Using Reserves to Finance the Increase in GovernmentInfrastructure Investment in China

Yin Hu∗

April 2, 2010

Abstract

In this paper I analyze the impact of increasing government infrastructure investmentby using existing large foreign exchange reserves in a fully optimizing model matchingthe Chinese economy. Even though the private investment falls in the nontradable sector,real expenditure and money balance decrease in the short run, the infrastructure investmentgreately enhances the efficiency and productivity of the private sector, and gives rise to anentire sequence of productivity increases. In the long run, private investment is enhanced,total output, real expenditure and money balance rise to a higher level with no negativeimpact on the budget of the central government.

JEL classification: E6; H54.Keywords: Infrastructure investment; Fiscal Policy.

1 IntroductionInvestment in social infrastructure has long been considered important for large developingcountries (LDCs). The infrastructure investment in LDCs is far below the average level of theindustrial countries. The stock of infrastructure is an important input in the production process,raising the efficiency and productivity in the private sector, and ultimately giving rise to a higheroutput and living standards.

Financing the new infrastructure investment is a difficult task for LDCs, especially in poor,resource-constrained developing countries with fiscal deficits. A common way for financing theinfrastructure investment is borrowing from abroad, or relying on aid programs. However, suchfinancing creates dramatic monetary management problems for LDCs, making them reluctantto pursue these avenues. A large amount of literature is focusing on those issues. In contrast,those problems do not hold for China. Even though China is an LDC, the Chinese governmentholds huge amounts of public savings in the form of foreign exchange reserves. In July 2009,

∗3rd year graduate student, Wylie Hall 210, Economics Department, Indiana University. Email address:yinhu@indiana.edu. Tel: 812-855-0179. I wish to thank Professor Edward Buffie for the great idea of this project,and helpful comments. Any errors in this paper are my responsibility. This is the draft of my 3rd year paper. Pro-fessor Edward Buffie is my committee chair, together with two committee members: Professor Fwu-Ranq Changand Professor Bulent Guler. I am grateful for all their helps during my research.

1

China’s foreign exchange reserves topped $2 trillion for the first time. The composition offoreign exchange reserves is presently regarded as a state secret in China, so there is no detailedofficial report on it, but it is commonly estimated that 60 % of the Chinese foreign reservesare in US dollars and bonds. According to a United States Treasury Department report, inOctober 2009, China held $798.9 billion in US Treasury bonds, $479.8 billion of long-termagency bonds, $24.5 billion of long-term corporate bonds and $100.8 billion in the US stockmarket, adding up to $1.4 trillion. The remainder is primarily invested in Japanese Yen, Euro,and British Pounds.

US dollar assets comprise a large portion of China’s foreign exchange reserves, and Chinadoes not have diversified channels to preserve the value of these reserves. The book valueof some of these assets have fallen significantly since 2000 due to a devaluation of the USdollar. Moreover, the interest returns on those US treasury bonds have fallen over time. Theinterest rates for 1-Year Treasury bonds in 1990 were 7.4%, and fell to 5.8% in 2000, andthe latest report from the Federal Reserve shows that the interest rates at 0.33% this Febuary.1 Hence, the interest return on those foreign exchange reserves is low. On the contrary, thereturn on infrastructure investment is high. The empirical estimates for the long-term returnon infrastructure investment are high in LDCs. 2 China has a very thin stock of infrastructure,even though the Chinese government started to increase the investment in public infrastructure.A recent empirical estimation shows that infrastructure investment spending comprises only6% of total investment before the stimulus package in 2008. There are too few highways,poor road conditions, urban congestion, lack of investment in education in the rural areas, etc.The insufficient infrastructure significantly affects the productivity and efficiency in the privatesector. With a decreasing return from foreign assets holdings, and an increasing return frominfrastructure investment, would it be a good idea for the Chinese government to increase itsinfrastructure investment by using the existing foreign exchange reserves?

