Permanent Land-Use Rights And Endowment Insurance: Chinese Evidence Of The Substitution Effect Ning Yu ∗ , School of Economics, Shanghai Jiao Tong University, 535 Fahuazhen Road, Shanghai, 200052, China Department of Economics, W. P. Carey School of Business, Arizona State University, University Drive and Mill Avenue, Tempe, AZ, 85287, U.S.A

Qinghua Shi, and Hongtao Jin School of Economics, Shanghai Jiao Tong University, 535 Fahuazhen Road, Shanghai, 200052, China

Abstract This paper studies the substitution effect of permanent land-use rights on endowment insurance in China. We first explain the rationality using an overlappinggenerations model with heterogeneous households possessing land-use rights or not, and find that economic agents profiting from land in the latter stage of their life tend to save less for retirement than their land-deprived counterparts. Empirical evidence from village-clustered Chinese survey data on rural households supports this finding, locating a significant negative effect of land on social and commercial endowment insurance purchase. Apart from the important policy implication of compensating land-deprived farmers with insurance, our theoretical and empirical models both yield unexpected informing findings. Key words: Land-use Rights, Endowment Insurance, Overlapping-Generations Model, China

∗ Corresponding Author. Email addresses: [email protected] (Ning Yu), [email protected] (Qinghua Shi), [email protected] (Hongtao Jin). 1 This research is supported by NSFC (70873102, 70703023, and 70673065). The authors would like to give thanks to Chinese Bureaux of Rural Longitudinal Observation for access to the precious panel data on tens of thousands of rural households. We also sincerely appreciate the assistance of Dr Xi Zhu in the laborious process

4 August 2009

of data management. Further, seminar participants in Nanjing Agricultural University and Zhejiang University provided useful suggestions, which are essential for the improvement of this paper. We also benefits substantially from experienced advice from Dr Scott Rozelle (Stanford University) and Dr Hanming Fang (Duke University). We are also grateful to referees for significant constructive comments.

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1

Introduction

After the inception of the People’s Republic of China, land reform redistributed farmland nationwide, following the principle of egalitarianism. At the climax of the Communist Movement, farmland was collectively both owned and cultivated by different organized groups of farmers. In 1978, the ruling Communist Party changed this unsustainable course and gradually issued land-use rights with fixed time intervals, typically 15 years, which were extended another 30 years in 1993. Krusekopf (2002), Dong (1996), Ho and Lin (2003), and Yang (1997) reported many anomalies in this era, including diverse land tenure, illegal land use, and large-scale inefficient allocations of land and labor, resulting partly from a complex hierarchical system of primary and secondary markets for land use rights; i.e., agricultural use of rural land should not be changed without going through the process of government acquisition. In 2006, Premier Wen Jiabao announced at the 4th session of the 10th National People’s Congress, “We say that we should secure farmer’s long-term landuse rights. This policy should not change in 15 years, 30 years, and even forever.” This was the first official guarantee that in the foreseeable future, the government will not reclaim land-use rights distributed after 1978. These are restrictive rights in the sense that farmers cannot unilaterally alter the agricultural use of the land or sell or mortgage it freely, but passing the rights to descendants is a common practice. Despite its limitations, this is still a great leap toward a land policy that respects property rights and makes the land-use rights of farming households much less susceptible to whimsical policy makers and profit-obsessive local governments. We thus hypothesize that farmers, when making economic decisions, have been taking into account that their land-use rights are a non-degenerate form of wealth and, in particular, that ownership of land influences endowment insurance purchase. Endowment insurance of farmers, as we define it, includes old-age and life insurance, both serving as saving mechanisms for retirement. As there exists no widespread rural pension system and the survey does not distinguish between social and private insurance purchases, we study the influence of land-use rights on overall endowment insurance consumption. These rights at least play a role of shelter from food shortage, as many migrant workers perceive according to our own yearly survey. Another incentive originates from the expectation of economic compensation from the government if these rights are called back as a result of rapid urbanization. In a word, a substitution effect should show up following our reasoning. To model the decision on endowment insurance consumption, we develop an overlapping-generations model (OLG), the debut of which, in the English literature, is possibly in Samuelson (1958). Geanakoplos (1987) is a useful review 1

