The multiplier assumes that the increase in government spending is financed by selling bonds to the public. When the increase in government spending is financed by raising taxes, this multiplier is called the balanced-budget multiplier. This name reflects the fact that in this case the fiscal action has no impact on the size of the government’s budget deficit or surplus.

An increase in government spending of one dollar increases aggregate demand by one dollar, but an increase of taxes by one dollar decreases aggregate demand by less than one dollar, because the extra dollar for taxes comes partly from reducing saving. Consequently, a net positive impact on aggregate demand results from a balanced-budget change in government spending. We can conclude that the Keynesian multiplier process does not necessarily require creation of a budget deficit.

The balanced-budget multiplier is quite small, however, rendering unconvincing the Keynesian plea for fiscal policy in this context. In very simple models of the economy it is easy to show that the balanced-budget multiplier is 1.0. More realistic models of the economy that incorporate automatic stabilizers, however, push this number well below 1.0.

The “world” real rate is a fictitious rate, thought to be determined by activity in a few large, stable financial markets such as those in the United States, Germany, Great Britain, and Japan. For expositional convenience, however, we consider the world real rate to be the rate prevailing in the United States, keeping in mind that the U.S. real rate can in reality be affected by financial activity in these other large countries. The forces described in our Canadian example come about because the Canadian financial market is quite small relative to the U.S. market. If the Canadian and other small markets were microcosms of the U.S. market, the rate prevailing in the U.S. market would undoubtedly also prevail in these smaller markets. They are not exactly the same as the U.S. market, however, if for no other reason than that they are located in another country, with bonds denominated in another currency. The U.S. market sets a standard, not just in terms of a numerical rate, but also in terms of the institutional structure associated with its financial transactions. Investing in a U.S. bond carries with it an implicit degree of riskiness, associated with the political stability, market liquidity, degree of business risk, and legal system characterizing the United States. The implicit degree of riskiness associated with, say, Canadian bonds, may be greater than with U.S. bonds (because of uncertainty caused by the possibility of Quebec separation or by the large size of the Canadian national debt), implying that the real rate in Canada must incorporate a risk premium and therefore be higher than in the United States to compensate for the difference in risk.

A major dimension of the risk factor is the possibility of changes in currency values, and for this reason the risk premium is sometimes called a currency premium. A U.S. investor buying Canadian bonds, for example, will be paid Canadian dollars when the bond matures, so the investor is running the risk that the value of the Canadian dollar may be lower at maturity than it was when he or she bought the bonds. Offsetting this danger is the possibility that the value of the Canadian dollar may be higher, but the point is that there is a risk. An investor will accept this risk only if a higher real rate of return is offered. An investor can purchase insurance to protect against this type of risk (this is called hedging), but at a cost that is of course higher, the higher is the risk. To cover this cost, the real interest rate on the Canadian bond must be higher to make it comparable to U.S. bonds in the eyes of U.S. investors.

A traveler also might notice that prices of nontradables—such as haircuts and hotel rooms—can differ markedly from country to country, at times by amounts dramatically different from what PPP would imply. Because PPP only applies to tradables, this phenomenon is not anomalous, but it does suggest that the exchange rate can be misleading if used to calculate cost-of-living comparisons.

Suppose you have been offered a job in France paying 160,000 francs per year. You check the newspaper, find that the exchange rate is five francs per dollar, and quickly calculate that this amount is equal to US$32,000. It would be a mistake to compare this figure to your current salary in the United States, because it may be that the cost of living in France differs markedly from the cost of living in the United States. To make a fair comparison, you would have to find out how much it would cost you to live your current lifestyle in France.

The real problem here is that the exchange rate does not reflect cost-of-living differences between countries. Instead, it reflects the forces of supply and demand for the dollar in the foreign exchange market, determined by the relative costs of tradables and by a variety of other factors (such as interest rate differences). To make cross-country cost-of-living comparisons, we need a different exchange rate, one explicitly designed to tell us the purchasing power of a franc in France compared to the purchasing power of a dollar in the United States.

The PPP exchange rate does just that. It is calculated by taking the ratio of the cost of a typical bundle of goods and services in francs in France to the cost of that same bundle in dollars in the United States.

