Household Saving, Financial Constraints and the Current Account Surplus

Transcription

1 Household Saving, Financial Constraints and the Current Account Surplus Ay³e mrohoro lu Kai Zhao August 2017 Preliminary Abstract In this paper, we present a model economy that can account for the increase in the saving and investment rates as well the current account surplus in China since the early 1990s. We show that while both the corporate and household saving rates are high in China, the increase in the household saving rate is relatively more important for understanding the current account surplus. The decline in family insurance against old-age risks due to the one-child policy resulted in large increases in household saving. However, the increased household saving was prevented from being invested in domestic rms due to nancial frictions and therefore showed up as the current account surplus. In addition, we nd that the large-scale scal stimulus program announced by the Chinese government in 2008 was an important cause of the sharp decline in China's current account surplus in the following years as it implicitly relaxed the nancial constraints facing domestic rms and thus encouraged domestic investment. Department of Finance and Business Economics, Marshall School of Business, University of Southern California, Los Angeles, CA ayse@marshall.usc.edu Department of Economics, The University of Connecticut, Storrs, CT , United States. kai.zhao@uconn.edu 1

2 1 Introduction In 2007, the current account surplus in China reached 10% of GDP sparking debate about its impact on global imbalances in the world economy. Such a high current account surplus was particularly puzzling since this was a period of high growth rates, high return to capital, and high investment rates in China, all of which would point to a current account decit in a standard model. While there is no consensus on the determinants of China's current account balance in the academic literature, several studies provide useful insights. Song, Storesletten, and Zilibotti (2011, thereafter SSZ), argue that a period of transition where traditional rms (those mimicking the state-owned enterprises) shrink and entrepreneurial rms expand could lead to a current account surplus if nancial constraints limit the amount of funds allocated to entrepreneurial rms. In this framework, it is the rise in the corporate savings (and the decline in the external funds domestic corporations use) that lead to the current account surplus. Bacchetta, Benhima, and Kalantzis (2013) model the central bank as a Ramsey planner in an economy where the central bank has access to international capital markets but the private sector does not. When the central bank has a limited set of instruments and is not able to relax the credit constraints, the optimal policy is found to be lending to the rest of the world. Figure 1a displays the evolution of the gross national saving and investment rates and the current account balance since the 1990s. Note that while the saving and investment rates have tracked each other fairly well, the gap between the two rates widened after the early 2000s during which the saving rate increased faster than the investment rate. There has also been marked dierences in the time series behavior of corporate, household, and government saving rates. Using the ow of funds data from the NBS of China, we decompose China's gross saving into three components: household, corporate, and government. As shown in Figure 1b, Chinese household saving has been an important contributor to national savings. Household savings as a percentage of GDP increased from an average of 20% in the 1990s, to 26% in The Chinese corporate saving has also been high and rising during this time period. It was approximately 15% of GDP in the 1990s, and increased to 21% in However, during the period of 2004 to 2008 where the current account surplus increased from 4% to 9%, the Chinese corporate saving was almost at (Figure 1b). In contrary, during this period the household saving increased from 20.8% of GDP to 23.6% of GDP, and the government saving as a share of GDP increased from 2.6% to 6.0%. 2 In an attempt to capture the rich dynamics behind the changes in the current account surplus, we propose a model that incorporates the saving behavior of households, corporations and the government. Our 1 Most of the research dealing with saving rates in China relies on ow of funds data to decompose gross saving between corporate, household and government. However, ow of funds data is subject to large revisions. Our decomposition is based on the most recent data, and it nds that household savings as a percentage of GDP increases from about 20% in the 1990s to 25.5% in It is also important to note that this is despite the fact that the household income as a share of GDP has been declining in this time period. Consequently, household saving rate as a percentage of household income has been increasing even at faster rates. Our nding is dierent from what Chamon and Prasad (2010) have documented in the earlier versions of the ow of funds data, that is, between 1993 and 2005 household savings as a percentage of GDP did not signicantly increase. 2 It is important to note that household savings as a share of GDP increased despite the fact that the household income as a share of GDP has been declining in this time period. Consequently, household saving rate (household savings as a percentage of household income) has been increasing even faster. 2

3 (a) Saving, Investment, and the CA (b) Decomposition of Gross Saving (as % of GDP) Note: the left vertical axis in panel (a) represents the current account (% of GDP), and the right vertical axis represents the gross saving and investment rates. The left vertical axis in panel (b) represents the decomposed saving rates, and the right vertical axis represents the current account (% of GDP). Data source: the World Bank, and the Flow of Funds data (NBS of China). Figure 1: Saving, Investment and the Current Account in China model consists of altruistic households as in Imrohoroglu and Zhao (2017) and rms that face borrowing constraints similar to SSZ. Households in this economy live at most up to 90 years. They face labor income risk during their working years, receive social security when retired and face health related shocks in old age. Parents and children pool their resources and maximize a joint objective function. Through intervivos transfers, parents insure their children against the labor income risk and children support their parents during retirement and insure them against health related shocks. Households in this economy save because of concerns about old-age risks and the decline in family insurance due to the one-child policy. The corporate sector is composed of rms that are owned by a fraction of households who have entrepreneurial skills. They are highly productive but face borrowing constraints. 3 We calibrate the borrowing constraints to match the average loan to asset ratio of the Chinese rms. Owners of these rms enjoy high returns due to high productivity while the rest of the households earn the return on bonds that are determined in a competitive banking sector which equals the rate of return on foreign bonds. Banks collect savings from workers and invest in loans to domestic rms and foreign bonds. Financial fractions restrict the amount of funds that can be allocated to the domestic rms. In addition, the government saves the excess tax revenues leading to government savings. Banks simply invest the dierence between domestic savings and domestic investment 3 As discussed in SSZ even the state owned enterprises in China nance about half of their investment through internal savings. In our framework, changes in the saving rate is not driven by the dierences between conventional versus entrepreneurial rms. Therefore, it is sucient to characterize the average rm in China as facing borrowing constraints. 3

