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The practice of econometrics: A feminist critique
Review o f Radical Political E c o n o m i c s , 31(3):40--52 All rights of r e p r o d u c t i o n in a n y f orm reserved.
© 1999 b y URPE ISSN: 0 4 8 6 - 6 1 3 4
The Practice of Econometrics: A Feminist Critique Brigitte H. Bechtold
A B S T R A C T : This paper defines feminist research methods and econometrics and then constructs a feminist critique of traditional m et hods of econometrics, notably regression and time series analysis. The role of academe and economics programs in maintaining masculinist econometric practices is also addressed. A list of remedies to be followed includes multimethod and interdisciplinary research, as well as increased reliance on inductive rather than deductive methods.
INTRODUCTION C r i t i q u e s o f e c o n o m e t r i c m e t h o d s go b a c k t o O s k a r Morgenstern's warning to econometric forecasters (1928), and have reemerged in the literature over the decades, most promin e n t l y w i t h t h e w o r k o f E . E . L e a r n e r ( 1 9 7 8 ; 1983). 1 W h a t is t h e feminist c r i t i q u e o f e c o n o m e t r i c m e t h o d s ? P e r h a p s t h e b e s t w a y t o a n s w e r t h i s q u e s t i o n is t o a s k i n s t e a d w h a t c o n s t i t u t e s a f e m i n i s t e c o n o m e t r i c m e t h o d . T h e r e is g e n e r a l l y n o a c c e p t e d d e f i n i t i o n . I n the introduction to Shulamith Reinharz's (1992) work on feminist methods in social research, we find some characterizations of feminist methods that post-modern and feminist researchers can agree on, and yet a definition that this same group may have disagreements w i t h . I n d e e d , a s R e i n h a r z w r i t e s (4), f e m i n i s t r e s e a r c h includes c o l l e c t i o n , c a t e g o r i z a t i o n , a n d e x a m i n a t i o n o f a multitude of female voices. However, these need not be female voices exclusively, and Reinharz's three definitions of feminist
1 Morgenstern warned that "forecasting in economics differs from forecasting in all other sciences in the characteristic that, in economics, the very fact of forecast leads to 'anticipations' which are bound to make the original forecast false" [as rendered by Marget 1929: 314]. This criticism was recently rediscovered by Lucas (1976).
7he Practice of Econometrics: A Feminist Critique r e s e a r c h m e t h o d s (4) a r e a l s o c o n t e n t i o u s . C o n t r a r y to h e r c l a i m s , f e m i n i s t r e s e a r c h m e t h o d s a r e not necessarily u s e d b y p e o p l e w h o s e l f - i d e n t i f y a s f e m i n i s t , t h e y a r e not necessarily m e t h o d s u s e d in r e s e a r c h p u b l i s h e d e x c l u s i v e l y in j o u r n a l s t h a t o n l y p u b l i s h f e m i n i s t r e s e a r c h , a n d t h e y a r e not necessarily u s e d e x c l u s i v e l y in research that has received awards from organizations that reward feminist research. A broader definition would see feminist research methods, i n c l u d i n g f e m i n i s t e c o n o m e t r i c s , a s m e t h o d s t h a t s t r i v e to b e i n c l u s i v e , n o t j u s t of all g e n d e r s , b u t of all c r o s s s e c t i o n s of s o c i e t y , r e g a r d l e s s o f t h e d e g r e e of t h e i r e c o n o m i c e n f r a n c h i s e m e n t . F e m i n i s t m e t h o d s a r e n o t g e a r e d to m e a s u r i n g p r o g r e s s , g r o w t h , e x p a n s i o n , or e v e n t h e m a i n t e n a n c e of t h e s t a t u s q u o , b u t to a n a c c o u n t of h u m a n w e l l b e i n g . T h u s , a f e m i n i s t r e s e a r c h m e t h o d is n o t m e r e l y c h a r a c t e r i z e d b y i n c l u s i v e n e s s of h u m a n c r o s s - s e c t i o n s , b u t a l s o in t e r m s of w h a t activity or s t a t e is b e i n g measured or observed. Dominant or masculinist theories, while not necessarily discarded, are at the very least supplemented with theories that have hitherto been marginalized by mainstream researchers. T h e a b o v e d e f i n i t i o n is c o n s i s t e n t b o t h w i t h t h e n e w c o u r s e curricula in feminist research methods, as well as recently p u b l i s h e d w o r k o n f e m i n i s t r e s e a r c h , for e x a m p l e t h e a r t i c l e s i n c l u d e d in Knowing Feminisms: On Academic Borders, Territories, a n d Tribes ( S t a n l e y 1997). T h i s w o r k s t r e s s e s t h e i n c l u s i o n of m a r g i n a l g r o u p s , e x p e r i e n c e s , a n d a s p e c t s , a n d t h e s t r e t c h i n g of a c a d e m i c b o r d e r s , c o n t r a r y to t h e e a r l i e r v i e w s t h a t f e m i n i s t r e s e a r c h is s o m e t h i n g d o n e o n l y b y w o m e n w h o s e l f - i d e n t i f y a s f e m i n i s t s a n d p u b l i s h in e x c l u s i v e l y f e m i n i s t j o u r n a l s , s u c h a s Signs or Feminist Studies. It a l s o r e c o g n i z e s t h a t f e m i n i s t j o u r n a l s a r e o f t e n r e l u c t a n t to p u b l i s h a r t i c l e s w i t h m a t h e m a t i c a l n o t a t i o n a n d e c o n o m e t r i c s , n o m a t t e r h o w f e m i n i s t t h e a u t h o r or h o w far the borders of academically acceptable research are being stretched. C o u r s e c u r r i c u l a in f e m i n i s t r e s e a r c h m e t h o d s c o m p r i s e t w o p a r t s . T h e y a p p r i s e s t u d e n t s of w h a t is a m i s s w i t h t h e s t a n d a r d mainstream methods of accumulating knowledge, and they p r e s e n t a d i v e r s e s e t of m e t h o d s t h a t p o s s e s s a t t r i b u t e s likely to be inclusive and not focus on materialist growth. Thus, by f o r m u l a t i n g t h e b i a s e s of e x i s t i n g m e t h o d s , w e o f t e n d i s c o v e r a b e t t e r , m o r e u n b i a s e d m e t h o d , a n d we c a n e x p a n d t h e t e r r i t o r i a l b o r d e r s of o u r s t u d i e s . F o r e x a m p l e , w h e n b i o l o g i s t s ' r e s e a r c h o n f r u i t flies w a s c r i t i c i z e d for i n c l u d i n g o n l y m a l e flies, a m o r e i n c l u s i v e , l e s s b i a s e d m e t h o d o l o g y w a s to i n c l u d e f e m a l e flies a s well. S i m i l a r l y , c r i t i q u e of a m e t h o d u s e d b y e c o n o m e t r i c i a n s o f t e n p o i n t s to a b e t t e r m e t h o d . Ten practices in traditional econometrics are decidedly nonf e m i n i s t , a c c o r d i n g to t h e d e f i n i t i o n i n t r o d u c e d a b o v e . T h e y are:
