Government Behavior on Urban Land Supply: Does it Follow a Prospect Preference?

Abstract

This paper investigates the role of the prospect theory preferences in influencing the relationship between performance goals and subsequent performances. We find an inverted-U relationship between the goal of the central government and the performance of local governments in land supply based on China’s land supply data between 2005 and 2013. The higher land supply goals of the central government initially increase and then decrease the land supply by local governments. We further explore the inverted-U relations by considering local governments’ prospect theory preferences theoretically and empirically. Our findings indicate that local governments are goal-dependent and risk-seeking in face of the extraordinarily ambitious goals set by the central government.

Appendices

Appendix 1 Value function of local governments with prospect theory preferences

Figures 5a and 5b show the value functions for a local government who has the prospect theory preference. Following Wu and Yang (2018), we assume the local performances m are the same in Figs. 5a and 5b, while the central goals n in Fig. 5a is lower than that in Fig. 5b. As we can see, the value increase (∆V) is much bigger in Fig. 5a than that in Fig. 5b.

That is, for local governments with prospect theory preferences, the value increase (∆V) from the better performance (m) is dependent on the target (n). The higher n, the lower marginal value (MB^V), as a result of the reference dependence and the sensitivity diminishing.

Fig. 5

Value function of local governments. Note: Figs. 5a and 5b are the value functions for local governments who have the prospect theory preference. m are the same in Figs. 5a and 5b, while n in Fig. 5a is smaller than that in Fig. 5b

Appendix 2 Impacts of β and λ on the goal-performance relationship

If local governments follow the prospect theory preferences, the risk seeking degree β would also have impacts on the n − m relationship. As shown in Fig. 6, a negative correlation dominates the relationship when the β value approaches zero, while a positive correlation dominates the relationship when the β value approaches one. There is the possibility to have a monotone positive n − m relationship when the β is extremely high (extremely low degree of risk seeking) and the marginal cost of land supply increasing is relatively low.

Fig. 6

Marginal benefits and costs in increasing land supply for local governmnets with prospect theory preferences, simulation of β. Note: According to Tversky and Kahneman (1992), λ=2.25. S₀ is normalized to 1

If local governments follow the prospect theory preference, the loss aversion parameter λ would also have impacts on the n − m relationship. As shown in Fig. 7, a negative correlation dominates the relationship when the λ value approaches one, while a positive correlation dominates the relationship when the λ value is high. There is the possibility to have a monotone positive n − m relationship when the λ is extremely high (extremely high degree of loss aversion) and the marginal cost of land supply increasing is relatively low.

Fig. 7

Marginal benefits and costs in increasing land supply for local governmnets with prospect theory preferences, simulation of λ. Note: According to Tversky and Kahneman (1992), β=0.88. S₀ is normalized to 1

Appendix 3 Impacts of β measured by political cycle on the goal-performance relationship

Table 6 shows the results with β measured by the political cycle, pre _ pcpc and aft _ pcpc. pre _ pcpc is a dummy variable equal to 1 for the preceding year of the provincial communist party congress dummy, and 0 otherwise. aft _ pcpc is a dummy variable equal to 1 for the year after the provincial communist party congress, and 0 otherwise. Political behavior is expected to be more risk averse before the end of an old cycle, and more risk seeking at the beginning of a new cycle, therefore pre _ pcpc indicates lower β and aft _ pcpc suggests higher β.

The inverted-U shape relation is robustly significant after controlling the β parameter measured by the political cycle dummy. Furthermore, as shown in the four bottom rows, when pre _ pcpc value changes from 0 to 1 (in columns 1 and 3), which indicates decreasing β, the symmetric lines in the inverted-U m − n relationship move left. When aft _ pcpc value changes from 0 to 1 (in columns 2 and 4), which indicates increasing β, the symmetric lines in the inverted-U m − n relationship move right. That is, as the theoretical model in Appendix 2 indicates, a negative correlation dominates the m − n relationship when β is low, while a positive correlation dominates the m − n relationship when β is high.

Table 6 Impacts of β measured by political cycle on the goal-performance relationship

Appendix 4 Utility function of local governments with expected utility preferences

Now we consider the condition where local governments follow an expected utility preference. All things are the same except the benefit function. If local governments follow an exponential expected utility preference, the utility improvement ∆U from increasing land supply from S₀ to S₁ should be ∆U = U(S₁) − U(S₀) = [(1 + m)S₀]^θ − (S₀)^θ. In that case, MB^Udecreases with m because θ<1, while MC still increases with m. Therefore, there is one internal solution ${m}_U^{\ast }$ when MC = MB^U. And it is obvious that $\frac{\partial \left({MB}^U\right)}{\partial n}=0$ and $\frac{\partial (MC)}{\partial n}=0$, which means the central target n has no impact on the marginal utility and the marginal cost, which indicates that ${m}_U^{\ast }$ has nothing to do with n. That indicates, for local governments that have the expected utility preference, the optimal local performance m is independent of the central target n. That cannot explain the findings in this paper.

It needs to mention that if the ${m}_U^{\ast }$ is no bigger than n, governments with the expected utility preference have one optimal ${m}_U^{\ast }$ which is independent of n; but if the ${m}_U^{\ast }$ is bigger than n, governments with the expected utility preference have the optimal ${m}_U^{\ast }$ equal to n. We provide a simple simulation for ${m}_U^{\ast }$ to solve this problem in Fig. 8. As we can see in Fig. 8, the intersected solutions ${m}_U^{\ast }$ are relatively small, ranging from 0.6 to 0.9 with alternatively different definitions of MC. And that may be an overvalued ${m}_U^{\ast }$ since lower θ means lower ${m}_U^{\ast }$, and higher S₀ means lower ${m}_U^{\ast }$. Even if θ equals to its upper limit 1, the ${m}_U^{\ast }$ is also relatively low. Since the central target n in the national residential land supply plan is relatively high as mentioned in Section 3, it could be expected that ${m}_U^{\ast }$ is no larger than n, and the optimal local performance is independent of the central target n for local governments with expected utility.

Fig. 8

Marginal benefits and costs in increasing land supply for local governments with expected utility preferences. Note: It plots the relationship between MB^U and MC if local governments follows the expect utility theory preference. The intersections of MB^U and MC are the optimal solutions ${m}_U^{\ast }$. In the simulation of MB^U, S₀ is normalized to 1; and according to Tversky and Kahneman (1992), we assume the θ in the utility is also 0.88. In the simulation of MC, since MC^′ > 0, thus we take three different forms of MC to make the MC^′′ > 0 (MC = m²), MC^′′ = 0 (MC = m), and MC^′′ < 0 (MC = m^0.4), respectively