2.1 The environment

We consider a village consisting of N households in which each household is described by an observable characteristic, ${x_i}$, and they must make a discrete choice about fuel use represented by ${Y_i} = \{{ - 1,1} \}$ such that ${Y_i} = 1$ means that a household chooses modern non-solid fuels and ${Y_i} ={-} 1$ is the choice to use traditional solid energy. The possible set of choices for the village is $Y = ({{Y_1}, \ldots ,{Y_N}} )$. We use the subscript $- i$ to code the choices of all households in the village other than household i, or ${Y_{ - i}} = ({{Y_1}, \ldots ,{Y_{i - 1}},{Y_{i + 1}}, \ldots ,{Y_N}} )$.

A household chooses fuel type to maximize utility, U. In the absence of social interactions, the standard discrete choice model assumes that the level of utility depends on the household's own fuel action ${Y_i}$, individual characteristic ${x_i}$, and a random component of utility defined as $\varepsilon ({{Y_i}} )$. As we further consider the dependence of fuel choice among households, the utility function not only includes a private component, but also a social component:

(1)\begin{equation}\begin{array}{*{20}{c}} {U({Y_i}) = u({Y_i}) + S({{Y_i},\mu_i^e({{Y_{ - i}}} )} )+ \varepsilon ({{Y_i}} ),} \end{array}\end{equation}

where $u({{Y_i}} )$ is private utility directly related to the household's own fuel choice, $S({{Y_i},\mu_i^e({{Y_{ - i}}} )} )$ is the social component of utility associated with the fuel choices of others, and $\varepsilon ({{Y_i}} )$ is a random utility term which is assumed to be independent across individuals. $\mu _i^e({{Y_{ - i}}} )$ represents a household's subjective expectations of others' fuel choices at the time of making its own fuel choice decision, and is specified as $\mu _i^e({{Y_{ - i}}} )= \bar{Y}_i^e = {({N - 1} )^{ - 1}}\sum\nolimits_{i \ne j} {Y_{ij}^e} \;$where $Y_{ij}^e$ denotes the subjective expectation of household i on household $j$'s choice for any household $j \ne i$. It is easy to see that $\bar{Y}_i^e$ is an expected average choice for the village from the view of household $i.$

Specifically, we consider the social utility as a form of strategy complementarity (see Blume et al., Reference Blume, Brock, Durlauf and Jayaraman2015), which consists of a parameter and an interaction term between the household's choice and the expected average village choice, $S({{Y_i},\; \bar{Y}_i^e} )= \lambda {Y_i}\bar{Y}_i^e$. This utility function setting indicates that the household's fuel choice and the average expected choice of the village determine the level of utility together, and the marginal utility of the household's choice changes with a change in the average expected village choice. The parameter $\lambda$ measures the degree of interdependence of fuel choices among households. It is necessary and convenient here to assume that parameter $\lambda$ is positive, ${\partial ^2}S({{Y_i},\bar{Y}_i^e} )/\partial {Y_i}\partial \bar{Y}_i^e = \lambda > 0$, which implies that the more people in the village that a household expects to abandon traditional fuels, the greater the marginal benefit of transition for the household. Yet, the increase in private utility brought on by fuel transition is limited.Footnote ³

Finally, we set the private utility to be an interaction between the individual characteristic and the household discrete choice,$u({{Y_i}} )= {x_i}{Y_i}$, which means that the marginal private utility of fuel choice is linear in the household's own characteristics. Thus, the complete utility function is $U({{Y_i}} )= {x_i}{Y_i} + \lambda {Y_i}\bar{Y}_i^e + \varepsilon ({{Y_i}} )$.

2.2 Equilibrium

Following Brock and Durlauf (Reference Brock and Durlauf2001), we specify the random term $\varepsilon ({{Y_i}} )$ as $i.i.d.$ extreme-value, which leads the difference between the positive and negative choice on the random term to be logistically distributed. When $\lambda > 0$, household fuel choice is no longer independent and the social interactions effect is just the effect of the average village choice (captured by $\lambda$).Footnote ⁴ Under a rational expectations assumption, all households from the same village have the same overall average expectation about village fuel transition. However, the solution – here, the optimal choice in transitioning to clean fuel or not – need not be unique, meaning that there is a possibility of multiple equilibria. This response function provides a means of visually understanding the potential for multiple equilibria. Detailed derivations are provided in the online appendix.

The intuition is that the equilibrium is determined by two parameters: ${x_i}$, which reflects marginal private utility, and $\lambda$, which reflects marginal social utility. In particular, the curvature of the response function is determined by the size of $\lambda$ such that a larger $\lambda$ corresponds to more curvature, and multiple equilibria may emerge when the social interactions effect is relatively larger than the private incentive.

