Saturday, May 2, 2009

Indicators For The Economy: Leads, Lags, and Coincidence

One common complaint from just about everyone is that economic data comes out at a fairly big lag. Malaysian quarterly GDP reports typically come out two months after the fact, which makes informed decision making difficult at best. I've laid out some of the reasons for the lag in this post here.

There are however some indicators that can give you a fairly accurate representation of what the economy is doing at much faster frequencies. The Department of Statistics issues monthly composite indexes that do exactly that. The Lagging Index is supposed to affirm the trajectory of the economy after the fact, the Coincident Index shows what the economy is doing right now, while the Leading Index gives an idea of how the economy will do in the future about 1 or 2 quarters ahead.

Here's what the indexes are showing up to February 2009:

All the Indexes are turning up, which gives some comfort that things are turning around. But how good really are these indexes relative to actual economic performance? The answer is: except for the Lagging Index surprisingly good.

I evaluated all three against real GDP (sample range 2005:1 to 2008:4), using both seasonal adjustment (x11) and with seasonal dummies. The quarterly index numbers are arrived at by averaging the monthly index numbers.

Only the Lagging Index didn't fit at all well. In terms of forecasting, the Coincident Index fit well in-sample but not forecasting out of sample (charts and results shown are for the non-seasonally adjusted regressions):

In-Sample Forecast (2005:1 to 2008:4):

LOG(RGDP_2005) = -0.63*LOG(IND_COIN) + 2.38*LOG(IND_COIN(-1)) + 3.36 + 0.01*D2 + 0.04*D3 + 0.03*D4

Out of Sample Forecast (2005:1 to 2007:4; dynamic forecast to 2009:1):

LOG(RGDP_2005) = 1.6729687*LOG(IND_COIN) + 3.69 + 0.01*D2 + 0.04*D3 + 0.04*D4

The Leading Index on the other hand is remarkably accurate:

In-Sample Forecast (2005:1 to 2008:4):

LOG(RGDP_2005) = 1.01*LOG(IND_LEAD) + 6.67 + 0.01*D2 + 0.04*D3 + 0.03*D4

Out of Sample Forecast (2005:1 to 2007:4; dynamic forecast to 2009:1):

LOG(RGDP_2005) = 1.02*LOG(IND_LEAD) + 6.63 + 0.01*D2 + 0.03*D3 + 0.03*D4

I admit to being surprised by these results. I would've thought the Lagging Index to be most accurate, and the Leading Index the least accurate - it turns out the opposite is true. The forecast standard error for the Leading Index is actually half that of the Coincident Index. I'd caution however that the above analysis is based on a rather short sample (reminder to self: a trip to DOS seems warranted). I'd love to know the exact composition of the Indexes and the source data - cointegration analysis would give a good idea of short term dynamics, as well as the relative importance of each component.

What does the Leading Index forecast say about 2009:1Q GDP? Based on the full sample:

Point forecast: RM128,236.1
Upper Bound: RM130,497.9
Lower Bound: RM125,974.4

The point forecast is equivalent to -0.7% growth y-o-y, and -9.5% growth q-o-q annualised, both down from 4Q 2008 growth but rather better than I expected. We'll see how accurate this is when the 1Q 2009 report comes out at the end of this month.


  1. bro hishamh

    Most enlightening. We are learning much from you. Keep up the first-class work, bro.

  2. Hi Hishamh,

    Some questions, hope you can enlighten me on:
    1. Which indicator (lagging, coincident, or leading) that the government (maybe BNM) looks at before taking action on policy changes ?

    2. Is it possible to tell how long is the lead for leading indicator, lag for lagging indicator ? Is the coincident indicator really coincident or with some lead or lag ?

    3. I saw from a book that for US, ratio of (coincident/lagging) tends to signal economic turnarounds ahead of leading indicator. Is this true for M’sia data ?

  3. 1. It would have to be BNM - fiscal policy works too slowly. As far as which index, TBH I don't know for sure, but if I have to guess it would be the coincident and leading indexes.

    2. The way I constructed this evaluation, it's hard to tell the lag structure. To figure that out I'd have to decompose GDP into monthly frequencies - not something I've studied yet. I'll revisit this topic when I have. But from my equations, it looks like both coincident and leading indexes are within one quarter of actual economic activity.

    3. That's a new one to me, but given how poorly the lagging index is in tracking GDP, I wouldn't rely on that metric too much. In any case, the ratio for Malaysia is still looking down.

  4. Hi Hishamh,

    Thx for your insights.
    On 3, the book that I mention is “The Atlas of Economic Indicators” by W. Stansbury Carnes and Stephen D. Slifer. It may be a book more for layman like me. Wonder whether its points are “correct”.
    Pg. 139 under short paragraph of : “the ratio of coincident to lagging indicator may be the best leading indicator of all”. It says this is due to business cycle.

    Early stage of economic upswing: coincident rise, lagging unchanged; thus ratio rise.
    Near peak: coincident rate of increase < lagging rate of increase; thus ratio begins to fall
    Near trough of recession: coincident rate of decline < lagging rate of decline; thus ratio rises

    It says this ratio “tend to signal economic turnarounds abt 2 months ahead of leading indicator”.

  5. Interesting theory - unfortunately not something we can check for Malaysian data as yet. The index series just don't go back far enough to test that hypothesis. I've just gotten data on these indexes from 1999, but that means testing based on just two business cycles, which isn't sufficient.