problem set 3

Applied Econometrics PROBLEM SET 3

Submitted by: Shahram Azhar

Part 1: Berndt Chapter 5

Question 1:

A) We find the arithmetic mean and the standard deviation of LNWAGE using the cps1978 data.

Variable | Obs Mean Std. Dev. Min Max

-------------+--------------------------------------------------------

lnwage | 550 1.681002 .490157 -.47 3.3514

The mean value of LNWAGE is equal to 1.681002 and the standard deviation is 0.49. The geometric mean is equal to the exponent of the mean of LNWAGE and is therefore equal to 5.37 dollars per hour. If a work year consists of 2000 hours then the implied geometric mean of annual wages is 10,740 dollars. Next, we exponentiate LNWAGE and find its mean, which comes out to be 6.062 dollars. This arithmetic mean is slightly higher than the geometric mean calculated in the previous step.

Last, we describe the mean and standard deviation of schooling and years of potential experience in the table below:


-------------+--------------------------------------------------------

Schooling | 550 12.53636 2.772087 1 18

Experience| 550 18.71818 13.34653 1 55

The mean value of schooling is 12.5 years of schooling and the mean for years potential experience is 18.7 labor market years of experience. The standard deviation is 2.7 and 13.3 respectively.

B) The mean and standard deviation of NONWH, HISP and FE, which are the

three dummies for nonwhite, Hispanic and female workers respectively are given in the table below:


-------------+--------------------------------------------------------

nonwh | 550 .1036364 .3050657 0 1

hisp | 550 .0654545 .2475513 0 1

fe | 550 .3763636 .484914 0 1

Since there are 550 observations in the 1978 sample therefore, multiplying the mean by the total number of observations for each category, we conclude that there are 57 Non White workers, 36 Hispanic workers and 207 Female workers in the sample. Therefore, 38% of the sample is composed of data for female workers. The following table compares the proportion of females, Hispanics and NonWhite people in the 1978 CPS with the 1985 CPS:

% in sample 1978 % in sample 1985Female 38% 46%Hispanic 10% 5%Non White 7% 13%

As we can see above, the proportion of Females has arisen by 8 percentage points in the new CPS while the percentage of Hispanics has fallen from 10 percent of the total sample in 1978 to only 5% in the new sample. The proportion of non white people has also increased from 7 to 13 percent in the more recent CPS.

C) We find the mean and standard deviation for the years of schooling (ed)

for males and females separately in the following table:

Mean and SD of ED by Sex (1978)Sex Mean Standard DeviationFemales 12.76 2.22Males 12.39 3.05

The mean years of schooling for females and males are 12.7 and 12.4 years respectively and the standard deviation is 2.2 and 3.1 respectively.

Next, the geometric mean wage rates are calculated by exponentiating the respective arithmetic means of LNWAGE for males and females. The respective arithmetic means of LNWAGE for males and females and the corresponding value of the geometric mean wage rate per hour are reproduced below:

Mean and SD of LNWAGE by Sex Sex Mean Standard Deviation Geometric MeanFemales 1.46 0.45 4.31Males 1.81 0.47 6.11

Table: Mean and SD of LNWAGE and Geometric Mean by Sex

The table above reports the mean and standard deviation of LNWAGE by sex and also reports the value of the geometric mean wage rate per hour for each sex. The geometric mean wage rate per hour is lower for females as compared to males (4.31 vs. 6.11 dollars per hour respectively) while the standard deviation is higher for males.

Next, we find the racial (White/Non white/Hispanic/) specificities of education by tabulating a table that summarizes education (ed) by sorting racial dummies. The table is reproduced below:

Mean and SD of ED by RaceRace Mean Standard DeviationWhites 12.63 2.67NonWhites 11.71 3.43Hispanic 10.3 3.65Non Hispanic 12.69 2.63

Table: Mean and SD of education (years) by Race.

It is important to remember that a large proportion of Non Hispanic people in the sample are White while a large proportion of non White people in the sample are Black people. Therefore, the mean and standard deviation of Whites and Non Hispanic people in the table above are similar. The mean years of schooling is 12.63 years for Whites and the standard deviation is 2.67, while the means years of schooling for Hispanic people is the lowest (10.3) in the racial subgroup and also has the highest standard deviation (3.65).

Next, we want to analyze the arithmetic and geometric mean wages rates per hour for each race. This can be done by finding the arithmetic mean of LNWAGE for each race and then exponentiating that mean value to obtain the geometric mean wage rate for each race:

Mean and SD of LNWAGE by Race Geometric MeanRace Mean Standard Deviation Whites 1.7 0.49 5.47NonWhites 1.51 0.5 4.53Hispanic 1.52 0.37 4.57Non Hispanic 1.69 0.49 5.42

Table:Mean and SD of LNWAGE and Geometric mean wage rate per hour by Race 1978

The table above reports the geometric mean and standard deviation of the hourly wage rates for each race. The highest geometric mean wage rate is for Whites (5.47 dollars/hour) with the

lowest standard deviation (0.49), while the lowest geometric mean wage rate per hour is for non White people (4.53 dollars/hour) with the highest standard deviation (0.50). Hispanics have the second highest geometric mean wages and the lowest within-group standard deviation.

D) Now, we repeat all the steps presented in A) to C) for 1985:

Part A for 1985:

Variable OBS Mean SD

LNWAGE 534 2.059181 .5277335Table: Mean and SD of LNWAGE for 1985

We find the arithmetic mean and the standard deviation of LNWAGE using the cps1985 data. The mean value of LNWAGE is equal to 2.05 and the standard deviation is 0.52. The geometric mean is equal to the exponent of the mean of LNWAGE and is therefore equal to 7.76 dollars per hour. If a work year consists of 2000 hours then the implied geometric mean of annual wages is 15,520 dollars per year. Next, we exponentiate LNWAGE and find its mean, which comes out to be 9.02 dollars per hour. This arithmetic mean is slightly higher than the geometric mean calculated in the previous step.

