OK, so welcome to the Seminar for solutions. So first of all, we're looking at this analytical question and then the next part will be looking at the views so.

We well the question was too.

Right these null hypothesis, so all part of the same H series the same null hypothesis in terms of the matrix big are the little vector R and the vector beta. So in other words to write it in the form our beta equal to little R and so.

This is what we start with. These are the three restrictions under the null hypothesis.

And initially so to put this into vector matrix form, we add in all of the other beaters into each equation, but obviously we multiply them by zero, so.

In the first equation we have beta 1, beta 5, beta 8, but we can also think about a zero times beta 2.

Zero Times Beta 3 zero times beta 4.

And then we have 0 times beta 6 and 0 times beta 7, so you're in here we have the three times beta one. We have the two times Beta 5.

We have the pizza 8 but we put zeros times the others. Let me do the same for the next 2 equations. So for this one we add in beta 1 beta 2 beta four and so on up to beta 8 each time multiplied by zero, which is the same for beta 7 and so now we have three equations in terms of all of the beaters and then we can write this week and see hopefully that this can be written in matrix and vector.

Form so with this matrix tree multiplying this vector where we have.

Beta one to beta 8.

Multiplying each element.

Of this room.

To get this side of the first equation.

And we have a four. Here we have a four here.

And then for the second equation we have the 2nd row times beta.

And then that's going to be equal to 0.

And for the third equation, sorry, but that I can't seem to unclick this. OK, so further third equation, here we have the 3rd row times by beta equal to 1.

And if that's not clear then let me know I can go into it in more detail, or perhaps just drop by my office hour. I can explain some more, but essentially now we have the matrix are holding the.

The coefficients on the beaters in each in each case, and in each equation, that's restricting the value of the beaters, and we have this vector comprised of beta one to beta 8. That's the entire beta vector in this case, and then we have this one here, which is little R.

So it's Big R beta equal to little R.

For these particular three linear restrictions.

So if there are non linear restrictions, we can't put the nonlinear restrictions into this form, but any linear restrictions in this kind of form we can put into matrix vector form RB2 equal to the law.

OK, so next is the evias.

So this is the eviews part of seminar full and I'm going to go into eviews via this button here.

I'm on the Apps anywhere server.

OK, so here we have the views.

And.

You will need to download the file and then navigate navigate to it from here. So import import from file and then go through your directory structure until you find the file and.

I'm just going to lose this one.

So.

Once you've found the file and clicked on it, you'll get to this and you can just click on finish because all of the settings work.

And we have the verbals here.

So the task initially is to estimate the model. One way to do that is to go to quick then estimate equation.

And you get this box where you can specify the equation and it gives. It gives the instructions to do that here.

But essentially we put in the dependent variable first.

Then see for constant.

Then the explanatory variables.

And then you have some options so.

Later on, we'll come to the issue of robust covariance matrices.

But we would just leave it how it is, so the default and we're using least squares estimation. Can see the lots of alternatives here.

Well.

These values should seem quite familiar by now, so we know we have significant negative correlation. Well and significant negative.

Relationship with log wage and positive relationship with square feet of housing area both very high T statistics and absolute value low P values.

So that's estimating the equation. We can do that programmatically as well, so I'll get into that a little later. But there was also the issue how to how to test for the joint significance of the coefficients on these two variables. So for that one way is to go to view.

Then coefficient diagnostics.

And then.

Volt test.

Which is not the test it's asked for in the question, so it's not the F test but the F test does appear as part of this, so this is how you get the F test.

So for that we went to view in this window here, but you could also do it from here.

So it's the same menu.

So if we do it from here.

The way you write in the restrictions is just in terms of this C notation, so we have beta one to beta K in our model. In Eviews they have C-12 whatever so.

It would be C1 to CK. So in our case in our model we have three variables.

So we have the constants of the vector of ones column of ones.

The column for the log age and for the square log, square, feet, and so the coefficient on C or the coefficient on the on the.

The column of ones the constant is this C1.

And for log age C2, and this is C3.

So, so I didn't mean that these are actually C1C2C3. I mean, these are the estimated coefficients for C1C2C3. In other words, beta 1, beta 2 beta 3, so we want to test whether the coefficient the true coefficient on age is equal to 0 and the two coefficient on lock square feet of housing is equal to 0. So whether C2 and C3.

Beta two and beta three are jointly equal to 0.

So there are two ways to do that. We can say that C2 is equal to 0 and C3 is equal to 0.

