Reserve Financing and Government Infrastructure Investment: An Application to China Yin Germaschewski∗ Department of Economics, Indiana University, Bloomington, IN 47405, United States
Abstract This paper proposes a novel financing scheme, reserve financing, for government infrastructure investment in China. A simple analytical model and a two-sector open economy model explore the consequences and implications of a big surge in infrastructure investment financed by international reserves. The results show that reserve financing, coupled with a managed float exchange rate system, can maintain the country’s fast growth rate while mitigating fiscal pressure on local governments. Productive infrastructure capital stimulates domestic demand, reducing the country’s dependence on exports. To promote growth and maintain price stability, three factors are critical: return on infrastructure investment, swift fiscal adjustment, and rapid infrastructure financing. Keywords: Government investment; Fiscal financing; Infrastructure; Open economy. JEL classification: O11; O23; F43; H54.
1.
Introduction
The slowing Chinese economy will struggle to achieve its minimum growth target of 7.5% this year. This is due to a nationwide real estate downturn, slowing imports, a broad deterioration in business conditions and declining consumer confidence.1 In recent years, China had been the leader in world economic growth, with annual growth rates averaging 9.5%. A Chinese downturn, even as Europe contends with a sovereign debt crisis and the US attempts to jump-start its recessed economy, could unnerve international investors with fears of a second global recession. As a main driver of China’s economic engine, government infrastructure investment has reduced the poverty rate, boosted productivity in the private sector, and most importantly, spurred private investment when the economy faces downward pressure. The Chinese government is responding to signs of economic slowdown by initiating a ∗ Corresponding author: Department of Economics, Wylie Hall 105, Indiana University, Bloomington, IN 47405, U.S.A. Present address (postal address): 12 Piper Lane, Lee, NH 03861, U.S.A. Tel: +1 603 953 7030. E-mail:
[email protected]. 1 According to the data released by The National Bureau of Statistics of China, growth in imports has risen just 0.3% in April 2012 from the same period a year earlier, construction and retail sales faltered, and fixed asset investment slackened to its lowest growth pace in nearly a decade, rising only 20.1% year on year to $1.73 trillion dollars in the first five months of 2012. (The growth rate in January-May period in 2011 is 25.8%.)
new round of infrastructure investment in roads, ports, airports, worth an estimated $160 billion. Though the hope is that this investment in infrastructure will foster growth and bolster a faltering economy, it fails to consider three potential problems: inflation, low return on public infrastructure investment and fiscal financing. Despite the government’s anti-inflationary efforts, prices in China have in recent years increased significantly (see Figure 1a). Climbing food, property and energy prices pushed the August 2011 consumer price index up 6.5% over 2010, and the actual numbers could be higher than officially reported.2 High inflation endangers China’s competitiveness in the world market and poses a threat to social stability as inflation further widens the income gap between rich and poor. The Chinese government has substantially increased its infrastructure investment in the recent past, but the demand for infrastructure services outpaces the supply due to continuous population growth and urbanization.3 In addition, most infrastructure expenditures are concentrated on big cities, neglecting the rural areas that need the investment the most.4 The infrastructure in large cities is similar to that found in wealthier nations, while the one found in the countryside closely resembles that observed in Third World countries. Table 1 compares China’s provisions of key infrastructure services with the US, South Korea, Malaysia and South Africa. The infrastructure capital stock in China lags behind these countries, especially in rural areas, which still suffer from a severe infrastructure deficiency. Thus, additional investment is urgently needed in order to achieve sustained rapid growth. On the other hand, continuous investing in urban areas would result in falling marginal returns on public investment, and can potentially result in an oversupply of infrastructure, dampening the growth effects of public investment. In the past, most Chinese infrastructure investment was financed by undisciplined bank lending, leading to the amassing of huge debts by local governments.5 The Chinese government countered this trend by tightening restrictions on bank lending and reducing the amount of money available for loans. Despite those measures, a new fear has arisen that more liquidity problems in the future will cause local governments to default on their debts, precipitating a wave of nonperforming loans at Chinese banks. A surge in infrastructure investment would make it harder for the government to stabilize prices and resolve local government debt issues. To address this ongoing policy dilemma that pits infrastructure investment against controlling inflation, promoting growth and preventing debt accumulation, this paper proposes a novel financing scheme, reverse financing. The Chinese government has accumulated a tremendous amount of international reserves over the past few years, 2
Chinese price index has longstanding methodological problems, the officially reported price index tends to underestimate the actual inflation. 3 Inadequate supply of infrastructure is common in China. According to an article from Shanghai Daily on September 7, 2012: “Shanghai may face a shortage of water supply if the population continues to soar. The current capacity of the city’s water supply was about 16 million tons per day, which is able to cover the demand of 26 million people. However, once the population reaches 30 million, the demand would rise to 18 million tons per day, exceeding the current capacity. And Shanghai will hit 30 million in about seven years.” Moreover, tens of millions of migrants have left the Chinese countryside for the cities, increasing the need for power and transportation. 4 China has experienced a nationwide energy shortage of 30-40 million kilowatts of power this summer, with the worst shortfalls in southern and eastern suburban and rural regions, where most factories are located. Power shortages have forced many factories to shut down their production lines, and some finished products did not meet the necessary specifications due to the lack of a steady supply of power. 5 There are several papers looking at the past and current government infrastructure investment in China and their sources of financing, see Chow (1993), Spear et al. (1997), Demurger (2001), Su & Zhao (2006).
2
mostly U.S. dollar assets (see Figure 1b).6 However, China lacks diversified channels through which to preserve the value of its international reserves. The book value for some of these assets has fallen significantly since 2000 due to a devaluation of the U.S. dollar, and their interest earnings are quite low. Rather than leaving them to earn low interest, investing China’s more than $3 trillion in foreign exchange reserves in infrastructure projects would diversify the nation’s portfolio. Reserve financing would not pile further fiscal burdens on already-stressed local governments, nor would it unleash a torrent of bank lending. Rather, skillful use of reserve financing could allow the government to reignite growth without revving up inflation. The contribution of infrastructure investment to economic growth has been studied extensively [e.g. Aschauer (1989); Glomm & Ravikumar (1994); Chatterjee et al. (2003); Angeletos & Panousi (2009); Barro & Redlick (2011), Buffie et al. (2012)]. The analyses in these studies, however, were mostly conducted in closed-economy setups, mainly focused on developed nations and using a taxation financing option: either lump-sum or distortionary taxes. In contrast to the existing literature on government infrastructure investment, this research deviates from the previous work in two ways. First, the financing instrument used in this research goes beyond the conventional financing choices. Second, a simple analytical model and a two-sector open economy model are developed to assess the macroeconomic consequences and implications of using reserves to pay for a 50% increase in public infrastructure investment in the context of a dynamic general equilibrium open economy framework. Briefly, in the reserve financing models, higher infrastructure investments are paid in full by international reserves, so that 55% of the country’s foreign exchange reserves are spent gradually over a few years. Government lump-sum transfer payments are adjusted over time to peg the long-run inflation rate at the government’s target level. Instead of a fixed peg, the government adopts a more flexible exchange rate system–a managed float–and manages the path of the exchange rate in an effort to reconcile a sharp and sustained increase in infrastructure investment with continuously lower inflation.7 Three factors are critical in regard to achieving a fine balance between stimulating the economy and managing inflation: return on public infrastructure, speed of fiscal adjustment and speed of infrastructure financing. Return on government infrastructure investment matters a great deal for the expansionary effects of infrastructure investment. Spending more money on infrastructure that has an adequate supply sharply reduces the return on public investment. An extremely low return (i.e. the net rate of return on infrastructure is 3% or less) can be harmful under current financing scheme, because the cost of investment: loss in international reserves and interest earnings on these reserves, can outweigh the benefit. Both models predict that as long as the return is not exceedingly low, 6 The composition of Chinese foreign exchange reserves is presently regarded as a top state secret, so there is no detailed official report available. It is commonly estimated that 60% of Chinese foreign exchange reserves are in U.S. dollars and bonds, especially U.S. long-term Treasury Bonds. According to a United States Treasury Department report, in October 2009, China held $798.9 billion of U.S. Treasury Bonds, $479.8 billion of long-term agency bonds, $24.5 billion of long-term corporate bonds and $108 billion in the U.S. stock market, adding up to $1.4 trillion. 7 China’s current exchange rate is predetermined by the central government, and the general consensus on the world market is that the Chinese currency is undervalued. Continued pressure exists from the rest of the world urging China to revalue its currency. A more flexible exchange rate policy would reduce the currency appreciation pressure from the rest of the world, and be more compatible with the nation’s current economic structure.
3
the accumulation of public infrastructure capital generates a positive wealth effect, which propels a consumption boom and reduces the time people spend working. Concurrently, rising productivity and efficiency increase the return on private investment. Both factors redirect the nation’s growth from exports to stronger domestic demand, a goal that Chinese policymakers have pursued for a long time. But wishing it were so is not enough, and problems may arise during the transitional periods. In the two-sector framework, the desire to consume more in response to an anticipated rise in income leads to an ex ante excess demand for nontraded goods. Since nontradables have to be produced at home, more resources are needed in the nontradable sector, and the relative price of nontradables has to rise to entice a shift of resources in the short run. The weak spot appreciation of the nominal exchange rate is not sufficient to counterbalance the increase in the relative price of the nontraded goods, and price levels then jump up on impact. Sluggish fiscal adjustment fails to anchor inflation expectations. The rate of inflation mounts by more than four percentage points, according to the typical calibration for the Chinese economy, and stays above the government’s target rate in the short and medium terms. Seeing higher inflation, agents immediately reduce their current demand for money, creating a liquidity shortage, which draws savings away from investment. Private investment contracts temporarily, falling 1.63%. The transitional dynamics highlight the crucial role played by the speed of fiscal adjustment in determining the path of inflation. A quick reduction in lump-sum transfer payments favorably affects the fiscal deficit, solidly anchoring ex ante inflation expectations and strengthening the pull of long-run fundamentals to immediately deliver a disinflationary outcome. The anticipation of lower inflation creates an incentive to accumulate real money balances, leading to a sharp decline in inflation ex post despite a strong increase in aggregate demand. In cases where the government reduces the lump-sum transfer payments to their long-run stationary level in fifteen years instead of thirty-five years, the rate of inflation falls to 4.07% initially and continues to decrease. Regrettably, it has often proven difficult for the government to implement a quick fiscal adjustment. An easy antidote for high inflation in the short run is to sell more international reserves than the amount needed for infrastructure financing each period. Under plausible conditions, pumping 19% of extra reserves into the economy significantly lowers the rate of currency depreciation, which far outweighs the rate of inflation in the nontradable sector.8 The overall rate of inflation then falls to 0.67% on impact and stays below its initial level thereafter. In addition, if the long-run inflation target is set at a lower rate than the inflation initially prevailing in the economy, the immediate decrease in inflation will be even more pronounced. A big surge in productive public infrastructure investment, combined with rapid fiscal adjustment or fast financing, would not worsen the local governments’ budget or exert any inflationary pressure. Output, consumption and private investment rise shortly after the reform, while the rate of inflation falls on impact and remains subdued. 8
The rate of inflation measured by consumer price index (CPI) is comprised of two parts: rate of currency depreciation and rate of inflation in the nontradable sector. Rate of currency depreciation can be thought of as the rate of inflation in the tradable sector, according to the model specification in this paper.