4 in foreign funds which results in a current account surplus for the country. Our results indicate that inadequate insurance through government programs during old age and the change in demographics due to one-child policy plays an important role in the increase in the household saving rate especially after 2000 as more and more families with only one child enter the economy. This feature plays an important role in the rise of the national saving rate. We also nd that the increase in the productivity of capital and the changes in borrowing constraints, which are both taken exogenously, are capable of generating the increase and the uctuations observed in investment in China. In our benchmark results, we examine the time series path of savings, investment, and the current account until and after 2008 separately. This is because in the following years of 2009 and 2010, as documented in Bai, Hsieh, and Song (2016), China launched a large scal stimulus plan that was equivalent to 12% of GDP and was largely nanced by o-balance sheet companies. Our counterfactual experiment suggests that the current account surplus of China would have been substantially larger after 2008 if the Chinese government had not embarked on this scal stimulus. As argued previously, the Chinese corporate saving has also been high and rising during this time period, but the corporate sector is not very likely to be a major driver of the rise in China's current account surplus in the 2000s. This point can be further conrmed by comparing the saving and investment behaviors of the Chinese corporations. Figure 2a presents the aggregate savings of non-nancial Chinese corporations together with their investments. All throughout this period, the Chinese corporations invested more than they saved, suggesting that they have been net borrowers. In addition, while their demand for external funds declined substantially around the year of 1999, their usage of external funds (i.e. the dierence between investment and saving) has been rather stable if not increasing in the 2000s. This implies that the increase in the current account surplus in the 2000s must come from the increased savings from either households or the government. Therefore, we conclude that to understand the evolution of the current account surplus in China, we need to concentrate on the evolution of savings, especially household savings. 4 The ow of funds data also allows us to decompose China's gross investment into private investment (corporate and household), and government investment. As shown in Figure 2b, while private investment has been much higher than government investment since the 1990s, both of them (as a share of GDP) were fairly stable during the period of rising current account surplus (highlighted by the two vertical lines). This nding further motivates us to investigate the role of saving in shaping the rising current account surpluses. Figure 1b also displays the government saving as a share of GDP since the early 1990s. While the government saving has been relatively low, it has gone through signicant changes since the late 90s. In this paper, we also incorporate government saving in our analysis. 4 After studying the Chinese corporate savings using rm-level data, Bayoumi, Tong, and Wei (2010) made a similar point. 4

5 (a) Corporate Sector and the CA (b) Decomposition of Gross Investment (as % of GDP) Note: in panel (a), the Cor I and Cor S measure the investment and saving of non-nancial corporations. As the Chinese corporations received substantial government subsidies which are an important source of nancing, we also include government capital transfers into the measure of corporate saving. In panel (b), the left axis represents the investments, and the private investment is the sum of corporate and household investments. In both panels, the right vertical axis represents the current account. Data source: the Flow of Funds data from NBS of China and the World Bank. Figure 2: Investment and the Corporate Sector in China 5

6 2 The Model In this section, we present the benchmark model for our analysis of China's saving, investment and the current account. The model consists of altruistic households as in Imrohoroglu and Zhao (2017) and nancial constrained rms that share similar features to the entrepreneurial rms in SSZ (2011). 2.1 Households The economy is populated with altruistic agents who derive utility from their own lifetime consumption and from the felicity of their predecessors and descendants. The decision-making unit is the household consisting of a parent and children. Each period t, a generation of individuals is born. All children become parents at age T+1 and face mandatory retirement at age R. After retirement, individuals face random lives and can live up to 2T periods. Depending on survival, an individual's life overlaps with his parent's life in the rst T periods and with the life of his children in the last T periods. A household lasts T periods. A dynasty is a sequence of households that belong to the same family line. At age T +1, each child becomes a parent in the next-generation household of the dynasty. The size of the population evolves over time exogenously at the rate g t 1. At the steady state, the population growth rate satises g = n 1/T, where n is the fertility rate. Working age individuals supply labor exogenously. Labor income is comprised of a deterministic component ε j representing the age-eciency prole and a stochastic component, µ j, faced by individuals up to age T. Parents face a health risk, h, that necessitates long-term care (LTC) where h = 0 represents a healthy parent without LTC needs. When h = 1, the family needs to provide LTC services to the parent. We assume that the cost of LTC services consists of two parts: a goods cost m and a time cost ξ. Here, ξ represents the informal care that requires children's time. For working individuals, the LTC cost also includes their own forgone earnings. Labor income of a family is composed of the income of the children and the income of the father. Once retired, the father faces an uncertain lifespan where d = 1 indicates a father who is alive and d = 0 indicates a deceased father. If alive, a retired father receives social security income, SS j. All children in the household split the remaining assets (bequests) equally when they form new households at time T + 1. After-tax labor earnings, e j, of all household with age-j children is given by [wε j µ j (n ξh) + wε j+t (1 h)](1 τ ss τ e ) if j + T < R e j = (1) wε j µ j (n ξh)(1 τ ss τ e ) + dss if j + T > R. Families are assumed to have heterogeneous skills, denoted by z. In each cohort, a ω fraction of the population are with entrepreneurial skills and own the rms (z = 1), and the rest are workers (z = 0). Firm ownership is inherited from parents. These families operate the rms, supply their own labor in the rm 6

