Heng-fu Zou

English

Research Papers in Economics

 
 
 
 
 
Foreign Asset Accumulation and Macroeconomic Policies 
 
in a Model of Mercantilism 
 
 
 
Heng-fu Zou 
(Revised at 2011) 
 
 
 
 
 
 
   2 
I. Introduction 
 
This paper examines the effects of macroeconomic policies on foreign asset accumulation in a 
small open economy. It obtains policy implications that are very different from many existing studies 
such as Turnovsky (1985, 1987) and, in particular, Obstfeld (1981). 
In an often-cited paper, Obstfeld (1981) presents three interesting results regarding the effects of 
government policies on foreign asset holdings: (1) foreign exchange intervention is found to have no 
real effects when official foreign reserves earn interest that is distributed to the public; (2) inflation 
leads to higher long-run consumption and foreign claims; (3) an increase in government consumption 
induces a surplus on current account in the short run and larger foreign asset accumulation in the long 
run. The intertemporal optimization framework used by Obstfeld in this study and some related studies 
Obstfeld, 1982, 1990) has also influenced the open economy macroeconomics in the past decade. 
In this paper, we are going to show that the policy implications of Obstfeld's model hinge on the 
special assumption of Uzawa's (1968) time preference and they are totally reversed and substantially 
changed in a dynamic optimization model with the wealth effect. The wealth effect approach developed 
in our paper is adapted from the models of Bardhan (1967), Kurz (1968), Calvo (1980) and Blanchard 
(1983) and defines the representative agent's utility function on foreign asset in addition to consumption 
and real balances. The main results derived from our model stand in striking contrast to the ones in 
Obstfeld paper: (1) foreign exchange intervention leads to more foreign asset holdings and more 
consumption in the long run; (2) if the utility function is separable in consumption and real balances as 
in Obstfeld (1981), inflation has no effect on the real variables in both short run and long run; if the 
utility function is nonseparable, inflation results in more foreign asset accumulation when the cross 
derivative of consumption and real balances is positive; (3) government spending always reduces 
foreign asset accumulation and crowds out private consumption.   3 
Our paper is organized as follows. Section II sets up a simple wealth effect model with money 
and discusses the stability and some policy implications of the model. Section III makes detailed 
comparative study on the effects of macroeconomic policies. We conclude our paper in Section IV. 
 
II. A Simple Model 
We consider a small economy in a competitive world market. The economy is populated with 
many identical people. We follow Bardhan (1967), Kurz (1968), Calvo (1980) and Blanchard (1983) 
and define a representative agent's instantaneous utility as 
) ( ) ( ) ( ) , , ( b w m v c u b m c U α + + =  
where c is consumption, m is real balance holdings, b is the foreign asset holdings, and α (α>0) 
measures the wealth effect. A negative b is foreign debt, and αw(b) is the disutility of debt as in 
Bardhan (1967) and Blanchard (1983). For a positive b, αw(b) reflects the wealth effects introduced by 
Kurz (1968). It is assumed that u'(c) > 0, w'(b) > 0, v'(m) > 0, u"(c) < 0, w"(b) < 0, v"(m) < 0. 
The representative agent maximizes a discounted utility over an infinite horizon: 
    ∫
∞ − + +
0 )] ( ) ( ) ( [ dt e b w m v c u
t ρ α             (1) 
where ρ 1is the time discount rate and 0<ρ< 1. 
The budget constraint is  
  m c x rb y a π − − + + =
.
               (2) 
  a=b+m                    (3)   
and the initial asset is given by b(0). Where where a dot over a variable is the time derivative, y is 
output, g is government spending, x is the government transfer, a is total wealth of the representative 
agent, π is the expected inflation rate and r is the returns on foreign bonds, which is given in the world   4 
capital market. Except for the preference and time discount rate, the set up of our model is identical to 
the one in Obstfeld (1982). 
The home price of the goods is p, and the corresponding world price is p
* . Assuming purchasing 
power parity, we have 
p = Ep
*                     (4) 
where E is the exchange rate. With proper normalization, p
* can be set to one. The Hamiltonian 
function is 
    ) ( ) ( ) ( ) ( ) ( 2 1 m b a m c x rb y b w m v c u H − − + − − + + + + + = λ π λ α  
The necessary conditions for optimization are 
    ) ( ' ) ( ' ) ( ' ) ( ' c ru b w c u m v + = − α π             (5) 
    c c u c u r b w ) ( " ) ( ' ) ( ) ( ' − = − + ρ α             (6) 
plus the budget constraints and transversality condition. 
The only new thing about these conditions is equation (5), which says that the marginal benefit of 
holding money   )) ( ' ) ( ' ( c u m v π −  is equal to the marginal benefit of holding foreign asset 
)) ( ' ) ( ' ( c ru b w + α at optimum. 
To fully spell out the dynamics, we need to specify the government sector. Government revenue 
comes from money creation and interest earnings from the central bank's reserves, i.e.,  rR p M + ) / (
.
, 
and R denotes the amount of reserves. Government also consumes goods, g, makes transfer, x, to the 
representative agent. So its budget is given by 
    rR p M x g + = + /
.
 
