经济计量学实习报告影响我国农村居民消费水平的主要因素分析.doc

经济计量学实习报告影响我国农村居民消费水平的主要因素分析 【摘要】：本文主要通过对农村居民消费水平的变动进行多因素分析，建立以农村居民消费水平为应变量，以农村人口自然增长率、农村居民人均可支配收入、商品零售价格指数以及农业生产资料价格指数为自变量的多元线性回归模型，并利用模型对农村居民消费水平这一社会现象进行数量化分析，揭示中国农村消费水平的现状及问题，并对如何提高农村居民消费水平提出一些可行性的建议。【关键词】:农村居民消费水平、农村人口自然增长率、农村居民人均可支配收入、商品零售价格指数、农业生产资料价格指数、建议前言: 当前全球面临60 年来最严重的金融危机之后的经济复苏期，而中国亦深受当前经济时势影响，外贸出口难度加大。我国地域辽阔，经济发展不平衡，人民生活由温饱向小康过渡，无论是市场容量还是未来发展，扩大内需的潜力都十分巨大。此外，当前工业化，城市化，现代化进程加快，经济结构调整升级，国内市场的需求进一步扩大。所以，对我国这样一个发展中大国来说，拉动经济增长的最主要力量仍然是国内需求， 而扩大国内需求的一个重要举措是刺激国内消费。而农民作为中国广大的消费群体，其消费水平和消费需求的变化直接关系到内需的政策的效果。目前，农民的经济状况仍然保持在“温饱有余、小康不足”的状态。“许多农民消费仍然不足，这已经影响到整个国民经济的健康发展。因此研究中国农村居民消费水平，对于我国制定、完善经济政策，改善消费结构，促进消费水平，提高农民消费质量有重要的意义。一、数据整理以及模型预测影响我国农村居民消费水平的主要因素分析年份农村居民消费水平y（元）农村人口自然增长率x1农村居民人均可支配收入x2（元)商品零售价格指数x3农业生产资料价格指数x4198534914.26397.6108.8104.8198637815.57423.8106101.1198742116.61462.6107.3107198850915.73544.9118.5116.2198954915.04601.5117.8118.9199056014.39686.3102.1105.5199160212.98708.6102.9102.9199268811.6784105.4103.7199380511.45921.6113.2114.11994103811.211221121.7121.61995131310.551577.7114.8127.41996162610.421926.1106.1108.41997172210.062090.1100.899.5199817309.14216297.494.5199917668.182210.39795.8200018607.582253.498.599.1200119696.952366.499.299.1200220626.452475.698.7100.5200321036.012622.299.9101.4200423015.872936.4102.8110.6200525605.893254.9100.8108.3200628475.283587101101.5200732655.174140.4103.8107.7200837565.084760.6105.9120.3200942505.055153101.497.5 数据来源：2009年中国统计年鉴根据上面的数据我们初步预测模型：y=b0+b1*x1+b2*x2+b3*x3+b4*x4+u其中：y农村居民消费水平x1农村人口自然增长率x2农村居民人均可支配收入x3商品零售价格指数x4农业生产资料价格指数u随机误差项二、模型设定回归模型参数估计根据数据用eviews软件对模型进行ols估计，得样本回归方程。结果如下：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:48sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c-207.4927163.4764-1.2692520.2189x1-0.7415855.960389-0.1244190.9022x20.7986720.01516052.684330.0000x37.9035243.1062042.5444310.0193x4-5.4543712.110245-2.5847090.0177r-squared0.998772 mean dependent var1641.160adjusted r-squared0.998526 s.d. dependent var1095.098s.e. of regression42.04608 akaike info criterion10.49227sum squared resid35357.46 schwarz criterion10.73604log likelihood-126.1533 f-statistic4065.108durbin-watson stat1.025801 prob(f-statistic)0.000000经过上述的初步回归分析，表明了最小的二乘估计的性质，证明了最小二乘法准则的合理性，但仍然不能完全保证现行回归分析的价值。原因是，模型本身未必一定满足要求，也就是模型的各个假设并不一定成立。最终的结果为：i = -207.4927-0.741585*x1+0.798672*x2+ 7.903524*x3-5.454371*x4t= (-1.269252) (-0.124419) (52.68433) (2.544431) (-2.584709) r2=0.998772 r2=0.998526 dw=1.025801 f=4065.108模型检验：经济意义检验：从得出的模型看，x1和x4的参数符号没通过经济意义检验。r2检验：经计算此模型的可决系数r2=0.998772，校正的可决系数r2=0.998526，表明模型拟合度高。t检验:再从五个参数的t检验值看，五个参数的t值分别为：t0=-1.269252, t1=-0.124419, t2=52.68433, t3=2.544431, t4=-2.584709 ，在5%显著性水平下自由度为n-k=25-5=20的t分布临界值为2.086，因此可知有部分t值是不显著的。f检验：模型的f值为：f=4065.108，而5%显著性水平下自由度分别为k-1=4和n-k=20的f分布临界值远小于模型的f值，说明模型在总体上是高度显著的。下面进行相关检验说明模型中可能存在多重共线性等问题，进而对模型进行修正。三、模型的检验和修正1.多重共线性检验:yx1x2x3x4y1-0.9081173817440.999151350318-0.45713591375-0.160979829436x1-0.9081173817441-0.9113872994820.5581729288970.231994327899x20.999151350318-0.9113872994821-0.463297625812-0.156835642896x3-0.457135913750.558172928897-0.46329762581210.837520186067x4-0.1609798294360.231994327899-0.1568356428960.8375201860671由上表可知，x1与x2相关系数高达0.9114，x4与x3相关系数高达0.8375，结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。