A Quantitative Evaluation of. the Housing Provident Fund Program in China

A Quantitative Evaluation of the Housing Provident Fund Program in China Xiaoqing Zhou Bank of Canada December 6, 217 Abstract The Housing Provident Fund (HPF) is the largest public housing program in China. It was created in 1999 to enhance homeownership. This program involves a mandatory savings scheme based on labor income. Past deposits are refunded when the worker purchases a house or retires. The program provides mortgages at subsidized rates to facilitate these home purchases. I calibrate a life-cycle model to quantify the effectiveness of these polices. My analysis shows that a housing program with these features is expected to increase the rate of homeownership by 6.7 percentage points and to raise the average home size by 21. These results are largely unaffected by the inclusion of employer contributions and rental markets in the model. I discuss the economic mechanisms by which these outcomes are achieved and which features of the HPF program are most effective. Keywords: Public housing program, Housing Provident Fund, Program evaluation, China, Life-cycle model, Homeownership, Average home size. JEL Codes: E2, E6, H3, R2, R3. Correspondence to: Xiaoqing Zhou, Bank of Canada, 234 Wellington St., Ottawa, ON K1A G9, Canada. Email: xzhou@bankofcanada.ca. Phone: (+1)613-782-8542. I thank Jason Allen, Joshua Hausman, Lutz Kilian and Dmitriy Stolyarov for helpful comments and discussions. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Bank of Canada. 1

1 Introduction Governments around the world take measures to promote homeownership. These actions are driven by the belief that housing, for most households, is both an important investment asset and a consumption good, and that homeownership promotes social and economic stability (see DiPasquale and Glaeser (1999)). The U.S. government, for example, has fostered homeownership by encouraging subprime lending and expanding secondary mortgage markets (see, e.g., Mian and Sufi (29) and Gabriel and Rosenthal (21)). Many Asian governments, in contrast, have adopted more centralized, mandatory savings plans intended to fund households housing needs. The Housing Provident Fund (HPF) in China is one such an example. Table 1 provides examples of similar programs in other countries. The HPF was first enacted in 1999 and has been applied to an increasing number of regions within China since then. 1 The policies stipulated by the HPF apply to all urban workers, regardless of the type of the firm they work for (state-owned, collective, or private). There are two key features of this program. First, it is a mandatory savings scheme intended to fund housing purchases. Specifically, the government requires each worker to deposit a mandatory fraction of his salary to the program until the worker purchases his first house, at which point the government refunds the worker s past deposits. If the worker never purchases a house during his working life, the HPF returns all past deposits to the worker at the time of retirement. Second, the program provides mortgages at below-market rates to participants. The HPF is the largest public housing program in China, both in terms of the number of workers enrolled and of the funds deposited and distributed. According to the annual report published by the Ministry of Housing and Urban-Rural Development in China, in 215, 124 million workers enrolled in the HPF (4 of urban employment), 1.5 trillion Yuan (2 of GDP) were deposited in the program, and 1.1 trillion Yuan were lent out for home purchases and building. Although compliance with the HPF program has been limited so far, it is expected that this program will eventually be extended to all urban workers. There has been much interest in the question of how effective the HPF program has been at stimulating homeownership (see, e.g., Logan et al. (1999), Li (2), Fu et al. (2), Huang and Clark (22), Buttimer et al. (24), Meng et al. (25), Yeung and Howes (26), Xu (216), 1 For further details on the HPF and a review of the history of related Chinese housing policies, see Xu (216). 2

and Tang and Coulson (217)). Empirically evaluating the success of this program is not easy. There are several challenges. For example, at the micro level, workers may select when to join the program. If this decision depends on unobserved characteristics, regression estimates suffer from selection bias. Alternatively, one may exploit regional variation in the timing of the implementation of this program. To the extent that the adoption of this program is anticipated by households, however, the causal effect will not be identified. Finally, at the national level, the length of time for which these policies have been in effect is too short to estimate the impact of the program, even if a credible counterfactual could be constructed. Given these empirical challenges, a natural alternative approach is to quantify the effectiveness of the HPF program based on a calibrated model. For this purpose, I develop a life-cycle model to evaluate the expected impact of the HPF program. The use of quantitative theory also helps understand the mechanisms by which these polices affect the housing market. I focus on the effect of the program on two outcome variables: the rate of homeownership and the average home size. The baseline model captures the consumption and savings behavior of Chinese households over their life cycle. Households can choose both the timing and the size of their home purchase. Within the same generation, households are heterogeneous in that each house purchase is associated with a random transaction cost. As a result, homeownership and average home size vary over the life cycle and across households. I calibrate the model based on household survey data from the Chinese Household Income Project Series (CHIPS). The model produces a rate of homeownership that is increasing with age, and a roughly flat path of the average home size over the life cycle. I then incorporate the two key features of the HPF program into this baseline model. First, the mandatory-savings feature is captured by a parameter that represents the fraction of income to be deposited into the program. Second, the mortgage subsidies are captured by the below-market mortgage rate. I set these parameters according to the values implemented by the HPF program. Finally, I compare the life-cycle path of homeownership and of the average home size with the corresponding paths in the baseline model. The objective is to capture the steady state effects of the HPF policies on housing demand when all urban workers are covered by this program. My analysis shows that a housing program with these features is expected to increase the rate of homeownership by 6.7 percentage points, which is equivalent to a 11 increase in the 3

