# Econometrics Final Exam Summer 2017

Econometrics Final Exam Summer 2017

This exam is divided into five parts. Please answer all the questions

as best as you can.

Part I

1. Give an example of a multiple regression equation

2. Give an example of a quadratic regression equation

Figure 1

2

Figure 1 shows the relationship between temperature and sales.

3. What kind of graph is this?

4. What kind of relationship is there between temperature and sales?

5. If the temperature is 13℃ would you expect high sales or low sales?

Part II

Figure 2

Figure 2 plots the Spending and revenue for an electronics company from 1960-2009.

1. On average would you say the company is profitable?

2. State one year when the company clearly made a profit.

3. Can you give any indication as to how the company will perform in the future?

4. Write an equation to investigate the relationship between Spending and Revenue.

3

4

Background to Parts III and IV: Female Labor Supply

Harvard economist Claudia Goldin attributes much of the rise of professional women in the U.S.

labor force to their ability to engage in family planning after the introduction of the birth-control

pill. In developing countries early childbearing is associated with lower levels of education and

more dependency of women on their husband’s earnings.

This question examines the effect of family size on female labor supply. The data set consists of

n = 254,654 married women (aged 21 – 35), as reported in the 1980 U.S. Census of the

Population (the data pertain to the full calendar year of 1979).

Variables in the Female Labor Supply Data Set

Variable Definition Wife’s weeks worked No. of weeks wife worked for pay in 1979 Husband’s weeks worked No. of weeks husband worked for pay in 1979 Same sex = 1 if first two children have same sex, = 0 otherwise 2 boys = 1 if first two children are boys, = 0 otherwise 2 girls = 1 if first two children are girls, = 0 otherwise Kids>2 = 1 if family has more than 2 children, = 0 otherwise Boy first = 1 if first child is a boy, = 0 otherwise Current age of mother age of mother in 1979 Age of mother at 1st birth age of mother at birth of first child Black = 1 if black Hispanic = 1 if Hispanic Other race = 1 if nonwhite/nonblack/nonHispanic

5

The questions in Parts III and IV refer to Table 2.

Table 2

Child Sex Composition, Family Size, and Labor Supply

(1) (2) (3) (4) (5) (6)

Dependent variable Kids>2 Kids>2 Wife’s weeks worke

d

Wife’s weeks worke

d

Wife’s weeks worke

d

Husband ’ s weeks worked

Estimation method OLS OLS OLS TSLS TSLS TSLS

Instruments Same sex 2 boys, 2 girls

Same sex

Regressors Same sex .0694*

* (.0018 )

2 boys .0599* * (.0026 )

2 girls .0789* * (.0026 )

Kids>2 – 8.04* * (0.09)

– 5.40* * (1.21)

– 5.16* * (1.20)

1.01 (0.63 ) Boy first -.0011

(.0019 )

-.0015 (.0026 )

-0.05 (0.08 )

-0.02 (0.08 )

-0.02 (0.08 )

0.03 (0.08 ) Current age of

mother .0304* * (.0003 )

.0304* * (.0003 )

1.33* * (0.01)

1.25* * (0.04)

1.25* * (0.04)

0.10* (0.04 ) Age of mother at 1st

birth -.0436* * (.0003)

-.0436* * (.0003)

– 1.36* * (0.17)

– 1.24* * (0.05)

– 1.24* * (0.05)

– 0.21* * (0.06)

Black .0680* * (.0042 )

.0680* * (.0042 )

10.83* * (0.19)

10.66* * (0.21)

10.64* * (0.21)

– 4.10* * (0.26)

Hispanic .1260* * (.0039 )

.1260* * (.0039 )

-0.04 (0.18 )

-0.38 (0.23 )

-0.41 (0.23 )

– 2.61* * (0.23)

Other race .0480* * (.0044 )

.0480* * (.0044 )

2.82* * (0.20)

2.70* * (0.21)

2.69* * (0.21)

2.02* * (0.18) N 254,654 254,654 254,654 254,654 254,654 254,654

F-statistic on Same sex 1413.0 F-statistic on 2 boys,

2 girl

s

725.9

J-statistic 3.24

Notes: Regressions (4), (5), and (6) are estimated by two stage least squares (TSLS) regression,

in which the included endogenous variable is Kids>2. 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. Regressions (1)

– (5) are estimated using data on married women for 1979, regression (6) is estimated using data

for the husbands of those married women.