7 and employ workers that belong to the other families. All workers earn the same wage rate. In this framework, since parents care about the utility of their descendants, they save to insure them against the labor income risk, and since children are altruistic toward their parents, they support them during retirement and insure them against health related risks. In addition, parents leave voluntary bequests to their children. In families who own the rms, children invest the bequests back in the rm. 5 A key dierence between the two types of households is that worker households put their saving in a bank, and the rest of the households invest all their saving in their rm. The state of a household consists of age j; assets a; the realizations of the labor productivity shock µ; and the health h and mortality d states faced by the elderly, and the entrepreneurial skill z Worker Families Worker families with n children face the following budget constraint: a j+1 + nc sj + dc fj + mh = e j + a j [1 + rt d (1 τ k )] + κ (2) where rt d is the before-tax deposit interest rate, τ e is the labor income tax rate, τ ss is the payroll tax rate to nance the social security program, and τ k is the capital income tax rate. Here, κ is the government transfer, which consists of two components, i.e., κ = κ 1 e j + κ 2. The rst component (κ 1 e j ) is proportional to household earnings and is used to balance the government budget constraint. The second component ( κ 2 ) guarantees a consumption oor for the most destitute, which we will discuss further later Entrepreneurial Families Families who own the rms face a dierent budget constraint since they earn prots from their own rm. The budget constraint facing an entrepreneurial family with own capital a j and loan l j is: a j+1 + nc sj + dc fj + mh = e j + a j + (1 τ k )[ρ t (a j + l j ) r t l j ]a j + κ (3) Here ρ t is the net return to capital of the rm, and r l t is the lending interest rate on bank loans, which is higher than the deposit rate. The dierence between the lending and deposit rates represents the iceberg cost of lending to rms. The maximization problem of households is to choose a sequence of consumption and asset holdings given the set of prices and policy parameters. Let V j (x) denote the maximized value of expected, discounted utility of a age-j household with the state vector x = (a, µ, z, h, d). The household's maximization problem is given by: V j (x) = max c s,c f,a [nu(c s) + du(c f )] + βe[ṽj+1(x )] (4) 5 In this framework we do not have to be concerned about opportunistic behavior of the children as in the SSZ model. 6 All children are born at the same time and face identical labor income shocks. The entrepreneurial skills of a household do not change over generations. 7

8 subject to the budget constraint 2 if z = 0, and to the budget constraint 3 if z = 1, and a j 0, c s 0 and c f 0, where 2.2 Banks V Ṽ j+1 (x j+1 (x ) for j = 1, 2,..., T 1 ) = nv 1 (x ) for j = T Banks collect savings from workers and invest in loans to domestic rms and foreign bonds. The bonds yield a net return r t. In a competitive equilibrium of the open economy, the rate of return on domestic loans must equal the rate of return on foreign bonds, r t, which in turn must equal the deposit rate, that is r t = r d t. However, there are nancial frictions that restrict the amount of funds allocated to domestic rms. This drives a wedge between bond yields and the marginal product of capital in this economy. 2.3 Technology A fraction ω of the households own the rms that operate in this economy. The rms produce a single good using a Cobb-Douglas production function Y t = A t Kt α Nt 1 α where α is the output share of capital, K t and N t are the capital and labor input at time t, and A t is the total factor productivity at time t. The growth rate of the TFP factor is γ t 1, where γ t = ( At+1 A t ) 1/(1 α). Capital depreciates at a constant rate δ (0, 1). Following SSK, we assume that the rm can only pledge to repay a share η of the value of the rm in the next period. This results in the borrowing limit faced by the rm. The current capital stock K t is comprised of the rms' own capital a and the bank loans they obtain l. Firms maximizes prots by solving the following problem:subject to V f (a) = max A t (a + l) α Nt 1 α δ(a + l) w t N t r t l (5) N,l subject to the incentive-compatibility constraint: (1 + r t )l η(1 + ρ t )(a t + l t ). The rm's optimization implies that the wage rate and the net return to capital are given by. w t = (1 α)a t (K t /N t ) α (6) ρ t = αa t (K t /N t ) α 1 δ (7) In this paper, we assume that the rm's credit constraint is always binding, that is, (1+r l t)l η(1+ρ t )K t. This assumption determines the level of loan for any given own capital, l = η(1+ρ t) 1+r l t η(1+ρt)a. 8

