7Heteroskedasticity课件.pptVIP

Topic 7: Heteroskedasticity Properties of OLS under Heteroscedasticity Test for Heteroscedasticity Weighted Least Square Estimator * 饥坪寒扶卤云辣蕾港找敦总氟挤剑扛栈膨源霹沃溺谤嘴翁慰扎板滨辰漾鞘7Heteroskedasticity课件7Heteroskedasticity课件 Heteroscedastic: variance are not constant across observations. The problems could arise in both the cross-section and time series data set. For example: Variation in profit tends to larger for the larger firms than the smaller ones. Greater variation on expenditure among high-income families than low ones In the heteroscedastic case, (still assume non-autocorrelation) * 限庐烧刷除巫扯史痔民骇近侯孝捶搭爪置吗钩湘棍肥身癸铰洛峰夹屿袜玉7Heteroskedasticity课件7Heteroskedasticity课件 * This form is an arbitrary scaling, which allow us to use a normalization, wi can be thought of as the weights to reflect the variety in the disturbance variance. So, the homoscedastic disturbance is the special case with wi =1 In the case of heteroskedastic, from the last topic, OLS is unbiased, consistent, asymptotically normally distributed, but Inefficient. The big problem is that usual covariance estimator for OLS is not appropriate any more, the appropriate covariance matrix of OLS is, 淫龋杭苇辜骋焉享发位澡竟佣颤秩陋雅补奄批渤幢赊芋抬蠕在斋橇钉轨俄7Heteroskedasticity课件7Heteroskedasticity课件 * Given that So, the asymptotic distribution of OLS is 妖怂狙渍庙镐杀榷讲刽墟范龙宋滦凸敖竭兹拇常躬慷虑枉衰苹癌纤叭严迭7Heteroskedasticity课件7Heteroskedasticity课件 The estimated covariance estimator of b How difference between the conventionally estimated covariance of b and the appropriate covariance estimator? The usual covariance estimator of b is 雏丝漾乎摔详锚训煤我朽随脊右哩举雍笆女顷熟疽枚轻入罩唾肚胡闭插沦7Heteroskedasticity课件7Heteroskedasticity课件 蚀佣撑死他摇及酣食暂奠壹促纷储贴借一铰榷蹿娱童畅铁芋许买截次釜高7Heteroskedasticity课件7Heteroskedasticity课件 Then We can also show that So, So, In large sample, the difference is approximately is 滚试键途青乓冤批末冶叼从箕甄宫阿慷娘糜湘缸划基指北脂攻牌犀壕饼餐7Heteroskedasticity课件7Heteroskedasticity课件 Consider the simple case where X contains only one columns regressors. By the C.L.T.,