Ekonomi Manajerial dalam Perekonomian Global Bab 4 : Estimasi & Peramalan Permintaan Bahan Kuliah Program Pascasarjana-UHAMKA Program Studi Magister Manajemen Dosen : Dr. Muchdie, PhD in Economics Jam Konsultasi : Sabtu, 10.00-12.00 Telp : 0818-0704-5737 Pokok Bahasan • Masalah Identifikasi • Pendekatan Penelitian Pemasaran untuk Estimasi Permintaan • Analisis Regresi – Regresi Sederhana – Regresi Berganda • Masalah dalam Analisis Regresi • Mengestimasi Permintaan Regresi Pokok Bahasan • Peramalan Kualitatif : – Survei & Jajak Pendapat • Peramalan Kuantitatif : – Analisis Deret Waktu – Teknik Penghalusan – Metode Barometrik – Model Ekonometrik – Model Input-Output • Ringkasan, Pertanyaan Diskusi, Soal-Soal dan Alamat Situs Internet Masalah Identifikasi Observasi Harga-Quantitas TIDAK SECARA LANGSUNG menghasilkan kurva Permintaan dari suatu komoditas Estimasi Permintaan: Pendekatan Riset Pemasaran • Survei Konsumen : mensurvei konsumen bgm reaksi tehd jumlah yg diminta jika ada perubahan harga, pendapatan, dll menggunakan kuisioner • Penelitian Observasi : pengumpulan informasi ttg preferensi konsumen dgn mengamati bgmana mereka membeli dan menggunakan produk • Klinik Konsumen : eksperimen lab dimana partisipan diberi sejumlah uang tertentu dan diminta membelanjakannya dalam suatu toko simulasi dan mengamati bgmana reaksi mereka jika terjadi perubahan harga, pendapatan, selera, dll • Eksperimen Pasar : mirip klinik konsumen, tetapi dilaksanakan di pasar yang sesungguhknya Analisis Regresi Scatter Diagram Year X Y 1 10 44 2 9 40 3 11 42 4 12 46 5 11 48 6 12 52 7 13 54 8 13 58 9 14 56 10 15 60 Persamaan Regresi : Y = a + bX Analisis Regresi • Garis Regresi : Line of Best Fit • Garis Regresi : meminimunkan jumlah dari simpangan kuadrat pada sumbu vertikal (et) dari setiap titik pada garis regresi tersebut. • Metode OLS (Ordinary Least Squares): metode jumlah kuadrat terkecil Menggambarkan Garis Regresi ˆ et Yt Yt Analisis Regresi Sederhana Metode : OLS Model: Yt a bX t et ˆ ˆ ˆ Yt a bX t et Yt Yˆt Metode OLS Tujuan: menentukan kemiringan (slope) dan intercept yang meminimumkan jumlah simpangan kuadrat (sum of the squared errors). n n n t 1 t 1 2 2 ˆ ˆ e (Yt Yt ) (Yt aˆ bX t ) t 1 2 t Metode OLS Prosedur Estimasi : n ˆ b (X t 1 t X )(Yt Y ) n (X t 1 ˆ ˆa Y bX t X) 2 Metode OLS Contoh Estimasi Time Xt 1 2 3 4 5 6 7 8 9 10 10 9 11 12 11 12 13 13 14 15 120 n 10 Yt 44 40 42 46 48 52 54 58 56 60 500 n n X t 120 Yt 500 t 1 n X 120 X t 12 10 t 1 n t 1 n Y 500 Y t 50 10 t 1 n Xt X Yt Y -2 -3 -1 0 -1 0 1 1 2 3 -6 -10 -8 -4 -2 2 4 8 6 10 n (X t 1 t 1 ( X t X )2 12 30 8 0 2 0 4 8 12 30 106 4 9 1 0 1 0 1 1 4 9 30 t X )2 30 106 bˆ 3.533 30 t X )(Yt Y ) 106 aˆ 50 (3.533)(12) 7.60 n (X ( X t X )(Yt Y ) Metode OLS Contoh Estimasi n X n 10 n X t 1 t n (X t 1 