Last, we describe the mean and standard deviation of schooling and years of potential experience in the table below:


-------------+--------------------------------------------------------

ed | 534 13.01873 2.615373 2 18

ex | 534 17.8221 12.37971 0 55

The mean value of schooling is 13 years of schooling and the mean for years potential experience is 17.7 labor market years of experience. As compared to 78, the mean years of education have increased slightly while the years of experience variable has slightly fallen indicating perhaps an entry of new and relatively inexperienced workers in the workforce. The standard deviation is 2.61 and 12.3 respectively for years of education and experience.

Part B for 1985:

The mean and standard deviation of NONWH, HISP and FE, which are the three dummies for nonwhite, Hispanic and female workers respectively are given in the table below:


-------------+--------------------------------------------------------

nonwh | 534 .1254682 .3315596 0 1

hisp | 534 .0505618 .2193066 0 1

fe | 534 .4588015 .498767 0 1

Since there are 534 observations in the 1985 sample therefore, multiplying the mean by the total number of observations for each category, we conclude that there are 67 Non White workers, 27 Hispanic workers and 245 Female workers in the sample. Therefore, 45% of the sample is composed of data for female workers.

PART C FOR 1985

We find the mean and standard deviation for the years of schooling (ed) for males and females separately in the following table:

Mean and SD of ED by SexSex Mean Standard DeviationFemales 13.02 2.42Males 13.01 2.7

The mean years of education have increased and become more equal since the last CPS1978 and the standard deviations have also become more similar for this data set.

Next, the geometric mean wage rates are calculated by exponentiating the respective arithmetic means of LNWAGE for males and females. The respective arithmetic means of LNWAGE for males and females and the corresponding value of the geometric mean wage rate per hour for 1985 are reproduced below:

Mean and SD of LNWAGE by Sex Sex Mean Standard Deviation Geometric MeanFemales 1.93 0.49 6.89Males 2.16 0.53 8.67

The arithmetic mean of LNWAGE is 1.93 and 2.16 for females and males respectively while the standard deviation is 0.49 and 0.53 respectively. The geometric mean hourly wage rate differential between males and females is now 1.78 dollars per hour whereas in 1978 the same differential was equal to 1.80 dollars per hour. The geometric mean wages per hour have risen by 2.58 dollars per hour for females and by 2.56 dollars per hour for males from 1978 to 1985.

Next, we find the racial (White/Non white/Hispanic/) specificities of education by tabulating a table that summarizes education (ed) by sorting racial dummies. The table is reproduced below:

Mean and SD of ED by RaceRace Mean Standard DeviationWhites 13.07 2.61NonWhites 12.64 2.6Hispanic 11.51 4.05Non Hispanic 13.09 2.49

The mean years of schooling is 13.07 years for Whites and the standard deviation is 2.61, and while the means years of schooling for Hispanic people has arisen since 1978 it is still the lowest (11.51) in the racial subgroup and its standard deviation is not only the highest but it has also increased since 1978 (4.05).

Next, we want to analyze the arithmetic and geometric mean wages rates per hour for each race. This can be done by finding the arithmetic mean of LNWAGE for each race and then exponentiating that mean value to obtain the geometric mean wage rate for each race:

Mean and SD of LNWAGE by Race Geometric MeanRace Mean Standard Deviation Whites 2.07 0.53 7.92NonWhites 1.96 0.49 7.10Hispanic 1.82 0.53 6.17Non Hispanic 2.07 0.53 7.92

Table:Mean and SD of LNWAGE and Geometric mean wage rate per hour by Race 1985

The table above reports the geometric mean and standard deviation of the hourly wage rates for each race. The highest geometric mean wage rate is for Whites (7.92 dollars/hour), while the lowest geometric mean wage rate per hour is for Hispanic people (6.17dollars/hour). Hispanics in the new data set have the lowest geometric mean wages.

Calculating the Geometric Mean of Real Wages in 1978 and 1985

The geometric mean of real wages can be calculated by discounting the respective nominal geometric mean of real wages by the price deflator. In 1978 prices, the geometric mean of real

wages is compared in the table below for the entire sample (1), for each gender (2), and for each Race (3).

ENTIRE SAMPLE

By Gender By Race

YearMale Female

Hispanic

White Non White

1978 5.37 6.11 4.31 4.57 5.47 4.531985 4.71 5.26 4.18 3.74 4.80 4.31

Real Change (%) -12%

-14% -3% -18% -12% -5%

Table: Geometric Real Mean of Wages using 1978 as Base Year and Deflating 1985

The table above displays the geometric real mean of wages for the years 1978 and 1985. The geometric real mean of wages has fallen for all categories based on 1978 prices. The value has fallen by 12% for the entire sample. However, the greatest decline has been seen for Hispanics, for whom the value fell by 18% from 1978 to 1985. The second greatest decline in the geometric real mean of wages was for males, who saw a 14% decrease in the geometric real mean of wages.

Comparing Years of Schooling between 1978 and 1985 by Gender and Race

The table below compares the years of schooling for the two years by each gender and race:

By Gender By Race

Year Male FemaleHispanic

White

Non White

1978 12.39 12.76 10.3 12.63 11.711985 13.01 13.02 11.51 13.07 12.64

Change (%) 5% 2% 12% 3% 8%Table: Years of Education by Gender and Race in 1978 vs. 1985

There has been an increase in the mean years of schooling in all racial and gender categories in the 7 years. However, the greatest increase has been for Hispanics (12 percent), followed by Non white workers (8 percent).

Implications for Human Capital Theory:

Human Capital Theory suggests that wages are an increasing function of investments in human capital, for example, schooling. An empirical confirmation of this theory would rest on some degree of association between additional years of schooling and rising wages. At the outset, however, it must be borne in mind that the period itself represents a general decline in real wages for all groups, albeit in different proportions. As a result, a comparison of the relative movement of years of schooling and percentage change in real wages must take this declining/recessionary environment into focus.

An analysis of the last two tables does not point towards a confirmation of the theory. For example, the mean years of schooling was highest between the two periods for Hispanics; the same group that saw the largest percentage fall in the geometric mean of real wages during the same period. Similarly, while the mean years of schooling increased by approximately 5% for males, the geometric mean of their real wages decreased by 14%. Put simply, during the time period, an average increase in years of schooling has not been associated with an increase in wages; on the contrary, the geometric mean of real wages has fallen across all groups. In addition, even if we take into account the recessionary nature of the time period under consideration, we should expect, at the very least that the percentage decrease in real wages over time would be lower for the groups that invested more in education. However, the patterns above show evidence to the contrary for even such a relaxed interpretation of the human capital theory.