4
In the rest of the paper, Section 2 lays out the two-sector model and its main characteristics. Section 3 then calibrates the model to match the Chinese economy. Section 4 presents the results from the simple analytical model and discusses the intuition behind the outcome. Section 5 reports the numerical results from the central model, while Section 6 concludes the paper.
2.
The Two-Sector Model
The core model is an open economy that produces nontraded goods and composite traded goods. There are no trade taxes, and all world market prices equal unity, so domestic prices of traded goods are set by the exchange rate e. The Chinese government has strict restrictions on private capital flows, so capital account is assumed to be closed. The model incorporates several features: elastic labor supply, costly investment adjustment, distorting taxes levied against consumption and capital income, and a managed float exchange rate system.
2.1.
Technology and the Supply Side
Technology is identical in both the tradable and nontradable sectors. Production functions take the CES functional form. Qn = aZ
η
QT = aZ η
σn −1 σn
b1 Kn
σT −1 σT
b2 KT
σn σn −1
σn −1 σn
σT −1 σT
!
+ Ln
(2.1)
σT σT −1
+ LT
(2.2)
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 goods and traded goods are produced by capital K and labor L. Government infrastructure Z increases productivity in the same manner as the Hicks-Neutral technological progress. Capital is mobile ex ante, but sector-specific ex post. Labor is intersectorally mobile. Firms in both sectors are perfectly competitive. With perfect competition and constant return to scale in capital and labor, the unit cost functions are C T (w, rT ) C¯T = aZ η
C n (w, rn ) C¯n = aZ η
(2.3)
where C i is the cost function of producing aZ η units of output; w is the wage rate determined by basic market forces; ri is the capital rental in sector i; and all measured in units of the traded good. The sectoral demands for capital and labor are Crn (w, rn )Qn aZ η C n (w, rn )Qn Ln = w aZ η
CrT (w, rT )QT aZ η C T (w, rT )QT LT = w aZ η
KT =
Kn =
(2.4)
Competitive firms earn zero profit in equilibrium, which links goods prices to factor prices. Letting Pn denote the relative price of nontraded goods to traded goods (Pn then is the inverse of the real exchange rate), the two 5
zero-profit conditions are Pn =
2.2.
C n (w, rn ) aZ η
1=
C T (w, rT ) aZ η
(2.5)
The Private Agent’s Optimization Problem
Consider an open economy inhabited by a large number of identical, infinitely-lived consumers who are endowed with perfect foresight. All economic decisions in the private sector are made by a representative agent who derives utility from consumption of traded and nontraded goods, from the liquidity services generated by holdings of domestic currency, and from leisure. Strict capital controls prevent the private agent from borrowing abroad or purchasing foreign assets. Domestic money and physical capital are therefore the only vehicles available for wealth accumulation. Preferences take the CES-CRRA functional form Z
∞
U= 0
1+1/φ 1−1/τ (M U (Cn , CT )1−1/τ Ls P ) + h1 − h2 e−ρt dt 1 − 1/τ 1 − 1/τ 1 + 1/φ
(2.6)
where ξ/(ξ−1) (ξ−1)/ξ U (Cn , CT ) = κ0 CT + κ1 Cn(ξ−1)/ξ is linearly homogeneous CES aggregator function; h1 and h2 are constant; κ0 and κ1 are share parameters; ξ is the elasticity of substitution between traded and nontraded consumption goods; ρ is pure time preference rate; τ is the intertemporal elasticity of substitution; φ is Frisch elasticity of labor supply to the real wage, holding the marginal utility of consumption constant. The private agent solves the optimization problem in two stages. In the first stage, Cn and CT are chosen to maximize U (Cn , CT ), subject to the budget constraint Pn Cn + CT = E. E is the total expenditure measured in units of the traded good. The optimal choices of Cn∗ and CT∗ give an indirect utility function V (Pn , E) =
U [Cn∗ (Pn , E), CT∗ (Pn , E)]
=
( c(PEn ) )1−1/τ 1 − 1/τ
where c(Pn ) = κξ0 + κξ1 Pn1−ξ
1/(1−ξ)
Therefore, the exact consumer price index can be written as P = ec(Pn ), and the rate of inflation is π =χ+γ
P˙n Pn
(2.7)
where χ is the rate of currency depreciation, defined as ee˙ , and γ = κξ1 Pn1−ξ κξ0 + κξ1 Pn1−ξ
−1
is the consumption
share of the nontraded goods. In the second stage, the private agent chooses consumption, real money balances, investment and leisure to maximize Z 0
∞
1−1/τ E c(Pn ) 1 − 1/τ
+ h1
1−1/τ m c(Pn ) 1 − 1/τ 6
1+1/φ Ls − h2 e−ρt dt 1 + 1/φ
(2.8)
subject to m ˙ = rT KT + rn Kn + wLs + T − (1 + v1 )E − (1 + v2 )Pk In +
v( KInn − δ)2 Kn 2
+ IT +
v( KITT − δ)2 KT 2
−χm
where m =
M e
(2.9) K˙n = In − δKn
(2.10)
K˙T = IT − δKT
(2.11)
is the real money balance measured in units of the traded good; T is a lump-sum transfer from I
the government; Ii is private investment in sector i; δ is the capital depreciation rate;
v( Ki −δ)2 Ki i
2
is the investment
adjustment cost function in sector i; v1 and v2 are the value-added taxes (VAT) on consumption and investment, respectively. The endogenous labor supply Ls introduces wealth effects to the model. Physical capital is produced by combining one unit of an imported input with bn units of nontraded inputs, thus, the supply price of capital Pk is given by Pk = 1 + bn Pn
(2.12)
The budget constraint, (2.9), states that savings increase over time whenever income exceeds spending on consumption and investment; (2.10) and (2.11) describe the rate of capital accumulation in the nontradable and tradable sectors. The necessary conditions for an optimum consist of
E c(Pn )
−1/τ = λ1 (1 + v1 )c(Pn )
h2 L1/φ = λ1 w s In λ2 = λ1 (1 + v2 )Pk 1 + v −δ Kn IT λ3 = λ1 (1 + v2 )Pk 1 + v −δ KT −1/τ m c(Pn ) λ˙ 1 = (ρ + χ)λ1 − h1 c(Pn ) 2 ˙λ2 = λ2 (ρ + δ) − λ1 rn − (1 + v2 )Pk v In − δ + (1 + v2 )Pk v In − δ In 2 Kn Kn Kn 2 ˙λ3 = λ3 (ρ + δ) − λ1 rT − (1 + v2 )Pk v IT − δ + (1 + v2 )Pk v IT − δ IT 2 KT KT KT
(2.13) (2.14) (2.15) (2.16)
(2.17) (2.18) (2.19)
λ1 , λ2 and λ3 are multipliers attached to the constraints seen in (2.9), (2.10) and (2.11). (2.13)–(2.14) state that the marginal utility of consumption equals the shadow price of wealth multiplied by the price of consumption, and that the marginal rate of substitution between leisure and consumption equals the real wage. (2.15) and (2.18) 7
define a Tobin’s q model of investment: λ2 /λ1 (1 + v2 )Pk (1 + v( KInn − δ)) is the ratio of the demanded price of capital to its supply price in the nontradable sector. (2.16) and (2.19) define a corresponding Tobin’s q model in the tradable sector. (2.17) is simply a Euler equation.
2.3.
The Public Sector
The public sector comprises the fiscal authority and the monetary authority. The balance sheet of the Central Bank ˙ + eR, ˙ so the changes of money supply depend on domestic credits DC and the accumulation of is M˙ = DC foreign exchange reserves R. The government’s flow budget constraint is given by " # v( KITT − δ)2 KT v( KInn − δ)2 Kn m ˙ = Pz Iz + T − rR − χm − v1 E − v2 Pk In + + R˙ + IT + 2 2
(2.20)
where Iz is the government investment in infrastructure; Pz is the supply price of infrastructure, which is given by Pz = 1 + bz Pn
(2.21)
Similar to private capital stock, infrastructure is produced by combining one unit of an imported input with bz units of nontraded inputs. The rate of infrastructure accumulation is Z˙ = Iz − δz Z
(2.22)
δz is the rate of infrastructure depreciation. As indicated by (2.20), the government has five sources of revenue: interest income on its international reserves; capital gains on reserves; money printing; consumption and investment VAT revenues; and inflation tax. Expenditure consists of the lump-sum transfer payments and infrastructure investment. The government sells foreign exchange reserves to pay for the increase in net infrastructure investment each period. R˙ = −Pz f (Iz − δz Z), f ≥ 1
(2.23)
where f measures the speed of financing. If f > 1, the government is selling more reserves than the amount needed to pay for infrastructure investment; if f = 1, reserves are sold to cover the exact cost of investment each period. Substituting for R˙ in (2.20) gives v( KITT − δ)2 v( KInn − δ)2 Kn m ˙ = Pz Iz + T − rR − χm − Pz f (Iz − δz Z) − v1 E − v2 Pk In + + IT + KT 2 2 (2.24) The government has its own target rate of inflation. In order to achieve the goal, the long-run transfer payments have to be fixed at9 T ∗ = rR∗ + χ∗ m∗ + v1 E ∗ + v2 Pk∗ (In∗ + IT∗ ) − Pz∗ Iz∗ 9
This can be obtained by evaluating (2.20) at its long-term stationary level. x∗ is the long-run steady state value of x.
8
(2.25)
so that the rate of inflation will be pegged at π ∗ in the long run. The lump-sum transfer payment then adjusts over time towards the long-term stationary level at T ∗ according to the rule T˙ = α(T ∗ − T (t)), α > 0
(2.26)
where α is the speed of fiscal adjustment.
2.4.
Market-Clearing Conditions
Temporary equilibrium in the economy is defined by the equality of demand and supply in the labor market and the nontraded goods market. Both markets clear when Ls = Ln + LT " Qn = Dn (Pn , E) + bn In +
v( KInn − δ)2 Kn 2
+ IT +
(2.27) v( KITT − δ)2 KT 2
# + bz Iz
(2.28)
where Dn (Pn , E) is the Marshallian demand function for consumer goods. (2.28) states that total output in the nontradable sector is equal to the demand for nontraded consumption goods plus the demand for nontraded inputs used in producing new capital goods and infrastructure.
2.5.
