分布滞后模型的估计

1、分布滞后模型的估计建立总量消费函数是进行宏观经济管理的重要手段。为了从总体上考察中国居民收入与消费的关系，下表给出了中国名义支出法国内生产总值GDP、名义居民总消费 CONS以及表示宏观税收的税收总额 TAX、表示价格变化的居民消费价格指数CPI(1990=100)，并由这些数据整理出实际支出法国内生产总值GDPC=GDP/CPI、居民实际消费总支出Y=CONS/CPI，以实际可支配收入 X=(GDP-TAX)/CPI，这些数据是1978-2006的时间序列数据，即观测值 是连续不同年份的数据。中国居民总量消费支出与收入资料年份GDPCONSCPITAXGDPCXY19783605.61759

2、.146.21519.287802.56678.83806.719794092.62011.547.07537.828694.27551.44273.219804592.62331.250.62571.709073.77944.24605.519815008.82627.951.90629.899651.88438.05063.919825590.92902.952.95700.0210557.39235.25482.419836216.22231.154.00775.5911510.810074.64983.219847362.73742.055.47947.3513272.811565.0

3、6745.619859076.74687.460.652040.7914966.811601.77729.2198610508.55302.164.572090.3716273.713036.58210.9198712277.46126.169.302140.3617716.314627.78840.0198815388.67868.182.302390.4718698.715794.09560.5198917311.38812.697.002727.4017847.415035.59085.8199019347.89450.9100.002821.8619347.816525.99450.9

4、199122577.410730.6103.422990.1721830.918939.610375.8199227565.213000.1110.033296.9125053.022056.511815.3199336938.116412.1126.204255.3029269.125897.313004.7199450217.421844.2156.655126.8832056.228783.413944.2199563216.928369.7183.416038.0434467.531175.415467.9199674163.633955.9198.666909.8237331.933

5、853.717092.5199781658.536921.5204.218234.0439988.535956.218080.6199886531.639229.3202.599262.8041713.138140.919364.1199991125.041920.4199.7210682.5845625.840277.020989.3200098749.045854.6200.5512581.5149238.042964.622863.92001108972.449213.3201.9415301.3853962.546385.424370.12002120350.352571.3200.3

6、217636.4560078.051274.026243.22003136398.856834.4202.7320017.3167282.257408.128035.02004160280.463833.5210.6324165.6876096.364623.130306.22005188692.171217.5214.4228778.5488002.174580.433214.42006221170.580120.5217.6534809.72101616.358623.136811.2解：阿尔蒙多项式估计法1、首先使用互相关分析命令cross，初步判断滞后期的长度。在命令窗口键入：cros

7、s y x，输出结果如下图所示:x与y各期滞后值的相关系数从上图中可以看出，消费总支出y与当年和前四年的实际可支配收入相关，因此，利用阿尔蒙多项式估计法估计模型时，解释变量滞后阶数为5利用EViews软件，输入样本数据，在命令窗口键入：LS y c pdl(x,5,2)得到以下回归分析结果：(=)Equation： UNTITLED Workfile UNTTTLED:hcf-OXView Proc Object PrintName FreezeEstimate ForecastStatsResidsDependentVariable: ¥Method: Least SquaresD

8、ate: 05701/13 Time. 12:&6Sample (adjusted): 1983 2005Included observations: 23 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C1794.192211,06883.5005080.0000PDL010.1331130.0204396.5126750.0000PDL020.0131370.0093491.4051620.1761PDL03-0.0141730007144-1.9838700 0619R-squared0.997444M

9、ean dependentvar1746093Adjusted R-squared0.997040S D. dependentvar6930192S E of regression485.0445Aka ike info criterion15.36643Sum squared resid4484853.Schwarz criterion15.56390Log likelihood-172.7139Hannan-Quinn enter.15.41609F-statistic2471.250Durtin-Watson stat0.955959Prob(F-statistic)0.000000La

