Monetary and Real Shocks With Flexible Exchange Rates

One often reads in the financial pages how the Bank of Canada has increased or lowered interest rates in Canada in an attempt to "cool down" or "kick start" the Canadian economy. Do these kind of statements make any sense? To what degree does the Bank of Canada control Canadian interest rates?

The Bank of Canada can control nominal interest rates in Canada but not real interest rates. Accordingly, it can not use changes in real interest rates as an instrument of monetary policy.

From the interest parity and efficient market conditions we have the following relationships between domestic and foreign real and nominal interest rates:

(1) id = if + rp + Ee

(2) rd = rf + rp - Eq

where id and if are domestic and foreign nominal interest rates, rd and rf are domestic and foreign real interest rates, rp is the combined country-specific and foreign exchange risk premium on domestic assets, Ee is the expected rate of change in the nominal exchange rate and Eq is the expected rate of change in the real exchange rate, with the latter defined as

(3) q = Pd/(ePf)

where Pd is the domestic price level, Pf is the foreign price level and e is the nominal exchange rate (domestic currency price of foreign currency).

We should also keep in mind the Fisher condition that gives the relation between real and nominal interest rates on each country's assets:

(4) id = rd + Epd

(5) if = rf + Epf

where Epd and Epf are the expected rates of change in the domestic and foreign price levels.

Looking first at equation (2) we can see that the Bank of Canada can only change the real interest rate in Canada if it can change the real rate of interest in the rest of the world, the risk premium on Canadian assets or the expected rate of change in the real exchange rate. Canada is such a small country that nothing the Bank of Canada does can affect real interest rates in the rest of the world. The government of any country could presumably raise the domestic real interest rates by talking incompetent nonsense and scaring investors into attaching a higher risk premium to domestic assets, but one cannot imagine this happening---governments like to present themselves as the epitome of stability and responsibility, thereby keeping the risk premium on domestic assets as low as possible. Since, apart from default risk, risk premia depend in a complicated way on the covariance structure of asset returns (on the correlation and amplitude of variability of the return of individual assets with respect to a "market" portfolio), it is unlikely that individual changes in the domestic money supply will much affect the risk premia on domestic assets. So the risk premium on Canadian assets is also beyond Bank of Canada control. Finally, there is strong evidence that the best prediction of next period's real exchange rate is this period's rate, given the random-walk nature of real exchange rate movements. Under these conditions, Eq will be zero.

Although it thus has no control over the expected rate of change in the real exchange rate, the Bank of Canada has a great deal of control of the expected rate of change in the nominal exchange rate. Hence, it can affect nominal interest rates in Canada. This can be seen by noting that, from the definition of the real exchange rate,

(6) Ee = Epd - Epf - Eq.

Equation (6) can be obtained from equation (3) by taking the relative rate of change and then passing the expectations operator through the resulting equation and reorganizing it. Although the Bank of Canada cannot affect Eq if the real exchange rate is perceived to be a random walk, it can easily affect the expected rate of inflation Epd by increasing the rate of money growth and, as a result, the actual rate of domestic inflation. Once people learn that the domestic rate of inflation has permanently increased, the expected domestic inflation rate will rise. Given the rate of inflation abroad, this will imply an increase in the expected rate of devaluation of the exchange rate, Ee, and from both equation (1) and the Fisher equation, a rise in domestic nominal interest rates.

When analysts in the popular press talk about the economy being "strangled" by high interest rates they are usually talking about high nominal interest rates. But nominal interest rates can be high without high real interest rates if there is a lot of domestic inflation. Moreover, domestic real interest rates can only be high if foreign real interest rates are high because the two are directly directly related. While high nominal interest rates are the responsibility of the Bank of Canada, and the high inflation that accompanies them is generally bad, nothing the Bank of Canada can do with respect to interest rates can "strangle" the economy. The Bank of Canada can "strangle" the domestic economy by decreasing the money supply but the effect of this monetary contraction on the real sector of the economy operates through an appreciation of the real exchange rate in the face of domestic price level rigidity, not through a rise in domestic real interest rates.

This having been said, there is a situation under which the Bank of Canada could manipulate the real interest rate for short periods, though the technique is rather crude. If the Bank of Canada reduces the domestic money supply and thereby appreciates the Canadian dollar and, given a sticky domestic price level, increases the real exchange rate, and the public happens to regard this real exchange rate appreciation as temporary, Eq will fall and the domestic real interest rate will rise (as indicated in equation (2)) at given levels of real interest rates abroad. But this depends critically on the public being convinced that the real exchange rate will fall in the future---it implies that the best forecast of tomorrow's real exchange rate is no longer today's rate! It is difficult to see how such policy moves could be systematically effective via a real interest rate channel because the real interest rate changes are expected to be temporary, lasting only until the real exchange rate has returned to its known equilibrium level. Meanwhile, the policy will be very effective in cooling down the economy because the appreciation of the real exchange rate will shift world demand off domestic goods---its effectiveness operates through the real exchange rate channel, not a real interest rate channel.

