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Do carnings differ by race? Using the Labor Force Participation 2011 data, wc run the following regression: EARNINGS B1 + 82S + BxETHW HITE +U, where EARNINGS is th...

Question

Do carnings differ by race? Using the Labor Force Participation 2011 data, wc run the following regression: EARNINGS B1 + 82S + BxETHW HITE +U, where EARNINGS is the hourly earnings in dollar, S is years of schooling, and ETHW HITE is dummy variable which equals to 1 if the individual is white and equals to 0 if the individual is non-white_ Please use the following regression output to answer the questions.SourceSSdfMSNumber of obs F( 2 _ 3592) Prob R-squared Adj R-squared Root MSE3595 114.86 0.

Do carnings differ by race? Using the Labor Force Participation 2011 data, wc run the following regression: EARNINGS B1 + 82S + BxETHW HITE +U, where EARNINGS is the hourly earnings in dollar, S is years of schooling, and ETHW HITE is dummy variable which equals to 1 if the individual is white and equals to 0 if the individual is non-white_ Please use the following regression output to answer the questions. Source SS df MS Number of obs F( 2 _ 3592) Prob R-squared Adj R-squared Root MSE 3595 114.86 0.0000 0.0601 0.0596 14.271 Model Residual 46783.3229 23391.6615 731501.896 3592 203. 647521 Total 778285.219 3594 216 551257 EARNINGS Coef Std. Exr P> Itl [95% Conf Interval] S ETHWHITE cons 1.176888 2.079192 1950893 0851246 5414326 1.231892 4 points) Interpret the coefficients of $ and ETHWHITE_ (4 points) Do earnings difer by race? Perform the relevant test and conclude. Use 5% significance level:



Answers

Use the data in WAGE2 for this exercise.
(i) Estimate the model
$$
\log (w a g e)
$$
$$
=\beta_{0}+\beta_{1} e d u c+\beta_{2} \text {exper}+\beta_{3} \text {tenure}+\beta_{4}
$$
$$
+\beta_{5} b l a c k+\beta_{6} s o u t h+\beta_{7} u r b a n+u
$$
$$
\begin{array}{l}{\text { and report the results in the usual form. Holding other factors fixed, what is the approximate }} \\ {\text { difference in monthly salary between blacks and nonblacks? Is this difference statistically }} \\ {\text { significant? }}\end{array}
$$
(ii) Add the variables $e x p e r^{2}$ and tenure$^{2}$ to the equation and show that they are jointly insignificant at even the 20$\%$ level.
$$
\begin{array}{l}{\text { (iii) Extend the original model to allow the return to education to depend on race and test whether }} \\ {\text { the return to education does depend on race. }}\end{array}
$$
$$
\begin{array}{l}{\text { (iv) Again, start with the original model, but now allow wages to differ across four groups of people: }} \\ {\text { married and black, married and nonblack, single and black, and single and nonblack. What is }} \\ {\text { the estimated wage differential between married blacks and married nonblacks? }}\end{array}
$$

Our spotter Out of 616 workers, 172 or 18% have no pension benefits or the rest those with positive benefits. Their range is from $7 to Almost $3,000. So it is appropriate to use the topic model or to you, you can tell in the first column of the table, we do not control for variable union being white and being mirror are both increases predicted pension benefits. Part three. We will use equations 17 point 22. We set the value of experience or tenure at 10 Age 35, education 16 years, zero dependence, single and be in white and being milled. Using the estimated equation in part two, we get the value of the index X. Beta head. So vector of X. Times vector of estimated coefficient to be 940 coin, 90. And given the estimated standard deviation of the error term Should be 600 77 74. We can calculate that the expected pension for this type of worker. Yeah, notice the different uh notations for The two different distribution. And we will get yeah 966.4 or a non white female with the same other characteristics. We get the index to be 488 66 and we do the same with the distributions and the value of the standard deviation of the error terms. We get the predicted pension for this person to be 582 and 10. The difference in pension benefits between the white male and non white female is 384 $0.3. Part four is the rig question Similar to Part two, but we add the Union variable. And this is there. The results are reported in the second column in the table from the left, the coefficient of this variable is quite large. But to evaluate the effect of this variable on predicted pension, we need to repeat what we have done in part three and see the difference. Okay, um the difference between union equals one and union equals zero, so all other variables are set maybe at their the sample mean values and we will calculate predicted passion when union is one, so the person is in the union and when union is zero, when the person is not participating in an union. Yeah, Part five. We have a different dependent variable. We will not use pension level, we use pension ratio. So I do not report the results here, but you may find that the two variables white and male are jointly insignificant. This means neither be white or being milk seem to have different effect for pension benefit. As a fraction of earnings, white males have higher pension benefits just because they have on average higher earnings.

