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7.6 EXERCISES 287 The estimated model (7.24) is
b ¼ "2:2833 þ 2:7500NJ
DFTE
(se) (1.036) (1:154Þ R2 ¼ 0:0146 The estimate of the treatment effect ^
d ¼ 2:75 using the differenced data, which accounts
for any unobserved individual differences, is very close to the differences-in-differences.
Once again we fail to conclude that the minimum wage increase has reduced employment in
these New Jersey fast food restaurants. 7.6 Exercises
Answers to exercises marked * appear at www.wiley.com/college/hill. 7.6.1 PROBLEMS
7.1 An economics department at a large state university keeps track of its majors’ starting
salaries. Does taking econometrics affect starting salary? Let SAL ¼ salary in
dollars, GPA ¼ grade point average on a 4.0 scale, METRICS ¼ 1 if student
took econometrics, and METRICS ¼ 0 otherwise. Using the data file metrics.dat,
which contains information on 50 recent graduates, we obtain the estimated
regression
b ¼ 24200 þ 1643GPA þ 5033METRICS
SAL
ðseÞ ð1078Þ ð352Þ ð456Þ R2 ¼ 0:74 (a) Interpret the estimated equation.
(b) How would you modify the equation to see whether women had lower starting
salaries than men? (Hint: Define an indicator variable FEMALE ¼ 1, if female;
zero otherwise.)
(c) How would you modify the equation to see if the value of econometrics was the
same for men and women?
7.2* In September 1998, a local TV station contacted an econometrician to analyze some
data for them. They were going to do a Halloween story on the legend of full moons’
affecting behavior in strange ways. They collected data from a local hospital on
emergency room cases for the period from January 1, 1998, until mid-August. There
were 229 observations. During this time there were eight full moons and seven new
moons (a related myth concerns new moons) and three holidays (New Year’s Day,
Memorial Day, and Easter). If there is a full-moon effect, then hospital administrators
will adjust numbers of emergency room doctors and nurses, and local police may
change the number of officers on duty.
Using the data in the file fullmoon.dat we obtain the regression results in the
following table: T is a time trend (T ¼ 1,2,3, . . . , 229) and the rest are indicator
variables. HOLIDAY ¼ 1 if the day is a holiday; 0 otherwise. FRIDAY ¼ 1 if the day is
a Friday; 0 otherwise. SATURDAY ¼ 1 if the day is a Saturday; 0 otherwise.
FULLMOON ¼ 1 if there is a full moon; 0 otherwise. NEWMOON ¼ 1 if there
is a new moon; 0 otherwise. 288 USING INDICATOR VARIABLES Emergency Room Cases Regression""Model 1
Variable Coefficient Std. Error t-Statistic Prob. C
T
HOLIDAY
FRIDAY
SATURDAY
FULLMOON
NEWMOON 93.6958
0.0338
13.8629
6.9098
10.5894
2.4545
6.4059 1.5592
0.0111
6.4452
2.1113
2.1184
3.9809
4.2569 60.0938
3.0580
2.1509
3.2727
4.9987
0.6166
1.5048 0.0000
0.0025
0.0326
0.0012
0.0000
0.5382
0.1338 R2 ¼ 0.1736 SSE ¼ 27108.82 (a) Interpret these regression results. When should emergency rooms expect more
calls?
(b) The model was reestimated omitting the variables FULLMOON and NEWMOON, as shown below. Comment on any changes you observe.
(c) Test the joint significance of FULLMOON and NEWMOON. State the null and
alternative hypotheses and indicate the test statistic you use. What do you
conclude?
Emergency Room Cases Regression""Model 2
Variable 7.3 Coefficient Std. Error t-Statistic Prob. C
T
HOLIDAY
FRIDAY
SATURDAY 94.0215
0.0338
13.6168
6.8491
10.3421 1.5458
0.0111
6.4511
2.1137
2.1153 60.8219
3.0568
2.1108
3.2404
4.8891 0.0000
0.0025
0.0359
0.0014
0.0000 R2 ¼ 0.1640 SSE ¼ 27424.19 Henry Saffer and Frank Chaloupka (‘‘The Demand for Illicit Drugs,’’ Economic
Inquiry, 37(3), 1999, 401–411) estimate demand equations for alcohol, marijuana,
cocaine, and heroin using a sample of size N ¼ 44,889. The estimated equation for
alcohol use after omitting a few control variables is shown in the chart at the top of
page 289.
