A Transparent, Numerical Solution to the Joint Estimation of Imputation Credit Value and Cash Dividend Value

Abstract

Multiple regression analysis leads to coefficient estimates that need to be jointly interpreted. This holds even if correlation amongst independent variables is at a level that researchers typically consider to be tolerable. In estimating the value of imputation credits using multiple regression, experts and regulators have typically considered estimates of the value of imputation credits in isolation. They apply the credit value estimates to pricing models under the assumption that cash is fully valued by the market. We call this problem selective interpretation. We address the challenge of selective interpretation by conducting an advanced “if-then” analysis. We ask if cash and credits are truly valued by investors at x and y, then what range of regression coefficients would occur if the regression could be repeated over and over again? This allows us to estimate confidence intervals for the value of cash dividends and imputation credits by making transparent assumptions about the independence of observations and the non-constant variance of error terms. Our paper has application to any research that relies on multiple regression analysis. The practical implication is that in the current tax regime, under which investors can receive a cash rebate for imputation credits, the market value of imputation credits lies within the range of 0.01 to 0.15. A dollar of cash is valued by the market at somewhere between 87 cents and 92 cents. But, at the lower end of the cash value (0.87), credits are worth between 0.13 and 0.15, and, at the higher end of cash value (0.92), credits are worth between 0.01 and 0.10. The value of imputation credits has moved over time in a direction consistent with the changing tax treatment. Prior to the introduction of the 45-day rule, credits had an estimated value within the range of 0.07 to 0.24, but the value decreased to a range of just 0.00 to 0.02 once the 45-day rule was introduced. Upon the introduction of the cash rebate, the value of credits has increased to a range of 0.01 to 0.15.