t 1 120 n Y 500 t 1 t n Yt 500 50 10 t 1 n Y t X ) 30 106 ˆ b 3.533 30 t X )(Yt Y ) 106 aˆ 50 (3.533)(12) 7.60 2 n (X t 1 X t 120 12 n 10 Uji Signifikansi Standard Error of the Slope Estimate sbˆ 2 ˆ (Yt Y ) ( n k ) ( X t X ) 2 e (n k ) ( X X ) 2 t t 2 Uji Signifikansi Contoh Perhitungan Yˆt et Yt Yˆt et2 (Yt Yˆt )2 ( X t X )2 44 42.90 1.10 1.2100 4 9 40 39.37 0.63 0.3969 9 3 11 42 46.43 -4.43 19.6249 1 4 12 46 49.96 -3.96 15.6816 0 5 11 48 46.43 1.57 2.4649 1 6 12 52 49.96 2.04 4.1616 0 7 13 54 53.49 0.51 0.2601 1 8 13 58 53.49 4.51 20.3401 1 9 14 56 57.02 -1.02 1.0404 4 10 15 60 60.55 -0.55 0.3025 9 65.4830 30 Time Xt Yt 1 10 2 (Y Yˆ ) ( n k ) ( X X ) 2 n n et2 (Yt Yˆt )2 65.4830 t 1 t 1 n ( X t X )2 30 t 1 sbˆ t t 2 65.4830 0.52 (10 2)(30) Uji Signifikansi Contoh Perhitungan n n t 1 t 1 2 2 ˆ e ( Y Y ) t t t 65.4830 n 2 ( X X ) 30 t t 1 2 ˆ (Yt Y ) 65.4830 sbˆ 0.52 2 ( n k ) ( X t X ) (10 2)(30) Uji Signifikansi Perhitungan : t-Statistic ˆ b 3.53 t 6.79 sbˆ 0.52 Derajat Bebas = (n-k) = (10-2) = 8 Critical Value at 5% level =2.306 Uji Signifikansi Decomposition of Sum of Squares Total Variation = Explained Variation + Unexplained Variation 2 2 ˆ ˆ (Yt Y ) (Y Y ) (Yt Yt ) 2 Uji Signifikansi Decomposition of Sum of Squares Uji Signifikansi Koefisien Determinasi Explained Variation R TotalVariation 2 373.84 R 0.85 440.00 2 2 ˆ (Y Y ) (Y Y ) t 2 Uji Signifikansi Koefisien Korelasi ˆ r R withthe signof b 2 1 r 1 r 0.85 0.92 Analisis Regresi Berganda Model: Y a b1 X1 b2 X 2 bk ' X k ' Analisis Regresi Berganda Adjusted Coefficient of Determination (n 1) R 1 (1 R ) (n k ) 2 2 Analisis Regresi Berganda Analysis of Variance and F Statistic Explained Variation /(k 1) F Unexplained Variation /(n k ) R /(k 1) F 2 (1 R ) /(n k ) 2 Masalah-Masalah dalam Analisis Regresi • Multicollinearity: Dua atau lebih variabel bebas mempunyai korelasi yang sangat kuat. • Heteroskedasticity: Variance of error term is not independent of the Y variable. • Autocorrelation: Consecutive error terms are correlated. Durbin-Watson Statistic Uji Autocorrelation n d 2 ( e e ) t t 1 t 2 n 2 e t t 1 If d=2, autocorrelation is absent. Langkah-Langkah Estimasi Permintaan dengan Regresi • Spesifikasi Model dengan Cara Mengidentifikasi Variabel-Variabel, misalnya : Qd = f (Px, I, Py, A, T) • Pengumpulan Data • Spesifikasi Bentuk Persamaan Permintaan Linier : Qd = A - a1Px + a2 I + a3 Py + a4 A + a5 T Pangkat : Qd = A(Px)b(Py)c • Estimasi Nilai-Nilai Parameter • Pengujian Hasil Qualitative Forecasts • Survey Techniques – Planned Plant and Equipment Spending – Expected Sales and Inventory Changes – Consumers’ Expenditure Plans • Opinion Polls – Business Executives – Sales Force – Consumer Intentions Time-Series Analysis • Secular Trend – Long-Run Increase or Decrease in Data • Cyclical Fluctuations – Long-Run Cycles of Expansion and Contraction • Seasonal Variation – Regularly Occurring Fluctuations • Irregular or Random Influences Trend Projection • Linear Trend: S t = S0 + b t b = Growth per time period • Constant Growth Rate: St = S0 (1 + g)t g = Growth rate • Estimation of Growth Rate : lnSt = lnS0 + t ln(1 + g) Seasonal Variation Ratio to Trend Method Actual Trend Forecast Ratio = Seasonal Adjustment Adjusted Forecast = = Average of Ratios for Each Seasonal Period Trend Forecast Seasonal Adjustment Seasonal Variation Ratio to Trend Method: Example Calculation for Quarter 1 Trend Forecast for 1996.1 = 11.90 + (0.394)(17) = 18.60 Seasonally Adjusted Forecast for 1996.1 = (18.60)(0.8869) = 16.50 Year 1992.1 1993.1 1994.1 1995.1 Trend Forecast Actual 12.29 11.00 13.87 12.00 15.45 14.00 17.02 15.00 Seasonal Adjustment = Ratio 0.8950 0.8652 0.9061 0.8813 0.8869 Moving Average Forecasts Forecast is the average of data from w periods prior to the forecast data point. w At i Ft i 1 w Exponential Smoothing Forecasts Forecast is the weighted average of of the forecast and the actual value from the prior period. Ft 1 wAt (1 w) Ft 0 w 1 Root Mean Square Error Measures the Accuracy of a Forecasting Method RMSE (A F ) t n t 2 Barometric Methods • • • • • • • National Bureau of Economic Research Department of Commerce Leading Indicators Lagging Indicators Coincident Indicators Composite Index Diffusion Index Econometric Models Single Equation Model of the Demand For Cereal (Good X) QX = a0 + a1PX + a2Y + a3N + a4PS + a5PC + a6A + e QX = Quantity of X PS = Price of Muffins PX = Price of Good X PC = Price of Milk Y = Consumer Income A = Advertising N = Size of Population e = Random Error Econometric Models Multiple Equation Model of GNP Ct a1 b1GNPt u1t It a2 b2 t 1 u2t GNPt Ct It Gt Reduced Form Equation Gt a1 a2 b2 t 1 GNPt b1 1 b1 1 1 b1 Input-Output Forecasting Three-Sector Input-Output Flow Table Producing Industry Supplying Industry A B C Value Added Total A 20 80 40 60 200 B 60 90 30 120 300 C 30 20 10 40 100 Final Demand 90 110 20 220 Total 200 300 100 220 Input-Output Forecasting Direct Requirements Matrix Direct Requirements = Input Requirements Column Total Producing Industry Supplying Industry A B C A 0.1 0.4 0.2 B 0.2 0.3 0.1 C 0.3 0.2 0.1 Input-Output Forecasting Total Requirements Matrix Producing Industry Supplying Industry A B C A 1.47 0.96 0.43 B 0.51 1.81 0.31 C 0.60 0.72 1.33 Input-Output Forecasting Total Requirements Matrix 1.47 0.96 0.43 0.51 1.81 0.31 0.60 0.72 1.33 Final Demand Vector 90 110 20 Total Demand Vector = 200 300 100 Input-Output Forecasting Revised Input-Output Flow Table Producing Industry Supplying Industry A B C A 22 88 43 B 62 93 31 C 31 21 10 Final Demand 100 110 20 Total 215 310 104