An Analogy

To start to understand the cause of current account deficits, consider the following simple analogy.  If an airline has an aircraft with 100 seats and sells 150 seats for a flight, how many seats will they be short by? Obviously 50.  It is the same with the economy.   Current account deficits occur when there are more tickets (money) issued than there are goods. 

To solve the seats problem, should the airline buy a bigger plane?  If it buys a 150 seat aircraft and now sells 250 seats for a flight, has the problem been solved? 

Of course the solution for the airline is to sell only as many tickets for a flight as there are seats on the plane.  That may be simple logic for an airline but most economists would laugh at the idea that bank credit should be managed to prevent current account deficits. 

Even so, the amount by which some countries are deficient (in that they have bought more than they have produced) is equal to the excess amount of additional money they have created.  The following is a graph of the excess amount of additional money created in New Zealand and the current account deficit for New Zealand.  

This graph clearly shows that the amount by which New Zealanders have bought more than they have produced is equal to the excess amount of additional money created from domestic sources.  The Reserve Bank of New Zealand identifies the excess amount of additional money and calls it M3R money. It says that this money is domestically funded. In reality, it is unfunded or what I have called unendowed.  

The same relationship between the current account deficit and domestic sources of money can be found in other countries such as Australia, the USA and the Philippines.  The central banks of these counties have not specifically identified domestic sources of money but it can be calculated approximately. 

Money that we earn does not cause us to buy more than we have produced and lead to current account deficits.  The money we earn is like a receipt from the economy for supplying products and that money entitles us to buy products from the economy up to the value of what we have produced.  This system also ensures that those with money have something to buy.  To use our airline analogy, it ensures that those who have tickets have a seat. 

The economy can create additional money that does not cause excessive spending.  To start identifying a formula for the current account deficit, we will start with sources of money that do not cause current account deficits.  Also, we need to clarify what we mean by the quantity of money.  

The Quantity of Money

Economists tend to talk of the quantity of money in terms of the supply of and the demand for money.  However, the amount of money in the economy is relatively simple to explain.  Regardless of whether it is supplied or demanded, there is a certain quantity of money in the economy and that is the money that we will deal with.  We are not concerned about whether the money was supplied or demanded.  It is the money that exists that we will consider.

Money from foreign reserves

So to start building a formula for the current account deficit, let us assume that an economy has fixed exchange rates, has no inflation and its only source of money is from the growth of foreign reserves.  (This additional money is earned and can be called endowed money.)  Foreign reserves accrue when money earned from exports and other foreign sources is greater than money spent on imports and other payments overseas.  The equilibrium quantity of money (supply and demand for money) would be given by:

            L_f = X/m                                              (1)

 Where  L_f  is the quantity of money from foreign reserves or endowed money;

            "X"  represents exports and other foreign receipts in a period of time; and

            "m" is the marginal propensity to import (or send money out to the economy) in the same period of time relative to the amount of money held.

Figure 1 below helps explains what that formula means. Let us assume that exports are $10 B.  In the period of time taken for the economy to spend that amount of money, people and businesses spend one third of that money on imports, and the remainder on domestic products.  In the first period, when exports start, the total amount of money held is $10 B.  One third, $3.3 B, is spent on imports, leaving $6.7 B in the economy.  In the second period, when exports are again $10 B, the money supply rises to $16.7 B (that is, the new money from exports plus the remaining money from the last period).   

Figure 1: Foreign source of money

The quantity of money will continue to grow until it reaches $30 B.  At this point there are $10 B of imports and they are equal to exports.  As imports and exports are equal, there is no further increase to the quantity of money.  Therefore, the quantity of money is stable, or at equilibrium.

