THE BIAS TOWARD ZERO IN IDENTIFYING RELATIONSHIPS: REPLY TO KENNEDY

We will argue that rational expectations has considered only the "misestimation" type of error, which can "cancel out" in the aggregate, but that with errors in identifying relationships, there is no similar cancelling out effect (Fremling and Lott [1996, 276]) Kennedy [1999] misses much of our point. When he extends our two-variable case to a three-variable case, he views agents as exclusively making the traditional "specification errors." As is well known, specification errors concern what variables to include when estimating a regression. He fails to address our main contribution - that people sometimes do not identify that a relationship even exists. When describing our argument Kennedy goes so far as to always replace our references to "[model] identification error" with the term "specification error." For instance, the way he refers to our footnote 5 (p. 279) gives the misleading impression that we ourselves are using the term "specification errors." Our footnote clearly uses the term "identification errors,"(1) and it is only because he switches these terms that he is able to conclude that "Fremling and Lott have violated one of their own assumptions ...." In our 1996 paper we showed the following. Individual actors sometimes are quite clueless as to an economic problem, failing to understand that two (or more) variables are related. We extensively described this "identification problem" on p. 278, and we stated: "The crucial argument in this paper is that at least some people fail to identify a true relationship, and therefore never take the next step, which is to estimate the strength of it. Failing to estimate the strength of a relationship is essentially equivalent to estimating it to be zero." Thus, many do not reach the regression-step at all. When aggregating across individuals making various mistakes, economic behavior at the group level resembles a situation where every individual estimates a regression but underestimates the regression coefficient. Even though all our actors are "rational" - and thus only make non-systematic mistakes in what variable(s) are omitted - the aggregate results could equally well have been generated by a group of non-rational actors systematically underestimating the regression coefficients. In other words, when observing aggregate behavior that contains aggregate systematic errors, one must be cautious not to erroneously infer irrationality on the part of the individuals. Now to Kennedy's numerical example with two independent variables rather than one. How should our analysis be applied? We maintain that there exists a total of eight possible cases: one of correctly recognizing all three variables as being connected, three of missing only one, three of missing two, one of missing all. Kennedy only recognizes four of the cases. This makes an enormous difference. If Kennedy had also included the implicit zero coefficients in the remaining four cases, he would have found a substantial "bias toward zero": for the representative individual, [Alpha] would have been only 4.05 (not 8.09) compared to its true value of 6. Kennedy never mentions his estimate of [Beta], but as a careful reader can deduce, this estimate is only 2.16, a serious underestimate. And including the four other cases with zero's would have yielded a mere average estimate of 1.08, way below its true value of [Beta] = 4. In our view, Kennedy's Monte Carlo experiment merely confirms our results.(2) Kennedy makes it appear that his numerical example corresponds to our macroeconomic modeling in section V. It does not, for he overlooks our explicit assumption that "the general price level cannot be perfectly and immediately observed by the workers ..." (p. 283). This a very classical assumption in macroeconomics and forms the basis for why changes in the nominal wage are sometimes confused with changes in the real wage. …