Part E:

Choosing the 1978 data set we calculate the mean and sd of LNWAGE for the entire data set. The mean value of LNWAGE is equal to 1.681002 and the standard deviation is 0.49. We want to divide the entire data set into six distinct groups using the mean value of w and the sd. The spread of LNWAGES around the mean, w, can be gauged by analyzing the number of observations below and above a certain number of standard deviations. In our case, w=1.68 and sd=0.49. Therefore, the relevant six categories are:

Category i) Wi <w-2sd = Wi<0.7: All people who are strictly 2 standard deviations below the mean

Category ii) w-2sd <=Wi<w-sd, or 0.7<Wi<1.19: All people who are between 2 sd below mean and one sd below mean

Category iii) w-sd<=Wi<w, or 1.19<Wi<1.68: All people who are between 1 sd below mean and the mean

Category iv)w<=Wi<w+sd, or 1.68<Wi<2.17: All people who are between the mean and 1 sd above the mean

Category v) w+sd<=Wi<w+2sd, or 2.17<Wi<2. 66: All people who are between 1 sd above the mean and 2 sd above the mean

Category vi) Wi>w+2sd, or Wi>2. 66: All people who are more than 2 sd above the mean

We wish to find the number of people in each of the six categories and the proportion of the total sample that they represent in order to comment on the degree of normality in the distribution. Using STATA we define a categorical variable CATG which takes a value of 1 to 6 depending on which of the aforementioned categories it belongs to. Then, using the summarize command we can find the number of observations in each category. The table below shows the number of people in every category and the proportion of the total sample that they represent:

Category

Number of Observations

Percentage of Sample

1 9 2%2 79 14%3 195 35%4 193 35%5 63 11%6 11 2%

Table: Percentage of Sample by Category

The graph below shows a graphical illustration of the spread:

1 2 3 4 5 60

50

100

150

200

250

300



According to the empirical rule, we should expect 68% of the sample to be within one standard deviation and about 95% to lie within two standard deviations for the distribution to be classified as normal. In our case, people within one standard deviation of the mean can be found by summing the percentages of the sample in category 3, which represents people one standard deviation below the mean and category 4 which represents people between the mean and one standard deviation above the mean. In total this represents about 70% of the total sample. Further, about 95% of the observations lie within two standard deviations (the sum of categories 2,3, 4, and 5. Therefore, it is fair to say that a normal distribution is an appropriate predictor for the data on LNWAGES.

We can confirm this with a Chi Square goodness of fit test for normality using STATA, which can be used to test whether each of the categories represent proportions that are similar to a normal distribution. For a normal distribution, we should expect 2.2%, 13.6%, 34.1%, 34.1%, 13.6%, and 2.2% of the sample to be in each of the aforementioned six categories respectively. We test this using STATA csconfig command and get the following result:

CATG expperc expfreq obsfreq |

|------------------------------------|

| 1 2.2 12.1 9 |

| 2 13.6 74.8 79 |

| 3 34.1 187.55 195 |

| 4 34.1 187.55 193 |

| 5 13.6 74.8 63 |

|------------------------------------|

| 6 2.2 12.1 11 |

chisq(5) is 3.45, p = .6316

The p value is 0.6, which implies that we cannot reject the null hypothesis that the LNWAGE distribution is the same as a normal distribution or in other words we find evidence that wages are log normally distributed.

Finally, we generate a new variable WAGE by exponentiating LNWAGE for each individual. We now test the normality of this distribution by similarly categorizing people in each of the six categories. The mean and standard deviation of the variable wage are 6.062766 and 3.257956 respectively. Using the aforementioned normal distribution categorization of expected observations around the mean we place individuals in each of the assigned categories using STATA.

Category


Percentage of Sample

1 0 0%2 45 8%3 278 51%4 164 30%5 45 8%6 18 3%

Table: No in each category using Wages.

1 2 3 4 5 60

50

100

150

200

250

300



Therefore, it is clear that the distribution of WAGES does not follow a normal distribution. This can be confirmed by the following chi square goodness of fit test result by STATA:

CATZ expperc expfreq obsfreq |

|------------------------------------|

| 2 15.8 86.9 45 |

| 3 34.1 187.55 278 |

| 4 34.1 187.55 164 |

| 5 13.6 74.8 45 |

| 6 2.2 12.1 18 |

+------------------------------------+

chisq(4) is 81.53, p = 0

The p value is 0 therefore we reject the hypothesis that the distribution of WAGES is normally distributed.

***************************************END OF BERNDT QUESTION 1*************************************

Question 5

A) Using the 1978 data, we summarize the means of all the variables in the table below.

Variable MeanLNWAGE

1.681002

FE0.37636

4

UNION0.30545

5NONWH

0.103636

HISP0.06545

5

ED12.5363

6

EX18.7181

8

EXSQ528.176

4

Next, we regress LNWAGE on the specified variables to obtain the table below. It is clear from the table that the coefficient on the UNION membership dummy is 0.207 and it is highly significant.

(1)Lnwage

Fe -0.306***

(0.0344)

Union 0.207***

(0.0369)

Nonwh -0.157**

(0.0550)

Hisp -0.0271(0.0688)

Ed 0.0746***

(0.0067)

Ex 0.0262***

(0.0047)

Exsq -0.000308**

(0.0001)

_cons 0.488***

(0.0983)N 550adj. R2 0.385

Standard errors in parentheses* p < 0.05, ** p < 0.01, *** p < 0.001

The Log Linear formulation of the model suggests that the wage differential between unionized and non unionized workers is approximately 21%. Our results confirm the hypothesized positive correlations between union and non union wage differentials with LNWAGES as outlined in section 5.3D of Berndt. The equation however, cannot give us an estimate of whether or not union workers earn premium wages or not. The direction of causality cannot be established in the aforementioned regression. It is not clear whether LNWAGES are higher because of union membership or whether high wage industries are more prone to unionization.