Significant at the: **1%, *5% significance level.

6

Questions for Part III (21 points).

1) Give the best reason you can why the OLS estimator of the coefficient on Kids>2 in Table

2, column (3) might be biased. (3 points)

2) Consider the hypothesis that, on average, U.S. parents want to have children of both

genders (that is, they prefer at least one girl and one boy to all girls or all boys). Does

Table 2 provide evidence in favor of this hypothesis, against this hypothesis, or neither?

Explain. (3 points)

3) Consider the following potential instrumental variables for Kids>2 in regression (3):

a) Whether wife came from large family (binary) (3 points)

b) The teen pregnancy rate in the wife’s city or town of residence (3 points)

For each proposed instrument, is the variable arguably a valid instrument variable? Briefly

explain.

4) Based on a combination of your judgment and the empirical results in Table 2:

a) Is Same sex a valid instrument in regression (4)? (3 points)

b) Is the pair of variables, 2 boys and 2 girls, a valid set of instruments in regression (5)?

(3 points)

5) The estimated coefficient on Kids>2 differs in regressions (3) and (4) (the OLS estimate is

more negative than the TSLS estimate). Provide a real-world explanation (an interpretation

of the results) that explains why the OLS estimate is more negative than the TSLS estimate.

(3 points)

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Questions for Part IV (17 points).

1) Consider a hypothetical regression (7),

Wife’s weeks workedi = β0 + β1Kids>2 + ui (7)

which would be estimated by TSLS, using Same sex as an instrument (so regression (7) is

regression (4) without the variables Boy first,…, Other race). For this question, assume

that Same sex is a valid instrument in regression (4) and in addition that Same sex is

distributed independently of all the control variables in regression (4), so E(Boy first|Same

sex) = E(Boy first), …, E(Other race|Same sex) = E(Other race).

a) Explain why Same sex would be a valid instrument in regression (7). (3 points)

b) Provide a reason why, despite the validity of Same sex as an instrument in regression

(7), you would still prefer regression (4). (3 points)

2) Some women are more ambitious professionally than others. Suppose that the effect on

labor force participation of having a large family is not the same for every woman,

specifically, the more ambitious the woman, the smaller is the effect (the most ambitious

women will work whether or not they have a large family). How – if at all – would this

change your interpretation of the results in regressions (4) and (5)? Explain your reasoning.

(5 points)

Use Table 2 to comment on the following statements. For each statement, do you agree or

disagree with the statement, and explain why (be specific).

3) Families with large numbers of children tend to be unusual in certain ways, in some cases

coming from certain religious/ethnic backgrounds (traditional Catholic families, Mormons,

etc.). So the analysis in regressions (4) and (5) is not providing a valid estimate of the

effect of family size on labor supply, it is just reflects this religious/ethnic effect. (3 points)

4) Even though having large families reduces female labor force participation, this is only half

of the story because their husbands will work more to compensate for the loss of the wife’s

earnings. (3 points)

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Background to Part V: The Term Spread and Output Growth

The U.S. Treasury issues bonds of different maturities. A 10-year bond is debt that is paid off

over 10 years. A one-year bond is debt that is paid off over one year. Usually, the rate of

interest on a 10-year bond exceeds the rate of interest on a one-year bond. If short-term interest

rates are unusually high, however, then the rate of interest on a one-year bond can exceed the

rate of interest on a 10-year bond. The difference between the rate of interest on a long-term

bond (here, the 10-year bond) and the rate of interest a short-term bond (here, the one-year bond)

is called the Term Spread. If the 10-year rate is 4.5 (percent) and the 1-year rate is 3.5 (percent),

then the spread is 1.0 (percentage points).

The Term Spread is often viewed as a measure of monetary policy. If monetary policy is

especially tight, then short term interest rates are high, relative to long term interest rates, and the

term spread is negative.

Over the past few months, the Term Spread in the U.S. has fallen, and just recently it became

negative for the first time since the onset of the recession in 2000.

The Term Spread data set contains quarterly time series data for the U.S. from the first quarter of

1960 (1960:I) through the third quarter of 2005 (2005:III). The data are plotted in Figure 1.

