founded 1348
DESCRIPTION
Charles University. Founded 1348. Austria, Linz 16. – 18. 6. . 2003. Johann Kepler University of Linz. Johann Kepler University of Linz. AN ANALYSIS OF. AN ANALYSIS OF. THE CZECH ECONOMY. THE CZECH ECONOMY. IN TRANSITION. IN TRANSITION. Jan Ámos Víšek. Jan Ámos Víšek. FSV UK. - PowerPoint PPT PresentationTRANSCRIPT
Founded 1348Charles University
Johann Kepler University of LinzJohann Kepler University of Linz
THE CZECH ECONOMYTHE CZECH ECONOMY
FSV UK
STAKAN III STAKAN III
Institute of Economic Studies Faculty of Social Sciences
Charles UniversityPrague
Institute of Economic Studies Faculty of Social Sciences
Charles UniversityPrague
Jan Ámos VíšekJan Ámos Víšek
IN TRANSITIONIN TRANSITION
AN ANALYSIS OFAN ANALYSIS OF
Austria, Linz 16. – 18. 6.. 2003
Schedule of today talk
definiton, properties and how to apply The least trimmed squares
definition The least weighted squares
They utilized -regression
Galileo Galilie (1632) Roger Joseph Bocovich (1757) Pierre Simon Laplace (1793)
(already Francis Ysidro Edgeworth …., 1887)
A motivation for robust regression
1L
(continued)
Schedule of today talk
separating market oriented part from the rest
Looking for the sense of division
dividing the industries into two groups - why
Analyzing the export from and FDI into the Czech republic – 1994
separating market oriented parts from the rest for each year
Analyzing the export from the Czech republic - 1993-1999
Why robust methods in regression ?
What about to consider a minimal elipsoid containing
a priori given number of observations.
So the solution seems to be simple !
continued
Why robust methods in regression ?
continued
Why robust methods in regression ?
(otherwise we lose some useful information)
I am sorry but we have to invent a more intricate solution.
So, for the OLS we have the breakdown point equal zero (asymptotically) !
Minimal number of observations which can cause that estimator breaks down.
Recalling that is breakdown point
Francis Ysidro Edgeworth, 1887
The method of the least squares is seen to be our best course when we have thrown overboard a certain portion of our data - a sort of sacrifice which has often to be made by those who sail the stormy seas of Probability.
One of really applicable 50% breakdown point estimator The Least Trimmed Squares - Rousseeuw (1983)
. )(r...)(r)(r 2)n(
2)2(
2)1(
and that the order statistics are given by
2p
1j
Tii
2i XY)(r
Let us recall that for any the residuals are given as
pR
The optimal . ]2/)1p[(]2/n[h
nhn . )(rminargˆ h
1i
2)i(
R
)h,n,LTS(
1p
Then for any
nh2/n
Continued The Least Trimmed Squares
- evidently 50% breakdown point - scale- and regression-equivariant
- -consistent and asymptotically normal - nowadays easy to evaluate
Advantages
- high subsample sensitivity, i.e. can be (arbitrarily) high
Disadvantage
n
Rousseeuw, Leroy (1987) – PROGRESS First proposal – based on LMS, in fact, the trimmed least squares.
k,h,1n,LTSh,n,LTS ˆˆ
Probably still in S-PLUS, e.g.. It did not work satisfactorily, sometimes very bad.
How to select How to select h h reasonablyreasonably??
Number of points of this „cloud“ is .
is only a “bit” smaller thanh 0k
0k
0kh 0kh
0kh
Algorithm for the case when n is large is described in:
Víšek, J.Á. (1996): On high breakdown point estimation. Computational Statistics (1996) 11, 137 – 146.Víšek, J.Á. (2000): On the diversity of estimates Computational Statistics and Data Analysis, 34, (2000), 67 – 89.Čížek, P., J. Á. Víšek (2000): Least trimmed squares. XPLORE, Application guide, 49 – 64.
One implementation is available in package XPLORE (supplied by Humboldt University), TURBO-PASCAL-version from me, MATLAB version from my PhD-student Libora Mašíček.
High subsample sensitivity, i.e.
