ECN225 exe10 - Lecturer: Stepana Lazarova PDF

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Lecturer: Stepana Lazarova...

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School of Economics and Finance Queen Mary University of London

Štµ epána Lazarová Semester B, 2019/20

ECN225 ECONOMETRICS 2 Class 10

Week 12

1. How would you transform the following models to estimate slope coe¢-

cients

j

?

(a)

Yit

=  +  1 X1 +  2 X2 + u ,

i

= 1; : : : ; n, t = 1; : : : ; T .

(b)

Yit

=  +  1X + u ,

i

= 1; : : : ; n, t = 1; : : : ; T .

i

;it

t

;it

it

it

it

2. The following regression has been estimated using data on variables for

48 US states for years 1982-1988: F atalityRate

=

(00 22) 45 :

BeerT ax

:

+0:028DrAge18  0:019 DrAge19 + 0:031 DrAge20 (0:066)

(0:040)

(0:046)

+0:013M andJ ail + 0:033M andComS erv (0:032)

(0:115)

+0:008AvgM il  0:063 U nRate + 1:81 ln (I nc) (0:008)

(0:012)

(0:47)

+StateF ixedE f f ects + T imeF ixedEf f ects where F atalityRate is the total number of tra¢c fatalities per 10,000 people, DrAge18, DrAg e19 and DrAg e20 are binary variables for a minimum legal drinking age of 18, 19 and 20 (so the omitted group is a minimum legal age of 21 or higher), M andJ ail and M andC omServ are binary variables for mandatory jail time or mandatory community service (the omitted group is less severe punishment), Avg M il is average vehicle miles per driver, U nRate is the unemployment rate and I nc is the real (1988 dollars) personal income per capita. The F -statistics for the test that the time …xed e¤ects are jointly equal to zero has a value of 11.44 (p-value < 0:001). (a) New Jersey has a population of 8.1 million people. Suppose that

New Jersey increased the tax on a case of beer by $1 (in $1988). Use the estimated regression above to predict the number of lives that would be saved over the next year. Construct a 95% con…dence interval for your answer. 1

The drinking age in New Jersey is 21. Suppose that New Jersey lowered its drinking age to 18. Use the estimated regression above to predict the change in the number of tra¢c fatalities in the next year. Construct a 95% con…dence interval for your answer. (c) Suppose that real income per capita in New Jersey increases by 1% in the next year. Use the estimated regression above to predict the change in the number of tra¢c fatalities in the next year. Construct a 90% con…dence interval for your answer. (d) Should time e¤ects be included in the regression? Why or why not? 3. Consider a product market with a supply function is = 0 + 1 i + is, a demand function s id = 0d + di , and a market equilibrium condition d s i , where i and i are mutually independent i.i.d. random i = variables, both with a mean of zero. (a) Show that i and is are correlated. (b) Show that the OLS estimator of 1 is inconsistent. (c) How would you estimate 0 , 1 and 0 ? 4. Consider the instrumental variable regression model i = 0 + 1 i + i is correlated with i and i is an instrument. 2 i + i , where Suppose that data on i are not available and the model is estimated omitting i from the regression. (a) Suppose i and i are uncorrelated. Is the IV estimator consistent? (b) Suppose i and i are correlated. Is the IV estimator consistent? 5. In an instrumental variable regression model with one regressor, i , and one instrument, i , the regression of i onto i has 2 = 0 05 and = 100. Is i a strong instrument? ( Use the homoskedasticityonly formula for -statistic.) Would your answer change if 2 = 0 05 and = 500? (b)

Q



Q

u

Q

Q



 P

u

u

u

P

u









Y

 W

u

X

u



 X

Z

W

W

Z

W

Z

W

X

Z

n

X

Z

R

:

Hint:

Z

F

R

n

2

:

6. (a)

The two stage least squares estimate of demand for cigarettes function gave

d

ln (Q ) = 9:72 i

(1:53)

 (01 32) 08 ln ( :

Pi

);

n

= 48;

:

where is cigarette consumption (number of packs of cigarettes sold per capita), is the average real price per pack of cigarettes including all taxes and is sample size. The numbers in parentheses are heteroskedasticity-robust errors. The instrument for ln ( ) is , the portion of the tax on cigarettes arising from the general sales tax, in dollars per pack. How is the coe¢cient on ln ( ) usually referred to? If Paul buys 100 packs of cigarettes at the current price, what is his predicted consumption when price per pack decreases by 5%? (b) Is a valid instrument for ln ( )? Discuss. (c) Looking at the least squares regression estimate Qi

Pi

n

Pi

SalesT axi

Pi

SalesT axi

Pi

d

ln (P ) = 4:63 + 0:031S alesT ax i

do you think

(0:03)

SalesT axi

(0:005)

i;

R

2

= 0:47;

is a weak instrument for ln ( )? Pi

3...