Ekonomi dan Keuangan Indonesia Vol 38, No. 4, 1990

Penurunan Data Bulanan dari Data Tahunan

Insukindro

Abstract

A method for deriving monthly data f r o m a n n u a l data is presented i n tni. paper. Using l i n e a r interpolation i n the first stage and iterative regressiik in the second one, the method is designed mainly for flow variables, sucl^ gross domestic product, investment, etc. V a r i a b l e s chosen as argumen i n the regression stage could be based on theoretical considerations, w e l l as trend and seasonal factors. In the e m p i r i c a l part o f the paper, author applies his method for obtaining monthly G D P data f r o m a n m a/ one.

a?

3 4 7

Insukindro

S a l a h s a t u p r a s y a r a t u t a m a d a p a t a t a u t i d a k n y a d i l a k u k a n p e n g u j i a n t e r h a d a p s u a t u m o d e l e k o n o m e t r i a d a l a h t e r s e d i a n y a d a t a s e p e r t i y a n g d i k e h e n d a k i o l e h s i p e m b u a t m o d e l . N a m u n d a l a m k e n y a t a a n n y a s e r i n g d i j u m p a i b a h w a d a t a y a n g d i i n g i n k a n t i d a k t e r s e d i a , t i d a k l e n g k a p a t a u t e r s e d i a d a l a m v a r i a s i w a k t u y a n g b e r b e d a . M i s a l n y a s a j a , d a t a y a n g d i ­k e h e n d a k i k u a r t a l a n a t a u b u l a n a n s e d a n g k a n y a n g t e r s e d i a d a t a t a h u n a n a t a u s e m e s t e r a n . K e l a n g k a a n d a t a s e m a c a m i n i m e r u p a k a n s u a t u p e r -s o a l a n y a n g t i d a k m u d a h d a p a t d i p e c a h k a n d a l a m p e m b e n t u k a n m o d e ! ( J o l m s t o n , 1 9 8 4 ) .

T e r k a i t d e n g a n u s a h a u n t u k m e m e n u h i k e b u t u h a n a k a n d a t a s e p e r t i y a n g d i h a r a p k a n o l e h s i p e m b u a t m o d e l e k o n o m i , t e l a h b a n y a k d i k e m -b a n g k a n s u a t u p e n d e k a t a n u n t u k m e n u m n k a n , m i s a l n y a , d a t a k u a r t a l a n d a r i d a t a t a h u n a n ( l i h a t m i s a l n y a : B e r g s t r o n et al. 1 9 7 5 : D i z , 1 9 7 0 d a n B a r t e n , 1 9 8 1 ) . P e n u r u n a n d a t a k u a r t a l a n d a r i d a t a t a h u n a n t e l a h p u l a b a n y a k d i c o b a d a n d i t e r a p k a n d a l a m p e n e i i t i a n e m p i r i s d i I n d o n e s i a ( l i h a t : A g h e v l i . 1 9 7 7 ; I n s u k i n d r o . 1 9 8 4 ; B o e d i o n o , 1 9 8 5 : P a r i k h e t a / , 1 9 8 5 ; d a n I n s u k i n d r o etal. 1 9 8 7 ) . T e n t u sa j a u s a h a y a n g d i s e b u t t e r a k h i r i n i t e l a h m a m p u m e m e n u h i k e b u t u h a n m e r e k a a k a n d a t a k u a r t a l a n d a n t e l a h p u l a m a m p u d i g u n a k a n u n t u k m e n j e l a s k a n g e j a l a a t a u p h e n o m e n a e k o n o m i y a n g d i a m a t i . N a m u n d e m i k i a n , d a l a m p e n e i i t i a n e m p i r i s s e r i n g p u l a m u n c u l p e r t a n y a a n : " b a g a i m a n a k a h m e n u r u n k a n d a t a b u l a n a n d a r i d a t a t a h u n a n " ? A p a k a h c a r a p e n u r u n a n d a t a k u a r t a l a n d a r i d a t a t a h u n a n d a p a t j u g a d i p a k a i u n t u k m e n u r u n k a n d a t a b u l a n a n ? S e m u a n y a i n i a d a l a h p e r t a n y a a n y a n g m u d a h , w a j a r d a n s e r i n g t e r u n g k a p k a n d a l a m s u a t u s t u d i e m p i r i s , w a l a u p u n t i d a k d e n g a n m u d a h m e n c a r i k a n j a w a b n y a .