homeownership rate relative to the baseline model. This increase is mainly due to the fact that many young households, who would otherwise buy a house later in life or who would simply choose never to buy a house, under this program choose to become homeowners. In addition, the average home size increases by 21 relative to the baseline model. This effect is driven by an increase in the size of new homes purchased in all age groups. My analysis also helps us understand which features of the HPF program are most effective. Two additional policy experiments shed light on this question. First, I consider a housing program that requires mandatory savings, but that does not offer mortgages at below-market rates. Second, I consider a program that offers subsidized mortgages, but that does not require mandatory savings. The first experiment shows that the mandatory-savings feature, as currently implemented in the HPF, has no impact on home purchase and consumption behavior. This is because when the mandatory savings are below the optimal savings in the absence of the policy, households keep the sum of their private and mandatory savings equal to the optimal savings in the absence of the policy. Since other conditions such as income, transaction costs and prices are unchanged, households make exactly the same decisions on home purchase and consumption. In contrast, the second experiment shows that the subsidized mortgages create a wealth effect by allowing households to borrow at a lower cost. This effect drives more households to purchase a house earlier in their life and to purchase a larger house. There are several ways of making the life-cycle model more realistic. For example, employers are often required by the government to contribute to workers HPF savings. Depending on how much an employers contributes, workers may change their home purchase decisions accordingly. Moreover, the baseline model abstracts from the existence of rental markets and renters choices. In Section 5, I investigate how these extensions affect the expected impact of the HPF program. I show that the baseline results are robust to these modifications. The remainder of the paper is organized as follows. Section 2 describes the baseline model and discusses how to incorporate the key features of the HPF program into the baseline model. Section 3 outlines the model calibration. Section 4 presents the results from a series of policy experiments. Section 5 extends the model to incorporate employer contributions and rental markets. Section 6 concludes. 4

2 Model The baseline life-cycle model is intended to capture households decisions about non-housing consumption, the timing of purchasing one s first home, and the size of this home purchase. This partial equilibrium consumption-choice framework has the advantage of allowing us to model more complicated household decisions such as discrete purchases and heterogeneous household behavior (see, e.g., Ortalo-Magne and Rady (26), Yang (29), and Berger et al. (217)). I abstract from the general equilibrium effects of the HPF program because my focus is on assessing how effective the program is at reaching its stated objectives rather than assessing its welfare implications. This approach avoids the difficult task of developing a fully specified model of the Chinese economy. Due to the presence of transaction costs and the requirement of a down payment in the life-cycle model, households first accumulate their wealth and then make one home purchase. In this purchase, they choose the size of the home. The model has two important features. First, I assume that households purchase a house, if at all, only once in their lives. This assumption appears realistic for the Chinese housing market. According to Huang and Yi (211), in 22, only 6.6 of urban households in China owned two or more homes. Second, a house purchase is associated with a randomly drawn transaction cost. This assumption creates heterogeneity in the timing of the purchase, in the size of the home purchased, and in non-housing consumption across households within the same generation. The advantage of a random transaction cost compared with idiosyncratic income shocks is that, in junction with heterogeneity in wealth within the same age group, it captures a range of additional unobserved determinants of home purchases in China such as local regulations and fees. It can be shown that the model with random transaction costs replicates key features of the Chinese housing market even in the absence of idiosyncratic income shocks. 2.1 Baseline Model The model is built on a discrete-time version of Leahy and Zeira (25) by introducing the housing collateral constraint and random transaction costs. The random transaction cost provides a source of heterogeneity across households of the same age. It captures unobserved characteristics 5

