我國糧食生產(chǎn)與相關(guān)投入計量經(jīng)濟學(xué)模型分析(一)

我國糧食生產(chǎn)與相關(guān)投入計量經(jīng)濟學(xué)模型分析

一.理論分析

二.建立模型

以1980——2003年各年糧食產(chǎn)量作為被解釋變量，解釋變量中，包括農(nóng)

業(yè)化肥施用量，糧食播種面積，成災(zāi)面積，農(nóng)業(yè)機械總動力，農(nóng)業(yè)勞動力。

模型設(shè)定為

Y=Bo+/3\X\+0%2+B、X3++B、X5

其中Y：糧食產(chǎn)量（萬噸）

XI：農(nóng)業(yè)化肥試用量（萬噸）

X2：糧食播種面積（千公頃）

X3：成災(zāi)面積1千公頃）

X4：農(nóng)業(yè)機械總動力（萬千瓦）

X5：農(nóng)業(yè)勞動力（萬人）

顯著性水平a=0.05

三.估計參數(shù)

假定模型中隨機項滿足基本假定，用OLS法估計參數(shù)，估計結(jié)

果如下：

DependentVariable:Y

Method:LeastSquares

Date:12/15/06Time:00:16

Sample:19802003

Includedobservations:24

VariableCoefficientStd.Errort-StatisticProb.

C-5410.50021545.53-0.2511200.8046

X18.1646181.6115125.0664330.0001

X20.1639010.1519251.0788300.2949

X3-0.2307920.103152-2.2373990.0381

X4-0.2516210.131533-1.9129190.0718

X50.6388690.4294961.4874850.1542

R-squared0.922443Meandependentvar42847.33

AdjustedR-squared0.900899S.D.dependentvar5325.186

S.E.ofregression1676.383Akaikeinfocriterion17.89898

SumsquaredresidSchwarzcriterion18.19350

Loglikelihood-208.7878F-statistic42.81740

Durbin-Watsonstat0.415364Prob(F-statistic)0.000000

估計方程為￥=-5140.5+8.16XI+().16X2-0.23X3-0.25X4+().64X5

t:(-0.25)(5.07)(1.08)(-2.24)(-1.91)(1.49)

R2=0.9224F=42.8174

由于X2,%4,X5未通過t檢驗，而且X4前的符號經(jīng)濟意義也不合理,

因此解釋變量鍵可能存在多重共線性。

四.多重共線性分析

1.檢驗簡單相關(guān)系數(shù)

Xl,X2,X3,X4,X5的相關(guān)系數(shù)表如下：

X1X2X3X4X5

X11.000000-0.8448520.3751090.9800340.396547

X2-0.8448521.000000-0.400823-0.822917-0.195668

X30.375109-0.4008231.0000000.500381-0.603832

X40.980034-0.8229170.5003811.0000000.268218

X50.396547-0.195668-0.6038320.2682181.000000

2.用Y分別關(guān)于Xl,X2,X-X5作一元線性回歸得：

變量XiX2X3X4X5

參數(shù)估計值4.255-0.3480.4690.2813.235

t統(tǒng)計量8.29-1.192.5285.1184.522

R20.75760.06060.22510.54350.4817

由上表知，解釋變量的重要程度依次為Xl,X4,X5,X3,%2

3.將各解釋變量按以上順序分別引入基本回歸模型中，并用OLS法估計。

先把X,引入模型，用Y關(guān)于X,X4做叵歸并用OLS法估計得：

DependentVariable:Y

Method:LeastSquares

Date:12/15/06Time:18:13

Sample:19802003

Includedobservations:24

VariableCoefficientStd.Errort-StatisticProb.

C29444.911146.28725.687210.0000

X110.230871.3090057.8157650.0000

X4-0.4845980.101949-4.7533260.0001

R-squared0.883222Meandependentvar42847.33

AdjustedR-squared0.872101S.D.dependentvar5325.186

S.E.ofregression1904.447Akaikeinfocriterion18.05824

SumsquaredresidSchwarzcriterion18.20550

Loglikelihood-213.6989F-statistic79.41445

Durbin-Watsonstat0.893524Prob(F-statistic)0.000000

Y=29444.91+10.231X1-0.485X4

R2=0.9224t(25.69)(7.82)(-4.75)

