On the Relevance of First Order Asymptotic Theory to Economics Esfandiar Maasoumi Dept. of Economics, SMU, Dallas, TX 75275-0496, maasoumi@mail.smu.edu On the occasion of its 100 th issue, the founders of the Journal of Econometrics, as well as its successive co-editors and editorial boards deserve our gratitude and thanks. It is easy to forget where we were at in econometrics publication in early 1970s. If you had something to say, you had to either please statistical outlets, or the few barons controlling Econometrica, or you shelved your work. Things have hardly improved with Econometrica, to say the least, but thanks to pioneering work of this journal, most of the real action is reflected elsewhere. There are numerous other outlets that are widely read and cited. Looking back and to the future deserves our attention, well beyond a few pages available here. But this collection will have great historical value, both for what is said and what is not. I will focus on only a few points. The first is, what have we achieved since about the publication of Bill Taylor's "On the relevance of finite sample distribution theory", Taylor (1983, Econometric Reviews)? The second is an informal set of where the most consequential developments may come from. There is a widespread belief, an official position of sorts, that we now have the "inference tools" to deal with much more complicated models and processes. Laws of large numbers (LLN) and central limit theorems (CLT) have been given under largely unverifiable and unlikely conditions for nonlinear, dynamic models/processes. Almost every function of the data you are likely to consider is consistent for something, is normally distributed, and gives rise to Chi-squared type statistics for testing any desired hypothesis. Any casual consideration of the rich tapestry of the random phenomena suggests that there is something wrong with this picture. It is practically tautological to say that most estimators are neither normally distributed nor even symmetric, and most test statistics are not Chi-squared. Finite sample distribution theory may not have given us a workable inference theory, but it gives us enough to assert the previous claim. Science is about approximation, to be sure, but the burden of proving adequacy and accuracy is with those proposing any approximation. In sciences it is widely accepted that the first term of Taylor series approximations, already merely locally valid, can be very poor. Asymptotic expansion, already less solid as an approximation concept, delivers even less. Still worse, in Maasoumi and Phillips (1982) a rather chilling characteristic of first order asymptotics was demonstrated. In the practically relevant “misspecified models” the limiting distribution may even fail to exist! This has recently been shown for GMM estimators by Alastair Hall and others. Monte Carlo evidence, though badly needing systematic compilation, provides frequent embarrassing evidence against first order asymptotic results. There are some experimental situations that are better than others. But where is the characterization work that may guide the users and empirical economists as to what to expect, when, where, and how? It is important to appreciate that most models are local approximations. Because of this we will often find evidence of “regime change” in the data. It is not a little comical then to pretend that larger samples serve a fundamentally small sample context. How can infinitely many observations pertain to an approximation valid for three points in time? It is no wonder to witness a widespread cynicism, and even outright rejection of "econometrics" in some quarters. See Jim Heckman's account in this issue, even though I am less worried about pre- renaissance economics rejecting econometrics, or trying to reinvent it to support an impressionist movement. But we have been warned: with or without econometrics, a good empiricist, familiar with his/her data and substantive context, can look at the square of her errors and decide that it is "relatively" large or not. A main claim of statistician/econometrician to usefulness in this process is the potential ability to provide a reliable probability level to such statements as economists need to make. That is, an inference theory with adequately characterized approximation levels and performance guarantees. We are not immune to laws of nature, even if we cook up the rules of the game so as to preserve the status quo. We need to change the incentives and the reward structure, may be a little like the mechanisms we teach our students and publish in elite journals, or face even greater irrelevance to the exciting economic world around us.