Dynamic System and Solution Technique
The solution to the model generates a dynamic system with five state variables, Kn , KT , Z, R, and T , and three jump variables, m, In , and IT . (2.9) and (2.24) are linked to solve for E as a function of endogenous variables, so that E is not a core variable in the dynamic system. v(IT /KT − δ)2 v(In /Kn − δ)2 Kn + IT + E = rT KT + rn Kn + wLs + rR + Pz f (Iz − δZ) − Pk In + 2 2 KT − Pz Iz (2.29) The first order conditions from the private agent’s optimization problem yield 2 v I r I I I n n n n n λ˙ 2 = λ1 (1 + v2 ) Pk (ρ + δ) 1 + v −δ − + Pk − δ − Pk v −δ Kn 1 + v2 2 Kn Kn Kn (2.30) 2 rT v IT IT IT ˙λ3 = λ1 (1 + v2 ) Pk (ρ + δ) 1 + v IT − δ − + Pk − δ − Pk v −δ KT 1 + v2 2 KT KT KT (2.31) To solve for the time paths of the three jump variables, it is necessary to take into account the induced variations in Ln , LT , rn , rT , w, and Pn . This involves solving the pseudo-static variant of the model in which the 9
eight endogenous variables are treated as exogenous variables. Details of the solution technique can be found in Appendix A. At the time the government increases its investment in infrastructure, it adopts a managed float exchange rate system, so χ is not a policy variable anymore and is instead determined by the basic market forces, but the government occasionally intervenes to influence the path of the exchange rate in an attempt to maintain price stability, especially when the economy is experiencing sharp and continuous increases in aggregate demand. (2.13) and (2.17) link χ to the endogenous variables in the dynamic system. −1/τ m 1 ˙ τ − 1 P˙n χ = (1 + v1 )h1 − E− γ −ρ E τE τ Pn
(2.32)
Making use of the equations (2.29) and (2.32), (2.30) and (2.31) can be used to solve for In and IT as functions of endogenous variables only. Expressing the solutions in general form, I˙n = F1 (In , IT , Kn , KT , Z, R, m)
(2.33)
I˙T = F2 (In , IT , Kn , KT , Z, R, m)
(2.34)
The above two equations together with the consolidated public sector budget constraint (2.24), capital accumulation in both sectors ((2.10) and (2.11)), rate of infrastructure accumulation (2.22), infrastructure financing scheme (2.23), and the adjustment process for government lump-sum transfer payments (2.26) form a system of eight differential equations. Analytical solutions are difficult to obtain, so I rely on numerical simulations.
3.
Model Calibration
The model is calibrated at an annual frequency to characterize the effects of public infrastructure investment that extends several decades into the future. Parameter calibrations are summarized in Table 2. The average value of consumption share of nontraded goods (γ) over the past twenty years in China was around 40%, with the lowest value at 31% in 1990, and the highest value at 43% in 2009,10 so 0.4 is assigned to γ. Elasticity of substitution between traded and nontraded consumption goods, ξ, is set to 0.5, which implies the compensated own-price elasticity of demand for the nontraded good is 0.25 initially, as this value tends to be small at high levels of aggregation.11 A moderately large value is chosen for the time preference rate (ρ), because it determines the real long-run return on private capital.12 Microeconomic evidence suggests that the Frisch elasticity of labor supply is small, so 0.3 is assigned to φ.13 There is an abundance of empirical literature estimating the intertemporal elasticity 10
Data used for this estimation comes from The National Bureau of Statistics of China. See Blundell et al. (1993) (Table 3b, P.581) 12 The time preference rate plays two roles in the model: it discounts future utility and determines the steady state return on capital. This creates something of a dilemma. A value of 0.5 is appropriate when ρ is used to discount future utility, but a value of 0.1-0.15 is more in line with the real return on capital in China, so 0.1 is chosen as a compromise. 13 Some of the empirical estimates suggested that φ is around unity or higher, but Sims (1996) pointed out that φ is small, well below unity (See Chapter 2 for detailed discussion). Results vary little when the value of φ changes. Sensitivity analysis on φ is available upon request. 11
10
of substitution (τ ). Most estimates place τ between 0.2 and 0.5 for emerging markets.14 China’s savings rate is very high, 40% on average, so 0.25 is chosen for the baseline model. For comparison purpose, two additional values are considered, one is 0.5, the other is 1.2. In specifying technology, the share of domestically produced capital goods (β) generally lies between 0.3 and 0.7, and is slightly higher in more developed countries as developing countries produce a limited range of capital goods, so 0.35 is set to β. The share of domestically produced infrastructure (ζ) is calibrated at 0.8 because infrastructure is mostly produced at home. Tobin’s q, the ratio of the demand price to the supply price, is used to calculate Ω. Most empirical estimation for the q-elasticity of investment spending lies between 0.2 and 2.15 The demand price of capital is estimated using stock prices. However, firms’ investment decisions do not react to the changes of stock prices that much, so it is highly possible that this parameter is under-estimated. A slightly large value is assigned to Ω.16 China is a labor-abundant country, and most industries are labor-intensive in general, so both θkn and θkT are less than 0.5 to reflect this characteristic. The nontradable sector is much more capital intensive than the tradable sector, so θkn is set to a greater value than θkT . The depreciation rate for private capital (δ) is set at a customary 6%, and for infrastructure, the value is calibrated at 10%, because the bulk of depreciation infrastructure investments are put into operations and maintenance in current public expenditure and have been financed by general tax revenue, not into public sector investment spending.17 Empirical estimates of the elasticity of substitution between capital and labor (σ i ) lie between 0.5 and 1, depending on whether the studies rely on time series or cross-sectional data sets.18 Without solid evidence for the Chinese economy, 0.5 is chosen for σ i in the baseline model, and sensitivity analysis on σ i is presented in Table 6. The fiscal parameters are calibrated to match the data from China. The ratio of foreign exchange reserves to GDP ( YR ) is set equal to the average value of this ratio over the past decade. The peak value of
R Y
is 0.58 at the end
of 2011, and the lowest value is 0.29 in the beginning of 2000.19 The initial gross rate of return on infrastructure (rzo ) and infrastructure investment to GDP ratio jointly determine the output elasticity of infrastructure (η).20 The larger the rzo , the greater the η, which implies that the diminishing return on infrastructure falls slowly when infrastructure capital accumulates. The value of rzo is in line with empirical estimations in developing countries.21 14 Garcia-Cicco et al. (2010) estimated τ to be equal to 0.5 for emerging markets; Guvenen (2006) further showed that τ is low for the poor; Reinhart et al. (1996) computed the mean value of τ to be 0.25 for the poorest countries. 15 To measure Tobin’s q, which is the ratio of the market value of a firm (as measured by the market value of its outstanding stock and debt) to the replacement cost of its assets. The estimates of Summers (1981) implied that the q-elasticity varies from 0.6 to 1.8; Hayashi (1982) estimated this value lies between 0.5 and 1.3. 16 1 Ω and δ pin down the degree of convexity of investment adjustment cost function. v = δΩ , which is the coefficient for the convex adjustment cost function. subsection 5.4 conducts sensitivity analysis on Ω. 17 See Rioja (2003). 18 Aschauer (2000) estimated the the elasticity of substitution around unity, and Griffin & Gregory (1976) showed that this value is on the order of 0.5. 19 Data comes from International Financial Statistics (IFS) and The People’s Bank of China. 20 According to the specification of production functions, the ratio of infrastructure investment to output ( PzYIz ) is initially equal to δz ηrzo . Even though this ratio has risen in recent years, it had been quite low over the past few years, so PzYIz is set to the average value of this ratio over the past twenty years. 21 World Development Report (1994) used a cost-benefit analysis estimating the return for World Bank projects. The result showed that
11
The ratio of money balance to consumption (µ) is set to 0.1.22 The long-run target rate of inflation is equated to its initial value at 5%. The average annual rate of inflation in China over the past thirty years is around 5%. The highest value was at 24.2% in 1994, and the lowest value was at -0.7% in 2002. I peg the world interest rate at 3%, consistent with the long-run real return paid by the U.S. Treasury Bonds. Consumption and investment VAT rates vary a great deal across emerging markets, ranging from a modest 5% to 35%. VAT is the most important tax collected in China, generating larger revenues than any other taxes. The VAT rate is 17% for most products and is 13% for some products, so a common rate 15% is assigned to both v1 and v2 .23 Two more policy parameters that have profound effects on the path of inflation are the speed of lump-sum transfer adjustment (α) and the speed of infrastructure financing (f ). 0.09 is set to α in the baseline model, which implies that the lump-sum transfer payment adjusts gradually towards its long-run stationary value. f is set to unity initially, so that the government sells reserves at the speed that exactly pays for the cost of investment each period. Given these parameters’ importance, an extensive sensitivity analysis is conducted on both of them.
4.
The Analytical Intuition
Prior to the analysis of the two-sector model in section 2, I developed intuition for the numerical solution by solving analytically a model that is considerably simpler. This setup contained only traded goods and eliminated private capital accumulation and labor-leisure choice, which allowed me to lay the groundwork for the development of a more complex model and highlighted some of the mechanisms at work in the numerical results.
4.1.
The One-Sector Model
The main equations and functional forms from the one-sector model are shown in Table 3. Solution paths can be obtained by linearizing the four equations from the dynamic system in Table 3 around the long-run stationary equilibrium (m∗ , R∗ , Z ∗ , T ∗ ). On the convergent saddlepath, ∗
m(t) − m
=
µ ∗ τ (rz
− δz − r)(ρ + χ + δz ) + v(rz ∗ − δz − r) − (δz + r) i τ (1
− ) + δz 1 (To − T ∗ )e−αt −i (1 − ) + α τ R(t) − R∗ = (Z ∗ − Zo )e−δz t
(Zo − Z ∗ )e−δz t (4.1) (4.2)
the average return on road projects is 29% and 11% for electricity projects. Canning & Bennathan (2000) stated that microeconomic costbenefit studies may potentially miss the positive externalities to infrastructure, so they used an aggregate production function to calculate the rate of return to infrastructure that captures the total social rate of return to infrastructure. Their estimation has found that the gross rate of return on electricity generating capacity in China is 54%, and on paved roads is generally high, around 40%, assuming the rate of depreciation is 7%. See Table 6, 7 in Canning & Bennathan (2000). Isaksson (2010) used a panel data set estimating the net return on hard infrastructure. The average return in developing countries varies from 48% to 57%. 22 This ratio is obtained using consumption to GDP ratio( YE ) and high-powered money to GDP ratio( m ) in the data. Y 23 China’s current VAT is of the GDP-type, so the tax base is GDP. Under the GDP-type VAT system, no deductions are allowed for capital investment and depreciation of capital when calculating the tax base. The tax is equivalent to a sales tax applicable to both consumption and capital goods. Detailed information on China’s value-added tax reform can be found at Lin (2008).
12
Z(t) − Z ∗ = −(Z ∗ − Zo )e−δz t
(4.3)
T (t) − T ∗ = −(T ∗ − To )e−αt
(4.4)
where xo represents the initial value of x; is the interest elasticity of money demand, defined as
χτ i ;
i = ρ + χ is
the nominal interest rate. Since there is only one jump variable m, it requires that
i τ (1
− ) > 0 to achieve a stationary outcome.