In this paper, I develop an open economy model to address the issue of using foreignexchange reserves to increase the government infrastructure investment. I investigate the shortterm and long term effects of increasing government infrastructure on private investment in bothtradable and nontradable sectors, aggregate investment, total expenditure, and real output in afully articulated, optimizing model matching the Chinese economy. Under the predeterminedexchange rate system, in the short run, large government infrastructure spending takes resourcesaway from the private sector, investment in the nontradable sector decreases, real expenditureand money holdings fall, but real GDP still increases slightly due to the boom in the tradablesector. Large foreign exchange reserves finance the surge of infrastructure investment, so thegovernment budget is balanced in both the short term and in the long term. Even though theinfrastructure investment has contractionary effect on the nontradable sector, the long run effectis expansionary. Higher infrastructure stock enhances the productivity and efficiency in theprivate sector, investment in both sectors rises, real GDP, expenditure and money holdings are allreaching a higher level without raising the inflation. However, the short run contractionary effecton the nontradable sector shows that the Chinese government should combine some stimulusplans for the nontradable sector together with the increase in infrastructure investment to offsetthe effects of contraction. (Literature review will be added.)

The rest of the paper is organized as follows. Section 2 outlines the model and its main

1FRED: Federal Reserve Bank at St.Louis, Economic Data2Canning and Bennathan, World Bank Working Paper

2

characteristics. Section 3 solves the dynamic system. Section 4 describes how the model wascalibrated, and provides a numerical examination of the transitional paths in response to anunanticipated, permanent increase in the infrastructure investment. Section 5 gives the sensitiv-ity check, and section 6 concludes.

2 The ModelThis paper focuses on the Chinese economy that produces a nontraded good and a compositetraded good. There are no trade taxes and all world market prices equal unity, so domestic pricesof traded goods are set by the exchange rate e. The exchange rate system is predetermined, sothe government fixes the rate of change of the exchange rate, but not the level. Capital accountis closed.

2.1 Technology and the Supply SideTechnology is identical in both tradable and nontradable sectors. Production functions take theCES functional form.

Qn = aZη

(b1K

σn−1σn

n + Lσn−1σn

n

) σnσn−1

(1)

QT = aZη

(b2K

σT−1

σTT + L

σT−1

σTT

) σTσT−1

(2)

where b1 and b2 are share parameters, and σi is the elasiticity of substitution (i = T, n). Qi

is the output in sector i. Both nontraded good and traded good are produced by capital K andlabor L. Government infrastructure stock Z creates a positive externality for the production inboth sectors, so the increase of infrastructure stocks can increase the productivities in general.Capital is mobile ex ante, but sector-specific ex post. Labor supply is inelastic.

Firms in both sectors are perfectly competitive. With perfect competition and CES tech-nology, the unit cost functions are

Cn =Cn(w, rn)

aZη(3)

CT =CT (w, rT )

aZη(4)

where Ci is the cost function for producing aZη units of output. w is the wage rate measuredin units of the traded good, and is determined by basic market forces. ri is measured in units ofthe traded good, and is the capital rental in sector i. The sectoral demands for capital stocks are

Kn =Cnr (w, rn)Qn

aZη(5)

KT =CTr (w, rT )QT

aZη(6)

3

Labor is not sector-specific, so labor is mobile across sectors. The sectoral labor demands aregiven by

Ln =Cnw(w, rn)Qn

aZη(7)

LT =CTw (w, rT )QT

aZη(8)

Competitive firms earn zero profits in equilibrium, so the zero profit conditions are

Pn =Cn(w, rn)

aZη(9)

1 =CT (w, rT )

aZη(10)

where Pn is the relative price of nontraded good to traded good. THe inverse of Pn is the realexchange rate.

2.2 Private Agent’s Optimization ProblemA representative agent derives utility from consumption of traded and nontraded goods, andfrom the liquidity services generated by holdings of domestic currency. The Chinese gov-ernment has strict capital controls, which prevent the private agent from borrowing abroad orpurchasing foreign assets. Domestic money and physical capital are the only vehicles availablefor wealth accumulation. Preferences take the CES-CRRA functional form

U =

∫ ∞0

[C(Cn, CT )1−1/τ

1− 1/τ+ h

(MP

)1−1/τ

1− 1/τ

]e−ρtdt (11)

where C(Cn, CT ) = [κ0C(βc−1)/βcT + κ1C

(βc−1)/βcn ]βc/(βc−1) is linearly homogeneous CES ag-

gregator function, h is constant; κ0, and κ1 are share parameters; ρ is the pure time preferencerate; τ is the intertemporal elasticity of substitution; βc is the elasticity of substitution betweentraded and nontraded consumption goods.