B) The table below tabulates, in a single table, the means and standard deviations of

LNWAGES, Sex (0 = Male and 1 = Female), Non White (0= White and 1= Non White), Hispanic, Years of Education, Experience and Experience squared by the unionized or non unionized status of workers. The final row shows the difference between the means and standard deviation for each category.

LNWAGES SexNon White Hispanic Education Exp Expsq

Mean SDMean SD Mean SD Mean SD Mean SD Mean SD Mean SD

Unionized 1.86 0.43 0.29 0.453 0.13 0. 0.042 0.2 12 2.53 22.5 13.3 683.6 660.3

3

Non Unionized 1.6 0.49 0.42 0.494 0.090.3 0.076 0.27 12.8 2.85 17 13 459.8 597.8

Difference 0.26 -0.1 -0.13 -0.04 0.04 0 -0.03-

0.06 -0.74-

0.32 5.51 0.23 223.7 62.51

Table 5B: Means and SD of all the variables based on union status.

It is clear from the table above that mean LNWAGES are approximately 0.26 units higher for unionized workers as compared to non unionized workers. Further, the distribution of LNWAGES is also more equal for unionized workers, as can be seen from the fact that standard deviation is lower. The proximity of the mean for a dummy variable can be used to assess whether or not it represents a higher or lower percentage of one or the other category for every workers union status. For example, a larger percentage of unionized workers are males, as can be seen from the fact that the mean is closer to 0. Similarly, it can be observed that an overwhelmingly large proportion of unionized workers are White. Hispanics are very unlikely to be unionized. An interesting fact is that while union and non union members are approximately equally well educated there is a substantial difference in their years of experience. The mean value of years of experience for unionized workers is 5.51 years higher than non unionized workers.

C) We regress LNWAGE on all the other variables separately for unionized vs. non unionized workers and get the following results:

(1) (2)Lnwage Lnwage

Fe -0.224** -0.326***

(0.0685) (0.0398)

Nonwh -0.233* -0.110(0.0918) (0.0689)

Hisp 0.0742 -0.0444(0.1562) (0.0762)

Ed 0.0399** 0.0852***

(0.0138) (0.0076)

Ex 0.0314** 0.0254***

(0.0099) (0.0054)

Exsq -0.000453* -0.000284*

(0.0002) (0.0001)

_cons 1.076*** 0.361**

(0.2002) (0.1117)N 168 382adj. R2 0.172 0.414


The regressions in column 1 and 2 refer to separate regressions for unionized members and non unionized workers respectively with LNWAGES as the dependent variable in both cases. It can be seen that wages are lower for females than males for both, unionized, and non unionized workers. However, while the wages for unionized female workers are 22.4% lower than their male unionized counterparts, the wages for non unionized females are 33% lower than their male non unionized co-workers. Non White unionized workers typically receive 23% lower wages than White workers. The coefficient on the Non White dummy is lower but not significant for non unionized workers (column 2). The coefficient on the Hispanic dummy is not significant in either case. Finally, the returns to education (one more year of schooling) are also different across unionized and non unionized workers. An additional year of schooling increases the wages of unionized workers by 4% and by 8% for nonunionized workers. The effects of education on log earnings are smaller in the union sector owing to effects of the seniority system presented by Berndt in his section on unionized vs. non unionized workers wage differentials.

Comparing estimates of age-earnings profile for union and nonunion workers Now, we compare the age earnings profile for union and nonunion workers using the formula described in Berndt equation 5.11. First, we calculate X* which is the value of experience that maximizes lnwages for each case (unionized and nonunionized). Plugging the coefficient values we get:

UNION:

X* = -(0.0314)/2x (-0.000453)=34

Non Union:

X* = (0.0254)/2x (0.000284)= 44

We know that X = Age –Edu -6. Using this formula and the value of experience that maximizes lnWAGES, X*, in each case we can calculate the age as:

Union case:Age= 34+12+6=52, assuming a person with 12 years of schooling in each case.

Nonunion case: 44+12+6=62

It is clear therefore that the age earnings profile is flatter for union workers than nonunion workers for any given value of education. We could graph these two equations and would find that the profile is indeed flatter for unionized workers than nonunionized workers. The evidence supports the claim made by Lewis(1986).

D) We now conduct a Chow test to check whether the coefficients estimated using separate regressions for unionized and non unionized workers are similar. To do this, in the first step we run a constrained regression of LNWAGE on the other variables without the Union Dummy. This pooled regression constrains the slope coefficients to be the same irrespective of union status and is in this sense a constrained regression. Next, we run two separate regressions for Union and Non Union workers. Extracting the squared residuals from these three regressions we can calculate the Chow statistic. The squared residuals for the unconstrained regressions are 24.8 and 53.2 for unionized and non unionized workers respectively. The squared residual for the constrained (pooled) regression is equal to 84.8. The value of k is 7 in our case since there are six independent variables and a constant. Thus, the number of parameters being tested is k=7. The number of observations in the two separate regressions is N1= 382 and N2=168 respectively. Plugging these values in the Chow statistic formula we get a Chow statistic value of F= 6.67. The null hypothesis for the Chow test is the equality of the coefficients across the three regressions. Since the

Chow statistic follows an F distribution with and degrees of freedom our statistic is significant at the 1% level. We therefore reject the null hypothesis and conclude that the coefficients are different across the three regressions.

E) We replicate Bloch and Kuskin (1978) in three steps. The goal is to differentiate between the wage differential that is associated with union membership from the wage differential that is associated with other variables. To do this, first, we calculate the difference in mean LNWAGES between unionized and non unionized workers. Next, we substract the sample means for nonunion workers from the sample means of union workers for each of the independent variables. The first two steps can be calculated using Table 5B below. Then, we weight each of these sample mean differences by multiplying them by their estimated parameters from the unconstrained regressions and then subtract the sum of these weighted differences in the regressors from the LNWAGE difference.

