finalprojecteconc142

Luke Chen

Econ C142 Final Project

Table 1:

All female male

Ttest (female vs male)

mean se mean se mean se t pvalue

Educ8.7239

9 0.02472 9.1515 0.04287

8.49442

0.03006 12.5489 < 2.2e-16

Age36.404

7 0.05502 36.3151

0.09216

36.4528

0.06857

-29.8542 < 2.2e-16

Y1.5671

6 0.00327 1.43867

0.00521

1.63616

0.00407 -1.1991 0.2305

Va3.0715

4 0.0038 2.94475

0.00677

3.13963

0.00447

-24.0223 < 2.2e-16

Education female male Y female male

418.13

0119.64

4 quantile 1

39.6859

17.0939

621.01

1626.66

36 quantile 2

22.2731

26.4843

920.73

9524.11

34 quantile 3

19.7502

27.8125

1227.99

919.84

99 quantile 4

18.2909

28.6094

1612.11

979.729

05 total 100 100 100 100

The blue smoothed histogram looks somewhat like the red one shifted to the left.

It is clear from the smoothed histograms that the distribution for the blues, while having a range very like that of the distribution for the reds (around 1.6 to 4.5), is much more skewed to the right, while the distribution of the reds is much more skewed to the left. This is one way to show va for females tends to be lower than va for males.

Also, a more obvious statistic is : both the female wage and va means are lower than the male wage and va means.

Table 2:

Coefficients: constant female educ age^3 s1 1.636162 -0.197495 s2

0.7791 -0.2496 0.082720.00000273

2 s3

0.5115 0.085520.00000259

6 s4

0.7893 0.081020.00000280

7

a. Both coefficients are negative in S1 and S2. After education and age effects are considered in S2, the coefficient is more negative in the S2 model

b. Coefficients for education and age are similar between female and male, while those for male are slightly larger. Oaxaca decomposition is done as below. When using female beta, the mean difference contributes 0.056 (education), 0.002(age), beta difference contributes 0.04(education), 0.01(age). Sum of them and the difference between constants is equal to 0.197, which explains all the wage difference between male and female.

Mean and Coefficients:

wage educ_mean age^3_mean educ_coef age^3_coef c female 1.438668 9.151496 55695.5 0.08552 0.000002596 0.5115 male 1.636162 8.494422 56518.37 0.08102 0.000002807 0.7893 diff 0.197 -0.657074 822.87 -0.0045 0.000000211 0.2778

Oaxaca Decomposition:

educ age const

mean diff (x_b-x_a)*beta_a

coef diff x_b*(beta_b-beta_a) mean diff coef diff const diff total

deco female beta

-0.056192968 -0.038224899 0.002136171 0.011925376 0.2778 0.197

deco male beta

-0.053236135 -0.041181732 0.002309796 0.011751751 0.2778 0.197

The contribution of education is larger in absolute value than the contribution of the coefficient on it, but in an opposite sign of the total difference for both the female beta and male beta decompositions. The contribution of age is in the same direction (positive) as the contribution of the coefficient on it, and both are in the same direction as the final difference, but the absolute value of the age contribution is smaller than the absolute value of the contribution of the coefficient on it. This shows how education seems to contribute oppositely to the gender gap, while age difference contributes positively but the returns to age difference contribute more than the age difference itself.

Figure 2: Women and Men Plots for each of the 5 Education Levels (with regression lines)

Figure 2b) Plots of each of the 5 Education Levels for both Men and Women(blue for men, red for women)

For both male and female, the best choice of K is K=2.

Figure 3 - Mean Squared Errors for Different K Values

Figure 4A and B : Spline v Cubic Regressions

Table 3:

Coeffs:

c female educ age^3 va M1

0.77910 -0.24960 0.08272 0.0000027

M2

0.13990 -0.19550 0.07060 0.0000027 0.23690

M3 (male)

0.50660 0.07049 0.0000028 0.25880

M4(female)

0.39640 0.07151 0.0000025 0.20080

M1:

Y = -0.25 * female + 0.08 * educ + 0.0000027 * age^3 + 0.779

M2:

Y = -0.19 * female + 0.07 * educ + 0.00000027 * age^3 +0.24*va+ 0.139

Gender gap explained by women working in less productive employer:

0.34938 * (-0.19 + 0.25) = 0.0189Where 0.34938 is the mean of femaleTotal gender gap is 1.636-1.439=0.197