of this subject. This model is a powerful tool in the study of resource allocation between different life stages, for it captures the balancing decision explicitly. Several researchers have used OLG models to analyze the Chinese pension system, including Li and M´erette (2005) and Yi (2009), which emphasized the effect of the aging population and the consequence of pension reform, respectively. However, the current system does not integrate rural residents, and thus none of these OLG models are suitable for the problem we discuss, let alone a model including land. Limited OLG models with land have been created for different purposes. Widasina and Wilson (1971) considered the welfare implications of land-value-maximizing local governments. Farmer and ˙ Randall (1997) was concerned with sustainability of land. While Imrohoroˇ glu et al (1971) indeed explored the interaction of two factors, land and social security, its model setting is essentially different from ours because land is privately owned in their model. Owing to the unique household registration system (also known as the Hukou system) and rural household responsibility system in China, our model differs from ordinary OLG models with land in many aspects. One of the distinctive features of our model is that holders of land-use rights can only benefit from rent income, but buying and selling of these rights are prohibited as the status quo in China. Further, only rural residents registered as farmers have access to land-use rights; i.e., there exist many rural residents without land-use rights because of their registration as non-farmers. The distinction is largely exogenous because the registration uses households as units, and thus children inherit the status of their parents. The introduction of exogenous heterogeneity among households facilitates comparison between those holders and land-deprived households. Within-household distribution of rent also has a bearing on the economic outcome; that is, the more rent individuals are to receive in old age, the less necessary it is for them to save for retirement when young. In our model, a transition to private ownership may not be all positive owing to reduced capital investment in the steady state. Testing the substitution effect involves rural survey data collected by the Chinese Bureau of Rural Longitudinal Observation. This program started in 1984 to collect detailed yearly panel data on the life and production behaviors of rural households in about 350 villages in all 31 province-level administrative districts in mainland China. The Bureau selected these villages and households at random to ensure that policy makers and researchers could draw valid conclusions. Over time, some households have moved out of the villages and dropped out of the program, but this does not cause much selection bias for this study is concerned about economic decisions made by rural residents. Moreover, because Premier Wen’s credible assurance of permanent land-use rights representing the government happened in 2006, we are unable to take advantage of panel data; however, the village-clustered structure allows us to control village-specific fixed effects, including geographic policy variations. 2

The use of cross-sectional data again alleviates the seriousness of the selection bias of our sample. In order to be more precise, we finally project the insurance purchase decision into whether to participate and how much to buy, thus adopting the Heckman selection model. At first sight, the substitution effect seems evident because the land-use rights can play a role as wealth that the farmers consume when they retire, but it is just the consistency of the land law and policy protecting permanent land-use rights that are in doubt. The split of land property rights into landuse rights and collective ownership is the cause of much confusion. Article 10 of the constitution 1 says that “Land in the cities is owned by the state. Land in the rural and suburban areas is owned by collectives except for those portions which belong to the state in accordance with the law; house sites and privately farmed plots of cropland and hill-side land are also owned by collectives. The state may, for the public interest, expropriate or take over land for public use, and pay compensation in accordance with the law. No organization or individual may appropriate, buy, sell or otherwise engage in the transfer of land by unlawful means. The rights to the use of land may be transferred according to law.” The loophole is that the law does not ensure permanent land-use rights and the compensation mentioned is not decided by the market or negotiations in which farmers have a say. In a nation-wide survey reported by Shi and Yu (2009) that lasted from 2002 to 2004, a 51% majority of rural residents considered the national government the de facto owner of rural land, among which 83% knew that the law points in another direction, that is, to the collectives. To make matters worse, the Communist Party has a notorious reputation among rural residents of issuing a policy in the morning and abandoning it in the evening. As a result, at the beginning of the research, we were not sure whether the rural residents had faith in the words of the premier and treated their land-use rights as a substitute for endowment insurance. Another practical significance of this paper lies in the troublesome land requisition compensation policy in the process of rapid urbanization in China, which constantly occupies national headlines. At large, this compensation is presently left to the discretion of rural officers in the form of a cash payment, investment portfolio, insurance, employment, or a combination of these. Owing to this undue flexibility, farmers, who are often deprived of their land and offered unfair compensation, resort to so-called mass incidents, demanding justice, for which Jin et al (2009, in Chinese) can be a useful reference. More often than not, farmers with the problem of dynamic inconsistency as other 1

The currently effective Constitution of the People’s Republic of China was adopted at the Fifth Session of the Fifth National People’s Congress on December 4, 1982 and amended at the First Session of the Eighth National People’s Congress on March 29, 1993.

