Autocorrelation as a tool for economic historians: New France and Lower Canada

I was working on my thesis and a weird idea struck me. More specifically, I was working on market integration between Quebec City and Montreal from 1688 to 1840. Generally, I used the coefficient of variation (standard deviation of observations over average). However, trends in market integration could be measured by the extent of serial correlation.

Normally, serial correlation (the past values of the dependent variable explain the present values) is a pain in the neck. But serial correlation could also be a sign of a violation of the efficient market hypothesis. The efficient market hypothesis were absent since this hypothesis states (in its strictest form) that all price changes should only come from new information as current prices reflect all the information available. Its like looking forward when you drive. If past values have large predictive power, this means that you drive forward by looking in the rearview mirror only.

However, if the predictive power of past prices evaporates progressively, this means that markets would have been working more efficiently (a necessary condition for market integration). So, does it work?

Between 1760 and 1840, the regression model shows that the log of wheat prices in Quebec follows this function:

Log Qc Price (1760 to 1840) = 0.42 * MtlLogPrice + 0.15 * QcLogPricePreviousYear + 0.38 *MtlLogPricePReviousYear + 0.08

All the variables, except the price of wheat in Quebec the year before, are statistically significant at the 99% level. The R2 is 0.74.  So what about the period of french rule for which I have prices from 1688 to 1760?

Log Qc Price (1688 to 1760) =  0.31 * MtlLogPrice + 0.30* QcLogPricePreviousYear + 0.43*MtlLogPricePReviousYear – 0.03

This time, all the variables are statistically significant at the 99% level and the R2 is higher (0.84). The changes in the predictive power of past values of wheat prices in the Quebec area would indicate that markets for grain grew more efficient in the era of British rule relative to the era of French rule.

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