# 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 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.

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.

I think you’re right about the bubbles – the deviation probably represents asset price increases , not volume increases.

I’d like to see the same graph with residential housing subtracted. I suspect the strong upward trend would largely disappear.

Wow minds think alike. I am sitting here about to make the same graph with residential investment subtracted. My guess is that it removes the 21st century weirdness of higher than fitted investment then lower. I don’t have a guess about the trend.

You might be right , but my thinking was that the bubble periods inflated the prices of the measured investments , probably due in large part to rising land prices of all types , but also for such things as internet and telecom components and machinery during the frenzy of the dot com bubble.

Oh , wait , land prices are not counted as investment , right ?

I need a new theory , I guess.

Another graph to add to my “It All Started In 1980” collection. So many things came uncoupled in the late 70s and early 80s, it shows up in Econ and other graphs almost daily.

I get very good results, similar to what you are looking for by making business investment a function of profits rather than GDP.

Noni Mausa: Viet Nam, and the fall of The Embassy in Siagon IS where is started to unravel.

Robert,

Maybe I have not read this sufficiently carefully, but your verbiage plus your first figure seem to be about the ratio of I to GDP, whereas the accelerator is about I being driven by changes in GDP. It seems that when you got to making your estimate, that is what you estimated with a lag. Is that right? You have actually tested lagged GDP as an independent variable on investment and found it holding strongly (with interest rate also)? If so, the verbal discussion is very unclear on this point and does not bring this out.