Monday, January 20, 2014

The Canada-US Exchange Rate and Central Banks' Key Interest Rates

The Canadian dollar lost 2.8 % of its value relative to the US dollar between January 3 and10. This phenomenon is called depreciation. While the Canadian dollar was depreciating, I have noticed that the overnight rate, which is the key interest rate of our central bank, the Bank of Canada, was also falling. Over the following week, one can still observe that the overnight rate was leading the Canada-US exchange rate, viz. changes in this latter variable were preceded by changes in the former variable. I will give two examples, to illustrate my observations. First, the Canada-US exchange rate, i.e., the value of one Canadian dollar in terms of the US dollar, rose from .916 to .92 on January 13. On January 10, the previous business day, the overnight rate rose from 1.0001 % to 1.0003 %. Second, on January 17, the Canada-US exchange rate fell from .9152 to .9123 after the rise the previous day of the overnight rate from 1 % to 1.0001 %. All this time, the US central bank, the Federal Reserve Bank, maintained its key interest rate, the federal funds rate, at the level of .07 %. As a matter of fact, a higher short-term interest rate in Canada induces an increase in the foreign demand of Canadian assets (bonds and treasury bills), which raises the value of the Loonie (Loonie or Buck, that is how our Canadian dollar is nicknamed).

I now show how the actual rate of change in the Canadian-US exchange rate relates to the past, current, and future values of the key interest rate in both countries.  To do that, I have used daily series on exchange rate and key interest rates over a very short period of time ranging from January 2, 2012 to January 16, 2014. My sample has 503 observations. Only business days that are common to both countries are considered in the sample. For instance, July 1st, Canada Day is a holiday for Canadians but not for our southern neighbors and on July 4, US citizens celebrate their independence whereas Canadians go about their businesses. Besides, I have retrieved data only over a short period of time to avoid what is called in the jargon structural breaks, which are shifts that can arise in the data due to the fact that central banks adjust over time the target for their key interest rates. In Canada, over the sample period the target for the overnight rate is 1 %, this means to keep inflation at the target of 2 % per annum, the Bank of Canada has to maintain the overnight rate around 1 %. The Federal Reserve Bank’s target range for the federal funds rate over the sample period is between zero and .25 %.    
 
Correlations between Past, Current, and Future Values of Key Interest Rates and the Actual Rate of Change in the Canada-US Exchange Rate
 
The above table displays the correlation coefficients between the actual rate of change in the Canadian-US dollar and the past, current, and future key interest rates.  I have computed the contemporaneous correlation coefficients as the correlation between the exchange rate and the key interest rates of the previous day because the information available when the exchange rate is determined is the key interest rates of the previous day.

The data show a positive contemporaneous correlation between the Canada-US exchange rate and the key interest rates. The intensity of the relationship between the exchange rate and the future values of the key interest rates turns out to be stronger in absolute value in most of the cases compared to the intensity of the relationship between the exchange rate and the lag of the key interest rates.  

Bibliography
Wickens, Michael (2008) Macroeconomic Theory, A Dynamic General Equilibrium Approach, Princeton University Press, pp 280-93.