Model specification: Reply to Loeb

REJOINDERS AND COMMENTARY

Ramsey, James B., and Paul Zarembka 1971 Specification Error Tests and Alternative Functional Forms of the Aggregate Production Function. Journal of the American Statistical Association, Applications Section 57:471 - 477. Submitted 9 October, 1984 Accepted 2 November, 1984

Model Specification: Reply to Loeb R i c h a r d G. F r i t z

Economics, Univ. of Central Florida, USA Charles Brandon

Accounting, Rollins College, USA James Xander

Economics, Univ. of Central Florida, USA

O u r o r i g i n a l p a p e r i n A n n a l s (I i : 2 1 9 - 229, 1984) p r e s e n t s a f o r e c a s t i n g procedure that combines time-series and econometric models and applies t h i s t e c h n i q u e to t o u r i s t a r r i v a l s b y a i r to Florida. S u b s e q u e n t l y , Loeb h a s i m p l i e d t h a t t h e m o d e l s , if misspecified, will g e n e r a t e f o r e c a s t s t h a t w o u l d n o t be o p t i m a l . In brief, he a r g u e s t h a t a " p r o p e r l y specified e c o n o m e t r i c model might indeed forecast better t h a n a forecast based on a c o m b i n a t i o n of m u l t i p l e m i s s p e c i f i e d m o d e l s . " F o r e c a s t i n g a n d Model S p e c i f i c a t i o n In f o r e c a s t i n g , m o d e l a d e q u a c y a n d e v a l u a t i o n is t r a d i t i o n a l l y m a d e b a s e d o n o n e of m a n y c r i t e r i a t h a t reflects t h e m i n i m i z a t i o n of " b a c k c a s t " error. T h i s is c o n s i s t e n t w i t h t h e goal of f o r e c a s t i n g models, w h i c h is obv i o u s l y to f o r e c a s t a s a c c u r a t e l y a s possible. It is t r u e t h a t a " p r o p e r l y specified" m o d e l m i g h t f o r e c a s t b e t t e r t h a n a m i s s p e c i f i e d s i n g l e or c o m b i n a t i o n model. However, it is also t r u e t h a t it m i g h t f o r e c a s t worse. Loeb presents no evidence that establishes a link between model specification and forecasting accuracy. Model s p e c i f i c a t i o n is critical for r e s e a r c h i n w h i c h t h e goal is to t e s t h y p o t h e s e s w i t h i n t h e c o n t e x t of a s t r u c t u r a l e q u a t i o n . A n o m i t t e d v a r i able, s i m u l t a n e o u s e q u a t i o n b i a s or i m p r o p e r s p e c i f i c a t i o n of t h e s t r u c t u r a l form of t h e r e g r e s s o r s c a n , a s n o t e d b y Loeb, lead to b i a s i n t h e e s t i m a t e d coefficients. However, t h i s is o n l y a s i g n i f i c a n t p r o b l e m if t h e m o d e l is to be u s e d to t e s t t h e o r e t i c a l l y b a s e d h y p o t h e s e s a n d n o t to forecast. As a n e x a m p l e , if t h e r e s e a r c h e r is i n t e r e s t e d i n t h e e s t i m a t i o n of t h e i n t e r e s t s e n s i t i v i t y of i n v e s t m e n t d e m a n d , t h e n b i a s i n t h e e s t i m a t e d coeff i c i e n t s c a n n o t be t o l e r a t e d s i n c e t h i s w o u l d be c o n t r a r y to t h e p u r p o s e for w h i c h t h e m o d e l w a s d e s i g n e d . However, if t h e m o d e l is m e r e l y d e s i g n e d to 256

