[speaker001:] Get into Microfit, when you're in the data input menu... I'd like you to call up the file Q M four FIT... Q M four FIT file... file. If you just look at the er [clears throat] the sheet, that we've handed out, they loaded from er from the computer it's that data that's in front of you, right, we've got three, three series, right, it's times data, right, from nineteen twenty three to nineteen forty five, right and the three variables are, textile consumption, United States er real, sorry is benevolence of the U S, so it's textile consumption, capita, real income er per capita income to be adjusted through inflation, so constant money terms and what the relative price of textiles P erm the price of textiles relative to the general level er the general price level. Okay what we're going to be doing is estimating a demand function... so we can specify the textile consumption as a function of real incomes per capita and also relative prices, alright. A priori, what sign would we expect on those two variables? Say the income, what sign would you expect to observe?... Yeah positive providing textiles are a normal good, you should observe positive er income consumption response okay. How about prices?... what code, what sign do we expect on the er the price variable there?... Yeah negative, right, textiles rise faster, the price of textiles rises faster than the general price level, the real increase in textile prices, therefore, we'd expect [clears throat] providing the first law of demand holds, that we get a negative response consumption, right. So that's what we expect a priori a positive coefficient, a negative, coefficient, positive on income, negative on prices. What we are actually going to do today is to look [clears throat] using this data, is to look at structural stability, right, we're going to ask ourselves are the parameters that we estimate over the entire sample, are they constant over time. There's no point in estimating a model if in reality those coefficients are not fixed, they're jumping all over the place. Right with those parameters, so if you just look at the er coefficional income, if we estimate the coefficional income to be nought point five right, over the entire sample, the then subsequently find out if that coefficient varies from year to year from minus six plus ten, right, having a one point estimate, right, er oh that coefficient is not going to be particularly useful to us, we want to know er whether our coefficients remain reasonably constant throughout our sample period, particularly if we're using this er equation to make out of sample predictions, right. The first thing we must er be sure of is that the coefficients within the sample are reasonably, er reasonably constant, right. If they are not reasonably constant, then not only is the model er a poor one, right, within sample but it can't really be used for out of sample predictions, because although on average er our coefficient that we estimate it might be nought point five, then the out of sample could well be minus six or something like that. Right, so you need to know that our model is characterized by constant parameters over the sample.... [clears throat] Now the data that we've got here has been artificially generated. the last six observations of it has, right, the first six observations, sorry the er the first twenty odd observations are real, right, that they haven't been made up but the last six observations have been made up, right, to er to illustrate structural change. [clears throat] We will assume that we don't know that there is structural change in this data, although a priori, we might expect it. Why, why might we expect structural change to occur in this example?... Anything in particular? Okay, yeah, that's right, this s this series a particularly volatile period of economic history in the nineteen thirties, the Great Depression, in addition what's at the end of the series? Yeah the Second World War, right, so er I can tell you now that in actual fact there's no structural change during the thirties here but there is structural change during the war. Textile consumption, or the parameters that we estimate during peacetime no longer er explain textile consumption during wartime. Right, I'm going to go through methods of how we can detect structural change by the non constant parameters. [clears throat] The first thing we'll do is look at the data, alright, so if you go from the action menu into option one, right, we're going to plot er go through to the transform edit
[speaker002:] [cough]
[speaker001:] option, go into the data processing environment, right, where your three variables are listed T C I P. Right, if you just give the command Plot T C Plot space T C then press the return key right, that's textile consumption over our sample. Now it's not immediately obvious from that time series that there's a structural break, right, textile consumption hasn't fallen dramatically, right, or risen dramatically over the post war period, oh sorry du during the er the war period. Nevertheless we can show that there is significant structural change er in the model that we'll
[speaker002:] [cough]
[speaker001:] estimate. Right, so by looking at the graph, I am just trying to impress upon you that structural change cannot always be spotted simply by looking at the data... right, anyway, let's now [clears throat] move on to estimate our first model. What we are going to be doing is trying to explain that series, right that er consumption series. So if you press the escape key we'll go back to the data processing environment, right. What we're going to do is to log all our variables, right, so if you let L N T C equal open brackets T C close brackets, right, we going to define a new variable L N T C. That's going to be the natural logarithm, right, of our original series T C textile consumption.... If you now plot L N T C... right, if you plot L N T C... you should have a very similar graph to the one that you had before. Alright, logging the data doesn't change the nature of the data, what it does do is that it re-scales the data, okay so the only thing that's, that's, that's changed by logging, right, is the scale of the cr is the vertical scale on the graph, right, but