. You also know the population of each neighborhood. How would you estimate the influence of income, home ownership, and school age children on the decision to vote for the bond?
8. You have estimated the following demand functions for grape juice:
GJ=150.83 -.75PGJ + .37POJ + .65Income + .23White + .17Highshchool
GJ = 168.19-.63Pgj + .46PPJ + .83Income
based on 350 observations. The residual sum of squares from the first equation is 496, and for the second equation is 553. Test the restriction that the coefficients on white and highschool are simultaneously zero.
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