可見，引入X4后，擬合優(yōu)度有所提高，但X4回歸參數(shù)的符號不對，所以應(yīng)該把

X4從模型中刪除。

按照上面的方法依次引入X5,X3,X1,經(jīng)過檢驗均可保留。

刪去不符合條件的解釋變量X4,得到Y(jié)關(guān)于Xl,X2,X3,X5的方程：

y=—33196.4+5.29X1+0.32X2-0.26X3+0.98X5

(-1.95)(8.51)(2.37)(-2.39)(2.34)

R2R.9067F=46.1480DW=0.38

DependentVariable:Y

Method:LeastSquares

Date:12/15/06Time:12:41

Sample:19802003

Includedobservations:24

VariableCoefficientStd.Errort-StatisticProb.

C-33196.4016990.03-1.9538700.0656

X15.2902390.6217618.5084710.0000

X20.3221970.1360352.3684980.0286

X3-0.2603400.108892-2.3908070.0273

X50.9777980.4177312.3407360.0303

R-squared0.906676Meandependentvar42847.33

AdjustedR-squared0.887029S.D.dependentvar5325.186

S.E.ofregression1789.857Akaikeinfocriterion18.00071

SumsquaredresidSchwarzcriterion18.24614

Loglikelihood-211.0085F-statistic46.14801

Durbin-Watsonstat0.380375Prob(F-statistic)0.000000

五.序列相關(guān)性分析

對上一步得到的回歸方程

A

K=-33196.4+5.29X1+0.32X2-0.26X3+0.98X5

做序列相關(guān)性分析，采用LM檢驗法：

1.2階滯后：已=為+小*Xl+42*X2+〃3*X3+A5*X5+0*e]+O*e，+J

Breusch-GodfreySerialCorrelationLMTest:

F-statistic24.93890Probability0.000009

Obs*R-squared17.89932Probability0.000130

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/15/06Time:13:05

PresamplemissingvaluelaggedresidualssetIozero.

VariableCoefficientStd.Errort-StatisticProb.

C5709.0289294.2960.6142510.5472

X10.0787650.3324010.2369590.8155

X2-0.0934320.075415-1.2388990.2322

X3-0.1035490.060792-1.7033260.1067

X50.2165530.2248040.9632970.3489

RESID(-1)1.2239900.1896966.4523910.0000

RESID(-2)-0.5186400.195301-2.6555860.0166

R-squared0.745805Meandependentvar1.33E-11

AdjustedR-squared0.656089S.D.dependentvar1626.789

S.E.ofregression954.0127Akaikeinfocriterion16.79772

SumsquaredresidSchwarzcriterion17.14132

Loglikelihood-194.5727F-statistic8.312966

Durbin-Watsonstat2.552423Prob(F-statistic)0.000262

得估計結(jié)果為：

e=5709.028+0.079*XI-0.093*X2-0.104*X34-0.217*X5+1.224*^/,-0.519*^2

t(0.61)(0.24)(-1.24)(-1.70)(0.96)(6.45)(-2.66)

R2=0.7458N=24P=2K=5(包含常數(shù)項)

LM=(N-P)*/?2=(24-2)*0.7458=16.4076

琉⑼⑵二5.99

由于LM>%：o>(2),而且e-，J」的回歸系數(shù)顯著不為零，表明此模型存在一階，

二階自相關(guān)

2.3階滯后:

呂=2300.225—().011*X?-0.09*X2—().077*X3+0.302*Xs+1.07*—0.20米e.2-030*6-

Breusch-GodfreySerialCorrelationLMTest:

F-statistic17.48614Probability0.000026

Obs*R-squared18.39076Probability0.000365

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/15/06Time:13:27

Presamplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C2300.2259626.9830.2389350.8142

X1-0.0114400.337259-0.0339200.9734

X2-0.0905930.074573-1.2147460.2421

X3-0.0770940.064103-1.2025960.2466

X50.3020660.2336371.2928830.2144

RESID(-1)1.0685910.2288634.6690250.0003

RESID(-2)-0.2018090.329957-0.6116210.5494

RESID(-3)-0.3025460.255535-1.1839710.2537

R-squared0.766282Meandependentvar1.33E-11

AdjustedR-squared0.664030S.D.dependentvar1626.789

S.E.ofregression942.9348Akaikeinfocriterion16.79707

SumsquaredresidSchwarzcriterion17.18976

Loglikelihood-193.5649F-statistic7.494061

Durbin-Watsonstat2.363537Prob(F-statistic)0.000442

得估計結(jié)果為:

