ISSUES AND STRATEGIES FOR AGGREGATE SUPPLY RESPONSE ESTIMATION FOR POLICY ANALYSIS

1. ISSUES AND STRATEGIES FOR AGGREGATE SUPPLY RESPONSE ESTIMATION FOR POLICY ANALYSIS by Octavio A. Ramirez and Samarendu Mohanty

2. Introduction • Supply equations are key components of increasingly sophisticated agricultural trade models built, maintained and continuously improved for policy analyses • The most common strategy for estimating supply response is to build separate econometric models for yield and acreage • In most applications, these need to be estimated at the state, regional or national level; which means that only relatively small samples are available for estimation

3. Introduction • This paper discusses key issues and exemplifies the use of the small-sample econometrics strategies to obtain reliable yield and acreage models under these circumstances • These will be presented throughout applications involving cotton supply response in the Southeastern U.S. • The development of proper confidence intervals for the supply response predictions is also discussed

4. Modeling Strategy • Since consistent parameter estimation is not feasible, we recommend estimating flexible but parsimonious models that provide for adequate representations of the data • Specifically, we use Ramirez’s pdf modeling approach where yields and acreage are specified as functions of sets of explanatory variables plus a flexibly distributed error term • The flexible error term is also needed for the development of proper confidence intervals • The model is estimated by ML procedures

5. Modeling Strategy • Initially, the error terms are specified as heteroskedastic, autocorrelated (acreage model), and non-normally distributed (pdf models) • The initial error term specifications are tested for homoskedasticity, symmetry and normality • Four misspecification tests are recommended to evaluate if the model is an adequate representation of the data-generating process: • RESET3 for functional form and omitted variables • White test for heteroskedasticity • ACF analysis and Box and Pierce Q test • D’Agostino-Pearson omnibus non-normality test

6. Modeling Strategy • The last three tests are applied to the standardized and normalized residuals from the pdf model • If the error term specifications in the flexible pdf models are correct, these residuals should be independently, identically and normally distributed random variables • Rejection of the null hypothesis in any of these tests points to possibility of improving the model in that particular aspect

7. Supply Response Predictions • In the context of policy analysis, a good supply response prediction must include a reliable confidence interval for that prediction • Ramirez’s pdf models provide more reliable confidence intervals than the standard models that assume error term normality • Another key issue is how to obtain proper confidence intervals when the predictions are based on forecasted values of some of the explanatory variables

8. Supply Response Predictions • The only sound alternative to derive the distribution of the dependent variable forecast in the general case where the model’s error term and some of the explanatory variables are not normally distributed is: • Model the joint probability distribution of the explanatory variables which values themselves had to be forecasted • Simulate joint realizations from this distribution into the future • Add the product of these simulated values times the corresponding simulated model parameters plus simulated error term values to the dependent variable forecast

9. Supply Response Predictions • Ramirez has also addressed the issue of how to jointly model and simulate the distribution of the a set of (explanatory) variables that might be non-normally distributed, heteroskedastic and/or autocorrelated • We recommend pure time series models, meaning that the means be initially specified as third-degree polynomial functions of time, the standard deviations as linear functions of time, and the error term as a non-normal first order autoregressive process • Misspecification testing procedures should also be applied in the case of these auxiliary models.

10. Yield Response Results • The “final” normal-error model passes all misspecification tests but its estimated t equation is 7.78+4.47t, which suggests that yield variability has increased 14-fold since 1965 • Once a statistically valid 50% volatility increase restriction is imposed (t=61.48+0.83t ), the residuals fail the normality test • In contrast, the final pdf model is homoskedastic • A LR test of initial normal-error model versus initial pdf model [12.10>2(2,0.01)=9.21] suggests that the later a far superior statistical representation of the data-generating process

14. Confidence Intervals for Yield Response • In short, when the error term is non-normally distributed, using confidence intervals from pdf model provides two empirical advantages: • The intervals would generally be narrower indicating that the corresponding predictions are more precise • They would also adhere more closely to “theoretical” expectations • These confidence intervals work well on reflecting the behavior of the yield data within sample • They will, however, be inappropriate to represent the stochastic behavior of the dependent variable out of sample (i.e. into the future) because the values to be undertaken by at least some of the explanatory variables become unknown

15. Confidence Intervals for Yield Response • The standard deviation of the “proper” probability distribution for the 2002 yield forecast (137.7 lbs/acre) is 40% larger than the one obtained when assuming that the explanatory variable values are known • The width of the 80% confidence interval is 298.67 lbs/acre versus 198.96 lbs/acre • This is due to the added uncertainty about the 2002 cotton and soybean prices and rainfall

16. Acreage Model • The initial acreage model includes an autoregressive error term specification • In regards to the variance function note that the typical zero-one dummy variable arrangement would result D65 and D97 encompassing only six and five observations, respectively • We propose using an “overlapping” dummy variable arrangement that provides for smoother shifts across policy periods and alleviates the econometric “instability” problem encountered when using the standard arrangement

17. Acreage Response • In the normal error model the standard deviation parameters have to be restricted so that no individual coefficient estimate deviates form the average of the four by more that 50% • Then, there appear to be two variance regimes and the autocorrelation coefficient is insignificant • The pdf model can be estimated without restrictions, is homoskedastic, includes one additional explanatory variable and a significant autocorrelation coefficient (=0.52) • The MVFL for the pdf model (-200.6) is much higher than the one for the normal model (-206.3)

20. Supply Response Forecasts • Note that in constructing the yield forecasts and confidence intervals above it was assumed that the number of acres planted was known, which would only be correct if supply response was being predicted right after planting • Then, the supply response forecast and its probability distribution would simply be obtained by multiplying the yield forecast and confidence intervals by the known acreage • Otherwise, more steps would be needed to finalize the task of obtaining theoretically sound and efficient cotton supply response forecasts for the Southeastern U.S.