Disadvantage of LTS
can be rather large (without control by design of experiment)
k,h,1n,LTSh,n,LTS ˆˆ
Víšek, J.Á. (1999): The least trimmed squares - random carriers.
Bulletin of the Czech Econometric Society, 10/1999, 1 - 30.
Víšek, J.Á. (1996): Sensitivity analysis of M-estimates.
Annals of the Instit. of Statist. Math. 48 (1996), 469 – 495.
Sensitivity analysis of M-estimates of nonlinear regression model: Influence of data subsets.
Annals of the Institute of Statistical Mathematics, 261 - 290, 2002.
See also
Víšek, J.Á. (2002): The least weighted squares I. The asymptotic linearity of normal equations. Bulletin of the Czech Econometric Society, no.15, 31 - 58, 2002. The least weighted squares II. Consistency and asymptotic normality. Bulletin of the Czech Econometric Society, no. 16, 1 - 28, 2002.
Disadvantage of LTS ……
nhn )(rwminargˆ n
1i
2)i(i
R
),n,LWS(
1p
non-increasing
,1)1(,0)0(),1,0()1,0(:)z( The Least Weighted Squares
Hence
)n/i(wi
relying on international trade The Czech Republic - small open economy
The export into EU increased in nineties from 8 billion US$ to 18.4 billion US$, i.e. annually 16.3%.
IN NUMBERS:
Export into EU - 70.7 % 1/3 Germany 1/12 Austria
European transition economies - 20.8 % 1/12 Slovakia
1/19 Poland
“Rest of world” - 8.4 %
HYPOTHESIS
There is an increasing segment of economy
In other words:
There is an increasing segment of economy
- as follows from the previous - oriented on EU.
which is export oriented
which resembles market economy.
91 industries, nearly 40 variables, year 1994
X - export S - sales
US - number of university students HS - number of high school students
TFPW - total factor productivity related to wages DP - price development after opening-up
FDI - foreigner direct investments
VA - value added W - wagesK - capitalBAL - Balasa index
IRS - increasing return from scale
R&D - research and development
CR3 - market power (concentration)
Pattern of variables
The goal of analysis – to find determinants of of the EXPORT and FDI
DATA ABOUT THE CZECH ECONOMY
i4i
i3
i
i2
i
i10
i
i 3CR*VA
K*
VA
HS*
VA
US*
S
X
ii7i6i5 DP*BAL*TFPW*
Variable t-value p-value
US / VA 0.115 0.021 5.298 0.000003
HS / VA 0.189 0.039 4.823 0.000016
K / VA -0.244 0.019 -12.355 0
CR3 1.486 0.322 4.610 0.000032
TFPW -0.979 0.227 -4.300 0.000088
Bal 0.271 0.202 1.339 0.086866
DP 1.180 0.158 7.467 0
52,91,LTS
· h=54
After a lot of experiments we arrived at the model
SEARCHING FOR MODEL FOR EXPORT
No of cases 53 54 55 56 57 58 59
US / VA 0.119 0.115 0.113 0.106 0.124 0.125 -0.051
HS / VA 0.187 0.189 0.201 0.192 0.203 0.426 0.237
K / VA -0.241 -0.244 -0.247 -0.245 -0.251 0.330 -0.233
CR3 1.404 1.486 1.274 1.345 1.153 1.163 2.650
TFPW -0.896 -0.979 -0.937 -1.026 -1.018 0.302 -1.661
Balasa 0.372 0.271 0.106 0.088 0.201 -0.209 0.589
DP 1.097 1.180 1.244 1.249 1.102 0.721 1.194
R-squared 0.850 0.853 0.845 0.831 0.823 0.636 0.650
Chi-square 10.34 7.357 9.937 8.331 9.921 26.34 33.71
Collecting results into the table ….
