Research Project for Economics Student(s)

I don't have a comparative advantage in doing this, so why not see if I can find someone who does?

If you are interested in Canadian monetary policy, and have basic econometric skills, you should be able to do this. And the answer you come up with might be interesting.

1. Read my old post (or posts, by just typing "core" in the search box on the right) on how we could properly test whether it is core or total inflation (or both) that central banks should be looking at when they decide on monetary policy. Remember that there's a distinction between what variable the central bank should be targeting (should it try to hold total inflation or core inflation constant at 2%?), and what indicator variable(s) the central bank should be looking at when it adjusts monetary policy to try to hit that target (if total inflation rises, and core inflation falls, should the bank tighten or loosen to hit its target?). The Bank of Canada has already answered the first question, by deciding to target total inflation. You are trying to help answer the second question: what should it look at and respond to if it wants to target total inflation? Before doing any econometrics you must first get a rough idea of why you are doing it and what the results might mean.

2. Get monthly data for the last (say) 20 years on: CPI inflation; core CPI inflation; the Bank of Canada overnight rate; and maybe a couple of other variables that you think the Bank of Canada might look at when setting the overnight rate (like unemployment rate and exchange rate?).

3. Estimate the Bank of Canada's reaction function. You are trying to find out whether the Bank of Canada has in fact responded to total and/or core inflation in the past, and how strongly it has responded to each. Remember that Statistics Canada publishes data with a lag, and there's a lag between the data being published and the Bank's next Fixed Announcement Date, and a lag between FADs. So there is no way the June overnight rate can respond to the June inflation rate. There will be a lag in the response. My guess is a couple of months. You might want to add other variables to the right hand side of the equation that you think the Bank might also respond to. Maybe unemployment rate and exchange rate? You might find the equation works better with the lagged overnight rate on the right hand side as well. Your call.

4. Estimate an "inflation forecasting equation". Remember that the Bank of Canada is supposed to be targeting 2% CPI inflation at a (roughly) two-year horizon. If the Bank of Canada is responding perfectly to the information it has available, deviations of CPI inflation from the 2% target should be unforecastable from anything the Bank had information on when it set the overnight rate two years back. That's testable. See what happens when you run a regression of inflation minus 2% on two year ago information, like total and core inflation. For example, if you find that core inflation is a good forecaster of two year ahead total inflation (with a positive sign) that means the Bank should have been responding more strongly to core than it actually did.

5. Report back your results. Don't be surprised if your results come out weird or meaningless; that's an occupational hazard. Don't be surprised if everybody else says you did it wrong, and suggests all sorts of possible changes to your regression equations; that too is an occupational hazard. (Actually, more of a certainty than a hazard, because they always do this.)  Don't blame me if the whole thing turns out to be a waste of time; that too is an occupational hazard. Empirical work is risky.

Good luck!

Comments

[John]

Not that risky...

Obvisouly if you dont get significant results, it is most likely a waste of time but even then some people are able (especially now) to sell their papers by saying that we though there was something but there is not... it is important because...

but does empirical macro is still publishable? I only see model and then estimation of model in seminars...

[Nick Rowe]

John: if you get statistically insignificant results in the second equation, that's OK. It means you cannot reject the hypothesis that the Bank has been doing it right. Which is an interesting result. Then you have to look at the first equation, to see what the Bank has been doing (and hope it makes sense).

[Mik]

Nick, the policy rule in ToTEM is a forward-looking Taylor rule with interest rate smoothing (publicly documented). If one's objective is to estimate that rule in a manner consistent with the conduct of monetary policy, it can't really be done by anyone outside of the Bank of Canada. Not only do you need a real time estimate of the Bank's output gap measure, but you also need access to the Bank's inflation forecasts.

If, on the other hand, the objective is to just estimate a hypothetical policy rule for the central bank, that is easy enough to do but not necessarily informative. Even if you deal with all the real time considerations, monetary policy doesn't mechanically react to any rule. In fact, it is impossible to summarize what the central bank looks at (numerous variables) in a simple regression without exhausting degrees of freedom.

[GVoss]

I'm not sure about the central bank's reaction function but as far as the fourth point is concerned, here is an example of what one might do: http://web.uvic.ca/~gvoss/Papers/Otto%20and%20Voss%20Manuscript.pdf, though allowing for near term considerations other than inflation. (I realize this is a bit self-serving but you did say report back your results.)

One qualification to the inflation forecasting equation is that the bank doesn't just target 2%. It has a 1-3 percent band, which is a little different. It's not impossible to accommodate this, just a bit of extra work.

[Chris Auld]

Graham, your link doesn't appear to work.

