Wednesday, December 10, 2008

Dr. Taylor’s Monetary Tonic

A Taylor rule ( named for John Taylor of Stanford) is a somewhat mechanical rule for monetary policy that suggests that an optimal policy should minimize the variation of inflation around its target and output around its potential. Its general specification is:


r =r* + β(π- π*) + γ(y – y*), where values with a *are steady-state or target values.



Even though the Bank of Canada is mandated solely to keep inflation near its target of 2%, it is not surprising that it responds to an output gap as well since an economy growing above potential is inflationary. An estimated rule reveals weights on the inflation and output gap of 1.88 and 0.38 – awfully close to the values of 2 and 0.5 suggested here: http://www.bankofcanada.ca/en/res/wp/2002/wp02-1.pdf. These estimates show a much heavier weight on excess inflation than on output, about what we should expect from an inflation targeting central bank.

Taylor rule for the target rate tracks the average quarterly overnight rate fairly closely, though suggests that the Bank should have started cutting earlier and more aggressively





UPDATE- Nick Rowe asks where the broken line comes from in the above graph - It represents my forecast (guess) at the future path of the output gap and inflation. Needless to say, i'm expecting inflation to not be a problem and for growth to disappoint to the downside. I've also added a second red broken line to show the Taylor rule path for the overnight rate based on the current BoC forecast (MP from Oct. 23). Thanks Nick.

















r = r* + β(π- π*) + γ(y – y*), where values with a * are steady-state or target values.



Even though the Bank of Canada is mandated solely to keep inflation near its target of 2%, it is not surprising that it responds to an output gap as well since an economy growing above potential is inflationary. An estimated Taylor rule reveals weights on the inflation and output gap of 1.88 and 0.38 – awfully close to the values of 2 and 0.5 suggested here: http://www.bankofcanada.ca/en/res/wp/2002/wp02-1.pdf. These estimates show a much heavier weight on excess inflation than on output, about what we should expect from an inflation targeting central bank.



A Taylor rule for the BoC target rate tracks the average quarterly overnight rate fairly closely, though suggests that the Bank should have started cutting earlier and more aggressively.







UPDATE- Nick Rowe asks where the broken line comes from in the above graph - It represents my forecast (guess) at the future path of the output gap and inflation. Needless to say, i'm expecting inflation to not be a problem and for growth to disappoint to the downside. I've also added a second red broken line to show the Taylor rule path for the overnight rate based on the current BoC forecast (MP from Oct. 23). Thanks Nick.







3 comments:

Nick Rowe said...

Where did you get that dotted line from? Was it from the Bank's own forecasts of output and inflation, plugged into the estimated reaction function?

Trouble is with those estimated Taylor rules, the real time output gap figures are very different from the final revised figures, I have heard.

You know, it seems to fit quite well from about 2003 on, but badly before that.

Shock Minus Control said...

The dotted line is my forecast (read: guess) for values of the output and inflation gap over the next 4 quarters.

I meant to plug in the BoC forecast to show the implication for a Taylor rule, but my my train ride to work ended before I had the chance. Perhaps i'll update it tonight.

Interesting that the fit is so poor prior to 2003 - any guesses as to why?

Nick Rowe said...

My knee-jerk reaction on simple Taylor Rules for Canada is: "What about the exchange rate?" (I'm the last living MCI guy.) When I played with this stuff in the past, I convinced myself that the y/y change in the exchange rate belongs in the reaction function. It's not obvious that including the exchange rate will fix that graph, but it's probably worth a shot.

But then those real time vs final revised numbers for potential output are also a big problem. Simon Van Norden told me, IIRC, that they have little relation to each other. That's why I like the unemployment rate instead, since it's real time data.

It's interesting to compare those two dotted lines on the graph. I'm going to make my forecast now: your "guess" will beat the Bank's guess.