that affect households home purchase decisions. The advantage of this approach compared with modeling idiosyncratic income shocks within the same age group is that in China home purchase decisions depend not only on income but also on local regulations and fees. The economy is populated with overlapping generations of households whose income and wealth differ across the life cycle. In each period, a mass of households is born and lives for J periods. In the first J y periods of life, households work and earn labor income. In the remaining J J y periods, households retire and receive retirement income. Households derive utility from consuming the non-housing good and housing services. Utility is additive in the two goods. Let u(c) denote the flow utility from consuming the non-housing good, where c is non-housing consumption (henceforth referred to as consumption). Let v(h) denote the flow utility from consuming the housing services generated by a home of size h. There is a minimum size of the house, h, that generates utility. Let v(h) = for h h, where h >. v(h) is increasing and concave for h > h, and is continuous at h. Households start their life without a house. In each period, households make decisions about consumption, about whether to become a homeowner if they are not already, about the size of the home they decide to buy, and about their savings for the next period. At the end of their life, households leave their wealth as a bequest, consisting of savings and the value of their house. In the baseline model, I assume that a house never depreciates. This assumption is relaxed in Section 5, where I discuss how the depreciation rate is relevant for household decisions and for the effects of the HPF program. A household maximizes expected lifetime utility, J 1 E β j [u(c j ) + v(h j )] + β J Φ(w J, h J ). j= The second term inside the expectation operator represents the discounted utility from leaving a bequest, specified by the bequest function Φ, the functional form of which is discussed in Section 3. w J denotes the wealth at the end of the household s life. The household problem has a recursive form. The value at the end of the household s life, V J, is given by the bequest function V J (a, h) = Φ ((1 + r)a + ph, h), 6

where a denotes savings, p denotes the house price, and r denotes the interest rate. For lifetime period j =,..., J 1, the value V j depends on whether the household owns a house at the beginning of the period. If the household owns a house of size h at the beginning of the period, the value is given by V j (a, h) = max c,a u(c) + v(h) + βv j+1 (a, h) s.t. c + a = y + (1 + r)a a γph. The first constraint is the budget constraint, where y denotes income. The second constraint is the housing collateral constraint. If the household borrows, the borrowing amount cannot exceed a fraction γ of the home value. Therefore, 1 γ denotes the down payment rate. If the household does not own a house at the beginning of the period, V j is the maximum of the value of purchasing a home, V P j The value of purchasing a home is, and of not purchasing a home, V N, i.e., { V j (a, f) = max V P j } (a, f), Vj N (a). Vj P (a, f) = max u(c) + βv j+1 (a, h ) c,a,h j s.t. c + a + ph = y + (1 + r)a f a γph, where f is an i.i.d. transaction cost drawn from a continuous distribution F. The value of not purchasing a home is Vj N (a) = max c,a [ ] u(c) + βe V j+1 (a, f ) s.t. c + a = y + (1 + r)a a, [ ] where E V j+1 (a, f ) = V j+1(a, f )df (f ). The second constraint is the liquidity constraint, which requires liquid savings to be non-negative. The presence of the collateral constraint and the liquidity constraint jointly imply that any positive borrowing amount must be collateralized by a house. The policy function is characterized by a cut-off rule. For each age j and a wealth level a, 7

there exists a cut-off transaction cost value, fj (a), such that the household purchases a house if f f j (a), and does not purchase a house if f > f j (a). 2.2 Modeling Mandatory Savings One important feature of the HPF program is a mandatory savings requirement for workers who are not homeowners. Specifically, the government requires each worker to deposit a mandatory fraction of his salary to the HPF until the worker purchases his first house, at which point the government refunds the worker for all past deposits. 2 The mandatory-savings policy affects the budget constraint of workers who choose not to purchase a house. After subtracting a fraction of their income, for j =,..., Jy 1, Vj N (a) = max c,a [ ] u(c) + βe V j+1 (a, f ) s.t. c + a = (1 θ)y + (1 + r)a a, where θ is the fraction of a worker s income taken away by the program. The HPF refunds the worker for all past deposits with interest if the worker purchases a house. The value of purchasing a house at age j = 1,..., Jy becomes Vj P (a, f) = max u(c) + βv j+1 (a, h ) c,a,h s.t. j 1 c + a + ph = y + (1 + r)a f + θ y k (1 + r) j k a γph. Finally, if the worker never purchases a house during his or her working life, the HPF returns all past deposits to the worker at the time of retirement. This implies that the budget constraint for a household who has not been a homeowner at the retirement age includes an extra income term, θ J y 1 k= y k(1 + r) Jy k. Since the mandatory-savings requirement does not apply to retired workers, the household problem during the retirement is the same as in the baseline model. k= 2 After the worker purchases the first house, the HPF still collects a fraction of the worker s salary every month, but refunds this amount to the worker usually within the same month. Therefore, income is not affected. Hence in the model, existing homeowners are not affected by the HPF program any more. 8

