第八次上机内容

1、 第八次上机作业教学目的：关于序列相关性的检验和修正的几种方法教学内容：一、序列相关性的检验和修正1 图示法：以回归方程的残差作为扰动项的估计，来反映扰动项的自相关。先对方程进行回归，观察残差 随时间变化的情况，若 随时间呈有规律变化，则说明存在自相关。2 一阶序列相关的D-W检验方法： 适合条件：（a）方程中无滞后因变量；（b）误差项一阶自相关，即 ，其中 满足基本假定的要求；（c）解释变量与 不相关；（d）样本容量N比较大。检验步骤：对方程进行回归，看输出表中的DW值（注意d值是否落在三个特殊点0（正自相关）、2（无自相关）和4（负自相关）的邻域内）。给定显著性水平，查DW表，得下、上临界

2、值 和 ，判断DW值在相应的哪个邻域内（具体请见教材P102的TABLE 6.1），得出在此显著性水平下自相关存在与否的结论。3 一阶序列相关的修正（1） Cochrane-Orcutt修正方法：在命令窗口输入“LS Y C X1 X2 Xk AR(1)”或在回归对话框中输入“Y C X1 X2 Xk AR(1)”，输出表中的AR(1)的系数即是一阶序列相关系数 的估计值。（2） Hildreth-Lu修正方法：选取一阶序列相关系数 的网格点值：0，0.2，0.9，1 .0（或更细网格点），作广义差分变换，对变换后的各方程进行OLS估计，选择残差平方和最小的方程作为最好的方程。4 有滞后因变量

3、时对序列相关性的检验Durbin h统计量检验方法：先对方程进行回归，由DW值计算 的估计值，构造h统计量（服从方差为1的正态分布），在一定显著性水平下，对无自相关性的原假设进行检验。细节及其变形请见教材P105。5 上机实习：（1） 以EXAMPLE 4-2中的数据和模型为例（即教材P104的EXAMPLE 6.6），检验模型的序列相关性，并应用上面的Cochrane-Orcutt方法和Hildreth-Lu方法对序列相关性进行修正。（2） 以我们曾做过的总消费函数模型为例（见教材P105的例6.7中的模型，数据是EX4.2），利用Durbin h检验法检验模型的序列相关性。二、模型确认失误

4、检验1 缺省变量的检验（预习）Bear in mind that: (1) The omitted variables test requires that the same number of observations exist in the original and test equations. If any of the series to be added contain missing observations over the sample of the original equation (which will often be the case when you add l

5、agged variables), the test statistics cannot be constructed. (2) The omitted variables test can be applied to equations estimated with linear LS, TSLS, ARCH (mean equation only), binary, ordered, censored, truncated, and count models. The test is available only if you specify the equation by listing

6、 the regressors, not by a formula. How to Perform an Omitted Variables Test？To test for omitted variables, first do the initial regression (not including the omitted variables), and then select “View/Coefficient Tests/Omitted Variables-Likelihood Ratio”. In the dialog that opens, list the names of t

7、he test variables, each separated by at least one space. Suppose, for example, that the initial regression is Ls log(q) c log(l) log(k)If you enter the list “log(m) log(e)”in the dialog, then EViews reports the results of the unrestricted regression containing the two additional explanatory variable

8、s, and displays statistics testing the hypothesis that the coefficients on the new variables are jointly zero. The top part of the output depicts the test results:Omitted Variables: LOG(M) LOG(E)F-statistic 4.267478 Probability0.028611Log likelihood ratio8.884940 Probability0.011767The F-statistic h

9、as an exact finite sample F-distribution under H0 (i.e. the two series do not belong to the equation, or the coefficients on the two variables are jointly zero) if the errors are independent and identically distributed normal random variables. The numerator degrees of freedom is the number of additi

10、onal regressors and the denominator degrees of freedom is the number of observations less the total number of regressors. The log likelihood ratio statistic (which we will discuss in the following chapters) is the LR test statistic and is asymptotically distributed as a with degrees of freedom equal

11、 to the number of added regressors. In our example, the tests reject the null hypothesis that the two series do not belong to the equation at a 5% significance level, but cannot reject the hypothesis at a 1% significance level. 2 多余变量的检验（预习）The redundant variables test allows you to test for the sta

12、tistical significance of a subset of your included variables. More formally, the test is for whether a subset of variables in an equation all have zero coefficients and might thus be deleted from the equation. The redundant variables test can be applied to equations estimated by linear LS, TSLS, ARC

13、H (mean equation only), binary, ordered, censored, truncated, and count methods. The test is available only if you specify the equation by listing the regressors, not by a formula.To test for redundant variables, first do the initial regression (including the redundant variables), and then select “V

14、iew/Coefficient Tests/Redundant Variables-Likelihood Ratio”. In the dialog that appears, list the names of each of the test variables, separated by at least one space. Suppose, for example, that the initial regression is ls log(q) c log(l) log(k) log(m) log(e)If you type the list“log(m) log(e)”in th

15、e dialog, then EViews reports the results of the restricted regression dropping the two regressors, followed by the statistics associated with the test of the hypothesis that the coefficients on the two variables are jointly zero. The test statistics are the F-statistic and the Log likelihood ratio.

