This morning I've been in email conversations with several economists who do not understand, or disagree with, something in the Bank of Canada's latest Monetary Policy Report (pdf). Specifically, Technical Box 2. These include some very good macroeconomists.
I think I do understand it. And I agree with the Bank of Canada. So I am going to give my interpretation of what the Bank is saying. I think the Bank is right, and it's an important point that we need to understand.
The Bank of Canada is saying that it expects output to return to normal, and inflation to return to target, before the policy rate returns to normal. And that this would not happen if the Bank followed a simple Taylor Rule, but will happen if the Bank gets policy right. A Taylor Rule is not always the best policy. It may not be the same as targeting the inflation forecast.
What may trouble some economists is that if output returns to potential, and inflation returns to target, shouldn't the Bank make the policy rate return to normal too? The Taylor Rule says it should.
Here's the diagram from the Bank's Technical Box 2. (Thanks Stephen!)
The Bank of Canada tries to keep inflation at target. Since there are lags in the Bank's response to shocks, and lags in the economy's response to the Bank's response, the Bank won't be able to keep inflation exactly at target. But it does try to adjust policy to keep its expectation of future inflation, post those lags, at target. It is targeting its own forecast of future inflation
And the way the Bank sees itself as doing this is by adjusting the policy rate of interest relative to some underlying natural (the Bank prefers the term "neutral") rate of interest. If the Bank sets the policy rate so that the actual real rate is above/below the natural rate, output will be below/above potential, and inflation will fall/rise relative to expected inflation and target inflation.
Suppose there is a shock to Aggregate Demand that lowers the natural rate of interest. And suppose it is a permanent shock, so that the natural rate is now permanently lower than where it was in the past. If the Bank observes this shock, soon after it happens, and knows that the shock is permanent, the Bank should permanently lower the policy rate of interest in response. There will be a temporary recession, and inflation will fall temporarily below target, because the Bank did nor respond instantly, or because the economy did not respond instantly to the Bank's response. But after a year or two, if the Bank gets it right, those lags have passed, and output returns to potential, and inflation returns to target. But the policy rate of interest stays permanently lower than where it was in the past. There's a new normal for the policy rate. 3% is the new 5%.
And the big problem with a simple rule for monetary policy like the Taylor Rule, is that it can't handle cases like that. The Taylor Rule, at it's simplest, sets the current policy rate as a function of the current output gap and current inflation gap only. So, if it followed a simple Taylor Rule, the Bank in this example would only set a permanently lower policy rate if output were permanently below potential (which can't happen in standard models) or if inflation were permanently below target (which can happen in standard models). The simple Taylor Rule can't handle a new normal.
The above was an extreme example, where the drop in the natural rate was permanent. It was just for illustration, because it's simpler to tell the story in that case.
Suppose, more realistically, that the shock to the natural rate is temporary, but lasts a long time. Specifically, it lasts longer than the lags in the economy's response to the Bank plus the Bank's response to the shock. And suppose the Bank knows this. In that case, the Bank should cut the policy rate in response to the shock, and the economy will eventually respond, so output returns to potential, and inflation returns to target, after a temporary recession. But the policy rate should remain below normal for some time after output returns to potential and inflation returns to target. The policy rate should remain below normal until the natural rate returns to normal.
But if the Bank were following a simple Taylor Rule instead, this would not happen. The policy rate will only be below normal (the old normal) if output is below potential and/or inflation is below target. And unless the policy rate is below normal (the old normal) output will be below potential and/or inflation will be below target. So, with a simple Taylor Rule, output will be below potential and/or inflation will be below target for as long as the natural rate stays below normal (the old normal).
And that is precisely what the Bank's two pictures are showing.
And this is important because I think the Bank's assumptions are reasonable. The global economy has been hit with a serious shock to demand, that has lowered the natural rate, and this shock to the natural rate will probably last for some time.
Here's a crude model:
Let P(t) be inflation (or the deviation of inflation from target), Y(t) the output gap, R(t) the policy rate of interest, and N(t) the natural rate of interest. (Both R and N are in real terms, to keep the equations simple. I have also ignored a lot of constant terms and set most parameters to 1 to keep the equations simple.)
IS Curve: Y(t) = N(t) - R(t-1)
This is fairly standard, except I have introduced a 1-period lag in the economy's response to the Bank's policy rate, so the Bank can't perfectly stabilise the economy.
Phillips Curve: P(t) = Y(t) + 0.5 E(t-1)P(t) + 0.5 E(t-2)P(t)
This is fairly standard, if you assume something like overlapping 2-period nominal wage contracts. E(t-1)P(t) and E(t-2)P(t) mean the expectations at time t-1 and t-2 of the inflation rate at time t.
Shocks to natural rate: N(t) = S(t) + S(t-1)
S(t) is a serially uncorrelated shock, so the natural rate follows an MA(1) Moving Average process.
[Update: Curses! I think this should have been an MA(2) process. Make it N(t) = S(t) + S(t-1) + S(t-2) instead.]
Run this model through two alternative policy rules:
2a. R(t) = Y(t) + P(t)
This is a Taylor-like Rule. Remember R(t) is the *real* policy rate, so this satisfies the Taylor/Howitt principle that the nominal policy rate responds more than on-for-one with inflation.
2b. R(t) = EtN(t+1) + bEtP(t+1)
This is the optimal monetary policy rule in this model for keeping next period's inflation on target in this model. The Bank sets the (real) policy rate equal to its expectation of next period's natural rate. (The second term isn't really needed; it's just to rule out indeterminacy of the inflation rate and satisfy the Taylor/Howitt principle).
Now suppose that S(t) < 0. All other S shocks are zero. Given the MA(1) structure to the natural rate, this means the natural rate falls at time t and stays below normal for 2 periods in total, then returns to normal.
With policy rule 2a, the Taylor Rule, you get something roughly like the Bank's figure 2a. The economy has a 2-period recession, with inflation below target for 2 periods, and the (real) policy rate below normal for 2 periods.
With policy rule 2b, you get something roughly like the Bank's figure 2b. The economy has a 1-period recession, and inflation below target for 1 period, and the (real) policy rate below normal for 2 periods.
I think I've got that right. Not 100% sure. Never could do math. Somebody else can solve the model and check for me. It's not my comparative advantage.