Econ 184b Practice problems for the final
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Econ 184b
Practice problems for the final exam
Part I: Multiple Choice
1. In the linear probability model, the interpretation ofthe slope coefficient is
a. the change in odds associated with a unit change in X, holding other regressors constant.
b. not meaningful since the dependent variable is either 0 or 1.
c. the change in probability that Y=1 associated with a unit change in X, holding others regressors constant.
d. the response in the dependent variable to a percentage change in the regressor.
e. (b) and (d).
2. In the probit model Pr(Y = 1 | X) =Ö(â0 + â1X), Ö
a. is not defined for Ö(0).
b. is the standard normal cumulative distribution function.
c. is the cumulative logistic distribution function.
d. can be computed from the standard normal density function.
e. (a) and (b).
3. In the expression Pr(deny = 1| P/I Ratio, black) = Ö(-2.26 + 2.74P/I ratio + 0.71black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person
a. is 4.8 percentage points.
b. is 6.1 percentage points.
c. is 2.7 percentage points.
d. is 2.3 percentage points.
e. none ofthe above.
4. The two conditions for a valid instrument are
a. corr(Zi, Xi) = 0 and corr(Zi, ui) ⃞ 0.
c. corr(Zi, Xi) ⃞ 0 and corr(Zi, ui) = 0.
5. When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows
a.
b.
c.
d.
6. Weak instruments are a problem because
a. the TSLS estimator may not be normally distributed, even in large samples.
b. they result in the instruments not being exogenous.
c. the TSLS estimator cannot be computed.
d. you cannot predict the endogenous variables any longer in the first stage.
e. (c) and (d).
7. To test for randomization when Xi is binary,
8. Experimental effects, such as the Hawthorne effect,
a. generally are not a concern in quasi-experiments.
b. typically require instrumental variable estimation in quasi-experiments.
c. can be dealt with using binary variables in quasi-experiments.
d. are the most important threat to internal validity in quasi-experiments.
e. none ofthe above.
9. Shrinkage estimators
a. are unbiased
b. shrink the estimator toward zero
c. are chosen to minimize the SSR
d. (b) and (c)
e. (a), (b) and (c)
10. The penalty term in the LASSO regression is
a.
b.
c.
d.
e.
Part II: True/False/Uncertain 1. Suppose that we estimated the following model: Pr(Y = 1 | M) = Ö(â0 + â1M), where Y is an indicator variable for whether or not the person is enrolled in school. Let M be an indicator for whether or not the person is male. Suppose the estimate of â1 =0.10 and is statistically significant. T/F/U: We interpret this estimate as: males are 10 percentage points more likely to enroll into school as females. 2. Using a logit model is a useful way to correct for omitted variable bias. 3. Estimation of the IV regression model requires exact identification or overidentification. 4. Suppose you want to estimate a regression with a single endogenous regressor: You have two instruments Z1i and Z21 . You run a TSLS regression and calculate a J-statistic of 2.58 with a 5% critical value of 3.84. T/F/U: You cannot reject the null hypothesis that all the instruments are exogenous. 5. The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor, the first-stage F-statistic must be statistically significant to indicate a strong instrument. 6. Conditional mean independence is a weaker assumption than the zero conditional mean assumption (e.g., E(ui | X1i, X2i) = 0). 7. Allowing regression coefficients to be biased can yield more accurate predictions than unbiased regression coefficients.
Part III: Short answer problems 1. Your textbook mentions use of a quasi-experiment to study the effects of minimum wages on employment using data from fast food restaurants. In 1992, there was a large increase in the (state) minimum wage in one U.S. state (New Jersey) but not in a neighboring location (eastern
Pennsylvania). To calculate theyou need the change in the treatment group and the change in the control group. To do this, the study provides you with the following
information:
|
PA |
NJ |
FTE Employment before |
23.33 |
20.44 |
FTE Employment after |
21.17 |
21.03 |
Where FTE is "full time equivalent" and the numbers are average employment per restaurant.
a. Calculate the change in the treatment group, the change in the control group, and . Did you expect the differences-in-differences estimator to be positive or negative?
b. Ifyou look at , is this number primarily due to a change in the treatment group or the control group? Is this what you expected? Explain.
c. The standard error for is 1.36. Test whether or not the coefficient is statistically
significant (n = 410 observations).
d. Why might you want to control for other factors in this model? What might some ofthose other factors be (provide at least two (good) factors)? Explain.
2. An economist is considering estimating the following equations using daily data from a New York City fresh fish market:
Demand:
Supply:
where: Qd = Qs is the quantity of fish purchased in the market on day t
P is the average price of fish purchased in the market on day t
a. If an economist estimated the demand equation using OLS, would she obtain consistent estimates of â1? Why or why not?
b. The economist is considering using wind speed in the Atlantic Ocean on day i as an instrument for the price of fish. Is this likely to be a good instrument? Why or why not? (In your answer you should be explicit about what makes an instrument good.)
c. Could the economist test whether the instrument was exogenous? Why or why not? How could the economist test whether the instrument was weak? Why would it matter ifthe
instrument was weak, as long as it was exogenous? Explain.