Money from bank credit

The other main source of money is bank credit.  This additional source of money is not initially earned and can be called unendowed money.  If we assume that for this example, there are were no international transactions, then the equilibrium quantity of money would be give by:

            L_c = dC_r/a                                            (2)

Where   L_c  is the quantity of money from bank credit or unendowed money;

            dC_r  represents the growth in bank credit in a period of time; and

            "a"  is the rate of loan repayment in the same period of time relative to the total amount of outstanding loans. (The inverse of "a" can be called the bank credit multiplier.)

The growth of the domestic source of money is shown in Figure 2.  In this example, loans are assumed to be $5 B per period and 25% of the outstanding balance at the end of the previous period is repaid in each period. From our formula we can work out that the equilibrium quantity of money from this source is $20 B (5/0.25). The money from bank credit continues to rise until repayments equal new loans.

Figure 2: Domestic source of money

If we assume an open economy with both money from bank credit and from foreign reserves, then in equilibrium, the total money supply would be given by:

            L = X/m                                               (3)

This is shown in Figure 3 where the two source of money from Figures 1 and 2 are combined. Initially the injections of export income and new credit are greater than the leakages on imports and loan repayments and the money supply grows quickly.  But then imports exceed exports and money leaks out.  Also, when the amount of loan repayments exceeds the amount of new loans, the injection of new money declines.  The money supply declines and reaches equilibrium at 30 (10/0.333) as given by equation (3).    

Figure 3: Interaction of Foreign and Domestic sources of money

To avoid mixing stocks and flows, we need to define the units of time in this analysis to be the time taken for all the money to be spent once. (The act of spending money includes the repayment of debt).  This assumption means that the quantity of money can be used as a proxy for national expenditure.  That is, it is an assumption that the velocity of circulation is equal to one.    

The formula for the equilibrium quantity of money is equivalent to the quantity of money from foreign reserves.  The reason for this is that in equilibrium, exports and imports must be equal.  That is from equation (3).

            mL = X                                                (4) 

By definition, mL is equal to spending on imports (assuming that this is the spending in the unit of time that it takes money to be spent once). 

The total quantity of money is equal to the sum of the two monetary sources.  That is:

            L =   L_f +  L_c                                        (5)

Therefore, the money from foreign reserves (endowed money) can be written as:

            L_f  =   L -  L_c                                        (6)

Note that the money from foreign reserves is also equal to the level of foreign reserves.

It is possible, by substituting equations (2) and (3) into equation (6) to derive the equilibrium or stable quantity of money from foreign reserves (which is equal to foreign reserves) as:

            L_f  =   X/m -  dC_r/a                                (7)

This formula assumes that the economy was already at equilibrium with monetary growth from foreign reserves before bank lending was introduced.  

This outcome is shown in Figure 4.  Note that the quantity of money starts at $30 B. The new credit initially increases the quantity of money and raises imports.  Then the leakage of money from imports reduces the quantity of money until it returns to equilibrium at $30 B. During this process, foreign reserves have fallen by the equilibrium level of money from bank credit (ie., $$20 B) and  reduce foreign reserves to $10 B.  Total bank credit is equal to the difference between the quantity of money line and the Foreign reserves/debt line.

Figure 4: Conditions for external balance with foreign reserves

Equation (7) explains the balance of payments in monetary terms. This equation reveals that if the equilibrium quantity of money created by bank credit is greater than the equilibrium quantity of money in the economy, then to a attain equilibrium, the country will have negative foreign reserves, or foreign debt. 

This is shown in Figure 5 where we assume that the rate of loan repayment is halved from 25 per cent to 12.5 per cent.  This raises the equilibrium level of bank credit from $20 B to $40B.  This is now $10 B greater than the equilibrium quantity of money.  The money from bank credit continues to be the difference between the Quantity of Money line and the Foreign Reserves/Debt line.

Figure 5: Conditions for external balance with foreign debt

Note that the rate of repayment of bank loans is particularly significant to the equilibrium level of money from bank credit.  The longer the term of the loans, the more likely it is that the equilibrium level of (unendowed) money from bank credit would be greater than the equilibrium level of (endowed) money from foreign reserves.

