A simple model of household borrowing in the US

Following on from last week’s post, if I am to test some of these predictions in a VECM, what variables will I test and what is the long run relationship that I am looking for?

Like the BdE paper, I would expect to see that consumption adjusts when borrowing it departs from its long run determinants. Thus, consumption and borrowing should be in the cointegrating vector and I should see an adjustment coefficient that shows that consumption is affected when borrowing is above or below it’s long run equilibrium.  

The Data

I have used the FRED database that is available from the St Louis Federal Reserve to get US data. To examine the debt or borrowing side of the equation, I have used Total liabilities – Balance sheet of household and non-profit organisations.

To test household wealth, I used the series called Real Estate – Assets – Balance Sheet of Households and Nonprofit Organizations, while for consumption I used Real Personal Consumption Expenditures. To turn the housing wealth and liabilities series into real variables, I deflated them by using the Personal Consumption Expenditures: Chain-type Price Index.

So my long run relationship will be something like:

Real liabilities=f(consumption, household housing wealth).

If consumption and debt have a long run relationship, I should find a cointegrating vector like that outlined above in this simple 3-variable model. Conversely, if a cointegrating vector does not exist between these series, then it would seriously question my assumptions about the long run importance of credit and debt.

The number of cointegrating relationships is determined by the Johansen maximum likelihood-based method in Eviews. The number of lags chosen was determined by the Schwarz Information Criterion (SIC).

What was found

Both the trace test and the maximum eigenvalue test indicated that there was one cointegrating relationship at the 0.05% level. This is what we expected at the very least. The main results are shown below:


Unfortunately, these results raise more questions than they answer. The normalised cointegrating coefficients are what were expected, but the adjustment coefficients, or the alphas, are curious. Like the BdE results, the adjustment coefficients were expected to be negative, implying that a disequilibrium in the borrowing level would have contractionary effects on consumption. These results signal caution in interpretation at this point, as they suggest that more rigorous testing of this data in needed before any firm conclusions can be drawn.

What I haven’t done

In my single-cointegrating VECM, I have not tested the weak exogeneity of my variables. The choice of lag length is also very important in the Johansen framework. In this simple example, I used the SIC to choose the lag length, but only minimal diagnostics were checked regarding this. A more thorough check might have suggested a different lag length.  

What could be done next

These unsatisfactory results suggest that a more rigorous model is needed to test my assumptions. It is probably advisable to test a system of cointegrating vectors in the Johansen framework and to see if I can find any evidence for the importance of credit disequilibrium in this model.

A possible extension to explore would be to test the unit root process of inflation expectations. If these were I(1), they could be tested in this long run equilibrium as well. Perhaps this would be worth exploring when we get to a multi-cointegrating vector model, where we try to model both consumption and borrowing jointly.

Moreover, if this modelling of US borrowing and consumption provides evidence of the importance of borrowing disequilibrium, the next country that could be tested is Australia. Australia is in a different situation to countries such as the US and UK in terms of its leverage cycle. Consumers in the US are deleveraging following the global financial crisis, but Australia has not had the housing bubble crash that these other countries have experienced. Hence, it would be interesting to see where Australian household borrowing is in terms of its fundamentals. One would presume that it is above it’s long run fundamentals, but testing this prediction in this Johansen framework would shed light on this.


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