ČESKÁ ZEMĚDĚLSKÁ UNIVERZITA V PRAZE
Provozně ekonomická fakulta
Econometrics
Analysis of influences in ICT sector
Autor:
Předmět:
Obor:
Ročník:
Jakub Liška
Ekonometrie – Úterý 12.15
Informatics
5.
INTRODUCTION & OBJECTIVES
Based on statistical data collected over the years 1996 – 2007 I've decided to analyse
influences of several economical aspects on added value and revenues in ICT sector of Czech
Republic.
1.
One-equation model
1.1 Economic model and econometric model
1.1.1 Economic model definition
Economic Value Added in ICT sector depends on :
• quantity of enterprises
• quantity of employees
• expenses for labor in ICT sector
• expenses for research & development in ICT sector
• investments in ICT sector
Expected relations :
• from long-term point of view all of those 5 factors are supposed to increase
added value in ICT sector
1.1.2
Econometric model definition
Variables:
Endogenous:
y1 = added value in ICT sector (mil. CZ Crowns)
Exogenous:
x1 = unit vector
x2 = quantity of enterprises
x3 = quantity of employees
x4 = expenses for labor in ICT sector (mil. CZ Crowns)
x5 = expenses for research & development in ICT sector (mil. CZ
Crowns)
x6 = investments in ICT sector (mil. CZ Crowns)
One-equation linear model:
y1 = func (x1, x2, x3, x4, x5, x6)
β11y1t = γ11 x1t + γ12 x2t + γ13 x3t + γ14 x4t + γ15 x5t + γ16 x6t + u1t
1. 1
Dataset
Correlation matrix computation:
added value
(mil. CZK)
quantity of
enterprises
y1
Variables
1995
39054
1996
48353
1997
55563
1998
65746
1999
73670
2000
84215
2001
100429
2002
112372
2003
120258
2004
130029
2005
131641
2006
149031
2007
163741
average
98008
variance
1488786191
standard deviation 38585
16531
17149
25102
20233
22362
24239
27768
28755
29052
29345
29108
29101
32654
25492
23832492
4882
YEARS
x2
expenditures
for research
&
development
(mil. CZK)
expenses
for labor
(mil. CZK)
quantity of
employees
x3
x4
94782
97182
99005
96744
92690
102448
110605
108900
107036
110386
112316
122490
130936
106578
115935482
10767
x5
11204
15085
17035
18273
19557
23202
28002
30666
32971
36141
39487
45218
51238
28314
140253971
11843
investments
(mil. CZK)
x6
327
301
584
654
839
1002
1156
1411
2772
3031
4205
5282
5923
2114
3493820
1869
23769
38433
53683
44822
35136
56173
57304
33171
22771
24695
21637
26708
29074
35952
158387573
12585
Following results do not comply with acceptable levels of multi-collinearity except of
investments. We can see strong dependence between all other variables.
added value
(mil. CZK)
added value (mil. CZK)
quantity of enterprises
quantity of employees
expenses for labor (mil. CZK)
expenditures for research &
development (mil. CZK)
investments (mil. CZK)
1
0.92
0.92
0.99
0.93
-0.44
quantity of
enterprises
0.92
1
0.84
0.9
0.78
-0.22
expenditures
for research &
investments
development
(mil. CZK)
(mil. CZK)
0.99
0.93
-0.44
0.9
0.78
-0.22
0.95
0.92
-0.31
1
0.96
-0.44
expenses for
labor (mil.
CZK)
quantity of
employees
0.92
0.84
1
0.95
0.92
-0.31
0.96
-0.44
1
-0.55
-0.55
1
Therefore I expressed added value in year-to-year differences to decrease the
level of mutual dependency, but there were still strong relations between the remaining 3
exogenous variables.
After expressing all variables except investments as year-to-year differences
the results seems satisfying. The only variable having unacceptable coefficient of correlation
is labor costs in relation with quantity of employees which is obvious even without correlation
matrix anyway. I decided to remove this variable for the sake of explanatory variables
parameters estimation accuracy.
added
value (mil.
