School Lahore of Economics
MPHIL Advanced Econometrics
Winter 2011
Quiz 3
Question 1. This question examine the relationship between the general level of education of citizens and the level of political
corruption.
The data below are cross-sectional for the 50 U.S. states on the following variables:
The following questions refer to Table 1.
Notes: Heteroskedasticity-robust standard errors appear in parentheses under
regression coecients, and p-values appear in parentheses under F -statistics.
All regressions include an estimated intercept, which is not reported. All regressions
are estimated using a cross-sectional data set consisting of 50 US states.
(A) Do you agree or disagree with the following statements? Explain.
(i) Because immigrants are less knowledgeable about the U.S. legal system, they are more susceptible to governmental corruption. The
regression results in Table 1 show that this is true: more foreign-born citizens, more corruption. (5 points)
(ii) The regression results in Table 1 are flawed because they use heteroskedasticity-robust standard errors: if the errors really are
homoskedastic, then these standard errors will be incorrect. The table should instead report standard errors that are correct even under
homoskedasticity. (5 points)
(B) Suppose that high levels of corruption result in low-quality public institutions, including low-quality schools, which in turn results
in lower levels of education. If so, what are the implications for the estimated effect on corruption of education in Table 1? Briefly
explain. (5 points)
(C) Explain if and why one could use following potential instrumental variables for LowEd share in regression (3). For each proposed
instrument, is the variable arguably a valid instrument variable? Briefly explain:
(i) Newspapers = average number of newspapers per capita in 1990. (5 points)
(ii) Alphabet = 1 if the state falls in the first half of the alphabet, = 0 otherwise (e.g. = 1 for Alabama, = 0 for Wyoming).
(5 points)
The following questions refer to Table 2.
Notes: Heteroskedasticity-robust standard errors appear in parentheses under regression coefficients,
and p-values appear in parentheses under F -statistics. All regressions include an estimated intercept,
which is not reported. All regressions are estimated using a cross-sectional data set consisting of 50 US
states, where the variables are defined in Table 1.
*The first-stage F -statistic is the F -statistic testing the hypothesis that the coefficients on the instruments
in the first stage regression all equal zero. The critical value of F can be taken as 11
(D) (i) From the regressions in Table 2, select one or more preferred regressions that you believe provide the most reliable basis for
inference about the effect of low education levels on corruption. Carefully explain your reasoning. (10 points)
(ii) Based on your preferred regression(s), what conclusions do you draw about the effect on corruption of the level of education?
Explain. (5 points)
Question 2. Suppose the log-likelihood function in a GLS estimation where the disturbances are multivariate normal distributed is:
Calculate the two first order conditions that one obtains when is trying to maximize with respect to and 2. Use these to calculate the
Maximum Likelihood estimates the in GLS estimation. (10 marks)
Question 3. Using the information given in the likelihood function in Question 4, derive the log likelihood function for the simple
case (where the error terms are homoscedastic and uncorrelated) and use this log likelihood function to prove that that maximum
likelihood estimator is equal to the OLS estimator. (10 marks)
Question 4. In their article, Returns to Capital in Microenterprises, Evidence from a Field Experiment, De Mel, McKenzie and
Woodruff (2007) conducted a field experiment to test the returns to capital in Sri Lanka Microenterprises.
(A) Briefly describe the experiment they conducted. Make sure to also discuss the randomization procedure. (5 points)
(B) The first estimation they perform is represented by:
The results they obtain are given below:
Briefly explain how the results in each column and each row are different (ie what is the difference between the rows and what is the
difference between the columns). Choosing any one estimate (for example Real Profits, FE with 1% level trim) explain what the
result implies in terms of the objectives of the experiment. (10 points)
(C) In their second estimation they wanted to look at the impact of capital stock on profits and due to the issue of endogeneity, they
used an instrumental variable analysis. The equation they estimated and the results are given below:
Carefully explain the first and second stage of the estimation and then using one particular estimate from the table above, explain what
is the measured impact of changes in capital stock on real profits (less 5.43 own hours). (10 points)
Question 5. This question revolves around an experiment run in Minnesota (USA) to try and examine the efficacy of various police
responses to domestic violence calls. Essentially, when police respond to a call they have some leeway in what they do they can
arrest the offender, take the offender away for a cooling off period, or attempt to talk sense into the offender. But which is best?
The experimental setup involved randomly assigning one of these three responses when called to a domestic violence situation. The
randomization was undertaken using color-coded notepads. Officers used this to determine the response. The outcome variable of
interest was a binary variable, simply whether or not they were called again to the same problem later. So an outcome of zero is good
(no return call), one not so good.
The regression to determine the effect was:
where X1i = 1 for taking away for a cooling off period (zero otherwise), X 2i = 1 for talking to the offender (zero otherwise), W 1i = 1 if
there was a gun involved, and W 2i = 1 if there was evidence of substance abuse (both zero otherwise). (Note that although the Y
variable is a zero-one variable, we do not need to use binary dependent variable methods since all the right hand side variables are also
binary, there are no functional form issues in this very special case).
(A) Explain how the randomization in the experimental setup helps ensure that the OLS estimates for 1 and 2 are unbiased. (10
points)
(B) Give a reason why it is useful to include the additional variables W 1i, W2i. Is there a problem if we omit them? Why is there
no variable for the cases where the officers arrest the perpetrator? (10 points)