As described in the introduction, the case of multiple equilibria has rich economic significance. In the online appendix, we show that in a situation of three equilibria, one is positive, one is negative, and one is not stable. The negative equilibrium means that most households in the village will choose traditional solid fuels; this equilibrium is the environmentally inefficient case. In contrast, the positive equilibrium is one in which a large number of households choose clean non-solid fuels, previously referred to as the high-level equilibrium. Brock and Durlauf (Reference Brock and Durlauf2001) show that both the low-level and high-level equilibria are locally stable, such that small deviations will not dislodge the equilibrium. In other words, if stuck at the low-level equilibrium, it may be very difficult for any household or village to escape the energy trap without a substantial outside force (substantial policy intervention).

3.1 Data

The data we use is from the China Family Panel Studies (CFPS). CFPS is a national-level, comprehensive continuous survey that documents changes in China's society, economy, population, education, and health, providing data for academic research and policy analysis. In 2010, CFPS implemented its baseline survey that covered 14,960 households. The CFPS baseline sample covers 25 provinces/cities/autonomous regions across the country, representing 95 per cent of China's population (Xie, Reference Xie2012). After the baseline survey, there were 5 subsequent waves of follow-up surveys implemented in 2012, 2014, 2016, 2018 and 2020. In total, we use all six waves of the survey to build a panel dataset.

We focus only on households in rural areas, and drop samples from urban areas according to the rural-urban division standard defined by the National Bureau of Statistics. Rural areas remain relatively underdeveloped with relatively poor infrastructure and household-based agricultural production, making rural residents more likely to use traditional solid fuels as cooking fuel. This setting provides us with an opportunity to study household fuel transition. Further, population mobility in rural areas is relatively small: most of the residents who come from the same village belong to several clans, which means that they are familiar with each other and their decisions affect each other's decisions. Therefore, we regard the household as the basic unit of analysis with the village as the reference group unit. We set the minimum group size to be six to allow every household to have at least five other households in the same village as its reference, and to avoid issues with highly isolated household clusters. After cleaning the data, we are left with a six wave, unbalanced panel dataset containing more than 38,000 total observations. The average group size (number of households per village) is 21.15.

3.2 Empirical methodology

Identifying the social interaction effects for household fuel choice requires that we manage the following two obstacles. The first is the reflection problem (Manski, Reference Manski1993), which is a confounding of the endogenous social effect and the contextual effect. This issue is particularly pernicious for the linear-in-means model. Fortunately, nonlinear models, like the logit model, are not plagued by the reflection problem because the binary choice framework imposes a non-linear relationship between individual behavior and group means (Brock and Durlauf, Reference Brock and Durlauf2001). The discrete choice interaction model described above, under the i.i.d. extreme-value random utility assumption, leads to a logistic regression model; therefore, by virtue of this nonlinear framework, the reflection problem is not a concern here. Another problem is how to separate the endogenous social effect from the correlated effect (Moffitt, Reference Moffitt, Durlauf and Young2001). The concern is that an observed convergence of fuel choice among households in the same village may stem from common environmental factors, such as village energy accessibility and availability, rather than the endogenous social effect. We follow standard empirical strategy and address this omitted variable problem via group-level fixed effects, which in our case is village-level.

The probability of individual fuel choice under the logit regression structure is:

(2)\begin{equation}\begin{array}{*{20}{c}} {Pr({{Y_i} = 1\textrm{|}{Z_i},\theta ,{\alpha_c}} )= F({\rho {{\bar{Y}}_{ - i}} + {X_i}\beta + {{\bar{X}}_{ - i}}\theta + {\alpha_v} + {\alpha_t}} ),} \end{array}\end{equation}

where $F:\mathrm{\mathbb{R}} \to [{0,1} ]$ is a standard logistic distribution function, ${Y_i}$ is the fuel choice for household $i = 1, \ldots ,\; N$, ${X_i}$ is a $1 \times k\; $vector of individual $i$'s characteristics such that the corresponding $k$-dimensioned coefficient $\beta$ captures the effect of private characteristics on fuel choice, ${\bar{Y}_{ - i}}$ is the leave-$i$-out mean of the fuel choices of the other $N - 1$ households in the village, and the coefficient $\rho$ is the endogenous social effect that captures the extent to which the probability that a household chooses non-solid clean fuel varies with the choices of its neighbors. Additionally, we investigate the extent to which the characteristics of household $i$'s neighbors, ${\bar{X}_{ - i}}$, influence household fuel choice via parameter $\theta$ (Manski, Reference Manski1993). The term ${\alpha _v}$ is the village-level fixed effect that captures the common shock to all households in the same village, and ${\alpha _t}$ is the time fixed effect.

3.3 Variables

3.3.2 Control variables

According to the energy ladder theory, the most important factor supporting household transition from solid fuels to clean non-solid fuels is income. We choose household annual net income to measure income, and take the natural logarithm of income to reduce the influence of relatively large values. Some studies find that the consumption of firewood or biomass is closely related to the farm size (Démurger and Fournier, Reference Démurger and Fournier2011; Pandey and Chaubal, Reference Pandey and Chaubal2011; Yang et al., Reference Yang, Li, Xu and Yi2020). Intuitively, agricultural activities directly provide households with biomass byproducts. Considering the heterogeneity of crops and land in our sample, we use the agricultural output value to measure the scale of household agricultural operations. Another economic factor is non-farm business: a household that owns a non-farm business has a higher opportunity cost of time, which we expect motivates the household to choose a relatively efficient energy type. We use a binary indicator to measure whether or not the household is predominantly engaged in non-farm business.

