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http://clevelandfed.org/research/workpaper Best available copy Working Paper 8603 PATTERNS AND DETERMINANTS OF INEFFICIENCY I N STATE MANUFACTURING By P a t r i c i a Beeson and S t e p h e n H u s t e d Working p a p e r s o f t h e F e d e r a l Reserve Bank o f C l e v e l a n d a r e o r e l i m i n a r y materials circulated t o stimulate d i s c u s s i o n and c r i t i c a l comment. The . views expressed a r e those of the a u t h o r and n o t n e c e s s a r i l y t h o s e o f t h e F e d e r a l Reserve Bank o f C l e v e l a n d o r o f t h e Board o f G o v e r n o r s o f t h e F e d e r a l Reserve System. P a t r i c i a Beeson, v i s i t i n g e c o n o m i s t a t t h e F e d e r a l Reserve Bank o f C l e v e l a n d i s o n l e a v e f r o m t h e U n i v e r s i t y o f P i t t s b u r g h , where she i s a s s i s t a n t p r o f e s s o r , Oepartment o f Economics. Stephen H u s t e d i s a s s i s t a n t p r o f e s s o r , D e p a r t m e n t o f Economics, U n i v e r s i t y o f P i t t s b u r g h . An e a r l i e r v e r s i o n o f t h i s p a p e r was p r e s e n t e d a t t h e R e g i o n a l S c i e n c e M e e t i n g s i n Denver i n November 1984. Research o n t h i s p r o j e c t was f u n d e d , i n p a r t , b y t w o F a c u l t y o f A r t s a n d S c i e n c e s ( F A S ) summer r e s e a r c h g r a n t s from the University of Pittsburgh. June 1986 F e d e r a l Reserve Bank o f C l e v e l a n d http://clevelandfed.org/research/workpaper Best available copy PATTERNS AND DETERMINANTS OF INEFFICIENCY I N STATE MANUFACTURING I. I n t r o d u c t i o n The r e l a t i v e e f f i c i e n c y of t h e manufacturing s e c t o r across r e g i o n s i n the U n i t e d S t a t e s has drawn c o n s i d e r a b l e a t t e n t i o n , i n view o f the r e g i o n a l r e s t r u c t u r i n g o f the manufacturing industry i n recent years. Some a n a i y s t s have s p e c u l a t e d t h a t t h e d e c l i n e i n t h e share of n a t i o n a l o u t p u t produced i n t r a d i t i o n a l m a n u f a c t u r i n g be1 t s t a t e s m i g h t be t h e r e s u l t o f a r e l a r l te d e c l i n e i n t h e e f f i c i e n c y of manufacturing f i r m s i n t h i s r e g i o n (see H u l t e n and Schwab C19841 and Beeson C19831). Efficiency, of course, i s n o t the o n l y f a c t o r d e t e r m i n i n g t h e growth and l o c a t i o n o f i n d u s t r y . important. Costs a r e a l s o Firms i n areas t h a t a r e l e s s e f f i c i e n t can compete w i t h f i r m s i n more e f f i c i e n t r e g i o n s , i f t h e i r i n e f f i c i e n c y i s o f f s e t by lower f a c t o r costs. regions. Other oapers have c o n c e n t r a t e d on d i f f e r e n c e s i n r e l a t i v e c o s t s ac ross (See S a h l i n g and Smith C19831; B e l l a n t e C19791; Newman C19831; and C a r l t o n C19831). This paper addresses t h e q u e s t i o n o f r e l a t i v e e f f i c i e n c y d i f f e r e n c e s across regions. Even i f t h e r e g i o n a l s h i f t of t h e m a n u f a c t u r i n g s e c t o r i s n o t the r e s u l t o f a change i n r e l a t i v e e f f i c i e n c y , b u t due r a t h e r t o changes i n r e l a t i v e c o s t s . r e l a t i v e e f f i c i e n c y l e v e l s across r e g i o n s m i g h t be i m p o r t a n t . If m a n u f a c t u r i n g a c t i v i t y i s moving t o r e g i o n s t h a t a r e r e l a t i v e l y l e s s e f f i c i e n t , t h e o v e r a l l e f f i c i e n c y o f t h e economy may d e c l i n e i f i n e f f i c i e n c y i s inherent t o the region. T h i s c o u l d have r a m i f i c a t i o n s f o r such issues as t h e i n t e r n a t i o n a l c o m p e t i t i v e n e s s o f U.S. i n d u s t r y . Thus, i f t h e r e a r e r e g i o n a l d i f f e r e n c e s i n e f f i c i e n c y , i t i s i m p o r t a n t t o determine why they exist. A number of e m p i r i c a l s t u d i e s have a t t e m p t e d t o examine the sources o f http://clevelandfed.org/research/workpaper Best available copy - 2i n e f f i c i e n c y a c r o s s r e g i o n s ( s e e , f o r example, Aberg 119731; Moomaw 11981a and 1981bl; and Beeson 119833). I n many o f t h e s e s t u d i e s . however, i t i s u n c l e a r what i s meant b y p r o d u c t i v e e f f i c i e n c y , and t h e methods used i n t h e e s t i m a t i o n are n o t always c o n s i s t e n t w i t h the t h e o r y of p r o d u c t i o n . I n t h i s p a p e r , a s t o c h a s t i c f r o n t i e r p r o d u c t i o n f u n c t i o n model i s used t o measure and compare p r o d u c t i v e e f f i c i e n c y i n t h e m a n u f a c t u r i n g s e c t o r a c r o s s states i n the United States. The model i s e s t i m a t e d u s i n g s t a t e l e v e l m a n u f a c t u r i n g d a t a f o r t h e p e r i o d 1959 t o 1972. I n contrast t o the standard approach o f e s t i m a t i n g t h e average p r o d u c t i o n f u n c t i o n f o r an i n d u s t r y or a r e g i o n , t h e f r o n t i e r p r o d u c t i o n f u n c t i o n approach e s t i m a t e s t h e p r o p e r t i e s o f the " best- practiced" technology. The i n e f f i c i e n c y o f a s t a t e i s t h e n measured i n terms o f t h a t s t a t e ' s average d e v i a t i o. n . from t h i s " b e s t - p r a c t i c e " f r o n t i e r . U s i n g t h i s a p p r o a c h , we f i n d t h a t t h e r e i s a s u b s t a n t i a l amount o f v a r i a t i o n i n t e c h n i c a l i n e f f i c i e n c y across s t a t e s . regional p a t t e r n t o t h i s inefficiency, There i s a l s o an a p p a r e n t w i t h t h e S o u t h e r n s t a t e s t e n d i n g t o be t h e l e a s t e f f i c i e n t , w h i l e t h e M o u n t a i n and West N o r t h C e n t r a l s t a t e s t e n d t o be t h e most e f f i c i e n t . T h i s p a t t e r n i s changed somewhat b y c o n t r o l l i n g f o r d i f f e r e n c e s i n i n d u s t r y m i x , e d u c a t i o n l e v e l s , u n i o n i z a t i o n r a t e s and t h e l e v e l o f u r b a n i z a t i o n across s t a t e s . Once t h e s e f a c t o r s have been t a k e n i n t o account, m a n u f a c t u r i n g i n the southern s t a t e s i s s t i l l s i g n i f i c a n t l y l e s s e f f i c i e n t than i t s counterpart i n other regions. States