Pub Econ Lecture 03 EmpericalTools

8/3/2019 Pub Econ Lecture 03 EmpericalTools

1/20

Public Finance

Dr. Katie Sauer

Cross-Sectional Regression Analysis

&

Difference-in-Difference Estimation


2/20

Data: March 2002 Current Population Survey

-unmarried women with a child youngerthan 19

n=8024

Variables:

TANF: total cash TANF benefits in previous

year (thousands $)

Hours: total hours of work in previous year

- weeks of work times usual hours

worked per week


3/20

Race: white, black, other

Age: age in years

Education: high school dropouts, high schoolgraduates w/ no college, some college,

college graduates

Urbanicity: central city, other urban, rural,unclear


4/20

Estimate a regression of the impact of welfare on hours of

work:

HOURSi = +TANFi + i

There is one observation for each mother, i.


5/20

HOURSi = +TANFi + i

is the constant term. It represents the estimated

number of hours worked if welfare benefits are zero.

is the slope coefficient. It represents the change in

hours worked per dollar of welfare benefits.

is the error term. It represents the difference for eachobservation between its actual value and its predicted

value.


6/20

TANF -107

(3.7)

Constant 1537

(10)

Rsquared 0.095

standard error in parenthesis

Regression Results: Effect of TANF on Hours Worked

Are these numbers statistically significant?

Divide the coefficient by the standard error. If you get anumber that is 2 or greater, then the results are

statistically significant.


7/20

TANF -107

(3.7)

Constant 1537

(10)

Rsquared 0.095



At a level of zero TANF benefits, the model predicts

that hours worked will be:

1537 hours

Each $1000 of TANF benefits will change the number

of hours worked by:

-107 hours


8/20

If a mother received $5000 in benefits, the model

predicts she would work how many hours?

She would work how many fewer hours?5 x -107 = -535

Ultimately, working for how many hours?

1537 - 535 = 1002 hours


9/20

Is the coefficient on TANF economically significant?


10/20

TANF -107

(3.7)

Constant 1537

(10)

Rsquared 0.095



The R2 is a measure of how well the statistical

regression is fitting the underlying data.

R2 = 1 means data are perfectly explained by

the model

R2 = 0.095 means 9.5% of the data are explained

by the model


11/20

Add the control variables to the regression.

HOURSi = +TANFi + CONTROLi + i


12/20

Statistically significant?TANF -107 -93

(3.7) (3.6)

White 181

(44)

Black 61

(47)

Dropout -756

(30)

HS grad -347

(25)

some college -232

(28)

age -9.3

(0.8)

central city -12

(30)

other urban 34

(29)rural -43

(31)

Constant 1537 2062

(10) (61)

Rsquared 0.095 0.183



When categorical variables

are included, always omit

one category from theregression.

All estimates are relative to

the excluded category.


13/20

TANF -107 -93

(3.7) (3.6)

White 181

(44)

Black 61

(47)

Dropout -756

(30)

HS grad -347

(25)

some college -232

(28)

age -9.3

(0.8)

central city -12

(30)

other urban 34

(29)rural -43

(31)

Constant 1537 2062

(10) (61)




$1000 of TANF benefitsresults in:

93 fewer hours worked

Whites are estimated to work181 hours more than:

other races

High School dropouts work756 hours less than:

college grads


14/20

TANF -107 -93

(3.7) (3.6)

White 181

(44)

Black 61

(47)

Dropout -756

(30)

HS grad -347

(25)

some college -232

(28)

age -9.3

(0.8)

central city -12

(30)

other urban 34

(29)rural -43

(31)

Constant 1537 2062

(10) (61)




High school graduates work347 fewer hours per year than:

college grads

Those with some college work232 fewer hours per year than:

college grads

Each year of age leads to:9.3 fewer hours of work


15/20

TANF -107 -93

(3.7) (3.6)

White 181

(44)

Black 61

(47)

Dropout -756

(30)

HS grad -347

(25)

some college -232

(28)

age -9.3

(0.8)

central city -12

(30)

other urban 34

(29)rural -43

(31)

Constant 1537 2062

(10) (61)




According to the R2, this

version of the model explains:18.3% of the data


16/20

Difference-in-Difference Estimation

Suppose we have a large sample of single mothers inArkansas and Louisiana for 1996 and 1998.

In 1997 Arkansas cut its benefit guarantee by 20% while

Louisianas benefits were unchanged.- AR is treatment

- LA is control

Other factors might have also influenced AR motherslabor supply decision (e.g. economic boom).

- likely to also have influenced mothers in LA


17/20

HoursAR, 1998 - Hours AR, 1996 = treatment effect + bias

HoursLA, 1998 - Hours LA, 1996 = bias

difference = treatment effect


18/20

1996 1998 Difference

Arkansas

Benefit Guarentee ($) 5000 4000 -1000

Hours of work per year 1000 1200 200

Louisiana

Benefit Guarentee ($) 5000 5000 0


A time series estimate for AR would be:

$1000 benefit reduction caused increased work

of 200 hours

4000-5000 / 5000 x 100 = -20%

1200-1000 / 1000 x 100 = 20%

elasticity = -1


19/20


Arkansas



Louisiana



But looking at LA we see that even though benefits werenot cut, the hours worked increased.

Some of the increase in hours worked in AR is probably

due to other factors than the cut in benefits.


20/20


Arkansas



Louisiana



Looking at the difference in hours worked in each of thestates, we can plausibly say that the cut in benefits led

women in AR to work:

200-50 = 150 more hours

1150 1000 / 1000 x 100 = 15%

elasticity = -0.75

Pub Econ Lecture 03 EmpericalTools

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