2.3 Modeling Below-Market Mortgage Rate In an effort to make housing more affordable, the HPF also provides mortgages at below-market rates. These rates are set by the People s Bank of China, the central bank of China. According to the People s Bank of China, the historical spread between the long-term market mortgage rate and the HPF s lending rate is about 2 percentage points. In modeling the mortgages provided by the HPF, I assume that households have two financial assets: liquid savings that earns a market interest rate, and a mortgage debt that is repaid at the rate specified by the HPF. I consider an interest-only repayment schedule that requires interest to be paid every period, but the principal can be paid when the mortgage contract terminates at the end of a borrower s life. Allowing two financial assets adds an additional state variable to the model, which greatly increases the computational cost of solving the model. The value V J at the end of the household s life becomes ( ) V J (a, h, b) = Φ (1 + r)a + ph (1 + r b )b, h, where a denotes liquid savings, r denotes the market interest rate, b denotes the amount of mortgage debt, and r b denotes the mortgage rate set by the HPF. For lifetime period j =,..., J 1, the value V j depends on whether the household owns a house and a mortgage at the beginning of the period, V j (a, h, b), if h > V j = V j (a, f), if h =, where V j (a, h, b) = max c,a u(c) + v(h) + βv j+1 (a, h, b ) s.t. c + a = y + (1 + r)a M a b = (1 + r b )b M, where M is the periodic interest repayment. b is the mortgage debt at the beginning of the next period. The liquidity constraint applies to liquid savings. 9

If the household does not own a house at the beginning of the period, V j is the maximum between the value of purchasing a house V P j and not purchasing Vj N. Vj N is the same as in the baseline model, because a lower mortgage rate would not affect households who choose not to buy a home. V P j becomes V P j (a, f) = max c,a,h,b u(c) + βv j+1 (a, h, b ) s.t. c + a + ph = y + (1 + r)a f + b a b γph. Given this analysis, it is straightforward to combine Sections 2.2 and 2.3 to model the two program features simultaneously. The model is solved numerically by backward induction using a two-step procedure. In the first step, I discretize the state space and then solve the value functions over fixed grids of the states. In the second step, I obtain the policy functions by solving the optimization problem over finer grids, given the value functions obtained in the first step. The numerical procedure is described in detail in the Appendix. 3 Calibration To quantify the impact of the HPF program, the model parameters are calibrated. A summary of the parameter values can be found in Table 2. Age is indexed by j =,..., J 1. The model frequency is five-year intervals. Households start their life at age 21, work for 4 years until age 6, and then live for 2 years in retirement, so J = 12 and Jy = 8. Households do not have initial liquid savings, i.e., a =. The discount factor is set to β =.93. The flow utility from consumption is u(c) = ln c. The flow utility from housing services is, s ln h, if h > h, v(h) = if h h, where s denotes the utility weight on housing services, and h is the minimum home size. I set 1

s =.25, so that the expenditures on housing account for 2 of total consumer expenditures. This is consistent with the expenditure share of housing and household goods in total consumer expenditures for urban households in China between 1998 and 22, according to the Statistical Yearbooks published by the National Bureau of Statistics of China. I set h to 1, so that the utility function is continuous and increasing. The bequest function is Φ(w) = η [u(w) + v(h)], where w denotes the wealth at the end of a household s life. u( ) and v( ) are specified earlier. η is the bequest parameter. Since a direct measurement of the bequest motive is hard to obtain from the data, I conduct a sensitivity analysis in Section 4.5. It shows that the effects of the HPF program are not sensitive to alternative values. Therefore, I set η = 1. I use survey data from the CHIPS for 22 to calibrate household income by age group. 3 The survey collects data on household income between 1998 and 22. I obtain a smooth income measure by averaging the income of a household across these years. I then regress the log of this income measure on the first and second polynomial of the household head s age. The coefficients from the regression can be used to construct a smooth income path over the life cycle. I then take the average of the estimated income within each age group, and normalize the income of age group 21-25 to 1. Figure 1 shows the age distribution of income used to calibrate the model. The down payment rate, 1 γ, is set to 22. This is consistent with the Chinese government regulations on residential housing markets during the 2s, which require a minimum down payment rate for the first home to be between 2-25. The i.i.d. transaction cost is assumed to be uniformly distributed with a lower bound of zero (f =). The upper bound is set to.6 to match the overall rate of homeownership in the data (f 1 =.6). The house price is normalized to p = 1. The mandatory fraction of income to be deposited into the program is set as θ =.12, consistent with the average of the workers contribution rate across cities in China from 1999 to 215. 4 The 3 The CHIPS are intended to measure the distribution of personal income in both rural and urban areas of China. These survey data were collected in 1988, 1995 and 22. Individual respondents reported their demographic characteristics, income, employment, and expenditures. I obtain the 22 CHIPS data from the ICPSR at the University of Michigan. 4 The required fraction of a worker s income deposited into the program varies across cities and years. Between 11