The dynamics will not be well behaved unless the economy is operating on the upward sloping portion of the seigniorage Laffer curve where < 1.24 Given this assumption, the equilibrium is saddlepoint stable. At the beginning of the reform, the government increases its infrastructure investment by 50% and adopts a managed float exchange rate system. International reserves are used to pay for higher public spending. Assuming χo = χ∗ , the long-run outcomes are25 dC ∗ = (rz ∗ − δz − r)dZ ∗ > 0
dm∗ = µ(rz ∗ − δz − r)dZ ∗ > 0
dT ∗ = [(rz ∗ − δz − r)(v + χµ) − (r + δz )]dZ ∗
(4.5)
These results agree with intuition: so long as the return on infrastructure is not extremely small (i.e. rz − δz > r), the economy will enjoy higher consumption and accumulate more money in the long run. Lump-sum transfer payments will be lowered if rz < (δz + r) 1 + ∗
1 v + χµ
(4.6)
For plausible parameter values, (4.6) will always hold.
4.2.
The Impact Effect
When infrastructure capital is sufficiently productive, public investment in infrastructure is expansionary over the long-term horizon. This does not ensure that the accumulation of infrastructure capital will be immediately and unambiguously disinflationary. Consider first the initial jump in the price level e. Since the nominal money supply M is predetermined, the impact effect on the price level can be found by examining the solution for the demand for real money balances at time t = 0. Subtracting mo , the initial value of the real money stock, from both sides of (4.1), yields m(0) − mo = µ(rz ∗ − δz − r)dZ ∗ −
µ ∗ τ (rz
− δz − r)(ρ + χ + δz ) + v(rz ∗ − δz − r) i τ (1
− ) + δz ∗ (rz − δz − r)(v + χµ) (r + δz )(δz − α) + − dZ ∗ i i i ( τ (1 − ) + δz )( τ (1 − ) + α) τ (1 − ) + α
24
dZ ∗ (4.7)
The revenue-maximizing inflation rate occurs when = 1. If > 1, the equilibrium is located on the downward sloping side of the seigniorage Laffer Curve. Such equilibria have a number of peculiar properties: an increase in the deficit lowers the steady-state inflation rate and there are an infinite number of convergent perfect foresight paths. 25 Note that dx∗ = x∗ − xo .
13
Substituting the solution for m(0) into equation for the price dynamics in Table 3. µ i τ (rz ∗ − δz − r)(ρ + χ + δz ) + v(rz ∗ − δz − r) ∗ χ(0) − χo = χ∗ − χo + dZ i | {z } τ m τ (1 − ) + δz 1 {z } | 2 i (rz ∗ − δz − r)(v + χµ) (r + δz )(δz − α) − − i dZ ∗ i i τm (1 − ) + α ( (1 − ) + α)( (1 − ) + δ ) z τ τ | {zτ } 3
1 − (rz ∗ − δz − r)(ρ + χ + δz )dZ ∗ τ C | {z }
(4.8)
4
Four factors determine the value of χ at the time the reform starts. According to the assumption χ∗ = χo , the first term in (4.8) is zero. The second term captures the effect of Z on the demand for real money balances and is positive. Expecting higher future income, the private agent has an incentive to dissave in the short run by running down his stock of real money balances in order to achieve consumption smoothing. The motive to smooth the consumption path is stronger, the smaller the intertemporal elasticity of substitution (τ ). The third term, though complicated, squares with intuition. It picks up the effect of infrastructure capital on the fiscal deficit and the growth rate of money supply. Since the base for inflation and consumption taxes expands when infrastructure investment raises income, the fall in the fiscal deficit will reduce the growth rate of money supply, and thus, lower the rate of inflation. But on the other hand, in order to pay for new infrastructure projects, the government will have to sell its foreign exchange reserves, which means the interest earnings on the reserves are also lost. Consequently, the fiscal deficit will grow. The greater the α, the faster the decrease in the lump-sum transfer payments, and the more likely the former effect dominates, and the fiscal deficit will decline. The last term represents the deflationary pull from long-run fundamentals. Higher output in the future strengthens the supply side and puts downward pressure on prices, provided that the return on infrastructure is not extremely small. The overall effect is ambiguous; much depends upon the combination of parameter values, especially the value for rzo , α and τ . It is highly possible that the rate of inflation will fall on impact. Table 4 displays the simulated initial responses of the key variables in this model economy. Demand for real money balances rises whenever α takes a large value. When private agents with perfect foresight foresee rapid fiscal adjustment, they will expect inflation to fall, which implies that the opportunity cost of holding money will be lower in the future, creating a strong incentive to immediately accumulate money. All entries for m(0) are positive, e(0) are negative and χ(0) are less than 5% unless α is extremely small (i.e. 0.07). When the intertemporal elasticity of substitution is small (i.e. τ = 0.25), the consumption smoothing motive dominates, and the current demand for money is relatively inelastic with respect to inflation, so the impact effects on the real money balances are weak. The results also highlight the critical role that the initial rate of return on infrastructure (rzo ) plays in determining short-run dynamics. When rzo takes a large value, two effects follow. First, higher investment in infrastructure brings in substantial revenue gains for the government, which has a favorable effect on the reduction of the fiscal 14
deficit, exerting a deflationary pull. The rate of inflation falls significantly, encouraging agents to save. Second, the diminishing return on infrastructure falls slowly when the stock of infrastructure capital accumulates, giving rise to a prolonged period of expansion, which, by contrast, discourages saving in the short run due to the consumption smoothing motive. The second effect counteracts the deflationary pull. Consequently, the quantitative changes in the demand for real money balances are much smaller on impact compared to the runs with rzo = 0.15.
4.3.
Pace of Infrastructure Financing
A quick cut in lump-sum transfer payments may be difficult or politically toxic, and policymakers are often averse to a high rate of inflation. An alternative solution for short-run inflation is to hasten the pace of infrastructure financing, which is easier to implement in practice, and can also achieve price stability. To model this scenario, I modify the infrastructure financing equation in Table 3 as follows R˙ = −f (Iz − δz Z), f > 1
(4.9)
Table 5 confirms the claim made earlier. Selling more reserves significantly lowers the rate of inflation, triggering a large increase in the demand for real money balances. While the one-sector model is a useful device for thinking about the intrinsic fundamentals that drive the outcome, it ignores the supply-side effects and focuses exclusively on issues related to the productivity of infrastructure capital, short-term inflation and the demand for real money stock. In contrast, the two-sector central model includes a nontradable sector, a labor-leisure choice, and sector-specific capital. These additions allow me to demonstrate the real exchange rate movement, changes in private investment, and the different dynamics for the tradable and nontradable sectors. But the basic principle remains: a rapid fiscal adjustment or speedy infrastructure financing anchors inflation expectations and stabilizes the prices, so that a surge in productive infrastructure investment will not exacerbate inflationary pressure, and can be disinflationary and expansionary even in the short run.
5.
Numerical Analysis of the Two-Sector Model
Armed with the above intuition, I now analyze the repercussions of a one-time, unanticipated, permanent increase in government infrastructure investment in the two-sector central model.
5.1.
Stationary Equilibrium
Examining long-run outcomes involves solving the following nonlinear system of equations, together with two production functions in both sectors ((2.1) and (2.2)): h1
E m
1/τ
ρ+χ = 1 + v1
h2 L1/φ s
E c(Pn )
1/τ =
w c(Pn ) 1 + v1
rT KT + rn Kn + wLs + T − (1 + v1 )E − (1 + v2 )Pk (In + IT ) − χm = 0 15
Dn (Pn , E) + bn (In + IT ) + bz Iz = Qn
Pz Iz + T − rR − v1 E − v2 Pk (In + IT ) − χm = 0
(5.1)
Table 6 shows a simulation of the equilibrium laid out in (5.1). The long-run effects of a 50% increase in infrastructure investment are significant and favorable. Productive public infrastructure investment greatly enhances efficiency and productivity in the private sector, giving rise to strong economic expansion and rapid growth without putting stress on the government budget. Consistent with the simpler setup, both the initial return on infrastructure and the intertemporal elasticity of substitution play important roles in determining long-run stationary outcomes. With a small value of rzo (i.e. rzo = 0.15, and net return is 5%), the return on infrastructure investment falls quickly when infrastructure capital accumulates, so the stimulative effects of higher public investment are significantly weakened. On the contrary, a large value of τ not only fosters private consumption and investment spending, but also increases the time spent working in response to the rising real wage. The overall expansion is quantitatively significant. Output increases by 11.33% instead of 7.62%, when τ = 025. More insights can be drawn from the two-sector framework. For instance, great elasticity of substitution between capital and labor in the nontradable sector (σ n = 1.5) strengthens the crowding-in effects of public infrastructure investment on private investment, so that the economy enjoys more consumption and leisure. When infrastructure investment mostly uses traded inputs (ζ = 0.4), it boosts the tradable sector, leaving the nontradable sector less affected. The overall efficiency gains are thus relatively small. The value of ζ also determines the longrun supply price of infrastructure capital.26 The smaller the ζ, the cheaper the infrastructure capital, therefore, less international reserves are needed to cover the cost of higher investment.
5.2.
Transitional Dynamics
Figure 2 plots the solution paths using the parameter calibration in Table 2. The dominant effect of a permanent increase in public infrastructure investment is the positive wealth effect, which raises the consumption for both traded and nontraded goods and reduces the hours worked, pushing up the real wage. The agent’s desire to consume more in response to the anticipated rise in productivity and efficiency results in an ex ante excess demand for nontraded goods. The relative price of nontradables has to rise to meet the demand. The capital account is closed, so the increase in aggregate demand cannot be reconciled by private capital inflows. A spike in the relative price of nontraded goods is not counterbalanced by the weak spot appreciation of the nominal exchange rate. The overall price level then rises immediately after the reform. The predictions of the simple model also match the numerical results here. The gradual fiscal adjustment as shown in Figure 2 fails to anchor ex ante inflation expectation, and excess demand in the nontradable sector aggravates inflationary pressure. Anticipating a higher rate of inflation, agents reduce their demand for real money 26
According to the specification of the model, in a stationary equilibrium, Pz =
16
1 . 1−ζ
balances ex post, further worsening inflation. As a result, the rate of inflation increases by four percentage points on impact and stays above the government’s target rate of 5% in the short and medium terms. The two-sector model highlights the asymmetric dynamics between the tradable and nontradable sectors over short-term horizons. The rise in the relative price of nontraded goods raises the real product wage in the tradable sector,27 causing it to release labor which is absorbed in the nontradable sector as the real product wage falls. The jump in employment in the nontradable sector shifts up the marginal product schedule for capital, spurring firms to invest more. The demand curve in the nontradable sector moves to the right, while the transfer of labor from tradable to nontradable sector shifts the supply curve to the left in the tradable sector, both of which pull in the same direction of an appreciation of the real exchange rate. Since real appreciation is in favor of the nontradable sector, the supply boom is concentrated there. By contrast, output shrinks in the tradable sector. The temporary contraction of tradable production outweighs expansion in the nontradable sector, and total output falls slightly in the short run. Effects on private investment depend on several factors. Real appreciation lowers the real supply price of capital in the nontradable sector and raises it in the tradable sector. Given the large share of imported capital goods in the production of private capital (small β), the real cost of capital falls significantly in the nontradable sector but rises a little in the tradable one. If these were the only factors at work, then total private investment would rise. However, the decrease in real money balances creates a liquidity shortage, which draws savings away from capital accumulation. Private investment decreases by 1.63% on impact, but quickly rebounds thereafter. Even though reserve financing does not immediately lead to a disinflationary outcome, it reduces the country’s dependence on the tradable sector and strengthens domestic demand. With a managed float exchange rate system, the path of the nominal exchange rate is not fully manipulated by the government, and is, instead, largely determined by basic market forces and agents’ expectations, which permit the exchange rate to fluctuate more freely, and pave the way for greater exchange rate flexibility in the future.