If the ratio is four, then the PPP exchange rate is four francs per dollar, so the 160,000-franc salary, in terms of its purchasing power in France, is equivalent to US$40,000. An innovative, albeit extreme, way of measuring the PPP exchange rate has been developed by the Economist magazine through checking the cost of a Big Mac in different countries. If, for example, a Big Mac costs eight francs in France and two dollars in the United States, the PPP exchange rate is four francs per dollar.

Using this alternative exchange rate to make cross-country comparisons can make a big difference. Recently, the International Monetary Fund calculated world income shares using purchasing power parity exchange rates instead of current exchange rates. The result vastly boosts developing countries’ share of the world’s GDP—to 34.4 percent from 17.7 percent. The explanation for this result is that the PPP exchange rate accounts for the fact that many nontradable goods and services in developing countries are much cheaper than in developed countries.

In 1997, U.S. per capita GDP was $29,326. Switzerland’s per capita GDP was $35,879 calculated using market exchange rates, but only $25,902 using PPP exchange rates. The market exchange rate for Swiss francs was about 1.45 francs per dollar, but the PPP exchange rate was about two francs per dollar because the cost of living was so high in Switzerland—in Switzerland two francs were needed to buy what in the U.S. would cost a dollar, but when a tourist exchanged dollars for francs she received only 1.45 francs per dollar. For Japan and Norway, also very expensive countries, the same phenomenon occurs—at market exchange rates per capita GDP appears to be higher than in the U.S., but using PPP exchange rates it is actually much lower. For countries with a lower cost of living, such as Mexico, Turkey, and the Czech Republic, using the PPP exchange rate raises their per capita GDP figure. Mexican per capita GDP was $4,298 in 1997 when calculated using market exchange rates (8 pesos/dollar) but was $7,697 using PPP exchange rates (4.4 pesos/dollar). PPP exchange rates can be found at www.oecd.org

Suppose U.S. inflation is 8 percent, but it is only 5 percent in the rest of the world, due to differing money-supply growth rates. With a fixed exchange rate, during the first year U.S. prices rise by 3 percent more than foreign prices. If nothing changes, during the following year the gap between U.S. and foreign prices widens by another 3 percent, and so on, year after year. It is not true, however, that nothing changes.

Prices in the United States are rising relative to foreign prices, so U.S. exports should fall and imports should rise. As a result, the United States should develop a balance of payments deficit, and the rest of the world should develop a balance of payments surplus. Under fixed exchange rates these developments should automatically decrease the U.S. money supply and automatically increase the foreign money supply. The fall in money-supply growth in the United States lowers its rate of inflation over the long run, and the increase in money-supply growth in the rest of the world increases foreign inflation over the long run. The pressure on both inflation rates continues as long as the U.S. inflation rate exceeds that of the rest of the world. Eventually, inflation and money-supply growth in the rest of the world should match those of the United States.

Does inflation in the rest of the world rise to match American inflation? Does American inflation fall to match foreign inflation? Or do they both move to an intermediate rate? From 1945 to 1971 when most countries were on a fixed exchange rate system, the Bretton Woods system, all countries fixed their exchange rates relative to the U.S. dollar so that in essence everything was measured in U.S. dollars. As a result, the United States could simply print U.S. dollars to cover its balance of payments deficit, eliminating any automatic contraction of the money supply. Consequently, the rest of the world was forced to experience U.S. monetary policy and inflation rate.

The bottom line here is that under a fixed exchange rate, a small, open economy loses control of its monetary policy, which is forced to be identical to that of the larger country to whose currency its exchange rate is fixed. Note that this analysis corroborates the result of the preceding chapter: monetary policy is ineffective under a fixed exchange rate.

Monetary policy in the context of a fixed exchange rate is ineffective because an expansionary monetary policy creates a balance of payments deficit, which automatically decreases the money supply, offsetting and eventually eliminating the original increase in the money supply. What if, however, the monetary authorities take monetary action to counteract the automatic change in the money supply, allowing the original monetary dose to be maintained? As the money supply decreases automatically in the preceding example, the monetary authorities could annually increase the money supply by exactly the same amount.

