an empirical investigation of economic growth and debt
TRANSCRIPT
University of PiraeusDepartment of Economics
An empirical investigation of economic growth and debt
Dimitrios KiritsisDonatela SalaiAntzela Ouroutsi
Piraeus, June 2015
05/02/23
Outline• Motivation• Graph• Model• Data• Results• Estimated Model• Robustness • Conclusions / References
Motivation
050
100
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050
100
1990 1995 2000 2005 2010
1990 1995 2000 2005 2010 1990 1995 2000 2005 2010 1990 1995 2000 2005 2010
Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden
aveY aveD
YEAR
Graphs by COUNTRY
050
100
150
200
gdpc
1
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
Data: Graphs0
5010
015
020
0IN
VESTM
ENT
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
grY
INVESTMENT
DEBT
DEBT2
SPENDING
NX
gdpc1
grL
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Model
• Solow (1956), Barro(1991), Checherita & Rother(2012)
• grY= ai+ a1 (Yt=o/popt=o) + a2 (Iit/Yit )+ a3 (grL/Yit )+ a4(Debtit/Yit)+a5 (Debtit/Yit)2+a6Zit + εit
Where, grY= Growth rate of GDP(constant 2005 US$) Iit/Yit= Investment (% of GDP)grL=Growth rate of labor (% of GDP)Debtit/Yit =Central government debt, total (% of GDP)pop=Population, totalZi, i=1,2,1= Net Exports (% of GDP) 2= General government final consumption expenditure (% of GDP)
• Expectations
a1 (-),a2 (+),a3 (+),a4 (?),a5 (?),a6.1 (+),a6.2 (-)
Data• Countries : Austria, Canada, Czech Republic, Denmark,
Hungary, Jordan, Nepal, Philippines, Sweden
• Time span : 1992/1995-2009
• Source : World Bank Indicator (WDI)
Results
legend: * p<0.05; ** p<0.01; *** p<0.001 chi2 6.4284401 12.240685 r2 .04197068 .04197068 .04172097 .04172097 F .98258207 .92213949 .9142853 59.628946 N 165 165 165 165 165 165 _cons -15.339304 -15.339304 -55.543446 -55.543446 -15.630745 -15.630745 spending1 -.04413878 -.04413878 -.04616899 -.04616899 -.04715415 -.04715415 nx1 .28741468 .28741468 .51525676* .51525676 .31738452* .31738452 DEBT2 -.07007356 -.07007356 .1672875 .1672875 -.03473157 -.03473157 debt1 .13477337 .13477337 -.16215063 -.16215063 .08004625 .08004625 grL -9.2102274 -9.2102274 -7.0790251 -7.0790251 -9.0514295 -9.0514295 investment1 .17164389 .17164389 .14412825 .14412825 .16441599 .16441599 gdpc1 -.05219032 -.05219032 .21033939 .21033939 -.05389926 -.05389926 Variable OLSdefault OLSrobust FEdefault FErobust REdeafault RErobust
Estimated Model: POOLED OLS• Hausman test between Fixed effects model and Random effects resulted in Random effects model.
After that, by having the xttest we resulted in OLS default model.