Variables in Term Spread Data Set

Variable Definition GDP growth quarterly growth rate of GDP, expressed in percent at an annual

rate (computed using the logarithmic approximation, GDP growth

= 400ln(GDPt/GDPt–1), where GDPt is the real Gross Domestic

Product of the U.S. in quarter t. (Quarterly GDP is the total value

of final goods and services produced in the United States in that

quarter.) Term Spread the interest rate on a 10-year U.S. Treasury bill, minus the interest

rate on a 1-year U.S. Treasury bill.

9

20

10

0

-10 1960q1 1972q3 1985q1 1997q3

2010q1 time Quarterly GDP growth at an annual rate

4

2

0

-2

-4

1960q1 1972q3 1985q1 1997q3 2010q1 time

Term Spread: 10-year minus 1-year

Figure 1. Time series plots of quarterly GDP growth and Term Spread, 1960:I – 2005:III

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The questions in Part V refer to Table 3.

Table 3

GDP Growth and the Term Spread

Dependent variable: GDP growtht

(1) (2) (3) (4) (5)

Sample period 1960:I – 2005:III

1960:I – 2005:III

1960:I – 2005:III

1960:I – 1984:IV

1985:I – 2005:III

Regressors Intercept 2.42*

* (0.38)

2.04* * (0.52)

1.85* * (0.45)

2.05* * (0.56)

2.07* * (0.57) GDP

growtht–1 0.27* * (0.08)

0.24* * (0.08)

0.26* * (0.07)

0.23* (0.10 )

0.25* (0.12 ) GDP

growtht–2 0.18

(0.14 )

GDP growtht–3

-0.06 (0.08 )

GDP growtht–4

0.01 (0.10 )

Term Spreadt– 1

0.67* * (0.25)

1.56* * (0.44)

0.18 (0.20 ) Quandt Likelihood Ratio

(QLR) statistic (p-value in

parentheses)

1.18 (0.41 )

1.71 (0.32 )

5.37 (0.03 )

2.59 (0.26 )

2.88 (0.24 ) T 183 183 183 100 83

SER 3.3 3.2 3.1 3.8 1.93 F-statistic testing zero

coefficients on GDP growtht– 2,. GDP growtht–3, and GDP

growtht–4 (p-value in parentheses)

1.27 (0.29 )

Notes: Estimation is by OLS, with heteroskedasticity-robust standard errors in parentheses. The

regressions are estimated over the sample period given in the first row. The QLR statistic is for

all the regressors in the regression, including the intercept. Heteroskedasticity-robust standard

errors are included in parentheses.

Significant at the: **1%, *5%, +

10% significance level.

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Questions for Part V (20 points).

1) The value of GDP growth in 2005:III was 4.1 (that is, in the third quarter of 2005, GDP

grew by 4.1% at an annual rate).

a) Use regression (1) in Table 3 to compute a forecast of GDP growth for 2005:IV. (3

points)

b) Suppose that the errors in regression (1) are normally distributed. Compute a 95%

prediction interval (forecast interval) for GDP growth in 2005:IV. (3 points)

c) Suppose that forecast errors come in clusters, for example, some years have more

volatile GDP growth than others, so that GDP growth is more difficult to predict in

some years than in others. Suggest a modification of regression (1) in Table 3 that

would produce more reliable forecast intervals if there is this forecast error volatility

clustering. (2 points)

2) Table 3 reports heteroskedasticity-robust standard errors. Should it report HAC standard

errors instead? Explain. (2 points)

3) In Business Week Online (January 9, 2006), David Wyss, chief economist for Standard and

Poor’s wrote about how the recent decline of Term Spread has created worries about a

slowdown in U.S. economic growth. Based on the results in Table 3, do you think that

these worries are justified? Fully explain your reasoning. (5 points)

4) Suppose the U.S. Federal Reserve Bank is considering setting Term Spread to 1.0, that is,

increasing Term Spread from its current value of approximately zero by 1.0 percentage

point. (Suppose that, because long rates are more sluggish than short rates, the Fed can do

this by lowing short-term interest rates until Term Spread equals 1.0.)

a) Use regression (5) to estimate the effect of this easing. (1 points)

b) In your judgment, do you think that your answer in (a) provides a good estimate of the

effect of this proposed policy intervention by the Fed? Why or why not? (4 points)

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