So what is the Bank of Canada doing when it announces and increase in interest rates from, say, 4 to 4.25 percent? It turns out that the Bank, when it does this, is only changing the interest rate at which it will make overnight loans to the Canadian banking system to finance short-falls of bank reserves. Normally, on any given day some banks will have surplus reserves and other banks will be short. There is an "overnight market" at which banks that are short can borrow reserves from the banks that happen to have too many reserves. The interest rate in this market is called the "Overnight Borrowing Rate". This rate is a free market rate that will vary with other short-term rates in the economy. The Bank of Canada can affect this rate for a day or two by providing additional reserves to the banking system or reducing the reserves available to the system. Within days, however, the Canadian banking system can acquire additional reserves or dispose of excess reserves by borrowing or lending outside the banking system and borrowing and lending abroad. So it is unrealistic to believe that the Bank of Canada can control the Overnight Borrowing Rate for periods of any length. Nevertheless, the Bank sets its "Bank Rate", the rate at which it will lend to commercial banks that are short of reserves, at some level above the Overnight Borrowing Rate. This Bank Rate setting is widely believed to be the upper bound to where the Bank of Canada would like the Overnight Borrowing Rate to be. And the Bank sets a desired lower bound to the Overnight Borrowing Rate at one-half a percentage point below the Bank Rate. Despite the perception that the Bank of Canada will maintain the Overnight Borrowing Rate between these limits, it sometimes goes outside them. And the Bank tends to adjust the Bank Rate to keep it above the market determined Overnight Borrowing Rate because it makes no sense to lend reserves to the commercial banks at an interest rate below the rate at which they can borrow them in the private market.

Although increases in the Overnight Borrowing Rate and the Bank Rate are generally perceived by the public as a "tightening" of monetary policy, there is no way of knowing whether an observed increase in these interest rates, or any other interest rates in the economy for that matter, are the result of a rise in real interest rates due to a rise in world real interest rates, an increase in the risk of holding Canadian assets, or an expected depreciation of the real exchange rate, or to an increase in the expected rate of inflation in the Canadian economy. The Bank of Canada controls the rate of domestic inflation by setting the rate of growth of the domestic money supply in relation to the rate of growth of the demand for money, so movements in Canadian nominal interest rates will reflect market perceptions about the future rate of inflation that will result from current Bank of Canada policy.

Outline the ways in which exchange rate overshooting can occur. Does it matter whether or not the real exchange rate is a random walk? Is "undershooting" possible?

Exchange rate overshooting is a short-run phenomenon whereby a shock to the equilibrium nominal exchange rate causes it to move past its long-run equilibrium level during the short run when adjustment is occurring. When the nominal exchange rate is overshooting, the real exchange rate will also deviate from its long-run equilibrium level.

The rationale behind overshooting can be seen by looking at a country's condition of monetary equilibrium.

(1) --- Md = Pd Ld(rw + rho - Eq, Yd)

where we assume that Md is the domestic nominal money supply, Yd is domestic real income, Pd is the domestic price level and rw is the world interest rate which, because of international capital mobility, also applies to the domestic economy after adjustment for the risk premium rho and the expected rate of increase in the domestic real exchange rate Eq. The domestic real exchange rate is defined as

(2) --- q = Pd/ePf

where e is the nominal exchange rate and q is the real exchange rate.

Now suppose, for example, that the authorities increase the domestic nominal money supply and the exchange rate is flexible. The analysis that follows will be the same for a decline in the domestic demand function for money L(...).

If prices are flexible and there is full employment, the increase in Md will result in an immediate proportional increase in Pd in equation (1) and equiproportional increases in Pd and e in equation (2). The excess supply of domestic money holdings results in an immediate devaluation of the domestic currency and a proportional rise in the price level until real money holdings have returned to their equilibrium level. No overshooting occurs.

