## A Bit More On Consumption

This is another entry into the series Rip Van Keynesian wakes up after 40 years and tries to analyse data up through 2013 with Paleo Keynesian concepts and statistical techniques. I’m pretty sure the main reason these notes can’t be published in any academic journal is that I will use old fashioned statistical techniques. It can be fairly safely assumed that no ratio of a coefficient to a standard error (t-statistic) reported here has a Student’s t distribution under the Permanent Income Hypothesis null. You have been warned.

So last time I noted that US aggregate consumption is very well fit by a constant times disposable personal income plus three variables related to wealth – the ratio of the S&P500 index to personal disposable income, the ratio of the US Federal debt to personal disposable income and the ratio of a house price index to the consumer price index (CPI). This totally dumb model fits the time series data quite well. However, the constant is about 0.88 which would imply a government spending multiplier of about 8 for a closed economy in a liquidity trap. Recall the relatively modest effects the stimulus bill and of reductions in state and local spending. Estimates of multipliers range from slightly less than one to 1.5 (Blanchard et al at the IMF). Clearly there is something else going on.

My guess is that the short run response of consumption to changes in income is less than one because of habit formation. So my guess is that consumption is best described with a model of myopic agents with habits (this is Stephen Marglin’s model which I saw presented as just an example of a model other than the PIH). Marglin’s point (which struck me with the force of a new idea after a delay of over 20 years) is that the patterns seen in cross sectional data of consumption by household can be explained equally well by the PIH and his model.

In the simplest version of this model consumption depends not on current income but on a lagged income with coefficients which decline exponentially. I think we know something about multipliers from painful experience. We know that consumption doesn’t depend only on current income (even if the time series are almost proportional). We don’t know if it depends on future expected income, past income or something else.

It seems to me that the first thing to do is to regress the log of the ratio of consumption to disposable income on leads and lags of the growth rates of personal income. Marglin predicts a negative coefficient on lagged growth (as consumers haven’t learned how to consume higher income or to reduce consumption to match lower income) . The PIH implies a positive coefficient on future income growth as discounted expected future income is part of permanent income.

I start with annual growth rates calculated with quarterly data (1947q1 through 2013q4). STATA says that Marglin was right. The coefficient on the change in log real personal disposable income since over the past 4 quarters (gr4rinc) is large and negative while the coefficient on the growth over the next four quarters is small and actually negative. This regression provides less than no support for the PIH and shows some evidence of habit formation.

. reg lnconsinc gr4rinc ldgr4rinc

Number of obs = 260

R-squared = 0.0521

Root MSE = .02573

lnconsinc | Coef. Std. Err. t

————-+—————————————-

gr4rinc | -.2900787 .0792252 -3.66

ldgr4rinc | -.0774749 .0792302 -0.98

_cons | -.1109063 .0040987 -27.06

More including totally naive calculations of multipliers after the jump

OK now income growth over the past 8 quarters (gr8rinc) and the next 8 quarters (ldgr8rinc)

. reg lnconsinc gr8rinc ldgr8rinc

Number of obs = 252

R-squared = 0.0889

Root MSE = .02521

lnconsinc | Coef. Std. Err. t

————-+———————-

gr8rinc | -.2132141 .0582193 -3.66

ldgr8rinc | -.1451357 .0577067 -2.52

_cons | -.1000141 .0051416 -19.45

Again the coefficient which should be positive according to the PIH is negative and the coefficient which should be negative if there is habit formation is negative.

Finally (just to report all the regressions I estimated) log income growth over the past quarter (grinc) and the upcoming quarter (ldgrinc)

. reg lnconsinc grinc ldgrinc

Number of obs = 266

R-squared = 0.0456

Root MSE = .02642

lnconsinc | Coef. Std. Err. t

————-+———————————————–

grinc | -.5615131 .1640519 -3.42

ldgrinc | .1396652 .1651578 0.85

_cons | -.1186457 .0025303 -46.89

The coefficient on the lead is now positive, but very small.

I decide again that expected future income (which must be positively correlated with achieved future income) doesn’t have much effect (this is consistent with full rationality if it is very hard to forecast future income). So an especially barbaric regression on a bunch of lagged growth rates. gr2rinc is the growth of log personal disposable income from two quarters ago to the present.

. reg lnconsinc grinc gr2rinc gr4rinc

Number of obs = 264

R-squared = 0.0671

Root MSE = .02586

lnconsinc | Coef. Std. Err. t

grinc | -.1758926 .231672 -0.76

gr2rinc | -.1219394 .2048533 -0.60

gr4rinc | -.2153378 .1156833 -1.86

_cons | -.1119228 .0030451 -36.76

The coefficients add up to about -0.513. The reckless interpretation of this regression as describing causation would imply that given lagged income, personal disposable income which is 1% higher causes consumption which is 0.487% of expected consumption higher. The average ratio of consumption to personal disposable income is about 0.89 so this means that consumption would be about 43% higher. Plugging this into an closed economy IS-LM model with a horizontal LM curve (in a liquidity trap) gives a government spending multiplier of about 1/(1-0.43) or about 1.77. This is quite reasonable.

If the regression also includes the growth of personal disposable income over the past 8 quarters the coefficients add up to about -0.566 giving a multiplier of about 1/(1-0.386) or roughly 1.63. This is also reasonable and very similar. If the regression also includes the growth over the past 6 quarters, the estimated multiplier falls to about 1.55.

The totally dumb model with myopia and habit formation fits the recent history of dramatic changes in government spending and changes in GDP not predicted by the IMF using other variables.

There is something bothering me about this sort of regression. But I can’t explain it very well.

Take an example of a closed economy with no government or investment. Then we know, just from the accounting, that current income would perfectly “explain” current consumption, with an MPC of 1.0, even if consumption was determined by the alignment of the planets.

Now add in investment. C+I=Y. If we run a regression of C on Y and some other variables X, how do we know whether we are estimating a consumption function or an investment function?

Just wait till I post about investment. Yeah it bothers me too. But the PIH would have implications for a closed economy with no G or I. It would be a statement about real interest rates and consumption (and GDP, NDP, and GNP which would all be equal).

Now I have almost always ignored interest rates in these posts on consumption. This is because, in fact, achieved ex post real interest rates or expectable real interest rates from IV (or GMM) have almost no association at all with consumption growth (excess smoothness).

For the very special case of additively separable logarithmic utility (and ignoring precautionary saving) the expected present value of future income should be a constant times current income– predictably high GDP growth corresponding to predictably high real interest rates so the present value of future income would be exactly proportional to current income (the constant being one over the rate of time preference).

The fact that the ratio of consumption to disposable income is pretty stable even with huge changes in achieved safe real interest rates (which were very high in the 80s) is a deadly problem for that particular model. Even PIHmodels with much lower intertemporal elasticities of substitution imply that there should have been a dramatic effect on consumption.

In any case, the PIH has implications even if consumption is equal to GDP because of an accounting identity. They aren’t the ones I’ve looked at much, because they are so wildly different from reality.

Thanks Robert. I’m getting myself into a philosophical muddle over this. I’m going to mull it over.