Ex ante versus ex post production

Most people agree GDP is probably a flawed tool. Results from a few papers I’ve recently read – which I’ll get to shortly – increase my curiosity. Ignoring its many other shortcomings, I want to focus on the difficulty of measuring realized GDP. My entire premise might be flawed, and definitely contact me if you can explain why. I might be very confused about the whole thing.

Consider an economy with households, firms, entrepreneurs, and banks. Households keep all their income as deposits in a bank, which invests in firms in the form of long-term debt, with residual business income accruing to entrepreneurs who hold equity.

Suppose tastes and preferences change and households no longer purchase widgets. Unfortunately at the beginning of this year firms had invested in large factories to scale their widget factory, financed largely by debt. Widget factories, having lots of unsecured debt, decide to default on the principal. Continuing operations is profitable for another year or two, however, and therefore they remain current on interest payments for another 2 years.

If widget factories decided to go bankrupt today, banks would have to writedown all their debt – taking a huge expense – and resulting in a sharp fall in production. Instead, widget factories will slowly default over the next decade, overstating ex ante GDP.

Now this effect might be moderated with a sensible requirement that banks immediately expense income for a loss reserve as they lend – with symmetric errors between reported and true earnings as borrowers default and recover. However my understanding is that the BEA uses current earnings excluding such accounting practices; and even if such were included the effect still remains large, especially when historical delinquency rates fail to capture the prevailing economic environment.

A working paper from Amir Sufi and Atif Mian prompted this question. In particular, they find that a one standard deviation increase in the household debt to GDP ratio over the last 3 years (6.2 percentage points) is associated with a 2.1 percentage point decline in GDP over the next three years, and outcome that seemed extremely large to me, especially given the econometric robustness they detailed.

Could it be that periods of substantive increase in household debt, and the rising delinquency rate that comes with it, make it harder to match economic revenues with economic expenses – perverting growth estimates? Even if the effect on GDP itself is small – which, if true, it cannot be given the meaningful role banks play in advanced economies – the effect on growth is meaningful. Consider valuation adjustments in financial inventories:

Screenshot 2016-02-02 00.48.50.png

Economic losses are unlikely to have been so concentrated. Non-recourse borrowers were economically delevered as soon as housing prices started to fall; and the ex post GDP in these years was much lower than that reported ex ante (not to be confused with revisions).

In this particular case, it is also likely the regression coefficient on HHD is also overstated. The increase in (Reported HHD / Reported GDP) is about 6% lower than that in (Economic HHD / Economic GDP) under standard calculations – where banks reserve losses at historical rates, growth is about 3% in the period of increasing debt, and the debt cycle gathered momentum over 10 years. In practice the effect is likely a little sharper as GAAP loss reserves are not included in the BEA estimate. In other words, the increase in the HHD/GDP ratio needed to achieve the same decrease in GDP is actually larger than estimated.

The particular problem I think this poses for economic analysis in general is from measurement error. Even if revised reported GDP is negligibly erroneous against perfectly reported GDP, both are meaningfully erroneous against perfectly reported economic GDP. There’s no good fix to this problem – it’s really hard to find out who has economically defaulted and who hasn’t. Doing a better job adjusting for loan reserves might help, but also open a host of other problems regarding standardized measures.

Of course the reported GDP eventually converges to the economic GDP, as losses must eventually be recognized. However, this process is subject both to institutional flaws, such as slow bankruptcy proceedings, as well as macroeconomic trends, such as low interest rates that allow borrowers to remain current on bad principal for a longer period of time.

Maybe more importantly, the measurement error attenuates regression coefficients and economic GDP turns out to be a lot more important than we gave it credit for.

I’ve worked out a back-of-the-envelope model to see the discrepancy that I’ll write about soon. In any case it generates an annualized 0.3% to 0.75% error in annualized growth rates under reasonable economic environments.

Some remedies might include a push towards using market, rather than face, value of debt. For example, sometime in 2007 the market value of subprime started collapsing even as no writedowns were realized – because investors realized the owners of these houses either had, or were going to, default and hence effectively unlevered.


The harder question is estimating the current, capitalized value of GDP. If there is any interesting writing on this topic, I’m interested.


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