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(1) t he r a n d o m s a m p l i n g issue, i.e., th e neglect to recognize t h a t d a t a u s e d for s t a t i s t i c a l i n f e r e n c e s s h o u l d r e s u l t from s i m p l e r a n d o m samples; (2) t he b u s i n e s s bias in th e d a t a ro u tin ely u s e d in model i ng, i.e., a t e n d e n c y to o v e r - r e p r e s e n t activity related to t h e "haves" in society; (3) t h e e m p h a s i s on m o n e t a r y v a r i a b l e s r a t h e r t h a n "people" v a r i a b l e s s u c h as literacy rates, p o v e r t y m e a s u r e s , h o u s i n g a d e q u a c y , a c c e s s to h e a l t h care, etc., t h u s m a k i n g t h e e c o n o m y look b e t t e r t h a n it is a n d f o s t e r i n g p r e s e r v a t i o n of t h e s t a t u s quo; (4) t h e p r a c t i c e of time s e r i e s a n a l y s i s w h i c h d e f a c t o c o n s i d e r s a time series as equivalent to a h o m o g e n e o u s string, o u t of w h i c h a n y piece c a n be c u t a n d a n a l y z e d , t h u s a g a i n limiting o n e s e l f to th e s t a t u s quo of t h e proc e ss studies; (5) t he focus of time series analysis on forecasting growth, e x p a n s i o n , a n d t r e n d s , w h i c h c o n s t i t u t e s a m a s c u l i n i s t methodology, g e a r e d to c o n t i n u o u s existence a n d m a i n t e n a n c e of existing e c o n o m i c society; (6) a distinction b e t w e e n exogenous a n d e n d o g e n o u s va r i a bl e s t h a t relegates marginal, u n p r e d i c t a b l e , a n d u n i m p o r t a n t p h e n o m e n a to t he m a r g i n s of th e s t u d y at h a n d ; (7) d u m m y v a r i a b l e s to d i s t i n g u i s h b e t w e e n categories, r e l e g a t i n g w h o l e g r o u p s (e.g., w o m e n ) to t h e m a r g i n of t h e s t u d y ; (8) s t u b b o r n r e f us a l by e c o n o m e t r i c i a n s to "see" t h a t time series d a t a c a n be "mixed up" in a r e g r e s s i o n model, j u s t as are cro s s -sectio n da t a , t h u s calling into q u e s t i o n all t r a n s f o r m a t i o n s a d d r e s s i n g "bad" D u r b i n - W a t s o n s a n d like s tatistics ; (9) t h e p r a c t i c e of forecasting, w h i c h always f oc u ses on b u s i n e s s activity; a n d (10) p a t r i a r c h a l pr a c t i c e s of a c a d e m e in general a n d economics departm e n t s in p a r t i c u l a r , w h e r e M.A. s t u d e n t s are t a u g h t h o w to do t h i n g s r a t h e r t h a n to q u e s t i o n t h e o r e t i c a l a n d p h i l o s o p h i c a l i m p l i c a t i o n s of t h e i r actions, t h u s leaving u n c h a n g e d the practice of e c o n o m e t r i c s in t h e r e a l m of b u s i n e s s a n d e c o n o m i c d e v e l o p m e n t planning. It will initially be u s e f u l to g ro u p t h e s e p r o b l e m s in t h r e e s e p a r a t e sections. The first deals with the stochastic r e q u i r e m e n t s of s t a t i s t i c a l e s t i m a t i o n a n d testin g a n d w i t h th e types of d a t a g a t h e r e d for u s e in e c o n o m e t r i c models. It also briefly a d d r e s s e s t h e f e m i n i s t c r i t i q u e of f o r e c a s t i n g in a s i m u l t a n e o u s e q u a t i o n f r a m e w o r k . The s e c o n d section deals with time-series a n a l y s i s as t he p o p u l a r a l t e r na t i ve to classical regression models, a n d related i s s u e s s u c h as t h e d i s t i n c t i o n b e t w e e n c r o s s - s e c t i o n a n d times e r i e s d a t a , a n d f o r e c a s t i n g p r a c t i c e s . A s e p a r a t e s e c t i o n is de vot e d to t h e typically m a s c u l i n i s t o r g a n i z a t i o n of a c a d e m e in g e n e r a l a n d of g r a d u a t e p r o g r a m s in e c o n o m i c s in p a r t i c u l a r . F u r t h e r reflections on t he t e n n o n - f e m i n i s t practices of traditional e c o n o m e t r i c s s h o w t h a t t h e y are all r e p r e s e n t a t i o n s of a l a c k of a t t e n t i o n to detail a n d to differences from average b e h a v i o r of th e d o m i n a n t gr oup in society. The p a p e r t h e n t u r n s to a s u m m a r y of guidelines to improve e c o n o m e t r i c practices to t a k e a c c o u n t of the f e m i n i s t critique. While s o m e of t h e s e g u i d e l i n e s are s t r a i g h t 42
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THE CENTRAL LIMIT THEOREM THE REGRESSION MODEL
AND
A s p e c t s of t he i n a d e q u a t e s t o c h a s t i c n a t u r e of econom e t r i c m ode l s , c o m p a r e d to t he r e q u i r e m e n t s imposed by limiting t h e o r e m s t h a t d e s c r i b e p r o p e r t i e s of t h e r e l e v a n t s a m p l i n g distributions, cover m o s t of t he above ten categories, in p a r t i c u l a r t h e r e q u i r e d r a n d o m n e s s of s a m p l e s (1), t h e i n c l u s i v e n e s s of v a r i a b l e s i n c o r p o r a t e d in e c o n o m e t r i c m o d e l s (2 a n d 3), t h e d i s t i n c t i o n b e t w e e n e x o g e n o u s a n d e n d o g e n o u s variables (6), the u s e of d u m m y va r i a bl e s to exclude categories from th e m o d e l s to be e s t i m a t e d (7), a n d t h e e q u i v a l e n c e of t i m e - s e r i e s a n d crosssection s a m p l e s from t he point of view of m a t h e m a t i c a l statistics (8). Probably t h e m o s t s e r i o u s criticism of applied e c o n o m e t r i c s is t he failure of t he m a j o r i t y of applied e c o n o m e t r i c i a n s to realize t h a t statistical e s t i m a t i o n a n d testing t e c h n i q u e s are b a s e d on the C e n t r a l Limit T h e o r e m , w h i c h s t a t e s that, in repeated same-size large r a n d o m samples, t h e s a m p l e m e a n ~ is d i s t r i b u t e d as follows:
~ N(#, a/~[-~, as the n u m b e r of samples - - ~
[11
w h e r e N i n d i c a t e s t h e n o r m a l distribution, n is t h e s a m p l e size, a n d # a n d a are t h e p o p u l a t i o n m e a n a n d s t a n d a r d deviation. While t h e r e q u i r e d large size of n is h a n d l e d p r a g m a t i c a l l y by u s i n g r u l e s of t h u m b , t h e r e are two o t h e r r e q u i r e m e n t s for th e t h e o r e m to hold: s a m p l e s m u s t be b o t h r a n d o m a n d at leas t t h e o r e t i c a l l y r e p e a t a b l e a n infinite n u m b e r of t i m e s . W h e r e l i m i t i n g t h e o r e m s r e q u i r e r a n d o m n e s s , it u s u a l l y is simple randomness, where each population unit has equal non-zero probability of belonging to a n y given sample. While this s a m p l i n g r e q u i r e m e n t is easily v i s u a l i z e d for s a m p l e s t h a t derive from e x p e r i m e n t s , it is m u c h m o r e t e n u o u s in a classical r e g r e s s i o n model e s t i m a t e d on t he basis of s e c o n d a r y n o n - e x p e r i m e n t a l data. We also n e e d to e m p h a s i z e t h a t s i m p l e r a n d o m n e s s of s a m p l e d a t a irrevocably implies t h a t the s a m p l e observations c a n be o r d e r e d in a n y a n d every way, from w h i c h follows t h e e q u i v a l e n c e of t i m e - s e r i e s a n d c r o s s - s e c t i o n data. T h u s , if the