LNWAG

ES Sex

Non White

Hispanic

Education Exp Expsq

MeanMean

Mean Mean Mean

Mean Mean

SD

Unionized1.86313

750.285

70.13

10.0416

7 12.0222.54

8683.559

52

Non Unionized 1.60090

050.416

20.09

20.0759

2 12.7617.03

4459.840

31

Difference0.26223

7-

0.1310.03

9-

0.0342 -0.745.513

6223.719

21

Weighted Difference

0.0292 -0.01

-0.0025 -0.03

0.1731

-0.10134

5Parameter estimate -0.22

-0.23

0.0742 0.04

0.031

-0.00045

Step 1: The difference in mean LNWAGES between unionized and nonunionized workers is equal to 0.26 (from table above)Step 2: The differences in the sample means for each of the independent variables are reported in the last row of the table above. Step 3: We weight these differences in step 2 by the parameter estimates calculated above for the regression with unionized workers only. These are found by multiplying the mean difference for each parameter by its estimate. The weighted mean difference is reported in row 4 above.Step 4:We subtract the sum of these weighted differences (found in step 3) from the

difference in mean LNWAGES found in step 1. Thus: 0.26 –(0.0292-0.01-0.03-0.0025+0.1731-0.1013) =0.2023. Step 5: Exponentiating this difference (value found in step 4) gives us 1.224 dollars per hour. The wage differential between unionized and nonunionized workers is approximately 22%. This represents the wage differential between union and non union members purely due to union membership since it subtracts the estimator weighted effect of other variables such as gender, race, education and experience from the difference in LNWAGES before exponentiation. The total mean difference in LNWAGES for union and nonunion members is equal to 0.26 . The proportion of this mean difference that is attributable to nonunion variables, such as fe, ed, exp etc. is 0.06, or 23%. Individually, 11% of this difference in LNWAGES is caused by FE or the sex dummy; it must be borne in mind that females are more densely represented in the nonunionized workforce so this relative over abundance of females in the nonunionized workforce propels mean LNWAGES down by 11% on its own accord simply due to gender discriminatory labor market distortions. The percentage effect on LNWAGES caused by racial specificities such as NONWHITE or Hispanic is miniscule, hovering around 3% and 1% respectively. The percentage effect of experience on LNWAGES is the highest and equal to 66.5% of the total differential in LNWAGES between union and nonunion members. It was noted earlier that the mean years of experience is much higher for unionized workers as opposed to non unionized workers. Finally, the impact of education as a proportion of the difference in LNWAGES is equal to 11.5%. The effect of experience squared is to bring down LNWAGES by approximately 38% for unionized members.

Therefore, the most important worker characteristic that explains the difference in LNWAGES between union and nonunion workers is years of experience. The difference in LNWAGES using a dummy variable approach pointed towards an approximately 1.23 dollar per hour differential (found in part A) between union and nonunion workers whereas the Bloch and Kuskin method points towards a slightly lower, 1.22 dollar per hour wage differential. The results are therefore very similar.

F) For this part we use exactly the same method as above but we use the weighting parameters from the nonunion regression. The relevant table with the new weighted differences (weighted using nonunion regression parameters) is reproduced below:

LNWAGE

S SexNon White

Hispanic

Education Exp Expsq

Mean Mean Mean Mean Mean Mean Mean

Unionized1.863137

50.2857

10.1309

50.0416

7 12.023822.54

8683.5595

2

Non Unionized 1.600900

50.4162

30.0916

20.0759

2 12.761817.03

4459.8403

1

Difference 0.262237-

0.13050.0393

3 -0.0342 -0.737975.513

6223.7192

1

Weighted Difference

0.04255

-0.0043

30.0015

2 -0.06288 0.14-

0.063536 Parameter estimate

(nonunion) -0.326 -0.11 -0.044 0.0852 0.025

-0.00028

Table: Weighted difference found using parameter estimates from the nonunion only regression.

We subtract the mean difference in LNWAGES between unionized and nonunionized workers from the sum of the weighted differences of all the other variables. This gives us a value of 0.19. Exponentiating this value gives us a value of 1.23. This value implies a wage differential of approximately 23 percent.

Comparing the three methods:

The dummy variable method, the weighting by unionized parameters method and the weighting by nonunionized parameters point towards very similar wage differentials between unionized and nonunionized workers. The dummy variable method approximates this difference as 21%. The latter two methods posit a difference of 22% and 21% respectively. While the differential impact of union membership is relatively the same according to the three methods I prefer method 2 and 3 since it weights the mean differences by parameter estimates calculated using the unconstrained regressions. This result provides a more robust theoretical argument in the sense that the case for unionization can be more strongly put forward by decomposing the effect of union membership into its component parts. In other words, it extracts the difference that is associated with gender and racial characteristics.

The merit of the first model (Dummy model) is that it is much simpler to execute and given that it posits a very similar result as models 2 and 3, it is perhaps preferable purely on grounds of simplicity.

G) Now, we repeat all the steps from a) to f) for the 1985 data set.

Part A for 85 data set: Report Means for Each Variable

We generate the means for each variable for the new data set. The table below gives the means for each of the specified variables.

Variable MeanLNWAGE 2.05FE 0.46UNION 0.18NONWH 0.13HISP 0.05ED 13.01EX 17.8EXSQ 470.6

Next , we run a regression of LNWAGE on each of the variables to get the following table:

(1)Lnwage

Fe -0.232***

(0.0386)

Union 0.212***

(0.0505)

Nonwh -0.125*

(0.0577)

Hisp -0.0807(0.0878)

Ed 0.0888***

(0.0080)

Ex 0.0345***

(0.0054)

Exsq -0.000527***

(0.0001)

_cons 0.625***

(0.1204)N 534

adj. R2 0.315

The coefficient on UNION is 0.212, which implies that the differential between the wages of unionized and non unionized workers is approximately 21%.

