Balbach and Brunner: A Missing Stop on the Road from Warburton to Friedman-Meiselman and St. Louis
指出，在弗里德曼和迈泽尔曼（1963）以及圣路易斯方程之前，布伦纳和巴尔巴赫已使用简化形式方程研究货币与支出对总需求的影响，并探讨了货币需求函数的稳定性，其工作应被视为重要先驱。
Abstract “The Relative Stability of Monetary Velocity and the Investment Multiplier in the United States, 1897–1958,” by Milton Friedman and David Meiselman (1963), typically is recognized as the original study that used a reduced-form equation to evaluate whether autonomous expenditures or the quantity of money was the dominant influence on aggregate spending. It also provided the foundation for the better-known St. Louis equation that followed. Missing from this evolution, however, are important precedents by Karl Brunner and Anatol Balbach that also employed a reduced-form framework to offer evidence on the same debate between the Keynesian expenditure theory and the quantity theory of money. Moreover, these authors also investigated whether the demand-for-money function was stable and inversely related to an interest rate, properties necessary in their reasoning before any more general model of national income determination could be developed. With this foundation, Balbach, in his 1963 PhD dissertation, then derived a reduced-form expression for personal income from an explicit theoretical model and, in its estimation, anticipated and addressed some of the empirical criticisms later directed at the work by Friedman and Meiselman and the early versions of the St. Louis equation. Taken together, the theoretical and empirical work reported in Balbach's dissertation and in a 1959 article by Brunner and Balbach suggest these papers are clear antecedents of later reduced-form expressions and should be recognized as such.