i n the t r a d i t i o n a l m a n u f a c t u r i n g b e l t r e g i o n a r e now f o u n d t o be t h e most e f f i c i e n t , w i t h the e x c e p t i o n o f t h e New England s t a t e s , w h i c h a r e f o u n d t o be s i g n i f i c a n t l y b e l o w the average l e v e l o f e f f i c i e n c y . I n s e c t i o n I 1 o f t h i s p a p e r , we d e f i n e e f f i c i e n c y i n p r o d u c t i o n and d i s c u s s t h e methods used i n t h e e s t i m a t i o n o f t e c h n i c a l i n e f f i c i e n c y . ' In s e c t i o n 111, we p r e s e n t t h e e s t i m a t e s o f i n e f f i c i e n c y by s t a t e and examine some p o s s i b l e s o u r c e s o f t h e i n e f f i c i e n c y . This i s followed by a b r i e f d i s c u s s i o n o f t h e r e l a t i o n s h i p between e f f i c i e n c y and economic g r o w t h . r e s u l t s a r e t h e n summarized i n s e c t i o n I V . The http://clevelandfed.org/research/workpaper Best available copy 11. Theory and Methodology S t u d i e s o f n a t i o n a l o r r e g i o n a l g r o w t h i n v a r i a b l y make use o f aggregate p r o d u c t i o n f u n c t i o n s as t h e u n d e r l y i n g t h e o r e t i c a l s t r u c t u r e f o r t h e i r empirical results. These s t u d i e s g e n e r a l l y e s t i m a t e a p r o d u c t i o n f u n c t i o n w i t h a two- sided e r r o r term, and hence, a r e e s t i m a t i n g t h e average economic p r o p e r t i e s . o f t e c h n o l o g y i n an i n d u s t r y o r r e g i o n . ' u s e f u l f o r a d d r e s s i n g a number of q u e s t i o n s . This f o r m u l a t i o n i s For example, when examining t h e impact of t h e o i l c r i s i s on p r o d u c t i o n i n an i n d u s t r y o r r e g i o n , i t may be i m p o r t a n t t o know the average r a t e a t which i n p u t s a r e s u b s t i t u t e d . when examining q u e s t i o n s of e f f i c i e n c y , However, the appropriate y a r d s t i c k i s n o t the average o u t p u t a c h i e v a b l e u s i n g a g i v e n v e c t o r o f i n p u t s , b u t r a t h e r t h e maximum o u t p u t a c h i e v a b l e u s i n g t h a t v e c t o r o f i n p u t s . ' I n t h i s case, i t would be d e s i r a b l e t o compare t h e o u t p u t c u r r e n t l y b e i n g produced i n a r e g i o n w i t h t h e o u t p u t t h a t c o u l d be produced i f a l l i n p u t s were used e f f i c i e n t l y . For a s t u d y o f r e g i o n a l e f f i c i e n c y , the f r o n t i e r production function. t h e a p p r o p r i a t e f o r m u l a t i o n , then, i s A f r o n t i e r production f u n c t i o n describes t h e maximum amount o f o u t p u t o b t a i n a b l e from a g i v e n q u a n t i t y o f a s e t o f i n p u t s - - t h a t i s , a p r o d u c t i o n f u n c t i o n i s an e f f i c i e n t f r o n t i e r . Output l e v e l s below those mapped b y t h e f u n c t i o n suggest i n e f f i c i e n c y i n p r o d u c t i o n . O u t p u t l e v e l s above t h e f u n c t i o n a r e i m p o s s i b l e , b a r r i n g t e c h n o l o g y shocks. R e c e n t l y , methods have been developed t o e s t i m a t e e m p i r i c a l l y t h e parameters o f p r o d u c t i o n (and c o s t ) f r o n t i e r s . " These methods n o t o n l y a l l o w f o r measurement o f i n e f f i c i e n c y i n p r o d u c t i o n , b u t a l s o p r o v i d e e s t i m a t e s o f models t h a t a r e c o n s i s t e n t w i t h t h e o r y . o f a f r o n t i e r model appears below as e q u a t i o n ( 1 ) : A typical specification http://clevelandfed.org/research/workpaper Best available copy or equivalently: (2> lny = ln(f(X)> + v - u where : y = output, X = vector of production inputs, = production function v = s t o c h a s t i c e r r o r term w i t h mean 0 and v a r i a n c e u = a one- sided e r r o r term w i t h mean p(>O> f(.) In 0: and variance ot = natural logarithm operator The two- part e r r o r term i n ( 1 ) and ( 2 ) above has t h e f o l l o w i n g interpretation. The component v r e p r e s e n t s t h e e f f e c t s o f s t o c h a s t i c shocks t o t h e p r o d u c t i o n process ( s u c h as t h e e f f e c t s of weather) o r n o i s e i n t h e measurement o f t h e dependent v a r i a b l e . The component u 1 0 c o n s t r a i n s o u t p u t t o l i e on o r below t h e s t o c h a s t i c f r o n t i e r and t h e r e b y r e p r e s e n t s t e c h n i c a l i n e f f i c i e n c y i n production. (See appendix 1 . ) I n order t o estimate ( 2 ) , a d d i t i o n a l assumptions a r e made about t h e two- part e r r o r . a r e assumed t o be independent o f X . o f the other. F i r s t , b o t h u and v Second, each i s assumed t o be independent F i n a l l y , one must assume a d i s t r i b u t i o n f o r b o t h components. Given a d i s t r i b u t i o n f o r u ( u s u a l l y h a l f normal o r gamma) and v (normal), then ( 2 ) can be e s t i m a t e d by maximum l i k e l i h o o d . sample a s i n g l e c r o s s - s e c t i o n o f d a t a . independent across o b s e r v a t i o n s . The usual p r o c e d u r e i s t o This ensures t h a t t h e e r r o r s a r e I n estimating ( 2 ) from a s i n g l e c r o s s - s e c t i o n , however, t h e r e i s no way t o d i s e n t a n g l e s e p a r a t e measures of v and u f o r each o b s e r v a t i o n . The b e s t one can hope f o r i s an e s t i m a t e of mean i n e f f i c i e n c y o v e r t h e e n t i r e sample ( i . e . , an e s t i m a t e of p ) . Even t h i s i s p r o b l e m a t i c however, s i n c e t h e e s t i m a t e o f p depends upon t h e assumed d i s t r i b u t i o n o f u. http://clevelandfed.org/research/workpaper Best available copy This discussion suggests three major problems of the estimation with stochastic production frontiers from a single cross-section of data. First, technical inefficiency is assumed to be independent of the choice o f the input mix. This may not be true in the real world. Second, in order to estimate the model and separate the effects of inefficiency from those o f noise, specific distributional assumptions must be made about the distribution of u and v , and the choice of distribution is not independent o f the resulting estimates. Finally, it is impossible, given only a single cross-section, to estimate technical inefficiency by observation. As