*5.3. Robustness Tests*

#### 5.3.1. Robustness Test I: Sensitivity Analysis

The key underlying assumption of the PSM method is that a farmer's decision to participate in LCP is solely dependent on observed factors [59]. However, the real-life decisions of farmers on whether to participate in the LCP are also affected to some extent by unobservable factors. As such, this section uses Rosenbaum bounds estimation for sensitivity analysis [60]. When γ = 1, this indicates that rural households are equally likely to participate in LCP. When different values are assigned to γ, Rosenbaum bounds estimates give the upper and lower significance levels of the impact of LCP at different levels of variation in likelihood, the Hodges–Lehmann point estimates of the upper and lower bounds, and the confidence intervals of the upper and lower bounds. These act as indications of whether heterogeneity in unobserved factors significantly alters the estimates. If unobservable heterogeneity significantly alters the estimation results, this indicates that the PSM method based on observable heterogeneity is not suitable for estimating the policy effects of the LCP.

According to the Table 7, even though there was more than twice the likelihood of a difference in the LCP due to unobservable heterogeneity, the effect of the LCP on land "stickiness" of rural labor was still positive, with significance levels below 1%. The Hodges–Lehmann point estimates and confidence intervals were greater than 0 at the 5% significance level. This indicates that the LCP had a significant positive effect on land "stickiness" of rural labor, and unobservable heterogeneity did not affect the estimation results. This suggests that the results obtained by the PSM method are robust.


**Table 7.** Rosenbaum bounds sensitivity analysis.

Note: sig+: upper bound significance level. sig− lower bound significance level. t-hat+: upper bound Hodges– Lehmann point estimate. t-hat−: lower bound Hodges–Lehmann point estimate. CI+: upper bound confidence interval (a = 0.95). CI−: lower bound confidence interval (a = 0.95).

#### 5.3.2. Robustness Test II: Replacement of LCP Variables

The issuance of certificates is the last part of the confirmation of the LCP, and at the same time, the land certificate is an important legal document to define the property rights of farmland. However, the latest LCP has problems such as the relative lag of the titling process [61]. Specifically, though the confirmation of farmland property rights in villages has been completed, the progress of issuing certificates is inconsistent among villages and some farmers have not yet even obtained farmland certificates. Firstly, due to the complex situation and unclear land boundaries in some areas, a resulting high error rate in land measurement has led to obvious differences in land area before and after titling. These discrepancies have slowed down the progress of certificate issuance. Secondly, due to historical legacy issues, the cadastral information of rural households has changed drastically since the second round of contracting. Conflicts concerning land among rural households, disputes between family members, and inter-generational conflicts are constant and often result in the temporary hold of certificate issuance. Thirdly, there is conflict in the objectives between farmers who go out to work and dedicate their time to apply for certification, the farmers who do not receive the certificates in time, and the certificates ending up being temporarily kept by the village collective.

In response to the inconsistent progress with the issuing of certificates to farmers within villages, this paper used the variable of "village level LCP" as a proxy variable for the LCP. The aim was to eliminate intra-village differences in rural household certificate holdings and to test whether the village level LCP has an impact on land "stickiness". Drawing on Sun et al. [62], this paper defined a village as a "certificated land village" if the certificate issuance rate of farmers was greater than or equal to 60%; otherwise, it defined a village as a "certificated land village". The nearest neighbor matching and kernel-based matching methods were also used to assess the policy effects of village level LCP on labor land "stickiness". The empirical results are shown in Table 8.


**Table 8.** The ATT of village level LCP on land "stickiness".

Note: Treatment group (T) and control group (C). \*\*\* denote significance at 1% level.

The results show that village level LCP had a positive contribution to the "stickiness" of rural labor. These results are consistent with the empirical results at household levels. Specifically, the matched ATT of village level LCP was 0.074, and both were statistically significant at the 1% level, as the promotion effect of village level LCP on land "stickiness" was 7.4%.

#### *5.4. Mechanism Analysis: How LCP Affect Land "Stickiness"*

Through our theoretical analysis, the theoretical framework of "LCP–land production function–land 'stickiness'" was constructed. In this part, the mediating effect model was used to verify whether there was a mediating effect of land production function.