G=23(X).225-0.011*XL().09*X2-().077*X3+().302*X5+L07&-0.20%-().30%

t(0.24)(-0.03)(-1.21)(-1.20)(1.29)(4.67)(-0.61)(-1.18)

R2=0.7663N=24P=3K=5(包含常數(shù)項)

LM=(24-3)*0.7663=16.0923〉城05)(3)=7.81,表明存在自相關(guān)；但由于巴川的

回歸系數(shù)不顯著，故不存在三階序列相關(guān)性。

3.運用廣義差分法進(jìn)行自相關(guān)的處理

DependentVariable:Y

Method:LeastSquares

Date:12/15/06Time:13:43

Sample(adjusted):19822003

Includedobservations:22afteradjustingendpoints

Convergenceachievedafter22iterations

VariableCoefficientStd.Errort-StatisticProb.

C-28788.979833.202-2.9277310.0104

X14.8123620.5116299.4059550.0000

X20.5602300.0907246.1751160.0000

X3-0.1841120.034253-5.3750180.0001

X50.0302050.3362940.0898170.9296

AR(1)0.7999790.2239273.5724940.0028

AR(2)-0.1932200.187475-1.0306480.3190

R-squared0.985985Meandependentvar43808.09

AdjustedR-squared0.980378S.D.dependentvar4410.156

S.E.ofregression617.7612Akaikeinfocriterion15.94345

Sumsquaredresid5724433.Schwarzcriterion16.29060

Loglikelihood-168.3780F-statistic175.8753

Durbin-Watsonstat2.504680Prob(F-statistic)0.000000

InvertedARRoots.40?.18i.40+.18I

結(jié)果表明，調(diào)整后的模型的DW=2.5()47>%=L78,廣義差分后的模型已不存

在序列相關(guān)性，得到的回歸方程為：

Y=-28788.97+4.81Xi+0.56X2-0.18X3+0.03X5

六.異方差性檢驗

1.采用懷特檢驗法，輔助回歸模型的估計結(jié)果如下:

WhiteHeteroskedasticityTest:

F-statistic2.936941Probability0.054487

Obs*R-squared19.69010Probability0.140219

TestEquation:

DependentVariable:RESIDA2

Method:LeastSquares

Date:12/15/06Time:14:08

Sample:19802003

Includedobservations:24

VariableCoefficientStd.Errort-StatisticProb.

C4.25E+081.49E+090.2859720.7814

X133760.9382018.730.4116240.6902

X1A20.7255983.1583020.2297430.8234

X1*X2-0.6906530.673699-1.0251660.3320

X1*X30.1291840.4770890.2707750.7927

xrx51.1287582.8949520.3899060.7057

X223241.7824004.530.9682250.3582

X2A2-0.1760490.106109-1.6591300.1315

X2*X3-0.0754480.093213-0.8094420.4391

X2*X50.6207110.5226491.1876450.2654

X38993.28513257.930.6783320.5146

X3A2-0.0545730.058213-0.9373820.3730

X3*X50.0543380.2370930.2291850.8238

X5-115713.965324.93-1.7713600.1103

X5A20.6278270.9646220.6508530.5314

R-squared0.820421Meandependentvar2536174.

AdjustedR-squared0.541075S.D.dependentvar3247638.

S.E.ofregression2200079.Akaikeinfocriterion32.31506

Sumsquaredresid4.36E+13Schwarzcriterion33.05134

Loglikelihood-372.7807F-statistic2.936941

Durbin-Watsonstat2.13G747Prob(F-statistic)0.054487

在同方差的條件下：nR2~/（份，］尸4,為解釋變量的個數(shù)

從上圖可知nW=19.6901,在顯著性水平a=0.（）5的情況下,

彳：5（4）=9.49,由于nR2>/；5（4）=9.49,故存在異方差性。

2.克服異方差，采用加權(quán)最小二乘法（WLS），以上為權(quán)數(shù)進(jìn)行WLS估計,

同

得估計結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:12/15/06Time:14:22

Sample:19802003

Includedobservations:24

Weightingseries:1/ABS(RESID)

VariableCoefficientStd.Errort-StatisticProb.

