The Twin-Deficit Identity

One of the important relationships among aggregate economic variables is the so-called Twin-Deficit Identity, a term in reference to a country’s government budget deficit and a simultaneous current account deficit. The name for this identity became commonplace during the 1980s and 1990s because at that time the US experienced deficits in both of these accounts. Now, as we will see later, the identity will be a misnomer in many circumstances since there is no reason that "twin" deficits need always appear together on these two national accounts. In fact, some countries will, at times, experience a deficit on one account and a surplus on the other. (witness Japan in 2000). Also, at times, a country will experience a surplus on both accounts.

Thus, a better title to this section would be, “The Relationship Between a Country’s Government Budget Deficit and its Current Account Deficit.” However, since the US currently (in 2004) finds itself back in the twin-deficit scenario, and since “twin-deficit identity” roles off the tongue much more easily, we will stick to this title.

To understand this identity it will be helpful to take a much more careful look at the national income identity. This time I will build up the identity in a stepwise fashion using a circular flow diagram to better visualize the flows of money within an economy.   A circular flow diagram is typically one of the first principles shown to students in an introductory macroeconomics class. Its purpose is to show the flow of money between the major players (or agents) within an economy. Circular flow diagrams can be either simple or complex depending on how many agents one introduces into the system and how finely one wishes to break down the money flows.

Circular Flow: Version 1

The simplest version of a circular flow diagram considers an economy consisting of two agents; households and firms. We imagine that firms produce goods and services using labor as an input.

 

The flow of money is shown in the adjoining diagram. The "C" arrow represents the dollar value of consumption expenditures made by households to purchase the goods and services produced and sold by firms. (The goods and services flow could be represented by an arrow in the opposite direction to C, but we leave that out for simplicity.) Since we assume in this case that there are only households buying goods, all of GNP consists of C. The money that flows to firms, from sales of consumption goods, is given to the workers in exchange for their labor services. This money flow is represented by the arrow labeled disposable income. Disposable income is all of the money households have to spend which in this case is equal to the national income (NI).

[Special Note: We use GNP rather than GDP as our measure of national income so that flows with the rest of the world later are properly defined.]

Circular Flow: Version 2

The circular flow can be extended one step by adding financial institutions. Financial institutions represent any company that facilitates borrowing and lending, the prime example being a bank. However, it may also include investment companies, pension funds and mutual funds. The presence of financial institutions allows some money to be diverted from the consumption flow. In the adjoining diagram these diversions are represented by S_HH, representing household saving and S_B, representing business saving. Some of the revenue earned by firms is not actually given out to workers in the forms of wages. Instead some money is "retained" in the form of profit and excess earnings. These retained earnings are generally used to purchase investment goods to help an industry replace worn-out capital equipment and to add new capital. Much of these retained earnings may be used directly to purchase new capital equipment, although some of it will be saved by depositing in a financial institution. For simplicity we will imagine that all such business saving flows through the financial system, hence the S_B arrow. In addition, households generally hold back some of their income from spending and deposit it into pension plans and savings accounts, etc. Thus we include the arrow from households. The easiest way to think of the diagram is to imagine that financial institutions take deposits from firms and households and then lend out the money to finance investment spending, I. With some exceptions, this is the way it will often work. One notable exception is that some of the money lent by banks is often used to finance consumption rather than investment. This occurs whenever households finance consumption spending using a credit card. However, we can avoid this complication by defining S_HH as being "net" saving, where the "net" means after subtracting household borrowing. With this definition in mind, it should be clear that S_HH can be negative - i.e., its flow reversed - if household borrowing exceeds household saving.

Looking at the diagram we can now identify several important relationships. The first one relates to an important decision made by households. They choose how much of their disposable income to spend on consumption and how much to save. You may recall from previous courses that the fraction of income spent on consumption goods (from an extra dollar of income) is called the marginal propensity to consume, while the fraction of income saved is called the marginal propensity to save.

A second relationship is shown to the left side of the firm box. This indicates that GNP is equal to the sum of C and I. This version of the national income identity would only be valid, though, if there were no government sector and no trade with the rest of the world.

A third important relationship is shown by noting the flow of money into and out of the financial sector. There we see two arrows flowing in, S_HH and S_B, and one flow outward, I. This leads to the following identity,

S_HH + S_B = I

indicating that the sum of household and business saving equals investment. A more common simplification of this relationship is shown by noting the following.

S_P = S_HH + S_B

where S_P is called private saving. Thus private saving equals the sum of household saving and business saving. This will simplify the above identity to,

S_P = I

or simply, private savings equals investment. Note that the term "private" is used here to distinguish it from government, or public sector, saving which we'll include next.

Circular Flow: Version 3

Next let's add in the government sector. The government is shown both to take money out of the circular flow and to inject money back in. Money is withdrawn first in the form of taxes, T. In the adjoining diagram taxes are represented as a flow of money directly from firms, as if it is entirely a tax on income. This is a simplification since in reality taxes are collected in many forms from many different agents. For example, governments collect profit taxes from firms and financial institutions, sales and property taxes from households, and tariffs on traded goods (not included yet). All these taxes are assumed to be lumped together in the T flow and withdrawn directly from national income.

Tax revenues can be spent in two separate ways. The TR flow represents transfer payments injected into the household income stream. Transfer payments include social security paid to retired workers, Medicaid and welfare payments, unemployment, etc. These are government expenditures which do not exchange for a particular good or service. The second type of expenditure is G. G represents spending by government for the purchase of goods and services produced by firms. It includes defense spending, education, police and fire protections, etc.