market savings rate is set at r =.5, consistent with the deposit interest rate in China. In all simulations, the HPF program creates an interest rate spread of 2 percent, i.e., r b =.3. 4 Policy Experiments In this section, I evaluate the impact of the HPF program on the rate of homeownership, defined as the fraction of homeowners in the population, on the average home size, defined as the average size of all owner-occupied homes, and on expected life-time utility, in steady state. This helps control for transition dynamics as the program is introduced. First, I use the baseline model to describe household decisions on new home purchase, consumption and savings. I simulate the life-cycle choices of 1, households, and use them to construct the average life-cycle path of homeownership, home size, consumption and wealth. 5 I then show that the program meets the government s objective of enhancing homeownership: the expected increase is 6.7 percentage points. The HPF also raises the average home size by 21. In addition, expected utility increases. Since the program has two distinct features, each of which may affect household decisions differently, I also investigate the impact of these two features separately. The results are summarized in Table 3. I conclude that the mandatory-savings feature, as currently implemented, has no impact on households home purchase decisions. Therefore, the effects of the HPF program are mainly driven by the feature of subsidized mortgages. 4.1 Pre-Policy Patterns The baseline model in Section 2.1 captures some of the key features of the Chinese housing market. For example, in the CHIPS data for 22, the homeownership rate is 61.5. The calibrated model generates a homeownership rate of 61. Moreover, the age profiles for homeownership and the fraction of new home buyers in the model are broadly consistent with the Chinese household survey data. Figure 2 shows the life-cycle profile of six key variables in the baseline model by averaging across 1, households within each age group. These variables include the rate of homeownership, 1999 and 215, this fraction fell in the range of 5-2 over the country, with 12 being the most commonly used value. 5 All results are robust to the number of simulations. 12

the average size of all homes, the fraction of new home buyers, the average size of new homes, consumption and wealth. The upper left panel captures a monotonically increasing pattern of homeownership over the life cycle. The difference in the homeownership rate between one age group and the previous age group represents the fraction of new home buyers, as reflected in the middle left panel. The youngest households, aged 21 to 25, choose not to buy a home because they have not saved enough for the down payment and the transaction cost. At age 26 to 3, about 9 of households buy a house and become homeowners. From age 31 to 4, the fraction of new home buyers keeps increasing, which explains the fast growing homeownership rate. By age 4, 43 of households are homeowners. After age 4, there are still households who become new homeowners, but at a decreasing fraction. At the end of the life cycle, only 2.7 of households never become a homeowner. The upper right panel shows the average size of all homes within each age group. Since no households in age group 21-25 buy a home, I set the average home size for this age group to. The average home value to income ratio ph/y, excluding the youngest age group is 3.6, which implies that on average the home value is 18 times the annual income. Over the life cycle, the average size of all homes is gradually increasing but not varying much. However, examining the average size of new homes in the middle right panel reveals that the size of new homes is increasing with age to a larger extent. Since households who have not been a homeowner constantly accumulate their savings as they grow old, they can afford a larger house when they choose to be a homeowner. The lower left panel shows a hump shaped life-cycle path of consumption. Before age 5, consumption is increasing due to the fact households are constrained by their borrowing capacity. After age 5, consumption is decreasing because households are impatient. Wealth is increasing before age 6 as households either become a homeowner, or build up their savings to prepare for future home purchase. Wealth is flat after 6, because homeowners do not downsize their house, and because the bequest motive prevents households to dissave. 4.2 Impact of the HPF Program Figure 3 shows the life-cycle profile of four variables, homeownership, the average size of all homes, the fraction of new home buyers and the average size of new homes, in the baseline model 13

(solid lines) and in the model including the HPF policies (dotted lines). Under the HPF program, homeownership increases in all age groups beyond age 3. The overall rate of homeownership increases by 6.7 percentage points, equivalent to a 11 increase in homeownership. At the end of the life cycle, only.4 of households are not homeowners. These facts imply that the HPF program pushes forward some households decisions on home purchase, and stimulates some households to become homeowners who otherwise would not. These effects can be seen from the change in the fraction of new home buyers. Under the program, the fraction of new home buyers substantially increases from age 31 to 45. By age 45, almost 7 of households already become homeowners. Later in life, the fraction of new home buyers is lower relative to the baseline scenario due to the pushing-forward effect of the program. The HPF program also increases the average home size by 21. A decomposition by age group in the upper right panel shows that the program raises the average size of all homes in all age groups. This comes from the fact that the program stimulates home buyers in all age groups to choose a large home, as shown in the lower right panel. Since the program features two distinct policies, mandatory savings and below-market rate mortgages, each may affect homeownership and home size differently. To understand the economic mechanism underlying each program feature and to quantify the extent to which each feature helps meet the policymaker s goal, I conduct two additional policy experiments. First, I consider a housing program that requires mandatory savings, but that does not offer mortgages at a subsidized rate. Second, I consider a program that offers a subsidized mortgage rate, but that does not require mandatory savings. 4.3 Effects of the Mandatory-Savings Policy in Isolation First, consider the effects of a mandatory-savings program that requires participants to deposit 12 (as currently implemented by the HPF) of their income every period until they purchase a home or retire, whichever is earlier. The program then returns the participants their previous mandatory savings with interest. It turns out that this program has no effect on households home purchase and consumption decisions. Homeownership and the average home size are the same as in the baseline scenario. The intuition is that if the mandatory savings are below the optimal savings 14