The variable definitions (sample means in parentheses) are as follows:
The dependent variable is the number of days alcohol was used in the past 31 days
(3.49)
ALCOHOL PRICE""price of a liter of pure alcohol in 1983 dollars (24.78)
INCOME""total personal income in 1983 dollars (12,425)
GENDER""a binary variable ¼ 1 if male (0.479)
MARITAL STATUS""a binary variable ¼ 1 if married (0.569)
AGE 12–20""a binary variable ¼ 1 if individual is 12–20 years of age (0.155)
AGE 21–30""a binary variable ¼ 1 if individual is 21–30 years of age (0.197)
BLACK""a binary variable ¼ 1 if individual is black (0.116)
HISPANIC"
"a binary variable ¼ 1 if individual is Hispanic (0.078) 7.6 EXERCISES 289 Demand for Illicit Drugs
Variable Coefficient t-statistic C
ALCOHOL PRICE
INCOME
GENDER
MARITAL STATUS
AGE 12–20
AGE 21–30
BLACK
HISPANIC 4.099
#0.045
0.000057
1.637
#0.807
#1.531
0.035
#0.580
#0.564 17.98
5.93
17.45
29.23
12.13
17.97
0.51
8.84
6.03 (a) Interpret the coefficient of alcohol price.
(b) Compute the price elasticity at the means of the variables.
(c) Compute the price elasticity at the means of alcohol price and income, for a
married black male, age 21–30.
(d) Interpret the coefficient of income. If we measured income in $1,000 units, what
would the estimated coefficient be?
(e) Interpret the coefficients of the indicator variables, as well as their significance.
7.4 In the file stockton.dat we have data from January 1991 to December 1996 on house
prices, square footage, and other characteristics of 4682 houses that were sold in
Stockton, California. One of the key problems regarding housing prices in a region
concerns construction of ‘‘house price indexes,’’ as discussed in Section 7.2.4b. To
illustrate, we estimate a regression model for house price, including as explanatory
variables the size of the house (SQFT), the age of the house (AGE), and annual
indicator variables, omitting the indicator variable for the year 1991.
PRICE ¼ b1 þ b2 SQFT þ b3 AGE þ d1 D92 þ d2 D93 þ d3 D94 þ d4 D95
þ d5 D96 þ e
The results are as follows: Stockton House Price Index Model
Variable
C
SQFT
AGE
D92
D93
D94
D95
D96 Coefficient Std. Error t-Statistic Prob. 21456.2000
72.7878
#179.4623
#4392.8460
#10435.4700
#13173.5100
#19040.8300
#23663.5100 1839.0400
1.0001
17.0112
1270.9300
1231.8000
1211.4770
1232.8080
1194.9280 11.6671
72.7773
#10.5496
#3.4564
#8.4717
#10.8739
#15.4451
#19.8033 0.0000
0.0000
0.0000
0.0006
0.0000
0.0000
0.0000
0.0000 290 USING INDICATOR VARIABLES (a) Discuss the estimated coefficients on SQFT and AGE, including their interpretation, signs, and statistical significance.
(b) Discuss the estimated coefficients on the indicator variables.
(c) What would have happened if we had included an indicator variable for 1991? 7.6.2 COMPUTER EXERCISES
7.5* In (7.7) we specified a hedonic model for house price. The dependent variable was the
price of the house in dollars. Real estate economists have found that for many data
sets, a more appropriate model has the dependent variable ln(PRICE).
(a) Using the data in the file utown.dat, estimate the model (7.7) using ln(PRICE) as
the dependent variable.
(b) Discuss the estimated coefficients on SQFT and AGE. Refer to Chapter 4.5 for
help with interpreting the coefficients in this log-linear functional form.
(c) Compute the percentage change in price due to the presence of a pool. Use both the
rough approximation in Section 7.3.1 and the exact calculation in Section 7.3.2.
(d) Compute the percentage change in price due to the presence of a fireplace. Use
both the rough approximation in Section 7.3.1 and the exact calculation in
Section 7.3.2.
