Tuesday, June 13, 2017

Modelling Consumption

I was running over things to write about over the next few weeks, and I decided to just casually see how much income and wealth explain consumption. I didn't expect to see anything spectacular, but I pulled the quarterly personal consumption expenditures series as well as disposable personal income and household and nonprofit net worth and ran a regression. The IPython notebook is here.

At first I ran the regression on all the data from 1952 on, and the result actually shocked me -- the first time I think I can say that while referring to statistics -- the R squared value was literally 1. I was too surprised to look at the p values or t-statistics for each variable, but I decided to only look at data after 1990 to see if that changed anything.

Here's the output for the regression on data after 1990:
I still suspect that I did something wrong here, but the fit is, in a word, impressive.

I also plotted the prediction given the coefficients from the regression against the actual data:

For good measure, these are the series IDs from FRED I used: Personal Consumption Expenditures: PCEC, Disposable Personal Income: DPI, Households and Nonprofit Organizations; Net Worth, Level: TNWBSHNO.

Update: I removed wealth from the regression, and the fit is still extremely high. I guess now the question is, if disposable income is such a good predictor of consumption, why does the Old Keynesian consumption function get routinely bashed for being inaccurate? Yes, I know the difference between average and marginal propensity to consume is important, but why insist on the consumption Euler equation given it's almost comical level of inaccuracy while ignoring the startlingly accurate Keynesian consumption function?

The results of the regression without household wealth:

Update 2: At Jason Smith's suggestion, I looked at the correlation with first differences (really 4 quarter growth rates) and found that the R squared went down to more normal levels, but that adding wealth does actually improve the fit considerably. The importance of wealth here is a partial win for the Permanent Income Hypothesis but ultimately still a loss for the consumption Euler equation. Here are charts for the new regression:


  1. Any thoughts on what might have been behind the large negative residual in 2011 (update 2)?

    1. There was an instantaneous drop in personal income in January 2013 that corresponds with sequestration, so I think a couple of factors are at play here.

      Higher income households probably intentionally shifted their income forward to take advantage of lower taxes -- the opposite of what they are doing now -- and people in general probably expected their incomes to fall because of how prominent the fiscal cliff was in the news cycle.

      Since the spike also appears in personal income (not only disposable personal income, which is personal income net of taxes), I think rich people shifting their income is probably the best explanation.


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