• grY= -15.33-0.05gdpc1+0.17investment1-9.2grL+0.13debt1-0.07DEBT2+0.28nx1-0.44spending1+ εit (0.51) (0.32) (1.18) (1.65) (0.46) (0.25) (1.89) 0.31)
Note: Number in parenthesis are t-valuesDiagnosticsNumber of obs = 165F( 7, 157) = 0.98 Prob > F = 0.4459 R-squared = 0.0420Adj R-squared = -0.0007 Root MSE = 84.294
Free: Multicolinearity, Hetteroskedasticity, Autocorrelation
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RobustnessDummies:
D for net exporting countries VS net importing countries.Group A= Net exporters: Hungary, Nepal, Jordan, Philippines, Czech RepublicGroup B= Net importers: Austria, Canada, Denmark, Sweden
grY= 18.72- 0.12gdpc1+0.05investment1-3.48grL-0.07debt1+0.04DEBT2+0.08nx1-0.08spending1+0.04D+εit (1.59) (2.01) (0.99) (1.27) (1.64) (0.47) (1.50) ( 1.84) (0.07)
Note:Number in parenthesis are t-values
DiagnosticsNumber of obs = 165F( 8, 150) = 0.74 Prob > F = 0.66 R-squared = 0.0377Adj R-squared = -0.0136 Root MSE = 36,37
Free: Multicolinearity, Hetteroskedasticity, Autocorrelation
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Conclusions
• a7: (Net Exports (% of GDP) positive effect and statistical significant
Daniel Lederman & William F. Maloney (2003): "Trade Structure and Growth”, World Bank Policy Research Working Paper, No. 3025
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Appendix1.Multicolinearity
0.0087 0.0000 0.7706 0.0477 0.3279 0.0019 spending1 -0.1908* -0.3427* 0.0221 0.1508* 0.0717 0.2250* 1.0000 0.5177 0.6236 0.0000 0.1889 0.8798 nx1 -0.0475 0.0360 0.4561* 0.1004 -0.0111 1.0000 0.5871 0.9230 0.9696 0.0000 DEBT2 -0.0399 0.0071 0.0029 0.8574* 1.0000 0.0294 0.0002 0.7210 debt1 -0.1656* -0.2772* 0.0280 1.0000 0.0000 0.1505 grL -0.4360* 0.1085 1.0000 0.0032 investment1 0.2142* 1.0000 gdpc1 1.0000 gdpc1 invest~1 grL debt1 DEBT2 nx1 spendi~1
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Graph matrix
INVESTMENT
DEBT
DEBT2
SPENDING
NX
gdpc1
grL
0
100
200
0 100 200
0
100
200
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0
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0
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-5
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-5 0 5 10
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2.Heteroskedasticity
Prob > chi2 = 0.0000 chi2(1) = 318.94
Variables: fitted values of grY Ho: Constant varianceBreusch-Pagan / Cook-Weisberg test for heteroskedasticity
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-500
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00R
esid
uals
0 50 100 150 200INVESTMENT -5
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Res
idua
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0 50 100 150 200DEBT
-500
050
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esid
uals
0 50 100 150 200DEBT2
-500
050
010
00R
esid
uals
0 50 100 150 200 SPENDING
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-500
050
010
00R
esid
uals
0 50 100 150 200NX
-500
050
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00R
esid
uals
0 50 100 150 200gdpc1
-500
050
010
00R
esid
uals
-5 0 5 10grL
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esid
uals
-500 0 500 1000Residuals, L
3.Autocorrelation
-500
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esid
uals
1990 1995 2000 2005 2010YEAR
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Histograms0
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity grYnormal grY
Den
sity
grY
Graphs by COUNTRY
0.0
2.0
4.0
60
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Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity investment1normal investment1
Den
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INVESTMENT
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0.01
.02
.03
.04
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.02
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity DEBT2normal DEBT2
