Net Exports

There are courses devoted to models dealing with international trade, financial flows and exchange rates. This is an extremely rich and multifaceted area. Our goal in this section is much more limited. We want to study the way in which imports and exports impact our model of economic fluctuations, and the basic microfoundations of why these relationships exist. Be aware that we are touching on only a tiny piece of an extensive body of knowledge.

In the standard IS/LM model, we regard net exports 𝑁𝑁𝑁𝑁 to be exogenous. But the truth is that net exports are endogenous. In fact, they depend both on GDP and on the interest rate. In this section, we will modify our IS/LM model to accommodate this feature and study the consequences.

Net Exports, Interest Rates and Income – Microfoundations

Here are the two basic relationships underlying the way in which an open economy impacts our model of macroeconomic fluctuations. Remember that net exports are defined as exports minus imports. It is a component of aggregate expenditures.

• Net exports fall when GDP 𝑌𝑌 rises.

• Net exports fall when the interest rate 𝑟𝑟 rises.

The first relationship is straightforward. When income rises, people are going to spend at least some of this income on imports. Rich countries can afford more imports than poor countries can. Thus, from an aggregate expenditures perspective, higher income 𝑌𝑌 reduces net exports.

The second relationship is intermediated by the exchange rate. Remember that the exchange rate is the value of the US dollar in terms of a foreign currency. When the exchange rate rises, we say that the dollar appreciates, meaning that it is more valuable in terms of a foreign currency. When the exchange rate falls, we say that the dollar depreciates, meaning that it is worth less in terms of a foreign currency.

Why do net exports fall when the interest rate rises? There are two steps to the argument.

1. When the interest rate rises, the exchange rate rises. The reason, in simple economic terms, is that demand for US dollars rises when the interest rate rises. When the US return on assets (the interest rate 𝑟𝑟) is high, foreigners demand more US dollars in order to buy these US assets. This demand pushes up the value of US dollars (the exchange rate).

2. When the exchange rate rises, two things happen. First, US exports become more expensive for foreigners to buy and so exports fall. Second, the US dollar becomes more valuable overseas and so imports of foreign goods by Americans rise. Overall, an increase in the exchange rate leads to a decline in net exports and a decline in aggregate expenditures on American goods and services.

To summarize, higher GDP means more income for Americans and means that Americans buy more imports. Thus, net exports fall as GDP rises. Higher interest rates mean that the US dollar appreciates, which makes American exports expensive and makes foreign imports cheap. Thus, net exports also fall as the interest rate rises.

Augmented IS/LM Model

From the previous section, net exports fall as GDP rises and they fall as the interest rate rises. Thus, rather than treating net exports as exogenous, we will model net exports as a function of GDP and of the interest rate.

𝑁𝑁𝑁𝑁 = 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟

Here, 𝑁𝑁 is the exogenous intercept. Net exports decline as income 𝑌𝑌 rises and they decline as the interest rate 𝑟𝑟 rises. The parameters 𝑚𝑚 and 𝑛𝑛 are the sensitivity of these relationships. When they are small, changes in 𝑌𝑌 and 𝑟𝑟 do not have a large impact on net export spending. As they become larger, changes in 𝑌𝑌 and 𝑟𝑟 have more impact on net exports.

We will solve for the IS/LM equilibrium with this new addition to the model. The four components of aggregate expenditures are as follows:

• _{𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)} • _{𝐼𝐼 = 𝐼𝐼0− 𝑑𝑑𝑟𝑟}

• _𝐺𝐺 is exogenous

• _{𝑁𝑁𝑁𝑁 = 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟}

This is the same as the standard model except for the endogenous formulation for net exports. The IS curve comes from the Keynesian equilibrium condition equating output and spending. To solve for IS/LM equilibrium, we first solve for the IS relation and isolate the interest rate 𝑟𝑟 at the end of the right side of the expression.

𝑌𝑌 = 𝐴𝐴𝐴𝐴 𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁 𝑌𝑌 = [𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)] + [𝐼𝐼0− 𝑑𝑑𝑟𝑟] + 𝐺𝐺 + [𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟] 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 − 𝑑𝑑𝑟𝑟 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑑𝑑𝑟𝑟 − 𝑛𝑛𝑟𝑟 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛)𝑟𝑟

The LM curve is the standard LM curve that equates supply and demand for money.

𝑀𝑀

𝑃𝑃 = 𝑚𝑚0− ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌 Solving the LM relationship for 𝑟𝑟 gives:

𝑟𝑟 =𝑚𝑚_{ℎ −}0 _{ℎ𝑃𝑃 + �}𝑀𝑀 𝑘𝑘_{ℎ� 𝑌𝑌}

To solve for the IS/LM equilibrium, we substitute this expression for 𝑟𝑟 back into the IS curve: 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛)𝑟𝑟

𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛) �𝑚𝑚_{ℎ −}0 _{ℎ𝑃𝑃 + �}𝑀𝑀 𝑘𝑘_{ℎ� 𝑌𝑌�}

We solve this expression for 𝑌𝑌 to find the equilibrium GDP.

𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛) �𝑚𝑚_{ℎ −}0 _{ℎ𝑃𝑃 + �}𝑀𝑀 𝑘𝑘_{ℎ� 𝑌𝑌�} 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − �𝑑𝑑 + 𝑛𝑛_{ℎ � 𝑚𝑚}0+ �𝑑𝑑 + 𝑛𝑛_{ℎ � �}𝑀𝑀_{𝑃𝑃 � − �}(𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ � 𝑌𝑌 𝑌𝑌 − 𝑏𝑏𝑌𝑌 + 𝑚𝑚𝑌𝑌 + �(𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ � 𝑌𝑌 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − �𝑑𝑑 + 𝑛𝑛_{ℎ � 𝑚𝑚}0+ �𝑑𝑑 + 𝑛𝑛_{ℎ � �}𝑀𝑀_{𝑃𝑃 �} 𝑌𝑌 �1 − 𝑏𝑏 + 𝑚𝑚 +(𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ � = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − �𝑑𝑑 + 𝑛𝑛_{ℎ � 𝑚𝑚}0+ �𝑑𝑑 + 𝑛𝑛_{ℎ � �}𝑀𝑀_{𝑃𝑃 �} 𝑌𝑌∗_{= �} 1 1 − 𝑏𝑏 + 𝑚𝑚 + (𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ � �𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − � 𝑑𝑑 + 𝑛𝑛 ℎ � 𝑚𝑚0+ � 𝑑𝑑 + 𝑛𝑛 ℎ � � 𝑀𝑀 𝑃𝑃 �� Using this last expression, we can study analytically the impact that the open economy has on economic policy.

Economic Policy in an Open Economy

In the standard IS/LM model, where net exports are exogenous, the IS/LM spending multiplier is:

𝜕𝜕𝑌𝑌∗

𝜕𝜕𝐺𝐺 =

1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘_ℎ

In our enhanced IS/LM model, with endogenous net exports, the IS/LM spending multiplier is:

𝜕𝜕𝑌𝑌∗

𝜕𝜕𝐺𝐺 =

1

1 − 𝑏𝑏 + 𝑚𝑚 + (𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ

The denominator is larger for our new enhanced model. Thus, the IS/LM spending multiplier is

lower in the model with endogenous net exports than it is in the standard model.

The key insight is that net exports reduce the value of the spending multiplier and thus they reduce the susceptibility of the economy to spending shocks. Exports and imports modulate the impact of spending shocks on the economy. In brief, net exports act as an automatic stabilizer.