5.3.
Return on Infrastructure, Fiscal Adjustment and Financing Speed
In theory, productive infrastructure investment can foster growth and buoy the economy. The prerequisite for this beneficial effect is that the return on infrastructure is not extremely low. In addition, fiscal adjustment and financing speed matter a great deal for the path of inflation. 5.3.1.
Return on Infrastructure Investment
The Chinese policymakers have to be careful on how they carry out the stimulus plan, because the macroeconomic consequences of reserve financing of infrastructure investment are sensitive to the return on the investment. Pouring all the money into urban infrastructure projects that have adequate supply can lead to falling marginal return, 27 A rise in the relative price of nontraded goods (Pn ) can be seen from the solution path of the real exchange rate in Figure 2, which is the inverse of Pn . A rise in Pn implies a decrease in real exchange rate, and thus, a real appreciation.
17
and may even worsen the economic downturn. Depending on the productivity of public infrastructure capital, the negative wealth effect from rising government spending and selling international reserves could dominate the positive wealth effect brought by higher infrastructure investment, resulting in small or even negative effects on output. In addition, the quality of investment matters both quantitatively and qualitatively for long-term growth effects. Some projects in China were built in a very short period of time without going through a series of strict safety checks. Collapsing bridges, roads and dams has been a serious problem in China, which can also make government investment contractionary at longer horizons. Figure 3 plots the responses when infrastructure capital is weakly productive: rzo = 0.15 (red solid lines), and repeats the solution paths in Figure 2 (blue dot-dashed lines), for comparison. The expansionary effect on public investment hinges crucially on the return on infrastructure, which is an important factor not only for determining the long-run stimulative effect of infrastructure investment, but also for the short-run dynamics. A small initial return suggests that the diminishing return on infrastructure falls quickly when infrastructure capital builds up. It is more profitable to accumulate capital and labor in the early stages of reform when the marginal products of inputs increase significantly, inducing agents to work and accumulate capital in response to higher expected returns in the short run. Demand for capital and labor then rises more in the nontradable sector and falls less in the tradable sector compared to the baseline case, boosting private investment. The positive wealth effect generated by higher public infrastructure investment is thus greatly weakened: the initial increase in real consumption is merely 0.09% and the reduction of hours worked is by 0.03% only, according to the model calibration. The overall revenue gains from VATs are small, thus, lump-sum transfer payments have to be cut further in order to peg the long-term inflation rate at the government’s target rate. 5.3.2.
The Role of Fiscal Adjustment
Both models drive home the point that sluggish fiscal adjustment cannot stabilize prices by pinning down the rate of inflation, so the natural policy response is to rapidly adjust the lump-sum transfer payments. Figure 4 contrasts the solution paths of inflation, real money balances and lump-sum transfer payments from two cases: a rapid fiscal adjustment (red solid line) and sluggish fiscal adjustment (blue dot-dashed line). When the government reduces the lump-sum transfer payments to their long-run stationary levels in about fifteen years instead of thirty-five years, inflation in the tradable sector and the overall rate of inflation jump down immediately and continue to decrease. Anticipating lower future inflation, agents immediately start accumulating money. This causes a sharp decline in the price level despite a strong increase in aggregate demand. Well-anchored inflation expectations trigger large decreases in inflation ex post. The rate of inflation falls to 4.07%, and the demand for money rises to 9.31% at the time the reform starts. Even though the rate of inflation in the nontradable sector rises on impact, it is far outweighed by the long-run deflationary pull. A quick cut of government lumpsum transfer payments favorably affects the reduction of the fiscal deficit and strengthens the pull of long-run 18
fundamentals to deliver an immediate, large decline in inflation. Table 7 further compares initial responses when the speed of fiscal adjustment varies. A rapid reduction of government lump-sum transfer payments (α = 0.25) quickly reduces the fiscal deficit, and thus, significantly lowers the rate of inflation; all entries for π(0) are less than 5%. A strong spot appreciation of the nominal exchange rate counteracts the rise in the relative price of nontraded goods. Not only inflation, but price levels also jump down significantly. Consistent with the analytical exercise, intertemporal elasticity of substitution (τ ) has important implications for how the public infrastructure investment affects the economy in the short run. The quantitative changes of the demand for real money are much less when τ takes a small value, because the current demand for money is less sensitive to its future return. 5.3.3.
Financing Speed
In reality, it is often difficult for the government to rapidly cut lump-sum transfer payments; sometimes, policymakers cannot withstand the pressure from the public and, eventually, are forced to slow down the reduction. The side effect of sluggish fiscal adjustment is the short-run high inflation that policymakers are opposed to. Alternatively, the government can accelerate the speed of infrastructure financing in order to tame inflation. By setting f = 1.35, the government sells more reserves than are needed to cover the cost of infrastructure investment each period. Instead of spending 55% of the nation’s total international reserves throughout the reform, the government could sell an additional 19%, which would significantly lower the rate of currency depreciation.28 Figure 5 plots the solution paths from the speedy financing scenario (red solid line), and from the baseline model (blue dot-dashed line). The overall rate of inflation falls considerably at time t = 0 and remains subdued thereafter, lowering the opportunity cost of holding money. The immediate increase in the demand for real money balances is more than 25%. Previous simulations were created under the assumption that the government’s long-run target rate of inflation was set at the same level as the initial rate. I relax this assumption by setting the long-run inflation target at 3%. Table 8 shows that a lower long-run inflation target positively affects the ex ante inflation expectation. Expected inflation, though not dependent of the inflation target, is certainly anchored by the target, leading to even lower inflation ex post. Both the speed of the fiscal adjustment and speed of financing can effectively combat short-run inflation, but each works through different channels. A quick cut in lump-sum transfer payments strengthens the favorable effect of higher infrastructure investment on the fiscal deficit, and ultimately, achieves price stability. Rapid financing fights short-run inflation by sufficiently lowering the rate of currency depreciation, so that the sharp decrease in the 28
Even after additional reserve sales, China still holds substantial amount of international reserves, about 25% of the nation’s GDP, much more than the optimal reserve level suggested by Ben-Bassat (1980), Obstfeld et al. (2010), Jeanne & Ranci´ere (2011) and many others. Appendix B has extensive discussions on the potential consequences and implications of Chinese reserve sales.
19
rate of currency depreciation counterbalances the inflationary pressure that stems from the ex ante excess demand for nontraded goods. The central insight from the analytical model carries over to the two-sector complex model.
5.4.
Some Robustness Checks
While the parameter calibration in the benchmark case represents a plausible description of the Chinese economy, the results are dependent upon this calibration. Thus, some alternative parameter values are considered here to prove the robustness of the results presented earlier. Figure 6 compares the transitional dynamics using different values for the cost share of nontraded inputs in the production of infrastructure (ζ). In the case where ζ = 0.4, some of the observations merit attention: • When infrastructure investment mostly uses tradable inputs (red solid line), both the short-run expansion in the nontradable sector and contraction in the tradable sector are much smaller when compared to the baseline model (blue dot-dashed line), producing small consumption and output responses to increases in government investment. • In response to the small efficiency gain, the desire to increase consumption is weak, so the rate of inflation in the nontradable sector is moderate; while the rate of currency depreciation falls on impact, lessening the short-run inflationary pressure. • The path of real money balance is volatile. The nominal money stock M is predetermined, the upward jump in the demand for real money at time t = 0 is due to the initial fall in the price level. Demand for money decreases later on the transition path when the rate of inflation rises. An important policy concern regarding public infrastructure investment is its effect on private investment. Will public investment crowd out private investment? Table 9 suggests that there are several factors influencing private investment: the share of the nontraded inputs in the production of capital (β), the q-elasticity of investment spending (Ω) and the intertemporal elasticity of substitution (τ ). A small β suggests that the real cost of capital falls sharply in the nontradable sector, but rises a little in the tradable sector when the relative price of nontraded goods increases, which strengthens the crowding-in effect of public investment on private investment. The incentive for immediate capital accumulation battles against the liquidity shortage, which discourages investment in the initial phase of the reform. The response pattern of private investment hinges on the value of intertemporal elasticity of substitution. According to the model specification, when τ is small (i.e. 0.25), the decrease in the demand for money significantly raises the marginal utility of money, causing the private agent to temporarily substitute away from investment toward the rebuilding of his real money stock. Thus, private investment is crowded out in the short run. Table 9 also illustrates the importance of Ω. The small value of Ω indicates that the cost of adjusting investment is high and that changes in investment are costly, which prevents firms from drastically varying their investment 20
spending. As the adjustment occurs over time, the duration of rise in the nontradable sector and fall in the tradable sector is also longer compared to the case when Ω = 8. These effects are quantitatively significant.
6.
Concluding Remarks
China’s economy continues to show signs of slowing, which calls for immediate economic stimulus, and infrastructure investment is ideal to counteract the economic downturn. However, by pumping up infrastructure spending, the country runs the risk of worsening inflation and local government debt. The primary contribution of this research is to propose a well-designed financing scheme for public infrastructure investment in China. The framework the paper developed accommodates two scenarios that are pertinent to the current Chinese economy, where excess infrastructure investment exists in some areas and deficient investment is common in others. Spending part of the nation’s enormous international reserves to ramp up infrastructure investment will release the funding pressure that most Chinese local governments have encountered in recent years. Productive infrastructure capital will boost domestic demand, reduce the country’s dependence on exports, and eventually, transform the country’s economy from being export-driven to becoming more dependent on domestic demand, enabling more sustainable, long-term growth. In the currency market, the government adjusts the path of the exchange rate to stabilize prices when infrastructure investment surges, and a managed float exchange rate regime is more compatible with the nation’s economic structure. In order to foster growth and maintain price stability, the following three factors are critical: return on infrastructure, speed of fiscal adjustment and speed of financing. In the past, government investment in infrastructure successfully helped the nation to sail through several regional and global financial crises, but most investments concentrated on urban areas, and very little money was spent on suburban and rural areas with the greatest infrastructure shortages. Continuous investment in big cities may potentially lead to an oversupply of infrastructure. Moreover, corruption, bad planning and poor quality construction can sharply reduce the return on public investment, hindering the beneficial effects of government investment at both short and long horizons. A sufficiently high rate of return on infrastructure is crucial for the effectiveness of infrastructure investment on energizing the sluggish economy. So long as the return on infrastructure is greater than the interest earnings on international reserves, higher public investment brings in substantial efficiency gains, which strengthen the stimulative effects of public infrastructure investment. In the early phase of the reform, the agent desires to increase consumption in response to the anticipated rise in productivity and efficiency, resulting in ex ante excess demand for nontraded goods. The relative price of nontradables rises, and the rate of inflation increases by four percentage points on impact. A rapid fiscal adjustment can be an effective way to combat this short-run inflation. Such a cut in government lump-sum transfer payments anchors the inflation expectation and quickly reduces the fiscal deficit, which triggers a sharp increase in the demand for real money balances. As a result, the rate of inflation falls to 4.07% on impact, and continues to 21
decrease. Unfortunately, it is generally difficult for the government to quickly reduce lump-sum transfer payments because a large portion of the population heavily depends on these government transfers. An alternative solution for short-run inflation is to speed up the pace of infrastructure financing. By selling 19% extra reserves, the government could sufficiently lower the rate of currency depreciation, so that the overall rate of inflation decreases in the short-run and remains below the government’s target level. The government has to carry out the stimulus plan carefully and effectively. Results have shown a risk of short-run inflation if fiscal adjustment or financing are done slowly, and a possibility of long-run contraction if infrastructure capital is unproductive. An interesting extension would be to estimate the maximum level of reserves the Chinese government could sell to pay for its fiscal stimulus without putting any risks to the nation’s economy under relevant scenarios, and at the same time, the government could still be able to buffer external shocks using the reserves that have been retained.