Subpopulations nested up to size 57 Selected subpopulation
Break in estimates of coefficients
Let us call it “main” subpopulation
(8) (8)(7) (7)(9) (9) (8)
crude petroleum, natural gas (111+112), non-ferrous ores (120+132), sand, stones (141+142), chemicals, minerals (143-145), processing and preserving fruits and vegetables (153), animal oil, fats (154), dairy (155), grain mill products, starches (156), feeds (157), beverages, beers (159), textile fibre (171), textile products (175), knitted and crocheted products (177), leather clothes (181), other outwears (182), furs (183), leather dressing (191), bags, luggages (192), foot-wear (193), impreg-nation of wood (201), plywood and laminboard (202), wood-products (203-205), paper products (212), petroleum-processing (232), pharmacy, botanical products (244), man-made fibres (247),rubber (251), plastics (252), prod. of glass, ceramics (262), bricks and baked clay (264), cement, lime and plaster (265-266), cutting, shaping and finishing stones, nonmetallic minerals (267-268), tubes (272), casting of metals (275), tanks, reservoirs, containers and boilers (282-283), knives, tools and metal products (284-287), machinery for production of power (291), machi-nery-tools (294), special and industrial machinery (295), domestic appliances (297), office machinery and computers (300), el. motors, generators and transformers (311), lighting equipment, el. lamp (315), radio and tv transmitters(322), radio, tv receivers, video recording (323), medical, surgical equipment (331), optical instru-ments, photo equipment (334), clocks, watches (335), motor vehicles (341), bicycles, motorcycles (354), furniture (361), gold and jewellery (362), sports goods, games, toys (364 – 365), production, distribution of electricity (401).
Industries in “main” subpopulation
i4i
i3
i
i2
i
i10
i
i 3CR*VA
K*
VA
HS*
VA
US*
S
X
,DP*BAL*TFPW* ii7i6i5
Variable t-value p-value
US / VA 0.098 0.070 1.389 0.177068
HS / VA 0.920 0.241 3.806 0.000814
K / VA 1.324 0.264 5.013 0.000036
CR3 1.550 1.131 1.369 0.182991
TFPW 3.564 0.994 3.582 0.001434
Balasa -0.079 0.630 -0.125 0.900952
DP 1.076 0.454 2.366 0.026028
33,37,LTS
· h=33
For “complementary” subpopulation - n = 37
Excluded: textile, ready made garment (174), agro- chemistry (242), musical instruments and records (363+223), weapons, ammunition, n.e.c. (296+366)
hard coal (101), lignite and peat (102+103), processing meat and meat products (151), processing fish and fish products (152), (other) food products (158), tobacco (160), textile weaving and the finishing of textiles (172+173), textile articles (174), knitted and crocheted materials (176), impregnation of wood (201), pulp and paper (211), publications and prints (221+222), oven-coke (231), basic chemicals (241), pesticide and agro-chemical products (242), paint-coating prod.(243), soap and detergents (245), manufacture of other chemical products (246), glass and glass products (261), iron and steel (271), metallurgy of iron and steel (273), precious and non-ferrous metals (274), structural metal products (281), other general purpose machinery (292), agriculture and forestry machinery (293), el. distr. equipment and control (312), cables and wires(313), other el. equipment (314-316), electronic components (321), measurement and test. devices(332), control equip-ment (333), trailers and semi-trailers (342),motor vehicles parts and accessories (343-355), buildingand repairing ships and boats (351),railway and tramway locomotives and rollingstock (352), air crafts and space crafts (353), music. instruments and records (363+223), weapons, ammunition, n.e.c. (296 +366).
Industries in “complementary” subpopulation
i
i
i
i
i
i
W
VA*0.558
W
X*0.226-11.13)
W
FDIlog(
iiii
i DP*0.311IRS*4.438VA
D&R*0.0003-
Model for “main” subpopulation
Coefficient of determination = 0.9199 Chi-square = 7.834
h = 54
Again after a lot of experiments we arrived :
SEARCHING A MODEL FOR Foreigner Direct Investments
Subpopulations nested up to the size 56
We decided for 54 due to the increase of sum of squares and partially also due to already known results for export.
(8)
i
i
i
i
i
i
W
D&R*0.0036
W
VA*1.5953.14
W
FDIlog )(
iii TFPW*3.288-IRS*3.026-
Model for “complementary” subpopulation
h = 36 Coefficient of determination = 0.5988 Chi-square = 8.119
Division of the population of 91 industries into the “main” and “complementary” subpopulation is nearly (except of two industries) the same as for export .