The final money flow, shown flowing out of the government, is labeled S_G, and refers to government saving. It should be obvious that the money collected by government in the form of taxes need not always equal government expenditures. In the event that tax revenues exceed expenditures, the government would have extra money left over. We imagine that this money would be saved in the financial sector since it is always better to collect interest when possible. Hence we draw the flow of excess funds, government saving S_G, flowing from government into the financial sector.

We can now represent the flow of funds into and out of the government sector with the following identity,

S_G = T - TR - G

When T exceeds the sum of TR and G, the government has extra saving that flows into the financial sector. These funds would then be available to lend out and finance additional investment.

Of course, what is more typical of many governments, is for the sum of TR and G to exceed tax revenue, T. In this case the flow of government saving, S_G, would be negative and would be represented in the diagram as a flow in the opposite direction. In this case the government would be borrowing money from the financial sector to finance its excess expenditures. We would also say that the government is running a budget deficit.

In short, negative government saving,

S_G < 0   implies a government budget deficit

which the government finances by borrowing from the financial sector.

Otherwise, positive government saving

S_G > 0   implies a government budget surplus

which results either in additions to saving or a repayment of previous debt.

Next, in this version of the circular flow, we can represent the national income identity as the flow of money into firms. In this case, GNP equals the sum of C, I and G. This version would only be accurate though when there is no trade with the rest of the world.

Lastly, with government included, we must rewrite the relationship representing the flows into and out of the financial sector. This now becomes,

S_HH + S_B + S_G = I

This identity says that the sum of household, business and government saving must equal private investment expenditures.

Circular Flow: Version 4

The final circular flow diagram extends the previous version to include trade flows with the rest of the world. The rest of the world (RoW) is shown at the very bottom of the adjoining diagram, below the dotted line which represents the border. Trade with the Row consists first of exports of goods, services, income and transfers, EX, represented by a flow into firms since money is being used by foreigners to purchase the exported products. Second, imports of goods, services, income and transfers, IM, are subtracted away from firms, resulting in an arrow from firms to the Row This adjustment accounts for the fact that measured expenditures made by households, the government, and firms in a open economy, will consist of purchases of both domestic and imported goods. Thus the C, I and G flows will include their purchases of imports, and these should not be included as part of GNP. In essence, the money used to buy imported products is redirected to the foreign firms, hence we have the outflow of money. (For a more complete explanation see, The Role of Imports in the National Income Identity)

This completes the national income identity with all major sectors included and now becomes,

GNP = C + I + G + EX - IM

which is represented by the flow of money into (and away from) firms on the left side of the diagram. However, as noted elsewhere, EX - IM, the balance on the current account, need not be equal to zero. If EX - IM > 0 then the country would have a current account (CA) surplus, whereas if EX - IM < 0 the country would have a CA deficit.

Consider when EX - IM < 0. In this case, more money flows out to purchase imports than flows back in to purchase exports. In essence there is a loss of money to the Row However, despite some exceptions, this money does not remain outside the country. Instead it is brought right back in and deposited into financial institutions (shown as the S_F flow on the diagram). In other words it is saved. This saving represents the country's financial account surplus which is equal and opposite to the CA deficit. [See Recording Transactions on the Balance of Payments for a more complete explanation]

The key point is that foreign saving offsets the CA deficit. This can be represented by the relationship showing the inflows and outflows from the Row, namely,

S_F = IM - EX

This says that foreign saving equals the CA deficit. From the perspective of the foreigners we would refer to S_F as money saved, or lent, to the domestic country. From the perspective of the domestic country, S_F would be considered money borrowed from the Row

Clearly, since a country may run a surplus on trade, that is EX - IM > 0, S_F could also be negative. In this case the Row would either be dissaving, meaning it is withdrawing previously accumulated saving from the domestic country, or, the Row would be borrowing money from the domestic country. This would occur if a domestic bank makes a loan to someone abroad. Alternatively, from the perspective of the domestic country we can say it is lending money to the Row when S_F < 0.

Finally, The Twin-Deficit Identity

The twin deficit identity is derived by accounting for the money flows into and out of the financial sector in version 4 of the circular flow. This results in the following identity,

(1)      S_HH + S_B + S_G + S_F = I

This says that the sum of household saving, business saving, government saving and foreign saving must equal private investment spending. An equivalent version can be written by recalling that household plus business saving equals private saving to get,

(1a)     S_P + S_G + S_F = I

The identity is best interpreted by noting that there are four key sources for funds in the financial sector that is not part of the consumption stream. The pool of funds to finance investment can be drawn from households, businesses, the government or from the Row Also, the sum of all funds not used for consumption, must be equal to the amount spent on investment goods.

It is important to note that this relationship is an accounting identity. This means that the relationship must be true as long as all variables are measured properly. This is NOT an economic theory, which is a proposition that may or may not be true. In practice, this identity rarely adds up, however, because the variables are not typically measured accurately.

To turn this identity into the "twin-deficit" identity we must merely take note of several previous definitions. Recall that,

S_G = T - TR - G

S_F = IM - EX

S_P = S_HH + S_B

Plugging these into (1) above yields,

S_P + T - TR - G + IM - EX = I

Reorder these to get the Twin-Deficit Identity,

(2)    (S_P - I) + (IM - EX) = (G + TR - T)

This is a popular way of writing the twin-deficit identity since it explicitly indicates two deficits. If the second expression (IM - EX) > 0, then the country has a current account deficit, i.e., a trade deficit. If the right-hand-side expression, (G + TR - T) > 0, then the country has a government budget deficit. The expression in total, then, demonstrates that these two deficits are related to each other according to this accounting identity. Indeed the difference between the government budget deficit and the trade deficit must equal the difference between private saving and investment as shown below,

(2a)    (S_P - I) = (G + TR - T) - (IM - EX)

International Finance Theory and Policy - Chapter 5-9: Last Updated on 6/3/04