T u l i s a n i n i b e r m a k s u d m e n g e t e n g a h k a n s a t u m e t o d e u n t u k m e n c o b a m e m b e r i k a n a l t e m a t i p j a w a b a n b a g i p e r t a n y a a n d i a t a s . D e n g a n d e m i k i a n d i s i n i a k a n d i k e t e n g a h k a n s a t u c a r a u n t u k m e n u r u n k a n d a t a b u l a n a n d a r i d a t a t a h u n a n , t e r u t a m a u n t u k d a t a y a n g s i f a t n y a a l i r a n (flow). L a n g k a h s e m a c a m i n i , s e p e r t i h a l n y a u s a h a s e j e n i s l a i n n y a , d i m a k s u d k a n a g a r d a t a y a n g d i k e h e n d a k i d a p a t d i p e r o l e h . T e n t u s a j a s e b a g a i d a t a t u r u n a n a t a u i n t e r p o l a s i , d a t a t e r s e b u t d i h a r a p k a n m a m p u m e w a k i l i d a n m e n c e r m i n k a n p e r i l a k u g e j a l a y a n g s e d a n g m e n j a d i p u s a t p e r h a t i a n k i t a . U n t u k m e n u n j a n g m a k s u d d i a t a s , p e r t a m a k a l i a k a n d i k e t e n g a h k a n c a r a d a n l a n g k a h p e n u r u n a n d a t a b u l a n a n d a r i d a t a t a h u n a n , k e m u d i a n d i k e m u k a k a n p u l a c o n t o h t e r a p a n n y a d a n d i s k u s i m e n g e n a i h a s i l p e n e ­i i t i a n e m p i r i s d e n g a n m e n g g u n a k a n d a t a P r o d u k D o m e s t i k B r u t o ( P D B ) d i I n d o n e s i a .

I . Cara dan Langkah Penurunan Data Bulanan

P a d a d a s a r n y a c a r a p e n u r u n a n y a n g a k a n d i k e t e n g a h k a n d a l a m t u l i s a n i n i

348

Penurunan Data Bulanan

m e r u p a k a n p e r l u a s a n l e b i h l a n j u t d a r i c a r a s e j e n i s u n t u k m e n u r u n k a n d a t a k u a r t a l a n d a r i d a t a t a h u n a n ( I n s u k i n d r o , 1 9 8 4 ) . D e n g a n d e m i k i a n a n g g a p a n d a s a r y a n g d i p a k a i d i s i n i p a d a d a s a r n y a s e g a r i s d e n g a n i t u . P e r t a m a , b a h w a l a j u p e r t u m b u h a n d a t a t a h u n a n y a n g d i a m a t i d i a n g g a p d i d i s t r i b u s i k a n m e r a t a s e t i a p b u l a n , d a n k e d u a , b a h w a j u m l a h d a t a b u l a n ­a n h a s i l t u r u n a n p a d a s a t u t a h u n t e r t e n t u s a m a d e n g a n d a t a t a h u n a n d a r i t a h u n y a n g b e r s a n g k u t a n . D e n g a n d a s a r a n g g a p a n t e r s e b u t , p e n u r u n a n d a t a b u l a n a n d a r i d a t a t a h u n a n d a p a t d i p e r o l e h d e n g a n r u m u s b e r i k u t :

y , . , = l / l 2 ( y , + i z M ( y ^ - y ^ j ) ) , / = 1 , 2 . . . 1 2 . ( 1 )

d i m a n a Y.^ m e r u p a k a n d a t a p a d a b u l a n k e / d a r i t a h u n t, a d a l a h d a t a p a d a t a h u n k e t d a n Y^ j m e r u p a k a n d a t a p a d a t a h u n s e b e l u m n y a .

