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1、案例分析以引子中所提出的问题为例，分析影响中国进口量的主要因素（数据如表9.3所示）。 表9.3 单位：人民币亿元、亿美元年份GDP进口总额IM（人民币）进口总额IMdollar（美元）汇率EXCHANGE19804517.8298.8000200.17149.840019814862.4375.3800220.15170.510019825294.7364.9900192.85189.260019835934.5422.6000213.90197.570019847171.0637.8300274.10232.700019858964.41257.800422.52293.660019861
2、0202.201498.300429.04345.2800198711962.501614.200432.16372.2100198814928.302055.100552.75372.2100198916909.202199.900591.40376.5100199018547.902574.300533.45478.3200199121617.803398.700637.91532.3300199226638.104443.300805.85551.4600199334634.405986.2001039.59576.2000199446759.409960.1001156.14861.8
3、700199558478.1011048.101320.84835.1000199667884.6011557.401388.33831.4200199774462.6011806.501423.70828.9800199878345.2011626.101402.37827.9100199982067.5013736.401656.99827.8300200089468.1018638.802250.94827.8400200197314.8020159.202435.53827.70002002105172.324430.302951.70827.70002003117251.934195
4、.604127.60827.7000 数据来源:中国统计年鉴2004中国统计出版社设定如下的模型。 （9.50）其中，是进口总额，是国内生产总值。为了分析此模型是否有变量设定误差，进行变量设定误差检验。有人认为，货物与服务的进口量受到一国的生产规模、货物与服务的进口价格、汇率等其他影响因素，而不能只仅用GDP来解释商品进口的变化。因此，设定的回归模型应该为： (9.51)其中：GDP为国内生产总值，为GDP的线性函数，Exchange为美元兑换人民币的汇率，为Exchange的线性函数。如果是这样，显然设定的回归模型（9.50）式中可能遗漏了变量GDP、Exchange以及两者的线性组合。那么
5、GDP、Exchange以及两者的线性组合是否被遗漏的重要变量呢？依据表9.3的数据，录入到EViews响应的数据表中，考证IM=f(GDP)基本关系图：对(9.50)进行回归,有回归结果se= (792.2620) (0.0142)t= (-2.0288) (16.2378) DW=0.5357 F=263.6657 并作(9.50)回归的残差图：显然，存在自相关现象，其主要原因可能是建模时遗漏了重要的相关变量造成的。1、DW检验:检验自相关模型的DW统计量表明，存在正的自相关，由于遗漏变量exchange或GDP 已经按从小到大顺序排列，因此，无需重新计算d统计量。对n=24和，5%的德宾
6、-沃森d-统计量的临界值为和，表明存在显著的遗漏变量现象。为此，进行如下的校正：Dependent Variable: IMMethod: Least SquaresDate: 07/08/05 Time: 15:40Sample (adjusted): 1981 2003Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-224.36321892.132-0.1185770.9069GDP1.1482590.1514337.5826060.0000GDP(-1)-0
7、.8224440.147359-5.5812130.0000EXCHANGE-4.2907468.348744-0.5139390.6135EXCHANGE2-0.0186370.008353-2.2311620.0386R-squared0.978691Mean dependent var8434.222Adjusted R-squared0.973956S.D. dependent var9025.326S.E. of regression1456.525Akaike info criterion17.59515Sum squared resid38186370Schwarz criter
8、ion17.84200Log likelihood-197.3443F-statistic206.6799Durbin-Watson stat1.962659Prob(F-statistic)0.000000其中，exchange的系数在统计意义上不显著，可以剔除，则有：Dependent Variable: IMMethod: Least SquaresDate: 07/08/05 Time: 15:43Sample (adjusted): 1981 2003Included observations: 23 after adjustmentsVariableCoefficientStd.
9、Errort-StatisticProb.C-1159.179511.0396-2.2682760.0352GDP1.1428970.1481197.7160700.0000GDP(-1)-0.8158420.143928-5.6684200.0000EXCHANGE2-0.0225690.003291-6.8578440.0000R-squared0.978378Mean dependent var8434.222Adjusted R-squared0.974965S.D. dependent var9025.326S.E. of regression1428.041Akaike info
10、criterion17.52277Sum squared resid38746720Schwarz criterion17.72024Log likelihood-197.5118F-statistic286.5846Durbin-Watson stat2.047965Prob(F-statistic)0.000000可以认为，这时模型设定无变量设定误差。2、LM检验按照LM检验步骤，首先生成残差序列（用EE表示），用EE对全部解释变量（包括遗漏变量）进行回归，有：Dependent Variable: EEMethod: Least SquaresDate: 07/08/05 Time: 1
11、5:45Sample (adjusted): 1981 2003Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C448.1584511.03960.8769540.3915GDP0.9122010.1481196.1585680.0000GDP(-1)-0.8158420.143928-5.6684200.0000EXCHANGE2-0.0225690.003291-6.8578440.0000R-squared0.727360Mean dependent var-
12、37.56085Adjusted R-squared0.684312S.D. dependent var2541.624S.E. of regression1428.041Akaike info criterion17.52277Sum squared resid38746720Schwarz criterion17.72024Log likelihood-197.5118F-statistic16.89632Durbin-Watson stat2.047965Prob(F-statistic)0.000014再计算，查表，显然，拒绝：受约束回归模型，接受无约束回归模型的假设，即确实存在遗漏变量。因此，在本章的引子中不能判断虽然简单但遗漏了重要变量的方程（1）比复杂的方程（2）更好
