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EKONOMETRIKA TERAPAN (Pertemuan #2) Pengajar: Dr. Vera Lisna, S.Si, M.Phil 1

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2 MODEL REGRESI LINIER BERGANDA DATA PANEL (Single Equation)

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Metodologi Ekonometrika Berdasarkan Jenis Data DATA CS TS PANEL UnivariateMultivariate Correlation Regression Multivariate analysis Regression AR, MA ARMA ARIMA ARCH, GARCH Correlation Regression Granger Causality VAR ECM, VECM Pooled Fixed Effect Random Effect 3

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1.Pooled Data Pooling of TS and CS data 2.Combination of TS and CS data 3.Micropanel data 4.Longitudinal data a study over time of a variable or group of subjects 5.Event history analysis studying the movement over time of subjects through successive states of conditions 6.Cohort analysis e.g. following the career path of 1965 graduates of a business school 4 Some Well-Known Panel Data Sets PANEL DATA PANEL DATA REGRESSION MODEL

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1.Panel data relate to individuals over time there is a bound to heterogeneity controlling for individual heterogeneity 2.By combining TS and CS data more informative, more variability, less collinearity among the varibles, more df, and more efficiency Note: df ↑ : distribusi mendekati normal 3.By studying the repeated CS of observation Better able to study the dynamics of adjustments 4.Better able to identify and measure effects that are simply not detectable in pure CS or TS data 5.Allow us to construct and test more complicated behavioral models than purely CS or TS data 6.By making data available for several thousand units minimize bias 5 Advantages of panel data PANEL DATA CAN ENRICH EMPIRICAL ANALYSIS

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1.Design and data collection problems includes coverage (incomplete account of individual or period), nonresponse (lack of respondent cooperation or interviewer error), recall (respondent not remembering correctly), frequency of interviewing, interview spacing, etc. 2.Distortions of measurement errors due to unclear questions, memory errors, inappropriate informants, misrecording or responses, and interviewer effects 3.Selectivity problems (due to self –selectivity, nonresponse, and attrition) data berkurang 4.Short time-series dimensions 5.Cross-section dependence panel unit root tests are suggested to account for CS dependence 6 Limitations of panel data

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Jenis-jenis data panel PANEL DATA Balanced panel Unbalanced panel 7 PANEL DATA Short panel Long panel N > T T > N

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Metode estimasi data panel 8 PANEL DATA Pooled OLS REM Pool all obs LSDV FE Within Group Pool all obs and assume that the intercept value are a random drawing from a much bigger population of CS data Pool all obs but allow each CS unit to have its own (intercept) dummy varb Pool all obs, but express each varb in each CS as a deviation from its mean value and then estimates OLS regression on such mean corrected

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Metode Estimasi Data Panel PANEL DATA FEM 9 PLS WG LSDV 2-way error comp B/W estimator GLS REM

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Kelemahan data CS: – Hanya dapat diamati pada satu titik – Contoh analisis pertumbuhan ekonomi: PDRB, investasi, tingkat konsumsi hanya di satu titik perkembangan ekonomi antar waktu tidak dapat dilihat Kelemahan data TS: – Variabel-variabel yang diobservasi secara agregat dati suatu uni invidu estimasi mungkin bias Kelebihan data panel: – Verbeek (2004): Kombinasi data S dan TS jumlah observasi lebih besar Model data panel variabel penjelas dilihat dari dua dimensi parameter yang diestimasi lebih akurat – Hsiao (2004) Lebih informatif Mengurangi kolinearitas antar variabel penjelas Meningkatkan df meningkatkan efisiensi Mampu mengontrol heterogenitas individy 10 Teori Data Panel Statis

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Dua pendekatan aplikasi data panel: – Fixed effect model (FEM) – Random Effect Model (REM) Perbedaan FEM dan REM: Asumsi ada/tidak korelasi antara error (e) dan variabel penjelas (X) Contoh: y it = α i + βX it + ε it Komponen error: One way error component model: y it = α i + βX it + it + u it Two way error component model: y it = α i + βX it + it + it + u it 11 Teori Data Panel Statis

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Menggunakan gabungan seluruh data (pooled) jumlah observasi = n x t ; n = jumlah unit CS t = jumlah series Model: y it = α i + βX it + ε it ; α i = α i Formula perhitungan: 12 FEM - Metode PLS

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Kelemahan: Parameter β bias arah kemiringan (slope) PLS tidak sejajar dengan garis regresi masing-masing individu (tidak dapat membedakan observasi yang sama pada periode berbeda) 13 FEM - Metode PLS Group 2 α 2 + βx it Group 1 α 1 + βx it Slope bias x it y it

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14 An illustrative example of panel data Data are taken from investment theory proposed by Y. Grunfeld (1958: “The Determinants of Corporate Investment”, unpublished Ph.D. thesis)

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Real capital stock Real gross investment X3X3 X2X2 Real value of the firm Y Y it = β 1 + β 2 X 2it + β 3 X 3it + u it i = 1, 2, 3, 4 CS identifier t = 1, 2, …, 20 TS identifier ↓ 80 observasi ↓ balanced panel Initial assumptions:1) X kit nonstochastic 2) E(u it ) N(0, 2 ) Grunfeld Investment Function Panel data BalancedUnbalanced t i = t I Not all of t i = t

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Y it = β 1 + β 2 X 2it + β 3 X 3it + u it i = 1, 2, 3, 4 t = 1, 2, …, 20 Futher assumptions (intercept, slope, error term): 1)The intercept and slope coefficients are constant across time and space and the error term captures differences over tima and individuals b jit = b j k,i,t and not all u it = u 2)The slope coefficients are constant but the intercept varies over individuals 3)The slope coefficients are constant but the intercept varies over individuals and time 4)All coefficients (the intercept and slope) vary over individuals 5)The intecept and slope coefficient vary over individuals and time Estimation of Grunfeld Investment Function

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1) ALL COEFFICIENTS CONSTANT ACROSS TIME AND INDIVIDUALS Dependent Variable: Y? Method: Pooled Least Squares Date: 10/24/14 Time: 09:06 Sample: Included observations: 20 Cross-sections included: 4 Total pool (balanced) observations: 80 VariableCoefficientStd. Errort-StatisticProb. C X1? X2? R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

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Dependent Variable: Y? Method: Pooled Least Squares Date: 10/24/14 Time: 09:06 Sample: Included observations: 20 Cross-sections included: 4 Total pool (balanced) observations: 80 VariableCoefficientStd. Errort-StatisticProb. C X1? X2? R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Dependent Variable: Y Method: Panel Least Squares Date: 10/24/14 Time: 09:19 Sample: Periods included: 20 Cross-sections included: 4 Total panel (balanced) observations: 80 VariableCoefficientStd. Errort-StatisticProb. C X X R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

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