Let us review the two exchange rate models that we have learned so far. The covered interest parity gives an understanding on how forward exchange rates should be determined. Any interest rate differentials between two countries produces an implied forward exchange rate. If we set an forward exchange rate that is too high or too low, there would be arbitrage opportunities. This, of course, makes sense in the absence of transaction costs, but for the most part, most academics and practitioners agree that the covered interest rate parity holds in reality. However, we want a model to understand the spot exchange rate or the exchange rate today. We want to somehow take the forward exchange rate as a given to make predictions on the spot exchange rate. The covered interest parity model gives us a way, but makes 2 additional assumptions so that we can substitute the forward exchange rate with future expectations about spot exchange rate. This is only possible if the forward exchange rate is redundant. Those two assumptions are 1) markets are efficient and therefore information is the same for the universe of investors and 2) investors on average are risk neutral. The latter assumption is possible if investors only care about expected returns and ignores risk. Therefore, the uncovered interest parity is a very simple asset pricing model because we are interpreting currency depreciation or appreciation as asset returns. Note that the no arbitrage assumption still applies in the covered interest parity. You can exploit the arbitrage opportunities from the deviations away from the uncovered interest parity just like you can with deviations away from the covered interest parity. However, these no arbitrage arguments assumes that our beliefs are on average accurate and correct. If our beliefs or expectations about the future are correct on average or that E hat e is on average equal to E in the future, then you can take advantage of violations of the uncovered interest parity through the same arbitrage steps you can take for the covered interest parity.

Last week’s homework hopefully informed you that the predictions of the uncovered interest parity is wildly different than reality. This is very common in all of economics and finance since we are dealing with human decision making, but it serves as a starting point to understand how reality deviates away from market efficiency.

Monetary Conditions and Exchange Rate

Today’s agenda is to combine the uncovered interest rate parity with money markets (that is, the supply and demand for cash) that you all might have seen in your other macroeconomics courses. Monetary conditions should be important determinants of exchange rates because they change the supply of money in the economy. Domestic monetary conditions can affect the domestic interest rates and thus the exchange rate through E. We will assume that the uncovered interest parity is satisfied.

Just to review why money is important: money has three basic functions 1) It is a medium of exchange: money helps make trade possible and less costly, 2) money is a unit of account: it helps us compare the value of goods between each other, and 3) it is a store of value: you can put your money away and use it again later to buy goods and services. It is a way to store future consumption.

The Value of Money Holdings

As mentioned before in the uncovered interest parity from an asset pricing approach last week, money or currency is an asset. It has returns, risk, and liquidity dimensions just like all assets. Its returns are small and potentially negative if there is inflation. Money expected returns are used in the uncovered interest parity. Its risk is low compared to most assets, but the risk of inflation of deflation can change its value. In the uncovered interest parity, we assumed risk neutrality, so the risk is ignored. Liquidity is the ease of transforming one asset into goods and services. Money is very liquid in general, except in the case of hyperinflation, such as the case in Zimbabwe.

Given these features, what are the incentives to holding and not holding money? What drives the demand and supply of money? To be more specific: what is the opportunity cost of holding money? The definition of opportunity cost is the forgone benefit of the next best alternative. So, to be more precise, what is the next best alternative to holding money? In most cases, if you are not holding money, you will deposit it in a bank account to protect your money from inflation. That is captured by R in our uncovered interest parity model, which is the domestic bond yield or nominal interest rate. Nominal here means that the interest rate has not been adjusted for inflation. That means we can decompose the nominal interest rate into two parts: the real interest rate and the inflation rate. So if holding money has 0 returns if we are not buying anything with it and the nominal interest rate is positive, that means our opportunity cost is positive, which means we will have negative returns. R therefore compensates for loss in inflation and the cost of not holding bonds.

So, the cost of holding money is therefore captured by R. The higher R is, the more expensive it is to hold money if you don’t plan on buying any goods with it, all else equal. Said differently, a rise in the nominal interest rate R reduces the demand for money. People may forgo some consumption today. The punchline is an increase in R reduces money demand. A decrease in R increases money demand. For the latter case, if the returns on saving is too low, you should consume today rather than delay consumption until tomorrow.

