# Consumption, Real Interest Rates, and Habit Formation

Many macroeconomists use models of aggregate consumption based on utility maximization by a rational representative agent. Some models also include liquidity constrained or rule of thumb consumers, but all micro founded models include inter-temporal substitution subject to a lifetime budget constraint. It is also standard to assume that utility is additively separable in consumption and everything else. In the simplest models, the utility function is time separable with a constant inter-temporal elasticity of substitution. Finally it is standard to assume that economic variables have stationary distributions around a balanced growth path. All this implies that the expected rate of growth of consumption is a constant (the inter temporal elasticity of substitution of consumption) times the expected real interest rate. The inter-temporal elasticity of substitution can easily be estimated with a regression of the rate of growth of consumption on the expectable real interest rate, that is with an instrumental variables regression of the rate of growth of consumption on the achieved real interest rate in which lagged variables are used as instruments.

Estimates of this constant are alarmingly tiny (generally around 0.1). The estimates imply extremely slow growth of consumption given measured real interest rates and even complete patience (zero subjective discounting). That is estimates based on first differences are inconsistent with estimates based on long term trends.

In order to reconcile the model with the data, it is necessary to modify the assumptions in a way which changes the short term correlation without changing the long term trend (or vice versa). This was an important impetus for the development of models of rational addiction, that is, of habit formation. Here the argument is that the marginal utility of consumption depends on the relationship between current consumption and past consumption. One way to interpret the models is that all consumption is addictive so doing without something to which one has become accustomed is very painful. Another is that people have to learn how to consume so high consumption becomes more efficient. A neutral description is that consumption changes slowly because of habit formation.

The standard new Keynesian DSGE model due to Smets and Wouters (based on the Eichenbaum, Christiano and Evans model) includes habit formation, as required to explain the low correlation of the rate of growth of consumption and the expectable real interest rate. This means that the short term evidence is consistent with the existence of a long term trend of increasing consumption. As an aside, it also means that the short term evidence of low correlation between the rate of growth of consumption and the real interest rate, is consistent with the belief that the key to long run growth is a high after tax real interest rate. I note in passing that this belief is not solidly based on evidence, but is held with great confidence by many economists.

Their claim must be that short run fluctuations in real interest rates don’t matter much, because of habit formation, but long run persistent variation matters a lot. This claim suggests a simple empirical investigation. Their argument must be that the average rate of growth of consumption over long periods of time is highly correlated with the average real interest rate over those periods. So as consumption growth and real interest rates are averaged over longer and longer periods of time, their correlation gets higher until the very strong long run association appears. This is an implication of models of habit formation.

As far as I know, no one has checked. In fact, it the regression coefficient of the change in log consumption on the average real interest rate does not increase markedly as the interval of time increases. This is true whether achieved real interest rates or real interest rates predicted using lagged variables are used. It is also true whether or not interest is compounded.

A few regressions

The regression of the change in seasonally quarterly log personal consumption expenditures (dlrcons) on the achieved real interest rate (ri3) — the real interest rate is the 3 month t-bill rate corrected for the change in the personal consumption expenditures deflator.

. reg dlrcons ri3

Number of obs = 267

R-squared = 0.0061

dlrcons Coef. t

ri3 .0242031 (1.27)

_cons .0079801 (14.59)

The coefficient on the real interest rate is tiny. It is extraordinarily small partly because this is a regression of consumption growth on the achieved real interest rate rather than a predicted real interest rate. To predict the real interest rate I use the fitted values (pri) from a regression of the real interest rate on the real interest rate lagged two quarters, the real interest rate lagged three quarters and the nominal interest rate lagged two quarters

. reg dlrcons pri3

Number of obs = 264

R-squared = 0.0082

dlrcons Coef. t

pri3 .0437429 (1.47)

_cons .0077503 (12.57)

Now consider changes over a year so, for example, one observation of the dependent variable (sdlrc4) is the change in log consumption is from the second quarter of 2000 to the second quarter of 2001 and the explanatory variable (sri4) is the sum of the real interest rates paid from the third quarter of 2000 through the second quarter of 2001. Since overlapping one year intervals are used, the standard errors are Newey West autocorrelation corrected standard errors with three lags.