S e l a n j u t n y a d a r i p e r s a m a a n ( 1 ) d a p a t d i p e r o l e h c a r a u n t u k m e ­n u r u n k a n d a t a b u l a n a n s e b a g a i b e r i k u t :

Yy, = 1 / 1 2 ( y , - 5 , 5 / 1 2 « y , - y , _ , ) )

y j , = 1 / 1 2 ( y , - 4 , 5 / 1 2 ( y , - y , _ , ) )

y , , = 1 / 1 2 ( y , - 3 , 5 / 1 2 ( y , - y , _ , ) )

d s t . ( 2 )

y , o , = i / i 2 ( y , + 3 , 5 / i 2 ( y , - y , _ , ) ) y j i , = i / i 2 ( y , + 4 , 5 / 1 2 ( y , - y , _ j ) ) y j j , = 1 / 1 2 ( y , + 5 , 5 / 1 2 ( y , - y , _ , ) )

d i m a n a y j ^ , y ^ ^ ? ' ' ' ^ \ 2 t m e r u p a k a n d a t a p a d a b u l a n k e 1 , 2 , 3 . . . d a n k e 1 2 d a r i t a h u n t .

D a r i p e r s a m a a n ( 2 ) d a p a t d i k e t a h u i b a h w a : ~ ~ ~ ^ i t d a n s e t e r u s n y a , a t a u s e c a r a u m u m d a p a t d i t u l i s s e b a g a i b e r i k u t :

f t - y u - i i f = i / 4 4 ( y , - y , _ i ) ( 3 )

D i s a m p i n g i t u d a p a t p u l a d i t u n j u k k a n b a h w a Y^^ + Y.^^ + . . . Y^^^t s a m a d e n g a n Y^ a t a u .

' i ' ^ u - ' ^ t ( 4 ) /= 1

3 4 9

Insukindro

S e t e l a h d a t a b u l a n a n d i p e r o l e h , l a n g k a h s e l a n j u t n y a a d a l a h m e m -b e n t u k s u a t u m o d e l u n t u k m e n a k s i r p e r i l a k u d a t a t u r u n a n i t u a g a r p a d a a k h i r n y a d i h a r a p k a n d a p a t d i p e r o l e h d a t a p e n a k s i r d a r i g e j a l a s e b e n a r n y a . L a n g k a h i n i d i h a r a p k a n p u l a m a m p u m e n g u b a h d a t a t u r u n a n k e a r a h d a t a r a w a k ( r a n d o m ) .

D a l a m t u l i s a n i n i d i a n g g a p b a h w a v a r i a s i J j ^ d i t e n t u k a n a t a u d i ­p e n g a r u h i o l e h 4 k o m p o n e n ' : T = k o m p o n e n t r e n d , S = k o m n o n e n m u s i m a n {seasonal component), 1 = k o m p o n e n y a n g t i d a k b e r a t u r a n (irregular component) d a n Y ^ . . = h i m p u n a n v a r i a b e l y a n g d i a n g g a p m a m ­p u m e n j e l a s k a n v a r i a s i . D e n g a n d e m i k i a n v a r i a s i L . ^ . d a p a t d i r u m u s k a n s e b a g a i b e r i k u t .

Y. = T + Z d.X.. + I. ( 5 )

d i m a n a Y^ a d a l a h d a t a b u l a n a n h a s i l t u r u n a n d i a t a s . 7 d i a n g g a p m e ­r u p a k a n t r e n d l i n i e r a t a u 7 = 0^ + a^i. S a d a l a h v a r i a b e l b o n e k a y a n g m e n c e r m i n k a n v a r i a s i b u l a n a n , d a n dj m e r u p a k a n k o e f i s i e n r e g r e s s i .

P e r s a m a a n ( 5 ) a k a n d a p a t d i e s t i m a s i d a n m e m b e r i p e n a k s i r y a n g b a i k b i l a v a r i a b e l y a n g d i a m a t i d a n t e r u k u r (Xj.) d a n v a r i a b e l y a n g t i d a k t e r u k u r ( T d a n S) d a p a t d i p i l i h d a n d i j a b a r k a n y a n g m e n u r u t t e o r i m a m ­p u m e n j e l a s k a n v a r i a s i Y.. N a m u n d e m i k i a n j i k a v a r i a b e l - v a r i a b e l t e r -m a k s u d s u l i t a t a u t i d a k c l a p a t d i p e r o l e h , p e r s a m a a n ( 5 ) m a s i h m u n g k i n d i t a k s i r d e n g a n m e n g g u n a k a n " K a l m a n F i l t e r " . T e h n i k f i l t e r K a l m a n i n i p a d a d a s a r n y a b e r k a i t a n d e n g a n i d e n t i f i k a s i , e s t i m a s i d a n p e r a m a l a n p e r i ­l a k u s u a t u s i s t e m d i m a n a p e n g e t a h u a n s i p e n e l i t i m e n g e n a i s i s t e m y a n g d i a m a t i s a n g a t t e r b a t a s . D e n g a n t e h n i k i n i k e s u l i t a n k i t a m e n e n t u k a n a t a u m e n c a r i v a r i a b e l y a n g m a m p u m e n j e l a s k a n v a r i a b e l Y. d a p a t t e r -p e c a h k a n , t e r l e b i h l a g i b i l a p a k e t k o m p u t e r m e n g e n a i h a l i t u t e r s e d i a . ^