The private agent solves the optimization problem in two stages. In the first stage, Cn andCT are chosen to maximize C(Cn, CT ) subject to the budget constraint PnCn+CT = E, whereE is the total expenditure measured in units of the traded good. The optimal choices of C∗nand C∗T give the indirect utility function V (Pn, E) = C[C∗n(Pn, E), C∗T (Pn, E)] =

( Ec(Pn)

)1−1/τ

1−1/τ ,

where c(Pn) = (κβc0 + κβc1 P1−βcn )1/(1−βc). Therefore, the exact consumer price index can be

written asP = ec(Pn) (12)

The rate of inflation is

π = χ+ γPnPn

(13)

where π = PP

is the inflation rate; χ = ee

is the rate of currency depreciation, and is controlledby the government; γ = (κβc0 +κβc1 P

1−βcn )−1κβc1 P

1−βcn is the consumption share of the nontraded

good.

4

In the second stage, the private agent chooses expenditure and money holdings to maximize∫ ∞0

[V (Pn, E) + hφ

(m

c(Pn)

)]e−ρtdt (14)

subject to

m = rTKT+rnKn+w(Ln+LT )+T−E−Pk

[In +

v( InKn− δ)2Kn

2+ IT +

v( ITKT− δ)2KT

2

]−χm

(15)

Kn = In − δKn (16)

KT = IT − δKT (17)

where m = Me

is the money balance measured in units of the traded good; φ(

mc(Pn)

)=

( mc(Pn)

)1−1/τ

1−1/τ ; T is the lump-sum transfer from the government; Ii is the investment in sector

i; δ is the depreciation rate;v( InKn−δ)2Kn2

is the investment adjustment cost function 3 Pk is thesupply price of capital, measured in units of the traded good. Physical capital is produced bycombining 1 unit of an imported machine with bn units of nontraded inputs, therefore

Pk = 1 + bnPn (18)

Equation (15) is the budget constraint, which states that the money holdings increase over timewhen income exceeds spending on consumption and investment; and equation (16) and (17)represent capital accumulations in the nontradable and tradable sectors, respectively.

The necessary conditions for an optimum consist of

VE(Pn, E) = λ1 (19)

λ2 = λ1Pk

(1 + v

(InKn

− δ))

(20)

λ3 = λ1Pk

(1 + v

(ITKT

− δ))

(21)

λ1 = (ρ+ χ)λ1 − hφ′(

m

c(Pn)

)1

c(Pn)(22)

λ2 = λ2(ρ+ δ)− λ1

[rn − Pk

v

2

(InKn

− δ)2

+ Pkv

(InKn

− δ)InKn

](23)

3The adjustment cost function is necessary to have well defined sectoral investment functions. Without this con-vex adjustment costs, the solution to the private agent’s optimization problem is of the big-bang variety: investmentis +∞ in the sector where the capital rental is highest, and −∞ in the other sector.

5

λ3 = λ3(ρ+ δ)− λ1

[rT − Pk

v

2

(ITKT

− δ)2

+ Pkv

(ITKT

− δ)ITKT

](24)

where λ1, λ2 and λ3 are the multipliers attached to the constraints (15), (16) and (17). Equation(19) state that the marginal utility of consumption equals to the shadow price of wealth. Equa-tion (20) and (23) define a Tobin’s q, λ2/λ1Pk

(1 + v

(InKn− δ))

= λ2/VEPk

(1 + v

(InKn− δ))

is the ratio of the demanded price of capital to its supply price in the nontradable sector; equa-tion (21) and (24) define Tobin’s q in the tradable sector. Equation (22) is simply an Eulerequation.

2.3 The Public SectorThe government comprises the fiscal authority and the monetary authority. The balance sheet ofthe Central Bank is M = DC + eR, so the changes of money supply depends on the domesticcredits and the accumulation of foreign exchange reserves R. The government’s flow constraintis given by

m = PzIz + T − rR− χm+ R (25)

where Iz is the government investment in infrastructure; Pz is the supply price of infrastructure,which is given by

Pz = 1 + bzPn (26)

Similar to the private capital stock, the infrastructure is produced by combining 1 unit of animported machine with bz units of nontraded inputs. The rate of infrastructure accumulation is

Z = Iz − δZ (27)

As indicated by equation (25), the government has four sources of revenue: interest in-come on its international reserves; capital gain on its international reserves; money printing,and inflation tax. The government expenditure consists of lump-sum transfers and the costof infrastructure investment. The government sells foreign exchange reserves to pay for theincrease in net infrastructure investment, thus

