# G and GDP during the current recovery

(Dan here update…other posts by Robert Waldmann on the issues can be found hereherehere, and here.)

G and GDP during the current recovery

update Stephen Williamson asks “Where’s the multiplier” (I have read only the title not the post). Since I regressed rates of growth on rates of growth, my coefficient of grGDP on grG = 0.339 is not an estimate of the multiplier. I am very traumetized to note that FRED seems to be down at the moment (normally this is 7:45 AM for me and I am asleep but I am in the Washington Area and it is 1:45 AM so I awake).

I looked up G and got in in 2008 (not an ideal year as G/GDP was high) I get \$ 2.88 Trillion GDP was 14.58 trillion so my back of the envelope and based on 19 observations estimate of the multiplier is change in Gdp/Change in G = (grGDP*GDP)/(grG*G)= 0.339*14.58/2.88 = 1.716 which is surprisingly close to the IMF estimate of 1.5.

Of course even if one believed the conventionally calculated OLS standard errors (which is crazy) and assume that there are no omitted variables which is crazy, one would get an +/-2 standard deviation interval from 0.248 to 3.184 so basically I totally misled the computer about the data generatingprocess but it still understands that 19 data points can’t prove or disprove anything.

The point of my post is that the evidence, weak as it is, tends to support the Keynesian view, yet anti-Keynesians look at news about G and GDP and perceive evidence against the Keynesian view.

end update 1

update2
Now I know what they were doing when FRED was down. They added 2014q3. I think they may have updated estimates of 2014q2 as well (or maybe the fact that they rounded growth rates is the issue)

Anyway the updated regerssion with 20 whole data points is

. reg grgdp grg if qtr>2009.5

Number of obs = 20

R-squared = 0.3220

grgdp | Coef. Std. Err. t
grg | .3618508 .1237726 2.92
_cons | .0071224 .0009988 7.13

grg is the growth rate of real government consumption plus investment (G) andgrgdp is the growth rate of real GDP

I can also include the third quarter of 2009 (which I call 2009.5)

. reg grgdp grg if qtr>2009.4

Number of obs = 21
R-squared = 0.2641

grgdp | Coef. Std. Err. t
grg | .3195651 .1223656 2.61
_cons | .0067221 .0009747 6.90

OK now drgdp is the change real GDP and drg is the change in G not the rate of growth (so I am estimating a multiplier)

. reg drgdp drg if qtr>2009.4

Number of obs = 21
R-squared = 0.2619

drgdp | Coef. Std. Err. t
drg | 1.639932 .6315393 2.60
_cons | 102.4702 15.13084 6.77

This is rather close to my back of the envelope calculation in update 1. It is also only very marginally more credible.

. reg rgdp rg qtr if qtr>2009.4

Number of obs = 21
R-squared = 0.9936

rgdp | Coef. Std. Err. t
rg | 1.792217 .4021076 4.46
qtr | 422.8802 22.19399 19.05
_cons | -840916.8 45806.65 -18.36

Above an absurd regression of real GDP and real G and a time trend. Do not do this at home kids. You may fail elementary econometrics if you let anyone see such an absurd regression. But the estimate is similar.

I think I understand where the anti Keynesians are coming from. They are thinking of an even more absurd regression with no trend. This corresponds to straw Keynesian who thinks government spending is the one and only cause of GDP growth. In fact real economists have noted that GDP usually grows and also ususally grows unusually quickly soon after it has declined. So one would expect positive GDP growth with no change in policy and, while adding a trend is totally absurd the regression without one is absurder

. reg rgdp rg if qtr>2009.4

ì Number of obs = 21
R-squared = 0.8645

rgdp | Coef. Std. Err. t
rg | -5.561926 .5050749 -11.01
_cons | 31850.86 1506.905 21.14

These last two regressions are grossly miss-specified and useless (especially the very last one in which I forced a coefficient with a t-stat over 20 to zero).

Now during the recession the pattern was completely different. I would say one can’t use regressions without considering a housing bubble bursting and a financial crisis. The regression starting in 2007q4 is based on the assumption that these shocks were irrelevant or uncorrelated with G.

Just for fun here is a multiplier with all the data available at FRED

. reg drgdp drg

Number of obs = 270
R-squared = 0.0185

drgdp | Coef. Std. Err. t
drg | .4559986 .2026528 2.25
_cons | 48.74642 4.39361 11.09

The government spending multiplier mostly not in a liquidity trap is about 0.5. Again this is the IMF estimate.

end update 2

Various non Keynesians have argued that the pattern of public spending and GDP in the USA during the current recovery (that is since June 2009) undermines the Keynesian hypothesis that the Government spending multiplier is positive. In particular John Cochrane and Tyler Cowen argue that, if Keynesians were right, sequestration should have caused at least a decline in GDP growth rates.

This shows they haven’t been FREDing. The Keynesian story refers to government spending, not US Federal Government spending. A substantial fraction of Government consumption plus investment (G) is done by state and local governments. An economist may not ignore the “50 little Hoovers” (P Krugman 2009) just because political reporters focuse inside the beltway (hey I’ve recently been inside the beltway for about one minute !).

As I note, sequestration did not have a noticible effect on G — it was anticipated (says my FedGov employed dad) and was a shift in Fiscal 2013 budgets which governed spending for the following 7 months. It didn’t cause a jump in Federal spending. It is impossible to guess when Sequestration occured from the time series of US real G.

In fact, during the recovery, percent growth of real G and real GDP are clearly positively correlated. This is exactly the evidence cited by anti-Keynesians. They are a few data points which form a very clear pattern (with an outlier 2014q1 due to weather).

https://research.stlouisfed.org/fred2/graph/?graph_id=213165

Clearly the percent change in real G and real GDP are positively correlated.

Here is a scatter graph with a regression line

For what it’s worth (not much) STATA is convinced that the null of zero correlation is rejected by the data

. reg grgdp grg if qtr>2009.5

Number of obs = 19
R-squared = 0.2432

grgdp | Coef. Std. Err. t
grg | .3387477 .1449474 2.34
_cons | .6951767 .1133052 6.14

19 data points can’t prove anything, but the few data support the Keynesian hypothesis about as strongly as could be imagined. I am impressed by the unreliability of casual empiricism conducted by idealogues. Some people look at this period and see the opposite of what I see. Even now, I am shocked that economists didn’t bother to look up the data on FRED before making nonsensical claims of fact.