协整检验和误差修正模型.doc

财政支出与财政收入的协整关系研究一 实验内容 根据我国1990-2007年间财政支出和财政收入的月度数据，研究财政支出和财政支出之间是否存在协整关系，进而做出二者的误差修正模型。二 模型设定 为了定量分析财政支出和财政收入的关系，弄清二者是否存在长期均衡关系，建立了财政支出和财政收入的回归模型。 其中表示财政支出；表示财政收入。数据如下：年份财政支出(亿元)财政收入(亿元)年份财政支出(亿元)财政收入(亿元)年份财政支出(亿元)财政收入(亿元)1990-1138.6138.361996-1370.94469.72002-11040.571511.331990-2152.55142.931996-2378.49330.822002-21124.2975.591990-3201.02227.611996-3429.21510.92002-31346.581320.891990-4224.17223.111996-4517.63626.172002-41488.051787.551990-5232.02221.221996-5573.17486.452002-51334.991465.971990-6277.02261.171996-6632.25578.842002-61962.971538.331990-7308.34298.781996-7629.63653.942002-71682.221715.241990-8298.05265.451996-8582.83504.782002-81607.451342.141990-9260278.941996-9645.93589.752002-91910.521512.881990-10276.97329.61996-10667.77680.122002-101513.861822.891990-11311.93229.841996-11780.06618.482002-111900.021495.331990-12397.92315.091996-121729.651358.072002-125141.712415.521991-1163.31209.251997-1492.29604.342003-11295.251994.641991-2147.9145.521997-2363.22420.132003-21097.11499.091991-3204.96231.041997-3539.46712003-31500.031711.471991-4229.65219.031997-4636.2727.942003-41734.52065.071991-5239.02241.691997-5644.62667.622003-51688.711769.711991-6302.6270.741997-6836.87810.042003-62350.251915.011991-7381.86328.21997-7742.86814.942003-71815.591967.441991-8293.54250.561997-8649.2580.562003-81703.671428.811991-9286.47294.961997-9707.99628.772003-92079.771780.611991-10345.55393.491997-10743.23839.762003-101683.012017.711991-11383.2312.061997-11868.37690.62003-111984.111624.411991-12408.57252.941997-122009.31195.422003-125717.941941.281992-1192.44221.741998-1507.43608.372004-11368.552534.561992-2151.21183.471998-2456.92511.12004-21361.962105.461992-3224.8276.781998-3602.15723.242004-31771.52304.171992-4266.88332.331998-4679.11812.812004-42099.662854.081992-5272.69311.361998-5772.31672.772004-51720.932174.251992-6331.23296.91998-6990.87929.862004-62480.262334.261992-7467.14413.081998-7804.38862.112004-71935.332503.021992-8348.58310.441998-8803.78645.582004-81976.4516671992-9363.89322.391998-9976.56773.622004-92429.941882.51992-10395.77301.571998-10870.57905.352004-101917.292255.281992-11389.68310.341998-111045.29872.492004-112531.821815.771992-12337.89202.971998-122288.821558.582004-126893.211966.121993-1176.95170.891999-1553.6859.962005-11555.583105.011993-2230.81212.91999-2529.76579.152005-21472.832157.611993-3283.55300.71999-3756.88885.342005-32180.942520.571993-4293.61248.911999-4794.83984.452005-42380.863278.671993-5299.66263.931999-5890.57847.162005-51995.142479.181993-6334.39248.461999-61118.891136.372005-62836.032850.281993-7463.36249.641999-7957.631037.752005-72239.262967.531993-8368.64226.541999-8839.96748.642005-82413.272056.611993-9362.5278.441999-91275.63830.632005-92876.032352.241993-10525.85382.311999-101035.71975.472005-102187.952952.51993-11539.02450.041999-111118.33941.42005-113188.392221.351993-12763.964671999-123311.641615.962005-1286042707.391994-1267.38318.252000-1776.571066.642006-12227.883870.981994-2224.17230.192000-2718.16737.042006-21559.672534.61994-3318.82380.962000-3878.691074.742006-32504.12894.381994-4357.2364.52000-41087.351186.322006-42728.524270.521994-5358.31335.752000-51022.15948.192006-52166.33060.481994-6447.47391.222000-61352.411227.232006-63414.623374.931994-7433.46388.212000-71048.451196.352006-72524.774043.81994-8421.68355.12000-81287.721042.832006-82604.922695.861994-9429.95431.162000-91278.311081.22006-93426.172876.761994-10494.14499.82000-101080.861246.292006-102670.563800.621994-11666.065412000-111375.581105.932006-113783.712660.661994-121374.061023.42000-123977.251482.462006-1210811.512676.611995-1341.582562001-1827.281340.662007-11870.865196.011995-2290.06260.962001-2950.831042.372007-22