Money Supply and Central Banks

Now that we understand why money is important and its relationship to interest rates, let’s try to understand where money comes from. Money, for the past several thousand years in the most advanced civilizations, are controlled by the central bank. This is the PBOC in China, the ECB in Europe, the Bank of England in the U.K., the Hong Kong Monetary Authority, and the Federal Reserve in the U.S. The central bank directly regulates the amount of currency in circulation through various methods such as open market operations such as buying and selling government debt. Buying government debt is a way of injecting money into the financial system. Selling government debt is a way of removing from the financial system. Buying government debt increases the demand for bonds, which increases bond prices, which lowers the yield. A lower yield makes bonds less attractive and so some people may prefer to hold cash now to consume today. Selling government debt increases the supply of bonds, which decreases bond prices, which increases the yield. A higher yield makes bonds more attractive and so some people will forgo consumption today and save for tomorrow. Therefore central banks’ direct impact on M0 will indirectly affect other aggregate measures of money such as M1, M2, and M3. M0 and M1 are called narrow money, which normally include coins and notes in circulation and other money equivalents that are easily convertible into cash. M2 includes M1 plus short-term time deposits in banks. M3 includes M2 plus longer-term time deposits. The exact definitions of the three measures depend on the country.

Since money is issued from central banks, they have several policy instruments to affect the interest rate. As mentioned before, they can engage in open market transactions where they buy and sell assets to adjust the overnight lending rate for banks. In the U.S., this overnight lending rate is called the federal funds rate, and is what banks charge each other for deposits. The interest rate at which commercial banks refinance is called the discount rate or bank rate. This is the interest rate to borrow funds from the central bank. The central bank functions as a lender of last resort, so changing the discount rate can affect the overnight interbank lending rate. Lastly, central banks can also change the deposit requirements for commercial banks. These are reserve requirements to limit the money multiplier effect. Here is an example of a money multiplier effect: If I deposit 100 dollars into a bank, that bank can loan that money to someone else. That person can then deposit that 100 dollars into another bank. So the initial 100 dollars created 200 dollars of deposits. This effect can explode the money base or the liability side of the central bank’s balance sheet. So, reserve ratios limits this money creation by banks because banks now have to keep a percentage of all deposits they receive.

Central Bank Balance Sheet

Let us get a visual understanding of what happens to the central bank balance sheets when it decides to use its policy instruments to adjust the money supply. This a typical central bank balance sheet. The left side are assets, which are mark to market, and the right side are liabilities. Net worth is just an accounting definition when we subtract liabilities from assets. W represent foreign assets and B represent domestic assets, specifically government issued bonds. These assets appear on the balance when the central bank give out short term loans through the discount or bank rate. SDRs are special drawing rights. They are rights to currency reserves owned by the international monetary fund. They act like a global currency. On the liabilities side, we have the monetary base, which is the M0, M1, M2, and M3. Note that the central bank can print money physically or electronically.

Open-market Intervention to Increase Monetary Base

Let us consider one type of policy instrument, namely the open-market intervention through the purchase of assets. To increase the monetary base, the central bank can buy either foreign or domestic assets by printing or creating new money. On the balance sheet, the central bank receives new assets, but that also increases the monetary base because new money is created.

Note that the interest rate that the central bank lends out to depositors reflects their expected default. Therefore, these assets act like collateral. Central banks doesn’t operate to make money, so it doesn’t care about returns on the balance sheet. If the central bank is risk neutral, it doesn’t matter if it holds foreign assets or domestic assets since they are perfect substitutes.

In any case, the takeaway is that one way the central bank can increase the monetary base is to buy assets by printing money.

Real Money Demand

Remember our goal is to understand the supply and demand of money to construct a model of the money markets. We have just discussed how the supply of money is determined. The central bank controls the money supply and it can change it at will by changing the monetary base through the bank rate or the open-market operations. The next step is to understand how money demand works. Much like all macroeconomic models, we are thinking individuals or households in aggregate. What is the aggregate demand of money? For now, we will make the assumption that aggregate household demand for money is determined by two things: 1) the nominal interest rate or bond yield and 2) the real national income or GNP. In order to get real money supply we will scale the nominal money supply by the overall price level of a country. Typically, this is the consumer price index or CPI. The CPI is the cost of a typical consumption basket. Just like calculating total revenue for a firm, we can calculate total demand for money by multiplying price by quantity demanded. We will call this quantity demanded for money the country’s liquidity preference. We will now build a simple model of a country’s liquidity preference.

We will assume that a country’s liquidity preference will be a function of two variables: 1) the nominal interest rate and the real national income. We will represent a country’s liquidity preference through the function L. To make our lives easier, we assume that L is continuous with respect both R and Y. This just means that if we change R and Y slightly, L will change slightly too. This assumption allows us to take derivatives so we know which direction L will move if we increase or decrease R or Y.