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economic agents spend their slim pure cash compensation quickly on consumptions and even lotteries rather than on investment or insurance and again find themselves in want of a channel for complaint. If the paper establishes that farmers with land do tend to ignore the importance of insurance, reasoning that there will not be a food shortage in their old age if only they can work on their land, insurance with the merit of preventing irrational spending certainly emerges as an indispensable compensation approach.

2

The Model

2.1 Model Description The well-known OLG model describes infinite-living households consisting of economic agents, each of whom lives for two periods. When these economic agents are young, i.e., in the first period of their lives, they provide labor, and save for retirement so that they can consume when old, i.e., in the second period of their lives. This saving-for-retirement structure meets our need to model the voluntary purchase of endowment insurance. There are L fixed households in our model, and each household contains two economic agents, one young and one old, in period t = 0, 1, 2, · · · . Each economic agent supplies 1 unit of labor and earns a wage of wt when young, then completely withdraws from the labor market when old, so the economy has a labor supply of L in each period. We rule out population growth so as to focus on the within-generation comparison, and the latter introduced time-invariance of technology is due to the same consideration. For v ∈ (0, 1), vL households each own the permanent use-rights of q units of land, and the others do not. There is a fixed amount Q = qvL of land. As for the rent zt q received by a representative household with land, an exogenous proportion of s goes to the young agent and 1 − s to the old. Young economic agents can only save in or borrow from private pension funds in the form of old-age or life insurance. In period t, a young agent without land saves iTt (T stands for tenant) and consumes cTY t = wt − iTt accordingly, and an old agent receives cTOt = (1 + rt )iTt−1 . A young agent with land saves iLt , negative when he or she borrows from the funds, which is possible because there may be substantial rent income in the next period. As a result, his/her consumption is cLY t = wt + szt q − iLt , and the old agent with land consumes cLOt = (1 + rt )iLt−1 + (1 − s)zt q. The pension funds earn zero profit owing to perfect competition. All young economic agents in period t have the same 1 overall utility function of U (cY t , cOt+1 ) = ln(cY t ) + 1+θ ln(cOt+1 ), with the rate 4

of time preference θ ∈ [0, ∞). Forward-looking agents maximize their utility function by choosing the optimal endowment insurance level when young. In this one-sector model, the constant-return-to-scale Cobb-Douglas production function in each period is specified by F (Q, Kt , L) = AQ1−α−β Ktα Lβ , where α > 0, β > 0, and α + β < 1. Here A represents time-invariant technology and Kt equals total endowment insurance bought by young agents in period t − 1. We can imagine this sector as agriculture, and a large number of small farms participate in the perfect competitive economy and earn zero profit. 2.2

Steady State Analysis

Because there is no population growth or technology change in this economy, the steady state keeps all variables unchanged between periods, greatly simplifying our analysis and allowing the dropping of time subscripts. To begin with, in this perfect competitive economy, land, capital, and labor earn their marginal product; that is,  −(α+β) α β  K L , and  z = A(1 − α − β)Q

r = AαQ1−α−β K α−1 Lβ , w = AβQ1−α−β K α Lβ−1 .

  

and

The maximization problem for agents without land becomes max {ln(w − iT ) + T {i }

1 ln[(1 + r)iT ]}, 1+θ

which yields

w . 2+θ For agents with land-use rights, the maximization problem is iT =

max {ln(w + szq − iL ) + L {i }

which yields iL =

(1)

1 ln[(1 + r)iL + (1 − s)zq]}, 1+θ

1 1+θ w + [s − (1 − s)]zq. 2+θ 2+θ 1+r

(2)

The comparison between Equations 1 and 2 tells us that whether agents with land-use rights purchase more endowment insurance than their counterparts (1 − s)]. This is very is determined by the positivity or negativity of [s − 1+θ 1+r intuitive because the more agents expect to earn in old age, the less necessary it 5

is for them to save in working age. In China, a long tradition of filial piety more or less retains some household decision power of family seniors. Moreover, the current household responsibility system of allocating land-use rights entitles senior farmers, as household heads, to the land-use rights. In summary, we expect a negative relation between land and endowment insurance.