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e x a m i n a t i o n of s e r i a l c o r r e l a t i o n i n c r o s s - s e c t i o n d a t a is d e e m e d "silly" s i n c e w e c a n r e - o r d e r t h e s a m p l e o b s e r v a t i o n s to get rid of it, t h e s a m e c o n c l u s i o n h o l d s for t i m e - s e r i e s s a m p l e d a t a , w h i c h a l s o s h o u l d b e c a p a b l e of b e i n g " m i x e d u p " if t h e y r e s u l t f r o m simple r a n d o m samples. Justification of the Error Term
The typical linear m-equation simultaneous equation m o d e l a n d its t y p i c a l e q u a t i o n a r e listed in e x p r e s s i o n s [2] a n d [3] below: Yt = a + A Y t
+
[21
B Z t + l.tt
w h e r e A is a s u b - d i a g o n a l m a t r i x of coefficients, Z is t h e v e c t o r of the predetermined (including exogenous) variables, and y and u are the vectors summarizing the dependent variables and the stochastic error terms. Y/t = f / ( Y t - 1 , Y t - 2 . . . . ; Xt,
Xt-1 . . . . ) "{-uit
[3l
w h e r e X is t h e v e c t o r of e x o g n e o u s variables. The model's stochastic nature is c a p t u r e d in the disturbances, since each sample observation has a stochastic c o m p o n e n t . E a r l y e c o n o m e t r i c w o r k , n o t a b l y b y Wold (Bentzel a n d W o l d 1946: 1 9 - 3 3 ; W o l d 1967: ch. 1), d e m o n s t r a t e d d e f i n i t e a w a r e n e s s of t h e d i f f e r e n c e s b e t w e e n e x p e r i m e n t a l a n d n o n e x p e r i m e n t a l a n a l y s i s . R e c e n t i n t e r p r e t a t i o n s of t h e e r r o r t e r m allow for a t l e a s t five r o l e s in t h e s p e c i f i c a t i o n of a n e c o n o m e t r i c m o d e l . 2 First, a s a l r e a d y m e n t i o n e d , d a t a for t h e v e c t o r s Y a n d Z i n e q u a t i o n [2] s h o u l d r e s u l t f r o m r a n d o m s a m p l i n g to p e r m i t reliance on limiting theorems about the underlying sampling distributions. Second, the predetermined and exogenous variables a r e g e n e r a l l y m o d e l e d i n s i m p l i f i e d f o r m a s fixed a n d l i n e a r . F o u r t h , t h e Y a n d Z i n c l u d 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 r e o f t e n c o n v e n i e n t m a t e r i a l c o u n t e r - p a r t s , or p r o t o c o l v a r i a b l e s , of t h o s e i n c l u d e d in t h e t h e o r e t i c a l m o d e l f o r m u l a t i o n ; a n d , fifth, Y a n d Z a r e f r a u g h t w i t h m e a s u r e m e n t e r r o r . Wold's i n t e r p r e t a t i o n falls u n d e r t h e s e c o n d a n d t h i r d of t h e s e s o u r c e s of error. T h e f e m i n i s t c r i t i q u e of t h e j u s t i f i c a t i o n of t h e e r r o r t e r m s is f a i r l y o b v i o u s . T h e u s e of s a l i e n t a n d p r o t o c o l v a r i a b l e s to s i m u l t a n e o u s l y j u s t i f y t h e s t o c h a s t i c n a t u r e of t h e e r r o r t e r m a n d t h e o m i s s i o n of a lot of v a r i a b l e s l e a d s to t h e c o n c e r n t h a t t h e i n c l u d e d v a r i a b l e s a r e t h o s e t h a t g e n e r a l l y a r e c o n s i d e r e d to b e
2 An excellent account of the role of the error term in rescuing the classical model from the randomness criticism is found in Darnell and Evans (1990: Ch. 4). 44
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i m p o r t a n t , a n d for w h i c h o b s e r v a t i o n s a r e r e c o r d e d o n a r e g u l a r b a s i s . S a l i e n t v a r i a b l e s t e n d to b e m o n e t a r y in n a t u r e , a n d m e a s u r e b u s i n e s s a c t i v i t y s u c h a s p r o d u c t i o n , a n d i n v e s t m e n t in d u r a b l e s , a n d are, t h e r e f o r e , r e n d e r i n g visible t h e a c t i v i t i e s of t h e " h a v e s " in s o c i e t y , w h i l e o t h e r m o r e m a r g i n a l i z e d g r o u p s a n d t h e i r a c t i v i t i e s a r e n o t c o n s i d e r e d . M o r e o v e r , W o l d ' s first a r g u m e n t - that the error term captures the fact that the model's equations are about individual behavioral units, while average group b e h a v i o r is to b e e x p l a i n e d - - l e a d s f e m i n i s t o r o t h e r c r i t i c s to a r g u e t h a t n o t all i n d i v i d u a l b e h a v i o r a l u n i t s a r e i n c l u d e d . T h a t , a t b e s t , t h e d o m i n a n t g r o u p ' s b e h a v i o r is b e i n g c a p t u r e d , w h i l e non-mainstream g r o u p s of s o c i e t y a r e s u m m a r i l y i g n o r e d , o r d i s s o l v e d in t h e e r r o r t e r m . W h i l e w e c a n d i s c u s s e r r o r t e r m s a n d t h e i r c o m p o n e n t s a t l e n g t h , t h e o n l y t w o w a y s to t r u l y a d d r e s s t h i s r a n d o m n e s s p r o b l e m a r e to i n c r e a s e t h e v a r i a b l e s t h a t a r e i n c l u d e d a s s a l i e n t in e c o n o m e t r i c m o d e l s , a n d to e n h a n c e t h e r a n d o m n e s s of t h e s a m p l e d a t a b y e q u a l i z i n g t h e p r o b a b i l i t y of e a c h m e m b e r of t h e p o p u l a t i o n to b e c o m e a m e m b e r of t h e s a m p l e , i.e., b y p r a c t i c i n g i n c l u s i v e n e s s in our modeling methodology. This conclusion also makes clear that the seemingly a l t e m a t i v e c r i t i q u e s of e c o n o m e t r i c m e t h o d s a n d p a u c i t y or l a c k of d i s a g g r e g a t i o n of s a m p l e d a t a are two s i d e s of t h e s a m e coin. T h e b a s i c m o d e l s h o w n in e q u a t i o n s [2] a n d [3] also calls i n t o question the sharp dichotomy between the Y variable and the X variables. In specifying an econometric model, one often begins by l i s t i n g t h o s e v a r i a b l e s t h a t will b e e n d o g e n o u s . T h e y a r e t h e " i m p o r t a n t " v a r i a b l e s , t h o s e w e a r e e x p e c t e d to m a k e i n f e r e n c e s a b o u t . T h u s , t h e d e c i s i o n b e t w e e n e n d o g e n o u s a n d e x o g e n o u s is n o t a t all i n d e p e n d e n t of d e c i s i o n s r e l a t e d to w h a t n e e d s to b e i n c l u d e d in t h e m o d e l a c c o r d i n g to t h e r e s e a r c h e r or t h e a g e n c y p a y i n g for t h a t r e s e a r c h e r ' s w o r k . S i m i l a r l y , n o n - m a i n s t r e a m g r o u p s a r e o f t e n a c c o u n t e d for b y m e a n s of a d u m m y v a r i a b l e , which essentially formalizes their marginality. A feminist's quest for i n c l u s i v e n e s s w o u l d t r a n s l a t e i n t o t h e q u e s t for e n h a n c e d e n d o g e n e i t y , r e d u c i n g t h e n u m b e r of X v a r i a b l e s a n d i n c r e a s i n g t h e n u m b e r of Y v a r i a b l e s , n o t m e r e l y b y s h i f t i n g Xs i n t o Ys, b u t a l s o b y i n c l u s i o n of n e w v a r i a b l e s in t h e overall d a t a b a s e , t h u s reducing reliance on dummy variables. Forecasting a n d Policy Simulations Forecasting within the classical model has typically b e e n g e a r e d to t h e f o r e c a s t of b u s i n e s s activity. T h e c l o s e s t a m a c r o m o d e l c o m e s to i n c l u d i n g i n d i v i d u a l p e o p l e of all w a l k s of life is to c o n s i d e r a c t i o n s b y c o n s u m e r s . To b e a c o n s u m e r , h o w e v e r , o n e n e e d s a n i n c o m e a n d a b i l i t y to p u r c h a s e , w h i c h l e a v e s o u t all p e o p l e in t h e m a r g i n s w h o do n o t p o s s e s s t h e s e attributes. Moreover, as consumers, the only action considered w o r t h y of i n c l u s i o n in t h e m a c r o m o d e l is t h e i r e x p e n d i t u r e o n
September 1999
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goods and services produced by the business sector (and s o m e t i m e s g o v e r n m e n t ) . T h u s , it is o n l y t h e i r s u p p o r t of t h e s t a t u s q u o of t h e m a r k e t e c o n o m y t h a t is w o r t h y of c o n s i d e r a t i o n . T h i s v e r y a s p e c t of m o d e l i n g a n d f o r e c a s t i n g b e c o m e s a c e n t r a l f e m i n i s t critique. Policy s i m u l a t i o n s w i t h t h e s i m u l t a n e o u s e q u a t i o n m o d e l a r e also d e c e p t i v e . A l t h o u g h s o m e look i n c l u s i v e , t h e r e a l i t y is q u i t e t h e r e v e r s e . C o n s i d e r , for e x a m p l e , t h e s i m u l a t i o n of t h e effect of m i n i m u m w a g e in a s i m u l t a n e o u s e q u a t i o n f r a m e w o r k . 3 O n e will find t h a t t h e m i n i m u m wage h a s a small positive effect on i n f l a t i o n a n d u n e m p l o y m e n t . H o w e v e r , it is u n w i s e to c o n c l u d e from this computation that the minimum wage has a minor d e t r i m e n t a l effect o n t h e e c o n o m y . A m i n i m u m w a g e rise t y p i c a l l y decreases the wage gap between low-wage workers and other w o r k e r s i n t h e e c o n o m y . S p e c i f i c a l l y , t h e g e n d e r w a g e g a p is n a r r o w e d , a n d a m i n i m u m w a g e policy c a n b e a n effective tool to m o v e t o w a r d g e n d e r e q u a l i t y in w a g e s , a n e f f e c t of w a g e e q u a l i z a t i o n n o t c a p t u r e d in m a c r o m o d e l s . E v e n if w a g e e q u a t i o n s a r e d i s a g g r e - g a t e d b y sex, t h e y a r e u n l i k e l y to h a v e t h e r e l e v a n t d e t a i l , s u c h a s t y p e s of w a g e s e a r n e d , g e n d e r i n c i d e n c e of v i o l a t i o n s , etc. M o v i n g b e y o n d t h e w a g e e q u a t i o n , it w o u l d be i m p o s s i b l e to c a r r y t h e e f f e c t of a g e n d e r - d i s a g g r e g a t e d w a g e i n c r e a s e t h r o u g h t h e r e m a i n d e r of t h e e c o n o m y in a s i m u l a t i o n e x e r c i s e , s i n c e o n e l a c k s d a t a to d i s a g g r e g a t e c o n s u m p t i o n a n d o t h e r r e l e v a n t e q u a t i o n s in t h e m o d e l a c c o r d i n g l y . T h e effect of a rise in r e a l m i n i m u m w a g e s a n d a n a r r o w i n g of t h e w a g e g a p in t h e e c o n o m y o n h u m a n dignity, p r o d u c t i v i t y , a n d h a p p i n e s s a r e m i s s i n g a l t o g e t h e r in m o d e l s i m u l a t i o n s . T h e r e m a y b e p r o d u c t i v i t y e q u a t i o n s in t h e m o d e l , b u t p r o d u c t i v i t y is t y p i c a l l y a c o m p u t e d v a r i a b l e , m e a s u r e d a s t h e w a g e bill d i v i d e d b y t h e n u m b e r of w o r k e r s . It d o e s n o t c a p t u r e i n c r e a s e d w o r k effort a n d h i g h e r q u a l i t y w o r k t h a t m a y derive f r o m a n i n c r e a s e d s e n s e of b e l o n g i n g a n d h u m a n dignity. Overall, a m i n i m u m w a g e i n c r e a s e likely h a s a positive effect on the economy. But this c a n n o t b e c a p t u r e d g i v e n t h e c u r r e n t d e t a i l in d a t a g a t h e r e d for the macroeconomy, a n d , t h e r e f o r e , detail i n c o r p o r a t e d in m a c r o e c o n o m i c s i m u l t a n e o u s e q u a t i o n m o d e l s . In criticizing l a c k of i n c l u s i v e n e s s , t h e f e m i n i s t c r i t i q u e a l s o i n c o r p o r a t e s l a c k of c o n c e n t r a t i o n o n a s p e c t s of e c o n o m i c p o l i c i e s in t h e r e a l m of sociology, p s y c h o l o g y , a n d e n v i r o n m e n t a l s t u d i e s , e.g., effects o n h u m a n dignity, s e l f - e s t e e m , a n d air quality.
3 I have done this elsewhere (Sellekaerts 1982) in the context of a modified version of the MPS model, in which new equations for wages, prices, and productivity were incorporated to model the effect of the minimum wage. 46
September 1999
The Practice of Econometrics: A Feminist Critique
T I M E - S E R I E S A N A L Y S I S TO T H E R E S C U E ? W h i l e t h e r e a r e s o l u t i o n s to a d d r e s s t h e f e m i n i s t c r i t i q u e w i t h i n c l a s s i c a l r e g r e s s i o n m o d e l s , t h e r e is m u c h l e s s h o p e for m o d e l s in t h e c a t e g o r y of t i m e - s e r i e s a n a l y s i s . To t h e n o n - f e m i n i s t p r a c t i c e s a l r e a d y m e n t i o n e d in r e l a t i o n to r e g r e s s i o n a n a l y s i s , we m u s t n o w a d d p r a c t i c e s [4], [5], a n d [6]. Briefly, VAR (vector a u t o r e g r e s s i o n ) h a s b e c o m e p o p u l a r s i n c e t h e d e v e l o p m e n t of B o x - J e n k i n s a n a l y s i s , a u g m e n t e d w i t h T.C. L i u ' s ( 1 9 6 0 ) c r i t i c i s m of t h e p a u c i t y of v a r i a b l e s in e c o n o m e t r i c e q u a t i o n s , in l i g h t of t h e o m i s s i o n of v a r i a b l e s a s t h e s t a n d a r d w a y of a c h i e v i n g i d e n t i f i c a t i o n , a n d w i t h t h e i n t r o d u c t i o n of c a u s a l i t y a n a l y s i s for e c o n o m e t r i c m o d e l s . R e l e v a n t a r t i c l e s d e v e l o p i n g t h i s field a r e t h o s e of G r a n g e r (1969) a n d S i m s (1972, 1982). A b a s i c VAR m o d e l is p r e s e n t e d by e q u a t i o n [4] below:
AY, + y_ CY,_, : u t
[4]
w h e r e t h e s u m m a t i o n r u n s f r o m l t h r o u g h k, w h i c h is t h e m a x i mum allowable by the data, and where the matrices A and C have d i m e n s i o n k x n . T h e t i m e s e r i e s a r e t h e n t r a n s f o r m e d to g u a r a n t e e s t a t i o n a r i t y . T h i s y i e l d s t r a n s f o r m e d v a r i a b l e s , so t h a t the model's specification becomes:
