How to test whether the LMI (LMCI) is a good indicator

The Bank of Canada calls theirs the "Labour Market Indicator". I now learn from Tim Duy (HT Mark Thoma) that the US Fed has one too, and calls theirs the "Labor Market Conditions Index". I think that LMI and LMCI are roughly the same sort of thing. It's an index number that is supposed to measure the amount of labour market slack [or tightness, for the LMCI], that is based on more than just the unemployment rate. (The Bank of Canada reports an LMI for the US too, and I don't know how much it agrees or disagrees with the Fed's LMCI.)

I read Tim as asking, quite reasonably, how we can know whether the LMCI is a useful indicator for the Fed to watch. Simon van Norden asked basically the same question about the LMI in a comment on my post. In particular, does the LMI/LMCI add any useful information for monetary policy that is not already in the unemployment rate?

Here's how to test whether the LMI is a useful indicator:

Suppose the central bank is watching indicator X(t) when it sets the interest rate R(t) to try to keep (2-period ahead) inflation P(t+2) equal to the 2% target. If it responds correctly to X(t), then E[P(t+2)/{R(t),X(t)}] = 2%.

1. Run a regression of R(t) on X(t). (Or on X(t-1) if there is an information lag).

2. Run a regression of P(t+2) on X(t). (Or X(t-1) if there is an information lag).

This is how we interpret the results:

Case A: A zero coefficient in both regressions means that X(t) is a useless indicator and the central bank is (quite correctly) ignoring it.

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.)

Case C. A zero coefficient in the first regression, and a non-zero coefficient in the second regression, means that X(t) is a useful indicator but the central bank is ignoring it.

Case D. If both coefficients have the same sign, X(t) is a useful indicator, and the central bank is not responding strongly enough to X(t).

Case E. If both coefficients have opposite signs, we can't tell whether X(t) is a useful indicator, but the central bank is responding too strongly to X(t).

Maybe throw a couple of other indicators into both equations too, if it helps tighten up the standard errors. Like current (or lagged) inflation.

If you want to, you can add both the LMI and the unemployment rate to both equations, to see if the LMI adds anything useful to the unemployment rate. Or, define X(t) as the difference between the LMI and the unemployment rate.

What it is not OK to do is simply see whether the LMI forecasts future inflation, then head off down the pub. One equation is not enough. You need two.

This shouldn't be too hard to do (for anyone except an incompetent like me). Both central banks should have done this already.

[This is just a repeat of my old posts about headline vs core inflation as useful indicators.]

Comments

[Majromax]

> 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.

[Nick Rowe]

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

[Carola Binder]

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:
http://carolabinder.blogspot.com/2014/07/thoughts-on-feds-new-labor-market.html

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.

[Majromax]

> 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.

[Nick Rowe]

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.