essentially we are still trying to model the same series and N T C is essentially the same series as T C. Okay, so if you press the escape key, once you've had a look at the data, er if you log all the other variables er if you let L N I equal log open brackets I close brackets let L N P equal log open brackets P close brackets, press the return key.... Okay has everyone created those three variables in logs?... Okay, right what we are going to er do now is create a constant, we'll need a constant for our regressions... so if you type the letter Q to come out of the data processing environment... right type the letter Q right and then go into the er constant creation menu, which is option one of the data processing menu... right,... you'll, you'll be asked for a name for if you like call it C or constant or Fred Bloggs, just supply a name... to your constant term.... ... By the way has everybody changed erm the password or their password, have you changed it to your date of birth, have you all done that because if you haven't, you've only got six grace log-ins on erm where your password is your user name. If you don't change
[speaker002:] [cough]
[speaker001:] your password within six er times of logging in then you will be excluded from the network. So you won't be able to log on to Microfit?...... Right, [clears throat] okay, so has everybody created a constant... right, what we are going to do now is to er estimate the first model right equation one on the sheets that you've been given, alright, you've created a constant, we've got our variables L N T C L N I L N P
[speaker002:] [cough]
[speaker001:] right so if press the letter Q to quit from the data processing environment and press the return key, head towards the action menu, right, when you are in the action menu, go to option two, which is the estimate option, right, and you should then be given a dialog box. If you then specify your equation, so it's L N T C your dependent variable space, whatever the name you called your constant then L N I space L N P. Now just specify the variables that you want in this regression, right, your dependent variable first... okay when you've specified the equation, sorry... once you specify the equation press the end key which is between the alphabetic and the numeric key pads, that will then submit that request, right. If you then er, it will then ask you over what period do you want to... right so if you press the end key that will submit the job erm it asks for the sample period, we're going to use the whole of the sample, so if you just press the return key, that's the default for the whole of the sample, right, it then asks you what procedure you want to use to estimate the model, we're going to use O L S option one, just press the return key O L S then [clears throat] the computer has estimated the model, right. Before we move on, let's just have a look at those numerical estimates, can we look at the coefficients on income, notice that in this model because we've logged both dependent and the independent variables, right, the coefficients that we estimate are elasticities, right, so we can read those coefficients off directly as elasticities and that's the case for any model in which all the variables are logged... right, in er, if we didn't log the data, in order to calculate the elasticity we have to multiply a coefficient the computer gives us by a erm price quantity ratio, price less, less part of the income constant ratio to obtain the income elasticities. Alright but in any double logged mode, right, the coefficients you estimate are elasticities, so we look at the incoming elasticity, we get a measure, or we get an estimate point six eight, right, that's a positive as we would expect suggesting that er erm textiles are a normal good, right. Notice that an incoming elasticity is less than unity, and that's less than one, as a result... textiles, textile industry in the Netherlands is going to be a declining sector in the economy, right, as incomes er per capita G D P rises, the textile sector will benefit, alright, because, because human demand for textiles either they're demanding proportionately less of any increases in incomes. Right, then so as a result the textiles would be a and relative decline to the rest of the economy. Is that a T ratio on that incoming elasticity? Is that coefficient statistically significant, is it significantly different from zero? Our estimate incoming elasticity, just the T ratio... would you say. T ratio of one point four nine.... Typically we use the rule of thumb to statistical significance so if we have a T ratio that's less than two we can infer that that coefficient to which the T ratio is attached is not significantly zero. In actual fact our incoming elasticity there with er nought point six is statistically significant zero, eighty five percent confidence level. Confidence right the figure in the square brackets next to the T ratio gives you the significance level of the coefficient, right. We normally use the five percent significance level or the ten percent significance level which corresponds er ninety five percent confidence or ninety percent confidence right. So this T ratio on income elasticity is for the bit right and if we were using the five percent or ten percent as our sort of cut off point, we'd actually discard income from our consumption, from our demand function.... Now as economists we should have strong prides about income in this model, we would all, we would expect income to be very important in explaining textile consumption although the model is telling us at the moment, income doesn't seem to be significantly explained in textile consumption so that's something to worry about, we're getting some, er sort of peculiar results here. We now look at the er price unity as a T ratio minus ten, right, so it's highly significant, right and the er figure in square brackets, the probability value next to the T ratio tells you that we get least ninety nine point nine percent confidence coefficiency price elasticity demand significantly different from zero... right, now is everybody happy interpreting the coefficient right and the T ratio? If not say now and we can go through it. It is vitally important that you know...
