econometrie subiect
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Subiecte Econometrie DOFINTRANSCRIPT
DOFIN - Bazele econometriei - 2010NR.2
I. (1,5p) Argumentali scurt gi la obiect validitatea urmdtoarelor afirmalii:1. Dacd P(A):0,1 , P(B):0,5 Si A(\ B =Q atunci P(lw B)= 0,0 .
2. DacdP(B):0,1qi AnB=/ atunci f(l1n)=ft.3. Dacd P(B):0,0s , p(.ql B)= 0,5 ei P(,tlE):0,01 atunci r(n1 t)= 0,8080.
4. Dac6, P(A):0,7 Si P(8):0,6 atunci f(l o B)>0,5 .
5. Dacd P(A):0,5 Si P(8):0,6 atunci este posibil ca Ao B = Q.
II. (1,5p) Argumentali scurt qi la obiect rispunsul la urmdtoarele intrebbri:l. Care sunt caracteristicile unui estimator ,,bun" in large sample?2. Care sunt elementele necesare pentru a efectua un test valid de tip Wald?3. Care sunt ipotezele necesare gi suficiente pentru a asigura consistenla estimatorului OLS
pentru un model liniar?Se considerd un model liniar caracterizat prin variabile explicative exogene qi inovaliiautocorelate. Estimatorul OLS este BLUE?Se considerd un model liniar caracterizat prin variabile explicative exogene qi inovaliiheteroskedastice. Este valid testul / construit pebaza erorilor standard clasice OLS?
III. (1,5p) Se considera un vector aleator bidimensional (X.)') care are funclia de densitate de
reparli{ie data de .f (", y)= (2 - x * y) .lro,,l(x)'1r0.,10).
1. Sa se determine funclia de densitate marginala pentru {'2. Sd se determine P(X < 0.5, Y 30.75), precum si P(f <0.75 | X < 0,5) .
IV. (1,5p) Pentru a analiza timpul scurs dintre doi cumpdrdtori succesivi dintr-un magazin se
urllizeazd. modelul statistic (Tr,Tr,....,f,) t.t.a unde Z este o variabil6 aleatoare avAnd funclia de
densitate de repartilie datd de f (x)= j exp(- i)' 1ro,-r("). Se qtie cd Elrl= e qi VARlrf= 0' .
1. Sa se determine estimatorul MLE pentru parametrul d;2. Sa se determine distribulia asimptotici a estimatorului 0rr, .
V. (1,5p)InurmaestimiriiprinOLSamodeluluiliniarderegresie Z,=fo+frX,+FrY,*q,undea[x]=0.0s,vARfxl=0.t , nlrl=0.r,runfrf=o.z , cov(x.r)=0, cov(Y.t):0 au fost
oblinutele rezultatele prezentate in Anexu.l. Comentali rezultatele;
2. Si se determine ElZ,l si VARlrl.
VI. (1,5p) Se considera urmdtorul model macroeconomic simplificat exprimat in formd structurald:
lY, = C, + NX, (t)
lq = Fo + f,.y, + €, (z)
unde I reprezintd devialia PIB-ul fatl de trend, C devialia consumului fala de trend. 1/X
devialia exporlului net fa![ de trend, E[]']= E[C']= f[,VX] :0. t, sunt inovalii sferice cu medie
0 gi variantd 6) .iar C)V(NX,,a,)= 0.
1. Sd se determine forma redusd a modelului:2. Sd se argumenteze o modalitate de estimare consistentd a parametrilor fi.mcjiei de consum
(i.e. ecuatia 2).
4.
Anexd
Deoendent Variable: Z
Method: Least SquaresSample (adjusted): 3 400
Included observations: 398 after adjustments
Variable Coefficient Std' Error t-Statistic Prob'
c -0.00202 0.001333 -1 515556 0 1304
x -0.320708 0.047913 -6.693574 0 0000
Y 0.197357 0.047658 4 141131 0 0000
R-squared 0.'121839 Mean dependent var -0 00178
Adjusted R-squared 0117392 S'D. dependent var 0'028244
S.E. of regression 0.026497 Akaike info criterion -4 416091
Sum squared resid 0.277318 Schwarz criterion -4'386042
Log likelihood 881 .8021 Hannan-Quinn criter' -4 404189
f-statistic 27.40171 Durbin-Watson stat 1 943491
Prob(F-statistic) 0
Wald Test:Equation: OLS
Test Statistic Value df Probability
F-statistic 0.100899 (2' 395) 0.904
Chi-square 0.201798 2 0'904
Null Hypothesis Summary:
Normalized Restriction (= 0) Value Std Err'
0.3 + C(2) -0.020708 0.047913
-0.2 + C(3) -0.002643 0 047658
Restrictions are linear in coefficients
Breusch-Godfrey Serial Correlation LM Test
F-statisticObs*R-squared
Coefficient Std
c -0 000524
x -0.053761Y -0.254188
RESID(-I) o.27 5916
RESID(-2) 0.105687
R-squared 0.006937
AdjustedR-squared -0.003171
S.E. of regression 0.026472Sum squared resid 0.275394
Log likelihood 883.1874
F-statistic 0.686311
Prob(F-statistic) 0.601773
1 372622 Prob. F(2,393)2.760884 Prob.Chi-Square(2)
0.25470 2515
Test Equation:Dependent Variable: RESID
Method: Least SquaresDafe. O2lO4l10 Time. 12:27
Sample: 3 400lncluded observationsi 398
Presample missing value lagged residuals set to zero
Vanable Error t-Statlstic Prob.
0.001383 -0.378855 0.7050.135257 -0.397474 0.6912
0.160651 -1.582243 0.11440.166996 1.652232 0.0993
0.'153445 0.688764 0.4914
Mean dependent var '1.17E-18
S.D. dependent var 0.02643
Akaike info criterion -4.413002Schwarz criterion -4.362921
Hannan-Quinn criter. -4.393165
Durbin-Walsonstat 1.992666
Heteroskedasticity Tesl: White
F-statistic 0.760469
Obs-R-squared 3.823456
Scaled explained SS 3.35825
Test Equation:Dependent Variable: RESID^2Method: Least SquaresDale: 02lo4l1o Time: 12:32
Sample: 3 400lncluded observations: 398
Variable Coefficient
aXx2
YY^2
0.00071 I0.000246-0.054677-0.065591-0.0009790.034725
Prob. F(5,392)Prob. Chi-Square(5)Prob. Chi-Square(5)
Std. Error lstatistic Prob.
0.57880.57510.6449
10.65468 0
o 144791 0.885-1.226356 0.2208-1.067318 0.2865-0.579163 0.56280.775832 0.4383
6.75E-05o.0017020.0445850.061454
0.001690.0447 59
R-squared 0.009607
AdjustedR-squared -0.003026
S.E. of regression 0.000933
Sum squared resid 0.000341
Log likelihood 2215.132F-statistic 0.760469
-statrstic) 0.578781
Mean dependent var 0.000697
S.D.dependentvar 0.000932
Akaike info criterion -11.10117
Schwaz criterion -11 04107
Hannan-Quinncriler. -11.07736
Durbin-Watson stat 2.039288
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Series: ResidualsSample 3 400Observations 398
Mean 1.17e-18Median 0.000413Maximum 0.076770Minimum -0.073472
Std. Dev. 0 026430Skewness 0.041635Kudosis 2.783442
Jarque-Bera O.892702Probability 0.639959
o bzs -o bso -o bzs 0.ooo o 025 0 oso 0 o7s
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