CZK)
added value (mil.CZK)
quantity of enterprises
expenses for labor (mil. CZK)
expenditures for research & development (mil CZK)
investments (mil. CZK)
1
0.06
0.64
-0.16
0.22
quantity of
enterprises
0.06
1
0.18
-0.11
0.38
expenditures
for research investment
&
s (mil.
development
CZK)
(mil. CZK)
0.64
-0.16
0.22
0.18
-0.11
0.38
1
0.25
-0.11
0.25
1
-0.67
-0.11
-0.67
1
expenses
for labor
(mil. CZK)
First off, it seemed I chose inappropriate variables but the last correlation
matrix is giving satisfying numbers so I decided not to change them.
1.3 Parameters’ estimation using OLSM
I need a matrix X for parameter estimation with variables chosen according to
the correlation matrix. For parameter estimation I'm using this equation: γ = (XTX)-1XTy
So I transposed vector of my endogenous variable (added value) yT and XT
yT
39054
48353
55563
65746
73670
84215 100429 112372 120258 130029 131641 149031 163741
Initial matrix X must be transposed as well:
matrix X T
1
16531
11204
327
23769
1
17149
15085
301
38433
1
25102
17035
584
53683
1
20233
18273
654
44822
1
22362
19557
839
35136
1
24239
23202
1002
56173
1
27768
28002
1156
57304
1
28755
30666
1411
33171
1
29052
32971
2772
22771
1
29345
36141
3031
24695
1
29108
39487
4205
21637
matrix XT y
The final econometric equation is then:
y1t = -7329,14 x1t + 0,55x2t + 4,15x4t – 8,21x5t – 0,25 x6t + u1t
1
29101
45218
5282
26708
1
32654
51238
5923
29074
1274102
34733453346.23
41958997813.55
3561768902.49
43056478927.16
matrix (XT X)-1 XT y
-7329.14
0.55
4.15
-8.21
-0.25
1.4. Economic verification
To verify the model I'm going to evaluate influences of particular variables on
the endogenous variable.
-7329,14
+0,55
… Relatively far from average, which is good
… positive value of quantity of enterprises variable conforms to expectations of added
value growth with increasing number of enterprises on the market
+4,15
… there are probably many angels of view for this fact. Let's say that the higher the
expenses for labor in ICT sector are the more qualified and experienced specialists are being employed. The
second explanation might be the fact that companies simply expand and increase such an amount of labor which
produces more added value. One way or another, the positive value of this parameter is expected and matches
economic expectations.
-8,21
… expenditures for research are very long time oriented and economic returnability or
projection into added value could last more then years.
-0,25
… ICT sector in general differs from the others that investments of all kinds
(equipment, technologies, know-how) come from abroad. For instance all kind of hardware which forms
significant part of investments into ICT sector is part of import to Czech Republic. From this implies that added
value grows abroad a lot. On the other hand in Czech Republic it does so only after the investments are reflected
in production growth.
1.5. Statistical verification
Statistical significance of parameters
A matrix for statistical verification of parameters:
matrix (X
T
X) -1
4.49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Calculation of regulated residual variance Su2
Su2=∑(yt-ŷ)/(n-p)= 12776833.53 / 9 = 1 419 648,17
variance of
estimated
parameters
quantity of
enterprises
unit vector
57349527.63
-3240.42
1370
-2976.67
-174.04
expenditures for
research &
development (mil.
CZK)
1370
-2976.67
-0.29
0.97
0.33
-1.43
-1.43
7.32
0
0.09
expenses for labor
(mil. CZK)
-3240.42
0.39
-0.29
0.97
-0.01
investments (mil.
CZK)
-174.04
-0.01
0
0.09
0.01
Calculation of test criterion, errors and parameter significance
errors
test criterion ( α=0,05)
t-value table ( α=0,05)
paramater significance
unit vector
quantity of
enterprises
7572.95
0.97
2.36
no
56.92
0.01
2.36
no
expenses for labor
(mil. CZK)
37.01
0.11
2.36
no
expenditures for
research &
development (mil.