Schmidt and Sickles (1984) point out, all of these problems can be overcome i f one has a set of panel data (that is, a pooled time series cross-section data set). In particular, using panel data estimation methodology (see Mundlak [I9781 and Hausman and Taylor [19811), it is possible to estimate technical inefficiency by cross-section unit without making distributional assumptions. Consider the following model: (3) Iny,, = a + InX', I3 + v , , - u , i = 1 , ....,N t = 1 , . . . . ,T. The data set contains T observations on N observational units (for example, firms, states, etc.). As before. the v , are two-sided errors representing statistical noise and are assumed to be uncorrelated with the regressors. The u , represent technical inefficiency and again are non-negative. We assume the u , are i id with mean p and variance independent of the v , , . A o: and are particular distribution may (but need not) be assumed for the u ,, and it is no longer necessary to assume that the u , are independent o f the X , , . Depending upon the assumptions that are made, several alternative estimators are available. We will consider two. If the u , are assumed to be fixed over time for each cross-section of observations, then they can be absorbed into the constant term. (x. This generates a model with N different http://clevelandfed.org/research/workpaper Best available copy intercepts (a, = a - u,). The r e s u l t i n g model can be e s t i m a t e d by (OLS) a f t e r suppressing t h e c o n s t a n t and adding N dummy v a r i a b l e s . ' This model i s known as the w i t h i n e s t i m a t o r . The w i t h i n e s t i m a t o r has s e v e r a l " n i c e " p r o p e r t i e s . F i r s t , since the u , a r e t r e a t e d as f i x e d , t h e y need n o t assumed t o be independent o f the X , , . Hence, e s t i m a t e s o f O a r e c o n s i s t e n t as e i t h e r N o r T-. the i n d i v i d u a l i n t e r c e p t s o f (a,) estimator i s simple t o c a l c u l a t e . r e q u i r e s T-. Consistency o f Second, t h e w i t h i n F i n a l l y , i t i s possible t o obtain estimates o f t h e u , ( t h e C f i x e d l i n e f f i c i e n c y o f each c r o s s - s e c t i o n u n i t ) . Given t h e N e s t i m a t e d i n t e r c e p t s , done as f o l lows. This i s 2 . 2,.. . . . A .a.. d e f i ne : . (4) G =max . &) t h e n , g i v e n t h e l o g a r i t h m i c s p e c i f i c a t i o n o f the p r o d u c t i o n f r o n t i e r an index of e f f i c i e n c y , (5) IE I E , can be c a l c u l a t e d as: = lOOe -ui = lOOe -6- h Oi) This amounts t o t r e a t i n g t h e most e f f i c i e n t u n i t o f o b s e r v a t i o n i n t h e sample as 100 p e r c e n t e f f i c i e n t . w i 1 1 be t r u e as N-. A l s o , as Schmidt and S i c k l e s (1984) p o i n t o u t , t h i s F u r t h e r , t h e e s t i m a t e s o f @and '? are c o n s i s t e n t as N and T*. Suppose t h a t t h e u . a r e t r e a t e d as random and u n c o r r e l a t e d w i t h t h e regressors. I n t h i s case, t h e a p p r o p r i a t e e s t i m a t o r (under m o s t c o n d i t i o n s ) i s t h e g e n e r a l i z e d l e a s t squares (GLS) e s t i m a t o r (see Mundlak 119781). The GLS e s t i m a t o r i s e s s e n t i a l l y a weighted average o f a t i m e s e r i e s ( t h e w i t h i n e s t i m a t o r d i s c u s s e d above) and a c r o s s - s e c t i o n e s t i m a t o r . The l a t t e r i s d e r i v e d f r o m a r e g r e s s i o n on t h e means over time o f t h e r e g r e s s o r f o r each http://clevelandfed.org/research/workpaper Best available copy cross- section u n i t . The GLS w e i g h t s a r e c o n s t r u c t e d from the c o v a r i a n c e m a t r i x , which i s a f u n c t i o n o f o: and 0;:. P r o v i d e d u n c o r r e l a t e d n e s s between t h e u , and t h e o t h e r r e g r e s s o r s , the GLS e s t i m a t o r produces c o n s i s t e n t e s t i m a t e s o f O and a* (=a - ':)p For samples such as o u r s , where T i s s m a l l , t h e GLS e s t i m a t o r i s e f f i c i e n t r e l a t i v e to the w i t h i n estimator. means o v e r t i m e of t h e r e s i d u a l s , E s t i m a t e s o f t h e a . can be o b t a i n e d as E , = Iny,, - 1nX' ,O. And, f o l l o w i n g t h e p r o c e d u r e d e f i n e d i n e q u a t i o n s ( 4 ) and ( 5 ) , t h e a , can be decomposed i n t o e s t i m a t e s o f c a n d C\ and an e f f i c i e n c y calculated. The e s t i m a t e s o f t h e ' ? 111. I n e f f i c i e n c y by S t a t e . index can be w i l l be c o n s i s t e n t as N and T-.' Estimation Results Our d a t a s e t i n c l u d e s o b s e r v a t i o n s on t o t a l m a n u f a c t u r i n g b y s t a t e for t h e 48 c o n t i g u o u s s t a t e s from 1959 t o 1973. We use v a l u e added i n m a n u f a c t u r i n g ( i n $100,000 o f 1972 d o l l a r s ) i n s t a t e i ( i = 1 , ..., 48) a t t i m e t ( t = 1, ..., 15) as o u r measure of o u t p u t . t a k e n f r o m v a r i o u s i s s u e s o f t h e Census of Manufactures. These d a t a were The p r i c e v a r i a b l e used t o d e f l a t e t h e nominal o u t p u t l e v e l s i s t h e i m p l i c i t p r i c e d e f l a t o r for t o t a l manufacturing. Accounts. T h i s was t a k e n from t h e N a t i o n a l Income and Product F o r o u r measure o f l a b o r we chose t o t a l p r o d u c t i o n workers hours ( i n 100s o f man- hours) i n m a n u f a c t u r i n g i n s t a t e i a t t i m e t . t h i s measure was a l s o v a r i o u s i s s u e s of t h e Census Our c a p i t a l s t o c k d a t a r e q u i r e more d i s c u s s i o n . of Our source f o r Manufactures. For some time, s t u d i e s o f p r o d u c t i o n a n d / o r p r o d u c t i v i t y a t t h e s t a t e l e v e l have been hampered b y t h e l a c k o f d a t a on s t a t e w i d e c a p i t a l s t o c k s . R e c e n t l y , however, r e s e a r c h e r s a t t h e F e d e r a l Reserve Bank o f Boston have c a l c u l a t e d e s t i m a t e s o f s t a t e l e v e l http://clevelandfed.org/research/workpaper Best available copy m a n u f a c t u r i n g c a p i t a l s t o c k u s i n g t h e p e r p e t u a l i n v e n t o r y t e c h n i q u e (see Browne, Mieszkowski, and Syron C19801). T h e i r s e r i e s r u n s f r o m 1954 t o 1976. I n o u r s t u d y , we r e s t r i c t o u r a t t e n t i o n t o t h e s h o r t e r sample p e r i o d , This i s f o r t h r e e reasons. 