or    rR m M M x g + = + ) / (
.
                 (7) 
Let the money growth rate be a positive constant:   5 
    θ = M M/
.
                    (8) 
Then we can write (7) as 
    g rR m x − + =θ                   (9) 
By definition, 
    m p p M M m ] / ) / [(
. . .
− =                (10) 
On the perfect foresight path, the expected inflation rate is equal to the actual inflation rate: 
    π = = = e E E p p / /
. .
                (11) 
where e is expected rate of exchange rate depreciation. Therefore 
    m m ) (
.
π θ − =                   (12) 
Substitute (12) into (5), and substitute (9) and (12) into (3), 
    )) ( " / 1 )]( ( ' ) ( ) ( ' [
.
c u c u r b w c − − + = ρ α           (13) 
    )) ( ' / )]( ( ' ) ( ' ) ( ) ( ' [
.
c u m m v c u r b w m − + + = θ α         (14) 
    g c rR rb y b − − + + =
.
               (15) 
To understand the stability of the system, we linearize (13), (14) and (15) around the steady state 
values c, m and b : 










−
− +
− −
=












r
c u b w m c u m v m c u c u m r
c u b w r p
b
m
c
0 1
) ( ' / ) ( " ) ( ' / ) ( " ) ( ' / ) ( " ) (
) ( " / ) ( 0
.
.
.
α θ
α










−
−
−
b b
m m
c c
  (16) 
The determinant of the 3x3 matrix is given by  
∆
) ( " ) ( '
) ( "
c u c u
m m v
   6 
which is negative if  ∆ is negative. In this case, the dynamic system has one negative and two positive 
characteristic roots because the product of the three roots is negative and the sum of the three roots is 
also positive and is given by the trace of the 3x3 matrix,  )) ( ' / ) ( " ( c u m m v p − . Therefore, the dynamic 
system has a unique perfect foresight path near the steady state. 
 
III. Policy Analysis 
In this section, we extend the basic model into a monetary economy and study the effects of 
inflation, government spending and foreign exchange intervention. 
We note that equations (13) and (15) are independent of real balances and inflation rate in both 
short run and long run: 
Proposition Four: With consumption and real balances separable in the preference, an increase 
in inflation (or exchange rate depreciation) has no effects on both the short-run and the long-run 
consumption and foreign asset holdings. 
Compared to Obstfeld (1981), this result is very strong. Following Uzawa's definition of time 
preference, Obstfeld has shown that inflation increases foreign asset accumulation in the long run and 
causes current account surplus in the short run when the utility is separable in consumption and real 
balances. If the severability assumption is retained in our wealth effect model, money is supernuetral in 
both the short run and the long run. 
In steady state, equation (37) is 
    ) ( ' ) ( ' ) ( ' ) ( ' c u m v c ru b w θ α − = + . 
As c and b  are not affected by inflation rate θ, a higher θ means a lower m in the new equilibrium: 
0 ) ( " / ) ( ' / < = m v c u d dm θ .    7 
In the wealth effect model, inflation will have real effects on consumption and foreign asset 
accumulation if the preference is not separable in c and m. We will focus on this case in the rest of this 
section. With non-separable preference in c and m, the representative agent maximizes 
    ∫
∞ − +
o
tdt e b w m c u
ρ α )] ( ) , ( [               (40) 
subject to the dynamic budget constraints (25) and (26). 
It is further assumed that assume  0 ) , ( > m c ucm , and u(c, m) is concave in c and m: 
    0 ) (
2 > − cm mm cc u u u                 (41) 
The necessary conditions for maximization are 
    ) , ( ) ( ' ) , ( ) , ( m c ru b w m c u m c u c c m + = − α π          (42) 
   
