Questions on Transmission Mechanism

I get a few questions regarding the use of VAR in topic 6. Here are some comments.

Exams requirement
As I mentioned in class, I expect you to be able to interpret the VAR results, but I don't require you to understand the econometrics of VAR. So just approach it like an end-user, rather than a developer.

VAR faqs
Disclaimer: My worst nightmare would be for you to skip all journal readings and just relying on my comments below. Below I intend only to clarify certain issues, and answer questions that were raised, so it is not comprehensive in any way. Also, in no way does the following aim to provide any hint about what's coming in exams!!!

What is VAR?

VAR or vector autoregression is a statistical model, which attempts to capture interdependence between various variables over time. It is purely statistical, so if you put in all the variables that really matter (and have not omitted anything important), then your model would be 'true', and would capture how these variables really co-move over time

VAR analysis returns an output in the form of many estimated coefficients, e.g. the response of inflation to interest rate 1 period ago, 2 periods ago, and so on. Because there are simply too many numbers, it is not very useful for us. One way to illustrate the implications of VAR is to ask..."what would be the impact of a one-time shock to variable x on variables z1, z2, z3 and so on, over time?". By one-time shock, we mean we let x go up or down by more than the model predicts by one period, and then return things to normal thereafter. The responses of other variables will take place over a number of periods, as the rich interactions between variables work through over time. If you plot these responses over time, you get the impulse-response analysis graphs, which I show on the last slide (these graphs were taken from a very good introductory paper by Stock and Watson (2001), "Vector Autoregressions", Journal of Economic Perspectives...a highly recommended read) . So all the changes of the various variables shown on each graph are due to that single one-time shock to one variable.

Impulse-Response Analysis: Interpretation

As an example, we can look at the last row of the Stock-Watson diagram. This is the result of impulse response analysis of a one-time positive shock to the interest rate. We see that this single one-time shock has no impact on inflation until after 4 quarters, after which the inflation will start to contract. Unemployment responds slowly also, with maximum impact felt after 8 quarters. The last graph shows that the model predicts the interest rate will gradually come down from the level at which it was shocked. Thus this type of analysis can help us quantify the time-lag involved after the policy variable changes, and also for us to check if the data really confirm our economic understanding that inflation should come down after interest rate is increased.

Why does unemployment come down eventually? Well, having done half a term of Friedman-Lucas-New Keynesian, this should not come as a surprise to us. We have pretty much reached a sure conclusion that monetary policy cannot affect real variables in the long-run. Once prices are allowed to adjust eventually, it does not matter if there's more money being printed, the unemployment should go back to its natural rate, and output should return to trend. VAR analysis gives us theorists confidence that our understanding is in line with the data.

How do I know from this graph, which transmission channel is more important?
Well we can't figure this out from this graph alone, because VAR here only includes interest rate, inflation and unemployment. For example, if you want to know how credit plays a part in the transmission mechanism, you simply add the credit variables into the VAR, and then see what kind of result the impulse-response analysis generates. If theory suggests interest rate shock should hit bank loans, and then shrinking loans hit the investment, and then investment hits GDP, then all these linkages can be checked within VAR framework. Dr.Piti's paper is an example of how this is done (page 14 onwards). For an end-user like us, life is very easy...we can readily infer from graphs what's going on.

What if there are many shocks at the same time?
We'd basically have to work that out in our head, as impulse-response only give us the marginal impact of each variable's one-time shock. The VAR developer can compute the net effect exactly in a special impulse-response exercise, but it would only be useful under special cases. Knowing marginal impact and the time lags involved tells us almost everything we need to know.

Other issues

What's 'Variance Decomposition' (e.g. Dr. Piti's paper, p.8)?
The impulse-response tells us how a shock to variable x affects variables z1, z2, z3... Variance decomposition tells us how variable x is responding to a shock to each of the other variables z1, z2, z3. E.g. does inflation respond more strongly to a shock to interest rate or a shock to unemployment? Variance decomposition basically gives you information on the other side of the coin.

What are stylised facts?
Stylised facts mean well-documented empirical facts, which can be taken as true beyond doubt. So any good theory should be able to at least replicate results that are in line with stylised facts. These are represented in short 'bullet-point' form, hence the term stylised. Recall earlier during the term, we noted that the traditional Keynesian model fails to explain the stylised fact that real wage, if anything, is weakly procyclical.