1959-73. F i r s t , 1959-73 r e p r e s e n t s t h e peak- to- peak o f two complete b u s i n e s s c y c l e s . Second, by d r o p p i n g t h e y e a r s 1974-76 f r o m o u r sampie, we e l i m i n a t e t h e p o t e n t i a l b i a s i n g e f f e c t s o f t h e 1974 OPEC o i l p r i c e shock. F i n a l l y , t h e year: from 1954 t o 1958 were dropped due t o p r o b a b l e e s t i m a t i o n problems i n h e r e n t i n t h e e a r l y c a p i t a l s t o c k data. ' The c a p i t a l s t o c k d a t a a r e measured i n m i l l i o n s o f 1972 d o l l a r s . Prior to e s t i m a t i o n , we s c a l e d t h e s e d a t a by t h e U . S . c a p a c i t y u t i l i z a t i o n r a t e f o r that year." Bulletin. D a t a on t h i ' s l a s t v a r i a b l e were t a k e n from t h e F e d e r a l Reserve We chose t h e t r a n s l o g p r o a u c t i o n f u n c t i o n as o u r e m p i r i c a l model o f the f r o n t i e r . T h i s model i s e s p e c i a l l y u s e f u l , s i n c e i t a l l o w s f o r n e u t r a l - and f a c t o r - a u g m e n t i n g t e c h n i c a l change as w e l l as n o n c o n s t a n t r e t u r n s t o I n a d d i t i o n , n e s t e d w i t h i n t h e t r a n s l o g s p e c i f i c a t i o n a r e t h e more scale. f a m i l i a r Cobb-Douglas and CES p r o d u c t i o n f u n c t i o n s . where Y ,, = output time t L ,, K ,, of s t a t e i ( i = 1 , . . . . , 48) a t (t = 1, . . . , 15). = l a b o r i n p u t i n s t a t e i a t t i m e t, ' = c a p i t a l i n p u t i n s t a t e i a t t i m e t, T = time trend, u , ( 2 0) = state- specific technical inefficiency, V, a, = random e r r o r , , R,, = parameters t o be e s t i m a t e d . The model i s g i v e n below: http://clevelandfed.org/research/workpaper Best available copy We w i l l s p e c i f y o u r aszumptions about the u , s h o r t l y . The v . a r e assumed t o be norma 1 1 y d i s t r i b u t e d , w i t h mean z e r o and v a r i a n c e a : , and a r e assumed t o be independent o f t h e u , . I n t a b l e 1 , we p r e s e n t o u r e s t i m a t e s o f t h e p r o d u c t i o n f r o n t i e r f o r t o t a l m a n u f a c t u r i n g u s i n g a l t e r n a t i v e l y , the w i t h i n and GLS e s t i m a t o r s . t a b l e shows, t h e f i t s a r e v e r y s t r o n g u s i n g e i t h e r e s t i m a t o r . As t h e Moreover, w i t h few e x c e p t i o n s , t h e e s t i m a t e s a r e v i r t u a l l y i d e n t i c a l , u s i n g e i t h e r e s t i m a t i o n Since t h e i n d i v i d u a l c o e f f i c i e n t s o f t h e t r a n s l o g a r e n o t r e a d i l y technique. i n t e r p r e t a b l e , we have c a l c u l a t e d the o u t p u t e l a s t i c i t i e s o f l a b o r and c a p i t a l ( E ~and E ~ r. e s p e c t i v e l y ) and the r a t e o f t e c h n i c a l change ( c r > . These e l a s t i c i t i e s a r e a l l e v a l u a t e d a t t h e means o f t h e d a t a and a r e p r e s e n t e d a t t h e b o t t o m of t a b l e 1 . The values o f these e l a s t i c i t i e s a r e c o n s i s t e n t w i t h many e m p i r i c a l s t u d i e s o f U.S. m a n u f a c t u r i n g u s i n g d a t a aggregated a t t h e n a t i o n a l l e v e l . The sum o f (RTS). E, and EK p r o v i d e s a measure o f r e t u r n s t o s c a l e Both e s t i m a t i o n t e c h n i q u e s produce e l a s t i c i t y e s t i m a t e s t h a t i m p l y i n c r e a s i n g r e t u r n s t o s c a l e i n manufacturing. The more e f f i c i e n t GLS e s t i m a t e s produce v a l u e s o f RTS s i m i l a r t o those r e p o r t e d by H a r r i s (1982) and N e r l o v e (1967). E s t i m a t e s o f t h e r a t e o f t e c h n o l o g i c a l change. Er, are e s s e n t i a l l y i d e n t i c a l and, a g a i n , a r e c o n s i s t e n t w i t h many s t u d i e s of U.S. aggregate m a n u f a c t u r i n g o v e r t h i s t i m e p e r i o d . I n t a b l e 2, we p r e s e n t t h e r a n k i n g of s t a t e s generated by o r d e r i n g t h e states according t o the size o f the individual s t a t e intercept. We a l s o r e p o r t t h e v a l u e o f t h e i n d i v i d u a l s t a t e i n t e r c e p t s produced u s i n g t h e two e s t i m a t i o n techniques and e s t i m a t e s o f t h e e f f i c i e n c y l e v e l s o f each o f t h e s t a t e s r e l a t i v e t o t h e most e f f i c i e n t s t a t e . These e s t i m a t e s o f e f f i c i e n c y (IEW f o r w i t h i n model and I E G , f o r t h e GLS model, columns 4 and 7) were c a l c u l a t e d a c c o r d i n g t o e q u a t i o n (5). Several p o i n t s emerge f r o m an e x a m i n a t i o n o f t a b l e 2. However, b e f o r e http://clevelandfed.org/research/workpaper Best available copy we c o n s i d e r these e s t i m a t e s , the q u e s t i o n a r i s e s as t o how t o d i s t i n g u i s h between t h e e s t i m a t o r s . C l e a r l y , t h i s i s r e l a t e d , i n p a r t , t o what one i s w i l l i n g t o assume about t h e u , . the u , a r e f i x e d e f f e c t s . One s a c r i f i c e s e f f i c i e n c y by assuming t h a t A l t e r n a t i v e l y , t h e GLS e s t i m a t e s a r e more e f f i c i e n t than t h e w i t h i n e s t i m a t e s i f t h e u , a r e independent o f t h e regressors. Hausman (1978) suggests a t e s t of t h i s assumption. The t e s t he proposes amounts t o adding the mean- differenced s e t o f r e g r e s s o r s t o t h e GLS s p e c i f i c a t i o n and t h e n t e s t i n g t h e j o i n t r e s t r i c t i o n t h a t t h e c o e f f i c i e n t s o f these a d d i t i o n a l v a r i a b l e s equal z e r o . We performed t h i s t e s t . s t a t i s t i c e q u a l s 16.57 and i s d i s t r i b u t i o n X i . The t e s t The v a l u e o f t h i s s t a t i s t i c i s s l i g h t l y s m a l l e r than t h e 5 p e r c e n t c r i t i c a l l e v e l , 16.32, and hence, we a r e u n a b l e t o r e j e c t t h e h y p o t h e s i s o f u n c o r r e l a t e d n e s s . Given t h i s l a s t r e s u l t , much o f t h e r e m a i n i n g d i s c u s s i o n w i l l c e n t e r on t h e GLS e s t i m a t e s . However, we n o t e i n p a s s i n g t h a t t h e r e a r e s e v e r a l s i m i l a r c h a r a c t e r i s t i