. .
) , ( ) , ( ) )( , ( ) ( ' m m c u c m c u r m c u b w cm cc c − − = − + ρ α       (43) 
plus the budget constraints and transversality condition. 
Again substitute (34) into (42), and substitute (31) and (34) into (25), and assume steady state: 
    0 ) , ( ) ( ' ) )( , ( = − + + m c u b w r m c u m c α θ           (44) 
    0 ) )( , ( ) ( ' = − + ρ r m c u b aw c               (45) 
    0 = − − + + g c rR b r y                (46) 
To find the effects of various macroeconomic policies on foreign asset accumulation, we totally 
differentiate (44), (45) and (46): 










−
− −
− + − +
o r
u r b w u r
u u r b w u u r
cm cc
mm cm cm cc
1
) ( ) ( " ) (
) ( ) ( " ) (
ρ α ρ
θ α θ










dm
db
dc
=










+
−
− −
rdR dg
d b w
d b w d uc
α
α θ
) ( '
) ( '
  (47) 
Denote the determinant of the 3x3 matrix as ∆”: 
+ − + + − + − = ∆ ] ) )][( ( " ) [( ) ( " ) ( " mm cm cm u u r b w r r u b w r θ α ρ α ρ    8 
0 ] ) [( ) ( < − + − cm cc cm u u r ru r θ ρ       (48) 
∆” is negative because  ) ( r − ρ is positive,  , 0 , 0 , 0 < < > mm cc cm u u u  and  . 0 ) ( " < b w  
With preference nonseparable in consumption and real balances, we have 
Proposition Five: If   , 0 > cm u  inflation increases foreign asset accumulation and consumption. 
From (47), 
    0 " / ) ( / > ∆ − = cm cu u r d db ρ θ             (49) 
and 
    0 ) / ( " / ) ( / > = ∆ − = θ ρ θ d db r u u r r d db cm c         (50)   
To provide some economic intuition to this result, we can rely on equation  
(45): 
    0 ) )( , ( ) ( ' = − + ρ α r m c u b w c               (45) 
Since the real balances and consumption is nonseparable in the utility function, an increase in the cost 
of real balances as a result of higher inflation rate leads people to lower money holdings and, in (45), 
the marginal utility of consumption will be smaller as ucm  is positive. In this case, the marginal utility of 
foreign asset is too high compared to marginal utility of consumption and people will invest more in 
foreign asset and consume less in the short run. That will lead to a short-run surplus in the current 
account. In the long run, there will be more foreign asset, more interest income and hence more 
consumption. As for the real balances, higher cost of inflation tends to reduce them and higher income 
tends to raise them; and the sign is ambiguous. 
As we mentioned earlier, Obstfeld (1981) has shown a surprising result that an increase in 
government spending leads to higher asset accumulation in the new equilibrium. In our wealth effect 
model, we have   9 
Proposition Six: Government spending always reduces long-run foreign asset accumulation and 
consumption. 
By Cramer's rule, (47) gives us 
    0 " / )] )( [( /
2 < ∆ − − = cm mm cc u u u r dg db ρ           (51) 
The whole expression is negative because  ) , ( , 0 ) ( m c u r > − ρ  is concave  
(see (41)), and  0 "< ∆ . 
The economic reason for this result is the same as in Proposition One of the last section. Again 
the short run implications of government spending are current account deficit and lower private saving. 
As for the long-run consumption, from (46), 
dc/dg = r(db/dg) < 0, 
That is to say, government spending reduces foreign asset accumulation, which in turn reduces interest 