多重共线修正处理：(1)采用逐步回归: 运用ols方法求y对各个解释变量的回归。结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。eviews过程如下y对x1回归：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:50sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c4168.325260.401016.007330.0000x1-256.284024.63966-10.401280.0000r-squared0.824677 mean dependent var1641.160adjusted r-squared0.817054 s.d. dependent var1095.098s.e. of regression468.3967 akaike info criterion15.21313sum squared resid5046096. schwarz criterion15.31064log likelihood-188.1641 f-statistic108.1866durbin-watson stat0.281126 prob(f-statistic)0.000000y对x2回归：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:50sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c57.4474316.439243.4945300.0020x20.7876350.006770116.33440.0000r-squared0.998303 mean dependent var1641.160adjusted r-squared0.998230 s.d. dependent var1095.098s.e. of regression46.07673 akaike info criterion10.57511sum squared resid48830.50 schwarz criterion10.67262log likelihood-130.1889 f-statistic13533.69durbin-watson stat1.178851 prob(f-statistic)0.000000y对x3回归：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:50sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c9234.5533086.9272.9915030.0065x3-72.1311729.26236-2.4649820.0216r-squared0.208973 mean dependent var1641.160adjusted r-squared0.174581 s.d. dependent var1095.098s.e. of regression994.9247 akaike info criterion16.71983sum squared resid22767128 schwarz criterion16.81734log likelihood-206.9979 f-statistic6.076134durbin-watson stat0.212411 prob(f-statistic)0.021595y对x4回归：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:51sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c3798.6572766.9471.3728700.1830x4-20.2209825.85028-0.7822340.4421r-squared0.025915 mean dependent var1641.160adjusted r-squared-0.016437 s.d. dependent var1095.098s.e. of regression1104.061 akaike info criterion16.92800sum squared resid28035877 schwarz criterion17.02551log likelihood-209.6000 f-statistic0.611890durbin-watson stat0.062338 prob(f-statistic)0.442056从上述四个表格分析可以得出：y对x2的线性关系强，拟合程度最优，则有回归方程：y=57.44743+0.787635*x2（2）逐步回归，将其余解释变量逐一代入上式引入x1：dependent variable: ymethod: least squaresdate: 01/16/11 time: 01:33sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob.c-4.86309690.75772-0.0535830.9578x14.1596915.9562290.6983770.4923x20.7982240.01663747.977700.0000r-squared0.998340mean dependent var1641.160adjusted r-squared0.998189s.d. dependent var1095.098s.e. of regression46.59859akaike info criterion10.63318sum squared resid47771.43schwarz criterion10.77945log likelihood-129.9148hannan-quinn criter.10.67375f-statistic6616.374durbin-watson stat1.185921prob(f-statistic)0.000000引进x3:dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:53sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c-69.95493170.5280-0.4102250.6856x20.7903170.007713102.46070.0000x31.1589831.5439330.7506690.4608r-squared0.998346 mean dependent var1641.160adjusted r-squared0.998195 s.d. dependent var1095.098s.e. of regression46.52028 