Econometrie,Dunca Lucian

8/8/2019 Econometrie,Dunca Lucian

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Table of content

TABLE OF CONTENT .......................................................................................................................2

PRIMARY DATA ................................................................................................................................2

GRAPHICAL REPRESENTATIONS AND CORRELATIONS ....................................................3

EXAMINATION OF CORELATION ................................................................................................4

ECONOMETRIC MODEL .................................................................................................................7

THE ANALYZE OF THE DATA FROM THE TABLE ...................................................................8

THE CHOW TEST ..............................................................................................................................9

DURBIN WATSON TEST ................................................................................................................. ..9

R EPRESENTATION OF ERRORS......................................................................................................................12

FORECASTING TWO AGRICULTURAL PRODUCTION .........................................................13

Primary Data

My project theme is the analysis of the factors that influenced the

agriculture production of our country between 1994 and 2009. The analysis is

made for 16 years and there are 3 variables that influence the agricultural

production:

Agricultural area ( measured in ha);

Land improvements;



Breeding Services;(Serviciile de reproductie);

So, we can see from the table that:

Y represent the agricultural production.

X1 represent the agricultural area.

X2 represent the land improvements

X3 represent the breeding services.

Graphical representations and correlations

The product moment correlation coefficient is a measurement of the

degree of scatter. It is usually denoted by r and r can be any value between -1

and 1. The product moment correlation coefficient can be used to tell us how

strong the correlation between two variables is.

A positive value indicates a positive correlation and the higher the value,

the stronger the correlation. Similarly, a negative value indicates a negative

correlation and the lower the value the stronger the correlation. If there is a

YearsAgriculturalproduction Agricultural area Land improvements Breeding Services

y x1 x2 x3

1994 644,38 401,03 33,321 0,925

1995 584,18 394,95 30,311 1.366

1996 689,79 405,26 35,591 0,502

1997 764,81 411,66 39,342 0,427

1998 435,63 376,76 22,884 0,954

1999 589,05 395,47 30,554 0,963

2000 517,41 387,43 26,973 0,788

2001 516,31 387,3 26,918 1,124

2002 519,89 387,72 27,097 1,343

2003 400,29 371,52 21,117 0,673

2004 673,91 403,81 35,116 0,739

2005 655,14 402,06 34,059 0,724

2006 670,06 403,46 34,605 0,596

2007 388,92 369,73 20,748 0,64

2008 637,86 400,4 32,995 0,517

2009 532,23 381,08 40,11 1,875



perfect positive correlation (in other words the points all lie on a straight line

that goes up from left to right), then r = 1.

If there is a perfect negative correlation, then r = -1.If there is no

correlation, then r = 0. r would also be equal to zero if the variables were relatedin a non-linear way.

Agriculture production

0

100

200

300

400

500

600

700

800

900

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Years

A g

r i c u l t u r a l p r o d u c t i o n

We can observe, in the table above, that there exists some corelatio-

ns between the depentend and the independent

variables.

Examination of corelation



Strong positive correlation between agriculture production and agricultural area

0

100

200

300

400

500

600

700

800

900

365 370 375 380 385 390 395 400 405 410 415

Agricultural area

A g r i c u l t u r a l p r o d u c t i o n

Fig. 1.1

So, as we can see in the figure 1.1, between the agriculture production and

the agricultural area, there is a strong positive correlation. Basically, this means

that whenever the agricultural area is bigger, the agricultural production

increases. The agricultural area it’s a fundamental factor for the development of

our agriculture production and we can say that in our country we have a wide

area for agriculture but, unfortunately, it s not enough because a large part of it it

s not used, the reason being the lack of funds.

In the 1.2 figure we can see that there exists also a strong positive

correlation between agricultural production and land improvements. This also

means that if the land improvements increase then the same thing will happen to

the agricultural area. So, this thing is logical because the better the land, the

bigger the agricultural production will be. In this case, there exist the following

improvements we can do: Hydrological improvement (Land levelling,

drainage, irrigation, leaching of saline soils, landslide and flood control)

Soil improvement (fertilization)

Soil stabilization/erosion control

Road construction

Afforestation, (water conservation and land

protection against wind erosion)



Strong positive correlation between Agricultural production and land improvements

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25 30 35 40 45

Land improvements

A g r i c u l t u r a l p r o d u c t i o n

Fig 1.2

In the 1.3 figure, we observe that the breeding services it’s in a weak

positive correlation with the agricultural production. That means that the

breeding service influences the agricultural production only in a small way.

When the Breeding services increase, the agricultural production increases also.

This represent a logical process because , for example, the majority of

agriculture in our country it s represented by the breeding services( an example

can be the production of potato, this year we plant the potato on a piece of land,

and the next year the potato will be planted on the same land).