9 2.4 Government In our benchmark economy, the government taxes both capital and labor income at rates τ k and τ e, respectively, and uses the revenues to nance an exogenously given stream of government consumption G t. A transfer that is distributed back to the individuals helps balance the government budget. In addition, the government runs a pay-as-you-go social security program that is nanced by a payroll tax τ ss. Note that this way of modeling the government signicantly simplies the government sector, but it misses the saving done through government investment. The Chinese government has been investing in nancial and physical assets during the past several decades. 7 To capture them, we introduce an exogenously given stream of government investment I g t consistent with the data in our simulation of the transition path, which will be discussed in details later. 2.5 Aggregation and the Current Account Surplus Let {X j (x)} T j=1 specied as: represent time-invariant measures of households. The aggregate capital and labor can be K = N = j,x [a j(x) + l j (x)]i z=1 X j (x) j,x [ε j(n ξh) + ε j+t (1 h)]x j (x) (8) In the competitive equilibrium of the open economy setting, the bank interest rate is equal to the world interest rate, and the current position of the net foreign assets is simply equal to the dierence between household saving and bank loans borrowed by the domestic rms. That is: NF A t = j,x a j (x)i z=0 X j (x) j,x l j (x)i z=1 X j (x) (9) The current account is simply measuring the change in net foreign assets over time. That is: CA t = NF A t+1 NF A t When the economy is closed, the net foreign assets and the current account balance are both zero, and the bank interest rate is determined endogenously by the market-clearing condition in the credit market, that is, the household saving equals the bank loans demanded by the rms. 7 See, for example, Ma and Yi (2010). 9

10 2.6 Equilibrium The denition of stationary recursive competitive equilibrium (steady state) in the benchmark model is standard and similar to that in Imrohoroglu and Zhao (2017). When the economy is open, a stationary recursive competitive equilibrium is dened as follows: Given a scal policy (G, τ e, τ k, τ ss, SS) and a fertility rate n, a stationary recursive competitive equilibrium is a set of value functions {V j (x)} T j=1, households' decision rules {c j,s(x), c j,f (x), a j+1 (x), l j (x)} T j=1, time-invariant measures of households {X j (x)} T j=1 with the state vector x = (a, z, µ, h, d), relative prices {w, ρ, r, rd, r l }, such that: 1. Given the scal policy and prices, households' decision rules solve households' decision problem in equation Factor prices solve the rm's prot maximization policy by satisfying equations 6 and Individual and aggregate behavior are consistent, that is, equation 8 is satised. 4. The net foreign assets position satises equation The measures of households satisfy: X j+1 (a, z, µ, h, d ) = 1 n 1/T {a,µ,h,d:a } X 1 (a, z, µ, 1, 1) = n Ω(µ, µ )Γ(h, h )Λ(d, d )X j (a, z, µ, h, d), for j < T, {a,µ,h,d:a } Ω(µ )X T (a, z, µ, h, d) where a = a j+1 (x) is the optimal assets in the next period. 6. The government's budget holds, that is, j,x κ 1e j X j (x) = τ k rk + τ e wn G 7. The social security system is self-nancing, and the expenditures for the consumption oor are nanced from the same budget: T j=r T +1 x R T d(ss j + κ 2 )X j (x) = τ ss [ j=1 e j X j (x) + x T R T +1 wε j µ j (n ξh)x j (x)]. x When the economy is closed, the denition of the stationary equilibrium is the same as in the open economy setting except that the net foreign assets position is always zero, and the bank interest rate is now endogenously determined by the market-clearing condition: K = j,x a j (x)x j (x) (10) 10

11 Our computational strategy is to start from an initial steady state that represents the Chinese economy before 1980 and then to numerically compute the equilibrium transition path of the macroeconomic aggregates generated by the model as it converges to( a nal steady state. Net national saving rate along the Y transition path for this economy is measured as t C t G t δk t Y t δk t ). The detrended steady-state saving rate is given by (γg 1) k ỹ δ k 3 Calibration where γ and g are the gross growth rates of TFP and population, respectively. Our calibration of the TFP growth rate, the individual income risk, the fertility rate, government expenditures, tax rates, and health related risks in China (both for the steady-state calculations and for the period) follows Imrohoroglu and Zhao (2017). Compared to the economy in Imrohoroglu and Zhao (2017) there are only two additional parameters that need to be calibrated. These are the parameters that correspond to the borrowing constraints faced by the rms and the share of the families that own the rms. 3.1 Demographics and Labor Income A newborn in this economy is 20 years old and live to be at most 90 years old. Retirement is mandatory at age 60 after which individuals face mortality risk. 8 (who are 20 years old) and form a household. An individual become a parent at age 55 to n children The average number of children per couple at the initial steady state is set to its value of 4 in the 1970s. In the model economy, this implies a fertility rate (number of children per parent) at the initial steady state of 2 (n = 2.0). The corresponding annual population growth rate is 2.0% (i.e., n 1/35 1 = 2.0%). The one-child policy implemented around the year 1980 restricts the urban population to having one child per couple and the rural population to having two children only if the rst child is a girl. However, despite the strong penalties imposed in the implementation of the one-child policy, the above-quota children are not unusual and the estimates of the the realized fertility rate after the one-child policy are approximately 1.6 per couple. This is the fertility rate we use for the period after 1980s and at the new steady state (the implied population growth rate at the nal steady state is -0.6% (i.e., n 1/35 1 = 0.6%)). With this calibration, the population shares of each age group (i.e., ages 20-40, 40-65, and 65+) generated by the model along the transition path mimic the data reasonably well (see Figure 6). We assume that a ω fraction of the population are entrepreneurs. The value of ω is chosen so that the capital-output ratio in the initial steady state matches the data. All workers, including those who own the rms face the same labor income process that is composed of a deterministic age-eciency prole ε j and a stochastic component (faced up to age 55) given by log(µ j ) = θlog(µ j 1 )+ν j. We take the age-specic labor 8 Survival probabilities are taken from the 1999 World Health Organization data (Lopez et al., 2001). See Imrohoroglu and Zhao (2017) for details. 11