Den
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DEBT2
Graphs by COUNTRY
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity debt1normal debt1
Den
sity
DEBT
Graphs by COUNTRY
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0.05
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity spending1normal spending1
Den
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SPENDING
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.04
.06
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0.02
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.06
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity nx1normal nx1
Den
sity
NX
Graphs by COUNTRY
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0.2
.4.6
.80
.2.4
.6.8
0.2
.4.6
.8
-5 0 5 10 -5 0 5 10 -5 0 5 10 -5 0 5 10
Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity grLnormal grL
Den
sity
grL
Graphs by COUNTRY
0.02
.04
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0.02
.04
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0.02
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.08
0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200
Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden Total
Densitykdensity gdpc1normal gdpc1
Den
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gdpc1
Graphs by COUNTRY
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Nepal Philippines Sweden
grY
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Nepal Philippines Sweden
DEBT
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Box Plots
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Nepal Philippines Sweden
INVESTM
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden
DEBT2
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Denmark Germany Hungary Jordan
Nepal Philippines Sweden
SPENDIN
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden
NX
Graphs by COUNTRY-5
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Austria Belgium Canada Czech Republic
Denmark Germany Hungary Jordan
Nepal Philippines Sweden
grL
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00gr
Y
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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DEBT
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
Time Series Plots
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INVESTM
ENT
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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DEBT2
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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SPEN
DIN
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1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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NX
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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gdpc
1
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
-50
510
grL
1990 1995 2000 2005 2010YEAR
Austria BelgiumCanada Czech RepublicDenmark GermanyHungary JordanNepal PhilippinesSweden
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OLS regression
_cons -15.3393 30.31154 -0.51 0.614 -75.21033 44.53173 spending1 -.0441388 .1402229 -0.31 0.753 -.3211056 .2328281 nx1 .2874147 .1522237 1.89 0.061 -.0132559 .5880853 DEBT2 -.0700736 .2819926 -0.25 0.804 -.6270623 .4869151 debt1 .1347734 .2947508 0.46 0.648 -.4474152 .7169619 grL -9.210227 5.576763 -1.65 0.101 -20.22539 1.804934 investment1 .1716439 .145282 1.18 0.239 -.1153156 .4586034 gdpc1 -.0521903 .1614234 -0.32 0.747 -.371032 .2666514 grY Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 1164430.82 164 7100.18792 Root MSE = 84.294 Adj R-squared = -0.0007 Residual 1115558.86 157 7105.47047 R-squared = 0.0420 Model 48871.9553 7 6981.7079 Prob > F = 0.4459 F( 7, 157) = 0.98 Source SS df MS Number of obs = 165
05/02/23
OLS ROBUST REGRESSION