R = −Pz(Iz − δZ) (28)

The consolidated public sector budget constraint is

m = PzIz + T − rR− χm− Pz(Iz − δZ) (29)

2.4 Market-Clearing ConditionsThe temporary equilibrium for the economy is defined by equality of demand and supply in thelabor market and the nontraded good market. Both markets clear when

L = Ln + LT (30)

Qn = Dn(Pn, E) + bn

[In +

v( InKn− δ)2Kn

2+ IT +

v( ITKT− δ)2KT

2

]+ bzIz (31)

6

where L is the fixed supply of labor; Dn(Pn, E) is the Marshallian demand function for con-sumer goods. Equation (31) states that the total output in nontradable sector is equal to thedemand for nontraded consumption goods plus the demand for nontraded inputs used in pro-ducing new capital goods and new infrastructure investment.

3 The Dynamic SystemThe perfect foresight solution to the model generates to a dynamic system with five state vari-ables, Kn, KT , Z, R, and m, and three jump variables, E, In, and IT . In order to form a systemof differential equations, we need to use the first order conditions obtained from the privateagent’s optimization problem. Equation (19) to (24) yield

VEEDn

(VEn

VEEDn

Pn +1

Dn

E

)= (ρ+ χ)VE − hφ

′(

m

c(Pn)

)1

c(Pn)(32)

where VEE = ∂2V/∂E2, and VEn = ∂2V/∂E∂Pn. The first order condtions from privateagent’s optimization problem yield

λ2 = λ1

[Pk(ρ+ δ)

((1 + v

(InKn

− δ))− rn + Pk

v

2

(InKn

− δ)2

− Pkv(InKn

− δ)InKn

](33)

λ3 = λ1

[Pk(ρ+ δ)

((1 + v

(ITKT

− δ))− rT + Pk

v

2

(ITKT

− δ)2

− Pkv(ITKT

− δ)ITKT

](34)

In order to solve the time paths for the three jump variables, it is necessary to take intoaccount the induced variations in Ln, Lt, rn, rt, Pn, and Pk. This involves solving the pseudo-static variant of the model in which the eight endogenous variables are treated as exogenousvariables. The solutions are

PnPn

=1

JPnQn

[γE + βPk

(1 + v

(InKn

− δ))

In + βPk

(1 + v

(ITKT

− δ))

IT

+

[βPk

v

2

(InKn

− δ)2

− βPkv(InKn

− δ)InKn

− rn −θnlθnkrn

a3LTa3LT + a1Ln

]Kn

+

[βPk

v

2

(ITKT

− δ)2

− βPkv(ITKT

− δ)ITKT

+θTlθTkrT

a1Lna3LT + a1Ln

]Kt −

η

ZPnQnZ

](35)

Ln =a3LT

a3LT + a1LnKn −

a1LTa3LT + a1Ln

KT +a2a3LT

a3LT + a1LnPn (36)

LT =a1Ln

a3LT + a1LnKT −

a3Lna3LT + a1Ln

Kn −a2a3Ln

a3LT + a1LnPn (37)

7

rn =1

θnk

(1 +

a2Lnθnl

a3LT + a1Ln

)Pn +

θnlθnk

LTa3LT + a1Ln

KT +θnlθnk

Lna3Lt + a1Ln

Kn + (1− θnl )η

θnkZ

(38)

rT =θTlθTk

a2Lna3LT + a1Ln

Pn +θTlθTk

LTa3LT + a1Ln

KT +θTlθTk

Lna3LT + a1Ln

Kn + (1− θTl )η

θTkZ (39)

where a1 = θnl (σnll + σnkk − 2σnlk) < 0, a2 = σnlk − σnkk > 0, a3 = θTl (σTll + σTkk − 2σTlk) < 0,and a4 = σTlk − σTkk > 0. J = θnl

a2a3a3+a1Ln/LT

+ (ε + γ)DnQn

, β = bnPnPk

is the cost share ofthe nontraded component in the production of capital good, ε is the compensated own-priceelasticity of demand for nontraded goods. θki is the cost share of factor i in sector k; σkij isthe Allen partial elasticity of substitution 4 between factors i and j in sector k. A circumflexdenotes the percentage change in a variable (x = dx/x).