About 0.0189/0.197 = 9.6% is explained by VA

Define: ~β as the estimate from (1), β as the estimate from OLS. Since a (productivity factor) is positively related to wage y, i.e. a > 0, we have ~β>β

Therefore if more productive employers hire workers with higher productivity, the workers’ wages tend to be higher.


log wageeduc_mean

age^3_mean va_mean

educ_coef age^3_coef va_coef c

female

1.43866

8 9.151496 55695.5 2.944748 0.07151 2.49E-06 0.2008 0.05431 male

1.63616

2 8.494422 56518.37 3.139626 0.07049 2.82E-06 0.2588 0.06563 diff 0.197 -0.65707 822.87 0.194878 -0.00102 3.26E-07 0.058 0.01132


educ age va const


coef diff x_b*(beta_b-beta_a)

mean diff coef diff

mean diff coef diff

const diff total

deco female beta -0.04699 -0.00866

0.002048

0.018425

0.039132

0.182098

0.01132

0.197

deco male beta -0.04632 -0.00933

0.002316

0.018157

0.050434

0.170795

0.01132

0.197

After renormalization (subtracting the lowest value of VA)


log wage educ_mean age^3_mean va_mean educ_coef age^3_coef va_coef c female 1.438668 9.151496 55695.5 1.241117 0.07151000 0.00000249 0.20080000 0.39640000 male 1.636162 8.494422 56518.37 1.435995 0.07049000 0.00000282 0.25880000 0.50660000 diff 0.197 -0.657074 822.87 0.194878 -0.00102 3.26E-07 0.058 0.1102


educ age va const


coef diff x_b*(beta_b-beta_a) mean diff

coef diff

mean diff coef diff

const diff total

deco female beta -0.04699 -0.00866 0.002048

0.018425

0.039132

0.083288 0.1102 0.197

deco male beta -0.04632 -0.00933 0.002316

0.018157

0.050434

0.071985 0.1102 0.197

Table 4:

Coefficients:

c age age^2 female dva C1

0.258371

2 -0.0099603 0.0001025 0.0759453

C20.422600

0 0.0635200 -0.0007875 -0.1981000 0.0034580

C3 (male)0.276200

0 -0.0102200 0.0000993 0.0831200

C4(female)0.227200

0 -0.0096330 0.0001108 0.0621000

The coefficients on dva are indeed all positive.

The coefficients for dva are smaller (<0.1) compared with those for va in M2-M4 (>0.2).

The reason is that age is now negatively correlated with dy.

In both models M3 and M4, and models C3 and C4, the coefficients of va for women are smaller than those for men. In other words, even though women work in more productive firms, they are not likely to be paid the same as men. Women may work in less-paid jobs in the same firm, or receive lower salary for the same jobs.

Table 5:

