第3章、虚拟变量.doc

第3章、虚拟变量虚拟变量（Dummy variable；binary variable）：也称为哑变量、定性变量和二进制变量等等。作用：采用虚拟变量来分离定性变量对被解释变量的影响，如性别、职称、肤色、季度、历史时期、政治等等。我们按照几个例子来学习如何正确使用、构造虚拟变量。1、比较均值1、“五年纷纭话股市”问题：上海和深圳两个股票市场（在过去5年内）的收益率有显著差异吗？分别建立如下回归方程上海：深圳：问题转化为检验是否显著不为0。建立如下含有虚拟变量的回归方程：其中是一个解释变量，也是虚拟变量：对复合方程进行回归，直接对解释变量实施t检验即可。2、Eviews实现的具体过程。使用series r=log(p)-log(p(-1)将收盘价序列转化为收益率序列。将Eviews数据（都是取最后1000个数据）copy到matlab，建立数据列向量和虚拟变量列向量。r=shr; szr;d=zeros(length(shr),1);ones(length(szr),1);将matlab数据copy到excel，再导入eviews。得到被解释变量r和解释变量dd（eviews不能用d这个记号，表示差分）。数据文件为dummy_stockmarket_camparingmean进行回归：ls r c dd，得到Dependent Variable: RMethod: Least SquaresDate: 10/24/04 Time: 12:27Sample: 1 2000Included observations: 2000VariableCoefficientStd. Errort-StatisticProb. C0.0007290.0006861.0625530.2881DD0.0003700.0009700.3814950.7029R-squared0.000073 Mean dependent var0.000914Adjusted R-squared-0.000428 S.D. dependent var0.021682S.E. of regression0.021687 Akaike info criterion-4.823215Sum squared resid0.939705 Schwarz criterion-4.817614Log likelihood4825.215 F-statistic0.145538Durbin-Watson stat1.966857 Prob(F-statistic)0.702877得到什么结论？2、保险公司的革新例子（来自于易丹辉数据分析与Eviews应用P49）：公司规模、类型与采取某项保险革新措施的速度之间有关系吗？为研究采取某项保险革新措施的速度y与保险公司的规模x1和保险公司类型的关系，选取下列数据：y是一个公司提出该项革新直至革新被采纳间隔的月数，x1是公司的总资产额（单位：百万美元），x2是一个虚拟变量，表示公司类型，其中1表示股份公司，0表示互助公司。建立如下回归方程双击数据文件dummy_yibookp49，进行回归ls y c x1 x2，得到Dependent Variable: YMethod: Least SquaresDate: 10/24/04 Time: 13:39Sample: 1 20Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C33.869871.56258821.675490.0000X1-0.1060890.007800-13.601740.0000X28.7679751.2864216.8157890.0000R-squared0.921478 Mean dependent var19.40000Adjusted R-squared0.912240 S.D. dependent var9.405486S.E. of regression2.786306 Akaike info criterion5.024791Sum squared resid131.9795 Schwarz criterion5.174151Log likelihood-47.24791 F-statistic99.75016Durbin-Watson stat2.462911 Prob(F-statistic)0.000000得到回归模型为：y33.869870.106089 X18.767975X2得到什么结论？3、政治性的投资周期各位读者：这个例子来自于：European JPE, 1991, 7: 141-157。选取这个例子，并不代表我支持或者反对这个观点。在我看来，这只是我们学习虚拟变量的一个例子而已。特此申明。双击数据文件political_investment_cycles，其中year、I、co、pi和dd分别是：yearinvestment rate as % of GNPconsumption rate of as % of GNPproductive investment as % of total investmentpower regimes as a dummy variableyear investment rate as % of GNPconsumption rate of as % of GNPproductive investment as % of total investmentpower regimes as a dummy variable195221.478.650.80195323.176.949.40195425.574.550.30195522.977.151.40195624.475.6710195724.975.158.80195833.966.182.31195943.856.286.91196039.660.497.41196119.280.878.50196210.489.663.60196317.582.563.90196422.277.860.80196527.172.970.70196630.669.468.91196721.378.782.21196821.178.978.51196923.276.876.21197032.967.171.81197134.165.976.21197231.668.478.71197332.967.173.71197432.367.775.41197533.966.173.41197630.969.179.31197732.367.770.91197836.563.571.81197934.665.464.10198031.568.554.50198128.371.746.80198228.871.246.40198329.770.352.50198431.2680858.60198533.766.357.70进行回归：ls i c i(-1) ddDependent Variable: IMethod: Least SquaresDate: 10/24/04 Time: 14:53Sample(adjusted): 1953 1985Included observations: 33 