# **_6.2 Empirical model estimation procedure_**

The empirical analysis began by estimating the response of net farm revenue _(V)_ (measured as net revenue nr2_3 in equation (1) to climate variables (F) only. The second model added soil variables (Z) to the first model to add spatial heterogeneity in net farm revenues. The third model added socio-economic variables (G) to the second model. The fourth model tested the effect of additional sources of water, in this case runoff, on farm net revenues. The fifth model added the interaction terms between mean annual climate variables (temperature and precipitation) to the fourth model to test whether access to other water supplies affects climate sensitivity.

The Zimbabwe Ricardian model specification assumed a quadratic relationship between net farm revenues and climatic variables to reflect the nonlinear relationship between net farm revenues and climatic variables that is consistent with Ricardian studies applied elsewhere (Mendelsohn et al. 1994, 1996; Kumar & Parikh 1998; Sanghi 1998; Sanghi et al. 1998; Mendelsohn & Dinar 1999, 2003). The quadratic term reflects the response function of net revenue as a function of climate variables.

Positive quadratic terms indicate that the net farm revenue function is U-shaped and negative quadratic terms indicate that the function is hill-shaped (Mendelsohn & Dinar, 2003). The expected relationship between net revenue and temperature based on agronomic research and past cross-sectional analyses is hill-shaped, (Mendelsohn & Dinar, 2003). The indication from this expectation is that a negative relationship is expected, implying that further increase in temperature would have an adverse effects on net farm revenues and hence agriculture. In addition, the estimation assumed a linear relationship between net farm revenues and other variables (soil, socio-economic and hydrological) that is also consistent with other Ricardian studies such as those mentioned above.

Econometric analysis with cross-sectional data is usually associated with problems of heteroscedasticity and multicollinearity and the effect of outliers in the variables. Although the study did not test for their presence, it was anticipated that these problems would arise in the estimation process. The study therefore used estimation methods that automatically correct for such problems, in this case quantile regression analysis. Though quantile regression analysis basically reduces the weight of outliers on the estimates, it can also be useful for correcting for heteroscedasticity and multicollinearity. Reducing the weight of outliers means that the estimation process reduces the variance of the estimates and hence helps correct for heteroscedasticity. In the estimation process highly correlated variables were dropped because of collinearity.

As a way of ascertaining which model best describes the relationship between net farm revenues and climate, soil, hydrological and socio-economic variables in Zimbabwe, the estimation did several runs of the above models. The study estimated three models for each regression model specification. The first included all the sample farming households, and the other two were rainfed only and households using irrigation. Farming households using irrigation in the study had some areas of rainfed and some areas under irrigation. No farmers exclusively used irrigation alone in their farming activities. The Stata statistical software was used to estimate the models.

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