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Use MROZ for this exercise.(i) Reestimate the labor supply function in Example $16.5,$ using log(hours) as the dependent variable. Compare the estimated elasticity (which is now constant) to the estimate obtained from equation $(16.24)$ at the average hours worked.(ii) In the labor supply equation from part (i), allow educ to be endogenous because of omitted ability. Use motheduc and fatheduc as IVs for educ. Remember, you now have two endogenous variables in the equation.(iii) Test the overidentifying restrictions in the 2 SLS estimation from part (ii). Do the IVs pass the test?

(i) Hence, the estimated elasticity of hours with respect to wage is 1.994349 of the model in whichlog(hours) is the dependent variable, which is higher than 1.26 of the model in which hours is the dependent variable(ii) It shall be noted that in this 2 $\mathrm{SL}$ S model, both log(wage) and educ are endogenous variables(iii)Yes, IVs pass the test

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Chapter 16

Simultaneous Equations Models

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Hello, everybody. And welcome to another econometrics tutorial. And on this what? We're going to be taking a look at some simultaneous equations. What you're gonna want to do first is open up your Wooldridge, um, package and then the MM Roz data set, which is a data set about labor statistics for a woman in the 19 seventies. As you can see here by all of these, So we're going to set up our model here, which this is a simultaneous equation because the dependent variable in our case, hours here and the main independent variable wage are actually both dependent. And they affect each other so you could put wages the dependent wages, the dependent variable, and then ours is the independent variable. So the fact that you can do both means it's a simultaneous equation Problem? Um, in this case, we're gonna be looking at hours as the, uh, dependent variable in wages, the independent variable. So we set up our model with the log of ours, um, against the log of wage education, age, the amount of kids that the woman has that are under six, and then I believe this is the, uh, the percent the family or that the wife makes of income in the house. Something like that. Um, yeah. Also, a little additional note here I added, plus one to the log because each of these data sets here the data for wage the data for hours. Some of the entries are actually zero because some of the females that answered the survey didn't have jobs, so they didn't have any hours, and therefore their wage was also zero. So that if you ran, if you run something that has a zero in the data, um, or will give you an airy and a fix for this is to just add plus one into the log. And because we're looking for elasticity here, the B two adding plus one actually doesn't change how you interpret the results, because elasticity is a percent change. So it does seem weird, but it works more or less. Um, and it's a way that you can work around the areas that are will give you. So we go get the elasticity, which is B to the beta that's attached to wage their, and we find that it is 0.45 So that means As your wage increases by 1% your hours are going to increase by 0.45%. As you see here, I mean ours. And wage could also be endogenous variables because, um, there are other Very There are other factors that could affect it that aren't measured in the the data sets here. Ability is one so like, what's your natural ability? Or you're a hard worker, that kind of thing. But we can still check for endogenous variables like your education could be, um, for example, if your parents are more well educated, it's more likely that you're going to be more well educated. And luckily enough for us in the data set, they do include father education and mother education. So we're going to use those instruments to test the education. So again, to do your instrumental variable test, you have to open up a ER and then you're good to do it. So just type an ivy rag test. The do the equation is normal again. Test log of ours against log of wage, um, plus the education age kids and then the wife stuff. And then the line is to let our know what the instruments are and what their instruments for so again, write everything the same, except for what you want. These two new instruments which have to be added on at the end to be instruments for So we write it again. Except we exclude education from it to let our know that we want mother education, further education to be instruments for education. And then we get ourselves the summary of that Make sure to put diagnostics true. So our gives you the tests that you want to check to make sure your instruments are good and that the variables are endogenous. So let's take a look at those now. So first of all, are those two instruments the weak instruments? No, they're not because the P value is very small. So Father, education and mother education are actually very strong instruments. The second one we want to be looking at is the surrogate test, which basically is testing whether, um, all of your instruments are valid. So this this only applies if you have more than one instrument, which we do in this case, and because the P value is pretty high here, we're not going to reject the null hypothesis, Which, for the sergeant test is that both of your are all of your instruments are valid. So, uh, with that, both both mother education and father education are valid instruments to use, um, in place of education there or with education, Rather. And then, of course, we're going to check if it actually is a Dodge Innis, which, since rejecting the P value on the Hosemann test, it is because the null hypothesis here is that your value is exogenous. So it's not. And therefore, in this example, it is better to do the instrumental value variable a technique, um, and yeah, they gave us instruments which work well in this scenario. Another note. If you do, if you do, um, the model without putting hours in log arrhythmic form, it will give you a You'll eventually get an elasticity. That's actually quite a bit higher than the elasticity we got here. Which does make a bit of sense because when you're not using the log form of your dependent variable, you're taking the elasticity at a specific point in the data. So at the average, the average amount of hours worked. So with this The elasticity is constant over the whole thing because you're flattening the curve of it. And yeah, that is everything for this example. Thanks. And I'll see you guys on the next one.

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