(e) Compute the percentage change in price of a 2500-square-foot home near the
university relative to the same house in another location using the methodology
in Section 7.3.2.
7.6 Data on the weekly sales of a major brand of canned tuna by a supermarket chain in a
large midwestern U.S. city during a mid-1990s calendar year are contained in the file
tuna.dat. There are 52 observations on the variables
SAL1 ¼ unit sales of brand no. 1 canned tuna
APR1 ¼ price per can of brand no. 1 canned tuna
APR2, APR3 ¼ price per can of brands nos. 2 and 3 of canned tuna
DISP ¼ an indicator variable that takes the value one if there is a store display for
brand no. 1 during the week but no newspaper ad; zero otherwise
DISPAD ¼ an indicator variable that takes the value one if there is a store display
and a newspaper ad during the week; zero otherwise
(a) Estimate, by least squares, the log-linear model
lnðSAL1Þ ¼ b1 þ b2 APR1 þ b3 APR2 þ b4 APR3 þ b5 DISP þ b6 DISPAD þ e
(b) Discuss and interpret the estimates of b2, b3, and b4.
(c) Are the signs and relative magnitudes of the estimates of b5 and b6 consistent
with economic logic? Interpret these estimates using the approaches in Sections
7.3.1 and 7.3.2.
(d) Test, at the a ¼ 0:05 level of significance, each of the following hypotheses:
H1 : b5 6¼ 0
(i) H0 : b5 ¼ 0,
H1 : b6 6¼ 0
(ii) H0 : b6 ¼ 0,
H1 : b5 or b6 6¼ 0
(iii) H0 : b5 ¼ 0, b6 ¼ 0;
(iv) H0 : b6 % b5 ,
H 1 : b 6 > b5
(e) Discuss the relevance of the hypothesis tests in (d) for the supermarket chain’s
executives. 7.6 EXERCISES 291 7.7 Mortgage lenders are interested in determining borrower and loan factors that may
lead to delinquency or foreclosure. In the file lasvegas.dat are 1000 observations on
mortgages for single-family homes in Las Vegas, Nevada, during 2008. The variable
of interest is DELINQUENT, an indicator variable ¼ 1 if the borrower missed at least
three payments (90 or more days late), but zero otherwise. Explanatory variables are
LVR ¼ the ratio of the loan amount to the value of the property; REF ¼ 1 if purpose
of the loan was a ‘‘refinance’’ and ¼ 0 if loan was for a purchase; INSUR ¼ 1 if
mortgage carries mortgage insurance, zero otherwise; RATE ¼ initial interest rate of
the mortgage; AMOUNT ¼ dollar value of mortgage (in $100,000); CREDIT ¼
credit score, TERM ¼ number of years between disbursement of the loan and the
date it is expected to be fully repaid, ARM ¼ 1 if mortgage has an adjustable rate,
and ¼ 0 if mortgage has a fixed rate.
(a) Estimate the linear probability (regression) model explaining DELINQUENT as
a function of the remaining variables. Are the signs of the estimated coefficients
reasonable?
(b) Interpret the coefficient of INSUR. If CREDIT increases by 50 points, what is the
estimated effect on the probability of a delinquent loan?
(c) Compute the predicted value of DELINQENT for the final (1000th) observation.
Interpret this value.
(d) Compute the predicted value of DELINQUENT for all 1000 observations.
How many were less than zero? How many were greater than 1? Explain
why such predictions are problematic.
7.8 A motel’s management discovered that a defective product was used in the motel’s
construction. It took seven months to correct the defects, during which time
approximately 14 rooms in the 100-unit motel were taken out of service for one
month at a time. The motel lost profits due to these closures, and the question of how
to compute the losses was addressed by Adams (2008).21 For this exercise, use the
data in motel.dat.
(a) The occupancy rate for the damaged motel is MOTEL_PCT, and the competitor
occupancy rate is COMP_PCT. On the same graph, plot these variables against
TIME. Which had the higher occupancy before the repair period? Which had the
higher occupancy during the repair period?