3. See the following Stata log file. The data set is information on housing loan applications and approvals where:
approve is a dummy= 1 ifthe loan was approved
ltotinc is log of monthly income
late is a dummy=1 if the applicant was late paying a previous mortgage
white is a dummy=1 ifthe applicant is white
whitelate = white*late
a. What fraction applicants are late paying a mortgage in the sample? What fraction ofwhite applicants are late paying a mortgage in the sample?
b. Compare regressions 2 and 3. Based on these regressions, do you infer that ltotinc and white are positively or negatively correlated? Explain.
c. Interpret the coefficient on ltotinc in regression 4 in words. How does the interpretation differ from that of the coefficient on ltotinc in regression 2?
d. In regression 5, interpret the coefficient on late and the coefficient on whitelate in words.
e. What question do you think regression 5 is trying to address? What do the results show?
use loanapp.dta
. summ ltotinc white late whitelate approve
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
ltotinc |
white |
late |
whitelate |
approve |
1985
1985
1985
1985
1985
8.337845
.8453401
.0105793
.0085642
.8780856
.5974066
.3616713
.1023362
.0921692
.3272693
5.010635
0
0
0
0
11.3022
1
1
1
1
. reg approve ltotinc
Source | SS df MS
-------------+------------------------------
Model | .659691042 1 .659691042
Residual | 211.837034 1983 .106826543
-------------+------------------------------
Total | 212.496725 1984 .107105204
Number of obs
F( 1, 1983)
Prob > F
R-squared
Adj R-squared
Root MSE
= 1985
= 6.18
= 0.0130
= 0.0031
= 0.0026
= .32684
------------------------------------------------------------------------------
approve | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ltotinc
_cons
|
|
.0305232
.6235883
.0122828
.1026748
2.49
6.07
0.013
0.000
.0064345
.4222264
.0546118
.8249501
------------------------------------------------------------------------------
. reg approve ltotinc white
Source | SS df MS
-------------+------------------------------
Model | 10.4486638 2 5.2243319
Residual | 202.048062 1982 .101941504
-------------+------------------------------
Total | 212.496725 1984 .107105204
Number of obs
F( 2, 1982)
Prob > F
R-squared
Adj R-squared
Root MSE
= 1985
= 51.25
= 0.0000
= 0.0492
= 0.0482
= .31928
------------------------------------------------------------------------------
approve | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ltotinc
white
_cons
|
|
|
.0169226
.1955104
.5717146
.0120787
.0199516
.1004394
1.40
9.80
5.69
0.161
0.000
0.000
-.0067657
.1563822
.3747368
.0406109
.2346386
.7686924
------------------------------------------------------------------------------
. reg approve ltotinc white late
Source | SS df MS
-------------+------------------------------
Model | 11.0180276 3 3.67267587
Residual | 201.478698 1981 .101705552
-------------+------------------------------
Total | 212.496725 1984 .107105204
Number of obs
F( 3, 1981)
Prob > F
R-squared
Adj R-squared
Root MSE
= 1985
= 36.11
= 0.0000
= 0.0519
= 0.0504
= .31891
------------------------------------------------------------------------------
approve | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ltotinc
white
late
_cons
|
|
|
|
.0188983
.1946545
-.1659416
.5577209
.0120936
.0199317
.0701347
.1004972
1.56
9.77
-2.37
5.55
0.118
0.000
0.018
0.000
-.0048192
.1555651
-.303487
.3606295
.0426158
.2337438
-.0283962
.7548123
------------------------------------------------------------------------------
. reg approve ltotinc white late whitelate
Source | SS df MS
-------------+------------------------------
Model | 11.5456536 4 Residual | 200.951072 1980 |
2.8864134 .10149044 |
-------------+------------------------------
Total | 212.496725 1984 .107105204
Number of obs
F( 4, 1980)
Prob > F
R-squared
Adj R-squared
Root MSE
= 1985
= 28.44
= 0.0000
= 0.0543
= 0.0524
= .31858
------------------------------------------------------------------------------
approve | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ltotinc
white
late
whitelate
_cons
|
|
|
|
|
.0213402
.1890994
-.4972257
.4077979
.5420687
.0121282
.0200592
.1613042
.1788523
.1006253
1.76
9.43
-3.08
2.28
5.39
0.079
0.000
0.002
0.023
0.000
-.0024451
.1497601
-.8135695
.0570395
.344726
.0451256
.2284387
-.1808819
.7585563
.7394113
------------------------------------------------------------------------------
4. In 1990, a law was passed expanding a public health insurance program (Medicaid) to make eligible some poor children who had previously not been eligible for the program, where “poor” was defined as having income below the federal poverty line. Not all poor children were made eligible, however. In particular, poor children born on or after October 1, 1983 were made eligible, while poor children born before that date were not made eligible.
a. Explain intuitively why the unusual targeting of this legislation is actually helpful in evaluating the effect of the legislation on health insurance coverage.
b. Below is an excerpt from a table in a paper studying the effect of this legislation (Card and Shore-Sheppard 2004):
Table 3: Medicaid Eligibility and Program Participation for Children Eligible and
Ineligible for 100 Percent Program, 1992-1993 SIPP Panels
2022-05-07