income and consumption. 
Another interesting comparison between Obstfeld's model and ours is the result of the central 
bank's foreign exchange intervention. In Obstfeld's model, if the central bank intervenes in the foreign 
exchange market by purchasing foreign bonds from the public with domestic currency, the total real 
asset in the economy is not affected, and, as the central bank's reserves also earn interest income which 
is distributed to the public in lump-sum form, the representative agent's real income and wealth remain 
the same. Therefore the central bank's intervention does not have real effects on foreign asset holdings3, 
1consumption and real balances. It only occasions a rise in the price level exactly proportional to the 
increase in money supply. In our wealth-effects model, the budget constraint does not change as the 
interest income earned by the central bank's reserves is still redistributed to the public, but, as foreign 
bonds are directly valued in the utility function, the symmetry of foreign bonds and the central bank's 
reserves in Obstfeld's model disappears. Shortly after the intervention of the central bank, the reduction 
of foreign bonds held by the private sector results in higher marginal utility of foreign asset, and the   10 
equilibrium conditions (44) and (45) no longer hold. In fact, when the initial equilibrium foreign asset is 
reduced by dR and real balances increased by dR, equilibrium condition (44) becomes 
. 0 ) , ( ) ( ' ) )( , ( > + − − + + + dR m c u dR b w r dR m c u m c α θ  
To restore equilibrium, the representative agent will in the short run cut consumption, reduce real 
balances and buy more foreign bonds. In the new equilibrium, as total asset (the sum of private asset 
and the central bank's asset) have gone up, private consumption and real balances also go up.  
Therefore we have 
Proposition Seven: The central bank's purchase of foreign claims from the public with domestic 
currency will lead to more foreign asset accumulation (the sum of central bank's reserve and 
private holdings), more consumption and more real balances. 
We also mention in passing that the wealth effects exert positive effect on foreign asset 
accumulation in this monetary model as in Proposition Three of the last section. From (47), 
    0 " / ]} ) [( ) ( ' ) {( / > ∆ − + − − = mm cm cm u u r u b w r d db θ ρ α     11 
IV. Conclusion 
In this paper, we have studies the effects of macroeconomic policies on foreign asset 
accumulation in a wealth effect model used by Bardhan (1967), Kurz (1968), Calvo (1980) and 
Blanchard (1983). Our results differ dramatically from the ones in Obstfeld (1981). In particular, we 
have shown that government spending always reduces foreign asset accumulation (or increases foreign 
borrowing). While Obstfeld's model turned the conventional Mundell-Fleming model on its head, our 
wealth effect approach has restored its validity. 
Evaluating the consequences of macroeconomic policies is complicated; and the results are often 
very sensitive to the optimization framework we have utilized. Our wealth effect model only provides a 
different perspective to the problems and it should be taken as complementary to many existing models. 
 