Weak p ositive correlation between Agricultural production and B reeding servi

0

100

200

300

400

500

600

700

800

900

0 0,2 0 ,4 0 ,6 0 ,8 1 1 ,2 1 ,4 1,6 1 ,8 2 2,2 2 ,4 2 ,6 2 ,8 3 3 ,2 3 ,4 3 ,6 3 ,8 4 4,2 4 ,4 4 ,6 4 ,8 5

Breeding service

A g r i c u l t u r

a l p r o d u c t i o n

Fig 1.3



The correlations between the variables can also be computed with the Correl

function. We can do this thing in Excel, and observe that we can speak about 2

types of correlations:

Positive correlation(if the value of the correlation is

positive) Negative correlation or inverse (if the value of correlation

is negative).

r y xi -0,018744409 0,986798138 0,858656362 0,018972632

0,778504152 0,051357893

Fig1.4

Econometric model

The structure of the econometric model is the following:

t t t t t t xa xa xa xa xaa y55443322110

ˆˆˆˆˆˆˆ +++++=

I used the table of regression from Excel, to establish the econometric model:

Fig 2.1



The analyze of the data from the table

We observe in 2.1 figure the following values: First of all, multipleR=0,997 this represent a strong correlation between the dependent and

independent variable. Second, R square= 0,994 this represent the validity of the

linear model.

The Fisher test ( which is ≈ 0) indicates a globally significant

regression.The P values for the variables are the following:

For the X Variable 1, P=0,0000;

X Variable 2, P= 0,0000;

X Variable 3,P=3929;

These P-values are very god. And the economic model is :

y th=-2287,139+6,9725x1+4,14244x2-0,0059x3

SUMMARY OUTPUT Y=f(x1,x2,x3)

Regression Statistics

Multiple R 0,9974

R Square 0,9949 Adjusted RSquare 0,9936

Standard Error 8,7679

Observations 16,0000

ANOVA

df SS MS F Significance F

Regression 3 178746,915 59582,305

775,037

0.000Residual 12 922,521 76,878

Total 15 179669,436

Coefficient

s

Standard

Error t Stat P-value

Lower

95%

Upper

95%

Intercept -2287,1390 97,9565 -23,3485 0,0000 -2500,5679 -2073,7102

X Variable 1 6,9726 0,2849 24,4766 0,0000 6,3519 7,5932

X Variable 2 4,1424 0,6046 6,8517 0,0000 2,8252 5,4597

X Variable 3 -0,0059 0,0067 -0,8862 0,3929 -0,0204 0,0086



The Chow test

This test refers to verification of the stability of coefficient s through

examination of the difference between the dependent variance SSR =square sumof residuals for the whole sample and the sum of the dependent variances

divided into two sub-samples SSR1 and SSR2.

We utilize the fisher test, who say :

if α

)1(2,1*+−+

≤ k nk F F , accept H0, the model is stable on the whole

period

If α

)1(2,1*+−+

> k nk F F , accept H1, the model is not stable on the

whole period

F* has the formula

)]1(2/[)(

)1/()]([

)]1()1/[()(

)]1()1()1/[()]([*

21

21

21

21

21

21

+−+

++−=

−−+−−+

−−−−−−−−+−=

k nSSRSSR

k SSRSSRSSR

k nk nSSRSSR

k nk nk nSSRSSRSSR F

So’ F*= 47,60 and I used Excel to compute F theoretical ( with Finv

function) and I obtained that F theo= 3,49. We observe that F* > F, so we admitthat we accept H1, The model is not stable on the whole period.

Durbin Watson test

The Durbin Watson test it’s used for establishing the presence or

absence of correlation of residuals. The formula is:

So, I compute in excel the residuals et first, then et-1( residual with one lag of time)as we can see in figure 3.1

y theo et et-1 et^2

(et-et-

1)^2

( )

∑

∑

=

=

−−

=n

t

t

n

t

t t

e

ee

DW

1

2

2

2

1



647,0954 -2,71543 7,373554

584,163 0,01699 -2,71543 0,000289 7,466115

685,9952 3,794756 0,01699 14,40017 14,27151

746,1584 18,65157 3,794756 347,8809 220,7248

434,6363 0,99368 18,65157 0,9874 311,8009

596,8656 -7,81558 0,99368 61,08327 77,60304

525,9731 -8,56307 -7,81558 73,32611 0,558738

524,8368 -8,52681 -8,56307 72,70652 0,001314

528,5055 -8,61549 -8,52681 74,22673 0,007864

390,782 9,507979 -8,61549 90,40167 328,4603

673,916 -0,00596 9,507979 3,55E-05 90,51498

657,3355 -2,19549 -0,00596 4,820161 4,794042

669,3596 0,700386 -2,19549 0,49054 8,386076

376,7728 12,14725 0,700386 147,5556 131,0306

641,3547 -3,49469 12,14725 12,21283 244,67

536,1101 -3,88009 -3,49469 15,05513 0,148539

Sum-> 922,5209 1440,439

Fig 3.1

Dw=1440,4/922,5 = 1,56



Fig 4.1

I used the figure 4.1 for finding D-L and D-U.The reason is that the

distribution of Dw test, depend on the values of x variables in my data. So, there

exist 2 cases:

Firs, When Dw statistic’s distribution it’s indicated by D-L’s, That

happens when X variables are not well behaved.