16、 The F-statistic has an exact finite sample F-distribution under H0 (i.e. the coefficients on the two redundant variables are jointly zero) if the errors are independent and identically distributed normal random variables. The numerator degrees of freedom are given by the number of coefficient restr

17、ictions in the null hypothesis. The denominator degrees of freedom are given by the total regression degrees of freedom. The LR test is an asymptotic test, distributed as a with degrees of freedom equal to the number of excluded variables under H0. In this case, there are two degrees of freedom.3 上机

18、实习案例以第四题中的数据(ex32.xls)及模型I和II为例，进行如上的检验：模型I为：Y=C1+C2（X1）+C3（X2）+C4（X3）+C5（X4）+C6（X5）模型II为：Y=C1+C2（X1）+C3（X2）+C4（X3）+C5（X4）检验模型I中的C6是否为多余？检验模型II是否缺省变量C6？多余变量的检验：先在检验模型I将Y关于X1，X2，X3，X4和X5 回归，在回归输出表中，击菜单“View/Coefficient Tests/ Redundant Variables-Likelihood Ratio”，在对话框中输入“C（6）”，看F值和p值（似然比以后再讲），判断。缺省变量

19、的检验：将Y关于X1，X2，X3，X4回归，在回归输出表中击菜单“View/Coefficient Tests/Omitted Variables-Likelihood Ratio”，在对话框中输入“C（6）”，观察F值和p值，判断。三、请根据下表资料建立反映我国城乡居民收入差距的线性模型，要求：1.把全部的解释变量引入模型进行估计，观察这一估计模型出现了哪些“病态”问题；运用“缺一个解释变量的可决系数”找出引起多重共线性的变量；采用“后退法”剔除引起多重共线性的“问题”变量，重建后的模型能通过两个基本检验吗？剔除这些解释变量会不会引起设定误差？请进行“确定检验”。yearyx1x2x3x4x

20、519783.4211.10.3540.1490.0690.21819793.369.90.2930.2110.0770.23419803.099.050.290.2260.0880.24119813.028.080.2670.2060.1070.25319822.747.450.2440.2030.1390.26819832.447.280.2350.2070.1650.27619842.397.020.210.1940.1820.319852.267.060.2050.1840.2160.31119862.66.980.180.1630.2070.32519872.646.920.1670

21、.1650.2160.33919882.496.880.1850.1650.2720.34819892.737.320.2120.1630.280.35519902.846.690.1850.1740.2440.35919912.927.270.2260.1720.2510.35819923.057.680.2540.1570.2760.38219933.279.820.360.150.270.39注：资料来源中国农村经济1995年第1期。指标含义和计算公式为：y代表城乡居民收入差；x1 代表二元结构系数，x1=城市非农产业比较劳动生产率农业比较劳动生产率；x2=(农产品价值农产品价格)农产品

22、价值；x3=城市居民人均隐性收入城市居民人均可支配收入；x4=农民人均非农产业收入农民人均可支配收入；x5=城镇总人口农村总人口。四测量误差的检验Hausman确认检验1Hausman确认检验的步骤：（1）先对原方程进行回归，讨论分析；（2）当怀疑某一自变量X有测量误差时，找出该变量的工具变量Z，将该自变量关于其工具变量回归，求出其残差序列，如用命令“Series sed_X=resid”生成新序列“ sed_X”；（3）将该残差变量加入原回归模型的自变量中，重新做回归，对残差变量sed_X的系数进行t检验，其中原假设为H0：X不存在测量误差，作出X有无测量误差的判断。2上机实习案例：仔细阅读教材P122 EXAMPLE 7.3的内容，然后检验自变量AID是否存在测量误差，其中数据可下载（表2-1房租数据）。五课后练习1某市百货公司的销售额X（万元）与流通费用率Y（%）之间是双曲函数模型Y=b0+b1/X+，其中满足基本假定的要求，对13个商店的销售额与流通费用率的统计资料如下:编号12345678910111213X1.54.57.510.515.516.519.522.525.521.513.57.56.5Y7.04.83.63.12.72.52.42.32.23.22.53.12.1要求：（1） 求估计方程；检验模型序列