So two restrictions separated by commas. We could also use this shorthand, so just saying C2 is equal to C3 is equal to 0.

We click OK and then we have the results for for the F statistic. I mean for the F test and for the CHI squared test for develop test.

So we do cover the belt. Test will come to it quite soon and the lectures. But now we're looking at the F test results. We have the value for the F test statistic and so we have the P value. We can see it's a very large F statistic and very low P value. We reject the null hypothesis that both coefficients are equal to 0 and you can also look at the degrees of freedom column here. So for the F test.

We have numerator and denominator degrees of freedom. The numerator degrees of freedom of the number of restrictions and the F test in the null hypothesis we have two because we're testing whether two coefficients are jointly equal to 0, and this is just N -- K in the unrestricted model.

So, um.

In in here.

Um, so where we going? So the coefficient diagnostics?

We can put all kinds of nandoni restrictions so you can see here we can. We can do things like 2 times so we we can put linear restrictions like this, But you can also times the see things together so you could test whether C one is equal to C 3 * C. Four things like that.

OK, um another thing I'm as well gives right now so.

When we come to heteroskedasticity testing, we'll be using this one, so residual diagnostics.

So you can go to heteroskedasticity tests.

And also.

To do a test for functional form, correctness of functional form, you got a quite basic test here. The Ramsey reset test.

OK, so the point and click methods is good for many purposes.

No, it's very useful for just doing quick estimations. I think that's why it's called quick, but sometimes it's useful to be able to do things programmatically.

One thing we can do from here actually is name the equation.

So we could call this equation.

And if we do that, you see it appears here so we can close all of this.

Now then, if we double click on this we get the estimated equation again.

So you can save your the equations that you've estimated so you can save your estimated results using different variables and so on.

Is one thing, but it is also possible to.

Um to all of what I've just done, but programmatically so.

If we go to file then you then program.

We get this area here in which to write some scripts. I mean some commands as part of a script.

And the first thing we need to do because Eve uses object orientated is to create an equation to declare an equation.

So we declare an equation like this.

Just like in one of the earlier Sessions seminar two another. What was it it was?

Lab one.

Was it?

Yeah lab one for social app and we went. We went into the programming and this was also how you had to declare vectors and matrices so.

You have to say equation and then the name of your equations.

Cool, it's in class 3.

OK, now hopefully we can run. So you see, we have an equation to appearing here, but so far there's nothing in it becausw we haven't done anything to equation 2. Haven't estimated it.

So what we can do?

Is performed least squares on equation 2.

The way that the way to do that is using dots, LS, and then you have to tell it the estimation you want it to do so. That includes the data that you wanted to use. So Ellen price. See Ellen age Ln square feet.

And so we run it again, and if I open that, you see now we.

Have our estimated results.

So I'm going to close that.

And then in here we can also do the Vault test while the F test. So to do that again, we're performing that on what's in equation 2. So after estimating, we're able to do this. We do a dot vault.

And then we need to put in the restrictions that we want it to perform or that we want it to test. So we have C 2 = C Three.

Equals 0.

Let's run that.

There we go.

And if I close that.

We open it.

OK, so just going back to the estimated equation.

OK, but if I run this again.

We get the F test result.

So there's more that can be done so we can do this with robust standard errors or yes. One thing I said in class that should say here.

Can I do that?

Let's do it from this one. So one thing is that when you do the.

Develop test for the joint significance of these two. It's actually something that's already on the screen.

So it's already in the regression results. This F test statistic. So if you just want to do the F test for overall significance without going into.

Into these options and changing things then. Then you don't need to do the test manually. You can just look at the regression outputs and see that this is the F test statistic and this is the P value. However, if you do find that you have heteroskedastic errors. So if you do a test for homoscedasticity and you reject the null.

Will come back to that in a later lecture. Then you probably want to use robust standard errors, and then there will be a difference between the value that you get.

Here, and the value that you get manually by specifying the linear restrictions on the coefficients. So then this one here will be. Just use using just assuming homoscedasticity, whereas the one that you compute manually will incorporate the heteroskedasticity assumption so.

That's something I'll come back to in later class.

OK, so you have two math 2 main methods within Eviews for estimating. You have the script method and at the point and click method.

You also have. You can put commands in here.

Yeah, but the advantage of creating a program file is that you can save it and use it later, so that's all for seminar four. Is there any questions and just let me know by email? I'd go through some more next time. Thank you.