Yt = ~ B y t - i + et
[51
w h e r e t h e Ys a r e n o w v a r i a b l e s r e p r e s e n t e d b y a s t a t i o n a r y p r o c e s s , all t h e a v a i l a b l e l a g s of all t h e Ys a r e i n c l u d e d o n t h e r i g h t - h a n d s i d e , a n d w h e r e t h e "error" v e c t o r is v i e w e d a s a n " i n n o v a t i o n " to t h e p r o c e s s . F o l l o w i n g t h e c h o i c e of t h e l o n g e s t l e n g t h of "/4' p o s s i b l e , c o n s i d e r i n g t h e a v a i l a b l e d e g r e e s of f r e e d o m , a d d i t i o n a l " s m o o t h n e s s " r e s t r i c t i o n s a r e a p p l i e d to f u r t h e r s i m p l i f y t h e m o d e l . Finally, p r e d i c t i o n s c a n b e m a d e , o n e p e r i o d a h e a d a t a t i m e . S i n c e n o o t h e r s o u r c e of "error" is allowed, a n d t h e b e h a v i o r of t h e s y s t e m is c o n s i d e r e d to b e u n c h a n g e d , government economic policies simply become "innovation shocks" to a n o t h e r w i s e d e t e r m i n i s t i c s y s t e m . I n its B a y e s i a n v e r s i o n (BVAR) t h e m e t h o d a l l o w s for t i m e v a r y i n g p a r a m e t e r s , in t h e s e n s e t h a t t h e c o e f f i c i e n t m a t r i c e s of t h e m o d e l follow a r a n d o m w a l k ( S i m s 1982: 140). E s t i m a t e s of t h e c o e f f i c i e n t s for t h e s t a r t of t h e s a m p l e p e r i o d a r e m o d i f i e d w i t h e a c h n e w o b s e r v a t i o n , u s i n g a K a l m a n filtering a p p r o a c h . A n o t h e r logical p r o g r e s s i o n in v e c t o r a u t o r e g r e s s i v e m o d e l i n g t a k e s u s to c o i n t e g r a t i o n ( H e n d r y 1 9 8 6 ) . T w o v a r i a b l e s a r e s a i d to b e cointegrated if t h e i r d i f f e r e n c e is s t a t i o n a r y , a p a r t f r o m a m u l t i p l i c a t i v e c o n s t a n t . T h i s b r i n g s u s b a c k to t h e b a s i c r e q u i r e m e n t for u n d e r l y i n g s t a t i o n a r i t y . September 1999
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Review of Radical Political Economics
Feministl Critique of VAR, BVAR, and Cointegration E c o n o m e t r i c m e t h o d o l o g y h a s f o c u s e d its c r i t i c i s m of t h e m e t h o d s a r o u n d t h e t h e m e t h a t t h e y a r e e q u i v a l e n t to m e a s u r e m e n t w i t h o u t t h e o r y . M o r e specifically, t h e i n c l u s i o n of o n l y a l i m i t e d n u m b e r of v a r i a b l e s , t h e c h o i c e of lag l e n g t h s o n t h e b a s i s of d e g r e e s of f r e e d o m , a n d p a r t i c u l a r l y t h e i m p o s i t i o n of s t a t i o n a r i t y of t h e t i m e s e r i e s h a v e b e e n s u b j e c t to f r e q u e n t c r i t i c i s m (see D a r n e l l a n d E v a n s 1 9 9 1 : 1 2 8 - 2 9 for a s u m m a r y ) . F u r t h e r m o r e , s i n c e VAR m o d e l s c a n in a s e n s e be s e e n a s r e d u c e d f o r m s of a s t r u c t u r a l m o d e l t h a t h a s b e e n explicitly s p e c i f i e d , a l a r g e n u m b e r of a l t e r n a t i v e s t r u c t u r a l f o r m s or e c o n o m i c t h e o r i e s c o u l d h a v e p r o d u c e d t h e r e d u c e d f o r m at h a n d , a n n i h i l a t i n g t h e p o t e n t i a l of VAR m e t h o d s to t e s t e c o n o m i c t h e o r i e s (Cooley a n d LeRoy 1985). To t h i s list, we c a n a d d t h r e e f e m i n i s t c r i t i q u e s . First, w h e n VAR f o r e c a s t s a r e c o m p a r e d w i t h t h o s e o b t a i n e d by other methods, such comparisons invariably focus on commercial f o r e c a s t s , w h i c h a r e t y p i c a l l y n o t r e p r e s e n t a t i v e of t h e b e s t results that can be obtained with traditional model simulations. Feminist criticism would also focus on the emphasis on c o m m e r c i a l f o r e c a s t s a n d activity, i.e., t h e e x c l u s i v e m a s c u l i n i s t n a t u r e of f o r e c a s t i n g in g e n e r a l . Second, e c o n o m i s t s a r e r e a l i z i n g m o r e a n d m o r e t h a t t h e e c o n o m i c p e r f o r m a n c e of a n a t i o n a n d t h e w e l l b e i n g of its p e o p l e a r e n o t well d e s c r i b e d b y m o v e m e n t s in t h e i r GNP, m o n e y s t o c k , a n d e x c h a n g e r a t e s . "Aggregates" reflect t h e t r a d i t i o n a l m a s c u l i n i s t v i e w s of e c o n o m i s t s of t h e 1 9 2 0 s . To g a t h e r i n f o r m a t i o n a b o u t t h e w e l l b e i n g of a n a t i o n ' s i n h a b i t a n t s , we m u s t m e a s u r e a n d e x p l a i n d a t a a b o u t e d u c a t i o n levels, h e a l t h c a r e a c c e s s , o w n e r s h i p p a t t e r n s , a n d so on, n o n e of w h i c h a r e f o c u s e d o n in t i m e - s e r i e s a n a l y s i s . Third, b y t h e i r v e r y n a t u r e , VAR m o d e l s m u s t v i e w t h e f u t u r e a s r e a s o n a b l y s i m i l a r to t h e p a s t . T h e r e f o r e , f u n d a m e n t a l c h a n g e s in s o c i e t y to e n h a n c e t h e lives of p e o p l e in t h e m a r g i n s a r e d i s c a r d e d a pr/or/. THE ROLE OF ACADEME ECONOMICS PROGRAMS
AND
T h e p r o l i f e r a t i o n of M a s t e r of A r t s in E c o n o m i c s p r o g r a m s , a n effort to t a p t h e i n t e r n a t i o n a l a n d d o m e s t i c m a r k e t s of g r a d u a t e s t u d e n t s w h o s e e k g r a d u a t e d e g r e e s b u t l a c k i n t e r e s t , skill, or f u n d s to e n t e r a P h . D . p r o g r a m , h a s c o n t r i b u t e d to t h e p r a c t i c e of b a d t r a d i t i o n a l m a s c u l i n i s t e c o n o m e t r i c s ( n u m b e r 10 of t h e n o n - f e m i n i s t p r a c t i c e s in t r a d i t i o n a l e c o n o m e t r i c s l i s t e d in t h e i n t r o d u c t i o n above), for five r e a s o n s . F i r s t , a c a d e m e is b y d e s i g n s l o w in a c c e p t i n g c h a n g e . As Liz S t a n l e y w r i t e s (1997: 181), " A c a d e m i c r e p r o d u c t i o n is in e s s e n c e a
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The Practice o f Econometrics: A Feminist Critique
