Climate and landscape mediate patterns of low lentil productivity in Nepal

yields estimates of β and γ where,g ¼ s2 U s2 2 0; 1 ½ �, and s2 ¼ s2 U þ s2 V . Hence, the model sepa- rates the residuals into a normally distributed random error and a one-sided error term reflect- ing technical inefficiency; the latter is related to input management and measures the degree to which a farmer was able to obtain the maximum possible output for a given vector of inputs. Several studies have been previously conducted using the two-stage stochastic production frontier model. In the two-stage stochastic production frontier analysis, the first stage involves the specification and estimation of stochastic frontier and prediction of technical efficiency score, while in the second stage determinants of the technical efficiency score are regressed. However, Battese and Coelli [62] and Wang and Schmidt [63] reported that the two-stage method is inconsistent and a single equation method is preferred because the two-stage method contradicts the assumption of an independently, identically and normally distributed inefficiency effect in the stochastic frontier function. Furthermore, Wang and Schmidt [63] pointed out that the first stage is biased if dependent variables of the first and determinants of the second stage are correlated. Kumbhakar et al. [64] and Reifschneider and Stevenson [65] specified a stochastic frontier model in which inefficiency effects were defined to be explicit functions of firm-specific factors, and all parameters are estimated in a single-stage maximum

likelihood procedure. In this study we applied the Battese and Coelli [62] model for the two years of cross-sectional data to derive unbiased estimates for lentil production in Nepal. Since both years were similar in terms of climatic parameters (wet winter), we amalgamated two years of survey data in order to develop a single production frontier. According to Battese and Coelli [62], the technical efficiency effects of U are obtained by truncation (at zero) of the nor- mal distribution with mean μi = Ziδ, where Zi is the farm specific explanatory variables and δ is the vector of parameters to be estimated. The stochastic frontier production function for lentil farming has a Cobb-Douglas type functional form and the production function estimation adopted in our study is defined as: Ln Yi ¼ b0 þ X 9 j¼1 bjLnðXijÞ þ X 9 k¼1 bkðDikÞ þ X 1 p¼1 X 1 r¼1 bpr Rpri þ Vi Ui ð2Þ Where, Ln Yi = Natural logarithm of output i = i-th farm (i = 1, 2, 3,. . ., 665) β = vector of parameters to be estimated Ln(Xj) = vector of input parameters Dk = vector of dummy variable related with lentil production Rpr = Total amount of rainfall differentiated by lowland production ecology V = N(0, σV distributed random error term U = non negative error term that represents technical inefficiency The non-negative error term is specified as a function of household-specific determinants of technical inefficiency, which can be specified as: Ui ¼ d0 þ X 7 l¼1 dlZli þ Wi ð3Þ Where, δ = vector of parameters to be estimated Zl = vectors of potential inefficiency determinants

W = N(0, σU) distributed random error, where σU is defined such that Ui � 0. PLOS ONE Climate and landscape mediate low lentil productivity PLOS ONE | https://doi.org/10.1371/journal.pone.0231377 April 16, 2020 5 / 19