c s between t h e two s e t s o f e s t i m a t e s . F i r s t , while the levels o f e f f i c i e n c y appear t o be somewhat h i g h e r u s i n g t h e GLS t e c h n i q u e , t h e r a n k i n g s are s i m i l a r u s i n g e i t h e r technique. The Spearman r a n k c o r r e l a t i o n c o e f f i c i e n t between these two s e t s o f r a n k i n g s i s 0.85, which i s s i g n i f i c a n t a t a l l l e v e l s o f confidence . Second, b o t h s e t s o f r a n k i n g s suggest a r a t h e r wide d i v e r g e n c e i n e f f i c i e n c y l e v e l s , b u t w i t h many s t a t e s bunched f a i r l y c l o s e l y t o g e t h e r i n t h e center o f the d i s t r i b u t i o n . For e i t h e r e s t i m a t o r , 75 p e r c e n t o f t h e s t a t e s l i e w i t h i n one s t a n d a r d d e v i a t i o n o f t h e mean l e v e l o f e f f i c i e n c y . The s t a t e s t h a t l i e above and below t h e one s t a n d a r d d e v i a t i o n bound a r e v i r t u a l l y i d e n t i c a l i n t n e two cases. I n f a c t , t h e same e i g h t s t a t e s appear a t t h e b o t t o m o f t h e two r a n k i n g s , a l b e i t i n s l i g h t l y d i f f e r e n t o r d e r . F i n a l l y , we n o t e t h a t r e g a r d l e s s o f our c h o i c e of e s t i m a t o r s , s t a t e s from t h e same o r nearby r e g i o n s o f t e n d i s p l a y s i m i l a r l e v e l s o f t e c h n i c a l efficiency. For i n s t a n c e , u s i n g t h e GLS r a n k i n g s . f o u r o f t h e 10 most http://clevelandfed.org/research/workpaper Best available copy efficient states come frorn the Mountain North Central (WNC) efficient are MTN (MTN) region and three from the Wejt region. Using the within estimator, five o f the 10 most states. and four are WNC. Using the GLS rankings,'our of the 10 least efficient states are from the Eas: South Centrai (ESC) region, and three are from the South Atlantic ( S A ) region. The comparable numbers for the within estimator are four from the ESC and two frorn the SA In summary, the results from tables 1 and 2 indicate the following general conclusions regarding aggregate manufacturing in the U.S.: 1. Estimates o f the production f r ~ n t i e rsuggest that aggregate U.S. manufacturing occurs under conditions of increasing returns to scale. This implies that any study of aggregate manufacturing that . . approximates the share.of one factor of production as unity, minus the sum of shares to other factors, will produce biased measures o f such important variables as total factor productivity growth. 2. There is evidence o f substantial technical inefficiency in U.S. manufacturing. 3. There is an apparent regional pattern to technical inefficiency in U . S . manufacturing. These three results argue strongly for the use of frontier estimation methodology employed in this paper. They also raise questions regarding regional patterns in technical inefficiency. two of these questions: inefficiency? In the next section, we consider First, what determines the level of technical Second, how does technical inefficiency in production relate to other aspects of production, such as total factor productivity and patterns of industrial location? http://clevelandfed.org/research/workpaper Best available copy Sources of Inefficiency. In the previous section, we noted substantial differences in the level of state technical inefficiency in manufacturing. What could lead to differences in inefficiency across states? Several factors come to mind. First, differences could simply be due to aggregation biases In particular, there are substantial differences in industrial mix across states. Second, differences could be due to basic differences in the quaiity of the labor force or in the labor-relations climate across states. possibility is that states differ by degree of urbanization. A third If the presence of larger cities led to a faster degree of dissemination of new technologies, then this could also help to explain state-by-state inefficiency levels. To test these variables as potential explanations, we estimated the fol lowing model : A (7) u , where = yo + y , D U R ,+ y,EDUC, + y UNION, + v ~ M E T R O + Regional Dummies + E 5? - level of technical inefficiency for state i calculated from the GLS estimates. (Equation C41 and column 6 of table 2 . ) OUR, = production of total manufacturing in state i accounted for by durable goods output. ' ' I Expected sign, uncertain. Source, Census of Manufactures. EDUC, = percent o f the labor force in state i with a minimum of a high school education (average of annual values 1959-73). Expected sign, negative. Source, Census of Population. METRO, = percent of the population in state i living in metropolitan areas (average of annual values 1959-73). Expected sign, negative. Source, Census of Population. UNION, = percent of production workers in state i that is unionized (1973-75 CPS surveys). Expected sign, uncertain. Source, Freeman and Medoff (1979, table 4 ) . http://clevelandfed.org/research/workpaper Best available copy We e s t i m a t e d e q u a t i o n ( 7 ) u s i n g o r d i n a r y l e a s t squares (OLS) under ;everal a l t e r n a t i v e hypotheses r e g a r d i n g r e g i o n a l a f f i l i a t i o n o f s t a t e s and c o e f f i c i e n t e q u a l i t y r e s t r i c t i o n on t h e r e g i o n a l dummy v a r i a b l e s . S p e c i f i c a l l y , we found i n two i n s t a n c e s t h a t s e v e r a l s t a t e s e x h i b i t e d p a t t e r n s o f b e h a v i o r t h a t were s i g n i f i c a n t l y d i f f e r e n t from t h e m a j o r i t y o f s t a t e s w i t h i n a U . S . Census r e g i o n . K e n t u c k y , f o r i n s t a n c e , appeared t o have a much lower l e v e l o f t e c h n i c a l i n e f f i c i e n c y t h a n t h e r e m a i n d e r o f t h e ESC r e g i o n . Since Kentucky seemed t o match more c l o s e l y t h e performance o f s t a t e s f r o m the ENC r e g i o n , and g i v e n K e n t u c k y ' s p r o x i m i t y t o t h a t r e g i o n , we changed the r e g i o n a l a f f i l i a t i o n t o ENC. S i m i l a r l y , Delaware, West V i r g i n i a , and Maryland d i d n o t appear t o have l e v e l s o f t e c h n i c a l i n e f f i c i e n c y t h a t matched we1 1 w i t h t h e r e m a i n d e r ' o f t h e SA r e g i o n s t a t e s . . Given t h a t t h e s e s t a t e s a r e c o