I I . Peneiitian Empiris : PDB Bulanan

U n t u k m e m p e r o l e h g a m b a r a n m e n g e n a i p e n e r a p a n c a r a t e r s e b u t d i a t a s , d i c o b a d i t u r u n k a n d a t a P r o d u k s i D o m e s t i k B r u t o ( P D B ) b u l a n a n d a r i

^ U n t u k k e p u s t a k a a n d a n d i s k u s i s e l a n j u t n y a , l i h a t m i s a l n y a ; H a r v e y , 1 9 8 5 ; H a r v e y et al, 1 9 8 6 ; C l a r k , 1 9 8 9 d a n C r a f t s e f al, 1 9 8 9 . D a l a m a r t i k e l m e r e k a k o m ­p o n e n t r e n d d a n m u s i m a n dianggap s t o k a s t i k .

^ P e n e r a p a n t e h n i k f i l t e r K a l m a n t e l a h b a n y a k d i l a k u k a n d a l a m anal i s i s e k o ­n o m i , t e r l e b i h l ag i se te lab d i k e t e m u k a n n y a p a k e t p r o g r a m k o m p u t e r s epe r t i S T A M P d a n R A T S ( l i h a t m i s a l n y a : C o o p e r , 1 9 8 8 , D o a n et al, 1 9 8 7 , H a r v e y etal 1 9 8 6 d a n C r a f t s , 1 9 8 9 ) .

3 5 0

Penurunan Data Bulanan

P D B t a h u n a n a t a s d a s a r h a r g a t e t a p t a h u n 1 9 8 5 . D a t a y a n g d i p e r g u n a k a n d a n d i a m a t i m u i a i t a h u n 1 9 8 3 s a m p a i 1 9 8 7 .

S e g a r i s d e n g a n c a r a d i m u k a , l a n g k a h p e r t a m a a d a l a h m e n u r u n k a n P D B b u l a n a n d e n g a n m e n g g u n a k a n p e r s a m a a n ( 2 ) . H a s i i p e r h i t u n g a n t a h a p i n i d i i a p o r k a n p a d a T a b e i 2 k o i o m 2 , d a n u n t u k s e l a n j u t n y a k i t a b e r i n o t a s i P D B l . T a b a p k e d u a , k i t a b e n t u k m o d e l u n t u k m e n g a m a t i , m e n g e s t i m a s i d a n m e r a m a i k a n P D B l . T e n t u sa j a d a i a m m e m b e n t u k m o ­d e l s e m a c a m i n i t e o r i y a n g b e r k a i t a n d e n g a n i t u t i d a k b o l e b d i l u p a k a n ; a g a r m o d e l y a n g d i b e n t u k m e m p u n y a i d a s a r y a n g i a y a k d a n d i h a r a p k a n m a m p u m e n j e l a s k a n v a r i a s i P D B 1 .

B e r k a i t a n d e n g a n u r a i a n d i a t a s , a n g g a p i a b b a h w a P D B l d i p e n g a r u h i o i e h T, S, G ^ p e n g e l u a r a n p e m e r i n t a h ) d a n P ( i n d e k s h a r g a k o n s u m e n m e n u r u t h a r g a t a h u n 1 9 8 0 ) . M u d a b d i p a b a m i d a n d i t e n t u k a n b a h w a a d a n y a k e n a i k a n G d a n P d i h a r a p k a n a k a n m e n d o r o n g k e n a i k a n p r o ­d u k s i n a s i o n a l , s e p e r t i y a n g s e r i n g d i b i c a r a k a n d a i a m t e o r i m u l t i p l i e r m a u p u n t e o r i p r o d u k s i . D e n g a n d e m i k i a n d i s i n i d i a n g g a p b a h w a h u b u n g ­a n a n t a r a P D B l d e n g a n T, G d a n P a d a l a h p o s i t i f , s e d a n g k a n d i k e n a i k a n -n y a v a r i a b e l S u n t u k m e i i b a t a d a t i d a k n y a p e n g a r u h v a r i a s i m u s i m a n t e r ­h a d a p P D B i . A n g g a p a n - a n g g a p a n t e r s e b u t m e i a b i r k a n h u b u n g a n b e r i k u t :

