计量经济学导论电子教案ch04章节幻灯片.ppt

Economics 20 - Prof. Anderson * Overall Significance A special case of exclusion restrictions is to test H0: b1 = b2 =…= bk = 0 Since the R2 from a model with only an intercept will be zero, the F statistic is simply Economics 20 - Prof. Anderson * General Linear Restrictions The basic form of the F statistic will work for any set of linear restrictions First estimate the unrestricted model and then estimate the restricted model In each case, make note of the SSR Imposing the restrictions can be tricky – will likely have to redefine variables again Economics 20 - Prof. Anderson * Example: Use same voting model as before Model is voteA = b0 + b1log(expendA) + b2log(expendB) + b3prtystrA + u now null is H0: b1 = 1, b3 = 0 Substituting in the restrictions: voteA = b0 + log(expendA) + b2log(expendB) + u, so Use voteA - log(expendA) = b0 + b2log(expendB) + u as restricted model Economics 20 - Prof. Anderson * F Statistic Summary Just as with t statistics, p-values can be calculated by looking up the percentile in the appropriate F distribution Stata will do this by entering: display fprob(q, n – k – 1, F), where the appropriate values of F, q,and n – k – 1 are used If only one exclusion is being tested, then F = t2, and the p-values will be the same Economics 20 - Prof. Anderson * Multiple Regression Analysis y = b0 + b1x1 + b2x2 + . . . bkxk + u 2. Inference Economics 20 - Prof. Anderson * Assumptions of the Classical Linear Model (CLM) So far, we know that given the Gauss-Markov assumptions, OLS is BLUE, In order to do classical hypothesis testing, we need to add another assumption (beyond the Gauss-Markov assumptions) Assume that u is independent of x1, x2,…, xk and u is normally distributed with zero mean and variance s2: u ~ Normal(0,s2) Economics 20 - Prof. Anderson * CLM Assumptions (cont) Under CLM, OLS is not only BLUE, but is the minimum variance unbiased estimator We can summarize the population assumptions of CLM as follows y|x ~