CZK)
54.56
0.15
2.36
no
(y 1 – y avg )2
Coefficient of multiple determination R2
•
equation
◦ R2 = 1 – (Su2/Sy2) =
= 1 - ( 8845500.13 / 1488786191.39 ) = 0,99
• from the value of R2 we can say that changes of
endogenous variable are explained by exogenous
variables from 99%
sum
Sy 2
Su2
Sŷ 2
R2
investments (mil.
CZK)
13.19
0.02
2.36
no
(ŷ 1 – y avg )2
3475601960.48
2465583884.66
1801558173.85
1040846719.7
592329781.89
190250604.96
5863245.01
206325755.61
495080026.31
1025354934.06
1131215271.65
2603315287.32
4320894842.56
19354220488.08
1488786191.39
8845500.13
3407587685.37
2059667632.08
1524729494.18
1221681195.67
759060480.29
323606105.33
5417048.39
319303639.3
361710753.65
883567661.46
1197894258.55
2330744084.81
4811831846.76
19206801885.84
1477446298.91
0.99
Residual auto-correlation with use of Durbin-Watson test DW
•
•
equation
◦ DW = ∑ (ut-u(t-1))2/∑ut2= 1,69
from the result we can say that there is not so alarming presence of autocorrelation in
the residuals. It's only 0,2 – 0,3 points under ideal level
1.6.
Model application
Coefficients of elasticity
•
•
Labor expenses elasticity for year 2007
◦ ∂y/∂x4*(x4/ŷ) = 4,15 * (51238 / 167375) = 1,27
◦ if labor expanses increase about 1% in comparison with the last period of time,
then added value increases about 1,27% in comparison with the last period of time
Investments elasticity for year 2007
◦ ∂y/∂x6*(x6/ŷ) = -0,25 * (29074 / 167375) = -0,04
◦ if investments increase about 1% in comparison with the last period of time, then
added value decreases about 0,04% in comparison with the last period of time
Scenario simulations
•
•
How much should expenses for labor increase for added value to increase to 1000 mil.
CZK ? X4 = ?, y1 = 1000, 4,15x4 = 1000 = > x4 = 240,96
=> expenses for labor would have to increase to 240,96 mil. CZK
How high the quantity of enterprises should be for added value to increase to 4000
mil. CZK? x6 = ?; y1 = 4000; 0,55x2 = 4000 => x2 = 7 272,73
=> quantity of enterprises must
increase to 7272,73 for added value to be 4000 mil. CZK
2.
Simultaneous model
2.1.
•
Economic model and econometric model
I chose two-equations simultaneous model with two endogenous variables: Revenues
and Added value
y1 = economic Value Added in ICT sector (mil. CZ Crowns)
y2 = revenues in ICT sector (mil. CZ Crowns)
x1 = unit vector
x2 = quantity of enterprises
x3 = quantity of employees
x4 = expenses for labor in ICT sector (mil. CZ Crowns)
x5 = expenses for research & development in ICT sector (mil. CZ Crowns)
x6 = investments in ICT sector (mil. CZ Crowns)
Economic Model
•
expenses for labor and research are shared by both endogenous variables because both
EAV and Revenues are very well explained by them. Investments and their cost
explains EAV because it is basically part of calculation of EAV. Quantity of
enterprises and employees influences primarily total revenues in ICT sector, but
obviously it has relation with EAV as well, so we'll see correlation matrix results
Econometric Model
•
based on gained data I put two equations simultaneuos model together :
β11y1t = β12y2t +γ11 x1t +γ14 x4t+γ15 x5t+γ16 x6t +u1t
β22y2t = β21y1t +γ21 x1t +γ22 x2t +γ23 x3t+γ24 x4t + γ25 x5t + u2t
2.2. Dataset
YEARS
Variables
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
average
variance
standard deviation
added value
(mil. CZK)
revenues (mil. quantity of
CZK)
enterprises
quantity of
employees
expenses
for labor
(mil. CZK)
expenses for
research &
development investments
(mil. CZK)
(mil. CZK)
y1
y2
x2
x3
x4
x5
x6
39054
48353
55563
65746
73670
84215
100429
112372
120258
130029
131641
149031
163741
98008
1488786191
38585
85948.44
127345.57
143454.09
160911.29
181936.33
239037.5
291030.34
332608.39
374802.74
444216.35
445108.89
518919.95
598771.55
303392
24828489896
157571
16531
17149
25102
20233
22362
24239
27768
28755
29052
29345
29108
29101
32654
25492
23832492
4882
94782
97182
99005
96744
92690
102448
110605
108900
107036
110386
112316
122490
130936
106578
115935482
10767
11204
15085
17035
18273
19557
23202
28002
30666
32971
36141
39487
45218
51238
28314
140253971
11843
327
301
584
654
839
1002
1156
1411
2772
3031
4205
5282
5923
2114
3493820
1869
23769
38433
53683
44822
35136
56173
57304
33171
22771
24695
21637
26708
29074
35952
158387573
12585
Correlation matrix computation:
• added value equation
I managed to get these results after expressing the values of added value and expenses for
labor and research in year-to-year differences.