va_previous va diff

women men women menwomen men

Q10.31388 0.2157 0.3469 0.1979

70.0330

2-

0.01773

Q20.2252 0.2633

20.2159

30.2447

2-

0.00928

-0.01859

Q30.24796 0.2507

60.2355

90.2813

1-

0.01237

0.030549

Q40.21296 0.2702

20.2015

8 0.276-

0.01138

0.005778

total 1 1 1 1 0 0

female male from to yl2 yl1 y yp1 yl2 yl1 y yp1

1 1 1.090181.09661

41.12507

71.14801

61.23042

51.23230

91.26972

31.29043

5

1 21.20107

51.20394

81.26198

71.29403

81.33349

41.32995

31.40003

21.42845

1

1 31.24805

11.25164

41.33248

61.35729

21.36298

21.35689

81.48636

81.52182

8

1 41.40351

71.40779

61.50730

91.54856

71.46838

11.46010

1 1.6251.65862

3

2 11.23535

81.24161

31.22686

91.24434

91.35510

11.35717

31.33932

71.36196

5

2 21.28071

91.30735

71.33806

11.36992

91.42894

11.43285

8 1.477141.49397

3

2 31.38250

1 1.37693 1.438081.45534

41.48321

51.49157

61.56388

61.59612

9

2 41.39452

51.40475

31.49381

11.52014

51.52464

6 1.529761.64534

81.67828

7

3 11.31651

51.34062

4 1.275211.30323

11.50454

61.50885

81.45681

71.46240

8

3 21.44741

4 1.448481.48400

11.53020

11.55141

11.55574

21.58218

21.61434

7

3 31.52172

91.50726

61.56762

11.55747

91.64572

21.64623

51.69957

31.71329

3

3 41.64459

71.66506

41.76400

71.78999

41.69404

11.70706

31.80547

21.84444

2

4 11.47464

81.49296

41.43655

61.45238

7 1.664671.67769

61.58318

61.61032

6

4 21.53662

7 1.545731.50803

71.54046

31.70081

21.71045

41.67279

51.69709

5

4 31.69258

41.71482

81.72946

71.75690

81.79522

51.80200

61.81722

51.84842

2

4 41.94395

11.96652

62.02591

92.05965

62.04960

12.06483

42.14593

12.17629

5

If employer productivity has a positive effect, the wage change from lower quantile to higher quantile should be positive, and negative in the other way. Check the change from quantile 1 to 4 for female, it is indeed positive (1.507309-407796), and the change from quantile 4 to 1 it is negative (1.436556 - 1.492964). The pattern for men is similar.

My analysis: If employer productivity has a positive causal effect on wages, the profiles for wage change should reflect a positive trend for workers who move to higher quantiles between different time intervals, and a negative trend for workers who move to lower quantiles between different time periods. We can check this by examining the mean differences between y and yl1 for females and males for those who moved from quantile 1 to 4 and 4 to 1 respectively. For females, this gives (1.507309-.407796) and (1.436556 - 1.492964). These indeed are positive and negative values.

Figure 5

Figure 6

By looking at Table 5 and Figure 5 and 6, we notice Moving from lower quantile to higher, wage increases. True for both men and women.

Wage changes are bigger for men. Change from 4->1 is different from 1->4, i.e. not symmetric. More men than women move from lower quantiles to the higher ones

We conclude that employer productivity is a factor for employee wage and male workers benefits more from moving from lower productivity employers to the higher ones.

My words: The data to tend to support that moving to higher productivity firm increases wages while moving to a lower productivity firm decreases wages, as evidenced by differences being positive and negative respectively for the two scenarios. This is true for both women and men. The figures also show the positive part of this relationship due to positive slopes (although not perfectly linear) for men and women who went through all the quantile increases (destination quantile 2, 3, 4 but not 1). However, the increase in wages for men due to moving to a higher productivity employer is higher than that for women, as suggested by comparing the slopes in the corresponding plots in Figures 5 and 6 (Figure 6 has smaller slopes), suggesting that women benefit less no matter what destination quantile from a quantile increase in employer productivity.

Table 6:


Wage wage (no va) educ_mean age^3_mean educ_coef age^3_coef c

female

1.438668 1.255799 9.151496 55695.5 0.08118 0.000002563 0.3701

male

1.636162 1.375197 8.494422 56518.37 0.07764 0.00000281 0.5569

diff 0.197494 0.119 -0.657074 822.87 -0.00354 0.000000247 0.1868

Decomposition

educ age const


coef diff x_b*(beta_b-beta_a) mean diff coef diff const diff total

deco female beta -0.05334

-0.030070254 0.00210902 0.013960037 0.1868 0.119

deco male beta -0.05102

-0.032396296 0.00231226 0.013756789 0.1868 0.119

VA contributions

va mean va coef va contribution

female 2.94474 0.0621000 0.182868851

8 0

male3.13962

60.0831200

0 0.260965713

male - female 0.078096862

Note 0.078096862 (gender gap of va) + 0.119457532 (gender gap without va) = 0.197494 (gender gap)

0.078096862/0. 197494 = 40%

Therefore about 40% of the gender gap is due to VA.

To decompose this into “due to different va means for male and female”, and “due to different returns to va for male and female”, we could hold the mean constant at the average of the 2 means, and then the coeff constant at the average of the 2 coeffs, and find the respective va contributions. Then difference them out, and divide those differences by the gender gap, which is .197494 to get the two respective percentages (first the coeff on va difference contribution and second the difference in mean va contribution).

Conclusion :

There is evidence that men and women are paid differently. Productivity of employer is a factor for a worker’s wage. Moving from lower productivity employers to higher productivity employers results in a wage

increase. Women benefit less from moving from lower productivity employers to the higher ones. This is

likely due to pay difference in the same employers. Less women move from less productive employers to the more productive ones. Productivity of employer is positively correlated to individual’s productivity.

finalprojecteconc142

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