Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Stochastic Partial Budgeting: A New Look at an Old Tool

Farm business managers are constantly making adjustments in their businesses for smoother operations and profitability. Many times, these choices involve actions to enhance the financial return of the farm business; while other times these decisions are made out of necessity to minimize the effects of unfavorable conditions or events such as drought or changes in the market conditions. Some of these decisions are relatively simple, requiring making choices among alternatives within an enterprise; while others are complex involving a total overhaul of the business and its enterprises. Alternative choices within an individual enterprise can have a differential impact on farm profitability. Therefore, making the best decision may make the difference between profit or loss for that enterprise. Partial budgeting is very useful in making such changes within an enterprise of a farm.