(b) Compute the average occupancy rate for the motel and competitors when the
repairs were not being made (call these MOTEL0 and COMP0 ) and when they
were being made (MOTEL1 and COMP1 ). During the nonrepair period, what was
the difference between the average occupancies, MOTEL0 " COMP0 ? Assume
that the damaged motel occupancy rate would have maintained the same relative
difference in occupancy if there had been no repairs. That is, assume that the
#
would have been MOTEL1 ¼ COMP1 þ
!damaged motel’s occupancy
"
MOTEL0 " COMP0 . Compute the ‘‘simple’’ estimate of lost occupancy
#
MOTEL1 " MOTEL1 . Compute the amount of revenue lost during the sevenmonth period (215 days) assuming an average room rate of $56.61 per night.
(c) Draw a revised version of Figure 7.3 that explains the calculation in part (b).
(d) Alternatively, consider a regression approach. A model explaining motel
occupancy uses as explanatory variables the competitors’ occupancy, the relative
21
A. Frank Adams (2008) ‘‘When a ‘Simple’ Analysis Won’t Do: Applying Economic Principles in a Lost
Profits Case,’’ The Value Examiner, May/June 2008, 22–28. The authors thank Professor Adams for the use of his
data. 292 USING INDICATOR VARIABLES price (RELPRICE) and an indicator variable for the repair period (REPAIR).
That is, let
MOTEL PCTt ¼ b1 þ b2 COMP PCTt þ b3 RELPRICEt þ b4 REPAIRt þ et
Obtain the least squares estimates of the parameters. Interpret the estimated
coefficients, as well as their signs and significance.
(e) Using the least squares estimate of the coefficient of REPAIR from part (d),
compute an estimate of the revenue lost by the damaged motel during the repair
period (215 days @ $56.61 # b4). Compare this value to the ‘‘simple’’ estimate in
part (b). Construct a 95% interval estimate for the estimated loss. Is the estimated
loss from part (b) within the interval estimate?
(f) Carry out the regression specification test RESET. Is there any evidence of model
misspecification?
(g) Plot the least squares residuals against TIME. Are there any obvious patterns?
7.9* In the STAR experiment (Section 7.5.3), children were randomly assigned within
schools into three types of classes: small classes with 13 to 17 students, regular-sized
classes with 22–25 students, and regular-sized classes with a full-time teacher aide to
assist the teacher. Student scores on achievement tests were recorded, as was some
information about the students, teachers, and schools. Data for the kindergarten
classes is contained in the data file star.dat.
(a) Calculate the average of TOTALSCORE for (i) students in regular-sized classrooms with full time teachers, but no aide; (ii) students in regular-sized classrooms
with full time teachers, and an aide; and (iii) students in small classrooms. What do
you observe about test scores in these three types of learning environments?
(b) Estimate the regression model TOTALSCOREi ¼ b1 þ b2 SMALLi þ b3 AIDEi þ
ei , where AIDE is a indicator variable equaling one for classes taught by a
teacher and an aide and zero otherwise. What is the relation of the estimated
coefficients from this regression to the sample means in part (a)? Test the
statistical significance of b3 at the 5% level of significance.
(c) To the regression in (b) add the additional explanatory variable TCHEXPER. Is
this variable statistically significant? Does its addition to the model affect the
estimates of b2 and b3?
(d) To the regression in (c) add the additional explanatory variables BOY,
FREELUNCH, and WHITE_ASIAN. Are any of these variables statistically
significant? Does their addition to the model affect the estimates of b2 and b3?
(e) To the regression in (d) add the additional explanatory variables TCHWHITE,
TCHMASTERS, SCHURBAN, and SCHRURAL. Are any of these variables
statistically significant? Does their addition to the model affect the estimates
of b2 and b3?
(f) Discuss the importance of parts (c), (d), and (e) to our estimation of the
‘‘treatment’’ effects in part (b).
(g) Add to the models in (b) through (e) indicator variables for each school
!
1 if student is in school j
SCHOOL j ¼
0 otherwise
Test the joint significance of these school ‘‘fixed effects.’’ Does the inclusion
of these fixed effect indicator variables substantially alter the estimates of b2
and b3? 7.6 EXERCISES 293 7.10 Many cities in California have passed Inclusionary Zoning policies (also known as
below-market housing mandates) as an attempt to make housing more affordable. These
policies require developers to sell some units below the market price on a percentage of
the new homes built. For example, in a development of 10 new homes each with market
value $850,000, the developer may have to sell 5 of the units at $180,000. Means et al.
