Recently I’ve been trying to learn some data analysis and econometrics to incorporate into my research. I thought I’d be able to show that Canada, from 1867-1935, had a more stable NGDP percent change from year to year than the U.S. And I thought this would be an easy and quick historical example that I could use to bolster my underlying theory. But things seem like they just ain’t so.
So why am I looking at old GDP figures? Well it has to do with my interest in NGDP targets and free banking. First off, I think there are very persuasive reasons to favour an NGDP target over the standard inflation target (as Scott Sumner has explained here).
More specifically, though, if NGDP growth was ~0% per annum, then we’d perhaps have the ideal policy – A Hayekian MV rule, or what George Selgin has called the productivity norm – where real GDP growth is negatively correlated with price level inflation. This is desirable because it allows for good inflation/deflation without creating any bad inflation/deflation (which I explained in my deflation post here). Basically, it keeps the the economic good at the hub of trade stable.
Standard free banking theory states that a fully unregulated banking system would follow a de facto NGDP target (a productivity norm) as an unintended, yet beneficial, consequence of a competitive banking environment. (For a more recent discussion on this, you can check out out one of Nicolás Cachanosky’s papers here). And within the free banking literature, early Canada is often held up as an example of a near free banking system. Therefore, I figured we should observe that this historical example had an NGDP growth trend resembling a productivity norm. At the least, it should follow a productivity norm closer than a country like the U.S, a country with heavier regulation on banking than Canada.
Figure 1 – Expected Results
Figure 1 is the actual NGDP data for the U.S. with hypothetical data from Canada to illustrate what I expected to find. Not a perfect 0% NGDP trend as Canadian banks weren’t perfectly free, but at least closer than the U.S. However, when I compared them, I didn’t see the expected results.
First I compared real GDP from Canada and the USA (between 1867-1935, from Canada’s beginning to when it got a central bank), which resulted in a Spearman correlation coefficient of nearly 99%, and so movement in the real economy between the two countries is strongly correlated. Next, the Johansen test for the existence of a cointegrated combination between the Canadian and US real GDP showed a statistically significant connection. The two economies are well integrated. I take this to mean that the two countries faced real economic shocks of nearly the same size and duration.
With the real GDP changes shown to be sufficiently similar, I then compared the Nominal GDP’s between the two countries during this time with the expectation that Canada’s percent change trend would be smoother (less spiky) than the U.S., due to the free(er) banks in Canada’s ability to hold MV stable (Figure 1 shows hypothesized results).
But a paired T-Test and Wilcoxon signed-rank test with actual Canadian and U.S. data (nominal GDP growth) showed that there is actually no significant difference (Figure 2).
Figure 2 – Actual Results
At least Canada did no worse in terms of NGDP fluctuations, but it’s still a big surprise to me that it wasn’t any better.
One possible problem is that, being from turn of the century, my data has some serious room for error. I calculated NGDP myself using real GDP per capita estimates, multiplied by population estimates, multiplied by price level estimates (email me if you are interested in more details).
So I looked around for more data and found the Macro History Database which has calculated US and Canada NGDP much different than I had myself. Perhaps with this alternative dataset I would see a less spiky Canadian NGDP? But when I did my paired t-test again, I got what is shown in Figure 3.
Figure 3 – Actual Results (Macro History Data)
Here it is visually obvious that Canada actually performed worse. This is confimed by both the paired T-Test and Wilcoxon signed-rank test, which show that there is a statistically significant difference between both time series. The average deviation of Canadian NGDP growth is much higher than in the US.
I tried running some more complex time series regressions as well with and without lagged regressors (for example a first-differenced model of logs of NGDP and Price level, bivariate vector error correction models of logs of NGDP and Price level), because maybe prices are sticky and, therefore, falls in P lag behind increases in Y. But these gave me no better results. Either Canada performed no better, or the U.S. actually performed better.
I also ran everything again but this time from only 1870-1914. Canada got a heavy dose of bank regulation that year, and with WW1 and the Great Depression, I thought maybe this later period was messing up my results. However, even limiting the time period did nothing to change the results.
Where Did I Go Wrong?
I love the way things have been going here on ppe.life, but one thing I wish we got more of was comments and interaction. So this post is a call for help. I doubt this is actually a problem for free banking. I find it much more likely, given the massive body of research on free banking and Canada, that I have made a mistake, or that I have missed some crucial data and/or papers.
So to anyone out there reading this who knows more about this stuff than I do, where did I go wrong?