12 eciencies, ε j, from He, Ning, and Zhu (2015) who use the data in CHNS to estimate them and set θ = 0.86 and the variance σ 2 ν as 0.06 based on the ndings in Yu and Zhu (2013). We discretize this process into a 3-state Markov chain by using the Tauchen (1986) method. The resulting values for µ are {0.36;1.0;2.7} and the transition matrix is given in Table 1. Table 1: Income Shock Γ µµ µ = 1 µ = 2 µ = 3 µ = µ = µ = Preferences and Technology The utility function is assumed to take the following form: u(c) = c1 σ 1 σ where σ is set to 3. The subjective time discount factor β is set to to match the gross saving rate in the initial steady state. The capital depreciation rate δ is set to 10% and the capital share α is set to The total factor productivity A is chosen so that output per household is normalized to one. The growth rate of the TFP factor γ 1 in the initial steady state is set to 6.2%, which is the average growth rate of the TFP factor in China between 1976 and We assume that the growth rate of the TFP factor in the nal steady state is 2%, which is commonly considered to be the growth rate at which a developed economy eventually stabilizes. Between 1980 and 2011, we use the observed growth rates of TFP. 10 For the period after 2011, we use the GDP long-term forecasts provided by OECD The Banking Sector Our model implies that in a competitive equilibrium, the rate of return on foreign bonds and the deposit rate are equal to each other, that is, r t = r d t. We set this rate to 0.04 in the current calibration. The rate of return on domestic loans contains an iceberg cost, which is assumed to be a xed fraction of the dierence between the return to capital and the deposit rate. That is, r l r d = ζ(ρ r d ), where ζ is calibrated so that the deposit interest rate in the initial steady state matches the data. The resulting value of ζ is As rms can only pledge to repay a share η of the rm value in the next period, the bank is willing to lend them up to a limit that their incentive-compatibility constraint holds. We set the value of η to 0.47 in the initial steady state to match the average loan-assets ratio of the Chinese rms, that is one half according to SSZ. 9 Same as in Bai, Hsieh, and Qian (2006) and Song, Storesletten, and Zilibotti (2011) 10 Y We construct the TFP series using A t = t. The detailed information about how the TFP series is constructed can K α t N 1 α t be found in Imrohoroglu and Zhao (2017). 11 The GDP growth data from can be found at the following webpage: As for the forecasts after 2050, we simply x the growth rate of the TFP factor at 2%. 12

13 Several existing studies have argued that the nancial constraints facing the Chinese rms have been changing over time, due to a variety of reasons such as the privatization of state-owned enterprises occurred in late 1990s, and the large-scale scal stimulus plan implemented by the Chinese government since This point can be clearly seen in the rst panel of Figure 5 which displays the amount of external funds used by the Chinese rms as a share of GDP (measured by the dierence between aggregate corporate investment and aggregate corporate saving) over time. To capture the changing nancial constraints, we allow the value of η to vary over time, and calibrate its value along the transition path to match the data on the amount of external funds used by the Chinese rms presented in the rst panel of Figure Health Risk Government provided health care programs in China do not provide full coverage of many health shocks that the elderly face. Imrohoroglu and Zhao (2017) use data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS) to document the expenditures associated with one of these, the Long Term Care costs. According to their ndings, the average expenditures of individuals in LTC status range from RMB 4466 to RMB 9124 during , that is, 26 37% of GDP per capita in the year. 12 In addition, according to the CLHLS data, individuals receive a signicant number of hours of informal care from their children and grandchildren. For those in LTC status, the average amount of informal care from children and grandchildren is approximately 40 hours per week during 2005 to Based on this information, we set the goods cost of LTC services m as 33% of GDP per capita in a given year in the model. As the total number of available hours (net of sleeping) is approximately 100 hours per week, we set the time cost of LTC, ξ, to We also assume that the probabilities of receiving the LTC shock, Γ j (0, 1), are age-specic, and calibrate their values to match the fractions of individuals in LTC by age. 13 The probability of exiting from the LTC status, Γ j (1, 0), is assumed to be constant across the age groups and is calibrated so that the probability of staying in LTC for more than three years in the model matches the data. 3.5 Government Policies Government expenditures, G, is set so that it is 14% of output in both the initial and the nal steady states. Along the transition path, the actual data on government expenditures for values of G t is used. The labor and capital income tax rates, in both steady states are determined so that tax revenues exactly cover government expenditures. At the initial steady state, both the labor and capital income tax rates are set at 17.5%. At the nal steady state, the capital income tax rate is set at 15.3% according to Liu and Cao (2007); the labor income tax rate is then set at 15.8% to balance the government budget. For the period we use the tax rates from Imrohoroglu and Zhao (2017). For the period after 2011, we assume that both government expenditures and the tax rate gradually converge to their nal steady state values in 10 years. 12 While these costs are high for individuals in LTC status, average expenditures per person (including those not in LTC status) for individuals aged 65+ range from approximately RMB 253 in 2005 to RMB 1490 in To this end, we assume that the probability is the same across agents within each age group, 55-75, 75-85, and

