THEAMERICAN ECONOMIC REVIEW JUNE 1985 TABLE1— ESTIMATEDⅤ ARIANCE DECOMPOSITIONS Population Name Estimate Estimate Percentage Market 68466 1959 02(B)H y2a2(S)(1-(1-H)p2 Covariance 2 ypa(B)a(s) 2Hypa(B)o(s) -2.159 Error 281.049 81.049 a2(r) 100.00 10000 Note:See text for sources and definitions, Totals may not add because of rounding results developed below, and then skip and the defensibility of industry-level analy Section Iv re again clear Ordinary least squares estimation of (4), In order to estimate the two remaining which appears in Figure 1 as the""Industry terms on the right of (5), it is necessary to be and Share Effects"model, yields a consistent more specific about what is meant by a non and unbiased estimate of 281.05 for a2(e). zero population correlation between market Following Searle's(chs. 9-11)treatment of share and market effects. Imagine the data variance components estimation in unbal- generation process first fixing the N, then nced models, I next compute consistent drawing the ps independently from their analysis-of-variance"estimates of the re- unconditional distribution, and finally draw maining quantities on the right of (5) ing the S's for each industry from the cond et the operator can"expected sum tional distribution determined by of squares about the sample mean, "let n be of B previously drawn. Assume without loss he total number of observations, let N, be of generality that the unconditional mean of the number of observations in industry j, the B's is zero and of the S's is u, I then and let M be the total number of industries. impose the following assumptions a bit of algebra yields (6)ESS(, -YS,) i=k =(N-1)2(a)+(N-G)02(B,E(S,S) (k2)2+o2(S) ()+(s)2(B,s)1≠k where (8b)E(BS)=p(B, S)o(B)o(S) The first part of(8a)and(8b)are not restric (7)G=∑(N)2/N tive,the second part of (8a) is consi tent with but does not impose normality These expectations are taken with respe If all industries had only one firm, G would to the unconditional population distribution equal one. If there were only one industry, G would equal N, since industry effects would not contribute to overall variance. In these data,G=15.55. Using y= 2304 and o(e) 15As a final check on the robustness of 81.05 from above, setting the expectation sion, I computed MIVQUEQO estimates of on the left of (6)equal to its sample value, firm, market, and error variance compone and solving yields an estimate of 68.47 for (r,.-ySiyj). See H. 0. Hartley et al., 1978 0(B). This is equal to 19.62 percent of the estimates of a(B)of 62.03 and 64.88,respectively.This of ple variance of the r. and 78.78 percent close to those in the text, further strengthening the case the sample variance of the R;. The or the qua e importance of in quantitative importance of industry effects these data