h o m o s o c i a l o n e i n w h i c h o l d e r m e n offer p a t r o n a g e to y o u n g e r m e n w h o i n r e t u r n offer t h e a p p e a r a n c e of h o m a g e . T h e s e a r e r e l a t i o n s of s u p e r - a n d s u b o r d i n a t i o n d e p e n d e n t o n t h o s e p o w e r relations that exist between teachers and taught, initiates and neophytes." This academic reproductive system maintains the s t a t u s q u o o v e r s c a r c e a c a d e m i c r e s o u r c e s , w h i c h is r e f l e c t e d in promotions, grant evaluations, required courses on college c u r r i c u l a , a n d f u n d i n g of h i g h e r e d u c a t i o n b y t h e l e g i s l a t u r e . 4 S e c o n d , f e m i n i s t e c o n o m e t r i c s , w h i c h r e q u i r e s a t t e n t i o n to b e t t e r data, more inclusive data, and more careful evaluation than usual of s t a t i s t i c a l t e s t s a p p l i e d , r e q u i r e s t h e level of s c h o l a r l y w o r k t h a t is g e n e r a l l y a s s o c i a t e d w i t h P h . D . s t u d y a n d d i s s e r t a t i o n r e s e a r c h . T h i r d , M.A. p r o g r a m s a r e o f t e n s p e c i a l i z e d in b u s i n e s s e c o n o m i c s or i n t e r n a t i o n a l e c o n o m i c s , a n d f o c u s o n a p p l i e d e c o n o m e t r i c s to t h e e x t e n t t h a t e s t i m a t e s or f o r e c a s t s a r e m a d e of o u t p u t , profits, i n v e s t m e n t s , etc., t h a t is, v a r i a b l e s t h a t e x p r e s s c o n c e r n s of t h e b u s i n e s s w o r l d . T h e r e is n o i n t e r e s t , n o r t i m e , for t h e s e s t u d e n t s to l e a r n a b o u t t h e pitfalls of t h e m e t h o d s t h e y a p p l y . F o u r t h , M.A. p r o g r a m s h a v e f a l l e n v i c t i m to t h e f o c u s o n f a s t t r a c k e d u c a t i o n , w h e r e g r a d u a t i o n is b a r e l y a y e a r after e n r o l l m e n t in t h e p r o g r a m . To t h e e x t e n t t h a t s t a t i s t i c s a n d e c o n o m e t r i c s r e m a i n p a r t of s u c h p r o g r a m s , t h e y b e c o m e a t o o l k i t , w h e r e s t u d e n t s l e a r n h o w to m a k e a c a n n e d p r o g r a m "work" a n d p r o d u c e " r e s u l t s " r a t h e r t h a n learning when the formulas that can be computed with such p r o g r a m s a r e v a l i d . F i n a l l y , t h e p r o l i f e r a t i o n of m i c r o c o m p u t e r s and the internet have rendered data gathering and tedious c o m p u t a t i o n s o b s o l e t e for s t u d e n t s . E a s e of a c c e s s to d a t a m a k e s t h e u s e r c o m p l a c e n t a n d l e s s critical t h a n w h e n d a t a c o l l e c t i o n is t h e r e s u l t of a t e d i o u s e x p e r i m e n t or s u r v e y . W h i l e t h e M.A. t r a c k in e c o n o m i c s p r o g r a m s f o s t e r s t h e n o n feminist practice of econometrics, t h e r e is a n a d d i t i o n a l d e t r i m e n t a l s p i l l o v e r effect. M a n y s t u d e n t s in s u c h p r o g r a m s a r e non-U.S, students, and some eventually become involved with p o l i c y m a k i n g i n t h e i r h o m e c o u n t r y . T h u s , t h e y c o n t i n u e to practice maintenance of t h e p a t r i a r c h a l status quo, and s o m e t i m e s fall p r e y to " S a c h s - i s t " a d v i s o r s f r o m U.S. i n s t i t u t i o n s .
WHAT THEN MUST WE DO? T h e f e m i n i s t s o l u t i o n is n o t to d i s c a r d e c o n o m e t r i c s , b u t to u s e t h e s e t o o l s m o r e c a r e f u l l y a n d w i t h m o r e a t t e n t i o n to data gathering. While bulky and seemingly detailed simultaneous equation macromodels as well as VAR models have major s h o r t c o m i n g s i n t e n t h s of i n c l u s i v e n e s s , a n d t h e b a s i c c l a s s i c a l
4 This was the central argument of Virginia Woolf in Three Guineas (1937). September 1999
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Review of Radical Political Economics r e g r e s s i o n m o d e l is l a c k i n g in s t o c h a s t i c q u a l i t i e s r e q u i r e d to a p p l y l i m i t i n g t h e o r e m s , all is n o t lost. S e v e n g e n e r a l g u i d e l i n e s t h a t go in t h e d i r e c t i o n of a d d r e s s i n g t h e f e m i n i s t c r i t i q u e follow. It is i m p o r t a n t to r e a l i z e t h a t all of t h e s e g u i d e l i n e s m u s t b e f o l l o w e d s i m u l t a n e o u s l y , b e c a u s e a d e t a i l e d , w e l l - w e i g h t e d s e t of data, cranked into a simultaneous equation model that loses this d e t a i l i n t h e i n t e r a c t i o n w i t h o t h e r e q u a t i o n s , is to n o avail. F u r t h e r , t h e g u i d e l i n e s t h a t follow h a v e n o p a r t i c u l a r o r d e r of i m p o r t a n c e a t t a c h e d . T h e o r d e r l i s t e d is o n e of c o n v e n i e n c e , n o t of e m p h a s i s . W i t h t h e s e q u a l i f y i n g r e m a r k s , I offer t h e following list of f e m i n i s t e c o n o m e t r i c h a b i t s . 5 First, in c l a s s i c a l m o d e l s , w e m u s t l o o k for h i g h e r t - v a l u e s rather than borderline o n e s . Second, r e l i a n c e o n l i m i t e d d e p e n d e n t v a r i a b l e m e t h o d s h e l p s a d d r e s s t h e s t o c h a s t i c limitat i o n s of s a m p l e d a t a . T h e s e m e t h o d s a r e f a i r l y s t a n d a r d for researchers doing detailed work in labor market studies and p o p u l a t i o n s s t u d i e s . Third, t e c h n i c a l c o r r e c t i o n s f o r s e r i a l correlation should be avoided, since they hide misspecification r a t h e r t h a n a d d r e s s i n g it. S u c h c o r r e c t i o n s i n c l u d e t h e m e t h o d s u s e d in t i m e - s e r i e s a n a l y s i s to o b t a i n s t a t i o n a r i t y . Fourth, t h e u s e of d u m m y v a r i a b l e s h a s t h e effect of excluding g r o u p s f r o m t h e main model specification, rather than including them. This inclusion must ideally take a different form, which includes gathering data and specifying verifyable theories based on these d a t a . Fifth, s u r v e y m e t h o d s a n d e x p e r i m e n t a l m e t h o d s c a n a d d r e s s b o t h t h e p a u c i t y of d a t a a n d t h e s t o c h a s t i c n a t u r e r e q u i r e d for c l a s s i c a l s t a t i s t i c a l i n f e r e n c e . Sixth, e c o n o m e t r i c s c a n n o t b e d o n e in a v i r t u a l i n f o r m a t i o n void. E c o n o m i c s a n d , hence, econometrics must be ideally conducted in an i n t e r d i s c i p l i n a r y e n v i r o n m e n t , r e l y i n g o n f i n d i n g s in o t h e r s o c i a l sciences, behavioral sciences, and environmental studies. Seventh, a c a d e m e s h o u l d i d e a l l y b e c o m e a p l a c e for c h a n g e , i n n o v a t i o n , a n d i n c l u s i v e n e s s , n o t a m a i n b a s t i o n of t h e s t a t u s quo. Eight, c o n s i d e r i n g the confinements of mainstream theories--their data and their verification in the deductive framework of hypothesis testing--econometricians should rely m o r e o n i n d u c t i v e m e t h o d s of a n a l y s i s . I n d u c t i o n is o n e of t h e m e t h o d s i d e n t i f i e d w i t h t h e d i s c i p l i n e of d e m o g r a p h y ( P r e s t o n 1993), a n d i n d u c t i v e p r o o f s a r e c o m m o n in m a t h e m a t i c a l a n a l y s i s w h e n e v e r a n i n t e g e r c o u n t e r is p r e s e n t . It is p u z z l i n g to s e e t h a t the powerful proof by induction, which is a s t a n d a r d m a t h e m a t i c a l tool, is h a r d l y e v e r u s e d b y e c o n o m e t r i c i a n s . Yet, every time we address sample data and population data that can b e n u m b e r e d c o n s e c u t i v e l y f r o m 1 to n or N , w e o p e n t h e