The economic intuition is easy to understand in an IS/LM framework. When there is a spending increase (a rightward shift of the IS curve), GDP and the interest rate increase. But both the GDP increase and the interest rate increase reduce net exports. This reduction offsets some of the initial increase in GDP, and so overall the multiplier effect of the spending shock on GDP is dampened. For negative spending shocks, the opposite is true. The reduction in interest rates and GDP will raise net exports and, at least in part, offset some of the negative impact on GDP.

However, this stabilizing effect of net exports is not necessarily the case for monetary shocks. In the standard model, the money multiplier is:

𝜕𝜕𝑌𝑌∗ 𝜕𝜕 �𝑀𝑀_{𝑃𝑃 �}= � 𝑑𝑑 ℎ� � 1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘_ℎ �

But, in our augmented model with endogenous net exports, the money multiplier is:

𝜕𝜕𝑌𝑌∗ 𝜕𝜕 �𝑀𝑀_{𝑃𝑃 �}= � 𝑑𝑑 + 𝑛𝑛 ℎ � � 1 1 − 𝑏𝑏 + 𝑚𝑚 + (𝑑𝑑 + 𝑛𝑛)𝑘𝑘_ℎ �

The numerator is larger in the new model with endogenous net exports, but the denominator is larger also. Thus, the new money multiplier could be higher or lower than the original multiplier.

Again, the intuition is straightforward in an IS/LM framework. When the money supply rises, the LM curve shifts right, causing GDP to rise and the interest rate to fall. The increase in GDP causes net exports to fall, but the reduction in interest rates causes net exports to rise. Overall, the impact of the open economy on a monetary shock could be to partially offset the increase in GDP, or it could be to reinforce and strengthen it.

The Open Economy in the United States

To finish with some perspective, the diagram below shows exports and imports in the US since 1947. Our trade position was basically balanced (exports and imports approximately equal) until the 1980’s, and since then imports have exceeded exports. The difference between the two exploded in the late 1990’s and early 2000’s, creating large trade deficits that have persisted ever since. In 2016, the US exported $2.21 trillion of goods and services but we imported $2.74 trillion of goods and services, leading to a $521 billion trade deficit with the rest of the world

The reasons for our large trade deficits are complicated and controversial. However, the basic accounting of international trade and capital flows suggests that the trade deficits are related to high levels of borrowing. When the US buys more from overseas than what it produces and sells overseas – when we consume more than what we produce – we have to pay for it by borrowing from foreigners (called net capital inflows in international finance lingo). In the case of the US, most of the net capital inflow borrowing has been government borrowing to cover government budget deficits; private savings just about covers private investment spending in the US. Essentially, government deficits have been financing low taxes, and then lots of this money is spent buying imports. This pattern leads simultaneously to a trade deficit and to a government budget deficit. For this reason, the problem has been called the twin deficits problem.

Unit 3.5: Money

In this section, we will cover the foundations of the role that money plays in macroeconomic models. We will first cover the demand side, then we will cover the supply side, and finally we will analyze the relationship between money and price levels. The money supply in each country is actively managed by its central bank. In the United States, the central bank is called the Federal Reserve Board. In a later section, we will cover optimal management of the money supply from a policy perspective. The purpose of this section is to provide an overview of the role of money in the macroeconomy.

Money Demand Why hold money?

On its face, money seems like a stupid way to hold wealth. After all, other financial assets like bonds pay some interest, but holding money generates zero return. Why then do we hold any of our wealth in the form of money? Classical macroeconomics offers three reasons:

1. Transactions motive – Income arrives periodically, but you have to buy things regularly. Thus, you need to keep some stock of money to buy things.

2. Precautionary motive – People might keep a stock of money in case they have an emergency need for quick, liquid funds. This is not much of an issue in the US since there are interest-bearing assets like CD’s that can be liquidated quickly and serve this precautionary function.

3. Speculative motive – If financial markets are unstable, people might want to hold some of their wealth as money just to avoid risk.

Among these, the most important by far is the transactions motive. Practically, this is the reason that most of us keep stocks of money.

