Download Note on Balance of Payments and Sovereign Debt

Riccardo Fiorito
Twin Deficits and Savings by Sector (PEC11_14)1
December 2011
1. Object
To show how foreign trade and government deficits are related, I will recall here a few basic
definitions helping to interpret the data.2
2. Reminders
2.1. Balance of Payments
Current Account (CA Over the line):
CA = Trade Balance (X- M) + Net Investment Income + Net Transfers,
where, in the national income and product (NIPA) accounts, X and M denote exports and imports
of goods and services, respectively [PEC11_1].
.
The current account reports all sources of incomes due to transactions, net income from capital
and net transfers which in practice amounts to income stemming from net aid. Since, in most cases,
the trade balance - i.e. the net export component (XN = X – M) - is the vast majority of the
aggregate, current account and net exports can be roughly equated in this simplified analysis.
Capital Account (KA Under the line):
KA = Foreign Holdings of Domestic Assets – Domestic Holdings of Foreign Assets.
[Capital Inflows]
[Capital Outflows]
Conversely, the capital accounts (KA) deals with assets, not with incomes (CA).
2.2. Savings
There is an important distinction between the closed and the open economy case: in the closed
economy case, savings and investment are equal while in the open economy they are not.
Closed Economy
In a closed economy there is no international trade and the GDP, denoted by Y, amounts to the
domestic demand only:
(1) Y = C + G + I,
where total consumption is the sum of private (C) and government consumption (G) and where total
investment (I)3 is the sum of private (Ip) and government investment (Ig):
1
This version slightly modifies a previous one (November, 2011), also available in the teaching section of my
homepage (www.econ-pol.unisi.it/fiorito).
2
For an introductory treatment, see: Blanchard’s Macroeconomics (Prentice Hall, several editions including an Italian
translation: Macroeconomia, Il Mulino). Another introductory textbook is: Obstfeld and Krugman (International
Economics, HarperCollins College Publishers, 1994) which is also available in Italian (Economia Internazionale,
Hoepli, 1994). For an advanced treatment, see: Obsfeld and Rogoff (Foundations of International Macroeconomics,
The MIT Press, 1999).
3
Inventory changes (inventory investment) are ignored to be simple.
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(2) I = Ip + Ig.
Similarly, total savings (S) are the sum of private (Sp) and government savings (Sg):
(3) S = Sp + Sg,
where government savings are the difference between current revenues (T) and current spending
which here includes government consumption to be simple4.
(4) Sg = T – G.
Once government is introduced, households spend (save) in the light of their disposable income
(YD) which is:
(5) YD = C + Sp,
i.e. the income available after net taxes are paid:
(6) YD = Y – T = (C + G + I) – T = C + I.
Assuming for simplicity that government consumption is the only public spending, there is no
government investment: hence, Ig = 0 and I = Ip in Eq. (2).
Assuming also that government consumption is fully financed by lump-sum5 taxation (T), the
household disposable income can be written as:
(7) YD = C + Ip,
given the equilibrium condition G = T. Thus, Sg = 0 and S = Sp in eq. (3). Therefore, equating (4)
and (7), Sp = Ip which also implies:
(8) S = I.
4
As far as revenues are concerned, in practice they are all current everywhere while, on the spending side, current
spending excludes capital spending which is made by government investment and other components that here can be
ignored. Notice that transfers too are ignored and also that government consumption is not a transfer (e.g. pensions,
welfare benefits etc., rather being the public provision of such services as health, education, justice or alike.
5
This is also made for the sake of simplicity, it being well known that most revenues are distortionary rather than
lump-sum. For excellent textbook treatments. see: J. Stiglitz (Economics of the Public Sector, Norton, 1988) or H.S.
Rosen (Public Finance, McGraw Hill, 2005).
2
Open Economy
The corresponding GDP definition now is the standard one:
(9) Y = C + I + G + (X - M),
where, assuming again that XN = X – M = CA, the current account measures the imbalances
between GDP and domestic demand:
(10) Y – (C + I + G) = CA.