Drawing on the Equations (5) and (6) to test the mediating effect in turn, it was assumed that the LCP enhanced the land "stickiness" of rural labor by strengthening the land production function, and the LCP significantly enhanced the land production function. Conversely, the land production function had no mediating effect. In this paper, we used "agricultural business income" as the proxy variable of land production function, and the higher agriculture income, the more significant the land production function. In the inverse scenario, the productive function of the land was weakened.

In Table 9, model I shows that the LCP significantly enhanced land production function, and model II shows that the effect of the LCP and land production function on land "stickiness" was significant at 1% statistical level. The results show that the LCP had a significantly positive effect on the land "stickiness" of rural labor, and land production function played an important role in it. In other words, the LCP exerted a significant influence on land "stickiness" via its influence on land production function. The research hypothesis is verified.


**Table 9.** Results of the test for mediating effects of land production function.

Note: Standard errors are shown in parentheses. \*\*\* denote significance at 1% level.

In addition, the mediating effect of the land production function was examined using two proxy variables, "village level LCP" and "village level LCP rate" (Table 9, Model III–Model VI), and the results are consistent with the above. Although there were differences in the titling status of rural households within villages, and some households had not yet received farmland certificates, rural households in these areas still had higher expectations of the effect of the LCP in terms of stabilizing contractual relationships. Thus, the property rights exclusion and incentive effects of the LCP strengthened the land production function and increased the land "stickiness" of rural labor.

#### **6. Discussion**

In this section, we discuss the potential contributions, interesting results and limitations of this research.

The first discussion concerns the major contributions to the existing literature. This paper contributes to the current studies in four ways. (1) We constructed an analytical framework of land "stickiness". Our analysis showed that the insecurity of land property rights is the internal cause of the weakening of the land "stickiness" of rural labor. We went on to explain the necessity of implementing the LCP in China from the perspective of land production function. (2) Though previous studies have examined the effect of the LCP on off-farm employment or rural out-migration [26–28], there is a relatively small amount of literature concerning the policy effect of the LCP on agricultural labor participation. Since agricultural labor participation is the external manifestation of land "stickiness", our paper is the first attempt to estimate the policy effect of the LCP on the land "stickiness" of rural labor. (3) Against the background of rural social division, we studied the heterogeneity of the policy effects in different rural household types and different farm sizes. In other words, we verified whether the policy effect of the LCP has preferences in terms of household types and farm size. (4) Although there are some studies investigating the impact of the LCP on labor reallocation, the mechanism of its influence remains unclear. In order to fill in the literature gap, in this study, we explored the effect of the LCP on land "stickiness" of rural labor with theoretical analysis and empirical tests, as well as the mediating role of land production function. Additionally, in the robustness tests section, we conducted a Rosenbaum bounds sensitivity analysis to determine the influence of unobservable factors on the policy effect of the LCP. Given the inconsistency in the progress of the LCP, this paper used the village level LCP to examine the policy effect and mechanism of the LCP on the land "stickiness" of rural labor.

The following discussion concerns the interesting findings. Firstly, using the PSM method, this paper found that the LCP has a significantly positive effect on land "stickiness" of rural labor and that the LCP promotes the agricultural labor participation. A few studies have shown that the LCP can promote the off-employment and migration of rural labor. For instance, de Janvry et al. [63] found that under the Mexican Land Certificated Program from 1993 to 2006, "households obtaining certificates were subsequently 28% more likely to have a migrant member". However, this does not contradict the conclusions of this paper. Due to the heterogeneity of the endowment of rural labor, not all rural labor will undergo the transition from agricultural production to off-farm employment. (1) During the long-term agricultural production, some farmers have formed high asset specificity, such as agricultural machinery and technology. If they abandon agricultural production, they will face high "sunk costs", and the stronger the asset specificity, the higher the sunk costs [64]. For this reason, these farmers will continue to engage in agricultural production after the LCP. (2) Some rural labor faces the constraints of human capital, such as aging and low education, and as such, they cannot leave the agricultural field [32]. Furthermore, Li [33] found that the LCP mainly promotes the off-farm employment of rural idle labor groups.