Quite one. The first order auto correlation for P. R. C. F 18 is 0.709 and that coefficient for unemployment is 0.95 So unemployment is a greater concern. It's likely to be a unit route. In Part two, we will use the first differences of PRC fatality and unemployment, but leave all other variables in their original form. This is our estimation. Result as you can see, eso. The three dots represent the seasonality, including the time trend and there monthly dummies. Here I Ali report the variables that are not time, trend or seasonality, which are we can't dummy first difference of unemployment and to binary variables, speed law and seatbelt Lee. As you can see, all these variables have centered error much longer than the magnitude of the estimated coefficient. Yes, and as we know the T's, that is the ratio of beta head to extended error. And when we get larger standard error than beta head, the T start would be less than one, and that implies the coefficient are not statistically different from zero. It means the change in peace. RC fat, the percent of fatality cannot be explained by the change in unemployment or any of their policy variables. And the reason why the our square is due quite okay is because the percent of fatality has some Yeah, seasonality. So if you look at the full regression result, you will see that some of the monthly dummies are statistically significant. Okay, In part three, we use what we get in part to to command on the statement and the results. We just got confirmed that we cannot always regrets the first difference estimation. In first, differences kill the interesting implications off the model estimate in level. This is not to say the level regression is valid, but as you will see in exercise 18.13, we can use the level of percent of fatality. It is not a unique route anyway, so we can use its level not first difference. And in general, the issue of whether to take first difference is a difficult decision even for professionals.

What's up, stat cats. In this video, we're given an example and asked to perform a one way unova, followed by a post hoc test if the results are significant. So let's go ahead two of My Excel spreadsheet, where I have the raw data coffee over. So this is weekly unemployment benefits between different states. We are told our awful level is 0.5 Let's go ahead and Duthie another test. So we're going to select all of our data. We do have labels and our off level is 0.5 Let's go ahead. Okay, so we have a significant result if our test statistic is larger than our critical value, so is 17 0.17 greater than 3.68? Yes, it is. So we do have a significant another result. So we can reject are null hypothesis. So there is evidence to support that at least one mean is not equal to another mean. And because we have a significant result, we can go ahead and do either a chef or a two key test. And if we look at our sample sizes, they are the same. So we will be performing a two key test. So in order to calculate our numerator, we're going to take the difference and means between our pairs. So I'm gonna pair Florida and Pennsylvania, Pennsylvania and main and mean and Florida. So let's take our difference of these, and then we're going to take the square root of our means square within group over our sample size, which is six. Okay, so this is our denominator, and this is our numerator. So to get our final value or just gonna go ahead and do that final calculation and we are getting some negative values, but on F value is never gonna be negative. So we can just go ahead and take the absolute value of these numbers. So just gonna consider them positive. And because we're doing a two key test, we find our critical value with the end table. So K is gonna be the number of our means. So that's three and V is gonna be our total population. So six times three, which is 18 and we're going to subtract K from that, so it'll be 15. So let's go ahead to our end table finer critical value. So three for K and 15 for Vita is 3.67 Okay, let's go ahead and go back to our whiteboard. So our Koukal value was 3.67 one in two was 8.17 2.91 in 5.27 Okay, so we know we have a significant pair if that value is greater than our critical value. So is 8.17 larger than 3.67? Yes. Is 2.91 new is 5.27 Yes. OK, so we have to significant pairs. So there is sufficient evidence use to conclude. Uh, there there exists a mean difference between hairs one in Teoh and three and one. Alright, guys, that's it for this video. I hope you learned a lot. I'll see you next time.


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