This dissertation is an essay on evaluating performance of econometric estimators, agricultural input choices under risk preference and welfare analysis with respect to different equilibrium models. In the first chapter, I use simulation methods with independent, relevant, and excluded instrumental variables, wherein they form a complete set of instruments, to quantify finite sample performance of selected estimators. In finite samples, I find that the bias and variance of estimators increase with the exclusion of instrumental variables. I also find that the mean squared error of the parameter estimates increase with the increase of number of omitted instruments in the model. The sensitivity due to the number of omitted instruments is not necessarily eliminated by increases in sample size. The equations containing more endogenous variables appear more sensitive to the omitted instruments. Simulation results also imply that the finite sample performance of 3SLS estimators also suffers under omitted instruments. In the second chapter, I develop a theoretical model to explore the choices of using plastics and pesticides to grow food as well as the potential negative spillover caused by plastic use in production agriculture that is transformed into microplastic pollution in the soil. I show that a growers' risk preference has an impact on the substitution between plastic and pesticides in that restrictions on these inputs do not necessarily trigger substitution for risk averse growers. In the third chapter, I focus on measuring and quantifying impacts of shocks along the supply chain for an agricultural sector in the context of a small economy. I show theoretically that the differences between the change in welfare estimated from GE and PE models are economically significant for a small economy. I show that the changes in consumer surplus predicted by the two models due to a domestic demand shock are statistically significantly different. I show that, the PE model produces larger welfare implication than hybrid model in response to demand shock, markup shock and capital demand shock compared to supply shock, labor demand shock and export shock. Results also show that the PE approach is more sensitive to the parameters of the behavioral equation.