Tuesday, August 7, 2012

NGDP Autoregressions and the Lucas Critique

Is NGDP growth sticky? In other words, does above NGDP growth in one period affect GDP growth in the next? Evan Soltas has previously shown that RGDP appears to be sticky. He constructed some impulse response functions and found that there is no instantaneous self-correction mechanism. On the nominal side, there is substantial evidence indicating that inflation is sticky. The correlation coefficient for the relationship between the current inflation rate and the inflation rate measured one quarter ago is 0.75. Another way of saying this is that about 50% of the variability in current inflation can be predicted by inflation one quarter ago.

Does NGDP, the sum of inflation and RGDP, suffer from the same stickiness? If it does, this could have serious implications for NGDP level targeting. If it takes a long time for past NGDP surges to slow down, this could affect the speed at which central banks can change expectations of NGDP. central banks may need to take even more drastic action to adjust NGDP at the necessary speed, causing monetary policy to be blunt and not credible.

To answer this, I looked at the NGDP time series from 1947 to today and constructed a multiple regression model to explain the current NGDP continuously compounded annual rate of growth as a function of the NGDP growth rate for the past six quarters. As only the coefficients for the past two quarters were statistically significant at the 95% confidence level, I settled with testing NGDP as an AR(2) model. The results of my regression are listed below:

lm(formula = n[, 1] ~ n[, 2] + n[, 3])

     Min       1Q   Median       3Q      Max 
-14.5968  -2.1681  -0.1866   2.0848  13.5262 

                 Estimate  Std. Error t value   Pr(>|t|)    
(Intercept)  2.82257    0.47431   5.951     8.93e-09 ***
n[, 2]         0.43320    0.06257   6.923     3.67e-11 ***
n[, 3]         0.13255    0.06250   2.121     0.0349 *  
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 3.943 on 251 degrees of freedom
Multiple R-squared: 0.2631,     Adjusted R-squared: 0.2572 
F-statistic:  44.8 on 2 and 251 DF,  p-value: < 2.2e-16 

From this, we can say that about 26% of the variability in current NGDP growth is explained by past NGDP growth. To get a better idea of what the relationship looked like, I also plotted the predicted values of NGDP versus the actual values:

While the intercept is not statistically significant different from zero, the slope is 1, with standard error of 0.10, suggesting that the model does do a reasonable job of estimating actual NGDP. So does this data prove NGDP is sticky, making instantaneous NGDP expectation adjustment impossible?

As with most economic questions, the answer is "not necessarily". Perhaps NGDP is sticky because of certain nominal frictions in the economy, such as staggered wage contracts or menu costs. These traits, while they endow nominal shocks with real effects, also mean that nominal levels in the economy have momentum. If wages are suppressed for extended periods of time, the economy would be able to stay at higher levels of aggregate activity for longer. Alternatively, information itself can be sticky. So even if economic agents stand at the ready to change prices and to be flexible, they don't observe economic conditions quickly enough, acting in a way that creates nominal momentum.

A first pass analysis would suggest that these frictions would fundamentally limit the ability of NGDPLT to achieve stability. If elevated current NGDP always predicts elevated future NGDP, then there would be no way for a central bank to credibly commit to quick NGDP corrections.

However, given some recent discussion of Milton Friedman's thermostat, we have to ask if this result is regime dependent. Take inflation for a concrete example. The Federal Reserve has, for most of its recent history, targeted the rate, not the level of inflation. What this means is that if the Fed overshoots one year, there's no expectation for the Fed to compensate with lower than normal inflation for the next year. There's no expectation for monetary policy to correct the elevated inflation, which allows all the frictions mentioned above to keep inflation persistent. But if there's an expectation that the Fed will engage in corrective policy as in level targeting, then inflation may not be as persistent. Higher inflation today would actually predict lower inflation tomorrow as the central bank quickly acts to restore the original price level trend. Applied to NGDP targeting, if people perceived that current NGDP growth was higher, they would have an expectation that future NGDP growth would be slower. They could then act on that expectation and quickly restore trend NGDP. We could also test this hypothesis by testing if inflation or NGDP autocorrelations are higher in rate targeting countries than level targeting countries. However, I do not know of any central banks that have a formal committment to any kind of level targeting, so I'm not sure how robust my results would be.

This discussion of autoregressions and NGDP stickiness is also an instance where the Lucas critique defends the effectiveness of monetary policy. While I can run a multiple regression and find "evidence" that NGDP growth is sticky, because my arguments are not microfounded I have no theoretical reason for why NGDP growth would stay sticky in a level targeting regime. So to fully understand how nominal persistence can affect NGDP targeting, we need a microfounded model that can analyze the intertrelated process of nominal frictions, policy and expectation formation: a hole that market monetarists must be able to fill.


  1. The Lucas Critique is actually a footnote to John Maynard Keynes's criticisms of Tinbergen and the econometricians. See the following book and the following review.



    In any case, while I think NGDP targeting might work, I think that econometrics needs a more rigorous statistical methodology. Benoit Mandelbrot, like John Maynard Keynes, criticized the econometricians for the assumption of the standard normal distribution without a goodness of fit test.

    A reformed econometrics would be more in line with Keynes and Mandelbrot's criticisms. (Financial economics, with it's ARCH-GARCH-and-so-on techniques, needs to follow Mandelbrot. Fluctuations in investment that are subject to decision-making under uncertainty/ambiguity, according to Dr. Michael Emmett Brady, are best done with the the techniques of non-parametric statistics.

  2. Yichuan,

    Check out Noah Smith's comments on those posts of mine.

    - Evan