# A Bit on Public Debt GDP Growth and Causation

Here I analyze the data set used by Reinhart and Rogoff (R-R) and by Herndon Ash and Pollin (HAP) in their critique and in particular the stata data set RR-processed.dta with data on public debt to GDP ratios and real GDP growth in 20 developed countries since 1946.

I show evidence that low growth causes a high debt to GDP ratio, so the correlation can’t be interpreted simply as the effect of debt on growth (damn fractions how do they work anyway). Of course this has been shown much better and much more thoroughly by HAP at PERI (warning the sudden traffic killed their hamster) and then their colleague Arindrajit Dube using non parametric regressions.

The following paragraph is pointless and may be skipped. <pointless nerdo twittosity>My added bit is a bit nerdo twitty — I note you can test whether the debt to GDP ratio is a good regressor or instrument (technically is it weakly exogenous) by considering it and another variable as instruments for it. The other variable should not affect growth except through the debt to GDP ratio. This motivates a regression on the debt to GDP ratio and the 5 year lagged debt to GDP ratio.</pointless nerdo twittosity>

This is a regression of one years real GDP growth on the debt to GDP ratio and the 5 year lagged debt to GDP ratio ( l5debtgdp)

OK that’s about it. If one trusts the standard error calculation, one concludes that there is very very strong evidence that, given debt now, it is much better to have been highly indebted already 5 years ago. This is the pattern one would expect if low growth caused a high debt to GDP ratio. Future growth is low if debt is higher than one would predict given debt 5 years ago — presumably because that is the result of disappointing growth and growth rates are serially correlated. Old debt is not so damaging. This means that it comes out looking as if old debt is positively a good thing (really the regression doesn’t show this it shows if you have debt it is better for it to be old).

Ooops I motivate the regression by assuming that growth rates are correlated over time, but the standard errors are calculated assuming they aren’t. Fortunately STATA makes it easy to correct standard errors for correlation of any kind within groups of data — in this case growth rates for the same country at different times.

Just type

. reg dRGDP debtgdp l5debtgdp if l5debtgdp!=.,cluster(cntry)

gives a new T-statistic on l5debtdgp of 3.19 markedly smaller than the uncorrected t-stat of 5.11 but still very significant.

The regression basically rejects the null (never stated but often insinuated by R-R) that the pooled OLS regression of read GDP growth rate on the debt to GDP ratio gives a valid estimate of a structural causal relationship.

Many more regressions and the batch program I used are here

This is a telling history:

1817-1821: U. S. Federal Debt reduced 29%. Depression began 1819.

1823-1836: U. S. Federal Debt reduced 99%. Depression began 1837.

1852-1857: U. S. Federal Debt reduced 59%. Depression began 1857.

1867-1873: U. S. Federal Debt reduced 27%. Depression began 1873.

1880-1893: U. S. Federal Debt reduced 57%. Depression began 1893.

1920-1930: U. S. Federal Debt reduced 36%. Depression began 1929.

1998-2001: U. S. Federal Debt reduced 9%. Recession began 2001

2004-2007: U. S. Deficit Reduced 61% (from $413B to $160B) Great Recession began 2008