Transactions motive – Portfolio balance problems

How much money to hold is a portfolio balance problem. In essence, it is about balancing out costs and benefits. Holding higher money stocks is more convenient and reduces the costs of having to get cash all the time. But holding higher money stocks also involves an opportunity cost – that wealth could have been invested in interest-bearing assets and earning a return. Maintaining a

money stock that is too low makes it inconvenient and costly to get money every time you need to spend it. But maintaining a money stock that is too high is costly because of the foregone interest.

Here is a simple model of how to choose the optimal stock of money to hold. Suppose you earn an income of 𝑌𝑌 each month, paid once a month. If you want your average money stock to be 𝑀𝑀, then number of withdrawals you need every month is:

withdrawals =_2𝑀𝑀𝑌𝑌

For example, if your income is $8000 a month and you want to have an average money balance of $4000, then you only need 𝑌𝑌

2𝑀𝑀= 8000

2⋅4000= 1 withdrawal. Your $8000 will be depleted at the end of

the month, so your average money holdings over the month will be $4000.

But if you want to reduce your average money balance to $2000, then you need 𝑌𝑌

2𝑀𝑀= 8000 2⋅2000= 2

withdrawals each month. In this case, you withdraw your $8000 twice a month ($4000 each), which would mean that you average a $2000 money balance over the month.

The cost of each withdrawal is 𝑞𝑞. This cost includes the inconvenience, time cost and monetary cost associated with making withdrawals.

total cost of withdrawals = 𝑞𝑞 �_2𝑀𝑀�𝑌𝑌

Choosing to keep a higher money balance 𝑀𝑀 reduces the total cost of withdrawals since you don’t have to visit the bank as often.

On the other hand, a higher money balance also increases the opportunity cost associated with the foregone interest. If the interest rate is 𝑟𝑟, then the opportunity cost associated with maintaining an average money balance of 𝑀𝑀 is:

opportunity cost of money balance = 𝑟𝑟𝑀𝑀

Combining the two pieces, the total cost associated with choosing to hold an average money balance 𝑀𝑀 is given by:

Now you can see the tradeoff. Higher money balances reduce transactions costs but they increase opportunity cost of lost interest. The objective is to choose a money balance 𝑀𝑀 to minimize the total cost associated with money holdings. To find the value of 𝑀𝑀 that minimizes total costs, we take the derivative of the expression with respect to 𝑀𝑀 and set it equal to zero.

𝑑𝑑 𝑑𝑑𝑀𝑀 = − 𝑞𝑞𝑌𝑌 2𝑀𝑀2+ 𝑟𝑟 = 0 𝑟𝑟 = 𝑞𝑞𝑌𝑌 2𝑀𝑀2 𝑀𝑀2 ₌ 𝑞𝑞𝑌𝑌 2𝑟𝑟 𝑀𝑀 = �𝑞𝑞𝑌𝑌_2𝑟𝑟

This model rationalizes the LM relationship that we developed earlier in the course. Money demand rises when income rises but money demand falls when the interest rate rises. Now we see why – at higher incomes, people spend more, so they keep higher money balances. But at higher interest rates, the opportunity cost of holding money balances is high, so people hold lower money balances and hold more of their wealth as interest-bearing assets.

Money Supply Definition of money

Money is a special kind of asset that is extremely liquid. There are many kinds of assets. Stocks, bonds, property, artwork, etc… are all assets with value, but these are at least somewhat illiquid. Out of all financial assets in the economy, only two things are considered to be money.

1. Currency (cash and coins)

2. Demand deposits (checking accounts)

Let 𝐶𝐶𝐶𝐶 designate the amount of currency outstanding and let 𝐷𝐷 be the total amount of demand deposits outstanding. The money supply (𝑀𝑀) is the amount of money in the hands of the public at any given time. Formally:

Fractional reserve system and the monetary base

Banks operate using a fractional reserve system, meaning that only a fraction of the total deposits at the bank are actually held in reserve. The banks lend the rest of the money out. Thus, much of what people think they have on deposit is illusory in a sense. If everyone tried to reclaim their demand deposits at the same time, a bank run ensues, which collapses the banking system.

