State Space Models

All state space models are written and estimated in the R programming language. The models are available here with instructions and R procedures for manipulating the models here here.

Monday, February 11, 2013

Should The Fed "Pop Bubbles"?


Recently, Matthew Yglesias posted a note on MoneyBox arguing that the US Federal Reserve should be trying to stabilize nominal GDP rather than attempting to "pop bubbles" (here). He was responding to a speech (here) by Jeremy C. Stein, a Harvard Economics Professor and member of the Board of Governors on the US Federal Reserve. Professor Stein was trying to figure out what caused the Financial Crisis of 2007-2008. Stein's hope was that some indicators of the developing "bubble" could be found that would signal the Fed to take some policy action. Yglesias, a Harvard alumnus and economics blogger, was arguing that the Fed should not pop bubbles but rather concentrate on stabilizing nominal GDP.

Yglesias bases his argument on the graph above. He feels that to characterize the Bush years as having launched with a "jobless recovery" is a mistake. Rather, he constructs a peak-to-peak trend line (the solid red line) and argues that the early Bush years were actually a period of "sub-trend GDP growth" and the supposed "bubble" is only a brief period between 2007 and the crash in 2008. A bubble this small and this brief would be hard for the Fed to recognize and monetary policy would not have been able to respond quickly enough to avert the crash. He concludes that the Fed should try to regulate guaranteed financial institutions, regulate fraudulent lending practices and "...stabilize the path of nominal GDP." To the last conclusion, my question is "Which nominal GDP path?"

If we construct a trough-to-trough GDP trend line we can see the end of the Clinton Bubble and the development of the Bush Bubble (the yellow line that I have placed in the graph above). The Obama years are simply a return to the linear trend line. This approach would have given the Fed five years to see the coming crash and potentially pop the developing bubble with tight monetary policy. In other words, whether we think the red line or the yellow line is the stabilized GDP path makes a lot of difference. How do we decide?

Proposals have been floated by analysts at Goldman-Sachs (GS, here) showing how to calculate a "nominal GDP target" that could be used by the Fed to guide monetary policy. It is also being argued (here) that Fed Chairman Ben Bernanke may have "capitulated" and now supports a nominal GDP target.

The graphic above is taken from the GS report. The "nominal GDP trend" line (target) looks very much like a peak-to-peak line. However, the GS line is drawn by extrapolation backwards from 2007Q4 assuming a 5.3% growth rate and extrapolating forward using a 4.5% growth rate. The forward projection is the sum of real potential GDP growth (2.5%) and inflation (2%). The report, however, argues that "The specific numbers matter less than the Fed's willingness to target a path that is anchored at a point like 2007, when the economy was near full employment..."

The peak-to-peak path is probably the path the most economists would say is correct or at least is the "full-employment GDP" line that policy should be directed at. It is obviously what the economy is capable of generating and must, in some sense, be optimal. If an economist believed that an economy could overheat, as Prof. Stein seems to in his speech, then maybe the trough-to-trough line provides a better "temperature" path for the economy.

In a number of other postings on "economic bubbles" (I will try to bring them together in a summary post) I have argued that drawing lines on graphs, whether based on peak-to-peak or growth-rate projections (exercises commonly done by financial analysts and economists) is arbitrary. We need a statistical model that can both fit the data and generate a path for the economy that is independent of shocks, bubbles and other random (or nonrandom) events that generate the data we are looking at (GS offers a "toy" model in their paper, it is not statistically estimated, has no error terms and does not produce prediction intervals for the policy experiments). If 2007 is the peak of the bubble then using 2007Q4 as the full-employment target is the same as arguing that the Fed should use monetary policy to generate another bubble.


My attractor path for real GDP (GDPC96*) was presented in an earlier post (here) and a close-up view of the Subprime Mortgage Bubble is presented above. How this graph was constructed is described in a technical note below. What is important to understand is that the lower 98% confidence interval (dashed blue line) for the model-based attractor path is very close to the trough-to-trough line while the peak-to-peak line is well outside the upper 98% prediction interval (dashed green line). It also should be pointed out that in 2010Q1, real GDP was right on GDPC96*.

This exercise makes a number of points about whether Fed policy should be directed a popping bubbles: (1) Bubbles are clearly visible if you draw a conservative trend line for target GDP. (2) Professor Stein's concerns then over finding other indicators (see the Technical Note below for the list of Stein's potential indicators) to tell whether credit markets are "over heating" would only be useful if you are trying to determine when the bubble will pop. (3) The politics of setting conservative target GDP trend lines are horrible. Financial pressure groups, such as Goldman-Sachs, will not accept conservative GDP targets and neither will any other member of the US political or economic elite. Everyone wants maximum economic growth and no one was happy with economic performance in 2010 when the economy was on the model-based attractor path. (4) The current problems the Fed is having with the zero-bound (interest rates are near zero, real interest rates are negative and the Fed funds rate is no longer a useful policy instrument) is the result of letting the bubble develop without gradually increasing interest rates starting in 2004. When we get to the peak of the bubble with low interest rates, there is no where to go when the bubble pops.

In summary, if the Fed could set a conservative path for target GDP (nominal or real) and if interest rates start increasing as the bubble starts forming (GDP above the target path), then the Fed has a chance of stabilizing GDP. If the Fed follows Mr. Yglesias, Goldman-Sachs and others who call for a peak-to-peak target path for GDP, the Fed doesn't have a chance of either stabilizing GDP or popping any bubbles.

TECHNICAL NOTE: The GDPC96* forecast was generated in a number of steps. First, five competitor time series models were estimated: (1) a random walk model, (2) a business as usual (BAU) model (similar to the GS forecasting approach), (3) a full-employment structural model (similar to a Keynesian full-employment model or a full-employment economic growth model) predicting GDPC96 from CE160V (Civilian Employment data from the St. Louis Fed), (4) a system model where GDPC96 is driven by the state of the US economy (state variables from the USL20 model) and (5) a system model where GDPC96 is driven by the state of the World economy (state variables form the WL20 model). The best model, based on step-ahead predictions and using the lowest AIC criterion was the BAU model.

The BAU model, however, was not that useful for defining GDPC96*. The AIC comparison was made using step-ahead predictions which are subject to error from the last period. To eliminate that error, each model was simulated starting in 1950 only using initial conditions and predicted input variables, if any. This is called a free simulation and produces an attractor path free of year-to-year error.  The best attractor model, again using the AIC criterion, was now the WL20 state-variable model. The time series graph above was constructed using a bootstrap free-simulation procedure to generate the 98% prediction intervals.

The input variables in the GDPC96 WL20 model contain none of the variables that Jeremy Stein looks at in his paper (here): high-yield share of corporate bond issuance and excess returns, syndicated leverage loan issuance, credit spreads on high-yield corporate bonds, payment-in-kind (PIK) bond issuance, covenant-lite loan issuance, dividend recapitalization loan issuance, average debt multiples of large corporate LBO loans, dealer financing of corporate debt, inflows into high-yield mutual funds, inflows into high-yield ETFs, total agency REIT assets, and collateral transformation transactions). These are all interesting dependent variables that could be forecast in the same way that GDPC96 was. If attractors can be found for these financial variables, departures from attractor values could be correlated with departures from GDPC96*. However, from a causality perspective, if the same bubble forces are pushing financial variables away from equilibrium there is likely to be a lot of confounding in such an analysis. From a control perspective, we need to take departures from GDPC96* and feed them back to control the input variables so that the bubble never happens.

The GDPC96 model was developed entirely in the public domain using the R programming language. Instructions for using the model are available here, here and here. The GDPC96 model is available to download here.

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