(2007)22 examine the effects of such policies on house prices and number of housing
units available using 1990 (before policy impact) and 2000 (after policy impact) census
data on California cities. Use means.dat for the following exercises.
(a) Using only the data for 2000, compare the sample means of LNPRICE and
LNUNITS for cities with an Inclusionary Zoning policy, IZLAW ¼ 1, to those
without the policy, IZLAW ¼ 0. Based on these estimates, what is the percentage
difference in prices and number of units for cities with and without the law? [For
this example, use the simple rule that 100[ln(y1) " ln(y0)] is the approximate
percentage difference between y0 and y1.] Does the law achieve its purpose?
(b) Use the existence of an Inclusionary Zoning policy as a ‘‘treatment.’’ Consider
those cities who did not pass such a law, IZLAW ¼ 0, the ‘‘control’’ group. Draw
a figure like Figure 7.3 comparing treatment and control groups LNPRICE and
LNUNITS, and determine the ‘‘treatment effect.’’ Are your conclusions about the
effect of the policy the same as in (a)?
(c) Use LNPRICE and LNUNITS in differences-in-differences regressions, with
explanatory variables D, the indicator variable for year 2000; IZLAW, and the
interaction of D and IZLAW. Is the estimate of the treatment effect statistically
significant, and of the anticipated sign?
(d) To the regressions in (c) add the control variable LMEDHHINC. Interpret
the estimate of the new variable, including its sign and significance. How
does the addition affect the estimates of the treatment effect?
(e) To the regressions in (d) add the variables EDUCATTAIN, PROPPOVERTY, and
LPOP. Interpret the estimates of these new variables, including their signs
and significance. How do these additions affect the estimates of the treatment
effect?
(f) Write a 250-word essay discussing the essential results in parts (a) through (e).
Include in your essay an economic analysis of the policy.
7.11 This question extends the analysis of Exercise 7.10. Read the introduction to that
exercise if you have not done so. Each city in the sample may have unique,
unobservable characteristics that affect LNPRICE and LNUNITS. Following the
discussion in Section 7.5.6, use the differenced data to control for these unobserved
effects.
(a) Regress DLNPRICE and DLNUNITS on IZLAW. Compare the estimate of the
treatment effect to those from the differences-in-differences regression of
LNPRICE and LNUNITS on the explanatory variables D, the indicator variable
for year 2000; IZLAW, and the interaction of D and IZLAW.
(b)^Explain, algebraically, why the outcome in (a) occurs.
(c) To the regression in (a) add the variable DLMEDHHINC. Interpret the estimate
of this new variable, including its sign and significance. How does the addition
affect the estimates of the treatment effect?
22
‘‘Below-Market Housing Mandates as Takings: Measuring their Impact’’ Tom Means, Edward Stringham,
and Edward Lopez, Independent Policy Report, November 2007. The authors wish to thank Tom Means for
providing the data and insights into this exercise. 294 USING INDICATOR VARIABLES (d) To the regression in (c), add the variables DEDUCATTAIN, DPROPPOVERTY,
and DLPOP. Interpret the estimates of these new variables, including their signs
and significance. How do these additions affect the estimates of the treatment
effect?
7.12 Use the data in the file cps5.dat to estimate the regression of ln(WAGE) on the
explanatory variables EDUC, EXPER, EXPER2, FEMALE, BLACK, MARRIED,
SOUTH, FULLTIME, and METRO.
(a) Discuss the results of the estimation. Interpret each coefficient and comment on
its sign and significance. Are things as you would expect?
(b)^(large data set) Use the data cps4.dat to re-estimate the equation. What changes
do you observe?
7.13^ (large data set) Use the data file cps4.dat for the following:
(a) Estimate the model used in Table 7.4. (i) Test the null hypothesis that the
interaction between BLACK and FEMALE is statistically significant. (ii) Test
the null hypothesis that there is no regional effect.
(b) Estimate the model used in Table 7.4 using ln(WAGE) as the dependent variable
rather than WAGE. (i) Discuss any important differences in results between
the linear and log-linear specifications. (ii) Test the null hypothesis that the
interaction between BLACK and FEMALE is statistically significant. (iii) Test
the null hypothesis that there is no regional effect.