Part B for 85:We can find the mean values by UNION status for each of the variables including LNWAGE. The following table reports these values along with their difference in the last row :

LNWAGES SexNon White

Hispanic

Education Exp Expsq

Mean Mean Mean Mean Mean Mean MeanUnionized 2.29 0.291 0.187 0.05 13.04 20.9 595.27 Non Unionized 2 0.49 0.111 0.052 12.88 17.14 443.27 Difference 0.29 -0.199 0.076 -0.002 0.16 3.76 152

For the 1985 data set the mean LNWAGES are approximately 29% higher for unionized workers. Other mean characteristics of the variables are similar to the 1978 data set. For example, a larger percentage of unionized workers are males, as can be seen from the fact that the mean is closer to 0. Similarly, it can be observed that an overwhelmingly large proportion of unionized workers are White. Hispanics are very unlikely to be unionized. An interesting fact is that while union and non union members are approximately equally well educated there is a substantial difference in their years of experience. The mean value of years of experience for unionized workers is 3.7 years higher than non unionized workers.

Part C:We regress LNWAGE on all other variables separately for unionized and nonunionized workers and get the following table:

(1) (2)Lnwage Lnwage

Fe -0.215* -0.226***

(0.0834) (0.0432)

Nonwh -0.0659 -0.140*

(0.0967) (0.0685)

Hisp 0.175 -0.109(0.1828) (0.0997)

Ed 0.0516** 0.0958***

(0.0166) (0.0090)

Ex 0.0561*** 0.0312***

(0.0125) (0.0060)

Exsq -0.00111*** -0.000430**

(0.0003) (0.0001)

_cons 1.178*** 0.547***

(0.2632) (0.1347)N 96 438adj. R2 0.266 0.295

The regressions in column 1 and 2 refer to separate regressions for unionized members and non unionized workers respectively with LNWAGES as the dependent variable in both cases. It can be seen that wages are lower for females than males for both, unionized, and non unionized workers. However, while the wages for unionized female workers are 21.5% lower than their male unionized counterparts, the wages for non unionized females are 22.6% lower than their male non unionized co-workers. Non White unionized workers typically receive 14% lower wages. The coefficient on the Hispanic dummy is not significant in either case. Finally, the returns to education (one more year of schooling) are also different across unionized and non unionized workers. An additional year of schooling increases the wages of unionized workers by 5% and by 9% for nonunionized workers.

Part E: We replicate Bloch and Kuskin (1978) for the 1985 data set. We report the mean differences in LNWAGES and all the other variables and then weight the mean differences of the independent variables by multiplying them with the parameter estimates from the union regression. We get the following table:

LNWAGE

S SexNon White

Hispanic

Education Exp Expsq

Mean Mean Mean Mean Mean Mean MeanSD

Unionized 2.29 0.291 0.187 0.05 13.04 20.9 595.2

7

Non Unionized 2 0.49 0.111 0.052 12.88 17.14443.2

7 Difference 0.29 -0.199 0.076 -0.002 0.16 3.76 152

Weighted Difference

0.04259

-0.0053

2 -0.0003 0.008160.210

6

-0.167

2 Parameter estimate(UNION) -0.214 -0.07 0.174 0.051 0.056

-0.001

1

Using the method outlined above we find the difference between mean LNWAGES for union vs non union and the sum of the weighted differences above. Exponentiating that number gives us a value=1.22; thus the model predicts that the differential between unionized and nonunionized wages is about 22%.

F) Now we use the parameter estimates for NONUNION workers to calculate the differential in wages. Using the calculation described above we get a value of 1.202, which points towards a 20.2% wage differential between unionized and non unionized workers.

G) COMPARING Union Wage Premium between 1978 and 1985

Finally, we compare the union and nonunion wage differential across the three models in the two years. The table below shows the approximate values of the premium predicted by the three models respectively for each of the time periods:

Model Union WagePremium 1978 1985Dummy 21% 21%Using Union Parameters 22% 22%Using Non Union Parameters 23% 20.20%

It is clear from the table above that union membership wage premium calculated by the three alternative methods gives relatively similar results across the two time periods. Barring the exception of method 3, which uses nonunion parameter estimates, and shows a decline in union premiums over the two periods the other two models predict that union premiums have not fallen. Therefore, we conclude that there has been little or no impact on union premiums from the 1978 CPS to the 1985 CPS.

Part 2: Gender Wage Gap-OLS meets Matching

A) Using a random sample of the 2000 Census Data we generate the mean values of the

variables shown below:

Total 2.775998 .098418 .0961363 13.12983 20.90014 478.6989 Male 2.654233 .1053408 .0894069 13.23739 20.87061 476.7962 0 2.891864 .0910518 .1032967 13.01538 20.93155 480.7234 sex lnwage black hisp hieduc exp exp2

The means of all the variables have been reproduced above. There is a typing error in the data set so that males have a value of 0 and females have a value 1 in the dummy variable on sex. Thus, the mean lnwages for males and females is 2.89 and 2.65 units respectively. Males and females are similar in terms of higher education and experience. Therefore, the differential in LNWAGES for males and females could be attributed to some structural and systematic discriminatory practices in the labor market rather than attributes such as skill or intelligence.

We test whether the mean LNWAGES are significantly different from one another by regressing LNWAGE on just the dummy variable sex. The constant is then simply the average LNWAGE for males and the difference between the coefficient on the dummy variable and the constant gives us the average LNWAGE for females. We then test the hypothesis that the two values are equal and we get:

F( 1, 5154) = 326.30

Prob > F = 0.0000The test result implies that we reject the null hypothesis that the two means are the same.

B) We ran the regression of lnwage on sex, experience, experience squared and higher education while controlling for race (Black and Hispanic) using heteroscedasticity robust standard errors. The results of this regression are shown below:

(1)lnwage

Sex -0.274***

(-15.24)

Black -0.0676*

(-2.05)

Hisp -0.0843*

(-2.51)

Hieduc 0.0894***

(21.85)

Exp -0.00786(-1.03)

exp2 0.000460*

(2.54)

_cons 1.675***

(17.79)N 5156

The coefficient on sex is -0.274 and it is highly significant. The differential in logwages is 0.274 higher for males than females. We test the null hypothesis that the coefficient on sex is equal to 0 and get the following results:

test sex==0 ( 1) sex = 0

F( 1, 5149) = 232.29

Prob > F = 0.0000

We therefore reject the null hypothesis that the coefficient on sex is zero at 1 percent level of significance.