 
 
 
 
 
 
 
 
 
 
 
 
   12 
 
References 
(1), Aiyagari, R., and McGrattan, E., The Optimum Quantity of Debt: Technical Appendix, Annals 
of Economics and Finance 4, 193-217, 2003. 
(2), Bardhan, P., "Optimal Foreign Borrowing," in Essays on the Theory of Optimal Economic Growth, 
edited by Karl Shell, MIT Press, 1967. 
(3), Barro, Robert, Optimal Management of Indexed and Nominal Debt, Annals of Economics and 
Finance 4, 1-15, 2003. 
(4), Blanchard, Olivier, "Debt and Current Account Deficit in Brazil," in Financial Policies and the 
World Capital Market, edited by Aspe Armella, Dornbusch and Obstfeld, University of Chicago 
Press, 1983. 
(5), Bruechner, J.K., Fiscal Decentralization in Developing Countries: The Effects of Local 
Corruption and Tax Ecasion, Annals of Economics and Finance 1, 2002, 1-18. 
 
(6), Buiter, Willem, "Time Preference and International Lending and Borrowing in an Overlapping-
Generations Model," Journal of Political Economy 89, No.4, 1981, pp.769-797. 
(7), Calvo, Guillermo, "Financial Opening, Crawling Peg and the Real Exchange Rate," mimeo, 1980. 
(8), Cheng, Wenli, and Dingsheng Zhang, The effects of foreign aid on the creation and distribution 
of wealth, Annals of Economics and Finance 9-2, 2008, 223-237. 
(9), Doi, T., Ihori, T., and Kondo, H., Government Deficits, Political Inefficiency, and Fiscal 
Reconstruction in Japan, Annals of Economics and Finance 3, 2002, 169-183. 
(10), Gong, Liutang and Heng-fu Zou, “Foreign aid reduces domestic capital accumulation and 
increases foreign borrowing: a theoretical analysis”, Annals of Economics and Finance 1, 
2000, pp. 147-163. 
(11), Huang Haizhou, and Padilla A.J.,  2002, Fiscal Policy and the Implementation of the Walsh 
Contract for Central Bankers, Annals of Economics and Finance 3, 27-42.   13 
(12), Kurz, Mordecai, "Optimal Economic Growth and Wealth Effects," International Economic 
Review 9, October 1968, pp.348-357. 
(13), Li Hongyi, and Heng-fu Zou, Inflation, Growth, and Income Distribution: A Cross-Country 
Study, Annals of Economcs and Finance 3, 2002, 85-101. 
(14), Obstfeld, Maurice, ”Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset 
Accumulation," Journal of Political Economy 89, December 1981, pp.1142-1161. 
(15), ______, "Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?" 
Quarterly Journal of Economics 97, 1982, 251-270. 
(16), ______, "Intertemporal Dependence, Impatience, and Dynamics." Journal of Monetary 
Economics 26, 1990, 45-75. 
(17), Shi Shouyong,. Liquidity, Bargaining, and Multiple Equilibria in a Search Monetary Model, 
Annals of Economics and Finance 2, 2001, 325-351. 
(18), Turnovsky, Stephen, "Domestic and Foreign Disturbances in an Optimizing Model of Exchange-
Rate Determination, "Journal of International Money and Finance 1985, pp.151-171. 
(19), ____ ,"Optimal Monetary Growth with Accommodation Fiscal Policies in a Small Open 
Economy," Journal of International Money and Finance, 1987, pp.179-193 
(20), Uzawa, Hirofumi, "Time Preference, the Consumption Function, and Optimal Asset Holdings." In 
Value, Capital, and Growth, edited by J. N. Wolfe, Chicago: Aldine, 1968. 
(21), Zou Heng-fu, “Dynamic Analysis in the Viner Model of Mercantilism”, Journal of 
International Money and Finance, 1997, pp. 637-651.  

Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?&quot;

Bargaining, and Multiple Equilibria in a Search Monetary Model,

Debt and Current Account Deficit in Brazil,&quot; in Financial Policies and the World Capital Market, edited by Aspe Armella, Dornbusch and Obstfeld,

Domestic and Foreign Disturbances in an Optimizing Model of ExchangeRate Determination, &quot;Journal of International Money and Finance

Financial Opening, Crawling Peg and the Real Exchange Rate,&quot; mimeo,

Fiscal Decentralization in Developing Countries: The Effects of Local Corruption and Tax Ecasion,

Fiscal Policy and the Implementation of the Walsh Contract for Central Bankers,

Government Deficits, Political Inefficiency, and Fiscal Reconstruction

Heng-fu, “Dynamic Analysis in the Viner Model of Mercantilism”,

Inflation, Growth, and Income Distribution: A Cross-Country Study,

Intertemporal Dependence, Impatience, and Dynamics.&quot;

Liutang and Heng-fu Zou, “Foreign aid reduces domestic capital accumulation and increases foreign borrowing: a theoretical analysis”,

Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation,&quot;

Optimal Economic Growth and Wealth Effects,&quot;

Optimal Foreign Borrowing,&quot; in Essays on the Theory of Optimal Economic Growth, edited by Karl Shell,

Optimal Management of Indexed and Nominal Debt,

Optimal Monetary Growth with Accommodation Fiscal Policies in a Small Open Economy,&quot;

The effects of foreign aid on the creation and distribution of wealth,

The Optimum Quantity of Debt:

Time Preference and International Lending and Borrowing in an OverlappingGenerations Model,&quot;

Time Preference, the Consumption Function, and Optimal Asset Holdings.&quot;

Foreign Asset Accumulation and Macroeconomic Policies in a Model of Mercantilism

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Foreign Asset Accumulation and Macroeconomic Policies in a Model of Mercantilism

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