in the absence of the policy, households dissave the same amount and keep the sum of their private and mandatory savings equal to the optimal savings in the absence of the policy. Since other conditions such as income, transaction costs and prices are unchanged, households make exactly the same decisions on home purchase and consumption. Thus, the mandatory savings feature of the current HPF program is ineffective. Figure 4 illustrates this intuition by plotting the wealth of households who are not yet homeowners when entering each age group (left), and the wealth of existing homeowners in each age group (right). For households who are not homeowners, their previous savings determines their home purchase and consumption. Under the current policy value, θ =.12, these households keep their wealth (defined as the sum of their private and mandatory savings) unchanged at the pre-policy level. For existing homeowners, their wealth determines their consumption. The wealth of homeowners consists of private savings and the value of their house, which is unaffected by the mandatory savings scheme. The reason why the mandatory savings feature of the HPF program has no impact on household decisions is that the mandatory savings are below the optimal savings in the absence of the policy. I explore two extensions where a mandatory-savings scheme can have actual impact. First, in Section 4.5, I consider alternative policy values for θ, the fraction of worker s income deposited to the program. I show that a high value of θ can distort household decisions. Second, in Section 5.1, I consider the case that employers can match workers mandatory deposits, and home buyers are refunded with both their own mandatory savings and their employer s contributions. This additional feature affects household decisions by generating a windfall wealth effect. In the latter case, the mandatory savings feature of the HPF program is somewhat effective but remains quantitatively unimportant. 4.4 Effects of Below-Market Mortgage Rates in Isolation I now consider the effects of a program that offers home buyers a mortgage rate below the market rate. This program replicates all the effects under the HPF program, as shown in Figure 3. Both homeownership and the average home size increase in all age groups beyond age 3. This policy affects household decisions mainly through a wealth effect brought about by the lower 15

borrowing cost. The wealth effect increases homeownership by pushing forward home purchasing decisions and by inducing some households to own a home who otherwise would not. Note that for households under age 3, this policy does not affect the timing of their home purchase (and hence their rate of homeownership), because at those ages most households have not accumulated enough wealth to pay for the down payment and the transaction cost. These payments are necessary to become a homeowner and to enjoy the program benefit. The wealth effect of mortgage subsidies can be illustrated by plotting the wealth and consumption of homeowners, who directly benefit from a lower borrowing cost. Figure 5 shows that the wealth and consumption of homeowners increase in all age groups when the policy is implemented. 4.5 Sensitivity Analysis I now examine how the rate of homeownership, the average home size and expected utility change for different values of the two policy parameters, the fraction of income deposited, θ, and the mortgage rate provided by the program, r b. I also investigate how sensitive the effects of the HPF program are to changes in the bequest parameter. Figure 6 plots the change in the rate of homeownership, the change in the home size and the change in expected utility relative to the baseline model as a function of θ, assuming the program also offers a mortgage rate of 2 percent below the market rate. For θ smaller than.15, the program has the same effects as in the HPF program where θ is set to.12. This result is consistent with the intuition from Section 4.3 that if the mandatory savings are below the optimal savings in the absence of the mandatory-savings policy, households keep their total savings, hence home purchase decisions, unchanged. For θ greater than.15, both homeownership and the average home size increase in θ. However, expected utility decreases. This is because when the required savings are above the optimal savings, households sacrifice their own consumption to fulfill the required savings, which leads to over-save. Later in life, households have more wealth due to the transfer of income from early life. This transfer of income increases the probability of buying a home and raises demand for a larger house. As θ increases further, households are forced to shift more of their income to later life, leading to a larger wealth effect that further increases homeownership and the 16

size of the home purchased. The increased homeownership and increased home size, however, come at the cost of lower expected utility, as households find it more difficult to smooth consumption. This point is illustrated in Figure 7, which plots the optimal savings of non-homeowners in the absence of mandatory savings, and their total savings under alternative θ. For θ greater than.15, total savings is above optimal savings, and hence creates distortion in consumption and home purchase decisions. Figure 8 shows the results of a similar exercise with θ fixed at.12 and the mortgage rate taking different values. The horizontal axes illustrate the intensity of these changes by a spread between the market interest rate and the subsidized mortgage rate. When the spread is zero, the policy boils down to a mandatory savings program, so the impact is zero. As the spread increases, homeownership, average home size and expected utility increase. These results are due to the wealth effect created by the lower borrowing cost. Households push forward their home purchase in response to this wealth effect, and they can afford a larger home as the interest rate spread increases. The wealth effect also raises consumption. Therefore, expected utility goes up as the spread increases. Since a direct measurement of the bequest motive is hard to obtain from the data, I now examine how sensitive the effects of the HPF program are to the change in the bequest parameter, η. I first recompute the baseline model for a given value of η as the pre-policy scenario. I then compute the model with this value of η under the HPF polices (θ =.12, r r b =.2). Figure 9 shows that homeownership, average home size and expected utility do not change much with different values of the bequest parameter. Based on the previous analysis, the HPF program affects overall homeownership mainly by pushing forward young households home purchase decisions. Young households, however, are less sensitive to the change at the end of the life cycle, such as a change in the utility weight of leaving a bequest. Therefore, changing the bequest parameter does not have much effect on homeownership. The HPF program also increases the average home size, mainly through the wealth effect, whether households value their bequest or not. Such increase is not sensitive to the change in the bequest parameter. 17