This formula suggests that bank credit should be used only for short term loans.  It should not be used for long term loans such as home mortgages.  Other forms of finance should be used for such loans (eg, savings bank loans, superannuation funds, etc).

It indicates that devaluing a currency will only help to reduce a balance of payments problem if it reduces the value of "m", the marginal propensity to import.

Also, it reveals the significance of financial deregulation for countries with fixed exchange rates.  That is, increased bank credit is likely to cause balance of payments problems. 

The current account balance with floating exchange rates

While this approach to explaining the balance of payments outcomes for a country with fixed exchange rates, it is not suitable for explaining the outcome for countries with floating exchange rates.

In countries with floating exchange rate systems, foreign reserves remain stable so that they do not affect the quantity of money.  

In such an environment, the growth in the quantity of money is determined by the growth of bank credit and the rate of repayment of banking loans. Yet it is apparent from the data that the growth of bank credit is linked to the current account deficit and so affects the level of foreign debt. 

This is evident in the relationship between bank credit and the accumulated current account deficit for Australia, New Zealand, the Philippines and the USA.  However, it is necessary to develop a new model to explain these outcomes. 

Floating exchange rate achieves external balance hypothesis

Some proponents of the floating exchange rate system believe that the exchange rate should adjust to bring about a balance between the foreign receipts and payments.  Let us assume that the exchange rate does adjust to balance imports and exports.  To start with we will assume that there are no capital inflows. We will assume the same situation as in Figure 5 above but with floating exchange rates.

In that case, exports would be given by:

            X = X/e                                                (8)

Where  "e"  is the exchange rate; and

           "X"  is the value of exports in term of foreign currency, which is assumed to be constant.  This means that if the exchange rate appreciates, the value of exports will fall in terms of domestic currency.  If the currency depreciates, the value of exports will rise in terms of domestic currency.

We will assume that imports are given by:

            M = emL                                              (9)

Without capital flows, under the floating exchange rate system, imports would equal exports.  That is:

            M = X                                                  (10)

Substitution equations (8) and (9) into equation (10) means that:

            emL = X/e                                            (11)

Which can be rewritten:

            e2 = X/mL

            e   = H(X/mL)                                       (12)

                                                                               (If you see an "H" in equation (12), the "H" represents a square root sign.)

In this example, as bank credit increases the quantity of money, imports increase.  However, the exchange rate depreciates to adjust exports up and imports down so that they are equal.  This outcome is shown in Figure 6

Figure 6: Credit growth with floating exchange rates

In this example, there is always external balance so there is no leakage of currency to imports.  The quantity of money grows by $40 B, following the introduction of bank credit of $5 B per period and repayments equal to 12.5% of loans outstanding.  The quantity of money has increased by the full amount of the growth in bank credit, rising from $30 B initially, to $70 B.  In the process, the exchange rate depreciates by about 35%.

Yet, while this is theoretically possible, there is no sustained period of time in the data for Australia, New Zealand, the USA and the Philippines where there is evidence of such an outcome.  Therefore, the exchange rate is not having this effect.  It is not bringing about external balance in these countries.  

The Capital Inflow Hypothesis

The other common explanation for the current account deficit is that it is caused by foreign capital inflows.      

Let us continue with the model used to derive Figure (6) but assume that foreign investors wish to invest $2 billion in foreign currency, in the economy. 

In that case, foreign currency receipts would be made up of exports and foreign capital given by:

           X = (X+K)/e                                          (13)

Where  "K"  is the value of foreign capital inflow in term of foreign currency, which is assumed to be constant. 

Substituting equations (9) and (13) into equation (10) defines the equilibrium situation of imports equalling exports and foreign capital with the exchange rate adjusting to bring about balance.    

            emL = (X+K)/e                                      (14)

Which can be rewritten:

            e² = (X+K)/mL

            e   = H((X+K)/mL)                                  (15)

                                                                               (If you see an "H" in equation (15), the "H" represents a square root sign.)