14 We set the average social security replacement rate at 15% for the whole population which represents the average coverage between the urban and the rural households. We assume that the social security program is self-nancing and that the social security payroll tax rate τ ss is endogenously determined to balance the budget in each period. The consumption oor, c is set to 10% as in Imrohoroglu and Zhao (2017). Table 2: Calibration Parameter Description Value α capital income share 0.5 δ capital depreciation rate 0.1 σ risk aversion parameter 3 A TFP factor 0.37 β time discount factor m goods cost of LTC services 33% of GDP per capita ξ time cost of LTC services 0.42 G government expenditures 14% of GDP SS social security replacement rate 15% 1 initial steady state TFP growth rate 3.1% γ 1 α final 1 nal steady state TFP growth rate 1% n initial initial steady state total fertility rate 2.0 n final nal steady state total fertility rate 0.8 rt d the deposit rate at the initial SS 0.02 ω popu. share with entrepreneurial skills 3 ζ iceberg cost parameter 0.2 η fraction of net prots can be pledged 0.45 γ 1 α initial Table 2 summarizes the main results of our calibration exercise. 4 Quantitative Results We start this section by examining the key aggregate statistics of the calibrated economy at both the initial and the nal steady states. The initial steady state is assumed to be a closed economy, and it is calibrated to mimic the economic and demographic conditions in China in 1980, while the nal steady state is an open economy, representing the one that the Chinese economy will eventually converge to. Next, we examine the time series path of the saving rate, investment rate, and the current account along the transition path. In the analysis of our benchmark model, we focus on the time period until This is because in the following years of 2009 and 2010, as documented in Bai, Hsieh, and Song (2016), China launched a large scal stimulus plan mainly nanced by o-balance sheet companies. In the next section, we examine the possible role of such a stimulus plan in shaping the large decline in current account surplus since 2009 in an extension of the model. We show that the current account surplus of China would have been substantially larger after 2008 if the Chinese government had not embarked on this scal stimulus. 14

15 4.1 Initial and Final Steady States The results presented in Table 3 show that the initial steady state of the calibrated model matches several key aspects of the Chinese economy in 1980, including the gross saving rate, the return to capital, and the demographic structure. The gross saving rate is 37.5% at the initial steady state, while the Chinese gross national saving rate was, on average, 35.6% around the year of The return to capital generated by the model at the initial steady state is 14.8%, which is mostly due to the relatively high TFP growth rate to which the initial steady state is calibrated. Bai, Hsieh, and Qian (2006) argue that the return to capital was, indeed, quite high in China in the 1980s, about 14% on average. However, most of the Chinese households did not get full access to the high returns to capital due to the nancial frictions. The bank deposit rate generated in the initial steady state is 2.0%, consistent with its data counterpart according to the World Bank. The demographic structure at the initial steady state is also consistent with the Chinese data. For instance, the share of the population aged 65+ at the initial steady state is 12.7%, while the share of the Chinese population aged 65+ was about 11% in The nal steady state of the economy is generated by simply changing the fertility rate from 2.0 to 0.8 and the growth rate of TFP factor from 6.2% to 2.0%, and opening up the economy while keeping the rest of the parameters the same as at the initial steady state. 14 The gross saving rate at the nal steady state is higher (i.e.42.3%) than that at the initial steady state. This is largely due to that the decline in family insurance triggered by the one-child policy encourages precautionary saving and capital accumulation. In addition, the changes in the bank deposit rate caused by the opening up of the economy also contribute to the change in the saving rate at the nal steady state, while the lower return to capital at the nal steady state is largely due to the increased capital accumulation and the lower TFP growth rate. Table 3: Properties of the Steady States Statistic Data Initial steady state Final steady state Gross saving rate 35.6% 37.0% 42.3% Elderly population share (65+) 11% 12.7% 25.1% Share of the elderly (65+) in LTC 10.2% 10.4% 11.0% Return to capital (ρ) 13.6% 14.8% 5.3% Bank interest rate (r) 2% 2.0% 2% Social security payroll tax (τ ss ).. 2.1% 5.1% Capital-output ratio The Rising Current Account Surplus Until 2008 In this section, we present our benchmark results where we examine the time path of the saving rate, the investment rate, and the current account along the transition path. We rst focus on the time period until 14 The payroll tax rate is also dierent between the two steady states. In the initial steady state, the social security replacement rate is set at 15%, which results in a payroll tax rate of 2.1%. At the nal steady state, a higher payroll tax rate (5.1%) is needed to balance the budget due to a much larger share of the elderly population. 15

