(i) Apply RESET from equation $(9.3)$ to the model estimated in Computer Exercise $\mathrm{C} 5$ in Chapter $7 .$ Is there evidence of functional form misspecification in the equation?
(ii) Compute a heteroskedasticity-robust form of RESET. Does your conclusion from part (i) change?

Answer

(i)This implies that there is no evidence of functional form mis-specification in the equation
$$
\log (\text {salary})=\beta_{0}+\beta_{l} \text { log }(\text {sales})+\beta_{2} r o e+\beta_{3} \text {rosneg}+u
$$
(ii) the conclusion did not change from what has been made when computing the usual OLS form RESET

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Introductory Econometrics

Chapter 9

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Dylan L.

November 7, 2021

Hello Are we able to see the video for the coding of this in STATA?It would be much appreciated!

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Video Transcript

Hi, everyone. Today we're gonna be talking about a question relating to a certain data model. Ah, and we're gonna be focusing on the Ramsey reset test of Ramsey. Reset test checks for functional for miss specifications. So, um, yes. So that's our question. So the first thing we need to do is have our correct packages installed. So first you'll need the Wooldridge package. This package has all of our data. Um, you'll notice for me. It says the package is already in use. That's because I found this a few times. Uh, we will also mean the sandwich package. This package allows the store just arc ovarian cysts for hetero skin elasticity, robust models. And then finally, we will need be element round. You don't actually need bl impress practice, but I find a little easier. But I will be showing you both ways to go about this with and without. So before we could do anything else, we have to load these packages in what's a library and then each of these up in our packages alone. So, um, what we're doing here is we're exploring functional form A specifications. Basically, if I have a model that says salary equals wages plus sales. Plus, um, return on every turn. About plus you. And then over here, we have our let's say I have this model. Now, um, you're the functional form of specifications. Checks. Hey, at any point should instead be instead of wages is very statistically significant. Wages square, even a way. Just cute. We're sale squared or seals. So functional form of specifications in and the Ramsey reset. Test check for these thes points, right. They check to see if we should be looking at a nonlinear mop. But before we could do any of this, um, are formula is logs out. Sorry. We load the data, Fraser, but we're using the CEO someone beta set from Woolridge. So if I actually now hit view CEO Sal one, I will get this, uh, bring here and that will show me everything from the CEO sound. One Data's whites clinching out so bad. But that's every So now, um, before we can do our formula, but we've been given for this problem is log salary cools and picks up, plus log sales. Most row close with Ross. And now you'll notice if I go back to the view screen. You look on the cop here. There is no Ross Neck. All right. All we have is Ross. That's because Ross neg is a dummy Variable. It's a problem inside this problem. So to set our dummy variable, what we're gonna do is we're gonna say rock snag equals if you know any coding, our little aero dash is sort of like equals or an assignment operator. So we're going to save raw snag equals if else cells being no, their leader of it is Ah, and then we So the function first takes a test. So we'll say if the Ross from CEO sell one. Right. So is that here and then the specific parameter here is less than zero. Brendan, you want Ross Nick to be once. Otherwise it'll be zero. Now if I view Theo, sell one rocks and I my view rocks leg What you should see. We just expand these out a little bit, so it's easier for me to move. You should see is here. Ross's positive, Positive, positive, Negative. And here in Ross neg 0001 and so on and so forth. So, uh, that's just created a dummy variable from Ross. So now we can start writing our formula. So we're going to create our primary model. And to create this, we're going to say we're going to use the L and Function BLM function, take a formula and a data set and it'll create a model out. So we will say, uh so L m l salary right. That's the log of salary. That's what we're picking from our model. I can say l salary because it's in the CEO. Salan data, by the way, is equal to that's the till Day log sales, plus Roe Ross neck. And then instead of writing CEO, sell $1 sign. For all of these things, I can just say data equal CEO Salva, Everything that's in there, it'll take from there and being like rock snag, it will just reference from the beta set that we've created for ourselves with the dummy. Very all right, I had entered here, and now if I typed summary of the model, I will get all of these different things, so I'll get the estimates for the coefficients. I'll get the standard errors, the T values, the probability, the significance every so Okay, Now, let's finally talk about our recent test. So to perform the reset test, we have two options. Our first option eyes the is slightly more manually driven. We're gonna have to put in a bit more work. So to do this option, we're going to create two new, very so are created to or fitted square. All right, this is gonna be the square off the entire model. In essence, it's going to be the square of our Why value? Because now we're performing the reset test. So we want to check a do any of the things in the Y value Should they be square? Right? And if none of them should be squared, then we contested the why. Value as a whole should be square. It's like F test First East teeth, that song. So we're gonna say Fitted to is gonna be pretty big. Our model where three is going to be, predict our model que So now we can create a new model. This is our unrestricted model. So are unrestricted. Model is gonna take our l m will have l salary. The people l sales broke looks Ross neck plus are fitted to gloves are fitted. Three data equal CEOs out one. So now if we summarize this one, you will get values for, um are fitted to included three. And now to compare these two, we're gonna use the function called a nova. So a nova does model model on reds and you can see it will now given analysis of the table. So we see, even though the degrees of freedom decreased from our first model to our second because we're adding in these new parameters. But the important point to look out for is ah, last calm. That says probability greater than F That's 0.2658 That's RPI value because 0.2658 is greater than 0.5 This result is not significant at the 5% confidence and in fact, it only becomes significant at a 27% confidence interval which we would never you. So because of that, we can say that this implies, uh, that there is no evidence off functional form, Miss stress if fication in the and be inquest, that's our answer to the Ramsey recent test. Ah, quicker way of doing this text is to just say reset test. Um And then we will say else look, pipe in our formula. The basic formula for the reset test goes all of this automatic and you can see we get that same p value of 0.265 That's something from the Ellen test. So great. We've established that there's no evidence of functional form A specifications for this model. But now we have to consider Would there be evidence in ahead Orosco Domesticity robust form of this month. So to figure that out, we're going to use the wall. That test. I believe this one is in the Elham cuts package so the wall test will take our model are unrestricted model and then it'll do something called vehicle, which is basically calculating the new variances for a hetero skin elasticity robust. So are the So we'll save e cough. That's the parameter is going to be equal to this function. V Cough HC, which will take our unrestricted model and then a certain type parameter. I guess that tells it how to manipulate back toe, achieve our head roads congested, be robust. When we run, our wall test will see that our probability is still greater than our 5% confidence level. So our conclusion does not change from the original OLS for And there you go. Brats calculating are reset test and our hetero skin elasticity robust. Reset. Test the wall test. All right. Hope you enjoyed. Thank you very much And have a good day.

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