11 P D B 1. = + a J / + ^,2 h.S. + h P . + cG. + d P D B i j + " i • • • ̂ 6 )

d i m a n a / m e n u n j u k k a n b u i a n d a n u. = N ( 0 , V ^ ) .

H a s i i e s t i m a s i p e r s a m a a n ( 6 ) d a p a t d i b a c a p a d a T a b e i i d a n n i l a i p e n a k s i r u n t u k P D B l d a p a t d i l i h a t p a d a T a b e l 2 k o i o m 3 , d a n u n t u k s e t e r u s n y a d i b e r i n o t a s i P D B 2 . L a n g k a h p e n a k s i r a n s e m a c a m i n i d i u i a n g l a g i d e n g a n m e n g g u n a k a n P D B 2 s e b a g a i v a r i a b e l g a y u t m e n g g a n t i k a n P D B l s e p e r t i a p a y a n g d i j a b a r k a n o i e h p e r s a m a a n ( 6 ) . B e g i t u s e t e r u s n y a , s e h i n g g a p a d a a k h i r n y a a k a n d i ­p e r o l e h n i l a i p e n a k s i r P D B y a n g t e r b a i k . D a i a m c o n t o h y a n g a k a n d i b i c a r a k a n i e b i h i a n j u t d i b a w a h i n i , l a n g k a h m e n g e s t i m a s i b e r u i a n g i t u h a n y a s a m p a i p a d a t a b a p y a n g k e e m p a t .

I I I . Pengujian dan Pemililian Hasil Studi Empiris

S e p e r t i t e i a h d i b i c a r a k a n d i a t a s , s e t e l a b d i p e r o l e h P D B l , l a n g k a h se­l a n j u t n y a a d a i a b m e i a k u k a n e s t i m a s i b e r u i a n g . H a s i i e s t i m a s i b e r u i a n g t e r s e b u t d a p a t d i b a c a p a d a T a b e i i d a n p e n a k s i r P D B d a r i e s t i m a s i i t u d a p a t d i l i h a t p a d a T a b e i 2 k o i o m 2 s a m p a i k o i o m 5 . N a m u n d e m i k i a n , s e b e i u m d i p i i i i i n i l a i p e n a k s i r m a n a y a n g d i a n g g a p t e r b a i k , t e r l e b i h d u l u

3 5 1

Insukindro

T a b e l 1 . H a s i l Estimasi Bertahap P D B B u l a n a n I n d o n e s i a : 1 9 8 4 ( 1 ) - - 1 9 8 7 ( 1 2 )

V a r . g a y u t P D B l P D B 2 P D B 3 P D B 4 P e r s a m a a n 1 2 3 4

V a r . t a k g a y u t :

1 .

2 .

3 .

I n t e r s e p 1 0 3 0 , 6 1 0 9 5 , 2 1 0 3 1 , 0 7 7 1 . 7 ( 5 4 9 , 3 ) ( 5 3 9 , 1 ) ( 5 1 8 , 2 ) ( 5 1 3 , 9 )

T r e n d ( 7 ) 2 , 4 3 2 3 2 , 3 7 9 4 2 , 1 9 2 3 1 ,8136 ( 1 , 7 1 0 5 ) ( 1 , 6 2 1 8 ) ( 1 , 4 9 2 1 ) ( 1 , 3 9 1 3 )

- 2 ! , 4 0 6 4 - 1 7 , 0 2 2 9 - 1 3 , 0 4 9 9 - 1 1 , 5 7 5 4 ( 1 2 , 1 6 7 3 ) ( 1 0 , 2 6 1 4 ) ( 8 , 3 5 2 8 ) ( 6 , 8 4 2 5 )