[GVoss]

Thanks Chris. Not sure what the problem is but a link to the paper, "Flexible Inflation Forecast Targeting: Evidence from Canada" is available at web.uvic.ca/~gvoss/research.html

[Too Much Fed]

"2. Get monthly data for the last (say) 20 years on: CPI inflation; core CPI inflation; the Bank of Canada overnight rate; and maybe a couple of other variables that you think the Bank of Canada might look at when setting the overnight rate (like unemployment rate and exchange rate?)."

Just out of interest, does anybody know if the bank of canada has something similar to the fed's flow of funds that shows currency denominated debt levels? Thanks!

[Nick Rowe]

Mik: yep, but: they don't actually follow the rule in their model, they just stuck that in as a rough approximation to make the model work. And, what the bank ultimately does is react to the information, and (so the bank says) all that information is publicly available. What we are trying to do here is see if they are responding correctly to that information.

GVoss: Thanks, I will check it later. The Bank says it is aiming for the mid-point in the 1%-3% band. I read that as 2%, and the only purpose of the band is just to acknowledge that it can't be expected to hit 2% perfectly. I read the band as a sort of "standard deviation" measure.

[Determinant]

While we're at it I have another suggestion. Stephen Gordon has blogged about the different between the GDP Delfator (reflecting Gross domestic incomes) and the Consumer Price Index. CPI has risen faster than GDI and I feel this is a major economic point. Stephen said the concept is the Labour Terms of Trade and that they are deteriorating. I want to know what items are causing that difference.

The idea is that in our economy we produce 8 apples and 5 oranges and consume 5 apples and 8 oranges. Thus we trade 3 apples for three oranges. I want to know what the real world counterparts are to the 3 apples and 3 oranges and which items are causing the divergence.

Research? Anybody?

[GVoss]

Nick: I don't disagree with your interpretation of the 2% but it is possible that we might be asking too much from a forecasting equation (or being unduly harsh using it to assess the Bank of Canada's record). An alternative interpretation is to ask whether any observed deviations outside of the 1-3 band were forecastable at a point in time where policy could have done something about them.

To be a little clearer. If the horizon is eight quarters, we could ask whether an episode such as 2003, where we left the band, could have been predicted eight quarters prior to this. If so, then the Bank should have done something differently. If not, then (conditional on whatever information set we are using) the Bank did all right.

I've posted a simple picture of this which I think is self-explanatory. The inflation measure is CPI ex Food and Energy, so it's like core.* The point is that the the while the variables used for forecasting here are all doing a good job --- evidence against the Bank doing all that it could as far as 2% is concerned --- no significant breach of the 1-3% bands are forecastable. It's not meant to be definitive, just a slight variation on the forecasting equation you suggested.

The picture is at: web.uvic.ca/~gvoss/Canada.pdf

*This is part of other work which also looks at provinces, which is why we are not using the Bank's core measure. It is a bit more volatile than core.

[Nick Rowe]

Graham: Neat paper and picture. We are thinking very much along the same lines here (though you have taken the econometrics farther than I can take it).

In your picture, is that a forecast of inflation at an 8 quarter horizon?? (It fits actual inflation far too well for that to be plausible??)

Suppose it were strictly true (as your findings suggest it's roughly true) that you cannot forecast deviations of inflation from 2% at an 8 quarter horizon. Then I would say the Bank is getting it right. And if estimating the Bank's reaction function shows (say) that the Bank responds to core but ignores headline, then I would say that core is what matters and headline doesn't.

[GVoss]

Nick: Thanks. The picture does show eight quarter ahead forecasts for inflation (with the s.e. bounds). And I am as surprised as you are at the forecast quality and we are still checking things. An important caveat is that these are in sample forecasts and the variables (wage, employment, and real gdp growth - all four quarter ended) have been selected after some search. Your interpretation --- that it appears that the Bank is getting it right --- is how I would interpret this as well; despite the apparent ability to forecast inflation.

I should emphasize that this is not actual core inflation but CPI ex food and energy (so it hasn't been stripped of indirect taxes) and particularly in the last ten years these two series have quite different inflation rates. I'm not entirely sure why they are so different.

The picture is based on work I am doing with Max Chaban at U Sask. It is still preliminary so all the usual caveats apply.

[Nick Rowe]

Graham: then your picture does look surprisingly good. Even allowing that you searched over variables to put on the RHS, and maybe functional form.

When I was playing with this stuff 10 years ago, I sometimes did a rolling sample version of the forecasting equation, to try to reduce the problem from fitting the equation based on a length of data series that was not available to the Bank at the time. I.e. I would estimate the equation using data up to 2000 to forecast 2002 inflation. Then data up to 2001 to forecast 2003 inflation, etc.

I have heard the argument (from people at the Bank) that it is better to use CPI net of indirect taxes as the target variable, since the Bank does not try to prevent "first round" effects of GST changes, etc., even if these GST changes are predictable.

[Nick Rowe]

BTW, David Tulk, now at TD, was at the Bank at the time, and doing the actual regressions for me. (I'm a komputer klutz.)