5 Extensions In this section, I consider two extensions to the model in Section 2 intended to make the model more realistic. First, I allow employers to contribute to worker s HPF savings by matching a fraction of workers HPF deposits. Second, I model rental markets and renters choices explicitly. I show that the results in Section 4 are robust to these extensions. 5.1 Employer Contributions Often, the employer of a program participant is required by the government to contribute to the participant s HPF savings. Both the worker s deposits and the employer s contributions are refunded to the worker with interest when the worker purchases a house or retires, whichever is earlier. How much an employer contributes, however, is chosen by the employer, and varies according to local regulations and the employer s profit condition. The HPF program requires that the amount the employer contributes to the worker s HPF savings should not exceed the worker s own deposits into the program. This additional contribution from employers is not accounted for in Section 2. In this section, I model the employer contribution by assuming that an employer has to match x of the worker s deposit, where x 1. Therefore, the total deposit of the worker to the program in period t is (1 + x) θy t. The case x = corresponds to no employer contributions, as modeled earlier. The case x = 1 means that the employer matches the worker s contribution dollar by dollar. First consider the program with a mandatory savings feature only, in which workers deposit 12 of their income to the program, consistent with the baseline calibration. In addition, let employers contribute to workers savings by matching x of their deposits. Both a worker s deposits and the contribution from his or her employer are refunded with interest when the worker purchases a house or retires, whichever is earlier. However, this program does not offer a subsidized mortgage rate. Figure 1 shows the results for this exercise. The left panel shows the change in homeownership in each age group as employers match 2, 4 and 6 of workers deposit, relative to no employer 18

contributions. When employers match 2 of workers deposits, the rate of homeownership is lower for young age groups. It gradually converges to the no-contribution case toward the end of the life cycle. This implies that employer contributions delay households decisions to purchase a home. This result is expected because workers treat their employer s contributions as windfall income, when they withdraw their program savings. This windfall income is larger if a worker deposits his or her own income for a longer time. Since no deposit can be made to the program once a worker buys a house, the worker may delay the purchase, and buy a larger house later when he or she can receive more windfall income. This delay effect is stronger as the contribution from employers increases. On the other hand, as shown in the right panel, buyers choose a larger home as the employer contribution increases, because they have more cash available. The lower panel of Table 4 summarizes the change in overall homeownership and the average home size for this exercise. Next, I reintroduce the below-market mortgage rate feature and quantify how much employer contributions can alter the effects of the HPF program. Figure 11 shows the change in homeownership and the average home size when the HPF program is characterized by a 2, 4 and 6 matching deposit from employers. The intuition from the earlier exercise survives here: households delay their home purchases in expecting a larger future windfall income from employer contributions. When they buy a house, they choose a larger size. The quantitative results are summarized in the upper panel of Table 4. To sum up, the results on the average home size are similar to Section 4, and the results on homeownership is similar if the matching deposit made by employers are small. To the extent that x is large on average, the average home size remains similar to Section 4, but the rate of homeownership decreases, making the program less effective. 5.2 Rental Markets In this section, I model the rental option explicitly by allowing households who are not homeowners to choose their housing services in the rental markets. 6 Unlike purchasing a home, renters can adjust their housing services without paying a transaction cost. However, the rental cost can be expensive relative to owner-occupied housing. This motivates renters to become homeowners. 6 Models in the previous sections can be considered as incorporating a simple rental market which provides houses of a size less than h, and the rental cost on such housing is negligible. 19