Secondly, based on the heterogeneity analysis, we found that the policy promotion effect of the LCP on labor land "stickiness" is mainly reflected in the group of non-professional agricultural production households, medium-sized farms, and small-scale farms, while its promotional effect on professional agricultural production households and large-scale farms is not significant. The possible reasons for this are as follows. (1) Professional agricultural production households have more advanced agricultural production machinery and scientific management methods, and their demand for agricultural labor input is lower than that of non-professional households. (2) Large-scale farms overcome the limitation of farmland fragmentation and increase the input of agricultural machinery, which in turn increases the mechanization level of agricultural production and has a certain substitution effect on agricultural labor input [65]. These findings also contribute to the LCP in other developing countries with plenty of smallholders.

The final discussion is about the limitations of this study. (1) We used mixed crosssectional data from 2016 and 2018. Due to data limitations, it was not possible to compose the panel data, and, therefore, this paper does not strictly reflect the dynamic changes of land "stickiness", especially against the background of the COVID-19 pandemic and the global grain crisis, during which the land "stickiness" of rural labor may have changed. In future research, we aim to use the latest panel data as the basis for detailed research to

further explore the effect of the LCP on land "stickiness". (2) According to our analysis, the promotional effect of LCP on land "stickiness" is the result of the combined effect of property rights exclusion effect and incentive effect. However, due to the research data, this paper cannot respectively distinguish the extent of the property rights exclusion effect and the incentive effect on land "stickiness". In the future, we will continue to deepen the effect mechanism of LCP. Specifically, we will estimate the extent of the impact of the property rights exclusion effect and incentive effect, respectively. (3) Due to the data limitations, we could not locate the data on the land quality in the CLDS data. We therefore used village topography as a proxy for the land quality variable. Meanwhile, the initial land allocation under the Household Contract Responsibility System (HCRS) was primarily egalitarian, according to the proximity, fertility, irrigation, and other conditions of plots. As a result, there were no significant differences in land quality between households within villages. In addition, this paper used the PSM method. The basic idea of matching was to find in a large uncertificated farmland group whose samples are similar to the certificated farmland group in all relevant pre-treatment individual characteristics, household characteristics, and village characteristics. Thus, it could correctly evaluate the pure policy effect of the LCP on farmland "stickiness". Therefore, the issue of omitted variable can be ignored in the case of this study.

#### **7. Conclusions and Policy Implications**

#### *7.1. Conclusions*

In this paper, we started from the premise that the "stickiness" of farmland is weakening. We went on to show that there is an urgent to improve the efficiency of agricultural production by stabilizing the property rights of farmland, improving its production function, and enhancing land "stickiness". Firstly, based on the perspective of land production function, this paper analyzed the LCP impact on land "stickiness". Secondly, the PSM method was applied to estimate the policy effects of the LCP on the land "stickiness" of rural labor. Thirdly, heterogeneity analysis of rural household type and farm size, as well as the necessary robustness tests, were also conducted. Finally, the mediating effect model was applied to examine the mechanism of the LCP on land "stickiness" at the household and village levels.

The results of our study revealed the following: (1) The LCP had a positive promoting effect on the land "stickiness" of rural labor, which in turn increased the agricultural labor participation rate by 4.8~4.9%. (2) The heterogeneity analysis of rural household types showed that the policy promoting effect of the LCP on land "stickiness" had a great impact on non-professional households compared to professional households. In terms of farm size, the promotional effect of the LCP on medium-sized farms was the largest, followed by small-sized farms, while the promotion effect on large-sized farms was not significant. (3) The robustness results confirmed that: first, unobservable factors did not affect the estimation results of the effect of the LCP; second, the policy promotion effect was still significant after adopting the village level LCP variables, and the estimation results were robust. (4) The mediating effect on land production function was significant. The LCP enhanced the "stickiness" of rural labor through enhancing land production function. Meanwhile, the village level LCP variables also further verified the mechanism of land production function.
