一道中级计量经济学的作业

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[color=rgba(0, 0, 0, 0.87)]某个学区进行一项实验，估计二年级的班级规模对考试分数的影响。学区将上一年的一年级学生的<span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="50%" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">50%50%编入小班二年级（每个教室18名学生），<span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="50%" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">50%50%编入常规班级二年级（每个教室21名学生）。新到该学区的学生则采用不同的编班方法：<span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="20%" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">20%20%随机编入小班，<span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="80%" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">80%80%编入常规班。在二年级末，每个学生都参加一次标准化考试。<span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="Yi" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119884;&#119894;Yi表示第<span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="i" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119894;i个学生的考分，<span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="X1i" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119883;1&#119894;X1i为二值变量，学生分入小班取值1，<span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="X2i" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119883;2&#119894;X2i也为二值变量，新注册学生取值1。<span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="β1" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#120573;1β1表示从常规班级到小班这样的减少班级规模对考试分数的因果效应。

[color=rgba(0, 0, 0, 0.87)]（1）考虑回归<span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="Y=β0+β1X1+μ" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119884;=&#120573;0+&#120573;1&#119883;1+&#120583;Y=β0+β1X1+μ。你认为<span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="E(μ|X1)=0" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119864;(&#120583;|&#119883;1)=0E(μ|X1)=0吗？<span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="β1" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#120573;1β1的OLS估计量是无偏和一致的么？请给出解释。

[color=rgba(0, 0, 0, 0.87)]（2）<span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="Y=β0+β1X1+β2X2+μ" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119884;=&#120573;0+&#120573;1&#119883;1+&#120573;2&#119883;2+&#120583;Y=β0+β1X1+β2X2+μ。你认为<span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="E(μ|X1,X2)" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119864;(&#120583;|&#119883;1,&#119883;2)E(μ|X1,X2)依赖<span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="X1" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#119883;1X1吗？<span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="β1" role="presentation" style="box-sizing: unset; display: inline-table; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">&#120573;1β1的OLS估计量是无偏和一致的么？请给出解释。

[color=rgba(0, 0, 0, 0.87)]楼主是计量小白，想问下各位大佬，上面两题该怎么做

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关键词：计量经济学 计量经济 经济学 OLS估计 OLS