If domestic prices are fixed and there is less-than-full-employment, the excess money holdings will again cause a purchase of assets abroad in order to reestablish domestic residents' portfolio equilibrium and the domestic currency will again devalue. Now, however, output will rise instead of prices as a result of the effect of the devaluation on the domestic trade balance. Yd will rise, increasing Ld(...) until the right side of equation (1) equals the left side. As e rises, the real exchange rate q falls. In the long run, Pd will rise and output will return to its full employment level. As this happens, e will adjust further until it has risen in exact proportion to the increase in Pd, which will rise in exact proportion to the increase in Md. Whether or not e will rise more in the short run than the long run (i.e., overshoot its long-run equilibrium level) will depend on how responsive the trade balance and output are to the fall in q. If the trade balance is not very responsive, a bigger increase in e will be required to bring about equilibrium in the short run than in the long run and there will be overshooting. On the other hand, if the trade balance is very responsive to the fall in q, output and employment may increase sufficiently to bring about short-run equilibrium without as big an increase in e as will be required in the long run when the price level adjusts. In this case there will be "undershooting".

Suppose, however, that in the very short run ---call it the immediate run--the trade balance does not respond at all to movements in the real exchange rate. Then in the absence of a change in Pd there is no way that domestic monetary equilibrium can be reestablished in this very short run. The nominal exchange rate e and real exchange rate q will shoot out of sight. There will clearly be overshooting.

But there must be an equilibrium even in the immediate run---that is, there must be bounds on the nominal and real exchange rates. There are two ways in which such bounds can be established.

First, there must be some value of q so low that agents realize that overshooting is occurring. When q falls below this level people will expect it to return towards its original level and Eq will become positive. This causes the domestic interest rate (rf + rho - Eq) to decline, making domestic residents willing to hold additional money balances. The equilibrium level of q in the very short or immediate run will that for which Eq has increased enough, and the domestic interest rate has fallen enough, to get domestic residents to hold the increment to their nominal money holdings. Subsequent adjustments of Yd when the trade balance responds to the devaluation, and Pd in the long run when the price level adjusts, will cause e to move back down towards its long-run equilibrium level and q to move back up towards its initial pre-shock level.

Note that this equilibrating mechanism will not work if the real exchange rate is perceived by market participants to be a random walk. If q is viewed as a random walk, Eq will always be zero. Since real exchange rates are generally perceived to be random walks, the overshooting movement of q would have to be much bigger than the kinds of shocks normally experienced to convince people that e has overshot its long-run equilibrium level. These magnitudes of exchange rate adjustment may be unnecessary, however, because there is a second avenue through which bounds to the real exchange rate are established in the immediate run.

This second equilibrating mechanism becomes obvious when we recognize that Pd really equals a weighted average of traded and non-graded goods prices

(3) --- Pd = wd Pud + (1 - wd) e Pf

where Pud is the price of the domestic non-traded good, Pf is the foreign currency price of the domestic traded good which we will assume equal to the foreign price level, and wd is the share of the domestic non-traded good in total domestic public and private consumption and investment expenditure.

Although it may be reasonable to assume that Pud is rigid in the short run, the domestic currency price of traded goods (e Pf) will surely rise with the exchange rate, given the level of prices in the rest of the world. So as e rises, Pd will rise. There is a rise in e sufficiently large to cause Pd to rise proportionally with the rise in Md, bringing about immediate-run equilibrium.

In fact we can determine how big an increase in e will be required. We know that if Yd, Eq and rho remain unchanged, Pd must rise proportionally with Md for equilibrium to be reestablished. And a given percentage change in e will result in a (1 - wd) percent change in Pd. Hence, the required percentage change in e must be [1/(1 - wd)] times the required percentage change in Pd and actual percentage change in Md. Since the long run percentage change in e will necessarily be equal to the percentage shock to Md, the long-run percentage change in e will be less than the immediate-run change in e if wd is less than 1. Since wd will always be less than unity if the country is involved in international trade, overshooting will always occur in a length-of-run too short for a devaluation of the real exchange rate to affect the trade balance and output.

Overshooting effects of money shocks on exchange rates are not observable in the data. This means that the notion of exchange rate overshooting is nonsense. True or False? Explain your answer.

Suppose that the United States conducts an expansionary monetary policy. Trace out the effects this policy might have on interest rates and output and employment in the United States. Then trace out the possible effects of such a policy on the Canadian economy. What would determine the magnitude and direction of these effects? Are the effects of the policy on U.S. output and employment dependent on what other countries do?

Since the United States is a large country, the monetary expansion there will (assuming it is unanticipated) lower the world real interest rate. The world LM curve will shift to the right, resulting in an expansion of output and employment in the U.S. in the short run and an increase in the U.S. price level in the long run.