Which direction should L go if we increase R or the nominal interest rate? If interest rates are high, then the opportunity cost to hold onto money is high. For some, it may not be worth it to consume goods and services today and will decide to invest in bonds instead. This means that there is less demand for money or liquidity. So if we take the partial derivative of L with respect to R, we should get something negative. That means if we increase R, L should decrease.

Which direction should L go if we increase Y or the real national income? If the aggregate real household income is higher, then everyone is richer overall. Some of these households may decide to consume more today and therefore demand for money will increase. In other words, more people will prefer to hold onto cash today. This means that there is more demand for money or liquidity. So if we take the partial derivative of L with respect to Y, we should get something positive. That means, if we increase Y, L should increase.

Again, nominal money supply should be equal to price times quantity demanded. However, if scale everything by price, then we can get real money demand. M^D divided P is equal to L.

Bond Yields and Monetary Policy

Let us try to get a better understanding of bond prices and bond yield or more specifically the nominal interest rate before moving on. First, let us review some terminology. The face value of a bond is sometimes called the par value. The par value is amount the bondholder gets at redemption. For simplicity, we are going to ignore coupon payments to make the math easier. Bonds typically trade at a discount of their face value. This is mainly due to the time value of money. For example, if a bond with par value of 1 dollar is trading at a 20 percent discount, the the bond price is 80 cents. That is 80 percent times 1 dollar. This price is the present value. Therefore, the yield of the bond is the required return on the present value such that the bondholder receives the par value in the future. The yield to maturity is therefore the face value divided by the present value minus 1. In the case in which a 1 dollar par value bond is trading at 80 cents, the bond yield is 25%. When the central bank purchases bonds, bond price will increase due to increased demand. A higher price means that the bond is trading at a lower discount. At a lower discount, the yield will decrease. For example, if the 1 dollar par value bond is now trading at 10 percent, then the bond yield is now 1 divided 0.9 minus 1 or 11 percent.

We will use this mechanism a lot to understand how money markets will relate to the exchange rate market.

Aggregate Real Money Demand

The link between the exchange rate market and the money market is the nominal interest rate or bond yield. Thus, the y axis is the nominal interest rate and the y axis is our aggregate liquidity preference of a country. Since we assumed that the increasing R will decrease a country’s liquidity preference, our aggregate real money demand will be downward sloping.

Money market Equilibrium

Money market equilibrium is determined when real money supply is set equal to real money demand. M^S divided P is freely chosen by the central banks. So, given a fixed M^S/P, we can now determine what the equilibrium nominal interest rate is when the two lines cross or when the money market clears.

Now that we have our graphical equilibrium model, how do real national income and potentially other macroeconomic variables impact R?

Increase in Real National Income

Consider the case in which there is an increase in real national income Y. We know that the aggregate liquidity preference is positively related to the real national income. So increasing Y will increase aggregate liquidity demand. With more real income, all households are now trying to sell assets to raise liquid money for consumption. They will sell bond holdings. The selling of bond holdings will lower bond prices and increase the bond yield. Therefore, the nominal interest rate R will increase. Graphically, the money demand curve will shift upward. Therefore, the new equilibrium nominal interest rate is at a higher level.

Short- and Long-Term Effects of Monetary Policy

Let us now introduce some typical macroeconomic frictions into our model. What all of you should be thinking now hopefully, for those who have had some exposure to macroeconomics, is why should the central bank have any sort of impact in the money market by changing the money supply? If the central bank changes the money supply, overall prices should inflate if the money supply increases and deflate when the money supply is cut. Either way, real money supply should be unchanged. Yes! That is true. If prices are not sticky or slow to adjust to money supply, then we don’t need central banks. But unfortunately, that is not reality. The reality is that prices are so called “sticky” and thus monetary policy has a real impact in the short run. In the long run, say 30 years, prices are fully flexible. That means that nominal interest rates should only be determined by real variables, such as real income. Monetary policy has no real impact.

Increase in Real Money Supply under Sticky Prices

To make sure everyone understand our short-run and long run assumptions, let us see what happens when we increase money supply under sticky and flexible prices. In the case of sticky prices, P doesn’t move when M^S increases. Thus, real money supply will shift rightward. The central bank can increase nominal money supply by printing money and buying bonds. Buying bonds will increase bond prices and thus the bond yield will decrease. Thus, the nominal interest rate will decrease.