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REJOINDERS AND COMMENTARY f o r e c a s t i n v e s t m e n t d e m a n d , b i a s in t h e c o e f f i c i e n t s is n o t a s i m p o r t a n t a s other concerns such as predictive accuracy. L o e b w a s c r i t i c a l of o u r m o d e l s " s e l e c t e d p u r e l y for p r a g m a t i c or a v a i l a b i l i t y r e a s o n s . " H o w e v e r , f o r e c a s t i n g b y its v e r y n a t u r e is p r a c t i c a l . A n o p t i m a l l y s p e c i f i e d m o d e l t h a t p e r h a p s i n c o r p o r a t e s a lag s t r u c t u r e for t h e r e g r e s s o r s t h a t r e n d e r s t h e m o d e l u s e l e s s d o e s little to d e v e l o p t h e a r t of f o r e c a s t i n g . To b e specific, o u r t h r e e p e r i o d l a g s t r u c t u r e w a s b a s e d o n t h e n e c e s s i t y of m a k i n g f o r e c a s t s t h r e e p e r i o d s a h e a d of t h e m o s t r e c e n t a v a i l a b l e d a t a o n t h e r e g r e s s o r s . If w e s h o r t e n e d t h e l a g w h i c h c o u l d h a v e b e e n d o n e o n a s c i e n t i f i c level, t h e m o d e l w o u l d h a v e b e e n u s e l e s s f r o m a p r a c t i cal s t a n d p o i n t . A l t e r n a t i v e l y , t h e r e g r e s s o r s c o u l d h a v e b e e n f o r e c a s t b u t t h i s p r o c e d u r e of c o n d i t i o n a l f o r e c a s t i n g w o u l d h a v e i n c o r p o r a t e d a n a d d i t i o n a l s o u r c e of e r r o r ( P i n d y c k a n d R u b i n f e l d 1981) a n d r e s u l t i n g in a d d i t i o n a l m o d e l d e v e l o p m e n t c o s t s . H e n c e , g i v e n t h e " g o o d " p e r f o r m a n c e of t h e m o d e l s e l e c t e d b a s e d o n w i d e l y a c c e p t e d m e a s u r e s of m o d e l a d e q u a c y , it w a s difficult to c o m p l i c a t e t h e m o d e l w i t h a n o t h e r l a y e r of f o r e c a s t i n g and additional costs when the expected benefits were apparently insignific a n t . In l i g h t of t h e m a g n i t u d e of t h e coefficient of d e t e r m i n a t i o n (.95), it h a r d l y s e e m s l i k e l y t h a t a s i g n i f i c a n t v a r i a b l e w a s i g n o r e d in t h e m o d e l s p e c i f i c a t i o n a s i m p l i e d b y Loeb. O t h e r t h e o r e t i c a l l y a p p e a l i n g v a r i a b l e s c o u l d h a v e b e e n a d d e d o r s u b s t i t u t e d for s o m e of t h o s e c h o s e n , b u t it a g a i n seems unlikely that the end result would have been a better forecasting model. L o e b p o i n t s o u t t h a t m o d e l s e l e c t i o n b y t h e c r i t e r i o n of R 2 o f t e n r e s u l t s in m i s s p e c i f i e d m o d e l s ( R a m s e y a n d G i l b e r t 1972; a n d R a m s e y a n d Z a r e m b k a 1971). H o w e v e r , t h e p u r p o s e of t h e r e s e a r c h b y R a m s e y a n d h i s c o a u t h o r s is coefficient e s t i m a t i o n b i a s , n o t f o r e c a s t a c c u r a c y . T h e r e a r e important differences between model selection given alternative objective f u n c t i o n s , In g e n e r a l , t h e p u r p o s e of e s t i m a t i n g a m o d e l is e i t h e r t h e verific a t i o n of t h e o r y (or n o n r e f u t a t i o n of t h e o r y ) v i a a n a c c u r a t e e s t i m a t i o n of t h e v a l u e of i n d i v i d u a l coefficients, or t h e p r e d i c t i o n of t h e v a l u e of t h e d e p e n d e n t v a r i a b l e in a f u t u r e period. If t h e p u r p o s e of t h e e s t i m a t i o n is to f o r e c a s t t h e v a l u e of t h e d e p e n d e n t v a r i a b l e , t h e n w e m a y i n c l u d e t h e i n t e r c o r r e l a t e d v a r i a b l e s a n d i g n o r e t h e p r o b l e m s of m u l t i c o l l i n e a r i t y , p r o v i d e d t h e s a m e p a t t e r n of i n t e r c o r r e l a t i o n of e x p l a n a t o r y v a r i a b l e s will l i k e l y c o n t i n u e in t h e f u t u r e ( K o u t s o y i a n n i s 1 9 7 7 : 2 5 2 ) . In t h e c a s e of m u l ticollinearity, excluding the collinear factors may indeed undermine the BLU c h a r a c t e r of o r d i n a r y l e a s t - s q u a r e s . T h e c h o i c e c l e a r l y d e p e n d s o n t h e o r i g i n a l o b j e c t i v e b e h i n d m o d e l e s t i m a t i o n . A m o r e o b v i o u s e x a m p l e of m o d e l s p e c i f i c a t i o n ( w h i c h is i g n o r e d b y Loeb) is in s e l e c t i o n of t h e t i m e s e r i e s c o m p o n e n t of t h e c o m b i n a t i o n f o r e c a s t model. T h e o r i g i n a l m o d e l s e l e c t i o n p r o c e d u r e a s o u t l i n e d b y Box a n d J e n k i n s (1971) is b a s e d on j u d i c i o u s e v a l u a t i o n of t h e a u t o c o r r e l a t i o n a n d p a r t i a l a u t o c o r r e l a t i o n f u n c t i o n s of t h e t r a n s f o r m e d n o n s t a t i o n a r y p r o c e s s , w i t h d i a g n o s t i c s b a s e d on t h e w h i t e n o i s e p r o c e s s r e s u l t i n g f r o m t h e m o d e l e s t i m a t i o n . H o w e v e r , t h i s d o e s n o t y i e l d t h e " b e s t " f o r e c a s t i n g m o d e l , o n l y o n e of many potential "adequate" model specifications. Alternative procedures 1985 ANNALS OF TOURISM RESEARCH