_cons -15.3393 36.83956 -0.42 0.678 -88.10441 57.4258 spending1 -.0441388 .0721213 -0.61 0.541 -.186592 .0983144 nx1 .2874147 .2141141 1.34 0.181 -.1355012 .7103306 DEBT2 -.0700736 .1229083 -0.57 0.569 -.3128408 .1726936 debt1 .1347734 .1985307 0.68 0.498 -.2573624 .5269091 grL -9.210227 6.510922 -1.41 0.159 -22.07053 3.650075 investment1 .1716439 .1327669 1.29 0.198 -.0905959 .4338837 gdpc1 -.0521903 .1028187 -0.51 0.612 -.2552767 .1508961 grY Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust
Root MSE = 84.294 R-squared = 0.0420 Prob > F = 0.4910 F( 7, 157) = 0.92Linear regression Number of obs = 165
05/02/23
FIXED EFFECTS REGRESSION
F test that all u_i=0: F(10, 147) = 0.77 Prob > F = 0.6555 rho .10715023 (fraction of variance due to u_i) sigma_e 84.912681 sigma_u 29.415749 _cons -55.54345 110.2938 -0.50 0.615 -273.5097 162.4229 spending1 -.046169 .321996 -0.14 0.886 -.6825083 .5901703 nx1 .5152568 .2222177 2.32 0.022 .0761027 .9544108 DEBT2 .1672875 .3560571 0.47 0.639 -.5363645 .8709395 debt1 -.1621506 .376068 -0.43 0.667 -.9053487 .5810475 grL -7.079025 6.372888 -1.11 0.268 -19.67334 5.515288 investment1 .1441282 .2174411 0.66 0.508 -.2855862 .5738427 gdpc1 .2103394 1.047617 0.20 0.841 -1.859996 2.280675 grY Coef. Std. Err. t P>|t| [95% Conf. Interval]
corr(u_i, Xb) = -0.6502 Prob > F = 0.4972 F(7,147) = 0.91
overall = 0.0275 max = 17 between = 0.1002 avg = 15.0R-sq: within = 0.0417 Obs per group: min = 12
Group variable: country1 Number of groups = 11Fixed-effects (within) regression Number of obs = 165
05/02/23
FIXED EFFECTS ROBUST REGRESSION
rho .10715023 (fraction of variance due to u_i) sigma_e 84.912681 sigma_u 29.415749 _cons -55.54345 82.9764 -0.67 0.518 -240.4264 129.3395 spending1 -.046169 .1136933 -0.41 0.693 -.2994935 .2071555 nx1 .5152568 .3167473 1.63 0.135 -.1905001 1.221014 DEBT2 .1672875 .2132061 0.78 0.451 -.3077652 .6423402 debt1 -.1621506 .2025012 -0.80 0.442 -.6133513 .2890501 grL -7.079025 5.426396 -1.30 0.221 -19.16979 5.011739 investment1 .1441282 .1232121 1.17 0.269 -.1304054 .4186619 gdpc1 .2103394 .4977539 0.42 0.682 -.8987255 1.319404 grY Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust (Std. Err. adjusted for 11 clusters in country1)
corr(u_i, Xb) = -0.6502 Prob > F = 0.0000 F(7,10) = 59.63
overall = 0.0275 max = 17 between = 0.1002 avg = 15.0R-sq: within = 0.0417 Obs per group: min = 12
Group variable: country1 Number of groups = 11Fixed-effects (within) regression Number of obs = 165
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RANDOM EFFECTS REGRESSION
rho .03090386 (fraction of variance due to u_i) sigma_e 84.912681 sigma_u 15.163361 _cons -15.63075 34.21572 -0.46 0.648 -82.69232 51.43083 spending1 -.0471542 .1594549 -0.30 0.767 -.3596799 .2653716 nx1 .3173845 .1610536 1.97 0.049 .0017253 .6330437 DEBT2 -.0347316 .2940462 -0.12 0.906 -.6110515 .5415883 debt1 .0800463 .3110469 0.26 0.797 -.5295944 .6896869 grL -9.051429 5.668779 -1.60 0.110 -20.16203 2.059173 investment1 .164416 .1572259 1.05 0.296 -.1437411 .4725731 gdpc1 -.0538993 .1838381 -0.29 0.769 -.4142153 .3064168 grY Coef. Std. Err. z P>|z| [95% Conf. Interval]
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.4907 Wald chi2(7) = 6.43
overall = 0.0414 max = 17 between = 0.2184 avg = 15.0R-sq: within = 0.0339 Obs per group: min = 12
Group variable: country1 Number of groups = 11Random-effects GLS regression Number of obs = 165
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RANDOM EFFECTS ROBUST REGRESSION
rho .03090386 (fraction of variance due to u_i) sigma_e 84.912681 sigma_u 15.163361 _cons -15.63075 29.46528 -0.53 0.596 -73.38163 42.12014 spending1 -.0471542 .0762171 -0.62 0.536 -.1965368 .1022285 nx1 .3173845 .2169167 1.46 0.143 -.1077644 .7425334 DEBT2 -.0347316 .040545 -0.86 0.392 -.1141984 .0447352 debt1 .0800463 .0630397 1.27 0.204 -.0435093 .2036018 grL -9.051429 6.076613 -1.49 0.136 -20.96137 2.858513 investment1 .164416 .1047209 1.57 0.116 -.0408332 .3696652 gdpc1 -.0538993 .0696405 -0.77 0.439 -.1903922 .0825937 grY Coef. Std. Err. z P>|z| [95% Conf. Interval] Robust (Std. Err. adjusted for 11 clusters in country1)