Increase in Real Money Supply under Flexible Prices

What do you think should happen to the real money supply under flexible prices? In the case of flexible prices, if money supply increases, price level should also increase the same proportion. Thus, money supply doesn’t move in the long run and the nominal interest rate stays the same, all else equal.

Money Supply and Central Banks

This slide is just to give you more background on money supply and central banks. Seignorage occurs basically when inflation or depreciation occurs. If take cash or fiat money from the central bank in exchange for valuable assets, inflation or depreciation can make the fiat money weaker. Trading fiat money back for your assets, the central bank can make money. For example, think about all those mortgage-backed securities that central banks bought up during the financial crisis at liquidation prices.

Lastly, a subtle note, monetary base and money supply are not quite the same. Monetary base is technically just cash. M1, M2, and M3 include cash but are created through short term and long term deposits. Deposits created from other deposits is a mechanism called the money multiplier. For example, if a commercial bank receives 1000 USD from the central bank and lends it out. The borrower can go on to purchase a good for 1000 USD. The goods seller can then deposit that 1000 USD with her bank. This can go on for infinity. The only way to limit this money multiplier or the expansion of the money supply is to require reserve ratios. That means for every deposit, the bank is required to keep a proportion of the deposit in the vault.

Money and Foreign Exchange Market Equilibrium

Now, given our exchange rate model from the uncovered interest rate parity and the money market model, we can now combine them together through the nominal interest rate or the bond yield. The macroeconomy can affect R and through liquidity demand affect E through the uncovered interest parity. We will assume that the uncovered interest parity holds.

Spot Exchange Rate and Expected Currency Returns

Note that the nominal interest rate is determined simultaneously from the money market and the exchange rate market.

Money and Foreign Exchange Market Equilibrium

This model allows us to study both how changes in domestic and foreign nominal interest rates can affect the domestic exchange rate E. We will assume that domestic and foreign money markets are similar. As we will see, the exchange rate response will depend on the degree of price flexibility. In the short run, we will assume that prices are sticky and fixed. In the long term, we assume that prices are flexible.

Temporary Increase in Domestic Money Supply under Sticky Prices

Let us first consider a temporary increase in the domestic money supply under sticky prices. Temporary means that our expectations about the future exchange rate is unchanged. P is also fixed. Increase in money supply means that the central bank buy bonds with newly printed money, bond prices increase, which decreases the bond yield or nominal interest rates. Investors will sell dollars for foreign currency to take advantage of better interests abroad. The dollar depreciates and thus E increases.

Temporary Increase in Foreign Money Supply under Sticky Prices

What happens in foreign central banks decide to increase their money supply. In the foreign central bank increases its money supply, they buy their own bonds, which increases bond prices and the bond yield decreases. So, R star decreases. The short story is that there is now better interest return on the domestic currency. Foreign investors will buy the domestic currency and appreciate the domestic currency. E will decrease. The long story using rational expectations is that E hat e is fixed. If E hat e is fixed, the dollar needs to depreciate between now and the future to wipe out interest gains on the dollar. Thus, you need to appreciate today and depreciate in the future to cancel out R minus R star.

Temporary Change to the Money Supply

This slide summarizes the short run impacts on exchange rates from temporary changes to the money supply. Note that neither R or E would change under flexible prices.

A Preview of the Long Term: E Traces P

What happens in the long run? As I will show you later graphically, the exchange rate will trace the price level. That is, exchange rates will increase when the price level increases. Let us go over an example. Suppose Toyota sells the same model car in the U.S. and in Japan. Thus, you should pay the same for them. From this single good alone, the exchange rate should be E = 1. Thus, 10000 JPY = 10000 USD. Now suppose the Federal Reserve doubles the monetary supply. What happens to prices? It should double. Thus, 20000 USD = 10000 JPY. We can no longer have E = 1. If E is still equal to 1, we want to buy Toyota as in Japan and sell them in the U.S. to get arbitrage profits. Everyone wants to sell USD. Thus, the exchange rate must depreciate such that E = 2. Nominal exchange rates move the same way as the increase in money supply.

Permanent Changes to the Money Supply

Permanent changes in money supply do affect exchange rates because expectations about the future exchange rates changes. Although in the long term, prices are flexible and the nominal interest rate is unchanged, the exchange rate will change due to rational expectations about the future exchange rate.

Permanent Increase in Domestic Money Supply under Sticky Prices

Permanent Changes and Overshooting

Overshooting: The Exchange Rate does the Job that Sticky Prices Do not Do