[speaker002:] [cough]
[speaker001:] how to distinguish a statistically significant coefficient, right, rule of thumb is that the T ratio has to be greater than two with absolute value... right and the figures in square brackets next to the T ratios tell us the exact level of significance, right, er of that coefficient, right, so the incoming elasticity of demand is statistically significant from zero only at the eighty five percent level, a correspondence of fifteen percent significance that incoming the price elasticity demand, highly significant, right, significance level as given by the probabil by the probability er unit in square brackets, the timing level therefore we could be very highly confident about that [clears throat] coefficient okay. So we've got this model, right, we've estimated the model, let's now have a look at the plot of actual and predicted. So if you press the return key... right, we just get a whole list of diagnostic test statistics that we won't look at at the moment, press the return key again, come to the post regression menu, you go into option three which is a list plot option. Now the plot actual and fitted, right, so we try to explain the actual block of textile consumption as the blue line and to do that we are using our model with those fixed estimates, the incoming elasticity and the price elasticity. As you can see there, the model is breaking down during the latter period of our sample. The notice that appears to track the data quite well up until about nineteen thirty, right and then after nineteen thirty it seems to get progressively worse.... Now we may suggest that that's the effect of the Second World War biasing alright biasing the estimates that we've just produced from the whole sample. Now because... I'll leave that for a moment... right, so one way we may test the structural change, right, is to construct what's called a dummy variable and a dummy variables in a wide variety of applications... they can be used to er get rid of er outlying observations, very very high or very very low observations. They can also be used for tests for structural change, right, what we're going to do is to say during peacetime... right, we'll estimate our model, we'll then estimate our model during wartime and we're going to assume that the coefficients or the income and price elasticity mark, don't change during between peace and wartime, all that happens is as they intercept this model shifts, right, now you may thinks that's not particularly er attractive, you might expect the price of income elasticities to change between two periods and we could actually use dummy variables to see whether that is the case, right, however, we'll get very similar results, right, if you just use a slope dummy so it'd intercept dummy, right, and all that's going to do is to say, well the model runs like this in peacetime, right, and then wartime it suddenly shifts up or down depending on the effect of er of the war on textile consumption. Right, so what we're going to do is create a dummy variable to test that hypothesis, right, so if you press the escape key, right, and work your way back towards erm the data processing sort of environment, so go back to the post regression menu through the backtracking menu erm, when you're in the backtracking menu, go to option six, which is the process plot edit option... right, now press the return key in the data processing menu, right, and that will get you to the data processing environment when we can start messing about with our variables. Right, what we are going to do now is create a dummy variable, right, let's call it D one right so if you type D one equals zero and press the return key... what you created there, right, is a new variable called D one and it assumes the value of zero, right, what I want you to do now is to edit this variable, so type edit space D one press the return key... right, if you type on edit space D one you'll then get a sheet that has all the observations for our variable D one. Using the cursor key move down to nineteen, the observation for nineteen forty... right when you've done that type the letter one... and then press the return key, right, and you'll see that the observation is changed, right, from zero to one. Move the cursor to nineteen forty one, right, and then press one again, press return key. Just go through the remainder... of the, of the observations, so that you should have zeros up until nineteen forty and then at nineteen forty through to nineteen forty five, right, you have ones. When you've finished doing that, press the end key. Right the end key will save the edit that you've just made... okay. Right, what we're now going to do is incorporate that dummy variable as the regressor in our model as an explanatory variable, so what's going to happen is that that dummy variable is turned off, alright in the first part of the sample right up until the war that dummy variable's going to be off, right so it has a value of zero, right, then in nineteen forty through to nineteen forty five it's switched on and what it's going to do is to pick up any differential effects, right, in the intercept between wartime and peacetime... right, we'll talk a little bit more, more about that in a second, we're going to add it in as a regressor, right, because it only comes on during the wartime it will pick up any shift in the intercept, right, that occurs due to the war if there is one, of course there may not be but it's quite likely that there, there may well be, so if you type Q to come out of the data processing environment, go back to the action menu and test estimate forecast... okay at the dialog box just add D one to your list of explanatory variables, alright then press the end key, right, yeah we're gonna use the full sample... right, we gonna use O L S, right you have now estimated the model with this dummy variable... now just to see what's happened to those coefficients... the er incoming elasticity was at nought point six is now doubled... right to one point one four... more importantly, right, its T ratio has jumped from one point eight five... right to six point eight, as a result, we now say that the incoming elasticity, the income coefficients, right, the significant zero, it's important to explain the textiles as such... the er, we are now getting a very different estimate for our our estimate for price elasticity is four and one to nought point eight minus one is one point eight, notice though that its ratio has jumped... considerably or has doubled... and the dummy variable itself... is very significant the T ratio ten... the coefficient on that dummy variable tells us the effect of the war on textile consumption, right so on average textile consumption rose by point two... er see what the units of measurement are... we don't actually have [LAUGHTER] units of er ah so we'll...