16 2008 because in the following years of 2009 and 2010, China launched a large scal stimulus plan (largely nanced by o-balance sheet companies) that needs a more detailed discussion. We examine the possible role of such a stimulus plan in shaping the time series of China's current account since 2009 in the next section. (a) Current Account (as % of GDP) (b) Gross Saving Rate and Investment Rate-Model (c) Gross Saving Rate and Investment Rate-Data Data source: dierent years of Chinese Statistical Yearbook from NBS of China, and the World Bank data. Figure 3: Benchmark: Key Statistics along the Transition Path We shock the initial steady state by imposing the one-child policy (i.e., the fertility rate is immediately reduced from 2.0 to 0.8), and then we open the model economy in 10 years after the transition path starts (i.e. 1990). The actual opening up of China's nancial accounts started around the mid 1980s, and the 16

17 process was gradual and lasted until the early 1990s. 15 In addition, we use the actual data on the TFP growth rate, government expenditures and taxes along the transition path and assume perfect foresight for all these components. 16 We compare the current account along the transition path generated by the model to the Chinese data to evaluate if the model is capable of accounting for the rise in China's current account surplus. Figure 3 displays the current account surplus generated by the benchmark economy versus the data starting in Overall, the time series path of the current account generated by the model tracks the data until 2008 reasonably well (before the vertical line). In the data, as summarized in Table 4, the current account surplus was fairly stable in the 1990s, and then increased substantially from 1.7% of GDP in 2000 to 9.1% in In the benchmark economy, the current account surplus was also at in the 1990s, and then increased from 3.4% in 2000 to 8.5% in Gross saving and investment rates along the transition path generated by the model are displayed in Figure 3. The model tracks China's gross saving and investment rates fairly well during the entire period, and in particular it captures the substantially dierent trends in the two rates in the 2000s. In the data, while gross saving and investment rates both declined slightly in the late 1990s, the saving rate increased much more than the investment rate in the 2000s. Similar results are generated in the benchmark model. As displayed in Figure 3, the gross saving rate also increased faster than the investment rate in the 2000s during the transition path generated from the benchmark model.. As argued previously, an important reason behind the dierent patterns in gross saving and investment rates since 2000 is the rise in household saving driven by the one-child policy during this period, and the nancial frictions preventing the increased household saving from being invested in domestic rms. Indeed, as displayed in Figure 3, the household saving rate (household saving as a share of household disposable income) increased dramatically during this period both in the model, consistent with the data. In section 5, we provide further analysis on the role of the one-child policy and household saving in understanding the rising current account. Table 4: Current Account (% of GDP) Along the Transition Path Economy Data Benchmark Counterfactual Experiments No One-child Policy Constant Financial Friction Data source: dierent years of Chinese Statistical Yearbook, NBS of China. 15 In the sensitivity analysis, we nd that opening up the economy in 1985 does not signicantly change our results. 16 In shown in both Imrohoroglu and Zhao (2017), and Chen, Imrohoroglu and Imrohoroglu (2006), the perfect foresight assumption does not have a large impact on the quantitative implications of the model of this type. 17

18 4.3 The Decline in the Current Account Surplus since 2009 In this section, we examine the benchmark model implication for the current account after As shown in Figure 3, the current account surplus generated by the benchmark economy also tracks the data after 2008 fairly well. In the data, as summarized in Table 4, the current account surplus substantially dropped after 2008, to 4.8% in 2009 and 2.5% in In the benchmark economy, the current account surplus also experienced a dramatic decline during the same period, decreasing to 4.0% in 2009 and 2.7% in Here the decline in the current account surplus since 2009 is simply due to the changing nancial constraints captured by the varying value of η during the transition. As shown in Figure 5, the amount of external funds used by the non-nancial Chinese rms (calculated as the dierence between corporate investment and corporate saving) dramatically increased after 2008, from 8.6% of GDP in 2008 to 12.5% in 2009 and 13.5% in In the benchmark calibration, we match the changing amount of external funds used by domestic rms by varying the value of η. The increased external funds encourage domestic investment and thus reduce the current account surplus after In the next section, we provide further analysis on the role of changing nancial constraint in shaping the current account time series, especially after Further Analysis 5.1 One-child Policy and the Current Account To highlight the role of the rising household saving rate in shaping China's current account surplus, in this section we consider a counterfactual case in which the household saving rate is expected to be much lower than in the benchmark case. As argued previously, the substantial increase in the household saving rate generated in the benchmark model is largely due to the loss of the original family insurance triggered by the one-child policy. Imrohoroglu and Zhao (2017) show in a closed economy that the rise in the Chinese saving rate would be much smaller if there was no one-child policy. To consider the impact of the one-child policy on the current account, we consider a counterfactual case in which the one-child policy is never implemented. 17 The results from this experiment are displayed in Figure xxx. Consistent with our theory, the current account balance is substantially lower during the entire period in this counterfactual economy, and there is no signicant rise in the current account surplus after This is largely due to the dierential responses from the saving and investment rates to the removal of the one-child policy. While households save substantially less in this counterfactual case (as shown in the last panel of Figure xxx), the investment behaviors in the economy are hardly aected by the policy change. 17 That is, the fertility rate is constant for the entire transition path. Imrohoroglu and Zhao (2017) also consider an alternative case that allows the fertility rate to gradually decline as the economy grows, and nd that the implications for saving are very similar. 18