The coefficient from the regression, -0.274, predicts a 27 % wage differential whereas the mean difference predicts a 24% differential between males and females. Therefore, the regression gives us a higher estimate of wage inequality due to gender than the same value enumerated by simply exponentiating the difference in LNWAGES.

C) We now run an alternative, unconstrained version of Equation 1.We run the regression

separately for males and females. The results for the three regressions are reproduced

below:

(1) (2) (3)lnwage lnwage lnwage

Sex -0.274*** -0.2606(-15.24)

Black -0.0676* -0.204*** 0.0479(-2.05) (-4.67) (1.01)

Hisp -0.0843* -0.121** -0.0572(-2.51) (-2.78) (-1.10)

Hieduc 0.0894*** 0.0770*** 0.104***

(21.85) (13.71) (17.35)

Exp -0.00786 0.0121 -0.0304**

(-1.03) (1.17) (-2.75)

exp2 0.000460* -0.0000155 0.00100***

(2.54) (-0.06) (3.81)

_cons 1.675*** 1.665*** 1.399***

(17.79) (12.65) (10.24)N 5156 2642 2514

Column 2 and 3 report the unconstrained regressions for Males and Females respectively.

A comparison of the three regressions reveals interesting results. Version A (column 1)

assumes that the slope coefficients on race, experience and higher education are the same

for both males and females. Versions B and C in columns 2 and 3 allow for male and

female specific coefficients. Comparing these three columns we find that while all Black

workers are 6% worse off than non Black workers, Black Male workers are much worse

off than Black Female workers (A highly significant 20 percent wage differential versus

an insignificant 4.8 percent differential). Similarly, Hispanic men earn a significant 12

percent less than non Hispanic men whereas Hispanic females earn an insignificant 5.8%

less than non Hispanic females. The returns to higher education are significant across all

three variants of the regression. A one unit increase in higher education leads to a 9%, 8%

and 10.4% increase in wages in the three regressions respectively. One more year of

education matters more for females than males. This is perhaps attributable to a kind of a

compensatory mechanism in the labor market which corrects gender wage discriminatory

tendencies only by means of additional schooling for women. Similarly, experience

seems to significantly matter only for females. Somewhat surprisingly however, an

additional year of experience is associated with a 3 percent fall in wages for women. The

labor market is discriminatory in more than one way. The results are seemingly

counterintuitive. More educated women earn more than less educated women. But more

experienced women are penalized

The coefficient on sex can be calculated for columns (2) and (3) by realizing that the difference

in the constants of the two regressions represents the coefficient for sex. The difference in the

constant terms from columns (2) and (3) above is the parallel shift in the male and female

specific regression lines. The value of this parallel shift is therefore equal to 1.399-1.665=-0.266.

In other words, running the regressions separately for males and females predicts a 26.6 percent

wage differential between males and females as compared to the 27.4 percent differential

predicted by the constrained regression. The constrained regression overstates the differential

because it assumes that the effect of all the other variables is the same across the two genders. As

a result, running the regressions separately allows for these effects to be taken into consideration

and slightly lowers the predicted wage differential. An alternative method of doing this is to

define interaction terms between race, gender,education and experience.

D) We test the equality of the beta coefficients across the three regressions by using the

SUEST command in STATA which estimates a joint variance covariance matrix across

models. We get the matrix1 and ask STATA to test the equality of the Beta coefficients

across the three regressions. We get the following results:

1 I have not reproduced the matrix here because of space considerations.

chi2( 2) = 28.53

Prob > chi2 = 0.0000

Based on the results above, we reject the null hypothesis that the Beta

coefficients are the same across the three regressions.

E) We generate a single factor variable DEM that contains all the

combinations of the variables by defining a group using STATA. Next,

we run the areg command of LNWAGES on sex with the absorb

function specifying DEM as categorical variable which is to be specified

as the dummy. The coefficient on sex indicates a wage differential of

28 percent between males and females. We generate the results below

in column (4):

(1) (2) (3) (4)lnwage lnwage lnwage lnwage

Sex -0.274*** -0.283***

(-15.24) (-15.27)

Black -0.0676* -0.204*** 0.0479(-2.05) (-4.67) (1.01)

hisp -0.0843* -0.121** -0.0572(-2.51) (-2.78) (-1.10)

hieduc 0.0894*** 0.0770*** 0.104***

(21.85) (13.71) (17.35)

exp -0.00786 0.0121 -0.0304**

(-1.03) (1.17) (-2.75)

exp2 0.000460* -0.0000155 0.00100***

(2.54) (-0.06) (3.81)

_cons 1.675*** 1.665*** 1.399*** 2.914***

(17.79) (12.65) (10.24) (232.06)N 5156 2642 2514 5156

F) We implement a simple matching estimator. First, we take the mean gap in lnwage by gender within each cell corresponding to a distinct value of DEM. This compares the means for LNWAGE for each gender for each value of DEM. Next, we take a weighted mean of the cell specific gap, weighting each cell by the number of women in each cell. This ensures that the value of the gender gap is not overemphasized in the case when a particular DEM is overrepresented by females. The results are reproduced below:

(1)Gender_Wage_Di

fferenceGender Wage Difference

0.312***

(0.00750)Adjusted R2 0.419


The gender difference is about 31% according to the matching estimators method while the value was approximately 28% for the fully saturated covariated model.

G) Finally, we add occupation controls to the constrained regression model. This gives us the following table:

(1)lnwage

Sex -0.300***

(-16.29)

Occ -0.000322***

(-8.54)

Black -0.0546(-1.67)

Hisp -0.0863**

(-2.58)

Hieduc 0.0759***

(17.71)

Exp -0.00422(-0.56)

exp2 0.000360*

(2.01)

_cons 1.990***

(20.41)N 5156

The coefficient on sex suggests that the gender wage differnetial is approximately 30%. However, including occupation as a control can be misleading because of the possibility of a high degree of correlation between occupation and other gender and racial characteristics. Women and ethnic minorities may be more likely to work in certain, typically low paying occupations. Thus, the effect on Occupation may be attributable to other racial or gender factors.

