Two sets of econometric models were used: one for analyzing the adoption of improved rice varieties and the other for estimating the impact of adoption.
Adoption model
The extent of adoption, measured here as percentage area under improved upland rice varieties, is a continuous variable that is limited between zero and 100 percent. A Tobit specification is appropriate for analyzing models with such limited dependent variables and has been used widely in adoption studies [
21].
The Tobit model, originally developed by Tobin (1958), is specified as:
where Y
i is the proportion of rice area under improved varieties, X
i is a vector of variables capturing the farm and household characteristics, β is a vector of unknown coefficients, and ε is an error term that is assumed to be independently distributed with mean zero and a constant variance. The coefficients βs can be used to measure the marginal effect of each of the exogenous variables on the extent of adoption. In adoption studies, exogenous variables specified typically include household characteristics, farm characteristics, and external factors such as prices, climatic conditions, and institutional factors [
22,
23,
24,
25].
In this study, the household-specific factors included were the endowments of land and labor and the share of terraced upland area in the total upland rice area. The theory of induced innovation predicts that the relative proportion of land and labor endowments of a household determines the relative desirability of adoption of land-intensive or labor-intensive technologies [
26]. A farm household with less land relative to family labor is more likely to adopt yield-increasing technologies than otherwise,
ceteris paribus. This variation in land/labor endowment among households could be a factor partially explaining the variation in the extent of the adoption of yield-increasing improved upland rice varieties.
Terracing of upland fields encourages the adoption of improved rice varieties. Terraced fields retain water and fertilizers better than sloping fields, resulting in higher productivity. The effect of terracing on the adoption of improved varieties is hence expected to be positive.
Adoption decisions are critically influenced by the presence/absence of technology extension programs. The presence of an active extension program to promote improved technology in a village is expected to have a positive impact on adoption. The government of Yunnan has made extensive efforts to promote improved upland rice varieties, but some villages are covered better than others while some villages are not covered at all. Thus, this variation in the extension coverage could be a factor explaining the observed variation in adoption.
The estimating equation for the Tobit model is specified in this study as:
where,
Yi is the proportionate area under improved upland rice variety for the i-th household,
X1i is the ratio of land/labor endowment for the i-th household,
X2i is share of terrace area in upland area for the i-th household,
X3 is the dummy for the extension program,
X4 represents the county dummy (with value 1 for Menglian county, 0 otherwise), and ε is the random error term.
The estimating equation is specified in a “reduced form” rather than in a “structural form” as the interest in the paper is in estimating the ultimate impact of exogenous variables on adoption. The use of the reduced form also avoids the potential problems of endogeneity that need to be considered in a structural model. In addition, the explanatory variables included are clearly exogenous in the cross-sectional data that reflect the household choices on rice varieties conditional on household resource endowments and the presence/absence of government programs on terracing/extension.
Impact model. Various econometric approaches exist for assessing the impact of an intervention [
27]. Of these, the propensity score matching method (PSM) has been a popular approach to estimate the treatment effects in diverse research fields in situations where the counterfactual is not observable [
28]. Self-selection by households into a program can lead to a bias in the estimation of treatment effects when the counter-factual is not observable as it is not possible to keep other factors constant while comparing the treatment effects in the more standard “with” and “without” framework. The PSM technique is now widely used to correct for potential self-selection biases in assessing the impact [
28]. The PSM uses a non-parametric estimation method [
29,
30] and reduces the dimension for matching between adopters and non-adopters that are similar in terms of their observable characteristics [
28,
31].
The propensity score is defined as the conditional probability of receiving a treatment given pretreatment characteristics [
32]:
where
p (X) denotes the propensity score under X, the multidimensional vector of pretreatment characteristics, T is the indicator of exposure to treatment, and Pr (T = 1|X) is the conditional probability which equals to the expectation with respect to the distribution of X.
Given Y
1 and Y
2 as the outcome “with” and “without” improved variety adoption, the average treatment effects on the treated group can be estimated as follows:
The required propensity scores were estimated by a logit model which is specified as follows:
where
is the probability of farmers’ technology adoption. In the propensity score matching method (PSM), only the variables that influence simultaneously the participation decision and the outcome variable but are unaffected by participation (or the anticipation of it) should be included. The explanatory variables include the ratio of land/labor endowment (
x1), share of terrace area in the upland area (
x2), extension program dummy (
x3), and county dummy (
x4).
s are the coefficients to be estimated.
The nearest neighbor matching method was implemented to estimate the average impact and the radius and kernel matching methods as alternative specifications for assessing the sensitivity of results with respect to matching methods. These matching methods are widely used to assess the sensitivity of results with respect to the alternative specification of counterfactual [
28]. The software STATA was used for estimation.