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Class Notes Economies

By:   •  June 7, 2016  •  Essay  •  1,351 Words (6 Pages)  •  1,563 Views

Page 1 of 6

Class #3

  1. Discrimination.

Wage = α + πMale

Where

  • Wage = hourly wage earned by subjects
  • Male = 1: person is a male; 0: person is a female

Table 1.  Confounders (or omitted variables) that could bias estimate of π and lead to incorrect conclusions about gender discrimination:

Confounder

Sign of relation with

Sign of indirect effect (sign of b*sign of c)

If we don’t control for confounder, then π will be?

Wage

Gender (male)

[a]

[b]

[c]

[d]

[e]

/a/ Name of omitted variable

/b-c/ Put a + or a – sign under the column to indicate the hypothesize correlation between the omitted variable an either wage or gender.

/d/ This should include the product of the sign you put under columns b and c

/e/ If the overall indirect effect is +, then /e/ will be smaller; if the overall indirect effect is -, then /e/ will be larger.

Tasks:

  1. Fill in the table with the three most important confounders you think matter
  2. What important confounders did you exclude?
  3. Could you possibly control for all confounders? Why? Explain

Table 2: Gender discrimination in returns to human capital. Outcome is natural log of monetary earnings from sale of goods + wage labor, among Tsimane’ Indians, Bolivian Amazon, ≥16 years of age: Panel data 2002-2010.  Multivariate regressions are OLS with robust standard errors and clustering by subject

Explanatory variables (X)s:

Outcome variable: natural logarithm of monetary earnings in previous two weeks

[a]

[b]

[c]

[d]

[e]

[f]

[g]

[h]

[i]

Male

1.80

1.78

1.45

1.30

1.10

1.02

1.02

1.02

1.57

Confounders or controls intentionally included? (yes, no)

Education

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Height

No

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Spanish

No

No

No

Yes

Yes

Yes

Yes

Yes

Yes

Alcohol

No

No

No

No

Yes

Yes

Yes

Yes

Yes

Age

No

No

No

No

No

Yes

Yes

Yes

Yes

Experience

No

No

No

No

No

No

Yes

Yes

Yes

Spanish

No

No

No

No

No

No

No

Yes

Yes

Survey year

No

No

No

No

No

No

No

Yes

Yes

Community FE*

No

No

No

No

No

No

No

No

Yes

Share of variation explained by all the X’s in any one column:

R squared

0.143

0.149

0.151

0.170

0.163

0.166

0.166

0.173

0.239

Male = 1: person is a male; 0: person is a female

Education=maximum years of education completed

Height = standing height in cm

Math=score 0-4 with 1 point for each of the four basic arithmetic operations

Writing and literacy coded as: 0=can’t, 1=with difficulty, 2=well

Alcohol: # of times person consumed alcohol in last week

Spanish: 0=no ability, 1=some ability, 2=fluent

[*] Community fixed effect [FE] = all variables at the community level that remain fixed during the study period (e.g., distance, altitude, # of schools)

Tasks:

  1. What is the male/female earnings differential without controlling for any variables? [Hint: The x, ‘male’, is a raw or linear variable]
  1. Is the gap large? Explain
  2. How much of the earnings variation is explained by gender?
  3. Why is the estimate unconvincing?
  1. What is the median differential in earnings based on the range of estimates in the table?
  2.  Based on the first three control variables (education, height, Spanish), does the trend in the male/female earnings gap conform to what you might have expected? Explain making explicit reference to indirect effects.
  3. What is the female/male earnings differential if one controlled only for education, Spanish, and age?
  4. Compared to the estimate in column [a],
  1. How much of the variation in earnings can be explained by all the explanatory variables in column [i]? [Hint: comment on levels and on changes in the share of variation that is explained]
  2. What explains the large difference in the share of the variation explained by the Xs of column [a] vs column [i]?
  1. K-M argue that community attributes (e.g., good schools) matter in the accumulation of human capital and earnings.  Can you find support for their thesis in the table above?
  2. Does the information in Table 2 support the idea that there is gender discrimination in the labor market?
  3. Assume that the estimates on the female/male earnings differential referred to a large organization that had multiple offices in the USA.  What firm-level policies would you implement to narrow the differential? Be very specific.

Common measures.

A.  Coefficient of variation (CV)=SD/mean

Deviation

Square deviation

Person

income

from mean

from mean

A

B

C=B^2

1

12

-54

2873

2

23

-43

1815

3

33

-33

1063

4

36

-30

876

5

52

-14

185

6

56

-10

92

7

62

-4

13

8

63

-3

7

9

85

19

376

10

234

168

28359

Total

656

35658

<=Total sum deviation

from mean squared (TSDM)

Mean (person 1…10)

65.6

n=# obs-1

9

SD=(TSDM/n)^0.5     (long hand)

63

SD=Excel formula (=stdev(b51:b60)

63

CV=

0.96


B.  Standard deviation of log (X) (not useful if X has many zeros or negative numbers). Logs normalize a distribution (Figure 1).

Person

income

Natural log

1

12

2.48

2

23

3.14

3

33

3.50

4

36

3.58

5

52

3.95

6

56

4.03

7

62

4.13

8

63

4.14

9

85

4.44

10

234

5.46

SD(log income)

0.80

C.  Kuznets ratio: ratio of top 10(20)%/bottom 10(20)%

Person

income

Share of total

Cumulative

Perfect equality

A=Area above B

1

12

1.829%

1.829%

10.00%

8.171%

<=Bottom 20%

2

23

3.506%

5.335%

20.00%

14.665%

<=Bottom 20%

3

33

5.030%

10.366%

30.00%

19.634%

4

36

5.488%

15.854%

40.00%

24.146%

5

52

7.927%

23.780%

50.00%

26.220%

6

56

8.537%

32.317%

60.00%

27.683%

7

62

9.451%

41.768%

70.00%

28.232%

8

63

9.604%

51.372%

80.00%

28.628%

<=Top 20%

9

85

12.957%

64.329%

90.00%

25.671%

<=Top 20%

10

234

35.671%

100.000%

100.00%

0.000%

Total

656

100.000%

Share of income of:

Kuznets ratio

Bottom 20%

5.34%

<=(5.34=1.82+3.50)

Kuznets ratio=48/5=9.6

Top 20%

48.63%

<=(48.6=12.9+35.6)

Examples: Sweeden=2.78; Denmark=2.86, N. Zealand=3.46, UK=4.07; Japan=4.17; USA=6.42

...

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