Transcript Why do we need econometrics?

STATA
Introductory manual
1
MADE
QUIZ (for the last time)
•
What are the main OLS
assumptions?
1. On average right
2. Linear
3. Predicting variables and error term
uncorrelated
4. No serial correlation in error term
5. Homoscedasticity
+ Normality of error term
2
MADE
Regression with STATA
• Refresh yourself how we did regressions?
– regress gdppc fdi trade inv school2
– regress gdppc fdi trade inv school2, nocons
Source
3
SS
df
MS
Model
Residual
2.0703e+09
691290985
4
88
517584509
7855579.38
Total
2.7616e+09
92
30017706.8
gdppc
Coef.
fdi
trade
inv
school2
_cons
508.1666
13.57583
-72.10749
110.629
-83.17579
Std. Err.
147.8113
12.64687
39.74305
10.25845
899.459
t
3.44
1.07
-1.81
10.78
-0.09
Number of obs
F( 4,
88)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.001
0.286
0.073
0.000
0.927
=
=
=
=
=
=
93
65.89
0.0000
0.7497
0.7383
2802.8
[95% Conf. Interval]
214.4226
-11.55717
-151.0885
90.24245
-1870.661
801.9106
38.70884
6.873478
131.0155
1704.31
MADE
Diagnostics with STATA
• Normality of the residual
– predict e, residual [directly after regress]
– sktest e [Jarque-Bery test]
Skewness/Kurtosis tests for Normality
Variable
Pr(Skewness)
e
0.025
Pr(Kurtosis)
0.057
joint
adj chi2(2)
Prob>chi2
7.73
0.0210
• RESET test
(so-called omitted variables or functional form test)
– ovtest, rhs
Ramsey RESET test using powers of the independent variables
Ho: model has no omitted variables
F(12, 76) =
3.30
Prob > F =
0.0007
4
MADE
First conclusions
• There is something wrong with the model
specification:
– residuals are not normal (although sample is not
that small)
– some variables seem to demonstrate nonlinearity
• We need to check if it causes problems for
estimation…
5
MADE
Diagnostics with STATA
• Heteroscedasticity
– hettest, rhs [Breush-Pagan test]
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fdi trade inv school2
chi2(4)
Prob > chi2
6
=
=
32.11
0.0000
MADE
Diagnostics with STATA
• Heteroscedasticity
– imtest, white [White test]
White's test for Ho: homoskedasticity
against Ha: unrestricted heteroskedasticity
chi2(14)
Prob > chi2
=
=
30.92
0.0057
Cameron & Trivedi's decomposition of IM-test
7
Source
chi2
df
p
Heteroskedasticity
Skewness
Kurtosis
30.92
9.28
1.43
14
4
1
0.0057
0.0545
0.2319
Total
41.63
19
0.0020
MADE
Diagnostics with STATA
• Autocorrelation
(we would need time, not this dataset)
– tsset t
– dwstat [Durbin-Watson test]
– bgodfrey, lags(1 2 3) [Breush-Godfrey test]
8
MADE
Conclusions
• Model specification is wrong
– sample small and no normality
– omitted variable problem
– for sure heteroscedasticity
(cannot trust standard errors)
=> There is something very wrong!
• Solutions
– we can use robust estimators, but it will not
solve the inconsistency problem
– we need a new model specification
9
MADE
Diagnostics with STATA
• Structural stability [Chow test]
–
–
–
–
–
–
–
–
–
–
10
gen d=0
gen dfdi=0
gen dtrade=0
gen dinv=0
replace d=1 if lat<0 (why so????)
replace dfdi=fdi if lat<0
replace dtrade=trade if lat<0
replace dinv=inv if lat<0
reg gdppc fdi trade inv school2 d dfdi dtrade dinv
test (d=0) (dfdi=0) (dtrade=0) (dinv=0)
MADE
Structure does not seem to be
driving this
Source
SS
df
MS
Model
Residual
2.0905e+09
671139673
8
84
261311169
7989758.01
Total
2.7616e+09
92
30017706.8
gdppc
Coef.
fdi
trade
inv
school2
d
dfdi
dtrade
dinv
_cons
526.6277
12.36589
-111.958
113.815
-3125.048
-53.68357
8.752883
137.5564
641.9922
Std. Err.
171.405
13.84263
47.72409
10.87722
2113.929
377.4741
75.44521
93.96076
1037.978
t
3.07
0.89
-2.35
10.46
-1.48
-0.14
0.12
1.46
0.62
Number of obs
F( 8,
84)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.003
0.374
0.021
0.000
0.143
0.887
0.908
0.147
0.538
=
=
=
=
=
=
93
32.71
0.0000
0.7570
0.7338
2826.6
[95% Conf. Interval]
185.7702
-15.16171
-206.8626
92.18447
-7328.828
-804.3323
-141.2782
-49.29488
-1422.141
867.4853
39.89348
-17.05342
135.4455
1078.732
696.9651
158.784
324.4077
2706.125
. test (d=0) (dfdi=0) (dtrade=0) (dinv=0)
(
(
(
(
1)
2)
3)
4)
d = 0
dfdi = 0
dtrade = 0
dinv = 0
F(
11
4,
84) =
Prob > F =
.
end of do-file
0.63
0.6421
MADE
Job for you now
• Start thinking 
– Maybe there are some variables we should
include in specification?
– Maybe we should start taking logs?
– Maybe interactions?
– Maybe model should be estimated on
subsamples?
• Try drawing things to prove your
approach
12
MADE