Regression with Newey-West standard errors Number of obs = 264

maximum lag: 3

sdlrc4 Coef. t

rin4 .0427988 (1.87)

_cons .0311175 (13.18)

The coefficient estimated with overlapping annual changes is slightly higher than the coefficient estimated with quarterly changes. This is a bit of evidence of habit formation. However, the coefficient is still tiny. This pattern would correspond to extremely slowly changing habits such that a year is still a brief interval.

Now a regression with overlapping two year periods

Regression with Newey-West standard errors Number of obs = 260

maximum lag: 7

sdlrc8 Coef. t

rin8 .0470761 (2.02)

_cons .0619985 (13.57)

The coefficient estimated with two year long intervals is almost identical to the coefficient estimated with one year long intervals. There is no further evidence of habit formation. The now medium term correlation of real interest rates and consumption growth remains miniscule.

Now consider overlapping five year intervals

Regression with Newey-West standard errors Number of obs = 248

maximum lag: 19

sdlrc20 Coef. t

rin20 .0511966 (2.04)

_cons .1540758 (11.33)

Again extending the interval has almost no effect. There is essentially no sign of a high long term correlation between real interest rates and consumption growth, that is no sign that the low quarterly correlation is due to habit formation.

Importantly interest paid over 5 years has enough variance to identify the coefficient. Simulations of standard macroeconomic models would probably not show a large and precisely estimated coefficient, because fluctutations of real interest rates are not persistent in such models. They certainly wouldn’t yield a tiny and precisely estimated coefficient. In fact there have been huge and highl persistent fluctuations in US achieved safe short term real interest rates with enormous rates in the 80s and very high rates in the 90s. The fact that the growth rate of aggregate consumption was similar in the 80s to that of other decades should have made it obvious that standard macroeconomic models with habit formation did not fit the data at all.

HI Robert,

A question… Redistribution of wealth could increase economic growth, and it could also suppress it in the long run. Mark Thoma writes about redistribution…

http://www.cbsnews.com/news/why-income-redistribution-doesnt-hurt-growth/

Do you see a possibility that consumption could increase with an increase in the real interest rate through an increase in the nominal rates? Are there different reactions that separate the short term from the long term? Wouldn’t we also have to look at the balance between capital income and labor income in relation to utilization of productive capacity?

“One way to interpret the models is that all consumption is addictive so doing without something to which one has become accustomed is very painful.”

It appears that just being in the presence of the consumption by others is enough to bring on a strong desire to consume similarly. Or is it just the possibility bringing on the urge?

At one time a mobile phone was considered a luxury, to be used only by those who could benefit financially by the use of one. Now everyone seems to want one and they are not cheap when you add the monthly service charges. How do people at the bottom of the income scale justify that expense?

From “Credit Expansion, 1920 to 1929, and its Lessons” – Charles E Persons – Quarterly Journal of Economics – November 1930 Pages 94 to 130:

In 1930 Charles Persons reported that the sale of electric refrigerators went from 11,000 in 1922 to 630,000 in 1929. (An increase of a factor of 56 in seven years) It appears that the individual refrigerator sold for about $287 in 1929. (My calculation)

He also reported that the sales of Radios went from 100,000 sets in 1922 to 4,200,000 in 1929. (An increase of a factor of 42 in seven years) It looks like the individual Radio cost about $130 in 1929. (My calculation)

These items appear very expensive for that time but once introduced the appeal seems to have been irresistible. The electric refrigerator may have offered a tremendous advantage over an IceBox but surely not the Radios.

HI Edward

Uh I don’t think I’m up to answering half of your questions. I tend to guess that redistribution has little effect on growth based on crude empiricism mostly.

I am quite confident that people form habits. My problem with standard models with habit formation is the intertemporal optimization part so I guess that long term changes have a lot to do with new habits. Evidence for habit formation is that if you regress aggregate consumption on current and lagged income, lagged income has a positive coefficient. I think there is also strong evidence in micro data.

On capital income vs labor income, I think a key issue is corporate profits vs the rest of net national income. Consumption is much better fit by personal disposable income (which doesn’t include reinvested profits) than by GDP. I think that national savings are higher if corporate profits are higher.

Hi JimH. the technical term is “keeping up with the Joneses”. The hypothesis is due to Adam Smith. It was resurrected by James Duesenberry. I think it is very strongly supported by the data. It is not really possible to tell habit formation from keeping up with the Joneses with aggregate data. I think that micro data show very strong evidence of keeping up with the Joneses.

http://economistsview.typepad.com/economistsview/2014/06/links-for-6-11-14.html