The monetary base, sometimes called high-powered money, is the amount of hard money that is outstanding at any point in time (not the money that exists only on bank balance sheets). The monetary base consists of currency in the hands of the public (𝐶𝐶𝐶𝐶) and bank reserves (𝑅𝑅𝐴𝐴).

𝑀𝑀𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝑅𝑅𝐴𝐴

The deposit multiplier

Banks are required by law to keep a fraction of their demand deposits on reserve. This is called the required reserve ratio (𝑟𝑟). In the US, 𝑟𝑟 = 0.1. Formally, reserves are:

𝑅𝑅𝐴𝐴 = 𝑟𝑟𝐷𝐷

Generally, people don’t want to have all of their money tied up in the bank. People want to hold some ratio 𝑐𝑐 of currency to demand deposits. Thus, currency holdings are:

𝐶𝐶𝐶𝐶 = 𝑐𝑐𝐷𝐷

Now, going back to the definition of the money supply, we substitute in the models above:

𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝐷𝐷 = 𝑐𝑐𝐷𝐷 + 𝐷𝐷 = (1 + 𝑐𝑐)𝐷𝐷

Similarly, substitute in the models above for the definition of the monetary base:

𝑀𝑀𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝑅𝑅𝐴𝐴 = 𝑐𝑐𝐷𝐷 + 𝑟𝑟𝐷𝐷 = (𝑐𝑐 + 𝑟𝑟)𝐷𝐷

𝑀𝑀 𝑀𝑀𝑀𝑀 = (1 + 𝑐𝑐)𝐷𝐷 (𝑐𝑐 + 𝑟𝑟)𝐷𝐷 𝑀𝑀 = �1 + 𝑐𝑐_{𝑟𝑟 + 𝑐𝑐� 𝑀𝑀𝑀𝑀} The coefficient 1+𝑖𝑖

𝑟𝑟+𝑖𝑖 is called the deposit multiplier. The deposit multiplier is the change in the

total money supply that results from each $1 increase in the monetary base by the Fed. Importantly, when the Fed injects an additional dollar into the monetary base, the injection increases the money supply by more than $1 because of the subsequent rounds of loans and deposits it creates.

Say the Fed injects $1000 into the monetary base. The money initially ends up deposited in Bank A. Bank A will lend out a chunk of the money, and that money will eventually end up deposited in Bank B. Bank B will lend out a chunk of the money, and that will end up deposited in Bank C, which can lend some of it out, etc… Thus, the total increase in demand deposits at banks is much greater than $1000. Of course, if everyone tried to go back and redeem their demand deposits at the same time, there would be a bank run since there is only $1000 of monetary base backing up all of these demand deposits.

For example, suppose 𝑟𝑟 = 0.1 and 𝑐𝑐 = 0. In this case, the deposit multiplier is: 1 + 𝑐𝑐

𝑟𝑟 + 𝑐𝑐 =

1 + 0 0.1 + 0 = 10

The multiplier is intuitive in this case. If each bank keeps only 10% of its deposits and there is no currency sucked out of the system, then the total deposits will be 10 times the monetary base.

But, suppose instead that 𝑟𝑟 = 0.1 and 𝑐𝑐 = 0.2. In this case, the deposit multiplier is: 1 + 𝑐𝑐

𝑟𝑟 + 𝑐𝑐 =

1 + 0.2 0.1 + 0.2 = 4

In this case, when bank deposits increase, people want to hold some of their new wealth as currency, so not all of the subsequent loans end up re-deposited in banks. Some of the funds are simply held as currency. This currency drain reduces the deposit multiplier.