I decided to do a bit more work with my Canadian gross-fixed capital formation series for the period 1870 to 2010 to see if I could estimate a simple regression model that might explain its fluctuations. If everything can be explained by a few simple economic variables, then the downward trend in the ratio since the 1970s might also be accounted for by economic determinants.

*chartsbin.com/view/oau*as a source for oil price data and I obtained a crude oil price in U.S.dollars per barrel from 1870 to the present expressed in 2009 values. I went onto Economic History Services (Eh.Net) and obtained a long-term interest rate series for U.S. interest rates. As we are a small open economy, oil prices as a proxy for resource prices in general and using U.S. interest rates seem like reasonable choices. I also obtained an annual population series for Canada. The dependent variable (gfky) is the ratio of gross fixed capital formation to GNP/GDP used in my earlier post.

I would expect population growth rates (popgrowthrate) to be positively correlated with capital formation as a demand side driver for new investment and infrastructure. On the other hand, if population growth rates outstrip capital formation growth there might be a negative relationship so a quadratic is probably a reasonable specification for that variable. I’m a little uncertain about the impact of oil prices. On the one hand, if they are a proxy for natural resource prices, then rising oil prices should result in increased investment and a rising investment-output ratio. On the other hand, rising investment demand could also lead to a rising price of capital and a substitution of labor for capital and eventually a falling investment output ratio. I use the annual percent change in oil prices as the regression variable (oilpriceg) and also specify it as a quadratic. Finally, I put in interest rates (interestrate) and just to be consistent specify that as a quadratic also. And naturally, I throw in a time trend (year) because over the course of 140 years, there does seem to be an overall upward trend in the series.

The results (Specification 1) are below (estimated with Stata with OLS as the estimation technique). The results find the time trend, interest rates and population growth to be statistically significant correlates of the investment/output ratio while oil prices are not. While rising interest rates seem to be correlated with a rising investment-output ratios, as they get high enough, they become associated with a decline. A similar pattern seems to be present with population growth rates. About 55 percent of the variation in the investment output ratio is accounted for by the regression. A plot of the actual versus the fitted value is provided also to provide some visuals on the fit. As well, the regression results from a second specification (Specification 2) that does not use a quadratic specification is provided below. It only explains about 45 percent of the variation.

Based on the results, it seems that time trend, population growth and interest rates can explain about 55 percent of the variation in the Canadian investment-output ratio over the period 1870 to 2010. What about the remaining 45 percent? Omitted variables? Animal spirits? However, the fitted values appear to have captured the downward trend in the investment output ratio since the 1970s, which suggests that economic or demographic factors are key in the decline and therefore there may not be a need for a massive infrastructure project to raise the investment-output ratio given the decline may simply reflect economic forces. However, the actual values since 2000 are substantially above the fitted values from the regression suggesting that there might be something else driving the uptick of the last decade in investment spending. Is there an unspoken exuberant optimism in Canada’s economic future that is driving the current increase in investment spending? On the other hand, this is obviously not the most robust methodological approach to analyzing this issue or specifying a regression equation. However, it has been a lot of fun.

Correlation with oil would improve the fit after 1950; before then Canada was not a producer, we were entirely a consumer. Alberta production did not start in force until the 1950's and the Oil Sands have taken even longer to bring online. The same with offshore Atlantic oil, there has been drilling since the 1970's (Ocean Ranger anyone?) but commercial production did not start until the 1990's with Hibernia.

Posted by: Determinant | December 06, 2011 at 07:53 PM

The slow downward trend since 1960 may have something to do with economies of scale.

Posted by: Alex Plante | December 07, 2011 at 08:54 PM