akaike info criterion10.62982sum squared resid47611.00 schwarz criterion10.77609log likelihood-129.8728 f-statistic6638.706durbin-watson stat1.209349 prob(f-statistic)0.000000引进x4dependent variable: ymethod: least squaresdate: 01/16/11 time: 01:34sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob.c117.3086121.85830.9626640.3462x20.7870920.006970112.91780.0000x4-0.5508271.110709-0.4959230.6249r-squared0.998322mean dependent var1641.160adjusted r-squared0.998170s.d. dependent var1095.098s.e. of regression46.85115akaike info criterion10.64399sum squared resid48290.66schwarz criterion10.79026log likelihood-130.0499hannan-quinn criter.10.68456f-statistic6545.116durbin-watson stat1.113382prob(f-statistic)0.000000经上面的分析，再次依据调整后的可决系数最大原则，选取调整后可决系数最大所对应的解释变量作为新进入模型的候选变量，将这个候选变量的调整后可决系数与上一步中进入模型解释变量的调整后可决系数加以比较，若是大于上一步的调整后可决系数，则将候选变量加入模型，若是小于，则将停止逐步回归。经查x3的调整后可决系数最大，故x3作为第二个解释变量进入回归模型。（3）继续逐步回归加入x1dependent variable: ymethod: least squaresdate: 01/15/11 time: 22:43sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c-82.54114176.0244-0.4689190.6440x12.8987446.5281120.4440400.6616x20.7970470.01707346.685460.0000x30.8784681.6950210.5182640.6097r-squared0.998361 mean dependent var1641.160adjusted r-squared0.998127 s.d. dependent var1095.098s.e. of regression47.39305 akaike info criterion10.70048sum squared resid47168.13 schwarz criterion10.89550log likelihood-129.7559 f-statistic4264.362durbin-watson stat1.202271 prob(f-statistic)0.000000加入x4dependent variable: ymethod: least squaresdate: 01/16/11 time: 01:35sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob.c-209.1116159.0920-1.3144070.2029x20.8002790.007746103.31550.0000x37.7558612.8024382.7675410.0115x4-5.3923312.001844-2.6936820.0136r-squared0.998771mean dependent var1641.160adjusted r-squared0.998595s.d. dependent var1095.098s.e. of regression41.04865akaike info criterion10.41304sum squared resid35384.83schwarz criterion10.60806log likelihood-126.1630hannan-quinn criter.10.46713f-statistic5686.745durbin-watson stat1.013575prob(f-statistic)0.000000根据上面的表格可知，由于，此次调整后可决系数最大的是x4，但与上一步的调整后可决系数相比要小，故可以认为逐步回归终止。由于在这里加入x4这个变量对于r2影响几乎不可计算，因此在这里不将x4放入模型。故修正后的模型是： y= -207.4927 +0.798672*x2+ 7.903524*x3y农村居民消费水平x2农村居民人均可支配收入x3商品零售价格指数x4农业生产资料价格指数2.异方差检验异方差分析：g-q检验：去除中间3个数据，剩下22个数据，此时自由度为11-2-1=8，查表的出临界值（9，9）=3.18对x2进行排序可得：子样一：dependent variable: ymethod: least squaresdate: 01/15/11 time: 21:01sample: 1 11included observations: 11variablecoefficientstd. errort-statisticprob. c-192.903276.94086-2.5071620.0365x20.7942360.01350158.828110.0000x32.2308310.7268763.0690680.0154r-squared0.998177 mean dependent var655.6364adjusted r-squared0.997722 s.d. dependent var295.4225s.e. of regression14.10154 akaike info criterion8.357447sum squared resid1590.829 schwarz criterion8.465963log likelihood-42.96596 f-statistic2190.440durbin-watson stat1.510644 prob(f-statistic)0.000000子样二：dependent variable: ymethod: least squaresdate: 01/15/11 time: 21:02sample: 15 25included observations: 11variablecoefficientstd. errort-statisticprob. c2656.866899.44402.9538990.0183x20.8482010.02369435.798680.0000x3-27.789339.499651-2.9253000.0191r-squared0.997180 