The above results are very intuitive. Eqution (35) states that Pn rises when higher con-sumption and investment spending strengthen demand, and falls when infrastructure accumula-tion increases supply. The capital accumulation in both sectors has ambiguous effects on Pn, butmore probably, the capital accumulation in the nontradable sector increases supply and resultsin a decrease in Pn, while the capital accumulation in the tradable sector may have negative im-pact on Pn. Equation (36) shows that both Kn, and Pn have favorable effects on labor demand,as the complementarity between labor and capital is high, and high price level decreases thereal cost of labor in the nontradable sector, so the demand for labor increases; while KT has theopposite effect on labor demand in the nontradable sector. Equation (37) indicates that similarto the nontradable sector, KT has favorable effect on labor demand in the tradable sector; whileKn and Pn have the opposite effects. Equation (38) says that the accumulation of Kn and KT

will drive down the capital rental in the nontradable sector, but the effect of Pn on rn is ambigu-ous. However, rT decreases with Pn, Kn, and KT . The accumulation of infrastructure stockwill result in a higher capital rentals in both sectors.

Use equation (35) to (39), equation (32), (33), and (34) can be solved for E, In, and IT asa function of the endogenous variables only.

E = f1(E, In, IT , Kn, KT , Z,m) (40)

In = f2(E, In, IT , Kn, KT , Z,m) (41)

IT = f3(E, In, IT , Kn, KT , Z,m) (42)

The above three equations together with the consolidated public sector budget constraint(equation (29)), and two capital accumulations in both sectors (equation (16) and (17)), and in-frastructure accumulation (equation (27)), infrastructure financing scheme (equation 28)) forma system of eight differential equations. It is impossible to derive a closed-form solution ana-lytically, so we will solve the above system of equations numerically.

4Uzawa, (1962)

8

4 Model Calibration and Numerical Solutions

4.1 CalibrationTable 1 lists the parameter values used to calibrate the model.

9

Table 1: Calibration of the Model

Parameter Valuesβ = 0.35, γ = 0.5, α = 0.6, βc = 0.5, Ω = 3δ = 0.05, ρ = 0.1, r = 0.03, η = 0.15θTk = 0.35, θTl = 0.65, θnk = 0.45, θnl = 0.55, a = 1.2µ = 0.1, σn = 0.5, σT = 0.5, χ = 0.14, τ = 0.5, R

Y= 0.4

Notationβ: cost share of nontraded inputs in the production of capitalγ: consumption share of the nontraded goodα: cost share of nontraded inputs in the production of infrastructureβc: elasticity of substitution between traded and nontraded consumption goodsΩ: q-elasiticity of investment spendingδ: depreciation rateρ: time preference rater: interest rateη: marginal utility of infrastructure stockθik: cost share of capital in sector iθil : cost share of labor in sector iµ: ratio of money balance to expenditureσi: elasticity of substitution between labor and capital in sector iχ: rate of currency depreciationτ : intertemporal elasticity of substitutionRY

: initial ratio of foreign exchange reserves to real GDP

From empirical evidence, the value of β lies between 0.3 to 0.65, but LDCs tend to havelower values of β as the capital market is not quite mature, thus 0.35 is chosen. On the contrary,the value of α tends to be big in LDCs, and the Chinese government will prefer to use morenontraded inputs in the production of infrastructure. The empirical estimate for the q-elasticityof investment spending is quite low, typically between 0.2 to 2. More recent studies suggest thatthese numbers understimate the true elasticity and the real value should be somewhere between2 to 5, so a slightly larger value is chosen here.5 The time preference rate is set quite largedue to the fact that it determines the net rate of return on private capital. The real interest rateis consistent with a value between the long-term real returns paid by U.S. stocks and treasurybonds. Those returns have been quite low in recent years. The Chinese economy is laborintensive in both sectors, especially so in the tradable sector, thus θTl = 0.65 and θnl = 0.55 arechosen to reflect this characteristic.

Since the Chinese government stimulus package, the domestic rate of inflation has goneup continuously, so a slightly high rate of currency depreciation is chosen to match this fact.Intertemporal elasticity of substitution tends to be small in developing countries, with an ex-tremely high savings rate in China, a relatively small value of τ is assumed. For the rest of theparameter values, the neutral values are chosen. One particular feature of the calibration hereis the initial ratio of foreign exchange reserves to real GDP, which is extremely large. It is usedto match the Chinese economy, as China held more than $2 trillion foreign exchange reserves

5Jovanovic and Rousseau,2007

10

by the end of 2009. The value of 0.4 is the average ratio of RY

from 2000 to 2009. Data used toestimate this value comes from IFS and the People’s Bank of China.