Using this equation, and the assumed capital inflow of $2 billion, the outcome was calculated and presented in Figure 7.

Figure 7: Capital inflow generating current account deficits and foreign debt

The current account deficit is evident as the amount by which imports exceed exports and it is accumulated each period as the "Accumulated current account deficit" line. This is also equal to the accumulated capital inflow which is an indicator of the level of foreign debt and equity accumulated.  It is evident that this graph does not reflect the relationship between the current account deficit and bank credit that is evident in the data for Australia, New Zealand, the USA and the Philippines.

In all four countries, the current account deficit is generally equal to the growth of bank credit.  Although the exchange rate has varied in each of these countries over the period shown, those variations have no effect on the basic relationship. (Note that there has been a recent case where foreign capital inflow may be driving the US current account deficit.  See bottom of the USA page for a possible explanation.)

The Supply Constraint Hypothesis

An alternative approach involves separating the intra-national and international transactions.  The quantity of money that people and businesses hold comes either from selling products in the domestic economy, selling exports, from bank credit or they had saved it.  That is:  

            L = N + X + dC_r + S                              (16)

Where   N  is income from the sale of products to the domestic market; and

            S  is the stock of money saved and not spent.

Note that saving here just means that the money was held.  If it were invested, it would be spent and would not be treated as savings.  A better term may be that the money was horded.          

The money that people and business have to spend is spent either on domestic products or imported products, or they can save (or hoard) it.  That is:

            L = N + M + S                                      (17)

The money that people and businesses have earned, borrowed or saved ("L" in equation (16)) is also the money that people and businesses spend or save ("L" in equation (17)). (The spending of one person is the income of another.)

Therefore, we can say substitute equations (16) into (17) and write that for the domestic economy to be balanced:

            N + M + S = N + X + dC_r + S                   (18)

This can be reduced to writing that the domestic market is balanced when imports are equal to exports plus the growth of bank credit:

            M = X + dC_r                                          (19)

Which may be written as the current account deficit is equal to the growth of bank credit:                               

            M - X  = dC_r                                          (20)

Under the floating exchange rate system, the international currency market is cleared when:

            M  = X + K                                            (21)

Which may be written:                                    

            M - X = K                                              (22)

Substituting equation (20) into (22), therefore, describes the conditions for both the domestic and the for both the domestic market and the foreign exchange market to be cleared. That is when the foreign capital inflow is equal to the growth of bank credit:

            K = dC_r                                                 (23)

This is the basic relationship we find for Australia, New Zealand, the USA and the Philippines.

If we apply the floating exchange rate system to the relationship considered in Figure 5, we need to start with equation (21) for the external balance and substitute in equation (23) so that we have:

            M  = X + dC_r                                         (24)

This is the same as equation (19).  However, we are now saying that this is the equation for internal and external balance: that is, when the domestic market is cleared and the foreign exchange market is cleared.  Substituting equations (8) and (9) into equation (24) gives:

            emL =  X/e + dC_r                                  (25)

Equation (25) can be rewritten as:

            mLe² - dC_re - X =  0                             (26)

Equation (26) is in the quadratic form  ax² + bx + c =0  which can be solved with the standard formula for solving a quadratic.  Therefore, the exchange rate that solves equation (26) is:

    e = (dC_r +/-  H(dC_r² + 4mLX) )/(2mL)               (27)

                                                                               (If you see an "H" in equation (27), the "H" represents a square root sign.)

Figure 8 plots these relationship, showing the accumulated current account deficit equal to the money supply.  This is relationship perceived in  Australia, New Zealand, the USA and the Philippines.  

Figure 8: Money supply and current account deficit with floating exchange rate system     

The relationship present in Figure 8 is a product of the floating exchange rate system.  Equation (27) provides an indication of the way the exchange rate must function to achieve internal and external stability under the floating exchange rate system. 