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h a v e b e e n d e v e l o p e d to s e a r c h for t h e m o d e l s p e c i f i c a t i o n w i t h t h e m o s t a c c u r a t e f o r e c a s t p o t e n t i a l . T h e A k a i k e C r i t e r i o n w a s u s e d in s p e c i f y i n g t h e t i m e s e r i e s c o m p o n e n t of t h e c o m b i n a t i o n f o r e c a s t m o d e l r e p o r t e d in our article. The Akaike Criterion ignores the autocorrelation/partial autoc o r r e l a t i o n i d e n t i f i c a t i o n p r o c e d u r e a n d f o c u s e s o n t h e r e l a t i v e a c c u r a c y of t h e e s t i m a t e d m o d e l (Ang, C h u a a a n d F a t e m i 1982). In brief, m o d e l s p e c i f i c a t i o n w a s n o t i g n o r e d , a l t h o u g h it w a s n o t g i v e n t h e s a m e a t t e n t i o n a s it m i g h t h a v e b e e n i f a s t r u c t u r a l e q u a t i o n w a s to be e s t i m a t e d for t h e p u r p o s e of t e s t i n g t h e o r e t i c a l h y p o t h e s e s . In a d d i t i o n , t h e m a j o r t h r u s t of t h e r e s e a r c h w a s to d e m o n s t r a t e by c a s e s t u d y t h a t a " p r o p e r l y " w e i g h t e d c o m b i n a t i o n of f o r e c a s t s will o u t p e r f o r m a s i n g l e f o r e c a s t . D e s p i t e t h e c r i t i q u e of m o d e l s p e c i f i c a t i o n by Loeb, t h e s a m e conc l u s i o n holds. [] []

REFERENCES Ang, James, Jess H. Chuaa, and All M. Fatemi 1982 How to Use the Akaike Criterion to Automatically Specify and Construct Box-Jenkins Models. Journal of Business Forecasting 1(3):38-42. Box, G. E., and G. M. J e n k i n s 1971 Time Series Analysis: Forecasting and Control. San Francisco, CA: HoldenDay. Koutsoyiannis, A. 1977 Theory of Econometrics (Second Edition). London: Macmillan. Pindyck, Robert, and Daniel Rubinfeld 1981 Econometric Models and Economic Forecasts (Second Edition). New York: McGraw-Hill. Ramsey, J a m e s B., and R. Gilbert 1972 A Monte Carlo Study of Small Sample Properties of Tests for Specification Error. Journal of the American Statistical Association, Theory and Methods Section 6 7 : 1 8 0 - 1 8 6 . Ramsey, J a m e s B., and Paul Zarembka 1971 Specification Error Tests and Alternative Functional Forms of the Aggregate Production Function. Journal of the American Statistical Association, Applications Section 57:471 - 477. Submitted 14 J a n u a r y 1985 Accepted 24 J a n u a r y 1985

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