Part 3: Term Paper Progress:

I have acquired all the necessary data and begun to replicate most of the results. I am definitely replicating AJR “Colonial Origins of Comparative Development”. I wish to include data on volume of atlantic trade in the original equation and test a trade immeserizing growth argument for Asia. I have acquired the data for volume of Trade using another paper by Acemoglu called “the rise of Europe”.

DO FILES: BERNDT************EXERCISE FIVE FROM BERNDT*************

*PART A

summarize lnwage fe union nonwh hisp ed ex exsq if year==1978

*

* REGRESS lnwage on several vars

reg lnwage fe union nonwh hisp ed ex exsq if year ==1978

est store a1

esttab a1 using firsttable.rtf, ar2 se(4)

*(PART B Mean of variables if union==1)

tabulate union if year==1978 , summarize (lnwage)

tabulate union if year==1978, summarize(fe)

tabulate union if year==1978, summarize(nonwh)

tabulate union if year==1978, summarize(hisp)

tabulate union if year==1978, summarize(ed)

tabulate union if year==1978, summarize(ex)

tabulate union if year==1978, summarize(exsq)

*

*PART C: REGRESS SEPARATELY FOR UNION VS NON UNION

keep if year==1978

reg lnwage fe nonwh hisp ed ex exsq if union==1

est store r1


est store r2

esttab r* using secondtable.rtf, ar2 se(4)

*

*PART D: Chow test

reg lnwage fe nonwh hisp ed ex exsq

*PART E:

*Step 1: Calculate the difference in mean LNWAGES between unionized and non unionized workers.

*Step 2 Substract the sample means for nonunion workers from the sample means of union workers for each of the independent variables.

*Step 3 Weight each of these sample mean differences by the estimated parameters

*Step 4 Subtract the sum of these weighted differences in the regressors from the LNWAGE difference.

*******Part F*********

*Done using Excel***

*Part G: For 1985

DO FILES: BERNDT

************EXERCISE FIVE FROM BERNDT*************

*PART A

summarize lnwage fe union nonwh hisp ed ex exsq if year==1985

esttab using tablenew.rtf ,cells("mean(fmt(a3) label(Mean)) p50(fmt(a3) label(Median)) max(fmt(a3) label(Maximum)) min(fmt(a3) label(Minimum)) sd(fmt(a3) label(Standard Deviation)) count(fmt(a3) label(Observations))") nonum noobs label nogap

* REGRESS lnwage on several vars

reg lnwage fe union nonwh hisp ed ex exsq if year ==1985

est store c1

esttab c1 using newwwtable.rtf, ar2 se(4)

*(PART B Mean of variables if union==1)

tabulate union if year==1985 , summarize (lnwage)

tabulate union if year==1985, summarize(fe)

tabulate union if year==1985, summarize(nonwh)

tabulate union if year==1985, summarize(hisp)

tabulate union if year==1985, summarize(ed)

tabulate union if year==1985, summarize(ex)

tabulate union if year==1985, summarize(exsq)

*

*PART C: REGRESS SEPARATELY FOR UNION VS NON UNION

keep if year==1985


est store x1


est store x2

esttab x* using second222table.rtf, ar2 se(4)

*

*PART D: Chow test

reg lnwage fe nonwh hisp ed ex exsq

*PART E:

*Step 1: Calculate the difference in mean LNWAGES between unionized and non unionized workers.

*Step 2 Substract the sample means for nonunion workers from the sample means of union workers for each of the independent variables.

*Step 3 Weight each of these sample mean differences by the estimated parameters

*Step 4 Subtract the sum of these weighted differences in the regressors from the LNWAGE difference.

*******Part F*********

*Done using Excel***

PART 2: OLS MEETS MATCHING:*************Part 2: OLS MEETS MATCHING****************************

*(A)

tabstat lnwage black hisp hieduc exp exp2, by(sex)

esttab using table11.rtf ,cells("mean(fmt(a3) label(Mean)) count(fmt(a3) label(Observations))") nonum noobs label nogap

* Test of means of lnwage - using intercept

reg lnwage sex

est store A

test _cons =2.653

*

*********PART B*************

reg lnwage sex black hisp hieduc exp exp2,r

esttab using tablehhpph.rtf

est store B

test sex=0

*

*************PART C******************

***TWO WAYS OF DOING THIS********

**C.**

generate blacksex=black*sex

generate hispsex=hisp*sex

generate hieducsex=hieduc*sex

generate expsex=exp*sex

generate exp2sex=exp2*sex

regress lnwage sex black hisp hieduc exp exp2 blacksex hispsex hieducsex expsex exp2sex

estimates store partc

test blacksex hispsex hieducsex expsex exp2sex

**D.**

reg lnwage sex black hisp hieduc exp exp2

estimates store partb

reg lnwage sex

estimates store parta

suest parta partb partc

test [ parta_mean=partb_mean=partc_mean], common

***Constrained*******

reg lnwage sex black hisp hieduc exp exp2,r

est store v3

***Unconstrained Regression****

***Males only****

reg lnwage black hisp hieduc exp exp2 if sex==0

est store v1

****Females Only***

reg lnwage black hisp hieduc exp exp2 if sex==1

est store v2

esttab v* using table1309887.rtf

suest v1 v2

*************PART D

suest A B C

* Do coefficients vary between groups? (Chow test)

test [A_mean]sex=[B_mean]sex=[C_mean]sex

***************PART E***************

egen dem=group(black hisp hieduc exp exp2)

areg lnwage sex, absorb(dem)

est store v4

esttab v* using table13ff3.rtf

****************************

************PART F****************************

gen lnwage_f = lnwage if sex==1

gen lnwage_m = lnwage if sex==0

egen N_D1_cell = mean(lnwage_m), by(dem)

egen N_D0_cell = mean(lnwage_f), by(dem)

gen b=1

egen Gen_Wage_Difference = N_D1_cell - N_D0_cell

label var b "Gender Wage Difference"

eststo: reg Gen_Wage_Difference b [aweight = Female],noconstant

esttab using tablefffggf.rtf, label replace nogap noobs se ar2

************PART G************

reg lnwage sex occ black hisp hieduc exp exp2,r

esttab using tablearff.rtf

problem set 3

Documents