This policy is called a sterilization policy because it “sterilizes” the automatic money-supply change that results from an imbalance in international payments under fixed exchange rates. Pursuing this policy maintains the original monetary policy dose and allows monetary policy to retain its effectiveness.

Unfortunately, there is a catch: the sterilization policy maintains the imbalance in international payments. In the example, the balance of payments deficit, which would normally disappear as it automatically decreased the money supply, now persists as this automatic mechanism is “sterilized.” What are the implications of of a continuing balance of payments deficit?

Consider how the government, through its agent the central bank, deals with the balance of payments deficit. The deficit means that the supply of dollars on the foreign exchange market exceeds the demand, so those unable to obtain foreign exchange for their dollars go to the government to exchange them at the fixed rate. The government sells foreign currency to them at the fixed rate, as it has promised to do, and in return obtains domestic dollars, which normally would thereby be removed from public circulation, thus decreasing the money supply. (Under a policy of sterilization, of course, the central bank arranges to have these dollars put back into circulation.) The key point here is that during this process the government is selling off its holdings of foreign exchange. As long as the balance of payments deficit continues, the government’s stock of foreign exchange—its foreign exchange reserves—steadily falls.

The major problem with sterilization policy should now be evident. By maintaining the balance of payments deficit, the sterilization policy causes the government’s foreign exchange reserves to run low, threatening its ability to continue this policy, and worse, alerting foreign exchange speculators that the dollar may soon have to be allowed to fall. The resulting foreign exchange crisis usually results in a devaluation (a substantive fall in the fixed exchange rate value), creating embarrassment for the government and profits for speculators. If a balance of payments surplus is being maintained by a sterilization policy, however, opposite results are obtained. Foreign exchange reserves cumulate to embarrassingly high levels, ultimately causing an upward revaluation of the currency and, once again, profits for speculators.

When the exchange rate is fixed, the balance of payments deficit created by a stimulating dose of monetary policy does not cause the exchange rate to fall. Instead, it causes a decrease in the money supply as the Fed buys dollars with foreign exchange to prevent the balance of payments deficit from lowering the exchange rate. The decrease in the money supply diminishes the stimulating effect of the policy dose, making monetary policy weaker in affecting the income level.

There is more to this story however. An increase in the money supply created the balance of payments deficit, and an automatic decrease in the money supply is decreasing the deficit. Consequently, only when the original money supply increase has been completely wiped out will the deficit be eliminated. The economy will regain equilibrium back where it started, so the end result of this monetary policy is no change. This reflects an extremely important general result: under a fixed exchange rate, monetary policy is completely ineffective as a policy tool. Monetary policy implicitly is being used to fix the exchange rate, so is not available for other purposes.

When the exchange rate is fixed, the balance of payments surplus created by a stimulating dose of fiscal policy does not cause the exchange rate to rise. Instead, it causes an increase in the money supply as the Fed buys foreign currency (the balance of payments surplus) with dollars. This increase in the money supply augments the stimulating effect of the policy dose, making fiscal policy stronger in affecting the income level.

An increase in government spending leads to an increase in income and an accompanying increase in the interest rate, causing some crowding out. The increase in income increases imports, creating a balance of payments deficit, but the increase in the interest rate causes capital inflows, creating a balance of payments surplus. Which will dominate? The consensus among economists on this empirical question is that the latter will outweigh the former. Because of the high mobility of international capital, a slight increase in our interest rate causes a substantial capital inflow, outweighing the impact on the balance of payments of the accompanying rise in imports.

Once this empirical question is settled, it is easy to see how international forces modify the impact of fiscal policy. Under a flexible exchange rate system, the balance of payments surplus created by a stimulating dose of fiscal policy causes the exchange rate to appreciate. This increase decreases exports—directly decreasing demand for domestically produced goods and services. It also in creases imports, thereby decreasing demand for domestically produced goods and services that compete against imports. The decrease in aggregate demand for domestically produced goods and services partially offsets the impact on the economy of the stimulating dose of fiscal policy, decreasing the strength of fiscal policy in affecting the income level. Where the terminology—such as “B of P” stands for “balance of payments” and “agg D for g & s'’ stands for “aggregate demand for domestically produced goods and services”—should be obvious.