19 (a) Current Account (as % of GDP) (b) Gross Saving Rate (c) Gross Investment Rate Data source: the ow of funds data and dierent years of Chinese Statistical Yearbook from NBS of China, and the World Bank data. Figure 4: One-child Policy and the Current Account 5.2 Financial Constraint and the Current Account To assess the role of changing nancial constraint in shaping the current account, we also consider a counterfactual economy in which the value of η is assumed to be constant along the transition path. As shown in the rst panel of Figure 5, the amount of external funds used by domestic rms (as % of GDP) became relatively stable during the transition path when the value of η is constant. 18 According to the second panel, the current account surplus of China would have been substantially larger after 2008 if the nancial con- 18 The remaining changes in the external funds are simply due to the TFP changes. 19

20 straint had not been relaxed after In addition, we nd that the tightening of the nancial constraint in the late 1990s also has a signicant impact on the current account surplus in the following years. When the value of η is constant, there is a level shift down in the current account during 1999 to Why has the nancial constraint been changing? Several existing studies have argued that the nancial constraints facing the Chinese rms have been changing over time, due to a variety of reasons. SSK argue that as the economy experienced the transition from nancial integrated rms (i.e. state-owned rms) to nancial constrained rms (i.e. private rms), the Chinese corporate sector on average became more nancially constrained over time. This can be particularly true in the late 1990s when the large-scale privatization of state-owned enterprises occurred (for instance, see He, et al, 2014). Bai, Hsieh, and Song (2016) on the other hand argue that the large-scale scal stimulus plan implemented by the Chinese government in 2009 was implicitly a nancial liberalization process for the Chinese rms. For tractability, our model captures these policy changes in a fairly reduced-form way by simply varying the value of η over time. It would be interesting to incorporate the details of these policy changes, in particular the scal stimulus plan, and examine their macro implications in a more realistic model, which we leave for future research. (a) Corp Investment minus Corp Saving (as % of GDP) (b) Current Account (as % of GDP) Data source: the data source for the rst panel is the ow of funds data, NBS of China, and the others are from dierent years of Chinese Statistical Yearbook and the World bank. Figure 5: Changing Financial Constraints: Key Statistics along the Transition Path 6 Conclusion In this paper, we develop a model economy that can account for the increase in the saving and investment rates as well the current account surplus in China since the early 1990s. Our quantitative analysis suggests that both investment and saving are important in shaping the current account time series in China. While 20

21 the rising current account surplus until 2008 was largely driven by the increase in household saving, the decline in the current account surplus since 2009 was mainly due to the increased domestic investments, most likely triggered by the large-scale scal stimulus program announced by the Chinese government in References [1] Bai, C., Hsieh, C. and Y. Qian The Return to Capital in China. Brookings Papers on Economic Activity, 37(2): [2] Chamon, M. and E. Prasad Why Are Saving Rates of Urban Households in China Rising? American Economic Journal: Macroeconomics 2 (1): [3] Chamon, M., Liu, K., and E. Prasad Income uncertainty and household savings in China. Journal of Development Economics 105: [4] Chang C., Chen, K., Waggoner, D., and T. Zha, Trends and Cycles in China's Macroeconomy, NBER Macroeconomics, University of Chicago Press. [5] Chen, K., mrohoro lu, A., and S. mrohoro lu, The Japanese Saving Rate, American Economic Review, 96(5): [6] Chen, K., mrohoro lu, A., and S. mrohoro lu, The Japanese saving rate between 1960 and 2000: productivity, policy changes, and demographics, Economic Theory, vol. 32(1), pages , July. [7] Coeurdacier, N., Guibaud, S. and K. Jin "Credit Constraints and Growth in a Global Economy." American Economic Review, 105(9): [8] Curtis, C., Lugauer, S., and N. Mark, Demographic Patterns and Household Saving in China. American Economic Journal: Macroeconomics, 7(2), pages [9] De Nardi, M., French, E. and J.B. Jones Why Do the Elderly Save? The Role of Medical Expenses. Journal of Political Economy, vol. 118 pages [10] Fuster, L., A. Imrohoroglu, and S. Imrohoroglu, A welfare analysis of social security in a dynastic framework, International Economic Review, vol. 44(4), pages , November. [11] Fuster, L., A. Imrohoroglu, and S. Imrohoroglu, Elimination of Social Security in a Dynastic Framework, Review of Economic Studies, vol. 74(1), pages [12] Gu, D., and D. A. Vlosky Long-Term Care Needs and Related Issues In China. Social Sciences in Health Care and Medicine, pp , Janet B. Garner and Thelma C. Christiansen, eds., Nova Science Publishers. 21