Appended Note 1-12 Estimation for Exchange Rates
- Japanese version
- English version
The all following indicated variables except for inflation rate 
, interest rate i, and the ratio of Cumulative Current Account to GDP are logarithms.
After consideration of the risk premium that foreign assets possess, the profit equality equation for domestic and foreign assets is as follows.
The expected depreciation rate for the nominal exchange rate is determined on the basis of the theory of purchasing power parity, depending on the following factors; (1) domestic and foreign inflation gap (2) degree of deviation of actual nominal exchange rate e and purchasing power parity level eE.
The following equation is derived from the equations of (1) and(2).
If it is assumed that the monetary policies of both countries exert influence on their interest rate and their risk premiums respectively, that is, the following cases are considered:
(1) If in comparison with economic activity scale (Nominal GDP) the stance for easy monetary policy is intensified and thereby monetary base increases, nominal interest rate decreases.
(2) At the same time, due to the increase in the ratio of possessing cash/deposits (In the case of financial institutions, it includes deposits for central banks) with low risk and profit, the tolerance of the risk-assets possession is intensified and the risk premium of foreign assets possession decreases. As the risk premium is basically influenced by fluctuations in the relative supply of external assets accumulated by net exports, it is difficult to measure how big the risk premium is in itself. However, under such a framework, a gap between domestic and foreign nominal interest rates can be explained by the relative difference in stance for the easy monetary policies and cumulative current account in both countries.
The following equation is derived by substituting (4) for (3).
As eE is a nominal term and that fluctuates depending on the time, the equation derived into a real term is as follows. (The base year for being converted to real terms = the first quarter of 1981)
(7) We estimated the equation, whose dependent variables are on the left side and explanatory variables are on the right side on the assumption of the first-order series correlation in the error term. ((): t value).
<Statistics Used>
Nominal Interest Rate: Ten-year government bond rate of the debenture's yield (For both Japan and the U.S.) Exchange Rate: Tokyo foreign exchange market inter-bank spot central rate
Price Index, Inflation Rate: GDP Deflator (National Account, Cabinet Office)
Nominal GDP: National Account, Cabinet Office
Monetary Base: Finance and Economic Statistics, Monthly, Bank of Japan
Cumulative Current Account: In order to calculate the amount of net external assets possessed in the private sector, a gap between the net external asset and the foreign currency reserve (National Account, Cabinet Office) at the end of 1979 was accumulated by the amount of shortage fund in the overseas section from "Flow of Funds," Bank of Japan and added the increase/decrease of foreign currency reserve.