Consumption Wealth ratios and Stock Market Returns II

I finally did a bit of empirical work related to Consumption/Wealth as a leading indicator (see older post).

I am reflecting on “consumers – in aggregate – have genuine foresight; this is why consumption-wealth ratios help predict equity returns.” I think I won’t restate exactly whom I am quoting.

My thoughts were that the variable which mostly varies in consumption-wealth ratios is wealth, which bubbles up and bursts down with asset prices, and that the main determinate of equity returns is the price earnings ratio, which bubbles up and bursts down. So my story about the simple correlation is that bubbles cause high measured wealth, which causes a low consumption wealth ratio, and that they are followed by busts so correlated with low equity returns (and vice versa panics cause low wealth, a high ratio of consumption to wealth and are followed by high returns).

I recently noticed that, in my story, consumption is working essentially as a trend. So if I am right, the evidence that fluctuations in aggregate consumption contains useful information because consumption-wealth ratios predict equity returns should equally support the claim that the fluctuations in an exponential trend contains useful information.

First I check the alleged correlation — it is there

. corr conswealth g20rsp500
(obs=208)

| conswe~h g20r~500
————-+——————
conswealth | 1.0000
g20rsp500 | 0.4481 1.0000

Conswealth is the ratio of real consumption to real wealth. Real wealth is net worth of households and nonprofits divided by the consumer price index. G20rsp500 is the growth over 5 years of the S&P500 index divided by the CPI. Both are quarterly series. The correlation is borderline significant when one corrects for overlapping 5 year intervals

. newey g20rsp500 conswealth,lag(19)

Regression with Newey-West standard errors Number of obs = 208
maximum lag: 19 F( 1, 206) = 3.75
Prob > F = 0.0543

|
g20rsp500 Coef. t

conswealth .0712455 1.94
_cons -1.078769 -0.92

Then I estimated the trend in ln real consumption (.0344805 per quarter) and use it to construct an exponential trend which I divide by real wealth to get ecw. All the information in ecw is due to the fluctuations in the denominator: real wealth. The numerator is just an exponential trend.

The regression says that the exponential trend has “genuine foresight”

. newey g20rsp500 ecw,lag(19)

Regression with Newey-West standard errors Number of obs = 208
maximum lag: 19 F( 1, 206) = 13.64
Prob > F = 0.0003

g20rsp500 Coef. t
ecw .103123 3.69
_cons -2.038214 -2.35

In fact if they are allowed to compete, the trend divided by real wealth is a much better predictor that consumption divided by real wealth

. newey g20rsp500 conswealth ecw,lag(19)

Regression with Newey-West standard errors Number of obs = 208
maximum lag: 19

g20rsp500 Coef. t
conswealth -.1977837 -6.49
ecw .2890798 6.91
_cons -1.56284 -2.79

I think these regressions very strongly confirm my guesses about what was going on.

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