Professor Allais' Theory of the Demand for Money: Rejoinder
I find myself in a situation like that of Moliere's M. Jourdain who was surprised to learn that he spoke prose. I am surprised to learn that-according to Maurice Allais, at least-I commit paralogisms. If all I wanted to do was dispute that, I would not take up space with this rejoinder; the law of diminishing returns applies with special force to these running controversies. The problem is, however, that Allais does not address himself directly to my criticism, and I think the criticism is important because it is fundamental. My point was a methodological one: that the tests of Allais' theory are probably quite weak. Allais' skirting of this point is unfortunate for two reasons. The first is that one might get the idea, from reading his reply, that his hereditary and relativistic formulation of the demand for money was under attack. The second is that one might think that he provides confirmation of his theory when I think that a careful scrutiny of his test procedures suggests otherwise. On the first point, nothing was further from my mind when I wrote my comment than an attack on the ideas in the hereditary and relativistic formulation of the demand for money. Quite the opposite was the case. I had then, and I continue to have, nothing but admiration for Allais' theory, which I think is original and may ultimately prove fruitful. I addressed myself only to the second point. The nub of the problem is that, in going from theoretical to empirical specification, Allais introduced an approximation which very likely robbed his tests of much power. That approximation consists of using velocity as a measure of the rate of forgetfulness (1966, p. 1135, equations (2.38) and (2.41)). That means that the estimated coefficient of psychological expansion' is a function, among other things, of past velocity. Since that coefficient is used to predict velocity, Allais' testing comes down to estimating velocity as function of its past. It could come perilously close, in other words, to estimating velocity as an autoregressive process. And if that is true, the test of the structural content of the theory is minimal. Allais' characterization of the above argument is that I accuse him of circularity. That is simply not true. What I suggest is that his tests have little power against the naive alternative of an autoregressive specification for velocity. It may be that velocity is a good measure of the rate of forgetfulness. But I have serious doubts as to whether we are going to be able to test that-or the other parts of the theory by appealing to the behavior of velocity. Allais in fact concedes that his test must be weak, although he does not say so explicitly. He grants that my argument is correct if we can identify measured with desired velocity (what he calls observed and estimated velocity): ... Scadding unfortunatelv fails to make the distinction between the observed and estimated values V and V*. In fact, his mathematical reasonings are valid only if V and v are replaced therein by V* and v* (p. 456). Yet in his original paper, Allais makes the same assumption in deriving the empirical form of his hvpothesis: . . but it can reasonably be suggested that the discrepancy between the actual and the desired value of money holdings is always relatively small. . . . It further follows that it is possible to write as a first approximation . . . (3.2) . .. (3.3) OD . . . * (1966, p. 1138).
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