Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the case of semiparametric M estimation. However, the resulting estimates of derivatives, as well as parameter estimates and inferences that depend on the derivatives, can be highly sensitive to the choice of the kernel and finite difference bandwidths. This paper discusses the theory of asymptotically optimal bandwidths for kernel and difference quotient estimation of the derivatives required for quantile and semiparametric M estimation, respectively. We do not present a fully automatic method for bandwidth selection.

Only in the last few years has the history of econometrics become established as an accepted field of research, with its own doctoral students and sessions at professional meetings. Yet, the first written histories of econometrics appeared as far back as the 1950s, when Carl Christ [4] reviewed the first 20 years' econometric work of the Cowles Commission and George Stigler [37] surveyed the early econometric analyses of consumer demand. Contributions in the intervening years have been sparse, with historical accounts such as Stigler [38], Humphrey [23], and Cargill [3] providing helpful landmarks, and additional insights coming from papers such as Gold-berger [16] and Griliches [17]. Now we have a new monograph on the history of the Cowles Commission by Hildreth [22], a number of journal articles, and Roy Epstein's 1987 book, A History of Econometrics, as further contributions to this small but rapidly expanding field.

This note presents a procedure which enables the user to check whether a monotonic transformation can change the sign of a regression coefficient. One possible use of this procedure is to examine the robustness of key regression coefficients.

There are some errors in the paper by Victoria Zinde-Walsh, “Some Exact Formulae for Autoregressive Moving Average Processes,” Econometric Theory 4 (1988): 384–402. The following is a list of corrections.

On page 393 the τ * τ matrices El,E2 should be replaced by their transposes ,, respectively, throughout. In (3.21) the expression (S3 – λλA3) should be replaced by (S3 – λλA3) in the definitions of both T1, and T3. In (3.8), (3.21), (5.1), and (5.2) the entry in the bottom right-hand corner should be pre- and post-multiplied by λ. In (3.6) the matrix is obtained as the negative of the matrix denoted in the previous section 3.1. In (3.19) the top bar was omitted in Ē2. The top bar was also omitted in Ē1 on the second to last line of p. 392. In (5.1) D′−1 rather than D−l should appear in all the matrix entries in the second column; D′−1 should premultiply the parentheses in the top left and bottom right corners instead of D−1 post-multiplying them. In (5.2) transposes were omitted on D in the second entries on the first and last lines; in the second line of the second column, the second time A2 appears it should be transposed.