Answer to Question #96174 in Economics for eliman

Question

The relationship between nominal exchange rate and relative prices. From annual
observations from 1985 to 2005, the following regression results were obtained,
where Y = exchange rate of the Canadian dollar to the U.S. dollar (CD_$) and X =
ratio of the U.S. consumer price index to the Canadian consumer price index; that is,
X represents the relative prices in the two countries:
ˆ 0.912 2.250 2 0.440
. 0.096
t t Y X r
s e
= - + =
=
（1）Interpret this regression. How would you interpret r2 ?
（2）Does the positive value of t X make economic sense? What is the underlying
economic theory?
（3）Suppose we were to redefine X as the ratio of the Canadian CPI to the U.S. CPI.
Would that change the sign of X? Why?

Answer 1

（1）We can mention that there are negative relation between Y and X. The regression is linear that can have its impact on the results we see in the regression. The value of r2 shows that X describes Y only for 53%, which means that there are other important variables absent in the regression equation. Standard errors may be smaller if the interval of observations will be increased.

（2) The economic interpretation of this relation can be explained with help of the conception of PPP (Purchasing Power Parity): National currency will have the tendency of declining, if the inflation rate inside the country (USA in our case) is higher than the inflation rate in abroad (Germany in our case). In the regression mentioned above, we see that 1 point raise of X, ceteris paribus, will cause decline in 4.13 point of Y. The value of intercept probably shows the approximate average level of Y, so it is equal to 6.68.

（3）If we were to redefine X as the ratio of the Canadian CPI to the U.S. CPI, that would not change the sign of X.