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1、2020计量经济 人民币汇率卓越假设影响人民币汇率的因素有，国内生产总值，货币和准货币M2，外汇储备三个变量，为方便量化，用货币供应量同比增长率来描述货币和准货币M2，用与100美元等值的人民币数值来近似描述人民币的汇率水平。搜集1991-2007年的数据如下：序号项目年份国内生产总值（亿元）货币和准货币M2（货币供应量同比增长率）外汇储备(亿美元)人民币汇率 人民币元（=100美元)11991532.320250.47.6217.121992551.523134.27.6194.431993576.226364.71121241994861.929813.411516.251995835.1
2、33070.51173661996831.436380.4111050.57199782939762.75.71398.981998827.942877.45.21449.691999827.846144.62.31546.8102000827.823072.32.31655.7112001827.7107449.72.32121.7122002827.7117208.322864.1132003827.7128958.924032.5142004827.7141964.526099.3152005819.2169996.42.38188.3162006797.2204556.12.31066
3、3.4172007760.42495302.315282.5一、 模型参数估计对模型进行多次试验，最终挑选出模型的形式：并对模型进行了参数估计，结果如下：Dependent Variable: LOG(EXCHANGE)Method: Least SquaresDate: 12/06/11 Time: 22:44Sample: 1991 2007Included observations: 17VariableCoefficientStd. Errort-StatisticProb. C5.0708000.20790324.390210.0000GDP-3.08E-065.55E-07-5.5
4、482960.0001M220.0001496.45E-052.3084140.0381LOG(RESERVE)0.2392850.0316787.5535960.0000R-squared0.829795 Mean dependent var6.642979Adjusted R-squared0.790517 S.D. dependent var0.158903S.E. of regression0.072729 Akaike info criterion-2.201825Sum squared resid0.068764 Schwarz criterion-2.005775Log like
5、lihood22.71552 F-statistic21.12611Durbin-Watson stat1.226706 Prob(F-statistic)0.000028经过参数估计的模型方程二、 模型的检验（一）对模型进行经济意义检验：表示当没有任何经济变量影响的时候，人民币汇率为5.070800，但数值本身没有任何意义；表示每当国内生产总值增加一个单位，人民币汇率的对数值会相应减少3.08E-06 个单位，国内生产总值和人民币汇率呈现负相关关系；表示每当货币供应量同比增长率的平方增加一个单位，人民币汇率的对数值会相应增长1.49 E-04 个单位，货币供应量和人民币汇率呈现正相关关系；表
6、示每当外汇储备的对数值增加一个单位，人民币汇率的对数值会相应增长0.24个单位，外汇储备和人民币汇率呈现正相关关系。符合经济学知识,模型通过经济意义检验。1 相关性检验拟合优度检验R2= 0.790517，说明人民币汇率中79.05%可由国内生产总值，货币和准货币M2，外汇储备解释，拟合程度比较好。2显著性检验整体线性关系检验（F检验）：Prob(F-statistic)=0.0000280.05，整体线性关系显著。回归系数显著性检验（t检验）：Prob.=0.00010.05，通过t检验；gdp对log(exchange)线性影响显著。Prob.=0.03810.05，通过t检验；m22对l
7、og(exchange)线性影响显著。Prob.=0.00000.05 未检验出存在异方差。进一步进行G-Q检验选取在上述OLS结果中未能通过T检验的M22进行G-Q检验。把M2的数据按升序排列，并将其分成三部分，选取第一部分1991-1997的数据和第三部分2001-2007年的数据分别按原方程进行回归。Dependent Variable: LOG(EXCHANGE)Method: Least SquaresDate: 12/17/09 Time: 20:35Sample: 1991 1997Included observations: 7R-squared0.993658 Mean de
8、pendent var6.649499Adjusted R-squared0.987316 S.D. dependent var0.133113S.E. of regression0.014991 Akaike info criterion-5.267110Sum squared resid0.000674 Schwarz criterion-5.298018Log likelihood22.43488 F-statistic156.6808Durbin-Watson stat1.965270 Prob(F-statistic)0.000856Dependent Variable: LOG(E
9、XCHANGE)Method: Least SquaresDate: 12/17/09 Time: 20:36Sample: 2001 2007Included observations: 6Excluded observations: 1R-squared0.913623 Mean dependent var6.647565Adjusted R-squared0.784058 S.D. dependent var0.181469S.E. of regression0.084328 Akaike info criterion-1.873490Sum squared resid0.014222
10、Schwarz criterion-2.012317Log likelihood9.620469 F-statistic7.051470Durbin-Watson stat0.689236 Prob(F-statistic)0.126725SSR的比值为SSR2/SSR1=0.014222/0.000674=21.10F0.05(3,3)=9.28，拒绝原假设，i存在异方差。对原方程进行加权数1/abs(e)，消除异方差，并进行回归。Dependent Variable: LOG(EXCHANGE)Method: Least SquaresDate: 12/17/09 Time: 19:22S
11、ample(adjusted): 1991 2007Included observations: 17 after adjusting endpointsWeighting series: 1/ABS(E)VariableCoefficientStd. Errort-StatisticProb. C5.1230750.19571326.176500.0000GDP-3.00E-063.62E-07-8.2976280.0000M220.0001561.94E-058.0619410.0000LOG(RESERVE)0.2315770.0284238.1476230.0000Weighted S
12、tatisticsR-squared1.000000 Mean dependent var6.712539Adjusted R-squared1.000000 S.D. dependent var14.87848S.E. of regression0.005674 Akaike info criterion-7.303547Sum squared resid0.000419 Schwarz criterion-7.107497Log likelihood66.08015 F-statistic24.33806Durbin-Watson stat1.308886 Prob(F-statistic)0.000013Unweighted StatisticsR-squared0.826616 Mean dependent var6.642979Adjusted R-squared0.786605 S.D. dependent var0.158903S.E. of regression0.073405 Sum squared resid0.070048Durbin-Watson stat1.184263再一次进行WHITE检验:White Heteroskedasticity Test:F-statistic
