Optimal Debt and Risk Balancing Behavior of Rural Households in China: Evidence from a Discrete Choice Experiment

ABSTRACT

Using an in-the-field discrete choice experiment on 336 farmers from rural China, this study aims to determine whether farmers optimize debt according to the optimal capital structure models and assess whether there is evidence of risk balancing behavior among Chinese farmers when they make financing decisions under risk constraints. Results suggest that farmers will increase leverage with greater profits, reduced interest rates, reduced business risk, lower risk aversion, and increasing prudence; they will reduce credit demand with increased collateral requirements, shorter repayment terms, and reduced loan usage flexibility. We also found significant heterogeneity among farmers and substantial differences across areas.

KEYWORDS:

• Optimal debt
• risk balancing
• risk management
• agriculture credit
• China

JEL:

• D14
• Q14
• P34

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/1540496X.2022.2104635

Notes

1. Although the optimal debt formula implies risk balancing, risk balancing does not necessarily imply optimal debt. Consider ${\sigma }_{ROE}^{\hspace{0.17em}}={\sigma }_{ROA}^{\hspace{0.17em}}{\left(1+\delta \right)}^{\hspace{0.17em}}$ and its total derivative $\mathrm{\Delta }{\sigma }_{ROE}^{\hspace{0.17em}}=\left(1+\delta \right)\mathrm{\Delta }{\sigma }_{ROA}^{\hspace{0.17em}}+{\sigma }_{ROA}^{\hspace{0.17em}}\mathrm{\Delta }\delta$. The first part on the right is the increase or decrease in absolute risk from changes to business risk. The second part is the incremental increase or decrease in absolute risk from changes in leverage, i.e., financial risk. Borrowing from de May et al. (2014), “Strong form” risk balancing results from a 1:1 balancing $\mathrm{\Delta }{\sigma }_{ROE}^{\hspace{0.17em}}=0$. Here, $\frac{\mathrm{\Delta }\delta }{\mathrm{\Delta }{\sigma }_{ROA}^{\hspace{0.17em}}}=-\frac{\left(1+\delta \right)}{{\sigma }_{ROA}^{\hspace{0.17em}}}<0$ is the exact rate that leverage must decrease in response to an increase in the total risk. More generally, if we assume, as Gabriel and Baker (1980) did, that there is a constraint for which total risk cannot increase above a threshold, i.e. $\mathrm{\Delta }{\sigma }_{ROE}^{\hspace{0.17em}}\le B$, then $\delta \le \frac{B-{\sigma }_{ROA}^{\hspace{0.17em}}\mathrm{\Delta }\delta }{\mathrm{\Delta }{\sigma }_{ROA}^{\hspace{0.17em}}}-1$. So long as the debt to equity does not exceed this value, the total risk will not be $B$ more significant. (Note that $B$ can allow for increases or decreases in total risk relative to the initial condition.) When this holds with a strict inequality and $B\ne 0$, then as business risk increases regarding leverage, financial risk will decrease, but not on a 1:1 basis. It is “weak form” of risk balancing. The equivalent weak form obtained from the optimal debt model is given as $\frac{\mathrm{\partial }{\delta }^{\ast }}{\mathrm{\partial }{\sigma }_{ROA}^{\hspace{0.17em}}}<0$ in Eq. (1).

2. See Supplemental C for commentary on including or excluding an opt-out option in choice experiments.

3. The card is translated from Chinese. The actual cards were presented in Chinese that represented the instructions, including the meaning of business risk, in a common language familiar to farmers. Each respondent was presented with nine cards (making up a randomly assigned block) that rotated the attributes identified in Table 1. Only three appear on this card, with other combinations appearing in the remaining eight cards of the block.

4. To determine the sample size, we use Johnson and Orme (2003), who suggested that the sample size required for the main effects depends on the number of choice tasks (t), the number of alternatives (a), and the number of analysis cells (c): (N>(500∙c)/(t∙a)).Considering our case, each respondent must complete nine choice tasks (t=9), each choice task displays three alternatives (a=3), and c equals the largest number of levels for any of the attributes (interest rate has the most levels, c=5). Thus, the minimum sample size required for the main effect given by (N>(500∙c)/(t∙a)) is 93. Moreover, regarding the optimal debt model, Eq. (1(1) ${\delta }^{\ast }=\frac{\overline{ROA}-i}{\rho {\sigma }_{ROA}^2}-1$(1) -5(5) $\frac{\mathrm{\partial }{\delta }^{\ast }}{\mathrm{\partial }\rho }=-\frac{\overline{ROA}-i}{{\rho }^2{\sigma }_{ROA}^2}<0$(5) ) also suggest some interaction relationships between the interest rate (i) and investment risk (σ_ROA^2), investment profitability ((ROA) ̅) and investment risk (σ_ROA^2), and interactions between risk aversion (ρ) and interest rate (i), investment profitability ((ROA) ̅), and investment risk (σ_ROA^2). If all these two-way interactions are considered, the minimum sample size required for interactions is 278. Our total number surveyed of 336 was greater than 278, which was enough to measure the interaction effect. Although Zhejiang’s sample size was less than the minimum requirement of 93, we can still do local regressions, and its results are still meaningful. The only limit of a small sample size is that it may prevent the detection of minor effects (de Bekker-Grob et al. 2015).