P 1 , 2 7 8 0 1 , 8 5 5 4 1 ,7945 1 , 0 5 5 4 ( 1 , 1 0 7 5 ) ( 0 , 9 7 0 0 ) ( 0 , 8 5 2 2 ) ( 0 , 8 1 1 1 )

G 0 , 0 0 1 4 0 , 0 0 0 8 0 , 0 0 3 5 0 , 0 0 1 1 ( 0 , 0 0 3 4 ) ( 0 , 0 0 2 9 ) ( 0 , 0 0 2 5 ) ( 0 , 0 0 2 1 )

P D B ( 7 ) . , 0 , 8 4 1 2 0 , 8 2 1 6 0 , 8 3 0 8 0 , 8 7 9 8 I — I ( 0 , 0 7 8 5 ) ( 0 , 0 7 7 7 ) ( 0 , 0 7 6 0 ) ( 0 , 0 7 7 6 )

2

R 0 , 9 9 6 4 0 , 9 9 7 3 0 , 9 9 8 1 0 , 9 9 8 7 _ -) R " 0 , 9 9 6 0 0 , 9 9 7 0 0 , 9 9 7 9 0 , 9 9 8 5

-) s~

2 0 , 0 5 9 7 1 6 , 9 5 6 1 1 3 8 3 4 8 1 1 3 3 8 8 F ( 5 , 4 1 ) * 2 2 6 7 , 0 2 9 4 7 , 1 4 1 2 1 , 2 5 7 1 8 , 7

i d i a g n o s t i k O t o k o r e l a s i : - S t a t i s t i k - h 0 , 9 3 2 1 1 , 0 9 8 0 1 ,2085 1 , 1 2 6 4 - V e r s i L M ( 1 2 ) 1 1 , 4 2 3 0 1 2 , 4 0 1 6 1 3 , 7 2 8 3 1 3 , 1 7 5 9 - V e r s i F ( 1 2 , 2 9 ) * 0 , 7 7 5 9 0 , 8 6 1 3 0 , 9 8 7 7 0 , 9 2 6 2 L i n i e r i t a s : - V e r s i L M ( 1 ) 0 , 5 2 8 9 0 , 0 0 3 5 0 , 8 0 8 0 5 , 0 9 8 9 - V e r s i F ( I , 4 0 ) * ' 0 , 4 5 5 2 0 , 0 0 3 0 0 , 6 9 4 8 4 , 8 4 9 8 H e t e r o s k e d a s t i s i t a s : - V e r s i L M ( 1 ) 1 , 2 7 6 1 1 , 2 2 0 0 1 , 1 0 6 0 0 , 9 1 3 8 - V e r s i F ( l , 4 5 ) * 1 , 2 5 5 9 1 ,1988 1 ,0835 0 , 8 9 0 8

A n g k a d a l a m k u r u n g m e n u n j u k k a n s i m p a n g a n b a k u k o e f i s i e n regressi . * ) D e r a j a t kebebasan u n t u k p e r s a m a a n 1 .

3 5 2

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T a b e l 2 . N i l a i Prediksi P D B B u l a n a n Indonesia 1 9 8 4 ( 1 ) - 1 9 8 7 ( 1 2 )

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3 5 3

Insukindro

p e r l u d i l a k u k a n u j i s t a t i s t i k t, F , a u t o k o r e l a s i , h e t e r o s k e d a s t i s i t a s d a n b e n t u k f u n g s i d a r i m o d e l k i t a .

D a i a m t u l i s a n i n i , p e r h a t i a n k i t a t i d a k d i p u s a t k a n p a d a n i l a i a t a u R , w a l a u p u n n i l a i e s t i m a s i u n t u k k e d u a b e s a r a n i t u m e n u n j u k k a n s e s u a t u y a n g s p e k t a k u l a r ( n i l a i n y a b e r k i s a r a n t a r a 0 , 9 9 6 0 d a n 0 , 9 9 8 7 ) . H a l i n i k a r e n a r e n d a h a t a u t i n g g i n y a R d a n R bukanlah prasyarat u n t u k m e i i b a t a t a u m e n i l a i a p a k a h s u a t u m o d e l d i s p e s i f i k a s i k a n d e n g a n b a i k a t a u t i d a k ( H e n d r y , 1 9 8 0 , p e r s a m a a n 4 s a m p a i 2 0 ; d a n D o m o w i t z et al, 1 9 8 7 ) . D i s a m p i n g i t u , n i l a i R t i d a k t e p a t u n t u k d i p a k a i s e b a g a i p e n d e k a t a n u n t u k m e n g u j i k e s e r a s i a n s u a t u m o d e l . U n t u k m e n g u j i k e -s e r a s i a n (goodness o f f i t ) s u a t u m o d e l , s e b a i k n y a d i p e r g u n a k a n b e s a r a n a t a u u j i - F ( P i n d y c k et al. 1 9 8 1 ) .

