计量经济学导论第四版部分课后答案中文翻译.docx

2.10(iii) From (2.57),Var() = ?2/. 由提示：：?, and so Var()? Var(). A more direct way to see this is to write(一个更直接的方式看到这是编写)?= , which is less thanunless= 0.(iv)给定的c但随着的增加，的方差与Var()的相关性也增加.小时的偏差也小.因此, 在均方误差的基础上不管我们选择还是要取决于,,和n的大小(除了的大小).3.7We can use Table 3.2. By definition, ? 0, and by assumption, Corr(x1,x2)? 0. Therefore, there is a negative bias in: E()? . This means that, on average across different random samples, the simple regression estimator underestimates the effect of the training program. It is even possible that E() is negative even though ? 0.我们可以使用表3.2。根据定义， 0，由假设，科尔（X1，X2）0。因此，有一个负偏压为：E（）。这意味着，平均在不同的随机抽样，简单的回归估计低估的培训计划的效果。 E（下），它甚至可能是负的，即使0。我们可以使用表格3.2。根据定义, 0,通过假设,柯尔(x1,x2) 0。因此,有一种负面的偏见:E()。这意味着,平均跨不同的随机样本,简单的回归估计低估了培训项目的效果。甚至可能让E()是负的,尽管 0。3.8Only (ii), omitting an important variable, can cause bias, and this is true only when the omitted variable is correlated with the included explanatory variables. The homoskedasticity assumption, MLR.5, played no role in showing that the OLS estimators are unbiased. (Homoskedasticity was used to obtain the usual variance formulas for the .) Further, the degree of collinearity between the explanatory variables in the sample, even if it is reflected in a correlation as high as .95, does not affect the Gauss-Markov assumptions. Only if there is a perfect linear relationship among two or more explanatory variables is MLR.3 violated. 只有3.8(ii),遗漏重要变量,会造成偏见确实是这样,只有当省略变量就与包括解释变量。homoskedasticity的假设,多元线性回归。5,没有发挥作用在显示OLS估计量是公正的。(Homoskedasticity是用来获取通常的方差公式。)进一步,共线的程度解释变量之间的样品中,即使它是反映在尽可能高的相关性。95年,不影响的高斯-马尔可夫假定。只要有一个完美的线性关系在两个或更多的解释变量是多元线性回归。三违反了。3.9 (i) Because is highly correlated with and , and these latter variables have large partial effects on y, the simple and multiple regression coefficients on can differ by large amounts. We have not done this case explicitly, but given equation (3.46) and the discussion with a single omitted variable, the intuition is pretty straightforward. 因为 是高度相关,和这些后面的变量有很