With rental markets, households who do not own a house can choose a rental house of size d at a unit rental cost of R per period. The flow utility of renters is u(c) + v(d). There is a minimum size of the rental house, d >, that generates utility. Therefore, v(d) = for d d. Households make other decisions such as home purchases and consumption as in Section 2. The model now has a new parameter to calibrate, the rental cost R. In the CHIPS data, homeowners report their own home value. They also give an estimate of how much they expect to charge if they rent their home out. The ratio of these two variables gives an empirical rent to price ratio, R/P, which pins down the value of R. In the data, R/P =.1 7. Figure 12 illustrates the key variables in the baseline model with rental markets. Incorporating this additional sector does not change household behavior much: homeownership and the average home size are monotonically increasing over the life cycle. Consumption exhibits a hump shape. Wealth is increasing at a faster rate early in life than later, and flattens out after retirement. Homeowners choose a larger home size than renters, because the rental cost is more expensive, and because renters have to accumulate their savings for being a homeowner in the future. Table 5 summarizes the steady-state impact of the HPF program in the model with rental markets. The program increases the rate of homeownership by about 8 percentage points and raises the average home size by 2, In addition, expected utility increases. I then examine the effects of each program feature in isolation. The mandatory-savings feature does affect household choices slightly, and increases both homeownership and home size. Unlike in the model of Section 2.2, households who are not homeowners have to pay for their rental services and hence reduce their optimal savings in the absence of the mandatory savings requirement. Therefore, the same policy rate of θ now can cause households to oversave, and distort home purchase decisions as discussed in the first sensitivity analysis. However, the effects from the mandatory-savings feature are negligible, as the program effects are mainly driven by the feature of below-market rate mortgages. This analysis shows that the results in Section 4 are robust to adding the rental markets that represent the current rental market conditions in China. Do the effects of the HPF program differ if alternative rental market conditions are considered? 7 r+δ Note that this empirical rent to price ratio is higher than the user cost of owner-occupied housing,, where β(1+r) δ is the housing depreciation rate, assumed to be zero in the model. This user cost is about.5 using the calibrated value of r and β 2

It can be shown that the more attractive the rental option is in the baseline scenario, the more effective the HPF policies are in raising homeownership and home size. First, I consider the effects of the HPF program when the rental cost increases. Second, I consider the effects of the HPF program when the user cost of owner-occupied housing increases. The intuition is that when the rental option is more attractive in the baseline scenario, more households stay renters and the rate of homeownership is lower. Therefore, the extent to which the program can stimulate home purchases is larger. Figure 13 shows how effective the HPF program is in increasing homeownership and the average home size for different rental costs. When the rental cost is small, more households choose to be renters in the baseline model, the rate of homeownership is low, and the average home size is small. In this case, the HPF program is more effective in raising homeownership. Since home buyers tend to choose larger homes than renters, the average home size is also larger. Figure 14 shows how effective the HPF program is when the housing depreciation rate changes. 8 This change leads to a change in the user cost of owner-occupied housing. As δ increases, owner-occupied housing is less attractive than rental housing, more households choose to be renters, and the rate of homeownership and the average home size is low. Therefore, the HPF program is more effective. 6 Conclusion There has been much interest in the question of how the HPF has affected homeownership in China. This question is of interest not only to Chinese authorities but to policymakers more broadly, because similar policies have been implemented in a range of countries. Addressing this question empirically is not straightforward because of selection bias, because of anticipation effects, and because of the short duration of this program to date. An alternative approach to quantifying the expected effects of this program is the use of quantitative theory. Existing theoretical studies of this question have relied on representative-agent models (see., e.g., Buttimer et al. (24) and Tang and Coulson (217)). Such models are not well-suited for studying the effect of these policies, because in representative-agent models either everyone or no one buys a house. The current paper introduces a life-cycle model with heterogeneous 8 To maintain the size of their home as in the previous period, homeowners have to spend on the cost of depreciation, i.e., δph. In earlier sections, δ is assumed to be zero. 21

agents that allows agents purchases of homes to depend on their age and unobserved characteristics. This model allows me to quantify the increase in homeownership one would expect in response to this program. I show that the HPF program is expected to increase the rate of homeownership by 6.7 percentage points in steady state. It also increases the average size of homes. These results are robust to allowing employers to match the workers contributions and to introducing the rental markets. One advantage of addressing this question based on a quantitative model is a better understanding of the mechanisms by which these policies affect economic outcomes. I find that the mandatory savings feature, as currently implemented, has no impact on household home purchase decisions because the mandatory savings are below the optimal savings in the absence of the policy. In this situation, households keep the sum of their private and mandatory savings equal to the optimal savings in the pre-policy scenario. Since other conditions such as income, transaction costs and prices are unchanged, households make exactly the same decisions on home purchases and consumption. Regardless of how long households are forced to save, the program also provides access to subsidized mortgages, which stimulate more households to become homeowners, and to purchase a larger home. This feature alone accounts for all of the estimated effects of the HPF program. However, households ability to take advantage of these mortgage subsidies depends on unobserved characteristics. In the calibrated model, the fraction of participating households who are unable to buy a house by the end of their life time is about.4. Although the model presented in this paper is more realistic than previous theoretical models of Chinese housing policies, the analysis in this paper is only a first step. I showed that the modeling device of a random transaction cost for potential home buyers in conjunction with heterogeneity in wealth within the same age group suffices to match some of the key features of the Chinese housing market. The model abstracts from heterogeneity in family size. This simplifying assumption is unproblematic to the extent that the one-child policy has largely eliminated this problem and that current efforts to increase population growth thus far have had little effect. An implicit assumption underlying my analysis is that the supply of housing is elastic. This assumption is supported by evidence in Wang et al. (212) whose estimates of the price elasticity 22