• B e r k a i t a n d e n g a n u j i - s t a t i s t i k s e p e r t i y a n g d i b i c a r a k a n d i m u k a . u j i - d i a g n o s t i k T a b e l 1 m e m u n g k i n k a n k i t a u n t u k r n e n g a n a l i s i s a p a k a h h i p o t e s i s : n o r h o t o k o r e l a s i , h o m o s k e d a s t i s i t a s d a n l i n i e r i t a s d a p a t t e r b u k t i a t a u t i d a k . S e l u r u h b a s i l e s t i m a s i d i t a k s i r d e n g a n m e t o d e O L S ( O r d i n a r y Least Squares) d e n g a n b a n t u a n p a k e t k o m p u t e r D A T A F I T ( P e s a r a n et al, 1 9 8 7 ) . N i l a i k r i t i s u n t u k u j i - s t a t i s t i k t e r k a i t d e n g a n v e r s i L M d a n F d a p a t d i p e r o l e h m a s i n g - m a s i n g d a r i t a b e l s t a t i s t i k K a i - k u a d r a t ( x ) d a n t a b e l s t a t i s t i k F; s e d a n g k a n a n g k a d a l a m k u r u n g m e n u n j u k k a n d e r a j a t k e b e ­b a s a n (degree of freedom) d a r i u j i - s t a t i s t i k t e r s e b u t .

S e c a r a u m u m , T a b e l 1 m e n u n j u k k a n b a b w a n i l a i b i t u n g u n t u k u j i : o t o k o r e l a s i , h e t e r o s k e d a s t i s i t a s d a n b e n t u k f u n g s i d a r i m o d e l b e r a d a d i b a w a b n i l a i k r i t i s m e r e k a p a d a t i n g k a t k e y a k i n a n m a r g i n a l ( m a r g i n a l significance level) s e b e s a r 5 p e r s e n . I n i b e r a r t i b a b w a h i p o t e s i s n o l n o n -o t o k o r e l a s i , h o m o s k e d a s t i s i t a s d a n b e n t u k f u n g s i y a n g l i n i e r t i d a k d a p a t d i t o l a k .

S e b a g a i i i u s t r a s i m e n g e n a i u j i - s t a t i s t i k t e r s e b u t k i t a a m a t i T a b e l 1 p e r s a m a a n n o m e r 1 . N i l a i b i t u n g u n t u k u j i o t o k o r e l a s i a t a u k o r e l a s i s e r i a l ( s e r i a l C o r r e l a t i o n ) b e r d a s a r k a n v e r s i L M ( 1 2 ) d a n F ( 1 2 , 2 9 ) m a s i n g - m a s i n g b e s a r n y a 1 1 , 4 2 3 d a n 0 , 7 7 5 9 ; s e d a n g k a n n i l a i t a b e l x ^ ( 1 2 ) d a n F ( 1 2 , 2 9 ) p a d a d e r a j a t k e y a k i n a n m a r g i n a l 5 p e r s e n m a s i n g - m a s i n g a d a i a b 2 1 , 0 2 6 d a n 2 , 1 0 . I n i m e n u n j u k k a n b a b w a m o d e l t i d a k m e n g a n d u n g a d a n y a o t o k o r e l a s i . K e s i m p u l a n i n i s e l a r a s d e n g a n b a s i l y a n g d i p e r o l e h b i l a d i ­p e r g u n a k a n u j i - s t a t i s t i k D u r b i n - b . D e n g a n c a r a y a n g s a m a d a p a t p u l a d i a m a t i u j i y a n g l a i n n y a .