543.713045.541995-3397.47510.442001-31054.871298.982007-32874.183542.071995-4475.89401.942001-41181.31553.962007-43220.475832.411995-5461.41445.942001-51309.951226.62007-52922.24107.51995-6547636.92001-61720.421409.782007-64488.574394.311995-7539.81542.552001-71363.811455.062007-73236.565212.321995-8506.46405.662001-81467.231247.582007-83426.673495.421995-9514.77536.982001-91603.941297.312007-94433.114091.321995-10535.29544.062001-101223.451502.382007-103560.255347.121995-11697.42572.792001-111801.411293.172007-114508.193913.11995-121516.561127.982001-124398.091718.182007-1212480.633126.91数据来源：统计年鉴三、实证分析1、数据处理由数据结构可以看出，数据存在季节波动。首先利用X-12季节调整方法对这两个指标进行季节调整，消除季节因素，然后去对数。2、单位根检验经济时间序列数据往往出现非平稳的情况，如果直接对数据建立回归模型，可能会出现伪回归的现象，因此在做回归之前，运用ADF方法，对数据进行单位根检验。对ln()、ln()及其一阶差分进行单位根检验，具体检验结果如下所示： ln()原值单位根检验Null Hypothesis: LNF_EX has a unit rootExogenous: ConstantLag Length: 5 (Automatic based on SIC, MAXLAG=14)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.5196860.9871Test critical values:1% level-3.4614785% level-2.87512810% level-2.574090*MacKinnon (1996) one-sided p-values.ln()一阶差分单位根检验Null Hypothesis: D(LNF_EX) has a unit rootExogenous: ConstantLag Length: 4 (Automatic based on SIC, MAXLAG=14)t-StatisticProb.*Augmented Dickey-Fuller test statistic-10.834460.0000Test critical values:1% level-3.4614785% level-2.87512810% level-2.574090*MacKinnon (1996) one-sided p-values.ln()原值单位根检验Null Hypothesis: LNF_IN has a unit rootExogenous: ConstantLag Length: 11 (Automatic based on SIC, MAXLAG=14)t-StatisticProb.*Augmented Dickey-Fuller test statistic0.7638500.9932Test critical values:1% level-3.4624125% level-2.87553810% level-2.574309*MacKinnon (1996) one-sided p-values.ln()一阶差分单位根检验Null Hypothesis: D(LNF_IN) has a unit rootExogenous: ConstantLag Length: 10 (Automatic based on SIC, MAXLAG=14)t-StatisticProb.*Augmented Dickey-Fuller test statistic-8.1614940.0000Test critical values:1% level-3.4624125% level-2.87553810% level-2.574309*MacKinnon (1996) one-sided p-values.汇总检验结果如下表所示：财政收入和财政支出的对数的原值和一阶差分的单位根检验结果指标ADF值P值ln()0.5196860.9871ln()的一阶差分-10.834460.0000ln()0.7638500.9932ln()的一阶差分-8.1614940.0000从上表中的ADF值和P值可以看出：当显著性水平为0.05时，对ln()和ln()的原值进行检验时，检验结果都表明不能拒绝“存在单位根”的原假设；而当对ln()和ln()的一阶差分进行检验时，检验结果都表明拒绝“存在单位根”的原假设。由此可以判定、的对数都是I（1）过程，即财政支出和财政收入的对数的月度时间序列数据为一阶单整的。为了防止应用最小二乘法导致伪回归现象的出现，所以必须分析变量间的协整关系，进而分析理论模型的长期关系。3、利用E-G两步法，进行协整检验首先，建立如下财政支出和财政收入的回归模型： 利用Eviews软件，得到如下回归结果：协整回归结果Dependent Variable: LNF_EXMethod: Least SquaresDate: 05/21/14 Time: 18:36Sample: 1990M01 2007M12Included observations: 216VariableCoefficientStd. Errort-StatisticProb.LNF_IN0.9531660.009390101.50390.0000C0.4020140.0643726.2451230.0000R-squared0.979652Mean dependent var6.880220Adjusted R-squared0.979557S.D. dependent var0.863309S.E. of regression0.123435Akaike info criterion-1.336985Sum squared resid3.260555Schwarz criterion-1.305733Log likelihood146.3944Hannan-Quinn criter.-1.324359F-statistic10303.03Durbin-Watson stat1.465547Prob(F-statistic)0.000000即 Se （0.06） （0.01）T （6.25） （101.50） 然后，对上式的残差e进行ADF检验，检验其平稳性由回归方程估计结果可得：对残差e进行ADF检验，由SIC准则确定滞后阶数，结果如下所示：残差序列的单位根检验Null Hypothesis: ECM has a unit rootExogenous: NoneLag Length: 2 (Automatic based on SIC, MAXLAG=14)t-StatisticProb.*Augmented Dickey-Fuller test statistic-5.2193100.0000Test critical values:1% level-2.5758645% level-1.94232410% level-1.615707*MacKinnon (1996) one-sided p-values.检验结果显示：残差e序列在1%的显著性水平下拒绝原假设，因此可确认残差e序列为平稳序列，即eI（0）。上述结果表明：1990年1月至2007年12月期间ln()和ln()之间存在协整关系。4、误差修正模型（ECM）的建立由上述检验可知，ln()和ln()之间存在协整关系，为了继续考察我国财政支出与财政收入之间的动态关系，现通过ECM模型来进行分析。以ln()和ln()的协整方程中平稳的残差序列e作为误差修正项，即令e=ecm可建立如下误差修正模型：其中：ecm（-1）是滞后一期的残差项利用Eviews软件，得到如下回归结果：ECM的回归结果Dependent Variable: D(LNF_EX)Method: Least SquaresDate: 05/21/14 Time: 18:39Sample (adjusted):