2.3 Optimal Within-Generation and Intergeneration Distribution of Rent

In this economy, capital is the only endogenous factor affecting production, so it is private savings given by Equations 1 and 2 that determine the level of production. We maximize capital K with respect to v and s. Propositions 1 and 2 exhibit the result of optimization. Proposition 1 (Optimal Within-Generation Distribution of Rent) 2 Under the former assumptions, v, the proportion of households possessing a claim to land-use rights, does not affect Kt , and thus F (Q, Kt , L). Although Proposition 1 depends crucially on the assumptions of the CobbDouglas production function and log-linear utility function, it still serves as a good example to show that inequality of property rights does not influence the productivity of the society, as long as inequality does not affect incentive to work. In China, there are always concerns that land-deprived farmers may lose their livelihood, so entities occupying the land are very often forced to provide jobs for these farmers. Inefficiency unavoidably emerges because those occupations are usually low-paid sinecures, for it is rare that the entities find farmers who are qualified employees. Markets for land-use rights should be established so that efficient farmers can return to the agriculture sector even when their own land-use rights are reclaimed by the government. Proposition 2 (Optimal Intergeneration Distribution of Rent) 3 Under the former assumptions, Kt and F (Q, Kt , L) are strictly-increasing functions of s, the proportion of rent going to the younger generation. The optimal value is 1, i.e., the younger generation collects all rent. If agents expect to receive much income in the form of rent when they retire, their incentive to save for retirement diminishes in their early years. As saving equals investment, the capital in the economy decreases. This philosophy is behind Proposition 2. To enlarge the economy, society should hand over the land-use rights to those who work in the field. 2 3

This is proved in the Appendix. This is proved in the Appendix.

6

The above analysis considers production as the object function, but maximization of the utility function is the ultimate goal of economic activities. It turns out that the condition on which s = 1 maximizes the utility function is not too demanding, but the exact description is quite complicated. For example, 1 a sufficient condition is α ≥ 3+θ for agents without land-use rights.

2.4

Comparison with Private Ownership of Land

If the government completely privatizes farmland and restricts the purchasing rights to a proportion v of the population, the steady state production can reduce, as we will show. We use all former notations and introduce p as the equilibrium price of land bought by the younger generation from the older one at the end of each period. Response of economic agents to this change is not desirable from a social planner’s point of view, which is summarized by Proposition 3. Proposition 3 (Diminution of Capital and Increase of Interest Rate) 4 In the economy with private ownership of land, capital investment K in the steady state is smaller than that with permanent land-use rights, and the interest rate r is higher. On one hand, Proposition 3 points out that land trade between generations squeezes out some capital investment in the economy, so the production level is lower in this case. This theoretical result provides a tentative partial explanation of the very high saving rate in China: restrictive land property rights prevent people from buying it. On the other hand, the interest rate r rises as capital K tumbles down; just as Keynes (1936) pointed out, “There have been times when it was probably the craving for the ownership of land, independently of its yield, which served to keep up the rate of interest; – though under Gesell’s system this possibility would have been eliminated by land nationalisation.” A policy implication can be naturally derived that the necessity to change the land-use rights to complete property rights may not be as apparent as some people claim. We are not suggesting that all countries nationalize land, but now that seminationalization is irreversible in China, it is unnecessary for this country to shock back in a hurry.

4

This is proved in the Appendix.

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3

The Microeconometric Study

3.1 Data Description

The survey data used for the microeconomic study were collected by the Chinese Bureau of Rural Longitudinal Observation in 2007. In this complex largescale household survey, 353 villages were selected from all 31 province-level administrative districts in mainland China, and the same approximately 20 thousand households have been surveyed every year since 1984. In 2007, the number of observations was 19,394.

Notes: The variable land uses the measure of Chinese acre, mou. 1 mou = 667m2 . The variable house uses the measure of square meters. The insurance, income, and med variables are in terms of Renminbi or Yuan, the official currency of P. R. China.

