*Heteroskedasticity
* Serial correlation
* Multicollinerity
* Normality
* Omitted variables
*
*What’s Heteroskedasticity?
*
Prototype
*
* Error learning  misal: belajar mengetik
* Sampel yang beragam  rumahtangga dgn pendptn, perusahaan
berbagai level
* Adanya outlier
* Omitting variables
* Sebaran data tidak normal
* incorrect data transformation (e.g., ratio or first difference
transformations) and
* incorrect functional form (e.g., linear versus log–linear models)
*  lebih sering terjadi pada data cross section
*
*BLUE?
* Linear Unbiased but not efficient  LU
Which is the
Homoscedastic?
Homoscedastic?
*KO
* Bagaimana estimasi yg diperoleh terkait varians yg tidak konstan?
* - Signifikansi ?
* - CI
?
*  misleading …
*
* Nature of problem (functional form review )
* Periksa Grafik residual
* Tes statistik
*
* Bahwa residual berkorelasi dengan varians
*Park Test
*  𝛽 signifikan  residuals are heteroskedastic
*  weakness: may not satisfy the OLS assumptions and may itself be
heteroscedastic
*Glejser Test
*  weakness: the error term vi has some
problems in that its expected value is nonzero,
it is serially correlated and ironically it is
heteroscedastic, some models are non linear.
*
H0: residuals are homoskedastic
H1: residuals are heteroskedastic
* Goldfeld-Quandt Test: the heteroscedastic variance, σ2i , is
positively related to one of the explanatory variables in the
regression model, ex:

*  σ2i
would be larger, the larger the values of Xi
* Weakness:
* - depend on which c is arbitrary,
* - for X > 1 Var, which X is correct to be ordered?
*
* Y = Income,
* X = Consumption,
* n = 30,
*c = 4
*
* Y = Income,
X = Consumption, n = 30, c = 4
* Breusch–Pagan–Godfrey Test
Ex: 
So, H0:
 residuals are Homoskedastic
* Weakness: - large sample needed  for small sample, depend much
on normality assumption
ESS = SSR
*
*𝜒2
1,5% = 3,8414
* White’s General Heteroscedasticity Test.
H0: residuals are homoskedastic
Or H0:

, df = # parameter -1
* Weakness: more variables will consume more df.
* Koenker–Bassett (KB) test.
Obtain residual, then estimate
* H0: residuals are homoskedastic
* Or H0: 𝛼2 = 0
* Tes hipotesis using t-test
*
* Find other references…
*
Perhatikan 𝛽1 &
𝛽2
Reparameterize before analize !
Reparameterize before analize !
* Practically, run OLS first, then run:
*  consistent estimator  large sample needed
*  𝛽 measure the elasticity
*
* Run the following (weighted) regression:
Apa
perbedaan
kedua model
ini?
* Compare with the unweighted
* White suggests:
* For RLB:
*
*
* Pelajari Gujarati, Basic
Econometrics, 14th edition,
* Ch. 11, section 11.7