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C11.227353.7476192.9958620.0054I(-1)0.5464080.1349284.0496280.0003DD4.0794391.8281512.2314560.0333R-squared0.497313 Mean dependent var28.66364Adjusted R-squared0.463801 S.D. dependent var6.824396S.E. of regression4.997208 Akaike info criterion6.142144Sum squared resid749.1626 Schwarz criterion6.278190Log likelihood-98.34537 F-statistic14.83965Durbin-Watson stat1.127080 Prob(F-statistic)0.000033进行回归：ls pi c pi(-1) ddDependent Variable: PIMethod: Least SquaresDate: 10/24/04 Time: 14:55Sample(adjusted): 1953 1985Included observations: 33 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C31.248447.1295884.3829240.0001PI(-1)0.4533600.1143223.9656530.0004DD12.364082.8821894.2898220.0002R-squared0.728784 Mean dependent var67.95758Adjusted R-squared0.710703 S.D. dependent var12.56386S.E. of regression6.757641 Akaike info criterion6.745733Sum squared resid1369.971 Schwarz criterion6.881779Log likelihood-108.3046 F-statistic40.30649Durbin-Watson stat1.927290 Prob(F-statistic)0.000000你得到什么结论？附录：如何在论文中报告计量结果在正文里指出，数据的频率（年度、季度，等）、样本个数、数据的来源（自己查的国家统计年鉴、某机构或者个人提供的数据、自己设计调查问卷所得到的调查数据等）等基本信息。1. 如果解释变量个数较多，建议直接copy软件的输出结果，去掉表的上面部分即可。这样处理的优点：一目了然，所有统计量全部给出了。表最好翻译成中文，因为很多人不认识英文。Dependent Variable: IMethod: Least SquaresDate: 09/19/04 Time: 20:49Sample: 1968 1982Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C-0.5090710.055128-9.2343940.0000T-0.0165800.001972-8.4089270.0000GNP0.6703830.05499712.189410.0000R-0.0023260.001219-1.9082700.0854INFLATION-9.40E-050.001347-0.0697680.9458R-squared0.972433 Mean dependent var0.203333Adjusted R-squared0.961406 S.D. dependent var0.034177S.E. of regression0.006714 Akaike info criterion-6.907967Sum squared resid0.000451 Schwarz criterion-6.671950Log likelihood56.80975 F-statistic88.18825Durbin-Watson stat1.963642 Prob(F-statistic)0.000000变为 Dependent Variable: IVariableCoefficientStd. Errort-StatisticProb. C-0.5090710.055128-9.2343940.0000T-0.0165800.001972-8.4089270.0000GNP0.6703830.05499712.189410.0000R-0.0023260.001219-1.9082700.0854INFLATION-9.40E-050.001347-0.0697680.9458R-squared0.972433 Mean dependent var0.203333Adjusted R-squared0.961406 S.D. dependent var0.034177S.E. of regression0.006714 Akaike info criterion-6.907967Sum squared resid0.000451 Schwarz criterion-6.671950Log likelihood56.80975 F-statistic88.18825Durbin-Watson stat1.963642 Prob(F-statistic)0.000000当然，一点都不删去也是可以的。这决定于个人的习惯和杂志的要求。2. 当解释变量个数较少、文章页面限制不能发表全部表格时，建议给出回归方程。如Dependent Variable: LOG(X)Method: Least SquaresDate: 10/20/04 Time: 20:20Sample: 1929 1967Included observations: 39VariableCoefficientStd. Errort-StatisticProb. C-3.9377140.236999-16.614880.0000LOG(L1)1.4507860.08322817.431370.0000LOG(K1)0.3838080.0480187.9930350.0000R-squared0.994627 Mean dependent var5.687449Adjusted R-squared0.994329 S.D. dependent var0.460959S.E. of regression0.034714 Akaike info criterion-3.809542Sum squared resid0.043382 Schwarz criterion-3.681576Log likelihood77.28607 F-statistic3332.181Durbin-Watson stat0.858080 Prob(F-statistic)0.000000LOG(X)= -3.937714+1.450786 LOG(L1)+ 0.383808 LOG(K1)(0.236999) ( 0.083228) ( 0.048018)R2=0.994627 D.W.= 0.858080 s.e.e.= 0.034714注意： 括号中的数值是系数的标准误差；s.e.e.是回归的标准误差（S.E.