Under a fixed exchange rate system, the government does not allow the forces of supply and demand to determine the exchange rate. Instead, the government fixes the exchange rate at what it believes is the “right” rate, and the central bank, armed with a stockpile of foreign exchange reserves, stands ready to buy or sell foreign currency at that rate. If there is a balance of payments surplus, the demand for our dollar by foreigners is greater than the supply, so some of these foreigners will seek extra, unavailable dollars. Under a flexible exchange rate, they would have to get dollars by offering more foreign exchange, but under a fixed exchange rate this higher cost can be avoided because the Fed will exchange their foreign currency for dollars at the fixed rate. When the Fed does so, it takes the extra foreign exchange (currency) and in return provides dollars. The most important implication of this process is that the domestic money supply increases by the increase in dollars times the money multiplier.

When there is a balance of payments deficit, the opposite occurs. We are supplying more dollars on the foreign exchange market (seeking foreign currency to take vacations abroad, for example) than there is foreign demand for dollars, so those of us unable to obtain foreign currency from foreigners go to the Fed to buy foreign exchange at the fixed rate. To buy the foreign currency we give the Fed dollars, removing them from public circulation and thereby decreasing the domestic money supply.

To summarize, if the economy has a fixed exchange rate, an imbalance in the international sector of the economy, measured by the balance of payments, automatically causes the money supply to change, in turn affecting economic activity.

Armed with these two general results—that international imbalance causes exchange-rate changes under a flexible exchange rate system and money-supply changes under a fixed exchange rate system—we can examine how monetary and fiscal policy are affected by repercussions from the international sector. To maintain simplicity, all analysis ignores price-level changes and inflation. Incorporating them would not change the general results, only the breakdown of nominal income changes into real changes and price changes.

Exactly what are the forces for change that an imbalance in the balance of payments engenders? This is a crucial question, the answer to which depends on whether the economy is operating on a flexible or a fixed exchange rate system. Let us first examine a flexible exchange rate system.

Under a flexible exchange rate system, the government allows the forces of supply and demand to determine the exchange rate. If there is a balance of payments surplus, demand for our dollar on the foreign exchange market exceeds its supply, so market forces cause a rise in the value of our dollar. Those who want the extra, unavailable dollars try to obtain them by offering extra foreign currency for them, so our dollar becomes more valuable in terms of foreign currency. This appreciation of our dollar is often described by the statement “The exchange rate has risen.”

This process operates in reverse if there is a balance of payments deficit. In this case, the demand for our dollar on the foreign exchange market is less than its supply, so market forces cause a fall in its value. This depreciation of our dollar is often described by the statement “The exchange rate has fallen.”

Note that under a flexible exchange rate system, any tendency toward a balance of payments surplus or deficit is automatically and instantaneously eliminated by a flexing of the exchange rate, so that our measure of the imbalance (the balance of payments) is always zero. The balance of payments measure is nonzero only if the government engages in some net buying or selling of foreign currency. In the context of a flexible exchange rate, the terminology “balance of payments surplus or deficit” must be interpreted as reflecting a surplus or deficit that would appear if the exchange rate were not permitted to adjust instantaneously.

Under a flexible exchange rate, therefore, the initial reaction of the economy to an imbalance in the balance of payments is a change in the exchange rate, which in turn creates additional forces for change in the economy. If, with other variables constant, the exchange rate rises, demand for our exports falls because foreigners find our exports more expensive in terms of their currency. Furthermore, imports become cheaper to us (because our dollar now buys more foreign exchange), so there is a fall in demand for domestically produced goods and services that compete with imports. Both phenomena imply that aggregate demand for domestically produced goods and services falls.

Similarly, if the exchange rate falls, demand for exports and import-competing goods and services should be stimulated, implying a rise in demand for domestically produced goods and services.

To summarize, if the economy has a flexible exchange rate, an imbalance in the international sector of the economy, measured by the balance of payments, automatically causes the exchange rate to change; this change in turn causes the import-competing and export sectors of the economy to adjust, thus affecting aggregate demand for goods and services.