Acknowledgements This paper is based on chapter two of my Ph.D. thesis written at Indiana University. I am especially grateful to Edward Buffie for constant advice and encouragement. I also wish to thank Robert Becker, Volodymyr Lugovskyy, and audiences at Eastern Economics Association Conference for helpful comments. The participants of several seminars at Indiana University also made useful suggestions.
22
Appendix A.
Solution Technique
The main solution procedure was discussed in section 2 of the text. In this appendix, I fill in the remaining steps needed to obtain the general solution for the two-sector central model.
Appendix A.1. Solving for the Pseudo-Static Variant of the Model As discussed in subsection 2.5, one needs to solve the pseudo-static variant of the model in which the eight endogenous variables are treated as exogenous variables.29 Making use of (2.1) to (2.5), plus the two market-clearing conditions: (2.27) and (2.28), routine manipulations yield " nP Q θL P˙n 1 a1 Ls φ/τ IT In n n = −δ + γ E˙ + βPk 1 + v I˙n + βPk 1 + v Pn JPn Qn E a1 Ln + a3 LT − Ls φ Kn KT 2 na L φ θ η v I In I 2 s n n L −δ I˙T + −1 Pn Qn Z˙ + βPk − δ − βPk v −δ − a1 Ln + a3 LT − Ls φ Z 2 Kn Kn Kn 2 n θL v I I IT a3 LT − Ls φ T T n P n Qn rn − n rn K˙ n + βPk − δ − βPk v −δ + θL θk a3 LT + a1 Ln − Ls φ 2 KT KT KT KT # a1 LT K˙ T (A.1) a3 LT + a1 Ln − Ls φ n where J = θL
a2 a3 LT −Ls φ(a2 +a1 τ −1 γ) τ a3 LT +a1 Ln −Ls φ
n n n n n n n + ( + γ) D Qn , a1 = θL (σLL + σkk − 2σ ) < 0, a2 = σ − σkk > 0,
T (σ T + σ T − 2σ T ) < 0, a = σ T − σ T > 0, β = a3 = θL 4 LL kk kk
b n Pn Pk .
is the compensated own-price elasticity
of demand for nontraded goods; σ i is the Allen partial elasticity of substitution in sector i (Uzawa (1962)). A circumflex denotes the percentage change in a variable (ˆ x = dx/x). (A.1) is very intuitive. It states that Pn rises when higher consumption and investment spendings strengthen demand, and falls when infrastructure accumulation enhances supply. The capital accumulation in the nontradable sector increases supply and leads to a decrease in Pn , while the capital accumulation in the tradable sector has the opposite effect on Pn . Using the above expression for
P˙n Pn ,
the solutions for w, Ln , LT , rn , rT can be written as
τ −1 τ −1 φLs /τ + f1 E( τ −1 τ γφLs + a2 Ln ) ˆ τ γφLs + a2 Ln τ γφLs + a2 Ln E− f4 In Iˆn − a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs τ −1 τ −1 ( γφL + a L )f K + L f K ( γφL + a L s 2 n 2 n n ˆ 3 T s 2 n ) + LT ˆ τ f5 IT IˆT − τ Kn − KT − Zˆ a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs f6 Z( τ −1 τ γφLs + a2 Ln ) + η(a2 Ln + a4 LT ) (A.2) a1 Ln + a3 LT − φLs
w ˆ = −
29 There exists a set of exogenous variables that the private agent views as parametric but which depend indirectly on the endogenous variables through economywide interactions. Because of this, one needs to solve the economy’s dynamics and the private agent’s intertemporal optimization problem jointly in a consistent manner.
23
ˆn = L
ˆT L
rˆn
f1 E(a2 a3 LT − φLs (a2 + a1 τ −1 a2 a3 LT − φLs (a2 + a1 τ −1 τ γ)) − a1 φLs /τ ˆ τ γ) E+ f4 In Iˆn + a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs a2 a3 LT − φLs (a2 + a1 τ −1 a3 LT − φLs + f2 Kn (a2 a3 LT − φLs (a2 + a1 τ −1 τ γ) τ γ) f5 IT IˆT + a1 Ln + a3 LT − Ls φ a1 Ln + a3 LT − Ls φ τ −1 KT f3 (a2 a3 LT − φLs (a2 + a1 τ γ)) − a1 LT ˆ f6 ZφLs (a2 + a1 τ −1 τ γ) ˆ ˆ Kn + KT − Z − a1 Ln + a3 LT − Ls φ a1 Ln + a3 LT − Ls φ a2 Ls φη − f6 Za2 a3 LT (A.3) a1 Ln + a3 LT − φLs
a3 φLs /τ + a3 f1 E( τ −1 a1 Ln − Ls φ − a3 f3 KT ( τ −1 τ γφLs + a2 Ln ) ˆ τ γφLs + a2 Ln ) ˆ E+ KT a1 Ln + a3 LT − Ls φ a1 Ln + a3 LT − Ls φ τ −1 τ −1 a3 f2 Kn τ −1 τ γφLs + a2 Ln ˆ τ γφLs + a2 Ln ˆ τ γφLs −a3 f5 IT IT − a3 f4 In In − a1 Ln + a3 LT − Ls φ a1 Ln + a3 LT − φLs a1 Ln + a3 LT − Ls φ τ −1 a4 Ls φη + a3 f6 Z( τ γφLs + a2 Ln ) ˆ a3 Ln + a3 f2 Kn a2 Ln ˆ + Kn − Z (A.4) a1 Ln + a3 LT − φLs a1 Ln + a3 LT − Ls φ τ −1 n θL φLs /τ f1 E f2 Kn n n τ γφLs + a2 Ln ˆ ˆ 1 + θ 1 + θL = + E + K n L n a L + a L − φL n θkn a1 Ln + a3 LT − φLs θK θ 1 n 3 T s k n τ −1 n θL θL Ln LT f3 KT τ γφLs + a2 Ln + n + n + 1 a1 Ln + a3 LT − φLs θk a1 Ln + a3 LT − Ls φ θk a1 Ln + a3 LT − φLs θkn ! τ −1 τ −1 f4 In f6 Z n n n τ γφLs + a2 Ln τ γφLs + a2 Ln ˆ ˆ +θL 1 + θL KT + n 1 + θL In + a1 Ln + a3 LT − φLs θk a1 Ln + a3 LT − φLs θkn τ −1 τ −1 a2 Ln + a4 LT η n n τ γφLs + a2 Ln τ γφLs + a2 Ln ˆ Z + θL + n 1 + θL a1 Ln + a3 LT − φLs θk a1 Ln + a3 LT − Ls φ a1 Ln + a3 LT − φLs f5 IT ˆ +1 IT (A.5) θkn = −
T L + f K ( τ −1 γφL + a L ) T T φL /τ + f E( τ −1 γφL + a L ) θL θL θL s 1 s 2 n ˆ n 2 n τ s 2 n ˆ τ ˆ E + K + K n T T a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs θkT θkT θk τ −1 τ −1 T LT + f3 KT ( τ γφLs + a2 Ln ) θL a2 Ln + a4 LT τ γφLs + a2 Ln + T f4 In Iˆn + a1 Ln + a3 LT − Ls φ a L + a L − φL a L θk 1 n 3 T s 1 n + a3 LT − Ls φ τ −1 T θT τ −1 η T τ γφLs + a2 Ln τ γφLs + a2 Ln ˆ + θL θL +1 T + L f Z Z f5 IT IˆT (A.6) 6 T T θk θk a1 Ln + a3 LT − φLs θk a1 Ln + a3 LT − Ls φ n θL θn a1 φLs /τ a3 LT −φLs Pn Qn 1 1 n where f1 = JPn Qn γ + θL E a1 Ln +a3 LT −φLs , f2 = − JPn Qn rn + θn rn a1 Ln +a3 LT −φLs , f3 = J1 KLT k η a2 φLs a1 LT 1 n a1 Ln +a3 LT −φLs , f4 = f5 = JPn Qn βPK , f6 = JZ θL a1 Ln +a3 LT −φLs − 1 .