Combining the disposable income definition (6) with the GDP definition (9), we obtain:
(11) C + S = (C + I + G + CA) - T,
which, in the balanced budget (G = T) case, implies:
(12) S = I + CA,
where savings are now affected by the current account balance (CA). From (12) it appears that for
S > I, CA > 0 as in Germany and in China, while for S < I, CA < 0 as in the US (see Table 1).
Twin deficits
Abandoning the government equilibrium assumption that spending and revenues are equal, more
realism is achieved. This also implies that public savings (Sg) can be positive (surplus) or negative
when a government deficit occurs. In turn, this implies a relation between government and
international balance which is often dubbed as the twin deficit case, i.e. the situation in which
excess government spending implies a negative current account balance.
Since public savings are the difference between revenues (T) and current spending (GCURR)
(13) Sg = T – GCURR,
which in our previous example was made by government consumption only (G) but that in a more
realistic case includes transfers and interest paid on government debt (B) where r is the average,
nominal, cost of the debt6:
(14) GCURR = G + Z + rB.
6
Actually, the relevant interest variable (r) is a weighted average of the debt maturity components. To be simple, in
Eq. (16) past debt refers to previous period only.
3
When Sg < 0, Eq. (13) is dubbed as (government) current deficit. Conversely, total spending
(GTOT) includes a usually small capital expenditure share which here includes fixed investment
(Ig) only:
(15) GTOT = Ig + GCURR.
Given that now deficits can occur and being accumulated, general government debt (B) is
introduced:
(16) B(t) = [(1+r(t)] B(t-1) + DPRIM(t),
where the primary deficit (DPRIM) is total deficit less the interest payment component:
(17) DPRIM(t) = [GTOT(t) – r(t)B(t-1)] - T(t),
and where primary spending is the expression in brackets.
Combining equations (2), (3), (4) the current account balance can be expressed as the difference
between savings and investment as in eq. (12), though now private and public components can be
separated:
(18) CA = Sp – I – (GCURR – T) = Sp + Sg – (Ip + Ig).
which is based on equation (4). However, what eq. (18) adds - and makes explicit - is that current
account is reduced by total government deficit (D) which includes government investment:
(19) D = (GCURR + Ig) - T,
where a deficit obviously requires that total spending (GCURR + Ig) > T.
Inserting (19) into (18) it appears that:
(20)
CA = Sp – Ip – D,
i.e. that CA is increased by domestic savings and reduced by government deficit. Some data on this
are shown below and include also the most recent data on 10-years government bond interest rates.
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Table 1 - Twin deficits (2010-11) and government cost of debt (2011) in several countries
Country
CA
November
2010, Latest
12 Months
-430.9
Current
Account
% of
GDP
2010
-3.3
Budget
Balance
% of
GDP
2010
-9.0
CA
November
2011,
Latest 12
Months
-469.9
Current
Account
% of
GDP
2011
-3.2
Budget
Balance
% of
GDP
2011
-9.0
Interest
rates (%)
on 10-year
government
bonds
2.04
United
States
Japan
188.1
3,3
-7.6
2.3
-8.3
1.07
China
289.1
4.9
-2.2
150.0
(Sept.)
259.3*
3.9
-1.8
3.64
France
-51.3
-2.0
-7.8
-2.5
-5.8
3.39
Germany
182.7
5.2
-3.7
5.0
-1.0
2.23
Greece
-35.6
-5.8
-7.9
-9.6
-9.1
30.0
Italy
-73.5
-3.1
-5.7
-3.7
-4.0
7.30
Spain
-73.8
-4.4
-9.6
-3.8
-6.5
6.20
Russia
77.0
4.3
-4.8
5.0
-0.8
4.73
Turkey
-33.6
-5.4
-4.2
-10.0
-1.7
9.76
Brazil
-47.3
-2.7
-2.3
-64.5
(Sept.)
193.7
(Sept.)
-29.9
(Sept)
-79.0
(Sept)
-56.8
(Oct)
86.3
(Q3)
-77.5
(Sept.)
-47.3
(Oct.)
-2.2
-2.7
11.1
Source: The Economist, November 2010 and December (3-9) 2011. CA = Current Account balance (latest
12 months ,$bn); * = estimate: Q3 = third quarted..
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