expenses for
expenses for research &
development investments
added value labor (mil.
(mil. CZK)
CZK)
(mil. CZK)
(mil. CZK)
added value (mil. CZK)
expenses for labor (mil. CZK)
expenses for research &
development (mil. CZK)
investments (mil. CZK)
y1
x4
x5
x6
1
0.64
0.64
1
-0.16
0.25
0.22
-0.11
-0.16
0.22
0.25
-0.11
1
-0.67
-0.67
1
• revenues equation
After I set up a correlation matrix for revenues equation there was high multiplicity all over
the matrix in practically each relation between random two vectors. I reduced it by computing
year-to-year differences for all vectors which was very satisfying but still there was only one
strong relation between expenses for labor and quantity of employees. It makes sense to
remove “quantity of employees
“ vector from the model for the sake of explanatory variables parameters estimation accuracy.
revenues (mil. CZK)
quantity of enterprises
expenses for labor (mil. CZK)
expenses for research &
development (mil. CZK)
1
0.09
0.74
0.09
1
0.18
0.74
0.18
1
0.03
-0.11
0.25
0.03
-0.11
0.25
1
2.3. Model identification :
•
•
endogenous variables: g = 2
predeterminated variables k = 6
1.equation:
β11y1t = β12y2t +γ11 x1t +γ14 x4t+γ15 x5t+γ16 x6t +u1t => k** = 2, g∆ = 1 => overidentified
2.equation
β22y2t = β21y1t +γ21 x1t +γ22 x2t +γ23 x3t+γ24 x4t + γ25 x5t + u2t => k** = 1, g∆ = 1 => exactly
identified
2.4. Parameters’ estimation using TSLSM and MMVR
TSLSM
1. equation:
Cii = K-1
K-1
0.00000007
0.00423637
0.00423637 253.58439781
-0.00000103
-0.06138426
0.00000072
0.04334294
0.00000005
0.00299251
-0.00000103
-0.06138426
0.00001497
-0.00001053
-0.00000074
0.00000072
0.04334294
-0.00001053
0.00000773
0.00000052
0.00000005
0.00299251
-0.00000074
0.00000052
0.00000004
Vector of estimated parameters:
β2
γ1
γ4
γ5
γ6
1.09
61665.63
-11.14
1.42
0.54
ŷ1t = 1,09y2t + 61665,63 - 11,14 x4t + 1,42 x5t + 0,54 x6t
2. equation:
Cii = K-1
K-1
0.00000007
-0.00430708
0.00000000
0.00000006
-0.00000033
0.00000045
-0.00430708
337.34334335
-0.00032868
-0.00449718
0.02246964
-0.03010631
0.00000000
-0.00032868
0.00000003
0.00000000
-0.00000002
0.00000007
0.00000006
-0.00449718
0.00000000
0.00000006
-0.00000031
0.00000041
-0.00000033
0.02246964
-0.00000002
-0.00000031
0.00000172
-0.00000240
Vector of estimated parameters:
β1
γ1
γ2
γ3
γ4
γ5
5.52
-335348.51
-0.59
3.79
-12.84
34.43
ŷ2t = 5,52y1t - 335348,51 - 0,59 x2t + 3,79 x3t - 12,84 x4t + 34,43 x5t
0.00000045
-0.03010631
0.00000007