4.2 Numercial SolutionAt t = 0, the Chinese government decides to increase the infrastructure investment by 50%using the foreign exchange reserves, therefore, infrastructure investment jumps up to a higherlevel. This is an unanticipated, permanent shock. Figure 1 shows the perfect foresight solutionsfor the base case in the benchmark model.6

Figure 1: Solution Paths for the Endogenous Variables 7

6The solution paths were generated by log-linearizing the model. Mathematica supplies the results for the loglinearization and numerical solutions for the transition path.

7 The plots show the percentage difference between all the variables at time t and their initial values at t = 0.The dashed line is the percentage change between the new steady state and the old steady state value.

11

The above solution paths are the core variables directly from the dynamic system. Totalexpenditure and money holdings are measured in units of traded goods. In order to have a betterpicture on the effect of the increase in government infrastructure investment, we need to solvefor the transtion paths for the real variables in the economy.

12

Fiture 2: Solution Paths for the Real Variables 8

The Chinese government increases the infrastructure investment at t = 0 by surprise, sothe infrastructure investment jumps to a higher level at t = 0, and stays constant thereafter.Foreign exchange reserves are used to finance the higher investment spending. As expected,foreign exchange reserves fall over time, and the stock of infrastructure increases continuously.However, both Z and R will not change immediately.

By the market clearing condition in the nontradable sector, when government infrastructureincreases, a large proportion of output from nontradable sector is taken away from the privatesector, therefore, the consumption of nontraded goods decreases, and the investment in thenontradable sector falls, creating a downward pressure on Pn right after the shock. The lowerPn has positive impact on the rental return on the tradable sector as equation (39) shows, so ITjumps up immediately, while the total investment increases. Inflation goes down immediately,so the real cost of holding money decreases, real money balances increases immediately afterthe shock.

8The plots also show the percentage differences, not in absolute term, except the rate of inflation, which ispresented in level term.

13

On the supply side, the lower level of Pn increases the real cost of capital in the nontradablesector, so the capital inputs decrease, which results in the decrease of output. Different fromthe nontradable sector, the price for the traded good goes up at a constant rate, so it is moreprofitable to invest in the tradable sector, KT increases continuoulsy, output rises in the tradablesector. Even though there exists a contractionary effect on the nontradable sector due to thehigher infrastructure investment, the boom in the tradable sector is greater than the bust, realGDP increases over time.

After the implementation of this new policy, perfect foresight private agents know thatthe government will draw down the reserves to pay for the infrastructure investment, so thegovernment will get rid of the ”unwanted” foreign reserves, which will result in the decrease inthe nominal money supply. Notice that τ is small here, so the private agents not only want tosmooth their consumption paths, but also would like to hold more real money balances when thenominal interest rate is low. The exchange rate system is predetermined, so the rate of currencydepreciation is controlled by the government, which means e will increase at a constant rate,that is 14%. Therefore, the excess demand for money creates a upward pressure on the pricelevel, real money balance goes down right after the initial upward jump.

Productivity starts to rise as Z increases continously. Expecting higher future income,people want to consume more, total expenditure goes up. Demand for the nontraded goodsrises sharply as Pn is temporarly lower. The excess demand for the nontraded goods drives upthe price, so Pn starts to rise, inflation goes up. Higher price level in the nontradable sectormakes the investment more profitable, so the investment in the nontradable sector rises. On thecontrary, investment in the tradable sector decreases partially because the higher Pn reduces therental return in the tradable sector, and also due to the ”competing asset effect”. The increasein the price level reduces the real money balances, creating a liquidity shortage, so the marginalutility of money balances rises sharply, which draws savings away from capital accumulation.Facing a severe liquidity shortage and an increasing rental return in the nontradable sector, theprivate agent may find it optimal to reduce the investment in the tradable sector in order torebuild the real money stocks. Total investment decreases.