S e t e l a b d i k e t a h u i b a b w a a n g g a p a n d a s a r m e t o d e O L S t e r p e n u h i , t i b a l a b s a a t n y a b a g i k i t a u n t u k m e m i l i b e s t i m a s i b e r u i a n g y a n g k e b e r a p a y a n g a k a n m e m b e r i p e n a k s i r P D B y a n g t e r b a i k . D e n g a n m e m p e r b a t i k a n u j i t, d i s a m p i n g u j i t e r s e b u t d i a t a s , d a r i T a b e l 1 d a p a t d i k e t a h u i b a b w a

3 5 4

Penurunan Data Bulanan

d e n g a n d e r a j a t k e y a k i n a n 5 p e r s e n e s t i m a s i t a h a p k e t i g a m e m b e r i k a n b a s i l e s t i m a s i y a n g r e l a t i f l e b i b b a i k d a r i p a d a y a n g l a i n n y a . P a d a t a b a p i n i t e r l i h a t , w a l a u p u n h a n y a s e c a r a m a r g i n a l , b a b w a v a r i a s i P D B 3 m a m p u d i j e l a s k a n o l e b v a r i a b e l t a k g a y u t y a n g k i t a p i l i b . D e n g a n s e n d i r i n y a e s t i m a s i t a b a p i n i l a b y a n g k i t a p i l i b , d a n P D B 3 m e r u p a k a n p e n a k s i r t e r ­b a i k b a g i P D B b u l a n a n .

Penutup

D a l a m t u U s a n i n i d i k e t e n g a h k a n s u a t u c a r a u n t u k m e n u m n k a n d a t a b u l a n a n d a r i d a t a t a h u n a n . S e j a u b y a n g p e n u l i s k e t a b u i , c a r a y a n g d i ­k e t e n g a h k a n d i s i n i m e r u p a k a n l a n g k a h a w a l d a r i u s a b a u n t u k m e n d a p a t -k a n d a t a b u l a n a n d a r i d a t a t a h u n a n d e n g a n p e n d e k a t a n i n t e r p o l a s i l i n i e r . C a r a y a n g d i k e t e n g a b k a n t i d a k b a n y a t e r b a t a s p a d a P D B , t e t a p i d a p a t d i t e r a p k a n p u l a u n t u k s e m u a d a t a y a n g m e m p u n y a i s i f a t a l i r a n (flow ) .

D i k e t e n g a b k a n n y a e s t i m a s i b e r t a h a p d i m a k s u d k a n a g a r d i p e r o l e h n i l a i p e n a k s i r d a r i d a t a y a n g d i a m a t i d a n d i h a r a p k a n m a m p u m e w a k i l i p e r i l a k u r a w a k d a t a s e b e n a r n y a . T a b a p m a n a y a n g a k a n d i p i l i h s a n g a t d i p e n g a r u h i o l e b b e r b a g a i f a k t o r d a n p e r t i m b a n g a n s i p e n e l i t i . D e n g a n d e m i k i a n , p a d a t a b a p d a n s i t u a s i t e r t e n t u , t i d a k d i t u t u p k e m u n g k i n a r b a b w a p e n e l i t i b a n y a m e m b u t u b k a n i n t e r p o l a s i t a b a p a w a l .

A k h i r n y a , s e b a g a i u s a b a u n t u k m e n u m n k a n d a t a b u l a n a n d a r i d a t ; t a h u n a n , c a r a y a n g d i k e t e n g a b k a n d i s i n i t i d a k l u p u t d a r i k r i t i k d a r m u n g k i n p e r l u d i k e m b a n g k a n l e b r b l a n j u t . H a l i n i k a r e n a a d a n y a s u a t i r u m u s a n y a n g l a i n m e n g e n a i c a r a t e r s e b u t , m e m u n g k i n k a n d i p e r o l e b n y ; d a t a t u m n a n y a n g b e r b e d a . N a m u n d e m i k i a n , s a m b i l m e n a n t i a d a n y ; p e r u m u s a n l a i n m e n g e n a i b a l s e r u p a , m u d a b - m u d a b a n c a r a p e n u m n a r t e r s e b u t m a m p u m e m e n u h i u n g k a p a n : " j i k a t i a d a r o t a n a k a r p u n h e r -g u n a " .

355

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Sumber data: 1 . B a n k I n d o n e s i a ( 1 9 8 8 ) , Statistik Ekonomi-Keuangan Indonesia. 2. I n t e r n a t i o n a l M o n e t a r y F u n d ( 1 9 8 9 ) , International Financial Statistics.

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