The variables we are interested in are the endowment insurance purchased in 2007 (insurance), the family total income (income), the amount of land for which the household possesses use rights (land), the number of family members (pop), the number of boys aged 18 or younger (boy), the number of girls aged 18 or younger (girl), the maximal number of years of formal education among family members (edu), the expense on medication in 2007 (med), the total housing area (house), and whether there are village officers in the household (officer). Merging and managing data sets decreases the number of observations to 18,476, 38.29% of which invested in endowment insurance, including life and old-age insurance. Life insurance, according to The American Heritage College Dictionary, guarantees a specific sum of money to a designated beneficiary upon the death of the insured or to the insured if he or she lives beyond a certain age, playing a role of pension investment, so we do not hesitate to introduce it into the dependent variable. Descriptive statistics are given in Table 1. 8

As we expected, the correlation coefficient between insurance and land is negative, with a value of -0.0478.

3.2 Simple Regression Analysis We proceed to test the hypothesis that land-use rights have a substitution effect on endowment insurance. Before doing so, some complications naturally emerge. First, our observations apparently do not satisfy the independent identical distribution (iid) assumption, owing to the sample stratification and clustering. Second, there are many important missing variables, for example, local government policies, attractiveness of policies issued by insurance companies, presence of active salesmen of insurance in the village, and convenience of payment. More importantly, it is credible that villagers share a similar culture and thus are protected by similar informal insurance mechanisms such as family networks, a factor influencing the demand for formal insurance. Fortunately, the village-clustering structure allows us to account for the abovementioned factors with village-specific intercepts. Specifically, we establish the cluster-specific effects regression model as insuranceic = αc +β1 incomeic +β2 landic +β3 popic +β4 boyic +β5 girlic +β6 eduic + β7 medic + β8 houseic + β1 officeric + ²ic , where i = 1, · · · , Nc , c = 1, · · · , C. Here, c represents different villages with different numbers Nc of households in the sample, and i pins down the household. We do not give the observations weights, following the convention of microeconometric study. The estimation can be easily carried out by unbalanced panel data estimation commands. Table 2 lists relevant results. To decide which model should be used for further discussion, we used the Hausman model-specification test to study whether RE estimators were significantly different from consistent FE estimators. The calculated p-value is 0.0340, so it is not safe to use possibly more efficient RE estimators. As for the coefficients of the CSFE model, income and land behave predictably. It comes as a surprise that numbers of family members and children do not seem to influence the amount of endowment insurance purchased even jointly, given fixed income and land. A tentative explanation is that children, although long thought of as insurance for old age in Chinese culture, are no longer so. Furthermore, education has a significant positive effect; that is, better-educated rural residents prepare better for their retirement. The positive significance of the officer variable is very interesting, taking into account that we have already considered many demographic variables. 9

Notes: 1. The random effects model is estimated by GLS regression, and the fixed effects model by within regression; 2. Estimations of intercepts are dropped due to limited space; 3. The first numbers are estimations of slopes, with one, two, and three stars denoting significance at the levels of 10%, 5%, and 1%, respectively; 4. The second numbers in parentheses are estimated standard errors robust to heteroskedasticity or clustering.

3.3 Two-Stage Regressions

The above analysis does not differentiate between the decision to participate in endowment insurance programs and the choice of an exact investment amount. The two-part model established by Cragg (1971) first explained whether to participate by a binary choice model, and then studied the exact amount only for those choosing to participate, thus befitting our need to decompose two decision-making processes. Nevertheless, those who buy a positive amount of insurance form a non-randomly selected sample, due to the endogenous nature of the decision to participate. Heckman (1979) provides a solution to this problem. We employ both models and compare the results in Table 3.

10

Notes: 1. For the two-part model, the first part is a binary logit model with cluster fixed effects estimated by a conditional logit option, from which 63 villages were dropped owing to uniform decisions; the second part only uses observations with positive investments in endowment insurance and is estimated within the regression; 2. The Heckman selection model is estimated by the standard method, controlling village clustering effects; 3. We do not log-transform insurance so as to facilitate comparison with Table 1; 4. Notations are the same as in Table 1.