n t i g u o u s , we separated them from t h e SA r e g i o n and grouped them i n t o a new r e g i o n , dubbed MSA. To t e s t the v a l i d i t y o f these g r o u p i n g s , v i s a v i s t h e census d e f i n i t i o n s , we r a n two s e p a r a t e r e g r e s s i o n s . A t e s t o f the n u l l h y p o t h e s i s t h a t t h e s t a t e s belonged t o t h e Census g r o u p i n g s y i e l d e d an F s t a t i s t i c o f 9.33, which i s s i g n i f i c a n t a t a l l u s u a l c o n f i d e n c e l e v e l s . " A f t e r r e d e f i n i n g r e g i o n a l a f f i l i a t i o n , we c o n s i d e r e d a v a r i e t y o f r e s t r i c t i o n s on e q u a l i t y o f r e g i o n a l dummies. A Meanofu,=.312 - R'=.61 The model t h a t y i e l d e d t h e h i g h e s t R2 i s : S . E . R. = .098 ( s t a n d a r d e r r o r s i n parentheses) The r e s u l t s above seem r e m a r k a b l y s t r o n g . The r e g r e s s i o n model e x p l a i n s more http://clevelandfed.org/research/workpaper Best available copy than 60 p e r c e n t o f the c r o s s - s e c t i o n a l v a r i a t i o n i n u . Both EDUC and METRO have t h e expected s i g n s and a r e s i g n i f i c a n t l y d i f f e r e n t from z e r o a t t h e 5 percent significance l e v e l . level. UNION i s a l s o s i g n i f i c a n t a t t h e 5 p e r c e n t The p o s i t i v e s i g n o f UNION suggests t h a t as t h e u n i o n i z a t i o n r a t e r i s e s across s t a t e s , so does t h e l e v e l o f t e c h n i c a l i n e f f i c i e n c y . does n o t seem t o be c o n t r o v e r s i a l . This r e s u l t F i n a l l y , t h e m i x o f o u t p u t between d u r a b l e s and nondurables across s t a t e s may c o n t r i b u t e t o t e c h n i c a l inefficiency. The c o e f f i c i e n t of DUR i s p o s i t i v e and s i g n i f i c a n t a t t h e 10 p e r c e n t l e v e l s u g g e s t i n g t h a t t e c h n i c a l i n e f f i c i e n c y r i s e s w i t h t h e share o f d u r a b l e goods o u t p u t i n t o t a l m a n u f a c t u r i n g . H o l d i n g t h e e f f e c t s of the economic v a r i a b l e s above c o n s t a n t , i t i s c l e a r from t h e s i g n s and f r o m the p r e c i s i o n of e s t i m a t i o n o f t h e r e g i o n a l dummies t h a t r e g i o n a l e f f e c t s are important. C l e a r l y , t h e South and the N o r t h East d i s p l a y h i g h e r l e v e l s of t e c h n i c a l i n e f f i c i e n c y , w h i l e s t a t e s from t h e MSA, ENC, and WNC d i s p l a y lower- than- average l e v e l s o f t e c h n i c a l i n e f f i c i e n c y . E f f i c i e n c y and Growth. I s technical i n e f f i c i e n c y important? The answer t o t h a t q u e s t i o n would seem t o depend upon t h e r e l a t i o n s h i p between t e c h n i c a l i n e f f i c i e n c y and o t h e r dimensions o f economic performance. Economic t h e o r y , which i s based on maximizing b e h a v i o r , o f f e r s v e r y l i t t l e guidance on t h i s i ssue. However, t h e r e l a t i o n s h i p between t e c h n i c a l i n e f f i c i e n c y and p r o d u c t i v i t y g r o w t h has been analyzed t o some e x t e n t . Caves (1984) argues t h a t t h e r e l a t i o n s h i p between t e c h n i c a l i n e f f i c i e n c y and p r o d u c t i v i t y growth c o u l d be p o s i t i v e o r negative. For i n s t a n c e , if t e c h n i c a l i n e f f i c i e n c y r e s u l t s f r o m " s u b - o p t i m i z a t i o n by o r g a n i z a t i o n a l c o a l i t i o n s , i t seems p l a u s i b l e t h a t t h e http://clevelandfed.org/research/workpaper Best available copy failing ihould affect both static if and dyndmic 9fficiency." On t 3 e 3tner productivity growth is embodied in capital and cannot be refitted to -i::d. old capital goods, ~nder-;nost empirical schemes for neasurins capital, high '~r,=.dth rates of producrivi::~ , @ u l d be stat'st'caliv technical ineff i cienc,:. LJs ing ,:or!-ei;tpd a single rros; c r- <ound 5GrTIe weak evidence to 5ugGest that . ; with !e,,els ;f noastry-!eve1 data, Cavej the r:2r-teiation betheen inefficieqcy and productivity growth is negative, implying tnat persistent tecnnical inefficiency reduces the likelhood for innovation and adoption of new methods 3 P production. He also briefly investigated this issue. Using data from Beeson (1986). ;;ions Setween values o f A u , and levels o f total we ran simple OL factor productiv~i, yo ,...- o y state. We consider two different dependent variables. First, T F P , , is the average rate of growth in total factor productivity growth in state manufacturing from 1959 to 1973. T ~ P , is the analogous variable over the shorter sample period 1965-73. The results of these regressions are m e a n o f T;P, = .a28 mean of T ~ P , = .025 -R ' = - -R - = .023 .021 S.E.R. S.E.R. = .006 = .009 (standard errors in parentheses) As the results suggest, there is virtually no evidence to support a l i n k between total-factor productivity growth and tecnnical inefficiency. coefficient of 3 in The the second regression is significantly positive at the 15 percent confidence level. This result is mildly contradictory to the industry http://clevelandfed.org/research/workpaper Best available copy findings reported by Caves. As we noted in our introduction, technical inefficiency may be a determinant o f industrial location. To test this hypothesis, we collected data o n various measures of state manufacturing activity for the five-year period immediately following the period covered in our study. These data included measures of the average annual change in real value added in manufacturing, in production worker hours, in total employment, and in The source for these data was the Census of production worker employment. Manufactures. In alternate experiments, these four variables were regressed on IEG--our measure of efficiency in production. If efficiency is a determinant o f industrial activity, we would expect the coefficient on IEG t o be positive. This was the case i'n all four regressions: 7 4 real value added = .001 + ( .026> ( .0004 IEG .0004> - m e a n o f d e p e n d e n t v a r i a b l e = .030 R L = .005 7' production worker hours = -.037 + .0006 IEG (.022> (.0003> mean of dependent variable = .008 %A total manufacturing employment - R' = .069 = mean o f dependent variable = .016 7~ production worker