This is something I posted on my blog tonight. Fun with regressions:

Here is a graph of household debt service payments as a percent of disposable personal income from 1980Q1-2005Q3, the latest period for which consistent data exist (total financial obligations show a similar pattern):

I wanted to see how the debt load related to economic downturns, so the
shaded areas are NBER dated recessions. It's hard to see a strong
association between the recessions and changes in debt. The next graph
plots the same series along with the *negative* of the unemployment rate. The
association appears much stronger:

To see if regression confirms the association, I ran OLS on

%Debt_{t} = β_{0} + β_{1}%Debt_{t-1} + β_{2}%Debt_{t-2} + β_{3}UN_{t} + e_{t}

and it does (debt data described here). The coefficient on UN is significant at the 5% level:

` Linear Regression - Estimation by Least Squares`

Dep Var PERCENTDEBT

Quarterly Data: 1980:03 To 2005:03

Usable Observations 101

Degrees of Freedom 97

Durbin-Watson Statistic 2.014351

Variable Coeff T-Stat Signif

***************************************************

β_{0} 0.468304856 1.49629 0.13782438

β_{1} 1.125298228 11.06370 0.00000000

β_{2} -0.150035410 -1.48249 0.14145135

β_{3} -0.024721984 -2.01484 0.04668936

As you interpret the second graph, remember that it's the negative of the unemployment rate. Thus, when the blue line is rising, unemployment is falling. In the regression results the actual unemployment rate, not the negative of it, is used. This is a fairly broad brush and it may hide detail such as differences by income class, and omitted variables are a concern, but in general these data and this model suggest unemployment and the debt percentage are negatively related.

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