As the table shows, the variable of lambda is significant in the Heckman selection model, so we should derive implications from it. In the first stage, coefficients of key variables do not change their behavior much. However, in the second stage, some surprising outcomes emerge. For example, land is not a significant variable, which implies that land ownership is crucial for the decision of whether to buy insurance, but the amount of investment is determined by other factors, such as income level and assets. House, as an important category of assets, becomes positively significant here, contrary to its performance in other models. A report by National Bureau of Statistics of China (2009, in Chinese) sheds some light on this phenomenon. It indicates that the transfer rate of land 11

operation rights is still low in Fujian province, which is not atypical, although there are numerous policies that legitimize or encourage this practice. As a reference, Ding (2003) claimed that rental market participation in some of the poorest provinces was 9.4% in 2000, exhibiting an upward trend. Considering that at the end of 2006 only 49.3% of farmers in Fujian received their major income from the agriculture sector, we should narrow down the causes of a low transfer rate. As the report suggests, their survey shows that land-use rights ensure basic living allowances for farmers when they are unable to migrate to work in the cities. They insist on the security of their land-use rights, and even allow other villagers to farm with zero rent in order to avoid acquisition by the village, for disusing farm land is prohibited. In summary, we can arrive at some logic behind the decisions made by rural residents in China. First, land and endowment insurance are both life-ordeath factors defining their old age. With memories or stories of the great famine of 1960 haunting them, Chinese people denied access to the social security system constantly worry about their future livelihood. Land produces food. It is no wonder that people with less or no land have much greater incentive to buy insurance. Second, farmland is of no collateral value according to jurisprudence and generates meager income in limited operations of the land market. When deciding how much to invest in insurance, people are subject to budget constraints that have little bearing on land-use rights, but housing is another story.

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Discussion

Based on the theoretical OLG model of heterogeneous households, we argue that land-use rights may have a negative effect on farmers’ investment in endowment insurance, resulting from their expectation of rent income in the later period of their life. To increase saving so as to encourage capital investment, the government should secure land-use rights for young farmers and should think twice before fully privatizing farmland. The empirical study supports our hypothesis of a substitution effect between land-use rights and endowment insurance, establishing a negative relation between exogenous land-use rights and chosen amount of investment in endowment insurance. There are also some interesting by-products of our study. For instance, bearing more children may no longer be considered a mechanism of informal insurance. There are some tentative policy implications of this research. Rapid reform on property rights of farmland may not be a good practice at this stage. First, it may increase inequality among farmers because farmland in Shanghai is 12

worth much more than that in western provinces if it is exchangeable. Since the Communist Party redistributed the land at the cost of landowners in 1949, it is not legitimate for this resulting distribution to be far from fair equality. Second, it may not narrow the gap between rural and urban residents because acquisition of full property rights of land does not improve farmers’ ability to earn a decent living. Anyhow, the amount of land these farmers have is quite limited, averaging 2.16 mou per person according to the 2008 Chinese Statistical Yearbook. Third, abuse of the land market may inevitably throw some farmers below the subsistence level, as some officials possess no notion of civil rights, especially when they are in conflict with economic interests. Dong (1996) arrived at a similar policy implication from another perspective. There are now different packages of compensations for deprivation of land-use rights in China. As this paper reveals, inclusion of endowment insurance is reasonable because of its substitution effect. A good proportion of farmers do not buy endowment insurance at all because they think land-use rights secure their access to food production and serve as insurance. Furthermore, it is more efficient than other means, such as mandatory employment by the occupier, for it is less likely to distort the land and labor markets. Another policy option that is rarely used is allowing land-deprived farmers to acquire new land-use rights in some well-designed system, such as auction. According to the author’s interview with farmers in Shandong Province, some villages used auctions to allocate land in the 1980s, and they were conscious that this mechanism is less susceptible to abuse of political and social power, and even power related to local gang activity. As Feldstein (1999) indicates, decades of social security reform should serve to bring in enough learning-by-doing expertise to guide the provision of retirement security for the entire Chinese nation instead of currently only urban workers. Resorting to insurance companies is the only means employed of compensating land-deprived farmers with endowment insurance, while it should not be. Admitting them to the social security system is also an option.

A

Appendix. Proof of Proposition 1 and 2

In the steady state, K = (1 − v)LiT + vLiL =

Lw 1 (1 + θ)(1 − s) + zqvL [s − ] 2+θ 2+θ 1+r 1 (1 + θ)(1 − s) Lw + zQ [s − ]. = 2+θ 2+θ 1+r 13

The last equality holds because Q = qvL according to our definition. We can plug in the expressions for z, r, and w and get 1 1−α 2 AQ1−α−β Lβ (K ) + [1 + θ + α − (2 + θ)β − (2 + θ)(1 − α − β)s]K 1−α − 2 2(2 + θ) (AQ1−α−β Lβ )2 α[β + (1 − α − β)s] = 0. 2 This equation implicitly gives K as a function of s. Because v plays no role here, Proposition 1 is sound. To simplify the analysis of optimal s, we set    C=     D =   E=     

