The concept of period length in the empirical application of cash-in-advance (CIA) models is introduced. CIA models posit that individuals and firms hold cash to purchase goods over a period. However, there has been no research into how long a period is. Existing empirical studies use quarterly or annual data in simulations or estimations of CIA models. This is inappropriate if individuals or firms conduct financial transactions at intervals which are more frequent than 3 months or 12 months. The period length which is empirically consistent with the theoretical restrictions imposed by a CIA model for 9 two-digit (SIC based) industries is determined to be one to six weeks, depending on the industry examined and money variable used. Unlike other empirical work using CIA models, the introduction of the concept of period length allows this model to display variability in the velocity of money. It is also found that the CIA binds between 1% to 13% of the time instead of nearly 100% as in other papers. The effectiveness of CIA in modeling the effect of money on firms and the demand for money by firms is demonstrated in two applications. Each application incorporates the period length concept described above. In the first application, it is found that money is not an omitted variable in the production function of a firm. This result is based upon the fact that the inclusion of money through the use of a CIA constraint into a model of production does not significantly affect the estimated partial elasticies of input substitution. This paper is the first empirical work reporting this result, and it casts some doubt on the results of several earlier papers which conclude that money does indeed belong as an argument in the production function. In the second application, the Euler equations of a firm subject to a CIA constraint are used to derive the firm' s money demand function. The CIA framework yields parameter restrictions for the money demand function which can be tested econometrically to evaluate the performance of the CIA model of money demand.
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