employment mean of dependent variable = S.E.R. .028 = S.E.R. .022 = -.021 + .0005 IEG (.020> (.0003> R' = .052 S.E.R. = -020 =-.028 + .00005 IEG (.021) (.00003> - .010 R' = .048 S.E.R. = 0.22 (Standard errors in parentheses) Given the poor performance of the first regression reported in this set, we http://clevelandfed.org/research/workpaper Best available copy cannot e s t a b l i s h a s t r o n g l i n k between t h e g r o w t h i n m a n u f a c t u r i n g a n d technical efficiency levels. The r e m a i n i n g t h r e e r e g r e s s i o n s , however, do seem t o p o i n t t o a p o s i t i v e and s i g n i f i c a n t r e l a t i o n s h i p between l a b o r u t i l i z a t i o n and t e c h n i c a l e f f i c i e n c y l e v e l s . IV. Conclusions I n t h i s paper, we sought t o examine t h e q u e s t i o n o f whether s t a t e s d i f f e r i n terms o f t e c h n i c a l i n e f f i c i e n c y i n t h e i r m a n u f a c t u r i n g s e c t o r s . f r o n t i e r p r o d u c t i o n approach and d a t a f o r t h e p e r i o d 1959-73, s i g n i f i c a n t differences i n inefficiency levels. Using a we have f o u n d Then. u s i n g d a t a on t h e c h a r a c t e r i s t i c s and r e g i o n a l a f f i l i a t i o n o f t h e v a r i o u s s t a t e s , we s e t o u t t o e x p l a i n the. p a t t e r n o f t h e s e i n e f f i c i e n c y l e v e l s . We found t h a t e d u c a t i o n , u n i o n a c t i v i t i e s , and u r b a n i z a t i o n l e v e l s were a l l s i g n i f i c a n t v a r i a b l e s i n explaining inefficiency. I n addition, very significant regional patterns i n i n e f f i c i e n c y emerged, w i t h t h e South and New England d i s p l a y i n g h i g h l e v e l s o f i neff i c i e n c y , and t h e t r a d i t i o n a l m a n u f a c t u r i n g be1 t r e g i o n s b e i n g more efficient. F i n a l l y , we l o o k e d t o see t o what e x t e n t s t a t e i n e f f i c i e n c y e x p l a i n e d o t h e r measures o f m a n u f a c t u r i n g performance. We f o u n d t h a t w h i l e t h e r e was no c o r r e l a t i o n between t h i s v a r i a b l e and t o t a l f a c t o r p r o d u c t i v i t y g r o w t h , t h e r e was some e v i d e n c e t o s u p p o r t t h e n o t i o n t h a t g r o w t h i n m a n u f a c t u r i n g employment i s p o s i t i v e l y r e l a t e d t o s t a t e e f f i c i e n c y . A number o f i n t e r e s t i n g q u e s t i o n s remain t o be c o n s i d e r e d . of the v a l i d i t y o f our r e s u l t ; industry level. A strong t e s t would be t o r e p l i c a t e o u r a n a l y s i s a t t h e I t would a l s o be i n t e r e s t i n g t o c o n s i d e r , u s i n g new d a t a , whether and how p a t t e r n s o f s t a t e i n e f f i c i e n c y change o v e r t i m e . http://clevelandfed.org/research/workpaper Best available copy Append i x Measures o f p r o d u c t i o n i n e f f i c i e n c y have been d e v e l o p e d b y F a r r e l l Let y (1957). = f(X,, X,) be a p r o d u c t i o n f u n c t i o n , w h e r e i n X , and X r a r e p r o d u c t i v e i n p u t s , and y i s a s i n g l e o u t p u t . Suppose f u r t h e r t h a t f ( . >d i s p l a y s c o n s t a n t r e t u r n s t o s c a l e , so t h a t f(XX,, XX,)=Xf(X, , X , > . Then l e t be t h e u n i t i s o q u a n t . 2 C o n s i d e r t h e i n p u t c h o i c e s ( f o r one u n i t of o u t p u t ) A , 8 , and C. Production of one u n i t i s t e c h n i c a l l y e f f i c i e n t i f t h e i n p u t mix chosen l i e s on t h e u n i t i soquant. " Thus, b o t h A and B r e p r e s e n t t e c h n i c a l l y e f f i c i e n t i n p u t However, o n l y A i s b o t h t e c h n i c a l l y choices. allocatively efficient, s i n c e g i v e n f a c t o r p r i c e r a t i o , w , A. r e p r e s e n t s t h e c o s t - m i n i m i z i n g i n p u t mix f o r u n i t a r y o u t p u t . ' ' g i v e n by: Ee = OEIOF. An index o f t h e l e v e l o f e f f i c i e n c y a t p o i n t B i s http://clevelandfed.org/research/workpaper Best available copy The i n p u t c h o i c e a t p o i n t C r e f l e c t s b o t h a l l o c a t i v e and t e c h n i c a l inefficiency. Ec An index o f t h e l e v e l of e f f i c i e n c y a t p o i n t C i s : = OEIOC = OEIOD ' OD/OC. where : OEIOD = index o f a l l o c a t i v e e f f i c i e n c y a t p o i n t C. ODIOC = index o f t e c h n i c a l e f f i c i e n c y a t p o i n t C. Thus, t o t a l e f f i c i e n c y i s t h e p r o d u c t o f a l l o c a t i v e and t e c h n i c a l efficiency.'Vy this definition, E, would have a v a l u e o f u n i t y . measure o f i n e f f i c i e n c y a s s o c i a t e d w i t h p o i n t s l i k e C would be 1 - A Ec. Notes 1 . T h i s s e c t i o n borrows h e a v i l y from Schmidt and S i c k l e s (1984). 2 . An a l t e r n a t i v e i n t e r p r e t a t i o n of these " average" p r o d u c t i o n f u n c t i o n s i s t h a t t h e y assume t h a t a l l f i r m s ( r e g i o n s ) a r e e q u a l l y e f f i c i e n t , and t h a t a l l e r r o r s a r e t h e r e s u l t o f t e c h n o l o g y shocks. This i s a t e s t a b l e , b u t seldom tested, hypothesis. 3. S t u d i e s , such as those by H u l t e n and Schwab (1984); G o l l o p and Jorgenson (1980); and K e n d r i c k and Grossman (19801, t h a t c a l c u l a t e r a t e s o f t o t a l f a c t o r p r o d u c t i v i t y growth based on f a c t o r shares use methodology c o n s i s t e n t w i t h t h e i r underlying theory. However, t h e s e l a t t e r s t u d i e s can be c r i t i c i z e d on http://clevelandfed.org/research/workpaper Best available copy two grounds. First, they rely on untested theoretical assumptions about the structure of the underlying technology, such as constant returns to scale. Second, standard statistical inference cannot be performed on the estimates from these studies. 4. For a detailed discussion o f this methodology, see Forsund, Lovell, and Schmidt (1980). 5. Alternatively, one could retain the constant and add N-1 dummies, or estimate the model by OLS after expressing all of the data as deviations from their cross-section means. 6. Hausman (19789 describes several tests of uncorrelatedness. 