# The Accelerator

I’ve decided to look at US economic aggregates using theory and statistical methods which were popular in the 1960s. I have long told students that the model of investment which best fits the data is the now ancient flexible accelerator. This is just a reduced form equation without theory. It just says that the ratio of fixed capital investment to GDP is high when GDP growth is high and low when the real interest rate is low. I tried to look up the parameters, and couldn’t find any estimates. So I decided to see how well US data could be fit with an old fashioned accelerator.

This means going back to very old style econometrics (which is just not allowed in peer reviewed journals these days in large part for good reasons). Very old style included trends as regressors, so the actual old regressions were (I guess) the investment to GDP ratio on the GDP growth rate, an estimate of real interest rates, and a trend. In any case they had better have included a trend since one is clear in the data. So this is very old fashioned econometrics with current data.

The old accelerator fits the data quite well — the R-squared of the regression is 0.745. This should be, at least, a stylized fact which micro founded models are supposed to match.

The ratio of US investment to GDP

The amazing part is that the fit up through the early 80s is almost exact, yet this is exactly when the accelerator was replaced in the literature.

footnote and one more graph after the jump

All data are quarterly data from FRED
The dependent variable is the ratio of
Real Gross Private Domestic Investment (GPDIC96) to real GDP (GDPC1) which I call invgdp

Growth of GDP is the rate of growth of real GDP from 5 quarters before the date of the dependent variable until 1 quarter before (so annual growth lagged one quarter which I call lagrgdp for lagged annual growth of GDP)

The real interest rate is Moody’s index of Baa corporate bond rates (BAA) minus the rate of increase of the GDP deflator over the previous year which I call rbaa.

The trend is the quarter AD which I call qtr so it is now 2014.00 for first quarter of 2014. In March it will be 2014.25.

So the regression is of invgdp on lagrgdp rbaa and qtr.

The Baa interest rate is the first I tried. The annual increase in the GDP deflator is the first variable for inflation I tried. I also did the annual growth of GDP up to the quarter of the dependent variable (so not lagged). Results are very very similar and I lagged just in a feeble feeble attempt to deal with endogeneity.

It is noticible that, during the 1950s and 1960s, the actual investment to GDP ratio moved up and down a bit less than the fitted values, and that it definitely moved up and down more since around 1985. I didn’t know that. This is the opposite of what one would guess based on the shift of GDP from manufacturing to services. Anyway I added an interaction term
lagrgdp(qtr-1947) which I call tlagrgdp. For what it’s worth (very very little) STATA is convinced that the coefficient on tlagrgdp is statistically significantly positive.

R-squared = 0.7852

invgdp | Coef. t
——-+—————————————————-
lagrgdp .050042 (1.17)
rbaa -.1286123 (-4.30)
tlagrgdp .0093771 (6.98)
qtr .0008603 (16.78)
_cons -1.567528 (-15.47)
——————————————————————

Now the fitted values of the ratio of investment to GDP look almost exactly like the actual measurements. There isn’t much left to explain.

fitted values from the regression just above

The main deviation is higher than predicted investment from around 1995 through 2008 then lower than predicted investment since the trough in 2009. This very much fits the story of two speculative bubbles (.com stuff then houses) followed by deleveraging.