(6)
(except of the statistical one that the subpopulations allow to built up reasonable models for EXPORT and for FDI)
Does the division make any sense?
(In other words, what about to study production functions in the respective subpopulations?)
What about a relation between LABOR and CAPITAL ?
DEPENDENCE of
on standardized labor (L / S)
standardized capital (K / W)
All 91 observations
DEPENDENCE of
on standardized labor (L / S)
standardized capital (K / W)
“Main” subpopulation
DEPENDENCE of
on standardized labor (L / S)
standardized capital (K / W)
“Complementary” subpopulation
Taking into account previous graphs, we should try to fit:
)1(i
i
i11
i
i
L
S*ba
W
K (1)
)2(i
i
i22
i
i
S
L*ba
W
K (2)
“Main” subpopulation “Complementary” subpopulation
h 50 51 52 53 54 55
“Main” 0.739 0.740 0.743 0.744 0.745 0.746
“Complementary” 0.180 0.181 0.168 0.137 0.130 0.131
Coeffs of determination of model (1)
h 41 40 39 38 37 36
“Main” 0.104 0.109 0.110 0.116 0.122 0.128
“Complementary” 0.557 0.549 0.557 0.542 0.544 0.535
Coeffs of determination of model (2)
Taking into account that IRS was significant factor for FDI-models:
h 50 51 52 53 54 55
2.69 2.71 2.73 2.74 2.76 2.77
determination .403 .407 .412 .415 .419 .422
Estimates for “main” subpopulation
h 41 40 39 38 37 36
-.97 -.96 -.95 -.94 -.93 -.93
determination .471 -.95 .462 .457 .452 .446
1,0,01,0
/L)1(KQ
CES
2
1
2
1
S/Lexp*W/Kexp
Estimates for “complementary” subpopulation
Conclusion from the analysis of 1994-data:
i.e. it was probably already market-economy-oriented group of industries.
There was (already in 1994) a part of economy which had standard production function,
61 industries, only 8 variables, years 1993 - 99
X - export
PE - export prices
K - capital L - labor DE - debts
FDI - foreigner direct investments
TAR - tariffs from the Czech republic into EU
M - import PI - import prices
VA - value added
DATA ABOUT THE CZECH ECONOMY
TAR - tariffs from EU into the Czech republic EU
CZ
(only EXPORT will be referred)
The goal of analysis - to find a model for the EXPORT and for the IMPORT.
Of course, the data were processed as panel data …..
determination Durbin-Watson White
0.963 1.639 31.430
p-values <.003 .000
it1t,i21it )Xlog(*)Xlog(
Result:
1t,iX
t-value p-value
intercept 0.337 0.208 1.617 [.107]
0.979 0.022 44.21 [.000]
by White estimate
…but also per years !
)PElog(*)PIlog(*)Xlog( 210
)VA/DElog(*)L/Klog(*)VAlog(* 543
)TARlog(*)FDIlog(* EU76
We arrived at the model
As we wanted to see a possible development of common factors (common for all years) in time, we tried to find factors which are significant (or nearly significant) throughout the whole studied period.
Similar analysis, as was presented for 1994, was carried out for every year starting with 1993 to 1999.
SizeOfSam. 33 34
35 36 37 38 39 40
Intercept 15.25 15.28 14.480 14.03 14.23 23.15 22.35 22.30
log(PI) -0.613 -0.626 -0.582 -0.549 -0.481 -0.785 -0.722 -0.699
log(PE) 0.405 0.407 0.373 0.364 0.277 0.145 0.120 0.098
log(VA) 0.408 0.398 0.381 0.396 0.392 0.695 0.614 0.613
log(K/L) -0.754 -0.741 -0.637 -0.592 -0.602 -1.430 -1.394 -1.391
log(DE/VA) 0.566 0.563 0.589 0.504 0.488 0.818 0.895 0.899
log(FDI) 0.538 0.541 0.542 0.497 0.473 0.302 0.369 0.378
log(TAR) -0.679 -0.671 -0.667 -0.500 -0.477 -1.435 -1.422 -1.428
Example of processing data for 1993
R-squared 0.980 0.975 0.972 0.964 0.959 0.972 0.970 0.968
D-W <0.997 <0.983 <0.983 <0.960 <0.883 <0.528 <0.333 <0.836
Chi-Square 0.451 0.633 0.579 0.302 0.195 0.017 0.170 0.178
Jarque-Bera 0.827 0.806 0.524 0.546 0.541 0.282 0.326 0.330
White 0.377 0.437 0.406 0.456For this sizes TSP did not give p-values
p-values of the respective tests
All explanatory variables are significant throughout 1993 – 99 except of log(DE/VA) in years 1996 and 1998.
Year 1993 1994 1995 1996 1997 1998 1999
Size of sub. 37 54 55 54 54 48 54
Intercept 14.23 17.19 15.92 11.84 11.84 12.77 12.26
log(PI) -0.481 -0.659 -0.552 -0.516 -0.516 -0.588 -0.518
log(PE) 0.277 0.396 0.400 0.551 0.551 0.707 0.588
log(VA) 0.392 0.607 0.668 0.861 0.861 0.818 0.857
log(K/L) -0.602 -0.906 -0.828 -0.498 -0.498 -0.663 -0.682
log(DE/VA) 0.488 0.546 0.403 0.350 0.350 0.101 0.252
log(FDI) 0.473 0.403 0.311 0.164 0.164 0.275 0.210
log(TAR) -0.477 -1.143 -0.915 -0.643 -0.643 -0.840 -0.741
Optimal models for individual years 1993 – 1999
Year 1993 1994 1995 1996 1997 1998 1999
Size of sub. 37 54 55 54 54 48 54
R-squared 0.959 0.809 0.799 0.867 0.856 0.929 0.886
0.072 0.448 0.454 0.228 0.347 0.166 0.302
D-W <0.883 <.918 1.677 <.980 <.819 <.711 <.458
0.195 0.569 0.252 0.711 0.154 0.671 0.031
Shapiro-Wilk 0.301 0.183 0.114 0.315 0.810 0.997 0.084
Jarque-Bera 0.541 0.428 0.329 0.686 0.703 0.934 0.516
LM-test 0.072 0.821 0.128 0.005 0.003 0.987 0.141
White test 0.377 0.393 0.242 0.225 0.290 0.959 0.111
Other characteristics of the “optimal” models for 1993 – 1999
2
2
p-values of respective tests
93 37 1 4 6 7 9 10 11 12 16 21 23 24
94 54 7 12 19 23
95 55 1 7 12 23 24
96 49 1 4 6 7 9 12 23 24
97 54 1 4 7 13 23
98 48 1 7 9 13 16 23 24
99 54 1 7 9 13 23
Year
Size
of
subp
opul
atio
n
List of atypical industries
Mea
tCor
nSu
gar
Coff
ee, t
eaO
ther
food
Drin
ksTo
bacc
oPe
ltSe
eds
Pulp
Iron
Coa
l, co
keG
asA
nim
al o
il
93 37 25 26 27 30 33 34 36 38 42 44 49 53 58
94 54 34 36 49
95 55 36 49
96 49 25 26 34 49
97 54 25 49
98 48 25 30 32 34 36
99 54 25 36
Year
Size
of
subp
opul
atio
n
continued
List of atypical industries
Veget
able
oil
Man
ufac
.oil
Org
an.ch
emist
r.
Pharm
acy
Parfu
mer
yPl
astic
sM
anuf
ac. p
lasti
cs
Leath
ers
Woo
dIr
on, s
teel
Met
al p
rod.
Bus
ines
s mac
hine
Tran
spor
t equ
ip.
Shoe
s
0
10
20
30
40
50
60
1993 1994 1995 1996 1997 1998 1999
SIZES OF SUBPOPULATIONS
WHICH WERE SELECTED
54
37
55
49
54
48
54
Floating exchange rate
Saving packages
Despite the government measures the economy is able to help itself.
Exaggerating a bit we may say:
THANKS for A
TTENTION