0.00000041
-0.00000240
0.00000363
MMVR
1. equation:
•
matrix (W* - kW)
Matrix (W*-kW)
•
56936289.4
14161469.41
14161469.63
3522309.25
roots k
D eterm inant of m atrix (W *-k W )
7.48E + 016
dis c rim inant
k1
k2
k2
-2.26E + 017
5.74E + 033
2.02
1.01
k
•
vector of parameters β
•
vector of parameters γ
Y1 = 4,02Y2 + 235694,64 - 53,6X4 + 31,17X5 + 2,62X6
1.52E + 017
β22=1
Β21=4,02
x1
x4
-235694.64
x5
x6
-31.17
53.6
-2.62
2. equation:
• matrix (W* - kW)
Matrix (W*-kW)
458243572.64
83009578.96
83009579.09
15036959.86
• roots k
Determinant of matrix (W*-kW)
7.48E+016
discriminant
k1
k2
k2
8.35E+032
1.39
1
-1.79E+017
k
1.04E+017
• vector of parameters β
Β22= 1
Β21= 5,52
• vector of parameters γ
Y2 = 5,52Y1 - 335348,51 - 0,59X2 + 3,79X3 - 12,84X4 + 34,43x5
x1
x2
335348.51
x3
0.59
x4
-3.79
x5
12.84
-34.43
control calculations:
1. equation:
• TSLSM
ŷ1t = 1,09y2t + 61665,63 - 11,14 x4t + 1,42 x5t + 0,54 x6t
98007,85 = 1,09*303391,65 + 61665,63 – 11,14*28313,78 + 1,42*2114,45
+0,54*35952
• MMVR
Y1 = 4,02Y2 + 235694,64 - 53,6X4 + 31,17X5 + 2,62X6
Verification v variable averages
average
y1
y2
x1
x2
x3
x4
x5
x6
98007.85 303391.65
1 25492.23 106578.38 28313.78 2114.45
35952
98007.85
=
98007.85
2. equation:
• TSLSM
ŷ2t = 5,52y1t - 335348,51 - 0,59 x2t + 3,79 x3t - 12,84 x4t + 34,43 x5t
303391,65 = 5,52*98007,85 + 335348,51 – 0,59*25492,23 + 3,79*106578,38 –
- 12,84*28313,78 + 34,43*2114,45
• MMVR
Y2 = 5,52Y1 - 335348,51 - 0,59X2 + 3,79X3 - 12,84X4 + 34,43x5
V erific ation v v ariable av erages y 1
y2
x1
x2
x3
x4
x5
x6
av erage
98007.85303391.65
1 25492.23106578.3828313.78 2114.45 35952
303391.65 =
303391.65
2.5. Economic verification
1. equation: parameters of variables of the model
expenses for
expenses for
research & investments
labor (mil.
development (mil. CZK)
CZK)
(mil. CZK)
61665.630 -11.138
1.420
0.537
235694.638 -53.604
31.171
2.624
added value revenues (mil.
1.equation Param eters
Constant
(mil. CZK)
CZK)
TSLSM
MMVR
1.000
1.000
1.086
4.021
1.086 / 4.021 …confirms, that if revenues increase added value increases as well
61665.63 / 235694.638 … both positive values in proper distance from an average
-11.138 / -53.604 … when expenses for labor increase, added value should increase !!
1.42 /
31.171 … increasing added value with increasing expenses for research is
supposed to be right
0.537 / 2.624 … correct
2. equation: parameters of variables of the model
2.equation
Parameters
TSLSM
MMVR
•
revenues (mil.