(c) Estimate the models used in Table 7.5. Carry out the test for the null hypothesis
that there is no difference between wage equations for southern and nonsouthern
workers.
(d) Estimate the models used in Table 7.5 using ln(WAGE) as the dependent variable
rather than WAGE. (i) Discuss any important differences in results between the
linear and log-linear specifications. (ii) Carry out the test for the null hypothesis
that there is no difference between wage equations for southern and nonsouthern
workers.
7.14* Professor Ray C. Fair’s voting model was introduced in Exercise 2.14. He builds
models that explain and predict the U.S. presidential elections. See his website
at http://fairmodel.econ.yale.edu/vote2008/index2.htm. The basic premise of the
model is that the incumbent party’s share of the two-party (Democratic and
Republican) popular vote (incumbent means the party in power at the time of the
election) is affected by a number of factors relating to the economy, and variables
relating to the politics, such as how long the incumbent party has been in power, and
whether the president is running for reelection. Fair’s data, 33 observations for the
election years from 1880 to 2008, are in the file fair4.dat. The dependent variable is
VOTE ¼ percentage share of the popular vote won by the incumbent party.
The explanatory variables include
PARTY ¼ 1 if there is a Democratic incumbent at the time of the election and "1 if
there is a Republican incumbent.
PERSON ¼ 1 if the incumbent is running for election and zero otherwise.
DURATION ¼ 0 if the incumbent party has been in power for one term, one if the
incumbent party has been in power for two consecutive terms, 1.25 if the incumbent
party has been in power for three consecutive terms, 1.50 for four consecutive terms,
and so on.
WAR ¼ 1 for the elections of 1920, 1944, and 1948 and zero otherwise. 7.6 EXERCISES 295 GROWTH ¼ growth rate of real per capita GDP in the first three quarters of the
election year (annual rate).
INFLATION ¼ absolute value of the growth rate of the GDP deflator in the first 15
quarters of the administration (annual rate) except for 1920, 1944, and 1948,
where the values are zero.
GOODNEWS ¼ number of quarters in the first 15 quarters of the administration in
which the growth rate of real per capita GDP is greater than 3.2% at an annual rate
except for 1920, 1944, and 1948, where the values are zero.
(a) Consider the regression model
VOTE ¼ b1 þ b2 GROWTH þ b3 INFLATION þ b4 GOODNEWS
þ b5 PERSON þ b6 DURATION þ b7 PARTY þ b8 WAR þ e
Discuss the anticipated effects of the dummy variables PERSON and WAR.
(b) The binary variable PARTY is somewhat different from the dummy variables we
have considered. Write out the regression function E(VOTE) for the two values of
PARTY. Discuss the effects of this specification.
(c) Use the data for the period 1916–2004 to estimate the proposed model. Discuss
the estimation results. Are the signs as expected? Are the estimates statistically
significant? How well does the model fit the data?
(d) Predict the outcome of the 2008 election using the given 2008 data for values of
the explanatory variables. Based on the prediction, would you have picked the
outcome of the election correctly?
(e) Construct a 95% prediction interval for the outcome of the 2008 election.
(f) Using data values of your choice (you must explain them), predict the outcome of
the 2012 election.
7.15 The data file br2.dat contains data on 1080 house sales in Baton Rouge, Louisiana,
during July and August 2005. The variables are PRICE ($), SQFT (total square feet),
BEDROOMS (number), BATHS (number), AGE (years), OWNER (¼1 if occupied by
owner; zero if vacant or rented), POOL (¼1 if present), TRADITIONAL (¼1 if
traditional style; 0 if other style), FIREPLACE (¼1 if present), and WATERFRONT
(¼1 if on waterfront).
(a) Compute the data summary statistics and comment. In particular, construct a
histogram of PRICE. What do you observe?
(b) Estimate a regression model explaining ln(PRICE=1000) as a function of the
remaining variables. Divide the variable SQFT by 100 prior to estimation.
Comment on how well the model fits the data. Discuss the signs and statistical
significance of the estimated coefficients. Are the signs what you expect? Give an
exact interpretation of the coefficient of WATERFRONT.
(c) Create a variable that is the product of WATER...
Â
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