5 Several of these are consistent with the five propositions to improve the study of discrimination, advocated by D. Figart (1997). 50
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The Practice of Econometrics: A Feminist Critique p o s s i b i l i t y for a p p l y i n g i n d u c t i v e p r o o f s . A m a t h e m a t i c a l p r o o f u s i n g i n d u c t i o n u s e s t h r e e s t e p s : (a) p r o v e t h e p r o p o s i t i o n at h a n d for t h e f i r s t e l e m e n t , (b) p r o v e it for c o n s e c u t i v e r e p r e s e n t a t i v e e l e m e n t s "k" a n d " k + l , " a n d (c) d r a w t h e c o n c l u s i o n t h a t it h o l d s for all e l e m e n t s i n t h e s a m p l e or p o p u l a t i o n u n d e r c o n s i d e r a t i o n . N o t e t h a t it is, b y d e s i g n , a n i n c l u s i v e p r o o f . W h e n i n d u c t i o n is u s e d a s a g e n e r a l tool of e c o n o m i c a n a l y s i s , we a t t a c h a n o t h e r m e a n i n g to t h e w o r d , i.e., t h e f a c t t h a t w e do n o t h a v e r e a d y t h e o r i e s a v a i l a b l e , a n d m a y h a v e to t r e a t d a t a we h a v e a v a i l a b l e w i t h s o m e m i s t r u s t , w h i c h e n c o u r a g e s u s to d r a w i n f e r e n c e s t h a t a r e r o o t e d i n t h e t o t a l i t y of a v a i l a b l e e v i d e n c e f r o m d i f f e r e n t m e t h o d s . A g a i n , i n d u c t i o n is s e e n to b e m o r e i n c l u s i v e t h a n is deduction.
REFERENCES B e n t z e l , R. a n d H. Wold. 1946. O n S t a t i s t i c a l D e m a n d A n a l y s i s f r o m t h e V i e w p o i n t of S i m u l t a n e o u s E q u a t i o n s . S k a n d i n a v i s k Actuarietidskrift 2 9 : 9 5 - 1 1 4 . Box, G . E . P . a n d G.M. J e n k i n s . 1 9 7 0 . Time Series A n a l y s i s : Forecasting and Control. S a n F r a n c i s c o , Calif.: H o l d e n Day. Cooley, T.F. a n d S.F. LeRoy. 1985. A t h e o r e t i c a l M a c r o e c o n o m i c s : A C r i t i q u e . Journal o f Monetary Economics 16: 2 8 3 - 3 0 8 . D a r n e l l , A d r i a n C. a n d J . L y n n e E v a n s . 1 9 9 0 . The Limits o f Econometrics. A l d e r s h o t , E n g l a n d : E. Elgar. F i g a r t , D e b o r a h M. 1 9 9 7 . G e n d e r a s M o r e t h a n a D u m m y V a r i a b l e : F e m i n i s t A p p r o a c h e s to D i s c r i m i n a t i o n . R e v i e w o f Social Economy 55: 1-32. Granger, C.W.J. 1969. Investigating Causal Relations by Econom e t r i c M o d e l s a n d C r o s s - S p e c t r a l M e t h o d s . Econometrica 37: 424-38. H e n d r y , D a v i d F. 1986. E c o n o m e t r i c M o d e l i n g w i t h C o i n t e g r a t e d V a r i a b l e s : A n O v e r v i e w . Oxford Bulletin o f Economics a n d Statistics 48: 2 0 1 - 1 2 . L e a r n e r , E.E. 1 9 7 5 . " E x p l a i n i n g Y o u r R e s u l t s " a s A c c e s s B i a s e d M e m o r y . Journal o f the A m e r i c a n Statistical Association 70: 88-93. 1983. Let's T a k e t h e "Con" o u t of E c o n o m e t r i c s . American Economic R e v i e w 7 3 : 3 1 - 4 3 . Liu, T.C. 1 9 6 0 . U n d e r i d e n t i f i c a t i o n , S t r u c t u r a l E s t i m a t i o n , a n d F o r e c a s t i n g . Econometrica 28: 8 5 5 - 6 5 . L u c a s , R o b e r t E. J r . 1 9 7 6 . E c o n o m e t r i c P o l i c y E v a l u a t i o n : A C r i t i q u e . I n T h e Phillips Curve a n d Labor Markets. Karl Brunner a n d A l l a n H. M e l t z e r (eds.). A m s t e r d a m : N o r t h Holland. M a r g e t , A r t h u r W. 1 9 2 9 . M o r g e n s t e r n o n t h e M e t h o d o l o g y of E c o n o m i c F o r e c a s t i n g . Journal of Political Economy 3 7 : 3 1 2 - 3 9 . S e p t e m b e r 1999
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Liu, T.C. 1960. U n d e r i d e n t i f i c a t i o n , S t r u c t u r a l E s t i m a t i o n , a n d Forecasting. E c o n o m e t r i c a 28: 855-65. L u c a s , R o b e r t E. J r . 1976. E c o n o m e t r i c Policy E v a l u a t i o n : A C r i t i q u e . In T h e P h i l l i p s C u r v e a n d L a b o r M a r k e t s . Karl B r u n n e r a n d A l l a n H. Meltzer (eds.). A m s t e r d a m : N o r t h Holland. Marget, A r t h u r W. 1929. M o r g e n s t e r n on th e M e t h o d o l o g y of E c o n o m i c Forecasting. J o u r n a l o f Political E c o n o m y 3 7 : 3 1 2 - 3 9 . P r e s t o n , S a m u e l H. 1993. T h e C o n t o u r s of D e m o g r a p h y : E s t i m a t e s a n d Projections. D e m o g r a p h y 30: 593-606. Re i nha rz , S h u l a m i t . 1992. F e m i n i s t M e t h o d s in Social R e s e a r c h . Oxford a n d New York: Oxford University Press. Sellekaerts, Brigitte H. 1982. I m p a c t of M i n i m u m Wage Legislation on Selected Macro Variables. E a s t e r n Economic J o u r n a l 8. Sims, C h r i s t o p h e r A. 1972. Money, I n c o m e , a n d C a u s a l i t y . A m e r i c a n E c o n o m i c R e v i e w 62: 540-52. 1982. Policy Analysis with E c o n o m e t r i c Models. B r o o k i n g s P a p e r s on E c o n o m i c Activity I: 107-52. S t a n l e y , Liz (ed.). 1997. K n o w i n g F e m i n i s m s : O n A c a d e m i c Borders, Territories, a n d Tribes. London, New Delhi: Sage. Wold, H e r m a n O.A. 1967. E c o n o m e t r i c M o d e l Building: E s s a y s on the C a u s a l C h a i n A p p r o a c h . A m s t e r d a m : North Holland. Woolf, Virginia. 1937. Three Guineas. London: Hogarth Press. Brigitte H. Bechtold D e p a r t m e n t of Sociology 137 A n s p a c h Hall Central Michigan University Mt. Pleasant, MI 48859 [email protected]
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© 1999 b y URPE ISSN: 0 4 8 6 - 6 1 3 4
The Practice of Econometrics: A Feminist Critique Brigitte H. Bechtold
A B S T R A C T : This paper defines feminist research methods and econometrics and then constructs a feminist critique of traditional m et hods of econometrics, notably regression and time series analysis. The role of academe and economics programs in maintaining masculinist econometric practices is also addressed. A list of remedies to be followed includes multimethod and interdisciplinary research, as well as increased reliance on inductive rather than deductive methods.