rˆT
=
Appendix A.2. Solving for the Transitional Dynamics Once the solutions for the pseudo-static variant of the model are obtained, the system of differential equations can be solved using the first order conditions from section 2. In order to get equations (2.33) and (2.34), differentiate equation (2.29) with respect to time, and make use of equations (A.1) to (A.6). g2 g3 g4 g5 g6 r E˙ = K˙ n + K˙T + I˙n + I˙T + Z˙ + R˙ g1 g1 g1 g1 g1 g1 24
(A.7)
where n θL θT φLs /τ rn φLs /τ rT w φLs /τ Ls − KT L + n θk a1 Ln + a3 LT − φLs E a1 Ln + a3 LT − φLs E θkT a1 Ln + a3 LT − φLs E n θT (a2 Ln + (τ − 1)φγLs /τ ) φLs /τ Kn θL w φLs + φLs − f1 n +w + 1 rn + KT L τE a1 Ln + a3 LT − φLs E θk a1 Ln + a3 LT − φLs θkT a2 Ln + (τ − 1)φγLs /τ τ −1 a2 Ln + (τ − 1)φγLs /τ rT − Ls w−w φγLs − βPk In + IT + a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs τ v(In /Kn − δ)2 Kn v(IT /KT − δ)2 KT a2 Ln + (τ − 1)φγLs /τ − φLs w − bz Iz Pn + 2 2 a1 Ln + a3 LT − φLs
g1 = 1 − Kn
g2 = KT
T n θL θL Ln rT Ln rn Ln w + K − Ls n n T θk a1 Ln + a3 LT − φLs Kn a1 Ln + a3 LT − φLs Kn θk a1 Ln + a3 LT − φLs Kn
1 w v(In /Kn − δ)2 Ln Ln − φLs − Pk + rn + Pk a1 Ln + a3 LT − φLs Kn a1 Ln + a3 LT − φLs Kn 2 n θT Kn θL (a2 Ln + (τ − 1)φγLs /τ ) τ −1 In + f2 n + 1 rn − w φγLs + KT L rT v(In /Kn − δ) Kn θk a1 Ln + a3 LT − φLs τ θkT v(In /Kn − δ)2 Kn v(IT /KT − δ)2 KT a2 Ln + (τ − 1)φγLs /τ − β In + IT + + Pk − φLs w a1 Ln + a3 LT − φLs 2 2 a2 Ln + (τ − 1)φγLs /τ a2 Ln + (τ − 1)φγLs /τ − Ls w − bz Iz Pn a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs
−φLs w
T n θL θL LT rT LT rn v(IT /KT − δ)2 + r + K − P − Ls n T k n θk a1 Ln + a3 LT − φLs KT 2 θkT a1 Ln + a3 LT − φLs KT LT IT Kn w 1 LT − φLs w + Pk v(IT /KT − δ) + f3 n rn a1 Ln + a3 LT − φLs KT a1 Ln + a3 LT − φLs KT KT θk n T θL (a2 Ln + (τ − 1)φγLs /τ ) θ a2 Ln + (τ − 1)φγLs /τ τ −1 wφγLs − Ls w + 1 + KT L rT − T a1 Ln + a3 LT − φLs τ θk a1 Ln + a3 LT − φLs a2 Ln + (τ − 1)φγLs /τ a2 Ln + (τ − 1)φγLs /τ v(In /Kn − δ)2 Kn − φLs w − bz Iz Pn − βPk In + a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs 2 2 v(IT /KT − δ) KT +IT + 2
g3 = KT
n (a L + (τ − 1)φγL /τ ) θL θT a2 Ln + (τ − 1)φγLs /τ τ −1 2 n s = f4 + 1 rn + KT L rT − w φγLs T a1 Ln + a3 LT − φLs τ θk a1 Ln + a3 LT − φLs a2 Ln + (τ − 1)φγLs /τ a2 Ln + (τ − 1)φγLs /τ In −Ls w − φLs w − bz Iz Pn − Pk 1 + v −δ a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs Kn v(IT /KT − δ)2 KT −βPk In + IT + + 2
g4
Kn θkn
n (a L + (τ − 1)φγL /τ ) θL θT a2 Ln + (τ − 1)φγLs /τ τ −1 2 n s φγLs = f5 + 1 rn + KT L rT − w T a1 Ln + a3 LT − φLs τ θk a1 Ln + a3 LT − φLs a2 Ln + (τ − 1)φγLs /τ a2 Ln + (τ − 1)φγLs /τ v(In /Kn − δ)2 Kn −Ls w − φLs w − βPk In + a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs 2 2 v(IT /KT − δ) KT IT +IT + − bz Iz Pn − Pk 1 + v −δ 2 KT 25
g5
Kn θkn
g6
n (a L + a L ) θL a2 Ln + a4 LT rT rn η η w 2 n 4 T T = KT T 1 + θL + Kn n 1 + − Pz f δz − Ls a1 Ln + a3 LT − φLs Z θk a1 Ln + a3 LT − φLs Z Z θk T θ (a2 Ln + a4 LT )η (a2 Ln + a4 LT )η 1 a2 Ln + (τ − 1)φγLs /τ Kn − φLs w + KT L rT + n T a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs Z a1 Ln + a3 LT − φLs θk θk n θL (a2 Ln + (τ − 1)φγLs /τ ) a2 Ln + (τ − 1)φγLs /τ τ −1 + 1 rn − Ls w−w φγLs − φLs w a1 Ln + a3 LT − φLs a1 Ln + a3 LT − φLs τ a2 Ln + (τ − 1)φγLs /τ v(In /Kn − δ)2 Kn v(IT /KT − δ)2 KT − βPk In + IT + − bz Iz Pn f6 + a1 Ln + a3 LT − φLs 2 2 The above equation, together with (2.30), (2.31) and (2.32), are used jointly to solve for the expressions for I˙n
and I˙T separately as shown in section 2 ((2.33) and (2.34)). Five negative eigenvalues are necessary for the system to converge to a stationary equilibrium.30
Appendix B.
Potential Consequences and Implications of Reserve Sales
Using reserves to finance a surge in public infrastructure investment spurs growth without putting pressure on local government budget, but at the cost of spending more than 50% of the country’s international reserves. One of the biggest concerns for reserve sales is its potential consequences on the global economy, especially, the Chinese and the US economies. Several factors have contributed to the accumulation of Chinese international reserves. Among those factors, continuous trade surplus and current account surplus are the main contributors. There is no empirical evidence on what would have happened if the Chinese government substantially sells its U.S. assets, and thus, a simple thought experiment is conducted here to assess the implications of reserve sales. Suppose China sells its U.S. assets, for example, U.S. Treasury Bonds. Those bonds would be sold to other investors, who would require higher interest rates. Rising interest rates may discourage private investment in the US. This may not be a concern for the Chinese government, but, if China, one of the biggest holders of U.S. Treasury Bonds, reduces its holdings, it would cause the overall foreign demand for U.S. assets to fall, this would devaluate the dollar-dominated assets, and result in a depreciation of the dollar. Thus, most of China’s existing U.S. assets would devaluate as well, and China’s trade surplus would fall. By contrast, the depreciation of the US dollar would narrow U.S. trade deficit with China, bolstering the US economy. On the other hand, reserves are spent on productive infrastructure investment, which strengthens domestic demand, and reduces the country’s dependence on exports. A reduction of Chinese trade surplus will not hurt China, because the economy is now mostly driven by domestic demand. Problems may exist if and only if the Chinese government suddenly and substantially sells its U.S. assets, which could potentially trigger a general financial panic, and induce other foreign holders to sell their U.S. assets. A rapid sell-off of foreign exchange reserves would not be in China’s economic interests, but modest and gradual reduction of its U.S. assets would have minor or even negligible effects on the world economy. For instance, from August 2004 to September 2007, 30 An economically meaningful saddlepoint solution requires that the number of state variables equals the number of negative eigenvalues, otherwise, the equilibrium is either indeterminate or out of reach.
26
Japan gradually reduced its U.S. Treasury Bonds holdings from $699.4 billion to $582.2 billion, this has little noticeable impact on both Japanese and the US economies. So long as the reduction is gradually carried out and phased in, a decline in Chinese trade surplus and a depreciation of the dollar could potentially be a win-win situation for both China and the US. After spending more than half of its international reserves, China will still hold a substantial amount of reserves, around $1.5 trillion, about 25% of the nation’s current GDP. In doing so, the Chinese economy will achieve a fine balance between growth and price stability, and for the US economy, a decrease in the trade deficit and a depreciation of the US dollar could generate an expansionary effect on its economy, boosting private consumption and investment. Historical experience shows that when the US dollar depreciated by about 40% in real terms and trade deficit declined continually in the late 1980s, the economic growth in the US was the strongest.
31
See Morrison & Labonte (2011) for empirical evidence and more discussions on this topic.
27
31
References Angeletos, G.-M., & Panousi, V. (2009). Revisiting the supply side effects of government spending. Journal of Monetary Economics, 56, 137–153. Aschauer, D. A. (1989). Is public expenditure productive? Journal of Monetary Economics, 23, 177–200. Aschauer, D. A. (2000). Public capital and economic growth: Issues of quantity, finance, and efficiency. Economic Development and Cultural Change, 48, 391–406. Barro, R. J., & Redlick, C. J. (2011). Macroeconomic effects from government purchases and taxes. The Quarterly Journal of Economics, 126, 51–102. Ben-Bassat, A. (1980). The optimal composition of foreign exchange reserves. Journal of International Economics, 10, 285 – 295. Blundell, R., Pashardes, P., & Weber, G. (1993). What do we learn about consumer demand patterns from micro data? American Economic Review, 83, 570–97. Buffie, E. F., Portillo, R., Zanna, L.-F., Pattillo, C. A., & Berg, A. (2012). Public Investment, Growth, and Debt Sustainability: Putting Together the Pieces. IMF Working Papers 12/144 International Monetary Fund. Canning, D., & Bennathan, E. (2000). The social rate of return on infrastructure investments. Policy Research Working Paper Series 2390 The World Bank. Chatterjee, S., Sakoulis, G., & Turnovsky, S. J. (2003). Unilateral capital transfers, public investment, and economic growth. European Economic Review, 47, 1077–1103. Chow, G. C. (1993). Capital formation and economic growth in china. The Quarterly Journal of Economics, 108, 809–42. Demurger, S. (2001). Infrastructure development and economic growth: An explanation for regional disparities in china? Journal of Comparative Economics, 29, 95–117. Garcia-Cicco, J., Pancrazi, R., & Uribe, M. (2010). Real business cycles in emerging countries?
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Economic Review, 100, 2510–31. Glomm, G., & Ravikumar, B. (1994). Public investment in infrastructure in a simple growth model. Journal of Economic Dynamics and Control, 18, 1173–1187. Griffin, J. M., & Gregory, P. R. (1976). An intercountry translog model of energy substitution responses. American Economic Review, 66, 845–57. 28
Guvenen, F. (2006). Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective. Journal of Monetary Economics, 53, 1451–1472. Hayashi, F. (1982). Tobin’s marginal q and average q: A neoclassical interpretation. Econometrica, 50, 213–24. Isaksson, A. (2010). Public capital, infrastructure and industrial development. United Nations Industrial Development Organization. Jeanne, O., & Ranci´ere, R. (2011). The optimal level of international reserves for emerging market countries: A new formula and some applications. The Economic Journal, 121, 905–30. Lin, S. (2008). China’s value-added tax reform, capital accumulation, and welfare implications. China Economic Review, 19, 197–214. Morrison, W. M., & Labonte, M. (2011). China’s Holdings of U.S. Securities: Implications for the U.S. Economy. CRS Report for Congress RL34314 Congressional Reserve Service (CRS). Obstfeld, M., Shambaugh, J. C., & Taylor, A. M. (2010). Financial stability, the trilemma, and international reserves. American Economic Journal: Macroeconomics, 2, 57–94. Reinhart, C., Ogaki, M., & Ostry, J. (1996). Saving behavior in low- and middle-income developing countries: A comparison. IMF Staff Papers, 43, 38–71. Rioja, F. K. (2003). Filling potholes: macroeconomic effects of maintenance versus new investments in public infrastructure. Journal of Public Economics, 87, 2281–2304. Sims, C. (1996). Advances in Econometrics: Volume 2: Sixth World Congress. Econometric Society Monographs. Cambridge University Press. Spear, A., Nailer, C., & He, S. (1997). China infrastructure: sectoral plans, reforms and financing. East Asia Analytical Unit, Department of Foreign Affairs and Trade, Australia. Su, M., & Zhao, Q. (2006). The Fiscal Framework and Urban Infrastructure Finance in China. World Bank, Transport and Urban Development Department, Urban Unit. Summers, L. H. (1981). Taxation and corporate investment: A q-theory approach. Brookings Papers on Economic Activity, 12, 67–140. Uzawa, H. (1962). Production function with constant elasticities of substitution. The Review of Economic Studies, 29, 291–99.
