Empirical Model Specification. The aim of this study is to examine the relationship between yield of three different rice crops (namely, Aus, Aman and Boro) and climate variables (namely, maximum temperature, minimum temperature, rainfall and humidity) to estimate the potential effects of climate change on rice crop productivity level. The dependent variable in this study is yield of different rice crops (such as, Aus, Aman and Boro) and following Lobell et al. (2007), Almaraz et al. (2008) and Sarkar et al. (2012) we have considered four climate variables as independent variable, that includes maximum temperature, minimum temperature, rainfall and humidity. Previous studies used different units of time, such as months, phonological periods and growing seasons, for climate variables. However, this study has used an average growing season maximum temperature and minimum temperature variables with average growing season rainfall and humidity variables, because the average growing season climate variables are able to capture the net effect of the entire range of the development process by which yields are affected by climate (Lobell and Field, 2007). Moreover, the average growing season temperature is a key determinant of average yield (Cabas et al., 2010). The monthly average growing season maximum and minimum temperature and the avearge growing season rainfall have been used in previous studies (Granger, 1980; Chang, 2002; Lobell and Field, 2007; Lobell et al., 2008).
Most of the studies on the possible impacts of climate change on food crops used indirect crop simulation models (Schlenker and Roberts, 2008) and regression models (Sarkar et al., 2012; Boubacar, 2010; Mendelsohn, 2009; Isik and Devadoss, 2006; You et al., 2005; Peng et al., 2004). Forecasts of the yield changes in response to changes in climate variables, from regression models based on historical climatic and yield data for specific crops are relatively accurate (Lobell and Asner, 2003; Lobell and Field, 2007; Mendelsohn et al., 1994; Lobell et al., 2007). Before estimate our model, at first we have checked the distribution of the yield of each rice crops (Aus, Aman and Boro) against time by drawing histograms. An inspection of the histograms shown that the yields of Aus, Aman and Boro rice seemed to follow a normal distribution. Thus, depending on the distribution of the yields (dependent variables) here we have chosen ordinary least squares (OLS) regression method to estimate three different rice crop models. However, there exists a significant and positive trends between rice yield and time. The results of the rice yields may vary due to change in non-climatic factors such as improved variety, management techniques, fertilizers, etc. Therefore, we need to remove the yield trend caused by non-climatic factors before run our linear regression model. In order to remove its trend and avoid heteroskedasticity in linear regression model, we can use log-linear regression model. Because log-transformation can transform absolute differences into relative differences. In this regard, we run the loglinear version of our regression models. Thus, on the basis of the distribution of the yields of three rice crops and other properties, the following regression models are employed: