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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 Presentation

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Page 1: Founded 1348

Founded 1348Charles University

Page 2: Founded 1348

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

Page 3: Founded 1348

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

Page 4: Founded 1348

(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

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Why robust methods in regression ?

What about to consider a minimal elipsoid containing

a priori given number of observations.

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So the solution seems to be simple !

continued

Why robust methods in regression ?

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continued

Why robust methods in regression ?

(otherwise we lose some useful information)

I am sorry but we have to invent a more intricate solution.

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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

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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.

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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

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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.

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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

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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.

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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

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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

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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%.

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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 %

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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.

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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

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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

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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)

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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

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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)

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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

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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)

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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)

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(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 ?

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DEPENDENCE of

on standardized labor (L / S)

standardized capital (K / W)

All 91 observations

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DEPENDENCE of

on standardized labor (L / S)

standardized capital (K / W)

“Main” subpopulation

Page 30: Founded 1348

DEPENDENCE of

on standardized labor (L / S)

standardized capital (K / W)

“Complementary” subpopulation

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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)

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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

Page 33: Founded 1348

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,

Page 34: Founded 1348

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.

Page 35: Founded 1348

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 !

Page 36: Founded 1348

)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.

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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

Page 38: Founded 1348

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

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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

Page 40: Founded 1348

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

Page 41: Founded 1348

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

Page 42: Founded 1348

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:

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THANKS for A

TTENTION