We also control for household demographic characteristics, including family size, age, and education. Family size refers to the number of permanent residents in the household, excluding those who work or study outside. The proportion of elderly people aged 60 and above, and the proportion of family members with a high school education or above, measure the age structure and education level of the household, respectively. Table 1 shows the variables, variable definitions, and provides descriptive statistics.

Table 1.

Definitions and descriptive statistics for variables

Notes: Family members do not include those who work or live outside the village.

3.5 Robustness checks

To ensure that our results are robust, we undertake four separate robustness checks. First, we set a minimum group (village) size to ensure that the peer reference group is adequate for all villages in the sample. Second, we use household-level fixed effects to account for any correlation effects that are not accounted for by our village-level fixed effects. Third, we conduct a series of placebo trials to ensure that the village reference groups we use are not generating spurious results. Fourth, we deploy an instrumental variables regression to ensure that our model does not suffer from reverse causality. In all cases, the results are consistent with our main reported results. Detailed results from these robustness checks are reported in the online appendix.

5.1 Which households are more likely to be influenced by others?

We are interested in heterogeneity in the magnitude of the endogenous social effect among different households because policies that leverage peer influence to accelerate rural energy transition will have a more immediate impact on those households that are more easily influenced by others. We select four household characteristics that are easily influenced by government policies to investigate this heterogeneity: income, education, agricultural production, and non-farm business. We add interaction terms between these variables and the average adoption rate of the village into the model in equation (2). Columns (1)–(4) of table 3 report the results: the interaction term for agricultural production is significantly positive, and the interaction term of non-farm business is significantly negative. These results indicate that the endogenous social effect has a greater impact on a household with a larger scale of agricultural production and/or that is not engaged in non-farm business. Therefore, we can conclude that intervention policies aimed at promoting household energy transition, because of the endogenous social effects underlying fuel choice, are more effective in groups with lower non-farm income households.

Table 3.

Heterogeneity analysis: which households are more likely to be influenced by others?

Notes: Robust standard error in parentheses.

Additionally, people now communicate in more ways than in previous times. The Internet has changed both communication between, and information sources of, rural residents, both of which may affect the social interaction effects. On the one hand, the Internet greatly facilitates daily communication among rural residents, and a higher frequency of information exchange strengthens the complementarity of others' choices in the same village, thereby enhancing the endogenous social effect. On the other hand, the Internet may provide rural residents with more information regarding cooking fuels and health, thereby weakening the peer influence, and reducing the social interaction effects. We investigate these issues by adding an interaction term between Internet use (measured as the proportion of family members using the Internet) and the endogenous social effect variable to the model. The estimated results are reported in column (5) of table 3, and we find that Internet use significantly increases the endogenous social effect. That is to say, the positive impact of the Internet on social interactions is greater than any negative impact.

5.2 Whose choice attracts more attention?

Our primary analysis assumes that when a household looks to its peers in determining its fuel choice it looks to all potential peers equally. However, it is possible that a household holds the decisions of particular neighbors in higher regard than others. For example, a household might look to more highly educated neighbors when considering adoption of a new technology in the anticipation that more highly educated neighbors might have a better understanding of the pros/cons of clean fuel. To test this hypothesis, we replace the average choice of neighbors in the village in the model with the average choice of neighbors with a higher education and with the average choice of neighbors with lower education. We also create similar groupings for income and agricultural production.Footnote ¹¹

Table 4 reports the results. In column (1), we can see that both the average choice of high-income neighbors and low-income neighbors has a significantly positive impact on household fuel choice. We test for a significant difference between the two coefficients, and we reject the null hypothesis that the two coefficients are equal at the 5 per cent significance level. The same situation holds in the model of high-education and low-education neighbors shown in column (2) of table 4, but not in the model of large-scale and small-scale agricultural production neighbors shown in column (3) of table 4. This implies that the fuel choices of households with a higher education and higher income have a greater spillover effect. If public policies such as straw processing technology and demonstrations of new energy kitchenware prioritize interventions targeting more highly educated and higher income households, then the effects on the fuel consumption structure of the entire village may change more readily towards clean fuel.

Table 4.

Heterogeneity analysis: whose choice attracts more attention?

Notes: Robust standard errors in parentheses. ‘High Income_peer’ and ‘Low Income_peer’ represent the average adoption rate of high- and low-income neighbors, respectively. ‘High Education_peer’ and ‘Low Education_peer’ represent the average adoption rate of high- and low-education neighbors, respectively. ‘High Agriculture_peer’ and ‘Low Agriculture_peer’ represent the average adoption rate of large- and small-scale agricultural production neighbors, respectively.