In the later phase of the reform, the continous increase in Pn reduces the real cost of capitaland labor in the nontradable sector, so the capital and labor inputs increase, higher infrastructurestock enhances the productivity, output in the nontradable sector rises. For the tradable sector,after the initial boom, investment falls due to the strong motivation of rebuilding the real moneybalances. Capital and labor inputs in the tradable sector keep falling, output decreases but stillmuch higher than the original level. Real GDP starts to decrease when capital stock in thetradable sector falls, but still higher than its initial steady state value.

In the long run, higher infrastructure investment increases the productivity and efficiencyin the private sector, real expenditure, real money holdings, real GDP, private investment, andcapital stocks all rise to a higher level. The rate of inflation returns back to its original level.Because the government finances the higher infrastructure investment by using the foreign ex-change reserves, so there is no fiscal deficit along the transition path, the public sector’s budgetis balanced. Foreign exchange reserves settle down at a lower level, but there still exists sub-stantial amount of international reserves.

The policy of increasing government infrastructure investment by drawing down the for-eign exchange reserves is quite successful in the long run. In a country like China with a thinstock of infrastructure but a huge amount of foreign exchange reserves, this policy increases the

14

general productivity and efficiency in the private sector. The depreciation of dollars, the lowerreturn from US dollar assets, and the higher return on infrastructure make it profitable for theChinese government to use those reserves to increase the infrastructure investment without anynegative impact on the public sector’s budget. However, this policy is not perfect. As can beseen from the transition paths, there exists an initial long period of lower level of investment,capital stock, and output in the nontradable sector, lower level of real expenditure and moneybalances, even though there is an initial boom in the tradable sector, and higher real GDP withlower level of inflation initially. The adjustment process is very slow. It takes nearly 40 periodsin order for the most variables converge to their higher new steady state level. In order to en-joy the higher output, income, and expenditure, the economy has to go through an initial longperiod of contraction in the nontradable sector. This is the price that needs to be paid for theimplementation of the policy.

5 Sensitivity AnalysisIn Figure 3, we carried out runs for an alternative value for τ . Instead of τ = 0.5, we setτ = 1.5, which means the intertemporal substitution is very large and marginal utility of moneyis small, so there will be less desire to smooth the consumption and accumulate more money.

Figure 3: Solution Paths for τ = 1.5 9

9Only the real variables are reported, not the nominal ones.

15

With the big value of intertemporal rate of substitution, the private agents do not havestrong desire to smooth their consumption path, so the magnitude of the initial prolonged periodof contraction in the nontradable sector is much smaller than the benchmark case, even though itstill takes a long time for the nontradable sector to recover from the contraction. The transitionalpaths are quite similar to the case when τ = 0.5, the only difference here is the expansionary

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effect is greater, the after shock steady state values are higher. The lowest values of the variablesduring the bust phase are much smaller. It still takes quite a long period of time for all thevariables to converge to their new steady state values. (This part is incomplete, need furtherrevision.)

6 ConclusionIn this paper we have analyzed the effects of increasing the government infrastructure invest-ment by using foreign exchange reserves in a model matching the Chinese economy. The de-creasing interest returns of foreign assets and the higher returns from infrastructure investmentmake it more profitable to draw down the foreign exchange reserves to finance the infrastructureinvestment. The solution path shows that the higher level of infrastructure increases the gen-eral productivity and efficieny of the private sector, making it more productive to invest in bothsectors. In the long term, investment, capital stock and output in both sectors, real GDP, realexpenditure and money holdings all rise to a higher level, even though there exists a transitorylong period of contraction in the nontradable sector. This may be the cost of this policy reform.Inflation goes down on the transition path due to the decrease of price level in the nontradablesector, however, the equilibrium rate of inflation is unchanged. The government effectively paysfor the cost of higher infrastructure investment using the foreign exchange reserves without anyadverse impact on government budget.

However, the prolonged period of contraction in the nontradable sector suggests that gov-ernment should use this policy with caution. A stimulus plan for the nontradable sector shouldbe combined with this policy reform to shorten the periods of lower output in the nontradablesector, and reduce the magnitude of contraction.

Labor supply is inelastic in our model, this is not a realistic assumption for the real econ-omy. The main task for future research is to analyze the effects of the same policy under theassumption of elastic labor supply. We hope the changes of labor supply will introduce thewealth effect into the model, so the labor supply and consumption will absorb the effect of theshock together, and the adjustment process will be faster with endogenous labor supply.

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