29
30
China 2,631 53.5 85 98 38.4 73 47
U.S. 12,914 67.4 94 100 78.2 106 802
South Korea 8,900 78.5 97 100 81.5 109 355
Malaysia 3,614 N/A 99 100 61 127 350
South Africa 4,532 N/A 79 99 20.9 127 162
Data come from World Development Indicators (the World Bank). N/A implies that no data is available for this particular infrastructure service. Years vary due to the availability of data.
Infrastructure services Electric power consumption (kwh per capita, 2009) Paved roads (% of total roads, 2008) Improved water source, rural (% of rural population with access, 2010) Improved water source, urban (% of urban population with access, 2010) Internet users (per 100 people, 2011) Mobile cellular subscriptions (per 100 people, 2011) Motor vehicles (per 1000 people, 2009)
Table 1: Comparison of key infrastructure supply
Table 2: Model Calibration Preference Consumption share of the nontraded good Elasticity of substitution between traded and nontraded consumption goods Time preference rate Frisch elasticity of labor supply Intertemporal elasticity of substitution Technology Share of nontraded inputs in the production of capital Share of nontraded inputs in the production of infrastructure Q-elasticity of investment spending Cost share of capital in the nontradable sector Cost share of capital in the tradable sector Rate of depreciation for private capital Rate of depreciation for infrastructure capital Elasticity of substitution between labor and capital in sector i Fiscal Parameter Initial ratio of foreign exchange reserves to GDP Initial ratio of infrastructure investment to GDP Initial gross rate of return on infrastructure investment Net rate of return on infrastructure investment Ratio of money balance to consumption Inflation Rate World interest rate Consumption value-added tax rate Investment value-added tax rate Speed of lump-sum transfer adjustment Speed of infrastructure financing
Parameter γ ξ ρ φ τ
Calibration 0.4 0.5 0.1 0.3 0.25
β ζ Ω θkn θkT δ δz σi
0.35 0.8 3 0.45 0.35 0.06 0.1 0.5
R Y Pz Iz Y rzo rzo − δz
0.45 0.05 0.35 0.25 0.1 5% 3% 15% 15% 0.09 1
µ π r v1 v2 α f
Table 3: The One-Sector Model. (A)
(B)
(C)
Private agent’s optimization problem R ∞ 1−1/τ 1−1/τ Preference U = 0 [ C1−1/τ + h m1−1/τ ]e−ρt dt Budget constraint m ˙ = aZ η + T − (1 + v)C − χm Dynamic system Rate of infrastructure accumulation Z˙ = Iz − δz Z Lump-sum transfer adjustment T˙ = α(T ∗ − T ), α > 0 Infrastructure financing R˙ = −(Iz − δz Z) Government flow budget constraint m ˙ = δz Z + T − rR − χm − vC Consumption function and price dynamics Consumption C = aZ η − δz Z + rR −1/τ Price Dynamics χ = − τ1C (rz − δz − r)(Iz − δz Z) + (1 + v)h m −ρ C −1/τ
v = tax on consumption m = real money balance aZ η = total output, which is a function of infrastructure stock only. T ∗ = rR∗ + vC ∗ + χ∗ m∗ − Iz∗ , long-run stationary level of lump-sum transfer payments.
31
Table 4: Impact effects on demand for real money balances, the price level, and the rate of inflation when the speed of fiscal adjustment and the net return on infrastructure investment vary. α 0.25 0.09 0.07
rzo = 0.35 m(0) 10.22 28.51 83.01 1.74 2.97 2.07 0.37 -2.01 -20.61
e(0) -10.22 -28.51 -83.01 -1.74 -2.97 -2.07 -0.37 2.01 20.61
χ(0) -2.12 -2.06 -1.41 1.72 3 4.27 2.5 4.48 7.71
rzo = 0.15 m(0) 11.92 32.21 94.81 1.3 0.22 -6.62 -0.41 -6.03 -35.03
e(0) -11.92 -32.21 -94.81 -1.3 -0.22 6.62 0.41 6.03 35.03
χ(0) -0.65 -1.52 -1.44 4.04 4.83 5.84 5.04 6.88 11.44
τ 0.25 0.5 1.2 0.25 0.5 1.2 0.25 0.5 1.2
Note: All entires are percentage deviations from their initial values, except the rate of inflation, which is actual percentage points.
Table 5: Impact effects on demand for real money balances and the rate of inflation with fast financing f 1.35
m(0) 17.73 38.36 36.4
e(0) -17.73 -38.36 -36.4
χ(0) -4.47 -2.04 1.11
τ 0.25 0.5 1.2
Note: All parameter values used for the simulations here are the baseline values, except f .
32
33
m c(Pn )
4.66 1.01 8.56 4.72 1.47 4.71 5.46 5.68 3.66 8.47
E c(Pn )
4.66 1.01 8.56 4.72 1.47 4.71 5.46 5.68 3.66 4.66
Kn 5.28 4.37 8.66 3.99 1.14 5.16 13.24 6.64 4.42 5.28
KT 2.82 1.81 6.55 3.47 1.43 3.1 4.07 12.56 1.87 2.82
I 4 3.04 7.57 3.81 1.3 4.14 8.48 9.71 3.09 4
Ln -0.56 1.83 2.63 -1.77 -0.78 -0.86 -4.71 0.64 -1.37 -0.56
LT -2.88 -0.67 0.64 -2.27 -0.49 -2.8 -1.74 -5.38 -3.78 -2.88
Ls -2 0.28 1.4 -2 -0.6 -2.02 -2.87 -3.09 -2.87 -2
Qn 9.49 6.14 13 8.15 2.47 9.25 10.7 10.85 8.59 9.49
QT 6.32 3.28 10.18 6.99 2.57 6.48 7.59 8.07 5.34 6.32
Y 7.62 4.46 11.33 7.68 2.53 7.64 8.85 9.21 6.67 7.62 -2.56 -3.06 -1.99 -2.59 -0.88 -2.56 -2.38 -2.32 -2.71 -2.73
T Yo
-24.77 -24.9 -24.77 -24.77 -8.32 -24.77 -24.74 -24.8 -24.77 -24.77
R Yo
Pn -1.13 -0.49 -1.13 -1.13 -0.38 -1.16 -1.3 -0.99 -1.13 -1.13
Note: the baseline case is using the calibrated parameter values in Table 2. All entries below the 2nd row report the long-run stationary outcomes when one parameter m value deviates from the baseline calibration. c(PEn ) represents real consumption; c(P is real money stock; YTo is the ratio of lump-sum transfer payments to initial n) R GDP; Yo is the ratio of foreign exchange reserves to initial GDP. All numbers are percentage deviations from their initial values.
Parameter Values Baseline rzo = 0.15 τ = 1.2 γ = 0.6 ζ = 0.4 β = 0.55 σ n = 1.5 σ T = 1.5 φ=1 χ∗ = 3%
Table 6: The long-run stationary outcomes.
Table 7: Impact effects on demand for real money balances, the price level, and the rate of inflation when the speed of fiscal adjustment varies. α 0.09 0.25
M P (0)
-0.04 -1.81 -11.73 9.31 23.32 57.72
e(0) -2.61 -0.72 9.54 -12.2 -26.5 -61.65
P˜n (0) 4.07 5.79 15.82 -5.52 -19.99 -55.37
P (0) 0.06 1.88 12.05 -9.53 -23.9 -59.13
χ(0) 5.61 5.88 6.93 0.91 0.08 0.52
πn (0) 13.51 13.6 14.42 8.81 7.8 8.01
π(0) 8.77 8.97 9.93 4.07 3.17 3.52
τ 0.25 0.5 1.2 0.25 0.5 1.2
Note: P˜n is the nominal price level in the nontradable sector, P is the consumer price index, and πn is the rate of inflation in the nontradable sector.
Table 8: Impact effects on demand for real money balances, the price level, and the rate of inflation in the fast financing scenario. χ∗ 0.05 0.03
M P (0)
e(0) -29.27 -35.13 -58.65 -31.96 -38.57 -69.01
25.2 31.19 54.14 27.81 34.52 64.21
P˜n (0) -21.05 -27.53 -51.26 -23.74 -30.97 -61.63
P (0) -25.98 -32.09 -55.69 -28.68 -35.53 -66.05
χ(0) -3.11 -0.75 0.97 -3.63 -1.19 0.42
πn (0) 6.34 8.08 9.57 5.82 7.64 9.03
π(0) 0.67 2.78 4.41 0.15 2.34 3.87
τ 0.25 0.5 1.2 0.25 0.5 1.2
Note: Parameter values are the same as the baseline case except f = 1.35 and χ∗ = 3%.
Table 9: Impact effects on private investment. Ω 3 8
β = 0.35 In 10.15 12.6 15.92 19.69 22.45 26.98
IT -12.55 -9.55 -5.64 -22.9 -19.06 -13.28
I -1.63 1.11 4.74 -2.41 0.91 6.09
β = 0.55 In 7.33 9.73 12.99 15.04 17.71 21.95
IT -14.18 -11.89 -8.92 -25.01 -22.69 -19.41
Note: All entries are percentage deviations from the initial values.
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I -3.27 -0.92 2.19 -4.69 -2.2 1.57
τ 0.25 0.5 1.2 0.25 0.5 1.2
(b) China’s foreign exchange reserves.
(a) The Inflation Rate in China.
Figure 1: The inflation rate and the accumulation of foreign exchange reserves in China. Inflation rate is the annual change on consumer price index. Source: The National Bureau of Statistics of China. Chinese foreign exchange reserves include foreign exchange, reserve position in the IMF and SDRs at end-period. Source: IMF, International Financial Statistics.
Figure 2: Transitional Dynamics for the baseline model. Solid lines: percentage deviations from initial values; dashed lines: percentage deviations across steady states. The solution paths for inflation rates are expressed in actual percentage points. 35
Figure 2 Continue
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Figure 3: Solution paths in an economy with weakly productive infrastructure: rzo = 0.15 (red solid lines) and corresponding percentage deviations across steady states (red dashed horizontal lines). For comparison purpose, responses from the baseline model (blue dot-dashed lines) and corresponding percentage deviations across steady states (blue dot-dashed horizontal lines) are also presented. 37
Figure 4: Solution paths in an economy with quick fiscal adjustment: α = 0.25 (red solid lines) and corresponding percentage deviations across steady states (red dashed horizontal lines). For comparison purpose, responses from the baseline model (blue dot-dashed lines) and corresponding percentage deviations across steady states (blue dotdashed horizontal lines) are also presented.
Figure 5: Solution paths in an economy with fast financing: f = 1.35 (red solid lines) and corresponding percentage deviations across steady states (red dashed horizontal lines). For comparison purpose, responses from the baseline model (blue dot-dashed lines) and corresponding percentage deviations across steady states (blue dotdashed horizontal lines) are also presented.
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Figure 6: Solution paths in an economy with ζ = 0.4 (red solid lines) and corresponding percentage deviations across steady states (red dashed horizontal lines). For comparison purpose, responses from the baseline model (blue dot-dashed lines) and corresponding percentage deviations across steady states (blue dot-dashed horizontal lines) are also presented. 39
