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