Economics 309 Exam Two Fall 2003
Please submit your answers Wednesday, October 22
1.(a) [25 pts] You collect data on the following two variables (creatively named X and Y):
|
Yi = |
0.3 |
1.6 |
0.8 |
3.9 |
2.0 |
5.2 |
3.4 |
6.0 |
-0.1 |
0.6 |
|
Xi = |
2 |
5 |
3 |
7 |
4 |
8 |
7 |
9 |
2 |
4 |
Assuming the relationship between X and Y to be causal and linear, write out the empirical model and estimate the slope and intercept coefficients.
1.(b) [25 pts] After you have completed (a) above, you find 10 more observations for the two variables, given below:
|
Yi = |
3.5 |
1.4 |
3.5 |
2.2 |
4.1 |
4.1 |
0.3 |
-0.9 |
5.1 |
1.4 |
|
Xi = |
8 |
3 |
6 |
4 |
8 |
7 |
2 |
1 |
8 |
5 |
You decide to estimate the same model as you did above, but using these new 10 observations (note, you used the first 10 obs. for the first estimate, and now use the second 10 obs. for this estimate.) What are your estimates of the intercept and slope coefficients for the two data sets? Explain why they are different (if they are.)
2. [30pts] Assume you wish to model the relationship between education, X (in years) and earnings, Y (in $1,000s) using the following equation:
ln Y = b0 + b1X + u, for each individual in the sample.
However, you feel that because you sample people from across the country (divided into regions: West, Mid and East) it might be important to account for region in your estimates of the effect of education on earnings (in the model the effect of education on earnings is given by b1). Using the dummy variable approach, define a set of dummy variables for region, then specify (and explain, showing how) the models you would use to estimate the following effects:
(a) people in each region have a different response to education, but ignoring education, all people earn the same.
(b) the average West person's response to years of education differs from that for Mid and East (which is the same), but all three groups earn different incomes if education is ignored.
(hint: you will have to consider both additive and multiplicative dummy variables to create these model specifications.)
3. [20 pts] Consider the simple experiment of rolling a die 2 times (or equivalently rolling 2 identical die).
(a) list the sample space for this experiment (eg. 11, 12, 13, etc.)
(b) what is the probability of getting two 6s?
(c) calculate the probability of obtaining a pair.
(d) Given that a 1 appears on the first roll, what is the probability of seeing a 2 on the second roll?
(e) what is the probability of throwing at least one 6?