C-38848.226162.635-6.3038330.0000

X15.6263340.05743597.960400.0000

X20.3996690.03619411.042280.0000

X3-0.2747060.020876-13.158680.0000

X50.8696750.0875939.9289660.0000

WeightedStatistics

R-squared1.000000Meandependentvar41264.31

AdjustedR-squared1.000000S.D.dependentvar179318.7

S.E.ofregression37.90557Akaikeinfocriterion10.29112

Sumsquaredresid27299.81Schwarzcriterion10.53655

Loglikelihood-118.4935F-statistic6319.212

Durbin-Watsonstat0.924452Prob(F-statistic)0.000000

UnweightedStatistics

R-squared0.904028Meandependentvar42847.33

AdjustedR-squared0.883823S.D.dependentvar5325.186

S.E.ofregression1815.075Sumsquaredresid

Durbin-Watsonstat0.387567

最終擬合的回歸方程為

/=-38848.22+5.63X1+0.40X2-0.27X3+0.87X5

t(-6.30)(97.96)(11.04)(-13.16)(9.93)

R2=1.0000

和初始方程比較，無論是擬合優(yōu)度還是個參數(shù)的t值都有顯著的改善。擬合

結(jié)果可以由下圖形象的看出：

七.模型的經(jīng)濟含義

經(jīng)過以上分析，得出模型的回歸方程為

A

Y=-38848.22+5.63Xi+0.40X2-0.27X3+0.87X5

/?2=1.0()()()表明，糧食總產(chǎn)量的變化可以完全由化肥施用量，糧食播種面積,

成災(zāi)面積和農(nóng)業(yè)勞動力的數(shù)值來解釋；

XI的回歸參數(shù)5.63表示：在其他條件不變的情況下，化肥施用量每增加1

萬噸，糧食產(chǎn)量增加5.63萬噸；

X2的回歸參數(shù)0.40表示：在其他條件不變的情況下，糧食播種面積每增加

100()公頃，糧食產(chǎn)量增加4000噸；

X3的回歸參數(shù)-0.27表示：在其他條件不變的情況下，成災(zāi)面積每減少1000

公頃，糧食產(chǎn)量增加270()噸；

X5的回歸參數(shù)0.87表示：在其他條件不變的情況下，農(nóng)業(yè)勞動力每增加1

萬人，糧食產(chǎn)量增加870()噸；

八.模型預(yù)測

以此模型預(yù)測2004年的糧食產(chǎn)量，由統(tǒng)計年鑒的數(shù)據(jù)知，2004年各解釋變

量的數(shù)值如下：

X1=4636.6X2=101606

X?=16297X5=30596

代入模型中得Y=49979.33

而2004年實際糧食總產(chǎn)量為50146.03,誤差率為0.059%,Eviews模型如下:

■^一____....................................................

ViewProcsObjectsPrint]NameFreezeEdit+/-Smpl+

YF

Lastupdated:12/16/06-11:54人

Modified:19802004//fit(^actual)y

1980198034941.60

1981198136138.20

1982198237678.73

1983198339139.61

1984198439419.28

1985198534803.68

1986198636348.43

1987198738115.78

1988198837991.84

1989198940754.99

1990199045166.09

1991199143918.59

1992199244313.20

1993199345621.52

1994199443409.60

1995199547362.36

1996199649894.03

1997199748557.74

1998199851062.20

1999199950862.85

2000200046910.56

2001200146970.09

2002200247405.46

2003—

2004

<IIL__isi??-??

EVi?v*-(fiiivRtinn:UITTTL?VorkfHii：TJ匚叵又

lil?till2bj?cltn”tractSick歸gx49V!?1?

V?Mtr?ciOli?ctx|〃??“2ttia*t4Stitt

Forecast:YF

Actual:Y

Forecastsample:19802004

Includedobservations:25

RootMeanSquaredError1589.413

MeanAbsoluteError1164.720

MeanAbs.PercentError3.011302

TheilInequalityCoefficient0.018265

BiasProportion0.004967

VarianceProportion0.010118

CovarianceProportion0.934915

附：中國糧食生產(chǎn)與相關(guān)投入資料

糧食產(chǎn)量化肥施用量糧食播種面積成災(zāi)面積農(nóng)業(yè)機械總動農(nóng)業(yè)勞動力

（萬噸）Y（萬噸）Xi千公頃）X2千公頃X3力萬千瓦X4（萬人）Xs

198032056.001269.400117234.022317