F =

1+θ+α−(2+θ)β AQ1−α−β Lβ , 2(2+θ) (2+θ)(1−α−β) AQ1−α−β Lβ , 2(2+θ) αβ (AQ1−α−β Lβ )2 , 2 α(1−α−β) (AQ1−α−β Lβ )2 . 2

and and and

It is apparent that D, E, and F > 0. We now have the equation 1 1−α 2 (K ) + (C − Ds)K 1−α − (E + F s) = 0, 2 and solving this quadratic equation gives us the only positive solution K 1−α (s) =

q

(C − Ds)2 + 2(E + F s) − (C − Ds).

It follows that D2 s − CD + F s DK 1−α + F s dK 1−α =q +D = q > 0. ds (C − Ds)2 + 2(E + F s) (C − Ds)2 + 2(E + F s) Since s ∈ [0, 1], its optimal value is 1; that is, s = 1 yields the greatest steady state capital and production, and thus we prove Proposition 2.

B

Appendix. Proof of Proposition 3

For (1 − v)L young agents in each period, the optimization problem is exactly the same as for agents without land-use rights in the former model, and thus their savings for retirement are given by Equation 1. For the other vL ones, their problem changes substantially as each of them must decide the amount of money to save and the amount of land to buy at the end of first period of their lives. The maximization problem is max {ln(w − iL − pq) + L

{i ,q}

1 ln[(1 + r)iL + (z + p)q]}, 1+θ 14

with first order conditions given by  1  ∂UL = − + ∂i w−iL −pq p  ∂U = − + ∂q w−iL −pq

1 1+r 1+θ (1+r)i+(z+p)q z+p 1 1+θ (1+r)i+(z+p)q

= 0, and = 0.

Solving these two simultaneous equations gives  p = z , and r iL = w − z q. 2+θ

r

So we have

Lw 1 − zQ . 2+θ r We can plug in the expressions of z, r, and w and get K = (1 − v)LiT + viL =

K 1−α =

αβ AQ1−α−β Lβ . (2 + θ)(1 − β)

For the economy with private ownership in the steady state, K 1−α =

αβ AQ1−α−β Lβ , (2 + θ)(1 − β)

while for the one with permanent land-use rights with s = 0 according to the Appendix, K 1−α =

q

q

(C 2 + 2E) − C =

[1 + θ + α − (2 + θ)β]2 + 4(2 + θ)2 αβ − [1 + θ + α − (2 + θ)β] 2(2 + θ)

AQ1−α−β Lβ .

So our task is to prove q

[1 + θ + α − (2 + θ)β]2 + 4(2 + θ)2 αβ − [1 + θ + α − (2 + θ)β] >

2αβ , 1−β

that is, q

(1 + β) [1 + θ + α − (2 + θ)β]2 + 4(2 + θ)2 αβ > (1 + β)[1 + θ + α − (2 + θ)β] + 2αβ. Squaring both sides and rearranging leaves 4(θ2 + 3θ + 3)αβ − 8(θ2 + 3θ + 2)αβ 2 + 4(θ2 + 3θ + 2)αβ 3 − 4α2 β > 0, equivalent to 4(θ2 + 3θ + 2)αβ(1 − β)2 + 4αβ(1 − α) > 0, 15

which is apparent. In addition, the expression for r in Section 2.2 shows that a decline of K will lead to larger r.

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National Bureau of Statistics of China, Report on transfers of rural land operation rights in Fujian province, Official Website (July 2, 2009). Samuelson, P. A., An exact consumption-loan model of interest without the social contrivance of money, Journal of Political Economy 66(1958), 1-18. Shi, Qinghua and Yu, Ning, Ownership of rural land: the gap between laws and farmer’s perception, Working Paper(2009). Wildasina, D. E. and Wilson, J. D., Imperfect mobility and local government behaviour in an overlapping-generations model, Journal of Public Economics 39(1971), 829-844. Yang, D. T., China’s land arrangements and rural labor mobility, China Economic Review 8-2(1997), 101-115. Yi, Xin, A computable overlapping generation model (OLG) of Chinese pension reform, PhD Doctorate(2009).

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C

Correlation Table

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