[speaker002:] elasticity whatever it's multiplied by
[speaker001:] That's right if you er... so this point two quantifies the effect of the war on our equation, and where is the so the intercept, well what you're saying is in peacetime the intercept is equation three point one seven, however, in war time the intercept shifts up and is now three point one seven plus point two,
[speaker002:] You could draw it like that you could say that this is the the war which cuts in this time of year line shifts up,
[speaker001:] Yes.
[speaker002:] so if you wanted it back, you would actually get a new value for the intercept which increases by nought point two three point
[speaker001:] Three point one okay so this is where the model, in effect what we've done which is a very crude way, right, of erm incorporating exogamous influences, right, we haven't said tha that the war is going to affect the income or price elasticity what we did do, right, all that we're doing is that we're allowing the intercept of our model to change, right, now as a result, we've got, we can prove the st the statistical significance of all the variables in our model, right, the co the actual coefficients that we've estimated have changed... quite significant, particularly in the er the incoming elasticity, right, the incoming elasticity was less than one, right, and insignificance before was now greater than one and height of R squared has also increased dramatically our measure of explanatory power. Now if you just press the return key a couple of times... right, and have a lot of actual and fitted, if you go into option three in the data post depression menu... you will notice that the fit of our model is very very different... right, so we are now getting a very very good correspondence between actual and fitted, notice that in our original model the thing started to break down at about nineteen thirty, right, just by allowing the intercept to vary, right, over the wartime we've now got a much better fit throughout the whole period... why is that the case? Why are we now getting a much better fit throughout the entire period simply by incorporating the dummy variable to the war period?... Any suggestions?... Well what's happening is it the, during the war, right, we're constraining the computer to estimate, like a single coefficient that is applicable to both war and peacetime er isn't the case, right,th there is a structural change, right, so when th when we constrain the computer to estimate the coefficients throughout the whole period, right, the coefficients are biased but if they don't apply either to the post er pre war peacetime sample neither do they er fit very well to the data during the wartime, right, if we allow the intercept to change but we're getting much better estimates both wartime and peacetime er parameter's okay because we haven't got rid of, we've got rid of that bias, right, in constraining the parameters to fit both wartime and peacetime er time periods. Okay, erm [clears throat] on this sheet, I don't think, well we won't go through it now because we've run out of time. On this sheet, on page two, we've er, we've performed equation two, right, on the sheet and the second page and it says that there's, there are two alternative ways of testing for structural change using dummy variables. One is to include corporate dummy variable of the intercept and see whether it's T ratio or significantly different, is, sorry it's greater than two... right or we can use an F test, right, now that F test that's given me that formula in the middle of the page is a very important [clears throat] test which was developed by a chap called Chow and as a result it become known as the Chow test and it's a, it's a test for parameter constancy, er do we have constant parameters in our model... now it tells you how to compute this Chow test, in this particular case we're only dummying the intercept, the Chow test gives exactly the same results of T tests, right, erm... we won't bother going through it, if you want to go through this er sheet in your own time calculate that, that Chow test and essentially what it involves is splitting with the s the whole sample now into two sub-samples, right, the first sub-sample, right, is peacetime, the second sub-sample wartime, right, and you just compare the residual sum of the squares on the unaccounted for variation, right, between actual and fitted values, just compare the residual sum of squares between these two sub periods, right and if you use the formula that's given there that will come out with exactly the same result, well in actual fact you can square, if you square the F statistic you get calculating one formula you will get T value, got from er the computer right, the er, the sheet goes on to say how we can er use dummy variables in slightly more complicated ways, right, we could see actually see whether the income or price elasticities of demand changed. Right, instead of letting the intercept change we could just let er our elasticities change. Anyway that's preferable because that's actually what's, what's happening, right, the war is likely to affect the elasticities of demand rather than this er bizarre concept intercept erm and the, the sheet on page three tells you how, how to do that... okay. But essentially all these tests do the same thing because they're seeing whether the parameters that we estimate over the entire sample are robust over all sub-samples, right, we can't, we wouldn't bother testing over all sub-samples though we can do, it's just if we have good reason to believe that behaviour in one sub-sample different for behaviour in another E G use er Chow test or equivalently a dummy variable on the intercept to see whether there was any change. Right, okay we'll leave it there, if you just press the escape key and then work your way out of Microfit towards the action menu, exit from Microfit and don't forget to log out of the network.... Okay, feel free to come down here at any time with this sheet and er going through the, the examples in greater detail Q M four FIT was the data file, you'll always be able to access, right... when you've logged out of the network feel free to go and a merry Christmas, see you next year.