mean dependent var2612.636adjusted r-squared0.996475 s.d. dependent var826.3828s.e. of regression49.06500 akaike info criterion10.85117sum squared resid19258.99 schwarz criterion10.95969log likelihood-56.68143 f-statistic1414.368durbin-watson stat1.081785 prob(f-statistic)0.000000从上两个表格求得：f1=19258.99/1590.829=12.10对x3进行排序：子样一：dependent variable: ymethod: least squaresdate: 01/15/11 time: 21:04sample: 1 11included observations: 11variablecoefficientstd. errort-statisticprob. c65.703321048.5600.0626610.9516x20.8142360.01595951.020520.0000x3-0.72351610.59494-0.0682890.9472r-squared0.997069 mean dependent var2129.909adjusted r-squared0.996336 s.d. dependent var906.7206s.e. of regression54.88365 akaike info criterion11.07531sum squared resid24097.72 schwarz criterion11.18383log likelihood-57.91420 f-statistic1360.681durbin-watson stat1.807882 prob(f-statistic)0.000000子样二：dependent variable: ymethod: least squaresdate: 01/15/11 time: 21:06sample: 15 25included observations: 11variablecoefficientstd. errort-statisticprob. c-69.27762161.1354-0.4299340.6786x20.7798430.006715116.13150.0000x31.2823331.4240730.9004690.3942r-squared0.999442 mean dependent var1039.273adjusted r-squared0.999303 s.d. dependent var989.7291s.e. of regression26.13108 akaike info criterion9.591129sum squared resid5462.668 schwarz criterion9.699646log likelihood-49.75121 f-statistic7168.785durbin-watson stat2.490933 prob(f-statistic)0.000000根据上两表求得：f2=24097.72/5462.668=4.41因为f1f2（9，9）=3.18 ，所以模型存在异方差。需要对其进行修正。异方差修正：dependent variable: ymethod: least squaresdate: 01/15/11 time: 21:09sample: 1985 2009included observations: 25weighting series: 1/abs(el)variablecoefficientstd. errort-statisticprob. c-100.421318.87623-5.3199890.0000x20.7875570.002494315.81420.0000x31.4632360.1808788.0896130.0000weighted statisticsr-squared0.999957 mean dependent var893.7122adjusted r-squared0.999953 s.d. dependent var1198.539s.e. of regression8.227519 akaike info criterion7.165013sum squared resid1489.225 schwarz criterion7.311278log likelihood-86.56266 f-statistic93346.88durbin-watson stat1.292238 prob(f-statistic)0.000000unweighted statisticsr-squared0.998310 mean dependent var1641.160adjusted r-squared0.998156 s.d. dependent var1095.098s.e. of regression47.02431 sum squared resid48648.29durbin-watson stat1.198471所以，修正后的模型为：y =-100.4213+0.787557*x2+1.463236*x3t=（-5.319989） （315.8142） （8.089613） r2=0.999957 f=93346.883.自相关性检验：dependent variable: ymethod: least squaresdate: 01/15/11 time: 20:53sample: 1985 2009included observations: 25variablecoefficientstd. errort-statisticprob. c-69.95493170.5280-0.4102250.6856x20.7903170.007713102.46070.0000x31.1589831.5439330.7506690.4608r-squared0.998346 mean dependent var1641.160adjusted r-squared0.998195 s.d. dependent var1095.098s.e. of regression46.52028 akaike info criterion10.62982sum squared resid47611.00 schwarz criterion10.77609log likelihood-129.8728 f-statistic6638.706durbin-watson stat1.209349 prob(f-statistic)0.000000查表可得其临界值为：dl=1.21 ， du=1.55 ，此时，d.w=1.209349dl=1.21 由此可见，模型存在正自相关。4-du=2.45自相关修正：dependent variable: ymethod: least squaresdate: 01/16/11 time: 02:55s