Second, ehen Dw statistic’s distribution it s indicated by D-U’s.That

happens when X variables are well behaved.

In my case, I have the following results:

The lower limit is 0,857.

The upper limit 1,728.

So, in conclusion, because The value of DW it’s between the value of

D-L and D-U , the model is inconclusive.



Representation of errors

Residual evolution

-10

-5

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

e t

Fig 4.1

Correlation of residuals

-10

-5

0

5

10

15

20

25

-10 -5 0 5 10 15 20 25

Fig 4.2

The both, Fig 4.2 and 4.2 are the proof that the model is inconclusive.



Forecasting two agricultural production

So, this allow us to establish two potential agricultural production

(having a theoretical value and an interval of confidence in which it can takevalues.)

The formula for calculating the interval of confidence is:

]1)([ˆ 122/

1 +′′±=+

−

+−−++ ht ht k nht ht X X X X t y ICy

ε

α

σ

In figure 5.1 we can see the matrix X, that I computed in excel:

Matrix X

1 401,03 33,321 0,925

1 394,95 30,311 1.366

1 405,26 35,591 0,502

1 411,66 39,342 0,427

1 376,76 22,884 0,954

1 395,47 30,554 0,963

1 387,43 26,973 0,788

1 387,3 26,918 1,124

1 387,72 27,097 1,3431 371,52 21,117 0,673

1 403,81 35,116 0,739

1 402,06 34,059 0,724

1 403,46 34,605 0,596

1 369,73 20,748 0,64

1 400,4 32,995 0,517

1 381,08 40,11 1,875

Fig 5.1

The calculation of the Matrix X, followed the next steps:



1. x'x

X'X

16 6279,64 491,741 1378,796279,64 2467049,139 193888,2418 544491,6279

491,741 193888,2418 15651,69552 41800,45945

1378,79 544491,6279 41800,45945 1865968,886

2. (x'x)^(-1)

(X'X)^(-1)

124,8163 -0,360314926 0,539832323 0,000818714

-0,36031 0,001055571 -0,001748857 -2,59807E-06

0,539832 -0,001748857 0,004754735 4,9157E-06

0,000819 -2,59807E-06 4,9157E-06 5,78956E-07

3. xt+h,(x19)

Xt+h,(X19)

1

500,25

42,12

0,23

4 X19’

X19'

1 500,25 42,12 0,23

5 xt+h,(x20)



Xt+h,(X20)

1

425,87

41,1

0,45

6 X20’

X20'

1 425,87 41,1 0,45

7 X19'*[(X'*X)^(-1)

X19'*[(X'*X)^(-1)

-32,69327214 0,094071998 -0,134762875 -0,000273787

8,689969489

8 X20'*[(X'*X)^(-1)

X20'*[(X'*X)^(-1)

-6,443496821 0,017341891 -0,009531634 -8,54296E-05

0,550105793

9

Then, in order to draw the forecast graphic I did the next steps:

yt+h add 1 *tau^2=var after sq root t value t*sqrtlim inf lim sup

19 8,689969489 9,689969489 744,9332442 27,29346523 2,178812827 59,46735214 1315,899889 2691,267

20 0,550105793 1,550105793 119,1670767 10,91636738 2,178812827 23,78472126 828,7362053 1681,257



I copied the values of the y theo for the first

16 values.

for the values 17 and 18, with the help of the

calculs I obtained the values of upper and lower limit

y theo Lower limit Upper limit

647,0954289 647,0954289 647,0954289

584,1630097 584,1630097 584,1630097

685,9952438 685,9952438 685,9952438

746,158435 746,158435 746,158435

434,6363199 434,6363199 434,6363199

596,8655785 596,8655785 596,8655785

525,9730666 525,9730666 525,9730666

524,8368118 524,8368118 524,8368118528,5054935 528,5054935 528,5054935

390,7820205 390,7820205 390,7820205

673,9159565 673,9159565 673,9159565

657,3354866 657,3354866 657,3354866

669,3596144 669,3596144 669,3596144

376,7727548 376,7727548 376,7727548

641,3546859 641,3546859 641,3546859

536,1100936 536,1100936 536,1100936

1375,367242 1315,899889 2691,267131

852,5209265 828,7362053 1681,257132

Forecasting for the salary

3100,00

3120,00

3140,00

3160,00

3180,00

3200,00

3220,00

3240,00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

R O N y th

low lim

up lim

Bibliography



www.google.ro

www.INSEE.ro

www.sofie.stern.nyu.edu

www.wikipedia.com

Econometrie,Dunca Lucian

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