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Sunday, March 01, 2015

Quality Premiums and GDP growth

I am still thinking about the working paper (which has since been revised) by Marco Del Negro, Marc P. Giannoni, and Frank Schorfheide of the New York Fed (pdf warning -- also not light reading). Del Negro, Giannoni and Schorfheide manage to fit the huge and persistent decline in real GDP of the great recession using a combination of the standard new Keynesian Smets Wouters 2007 (SW) model and the Bernanke Gertler and Gilchrist (1999) (BGG) financial accelerator model. The paper is mathmatically difficult.

BGG 1999 isn't all that mathematically simple either, but the BGG story is simple: there are periods of financial distress when firms have to pay high interest rates to borrow. This causes low investment which exacerbates the financial distress. The story is very old (BGG added the not so simple math). In fact old old business cycle analysts used differentials on corporate bonds with different ratings (and treasury notes) to forecast. The crisis of 2008-9 made people focus on that issue and that type of variable.

I had some fun playing with data today. I think there might be two useful lessons which I should state before the long wandering vague post. First it is very hard for me to resist the temptation to fiddle with specifications until I like the fit if I play with data with no discipline from theory or standard empirical practice. Second, it is easier to fit the severity of the downturn than its duration. I actually have a question for Del Negro, Giannoni and Schorfheide. They show forecasts for GDP and inflation, but not for the interest rate differential. I think their model might imply a forecast of a persistently high differential not the huge spike and then rapid return to near normal. This is not at all typical. To me the mystery of the sluggish recovery is that GDP remained far below trend when the initial shock was long over. My guesses of the reasons aren't related to their model at all -- I guess they are low residential investment largely because of low expected house price appreciation and low public spending. The point of this post (if any) is that a financial frictions based explanation of the sluggish recovery requires evidence that severe financial frictions lasted during the recovery. This evidence does not appear in interest rates (including the mortgage interest rate)

OK off to play with data.

To start I show Moody's Seasoned Baa Corporate Bond Yield (c) minus Moody's Seasoned Aaa Corporate Bond Yield (c)

Clearly the differential rises during recessions. There isn't much evidence that sudden fear of corporate default is the cause of recessions -- the differential rises during the recession. If anything it peaks at the trough (as if fear of a wave of bankruptcies is what causes the Fed Open Market Committee (FOMC) to relent and reflate). This is why the model is called the financial accelerator. The idea is that, generally, something else causes low GDP and financial distress and the risk premium effect makes the decline in GDP worse.

I see two cases in which an increase in the differential was, arguably, the result of something other than a general downturn (maybe because I have vivid memories of both). One, of course is the gigantic spike when Lehman failed. The other occurred when Enron failed. If you look closely at the tiny 2001 recession, you can see that the differential spiked during the recovery.

For some reason I decided to do some embarrassingly primitive calculations related to the differential and real GDP growth (the motive was it's fun to play with data and I wanted to decide how impressed to be with Del Negro, Giannoni and Schorfheide 2013). I think the exercize is useful for two reasons.

First it is a warning about what can go wrong if one starts playing around with numbers completely unrestricted by any theory. It is very hard to resist data dredging and cherry pickign while looking at time series and fiddling with ad hoc specifications. In any case, I can't resist and just don't take the results of the fiddling seriously.

First a regression of the annualized percent growth rate of real GDP on the interest rate differential (in percent)

. reg grgdp00 idiff

Number of obs = 267

R-squared = 0.0961

grgdp00 | Coef. Std. Err. t

idiff | -2.715849 .5115451 -5.31

_cons | 5.712052 .5345035 10.69

A very large t-statistic. I should stress that this isn't really a forecasting equation as the interest rate data aren't lagged -- the idea is that people observe interest rates immediately long before real GDP has been calculated. Also I use all the available data for the regression including data from the great recession

Now I predict the annualized growth rate of GDP using the simple regression and see that it doesn't fit the great recession well

| qtr pgrgdp00 grgdp00 |


242. | 2007.25 3.240629 3.056305 |

243. | 2007.5 3.322104 2.677107 |

244. | 2007.75 3.050519 1.456368 |

245. | 2008 2.208606 -2.70417 |

246. | 2008.25 1.937021 1.972044 |

247. | 2008.5 1.475327 -1.989932 |

248. | 2008.75 -2.489813 -8.796125 |

249. | 2009 -2.272546 -5.63592 |

250. | 2009.25 -.9960956 -.423468 |

251. | 2009.5 1.937021 1.266436 |

252. | 2009.75 2.643142 3.788124 |

The prediction is of a brief mild recession.

So I decided to play with the specification (or rather played with the specification because I can't resist). I added a lag of the interest rate differential (I expected a negative coefficient)

. reg grgdp00 idiff lidiff

Number of obs = 267

R-squared = 0.1338

grgdp00 | Coef. Std. Err. t

idiff | -6.371246 1.18959 -5.36

lidiff | 4.027055 1.18828 3.39

_cons | 5.362076 .5343076 10.04

This is what happens when you add 2 similar variables. I used this silly regression to predict real GDP growth and find that it matches the severity of the 2008 4th quarter downturn 2008 but not the fact that it continued in 2009 and also predicts a dramatic recovery in the third quarter of 2009.

Totally losing all intellectual self discipline, I couldn't resist regressing real GDP growth on the current quarter's interest rate differential and the differential lagged two quarters

. reg grgdp00 idiff l2idiff

Number of obs = 266

R-squared = 0.1800

- grgdp00 | Coef. Std. Err. t

idiff | -5.906914 .7877269 -7.50

l2idiff | 4.026046 .7861379 5.12

_cons | 4.941499 .5353582 9.23

. predict p2grgdp00

(option xb assumed; fitted values)

(2 missing values generated)

The blatant trick makes the effects of a spike in the diffential last two quarters so 2009q1 is fit as well.

The only point of this last bit with the differential lagged 2 quarters is as a warning about the temptations t data dredge. Looking at the graph, I realized I had gone too far.

update: I need help. Stop me before I regress further. For what it's worth I did regressions using only data from before 2008. The coefficients are a bit larger. the predicted values over fit the great recession and include a very dramatic recovery.

But the thing that really alarms me is that I estimated

reg grgdp00 idiff ddiffsilly l2idiff lidiff lgrgdp00

Where lgrgdp00 is the lagged growth rate of real GDP and ddiffsilly is idiff minus idiff lagged two quarters if idiff is greater than idiff lagged two quarters or zero if idiff is less than idiff lagged two quarters. Here I went back to using all available data for the regression. The regressions before the update are silly because they don't include lgrgdp00 or any recognition of the univariate dynamics of the GDP time series. However including ddiffsilly is obviously just a way to avoid predicting a dramatic recovery.

Here is a graph Finally I estimate that last crazy regression using only data from before 2008 (so 3rd quarter 1947 through fourth quarter 2007). reg grgdp00 idiff ddiffsilly l2idiff lidiff lgrgdp00 if qtr<2008

1 comment:

reason said...

Robert, very interesting and tends to confirm my view that we are wasting our time with general equilibrium models and need to concentrate on proper dynamic models (I don't regard DSGE models as dynamic - in my view general equilibrium, if it exists at all, must arise from the dynamics - not the other way around).

By the way, I think the "stochastic" bit is also wrong headed. The stochastic bit has to really look at the effect of risk - and not just on lenders, on borrowers as well. The "quality premium" just looks at lenders risk perception. Borrowers perception of risk (whether they think they will get their money back / can afford to pay of the loan) are at least as important.