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> Case B. A zero coefficient in the second regression, and a non-zero coefficient in the first regression, means that X(t) is a useful indicator and the central bank is responding to it correctly. (This is an immediate consequence of orthogonality of forecast errors with respect to the information set under rational expectations on the part of the central bank.)

One caveat here is that this could be true even if the central bank does not use the LMI itself in its policy-setting. It could be that whatever useful information is contained within the LMI is also contained in other, monitored variables such as GDP growth.

Majromax: true. good point. We maybe need to distinguish between utility and marginal utility!

Nick and Majromax, as I discussed in a previous post, the LMCI has a correlation coefficient of -0.96 with the unemployment rate. It seems likely that any useful info contained in the LMCI is contained in the unemployment rate:

Also, the Fed has a dual mandate so it is not just targeting 2% inflation but also employment variables that are not orthogonal to the LMCI, so that may need to be taken into account in your two equations.

> Also, the Fed has a dual mandate so it is not just targeting 2% inflation but also employment variables that are not orthogonal to the LMCI

Is there any evidence that the Fed has been acting on that dual mandate, or is it something of a legal fiction? Since adopting the dual mandate, the US inflation rate has been far more stable than the unemployment rate:

If the Fed truly has been targeting the unemployment rate in its own right rather than as a datum on expected future inflation, then it's been doing a terrible job of it.

Carola: I've been thinking about that -96% correlation. If the correlation were too low, I would be very suspicious of the LMCI. But being as high as -96% does suggest it can't add much at the margin. But if it followed the unemployment rate closely 96% of the time, but were very different the other 4% of the time, it might (or might not) still be a very useful indicator on those rare occasions. Dunno.

And the Bank of Canada's LMI for the US does track the US unemployment rate quite closely, but right now is equivalent to about a whole percentage point of difference in the unemployment rate, which seems quite a lot to me. (The graph is on my old post).

Dunno. But it would still be interesting to see if it works better than the raw unemployment rate.

I've never got my head around the dual mandate. Given any version of the natural rate hypothesis, it doesn't seem to make sense. Unless we interpret it as "flexible inflation targeting", which means you don't try to get inflation back to target instantly, because that would cause larger fluctuations in unemployment around the natural rate, but instead (like the BoC) have something like a 2-year targeting horizon for inflation. That makes sense to me, if we interpret it that way.

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