10、g Distribution of XiCoefficientStd. Errort-Statistic100.050150 0241420775510.105900.Q15956.634111720133110.020446.512671J30.132080016707 90985140.102700016306257761 050.044970 045190 99497Sum of Lags0.56890Q.0165634.3414估计结果：Ay =1794.192 -0.05015Xt -0.10580Xt4 -0.13311X2 °.13208* 0.10270*丄 0.04

11、497Xtt =(2.07755)(6.63411)(6.51267)90985)(6.26776)(0.99479)2R 巾997444，F =2471-250，DW-0-9559592其中括号内的数为相应参数的T检验，R是可决系数，F和D.W.是有关的两个检验统计量。2、模型检验= Equation: UNTTTLED Worfcfile: UNUTLED:hcf-口 XView Proc Object Print Name Freeze Estimate Forecast Mats ResidJ从回归估计和残差图可以看出模型的拟合程度较好。从截距项与斜率项的t检验值看，均大于5%显著性水

12、平下自由度为n-2=27的临界值 匕025（27） =2.052，认为中国总量消费与支出以及与各滞后消费间线性相关性显著，并且解释变量间不存在多重共线性。工具变量法1、利用OLS法估计分布滞后模型 （滞后期长度为5），在命令窗口输入：LS y c x（0 to -5） 估计结果如下表所示：回 Equation: UNTITLED Woricfile: UNHTLED:hcf-B XProcObjectPrintFreeze EstimateForecastStatsResidsViewDependent Variable: YMethod: Least SquaresDate: 05/OV13

13、 Time: 13:09Sample (adjusted): 1983 2005Included observations: 23 after adjustmentsVariableCoefficient Std Error t-Statjstic Prob.12 3 4 5 亠 一 一 /A rf. /V- /It /It X X X X1980.009168509511.750130000000305B30 0202121 5130710 14980 32434800829273 9112390182505-031062207601*0.0616210.196

14、766*0.3141850.75740.1633680.191S3S0.85160S0.40700164504011573114214330 1744R-squared0996734Mean dependent var17460 93Adjusted R-sqljared0996260S D. dependentvar8930.192S.E. of regression372,5363Aka ike info criterion14 92434Sum squared resid2220532Schwarz criterion15.26992Log liKeiihcod-164.6299Hann

15、an-Quinn cniter.15.01125F-statistic2104.291Durbin-Watson stat1.337724Prob(F-statistic)0 000000根据以上回归结果得：Ay =1980.009 0.030585“ 0.324348 %丄0.056690 xt< 0.061821 %0.1633680.164504t = (1.513071)(3.911239)(-0.310622)(-0.314185)(0.851605)(1.421433)在命令窗口键入：LS Y C X YF(-1) AR(1) AR(2)得如下表回归结果:View Pro&l

16、t; Object PrintFreeze Estimate Forecast Stats ResidsDependentVariable: YMethod: Least SquaresDate: 05/01/13 Bme: 1246Sample (adjusted): 1995 2005included observations: 21 after adjustmentsConvergence achieved after 15 iterationsVariableCoefficientStd. ErrorStatisticProbC1836.1 B435457735.1785160.000

17、1X0,4337500.01788024.2597600000YFM)0 0387120.01676523091690.0346AR*1.0718780908186-1R-0.7694571.110482*0.6939030.4983R*squared0.962937Mean dependent var18434.60Adjusted R*squared0.953671S,D. dependent var8732210S E of regression1879 533Akaike info criterion18,11969Sum squared resid56522333Schwarz criterion1836839Log likelihood-185.2568Hannan-Quinn cniter18,17366F-statistic103.9240Durbin-Watson stat1.632513ProbtF-statistic)0 000000Inverted AR Roots-54+ 69i-54-.69i上述回归结果不存在自相关，估计模型为:yt =1836.184 +0.433750 Xt +0.038712 丫匚(24.25876)(2.309169)y