7. If uncorrelatedness cannot be rejected, another estimator is available. This is the maximum likelihood estimator (MLE). Maximum likelihood estimates can be obtained, provided one assumes distributions for the u , and the v . Pitt and Lee (1981) have derived the likelihood function for the case where the v , , are normal, and the u , are half normal. Other cases are possible, but have not appeared in the literature. The reader should note that the asymptotic properties o f the MLE estimator have not been fully developed, although Schmidt and Sickles (1984) make some conjectures about these properties. 8. For more on this point, see Beeson (1983). http://clevelandfed.org/research/workpaper Best available copy 9 . D a t a o n c a p a c i t y u t i l i z a t i o n by s t a t e a r e n o t a v a i l a b l e 10. T h i s v a r i a b l e was c o n s t r u c t e d as t h e a v e r a g e o f v a l u e s o f t h e f o l l o w i n g f o r m u 1a : DUR, = [ s t a t e i i s o u t p u t i n S I C ' S 24, 2 5 , 32-391f t o t a l manu- f a c t u r i n g i n s t a t e i f o r t h e y e a r s 1958, 1963, 1967, 1972, and 1977. 1 ' . E v i d e n c e t h a t homogeneity i n a v a r i e t y o f c o n t e x t s does n o t e x i s t w i t h i n Census r e g i o n s can be found i n Murphy and H o f l e r i n (1984) and Beeson ( 1 9 8 3 ) . 12. F o r m a l l y , p r o d u c t i o n i s t e c h n i c a l l y i n e f f i c i e n t i f , f o r t h e p r o d u c t i o n plan .- where 7 i s a v e c t o r o f p r o d u c t i o n i n p u t s- - y o < f (?>. 13. F o r m a l l y , t h e p r o d u c t i o n p l a n ( y o , 7 )i s s a i d t o be a l l o c a t i v e l y e f f i c i e n t i f , f o r g i v e n i n p u t p r i c e s , w , , and a , , f , ( ? ) If,(??"'= W, Iw, . 14. P r o d u c t i o n can a l s o be s c a l e - i n e f f i c i e n t . T h i s would be t h e case i f p r o d u c t i o n d i d n o t o c c u r a t t h e p o i n t where p r o f i t s a r e maximized. http://clevelandfed.org/research/workpaper Best available copy TABLE 1 PARAMETER ESTIMATES OF THE PRODUCTION FRONTIER Mean Within GLS Variable v a l ue estimate estimate (1) (2) (3) Constant ( .008 .372) 1.103 1.040 R.T.S. NOTE: Standard e r r o r s i n parentheses. *indicates c o e f f i c i e n t i s s i g n i f i c a n t l y d i f f e r e n t from zero a t the 1 percent l e v e l . - http://clevelandfed.org/research/workpaper Best available copy TABLE 2 RANKING OF STATES BY EFFICIENCY LEVELS Within estimates State Region (1 1 Intercept s.e. (2) GLS e s t i m a t e s State (3) IEW ( i n %I (4) Region Intercep t (6) Utah (MTN > .320 100.0 (5) IEG ( i n 1) (7) 1 . Nevada (MTN ) -.763 .501 .100.O 2. Utah (MTN) -.998 .590 79.1 Nevada (MTN) .308 38.8 3. N . Dakota (WNC) - 1.034 .519 76.3 Delaware (SA) .275 95.6 4. Wyoming (MTN) - 1.041 .521 75.7 Minnesota (WNC) .I93 88.1 5. Delaware (SA) - 1.063 .600 74.1 Colorado (MTN 1 .I84 87.3 6. S . Dakota (WNC) - 1.084 ,525 72.5 Iowa ( WNC) .I69 86.0 7. C o l o r a d o .(MTN> - 1.208 .611 64.1 Arizona (MTN) .I59 85.1 8. Arizona (MTN Washington (PAC) 9 . Nebraska (WNC) Kentucky (ESC) 10. Iowa (WMC) Mi s s o u r i (WNC) 1 1 . Minnesota (WNC) Kansas ( WNC) 12. Kansas ( WNC) Nebraska ( WNC) 13. Vermont (NE) California (PAC) 14. Washington ( PAC New York (MA) 15. K e n t u c k y (ESC) W. V i r g i n i a (SA) 16. W. V i r g i n i a (SA) New J e r s e y (MA) 17. N . Mexico (MTN) Connecticut (NE) 18. M i s s o u r i (WNC) N. Dakota ( WNC) 19. Montana ( WNC) Massachusetts (NE) 20. I d a h o ( MTN) Wyomi n g (MTN) 21. C a l i f o r n i a (PAC) S. Dakota (WNC) > http://clevelandfed.org/research/workpaper Best available copy TABLE 2 (CONT'D) RANKING OF S T A T E S BY EFFICIENCY LEVELS State Region Within estimates Inters.e. IEW ( i n %) cept (3) (4) (2) State (5) GLS e s t i m a t e s Region I n t e r ce p t (61 IEG ( i n %I (7 > 22. New J e r s e y (MA) - 1.395 .613 53.2 Wisconsin (ENC) .060 77.1 23. Oklahoma (WSC) - 1.398 .612. 53.0 Mary1 and (SA) .039 75.5 24. New York (MA 1 - 1.399 .600 52.9 Illinois (ENC) .Oll 73.4 25. C o n n e c t i c u t (NE) - 1.406 .621 52.6 Louisiana (WSC) .011 73.4 26. Maryland (SA) - 1.419 .622 51.9 Michigan (ENC) -.001 72.5 27. L o u i s i a n a (WSC) - 1.420 .622 51 .a Oklahoma (WSC) -.002 72.5 - 1.420 .608 51.8 Texas (WSC) -.014 71.6 - 1.427 -620. 51.5' Florida (SA) -.015 71 . 5 - 1.427 .619 51.5 Vermont (NE) -.015 71.5 28. Rhode I s l a n d (NE) 29. Wisconsin (ENC) 30. Massachusetts(NE> 31. F l o r i d a (SA) Rhode I s l a n d (NE) 32. I l l i n o i s (ENC) Ohio ( ENC) 33. New Hampshire(NE) Idaho (MTN 1 34. Texas (WSC) Montana (MTN 1 35. M i c h i g a n (ENC) Oregon ( PAC 36. Oregon ( PAC I n d i ana (ENC) 37. Ohio (ENC) N. Hampshire (NE) 38. I n d i a n a (ENC) Virginia (SA) 39. V i r g i n i a (SA) - 1.595 .622 43.5 N. Mexico (MTN) -.I40 63.1 40. Tennessee (ESC) - 1.620 .621 42.4 Tennessee (ESC) -.I40 63.1 41. Arkansas (WSC) - 1.628 .615 42.1 Pennsylvania !MA) - . 164 61.6 42. P e n n s y l v a n i a ( M A > - 1.659 .599 40.8 Alabama (ESC) -.I99 59.5 43. Alabama (ESC) - 1.665 .622 40.6 Georgia (ESC) -.200 59.5 44. G e o r g i a (ESC) - 1.684 -621 39.8 Arkansas (WSC) -.206 59.1 45. M i s s i s s i p p i (ESC) - 1.718 .616 38.5 N. C a r o l i n a (SA) - . 241 57.1 http://clevelandfed.org/research/workpaper Best available copy TABLE 2 ( C O N T ' D ) RANKING OF STATES BY EFFICIENCY LEVELS State Region Within estimates Inters.e. IEW ( i n Y!) cept (2 (3) (4) State (5) GLS e s t i m a t e s Region I n t e r cept (6) IEG ( i n %) (7) 4 6 . N. C a r o l i n a (SA) - 1.749 .612 37.3 Mississippi (ESC) -.289 54.4 4 7 . S. C a r o l i n a (SA) - 1.763 .621 36.8 5. Carolina (SA) - .290 54.3. 48. Maine (NE) - 1.769 .613 36.6 Maine (NE) - . 364 50.5 http://clevelandfed.org/research/workpaper Best available copy References Aberg, Y.. " R e g i o n a l P r o d u c t i v i t y D i f f e r e n c e s i n Swedish M a n u f a c t u r i n g , " R e g i o n a l and Urban Economics, v o l . 3, no. 2 (May 1 9 7 3 ) , p p . 131- 56. Beeson, P. "Essays i n R e g i o n a l P r o d u c t i v i t y , Ph.D. T h e s i s , U n i v e r s i t y o f Oregon, 1983. . " T o t a l F a c t o r P r o d u c t i v i t y Growth and A g g l o m e r a t i o n Economies i n mimeo, U n i v e r s i t y of P i t t s b u r g h , 1986. Manufacturing, i959-73." B e l l a n t e , D . "The N o r t h- S o u t h D i f f e r e n t i a l and t h e M i g r a t i o n o f Heterogeneous L a b o r , " 4merican Economic Review, v o l . 69, n o . 1 (March 19791, p p . 166-75. 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