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0929 Wald chi2(7) = 12.24
overall = 0.0414 max = 17 between = 0.2184 avg = 15.0R-sq: within = 0.0339 Obs per group: min = 12
Group variable: country1 Number of groups = 11Random-effects GLS regression Number of obs = 165
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HAUSMAN TEST
Prob>chi2 = 0.9238 = 2.54 chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
Test: Ho: difference in coefficients not systematic
B = inconsistent under Ha, efficient under Ho; obtained from xtreg b = consistent under Ho and Ha; obtained from xtreg spending1 -.046169 -.0471542 .0009852 .279742 nx1 .5152568 .3173845 .1978722 .1531093 DEBT2 .1672875 -.0347316 .2020191 .2007823 debt1 -.1621506 .0800463 -.2421969 .2113693 grL -7.079025 -9.051429 1.972404 2.911811 investment1 .1441282 .164416 -.0202877 .1502021 gdpc1 .2103394 -.0538993 .2642386 1.031361 FEdefault REdeafault Difference S.E. (b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients
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XTTEST
Prob > chibar2 = 0.1501 chibar2(01) = 1.07 Test: Var(u) = 0
u 229.9275 15.16336 e 7210.163 84.91268 grY 7100.188 84.26261 Var sd = sqrt(Var) Estimated results:
grY[country1,t] = Xb + u[country1] + e[country1,t]
Breusch and Pagan Lagrangian multiplier test for random effects
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OUTLIERS
4
5
67
8910111213
1415161718222324252627
28
293031323334
35
363839404142434445
46474849505152535456
57
5859
60
6162636465
66
67686970
71
75
76777879808182838485
86
87
88
89
919293949596979899100101102103104
106107
108109110111112113114
115116
117118
119
121
122
123124125126127128129
130131132
133
134
135
136137
139140141142143144
145146147148149150151152153154157158
159
160161
162163
164
165
166167
168175176177178179180181182183184185186187188
0.0
5.1
.15
.2.2
5Le
vera
ge
0 .2 .4 .6 .8Normalized residual squared
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MODEL ESTIMATED WITH DUMMIES
_cons -14.23622 32.29801 -0.44 0.660 -78.03407 49.56163 D 2.119791 20.92297 0.10 0.919 -39.20908 43.44866 nx1 .2750279 .1956191 1.41 0.162 -.1113761 .6614319 spending1 -.0448741 .1408541 -0.32 0.750 -.3231014 .2333533 DEBT2 -.0805595 .3012248 -0.27 0.789 -.6755651 .5144462 debt1 .142824 .3061754 0.47 0.642 -.4619605 .7476084 grL -9.263999 5.619544 -1.65 0.101 -20.36421 1.836215 investment1 .1677051 .1508384 1.11 0.268 -.1302442 .4656543 gdpc1 -.0540443 .1629653 -0.33 0.741 -.3759476 .267859 grY Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 1164430.82 164 7100.18792 Root MSE = 84.561 Adj R-squared = -0.0071 Residual 1115485.47 156 7150.54786 R-squared = 0.0420 Model 48945.3524 8 6118.16905 Prob > F = 0.5554 F( 8, 156) = 0.86 Source SS df MS Number of obs = 165
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MODEL ESTIMATED WITHOUT OUTLIERS
_cons 18.8192 13.27504 1.42 0.158 -7.411017 45.04943 D .148982 9.069299 0.02 0.987 -17.77109 18.06906 nx1 .0875015 .0819643 1.07 0.287 -.0744521 .2494552 spending1 -.082107 .0580944 -1.41 0.160 -.196896 .0326819 DEBT2 .0573976 .1683864 0.34 0.734 -.275318 .3901132 debt1 -.0846599 .1689968 -0.50 0.617 -.4185816 .2492617 grL -3.430181 2.656401 -1.29 0.199 -8.678978 1.818616 investment1 .0577803 .062812 0.92 0.359 -.0663302 .1818908 gdpc1 -.1222888 .0692928 -1.76 0.080 -.2592049 .0146272 grY Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 184211.26 158 1165.89405 Root MSE = 34.377 Adj R-squared = -0.0136 Residual 177262.012 150 1181.74675 R-squared = 0.0377 Model 6949.24851 8 868.656064 Prob > F = 0.6604 F( 8, 150) = 0.74 Source SS df MS Number of obs = 159