CZK)
added value
(mil. CZK)
Constant
1.000000000 5.520369788 -335348.514093023
1.000000000 5.520369790 -335348.514168253
expenses for
research &
development
(mil. CZK)
-0.591965655 3.785323428 -12.836305711 34.430551000
-0.591965655 3.785323429 -12.836305717 34.430551008
quantity of
enterprises
quantity of
employees
expenses for
labor (mil. CZK)
parameters of explanatory variables estimated by both methods are almost
identical
-335348 … negative constant value seems a bit invalid
• anyway the rest of the parameters seems perfectly valid and well founded
• expenses for labor behave the same way as they do in the previous equation in relation
with added value. It could be the case, that enterprises might spend more funds for
labor and narrow their budget down so that added value is produced by additional
labor force but potential added value is not produced by the other means then
2.6. Statistical verification
statistical significance of estimated parameters:
1. equation:
y1t = 1,09y2t + 61665,63 - 11,14 x4t + 1,42 x5t + 0,54 x6t
sy2
su2
cor su2
1606937339.21
111763156.19
161435670.05
0.93
0.87
R2
kor R2
•
a value of R tends to be a little higher and expresses higher dependency between
explanatory variables
Sii
Sbi
T-value
t-value table (α=0,1)
t-value table (α=0,05)
paramater significance
y2
11.53
3.4
0.3197
1.83
2.62
no
x1
40937567175
202330.34
0.3048
1.83
2.62
no
x4
2416.08
49.15
-0.2266
1.83
2.62
no
x5
1247.34
35.32
0.0402
1.83
2.62
no
x6
5.96
2.44
0.2199
1.83
2.62
no
2. equation:
y2t = 5,52y1t - 335348,51 - 0,59 x2t + 3,79 x3t - 12,84 x4t + 34,43 x5t
sy 2
su2
cor su2
R2
cor R2
•
24878872137.18
147848672.81
240254093.31
0.99
0.99
a value of R is high and expresses strong dependency between explanatory variables
Sii
Sbi
T-value
t-value table (α=0,1)
t-value table (α=0,05)
paramater significance
y2
15.98
4
1.38
1.86
2.31
no
x1
81048119090.64
284689.51
1.18
1.86
2.31
no
2.7. Matrix B, Γ and matrix M
x2
7.33
2.71
0.22
1.86
2.31
no
x3
14.64
3.83
0.99
1.86
2.31
no
x4
412.53
20.31
0.19
1.86
2.31
no
x5
872.29
29.53
1.17
1.86
2.31
no
matrix Β
matrix Γ
matrix M
1
-5.52
x1
-61665.63
335348.51
-1.09
1
x2
60563.6
-1015.03
matrix -Β −1
0.2
1.11
0.22
0.2
matrix -Β
-1
5.52
1.09
-1
x3
x4
x5
x6
0
0.59
0
-3.79
11.14
12.84
-1.42
-34.43
-0.54
0
0.13
0.12
-0.82
-0.76
5.02
14.88
-7.77
-8.47
-0.11
-0.59
reduced form
y1 = 60563,6x1 + 0,13x2 – 0,82x3 + 5,02x4 - 7,77x5 – 0,11x6
y2 = -1015,03x1 + 0,12x2 – 0,76x3 + 14,88x4 - 8,47x5 – 0,59x6
•
•
differences between structural and reduced form
models in reduced form express dependencies of endogenous only on predetermined
variables, while in structural form endogenous variables are being influenced by
predetermined variables and the others explanatory variables
in the multiplicator matrix of mine we can see that those predetermined variables,
which haven't been part of original equations, have reduced form as a result of
mediation between explanatory variables
2.8. Model application
coefficients of elasticity for 1.equation
• expense elasticity for the last year
expenses for labor
∂y/∂x4*(x4/ŷ) = -11,138 * (51238/165080,3) = -3,46
=> increase of expenses for labor causes decrease of added value about 3,46% in
comparison with the last one
expenses for research
∂y/∂x5*(x5/ŷ) = 1420 * (5923/165080,3) = 0,05
=> increase of expenses for research causes increase of added value about 0,05% in
comparison with the last one
•
investments elasticity for the last year
∂y/∂x6*(x6/ŷ) = 0,537 * (29074/165080,3) = 0,09
=> increase of investments causes increase of added value about 0,05% in comparison
with the last one
3. Conclusion
I suppose this analysis fulfilled the objectives well except of the fact that testing
showed that most of the variables are statistically insignificant which might be influenced by
many factors. For instance it is good to say that the amount of variables I used to explain the
dependencies is not enough to cover this huge sector of market.
References:
http://czso.cz/csu/redakce.nsf/i/ict_sektor – Category “ICT sektor - celkem”