Thursday, April 16, 2015

There is No Evidence that the Economy is Self-Correcting (Very Wonkish)

David Andolfatto asks in a twitter exchange for evidence that deviations of GDP from trend are non-stationary. Here is the raw data. Figure 1 is the residual from a regression of the log of real GDP on a constant and a time trend for quarterly US data from 1955q1 through 2014q4. I will refer to this series as "X".
Figure 1: X = Log of Deviation of Real GDP from Trend

Table 1 reveals the regression of X on itself lagged and on a constant. Remember that these data describe deviations from trend so persistence reflects potentially permanent deviations from the trend growth path. Notice that the coefficient on lagged X is 0.996. That of course, does not establish that the data has a unit root. 
Table 1: Regression Results

There are two approaches to testing formally for a unit root. For one group of tests, for example, the augmented Dickey Fuller test, the null hypothesis is that the series is non-stationary. For a second group, for example the KPSS test, the null hypothesis is that the series is stationary.

Table 2 presents the results of a Dickey Fuller test where the null hypothesis is that X has a unit root. Here we are looking for a test statistic that is small in absolute value if the series has a unit root, reflecting the fact that there is nothing pulling the series back towards trend. The null hypothesis that X has a unit root cannot be rejected at the 1%, the 5% or the10% level. 
Table 2: Augmented Dickey Fuller Test
The Dickey Fuller test is known to have very little power over the alternative of a root close to unity and sometimes it helps to look at additional evidence. Table 3 presents the KPSS test for which the null hypothesis is stationarity. Here we are looking for a large test statistic if the series has a unit root.
Table 3: KPSS Test
Notice that here, the null hypothesis of stationarity is overwhelmingly rejected. 

What do we learn from this? Much the same as we learn from the fact that unemployment has a unit root. Just as unemployment can remain persistently high, so GDP can remain persistently below trend. There is no evidence that the economy is self-correcting. 


  1. Very interesting post. I have a couple of questions about the ADF test you use:

    1. Since your null hypothesis is a unit root with drift and the alternative is trend-stationary, why not just run the test on the series itself (in levels) with a constant and a trend, and test the joint hypothesis of a unit root and no
    deterministic time trend?

    2. If you do choose to detrend the data first, wouldn't it be better to apply the GLS detrending first as in Elliott, Rothenberg and Stock (1996)?


  2. Itamar
    I wanted to make the point that, when there is a unit root, removing a time trend still leaves a non stationary series. Thanks for the pointer to the ERS paper. I will take a look at it.

  3. From your analysis (which I admit is well outside of my comfort zone), you conclude that "just as unemployment can remain persistently high, so GDP can remain persistently below trend. There is no evidence that the economy is self-correcting."
    The problem revealed by your analysis can most likely be explained by the fact that you are looking at national data (USA), whereas economists have convinced everyone that we should look at the world as an international system. You might find a different result if you used international data.
    While we continue to worship at the foot of Ricardo's 1820 theory of comparative advantage (which reduces the economic role of nation-state governments), there is little national governments can do to redress the problem of stratified unemployment within their own systems while continuing to promote free trade as a part of their economic solution package.
    Having insisted that every business has to compete with everyone else in the world, the only weapons left for governments are targeted fiscal stimulus and national-economy-wide monetary policy.
    Neither provides the flexibility necessary to fix the problem of the loss of jobs for those of lesser skills or education level.
    Education is not a permanent solution, since even more highly skills jobs are in danger of moving to the emerging world in the next 20 years.
    It is time that economists came up with a model that restores power to national parliaments and governments in relation to trade. Such a model should enable each nation-state to implement policies to ensure that jobs are potentially created for people of every skill and education level.
    There seems little chance of this happening in the near future, since economists cannot see past the danger of the continuing lover-affair with free trade, despite the fact that there is limited evidence of free trade pulling really poor countries out of poverty.
    Japan, Korea and China are not examples, since they have used managed trade to develop their own diverse economies (just as the US did in the 19C), not unrestrained free trade.

  4. Roger - what if you "de-trend" using the HP filter? Does the resulting cyclical component exhibit the same characteristics? (Not that I'm saying that I favour the use of the HP filter! :-) )

    1. Dave
      No. Isn't it true that every HP filtered series is stationary by construction? At least I thought I had seen that theorem somewhere....

  5. Roger - You're right, I think it was Cogley and Nason (?) who showed that unit roots up to the order of the data frequency will be removed by the HP filter. So with quarterly data the HP filtered series should not be I(1), I(2), I(3) or I(4). (If you even believe that anything above I(2) is possible for economic data.)

  6. You are showing... what? That during the golden age of macroeconomic manipulation that the economy showed the ability to fail to return to trend? Some might conclude you have showed nothing whatsoever about the economy's self-correcting tendencies.

  7. Since you detrended first, the critical values in the tables are wrong. With detrending, the ADF c.v. gets bigger and the KPSS gets smaller. But the correction strengthens your conclusion.

  8. Thanks for pointing that out David!

  9. Hmm, I am not convinced. There is no reason to assume that technological innovation is a stationary process. And, for what it is worth, a random walk process with a drift seems to be a good approximation for the Solow residual. In which case, removing a linear trend from the data will produce non-stationary series. But is it appropriate to interpret these series as a "cyclical component"? Well, what's the definition? This is precisely the point raised by Prescott (1986) in "Theory ahead of business cycle measurement", that the term "cyclical" needs to be defined in terms of the statistical properties of the series. I think Prescott follows Lucas in defining them as temporary deviations of output about a trend. The construction of the HPand the band-pass filters is based on this definition. If we reject it, we need a new definition so as to measure the "cyclical" component as alternatively defined. So what is the new definition? I didn't see one above.


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