5. In any case, the farmer respondents were provided an incentive of 30 RMB (approximately $4.42, which was about one-fourth to one-third of a typical daily labor wage).

6. One mu = 0.1647 acre, or one acre is about six mu.

7. It is often more convenient to express logit results in terms of the odds ratio rather than marginal effects when attributes are ordinal or not continuous Given Eq. (s.9), Eq. (s.10), and Eq. (s.11)(see Supplement B), we can interpret utility $U_{ij}=LN\left(\frac{P_{ij}}{1-P_{ij}}\right)$ as the log of the odds ratio of selecting $\left(P_{ij}\right),$ or not selecting $\left(1-P_{ij}\right),$ a set of attributes. Then, marginal utility concerning any attribute is given by $\frac{\mathrm{\partial }{U}_{ij}}{\mathrm{\partial }{x}_j}=e^{{\beta }_j}$. In other words, the marginal utility from changes in any of the attributes is given by the percentage change in the odds that the attribute will be favored, all other things held constant.

8. We find conformity and consistency in the CLM and MLM results with the optimal debt decision (i.e., Eq.1)(1) ${\delta }^{\ast }=\frac{\overline{ROA}-i}{\rho {\sigma }_{ROA}^2}-1$(1) and risk balancing, except for the second-order interaction between risk and risk aversion. The difference could be due to restricting utility in the theoretical model to negative exponential utility and the normal assumption, while the CLM and MLM are of flexible form. To evaluate this further, we have run separate conditional logit models for each class (cluster) of risk aversion. The results indicate that as farmers become more risk averse, they are more likely to reduce debt when investment risk increases. Specifically, if investment risk increases by one level, respondents with high risk aversion would be $1-e^{-0.608}=0.4561$ or 45.6% less likely to borrow. In contrast, low risk aversion farmers would be $e^{-0.311}$ or 26.7% less likely to borrow. Compared with the results in Table 2, these additional logits indicate that the second-order conditions on risk and risk aversion concerning optimal debt and risk balancing are indeed satisfied.

9. The percentage can be calculated from the cumulative distribution function of the normal distribution. Suppose ${\beta }_k\sim N\left({\mu }_k,{\sigma }_k^2\right)$, where ${\beta }_k$ is the coefficient for the k^th attribute with mean ${\mu }_k$ and standard deviation ${\sigma }_k$. The probability that ${\beta }_k$ is not greater than zero is given by: $Pr\left({\beta }_k\le 0\right)=\mathrm{\Phi }\left(-\frac{{\mu }_k}{{\sigma }_k}\right)$, and $Pr\left({\beta }_k>0\right)=1-\mathrm{\Phi }\left(-\frac{{\mu }_k}{{\sigma }_k}\right)$. For example, the probability that the PROFIT coefficient is greater than zero equals $1-\mathrm{\Phi }\left(-\frac{0.327}{0.428}\right)=77.76\mathrm{\%}$.

10. As described, MLM is a random coefficient model with $\left(\bar{\beta }+{\xi }_i\right).\mathrm{B}\mathrm{Z}\sigma \mathrm{i}$ gives the confidence intervals around the mean coefficient. Of interest is the positive or negative preference associated with a particular attribute, that is, $Prob\left(\bar{\beta }+{\xi }_i\right)<0$, $Prob\left(\bar{\beta }+{\xi }_i\right)=0$, or $Prob\left(\bar{\beta }+{\xi }_i\right)>0.$ The probability in this context is measured by the likelihood (or population frequency) that any individual prefers the attribute.

11. The distribution of coefficients across respondents for profits is assumed to be normally distributed, that is, ${\beta }_{Profit}\sim N\left(0.591,0.469\right)$. Then the likelihood that an individual will have $Prob\left({\beta }_{Profit}\ge 0\right)=89.62\mathrm{\%},$ which is hypothesized under the optimal debt model. However, in the population $Prob\left({\beta }_{Profit}<0\right)=0.38\mathrm{\%},$ which suggests (at least) that about 1 in 10 farmers are less likely to borrow as profits increase.

Additional information

Funding

This work was supported by the [National Nature Science Foundation of China] under Grant [71903141].