計(jì)量經(jīng)濟(jì)第四章ppt課件(存儲(chǔ)版)
【正文】 準(zhǔn)檢驗(yàn)時(shí)bbExample: Campus Crime and Enrollment 例子：校園犯罪與錄取 ? Question: Will 1% increase in enrollment increase campus crime by more than 1%? 問(wèn)題：錄取量提高 1%是否會(huì)導(dǎo)致校園犯罪增加超過(guò) 1%? ? Suppose total number of crimes is determined by 假設(shè)犯罪總數(shù)由下式?jīng)Q定 crime=exp(b0 )enrollb1exp(u). ? One can estimate 可以估計(jì) log(crime)=b0 + b1 log(enroll)+u Example: Campus Crime and Enrollment 例子：校園犯罪與錄取 ? And test H0: b1 = 1 H1: b1 1. ? Using data from the FBI’s uniform Crime reports (97 observations), the estimated equation is ? 利用 FBI犯罪報(bào)告（ 97個(gè)觀察值）的數(shù)據(jù)，估計(jì)得到方程 ^log(crime)=+(enroll) () () () The correct t ratio=()/=. The 1% onesided critical value for a t distribution with 95 degrees of freedom is . Therefore reject the null. t值 =()/=。對(duì)于雙邊檢驗(yàn) pvalue=P(|T||t|). Computing pvalues for t Tests 計(jì)算 t檢驗(yàn)的 p值 pα/2 pα/2 In the above example, it must be true that 1%p5%. pvalue=P(|T|) =2P(T) =. 。標(biāo)準(zhǔn)正態(tài)分布的在 5%的顯著水平對(duì)應(yīng)的臨界值為 。在5％顯著水平下，臨界值位－ ? Because –, we fail to reject the null. 由于 ，我們不能拒絕零假設(shè) Example: Student Performance and School Size 例子：學(xué)生表現(xiàn)與學(xué)校規(guī)模 ? If we are also interested in asking whether betterpaid teachers leads to better student performance, we can test 如果我們同樣感興趣是否高收入的教師會(huì)使學(xué)生表現(xiàn)更好，我們可以檢驗(yàn)： ? H0 :βtotp=0 versus H1 :βtotp0 ? The calculated t statistic equals . Since , therefore rejecting the H0 at 1% level. 計(jì)算得到的 t統(tǒng)計(jì)量為 。 Background Review 背景知識(shí)回顧 ? The critical value of the test statistic is the value of the statistic for which the test just reject the null hypothesis at the given significance level. 檢驗(yàn)統(tǒng)計(jì)量的 臨界值 是使得零假設(shè)剛好在給定顯著性水平上被拒絕的統(tǒng)計(jì)量的值。 CLM Assumptions 經(jīng)典線性模型假設(shè) ? We can summarize the population assumptions of CLM as follows 我們對(duì)總體的經(jīng)典線性模型假設(shè)做個(gè)總結(jié) ? y|x ~ Normal(b0 + b1x1 +…+ bkxk, ,s2) ? While for now we just assume normality, sometimes this is not the case 盡管現(xiàn)在我們假設(shè)了正態(tài)，但有時(shí)候并不是這種情況 CLM Assumptions 經(jīng)典線性模型假設(shè) ? What should we do when the normality assumption fails? 如果正態(tài)假設(shè)不成立怎么辦？ ? Using a transformation, especially taking the log, often yields a distribution that is closer to normal. 通過(guò)變換，特別是通過(guò)取自然對(duì)數(shù)，往往可以得到接近于正態(tài)的分布。 CLM Assumptions 經(jīng)典線性模型假設(shè) ? Assumptions – are called the classical linear model (CLM) assumptions. 假設(shè) ? We refer to the model under these six assumptions as the classical linear model. 我們將滿足這六個(gè)假設(shè)的模型稱為經(jīng)典線性模型 ? Under CLM, OLS is not only BLUE, but also the minimum variance unbiased estimator, that is, among linear and nonlinear estimators, OLS estimator gives the smallest variance. ? 在經(jīng)典線性模型假設(shè)下， OLS不僅是 BLUE，而且是 最小方差無(wú)偏估計(jì)量 ，即在所有線性和非線性的估計(jì)量中， OLS估計(jì)量具有最小的方差。如果為 5％的檢驗(yàn)中錯(cuò)誤地拒絕零假設(shè)。 The t Test (cont) ? ?? ?0?j0?j
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