When the U.S. money supply expands, U.S. residents will try to buy assets in the international market. Because they make up a significant share of that market, the world interest rate must decline until world residents no longer have an excess demand for non-monetary assets. The residents of other countries, Canada among them, faced with a fall in the world interest rate will want to hold more money and will end up trying to sell domestic assets to U.S. residents to obtain some of the surplus money there. To do this, however, U.S. funds must be converted into domestic funds on the foreign exchange market. The resulting excess demand for domestic currency on that market will cause the U.S. dollar to depreciate and other countries' currencies to appreciate.

If the Bank of Canada holds the domestic money supply constant in the face of the fall in world (and hence Canadian) interest rates, an appreciation of the Canadian dollar sufficient to drive the domestic IS curve to the left to cross the original LM curve at the new lower interest rate will take place. Output and employment in Canada will fall. The Bank of Canada could prevent the fall in output and employment by increasing the Canadian money supply sufficiently to moderate the appreciation of the Canadian dollar to where the new IS curve crosses the new world interest rate line at the full-employment level of output. If the Bank of Canada wants to keep the Canadian dollar from appreciating at all it will have to increase the money supply roughly in proportion to the increase in the U.S. money supply so that Canadian residents will want to buy additional assets to the same degree that U.S. residents do and the fall in the interest rate will occur with out any attempted international exchange of money for assets or assets for money.

If all countries, in response to the upward pressures on their exchange rates from the U.S. monetary expansion, increase their money supplies sufficiently to keep their home currencies from appreciating, they will have to increase their money supplies roughly in proportion to the increase in the U.S. money supply. This will make the fall in the world interest rate greater (because the world money supply will increase by more) and cause output and employment to rise by roughly the same amount in all countries (assuming that the structure of countries' economies are not much different). This will have both positive and negative effects on U.S. output and employment as compared to the case where all other countries kept their money supplies constant. On the one hand the world (and U.S.) interest rate will fall by more, increasing U.S. output as it moves further down along its IS curve; on the other hand, the U.S. dollar will not devalue and shift that country's IS curve to the right, as it would if other countries kept their money supplies constant, and a shift of aggregate demand from the rest of the world to the U.S. will thereby have been prevented, making the increase in output and employment in the U.S. less than it otherwise would be.

Suppose that, because of the rhetoric of a Federal election campaign in Canada, people decide that they don't want to hold as many Canadian assets. Is it the case, as the financial press would assert, that the result will be a fall in the value of the Canadian dollar? If so, explain the mechanism by which that fall will occur. Will the Canada's real exchange rate with respect to the U.S. fall too? The press also reported that an observed rise in the Canadian dollar in terms of the U.S. dollar was the result of a loss of confidence in the U.S. economy by the market as a result of the year 2000 Presidential election fiasco in that country. Does this make any sense? How would you make a simple test of the proposition?

If the market perceives Canadian assets to be more risky than before, the risk premium on Canadian assets will increase and interest rates in Canada will rise relative to the world (and U.S.) interest rate. If Canadians and foreigners agree on the magnitude of the increased riskiness, no international exchange of assets will occur--Canadian interest rates will simply rise until world residents are again willing to hold the existing stocks of Canadian assets.

When interest rates rise in Canada the cost of holding domestic money goes up and people will choose to hold less of it, trying to exchange their excess money holdings for non-monetary assets. This attempt on the part of Canadian residents (and perhaps some foreign residents too) to shift their portfolios from Canadian money to non-monetary assets will create an incipient deficit in the Canadian balance of payments, causing the Canadian dollar to depreciate in the foreign exchange market. It is hard to imagine how the riskiness of holding Canadian relative to U.S. assets would not in this way cause the Canadian dollar to devalue.

The argument that an increase in the risk of holding U.S. assets will cause the Canadian dollar to appreciate would have to hinge on the U.S. dollar devaluing in terms of all other currencies (assuming the situation in all the other countries unchanged). It is hard to imagine why the Canadian dollar would appreciate in terms of the U.S. dollar as a result of the election fiasco if other countries' currencies did not also do so. The way to test this argument is to look at the data to see whether other countries' currencies also appreciated in terms of the U.S. dollar. If they did not, then the observed appreciation of the Canadian dollar in terms of the U.S. dollar was probably due to something that was happening in the Canadian economy and not to the U.S. election fiasco.

There is also the possibility, of course, that speculators, anticipating a future appreciation of the Canadian dollar for whatever reason, may bid up the forward price of the Canadian dollar in terms of the U.S. dollar. This also will have the effect of raising Canadian interest rates because arbitrage will ensure that the interest parity condition will hold. If such an appreciation were not based on fundamentals (i.e., on a real reason why the Canadian dollar would be expected to appreciate in the future) it will be short-lived if the foreign exchange market is efficient.