The difference between imports and exports must also be met by foreign capital inflow.  However, foreign capital does not normally drive the outcome. It is the bank credit that drives the flows in the studied countries. 

The optimum exchange rate system and the guided exchange rate system are exchange rate systems that take into account the significance of monetary growth for the external balance.  Both system manage the growth of bank credit so that the money from bank credit does not cause balance of payments difficulties.

The Supply Constraint Hypothesis with Net Capital Outflow

While the supply constraint hypothesis may apply to countries such as the USA and Australia with net capital inflow, the question arises as to whether it explains the outcomes of countries such as Japan that have a current account surplus. 

To assess this question, we will assume again as in equation (16) above that the money people and businesses have can come either from selling products in the domestic economy, selling exports, from bank credit or they can save it.  That is:  

            L = N + X + dC_r + S                              (16)      

The quantity of money that people and business have to spend is spent either on domestic products, imported products, saved or they can invest it overseas.  That is, we add investment overseas to equation (17) such that:

            L = N + M + S + I_O                              (28)

Where   I_O is the amount of money people choose to invest overseas.

The quantity of money that people and business have earned, borrowed or saved ("L" in equation (16)) is also the quantity of money the same people and business spend, saver or invest overseas ("L" in equation (28)).

Therefore, we can say substitute equations (16) into (28) and write that for the domestic economy to be balanced:

            N + M + S + I_O =  N + X + dC_r + S          (29)

This can be reduced to writing that the domestic market is balanced when:

            M + I_O = X + dC_r                                   (30)

Which may be written:                               

            M - X = dC_r - I_O                                     (31)

We will restate equation (22) which defines the situation under the floating exchange rate system, when the international currency market is cleared:                           

            M - X = K                                              (22)

Note that "K" represents net capital inflow.  Substituting equation (31) into (22), therefore, describes the conditions for both the domestic and the for both the domestic market and the foreign exchange market to be cleared. That is:

            K = dC_r - I_O                                           (32)

To attain the domestic and international balance under the floating exchange rate system, we substitute equation (32) into equation (21) for the external balance so that we have:

            M  = X + dC_r  - I_O                                  (33)

This is similar to equation (31).  Substituting equations (8) and (9) into equation (33) gives:

            emL =  X/e + dC_r - I_O                            (34)

Equation (25) can be rewritten as:

            mLe² - (dC_r-I_O)e - X =  0                        (35)

This equation is in the quadratic form  ax² + bx + c =0  which can be solved with the standard formula for solving a quadratic.  Therefore, the exchange rate that solves equation (26) is:

    e = ((dC_r-I_O) +/-  H((dC_r-I_O)² + 4mLX) )/(2mL)   (36)

                                                                                          (If you see an "H" in equation (36), the "H" represents a square root sign.)

Figure 9 plots the outcome. This model is similar to those above except that it assumes investment overseas of $2 B in each period. (Note, rather than plotting the current account deficit, Figure 9 plots the current account balance, so that a current account deficit would be represented as a negative flow rather than as a positive flow as represented in earlier diagrams.)  

Figure 9: Investment overseas and current account balance with floating exchange rate system

Initially, the growth in net bank credit is greater than the investment overseas.  This causes current account deficits.  But as loan repayments increase and the investment overseas exceeds the growth of bank credit, the current account balance is reversed and the economy experiences current account surpluses.

This is the experience of countries such as Japan whose net overseas investment is greater than the their net growth in bank credit.  The Japanese economy was impeded when the growth of bank credit was severely constrained following the business and bank failures in the early 1990's. 

Thus, it is possible to find a unifying theory and a formula explaining the current account balance  for countries with both fixed and floating exchange rates.

  

See also Money and Inflation, Money and Unsustainable Debt

Impact of the floating exchange rate system on employment and growth

Impact of the floating exchange rate system on debt

and Free Trade.