INTRODUCTION C r i t i q u e s o f e c o n o m e t r i c m e t h o d s go b a c k t o O s k a r Morgenstern's warning to econometric forecasters (1928), and have reemerged in the literature over the decades, most promin e n t l y w i t h t h e w o r k o f E . E . L e a r n e r ( 1 9 7 8 ; 1983). 1 W h a t is t h e feminist c r i t i q u e o f e c o n o m e t r i c m e t h o d s ? P e r h a p s t h e b e s t w a y t o a n s w e r t h i s q u e s t i o n is t o a s k i n s t e a d w h a t c o n s t i t u t e s a f e m i n i s t e c o n o m e t r i c m e t h o d . T h e r e is g e n e r a l l y n o a c c e p t e d d e f i n i t i o n . I n the introduction to Shulamith Reinharz's (1992) work on feminist methods in social research, we find some characterizations of feminist methods that post-modern and feminist researchers can agree on, and yet a definition that this same group may have disagreements w i t h . I n d e e d , a s R e i n h a r z w r i t e s (4), f e m i n i s t r e s e a r c h includes c o l l e c t i o n , c a t e g o r i z a t i o n , a n d e x a m i n a t i o n o f a multitude of female voices. However, these need not be female voices exclusively, and Reinharz's three definitions of feminist
1 Morgenstern warned that "forecasting in economics differs from forecasting in all other sciences in the characteristic that, in economics, the very fact of forecast leads to 'anticipations' which are bound to make the original forecast false" [as rendered by Marget 1929: 314]. This criticism was recently rediscovered by Lucas (1976).
7he Practice of Econometrics: A Feminist Critique r e s e a r c h m e t h o d s (4) a r e a l s o c o n t e n t i o u s . C o n t r a r y to h e r c l a i m s , f e m i n i s t r e s e a r c h m e t h o d s a r e not necessarily u s e d b y p e o p l e w h o s e l f - i d e n t i f y a s f e m i n i s t , t h e y a r e not necessarily m e t h o d s u s e d in r e s e a r c h p u b l i s h e d e x c l u s i v e l y in j o u r n a l s t h a t o n l y p u b l i s h f e m i n i s t r e s e a r c h , a n d t h e y a r e not necessarily u s e d e x c l u s i v e l y in research that has received awards from organizations that reward feminist research. A broader definition would see feminist research methods, i n c l u d i n g f e m i n i s t e c o n o m e t r i c s , a s m e t h o d s t h a t s t r i v e to b e i n c l u s i v e , n o t j u s t of all g e n d e r s , b u t of all c r o s s s e c t i o n s of s o c i e t y , r e g a r d l e s s o f t h e d e g r e e of t h e i r e c o n o m i c e n f r a n c h i s e m e n t . F e m i n i s t m e t h o d s a r e n o t g e a r e d to m e a s u r i n g p r o g r e s s , g r o w t h , e x p a n s i o n , or e v e n t h e m a i n t e n a n c e of t h e s t a t u s q u o , b u t to a n a c c o u n t of h u m a n w e l l b e i n g . T h u s , a f e m i n i s t r e s e a r c h m e t h o d is n o t m e r e l y c h a r a c t e r i z e d b y i n c l u s i v e n e s s of h u m a n c r o s s - s e c t i o n s , b u t a l s o in t e r m s of w h a t activity or s t a t e is b e i n g measured or observed. Dominant or masculinist theories, while not necessarily discarded, are at the very least supplemented with theories that have hitherto been marginalized by mainstream researchers. T h e a b o v e d e f i n i t i o n is c o n s i s t e n t b o t h w i t h t h e n e w c o u r s e curricula in feminist research methods, as well as recently p u b l i s h e d w o r k o n f e m i n i s t r e s e a r c h , for e x a m p l e t h e a r t i c l e s i n c l u d e d in Knowing Feminisms: On Academic Borders, Territories, a n d Tribes ( S t a n l e y 1997). T h i s w o r k s t r e s s e s t h e i n c l u s i o n of m a r g i n a l g r o u p s , e x p e r i e n c e s , a n d a s p e c t s , a n d t h e s t r e t c h i n g of a c a d e m i c b o r d e r s , c o n t r a r y to t h e e a r l i e r v i e w s t h a t f e m i n i s t r e s e a r c h is s o m e t h i n g d o n e o n l y b y w o m e n w h o s e l f - i d e n t i f y a s f e m i n i s t s a n d p u b l i s h in e x c l u s i v e l y f e m i n i s t j o u r n a l s , s u c h a s Signs or Feminist Studies. It a l s o r e c o g n i z e s t h a t f e m i n i s t j o u r n a l s a r e o f t e n r e l u c t a n t to p u b l i s h a r t i c l e s w i t h m a t h e m a t i c a l n o t a t i o n a n d e c o n o m e t r i c s , n o m a t t e r h o w f e m i n i s t t h e a u t h o r or h o w far the borders of academically acceptable research are being stretched. C o u r s e c u r r i c u l a in f e m i n i s t r e s e a r c h m e t h o d s c o m p r i s e t w o p a r t s . T h e y a p p r i s e s t u d e n t s of w h a t is a m i s s w i t h t h e s t a n d a r d mainstream methods of accumulating knowledge, and they p r e s e n t a d i v e r s e s e t of m e t h o d s t h a t p o s s e s s a t t r i b u t e s likely to be inclusive and not focus on materialist growth. Thus, by f o r m u l a t i n g t h e b i a s e s of e x i s t i n g m e t h o d s , w e o f t e n d i s c o v e r a b e t t e r , m o r e u n b i a s e d m e t h o d , a n d we c a n e x p a n d t h e t e r r i t o r i a l b o r d e r s of o u r s t u d i e s . F o r e x a m p l e , w h e n b i o l o g i s t s ' r e s e a r c h o n f r u i t flies w a s c r i t i c i z e d for i n c l u d i n g o n l y m a l e flies, a m o r e i n c l u s i v e , l e s s b i a s e d m e t h o d o l o g y w a s to i n c l u d e f e m a l e flies a s well. S i m i l a r l y , c r i t i q u e of a m e t h o d u s e d b y e c o n o m e t r i c i a n s o f t e n p o i n t s to a b e t t e r m e t h o d . Ten practices in traditional econometrics are decidedly nonf e m i n i s t , a c c o r d i n g to t h e d e f i n i t i o n i n t r o d u c e d a b o v e . T h e y are:
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(1) t he r a n d o m s a m p l i n g issue, i.e., th e neglect to recognize t h a t d a t a u s e d for s t a t i s t i c a l i n f e r e n c e s s h o u l d r e s u l t from s i m p l e r a n d o m samples; (2) t he b u s i n e s s bias in th e d a t a ro u tin ely u s e d in model i ng, i.e., a t e n d e n c y to o v e r - r e p r e s e n t activity related to t h e "haves" in society; (3) t h e e m p h a s i s on m o n e t a r y v a r i a b l e s r a t h e r t h a n "people" v a r i a b l e s s u c h as literacy rates, p o v e r t y m e a s u r e s , h o u s i n g a d e q u a c y , a c c e s s to h e a l t h care, etc., t h u s m a k i n g t h e e c o n o m y look b e t t e r t h a n it is a n d f o s t e r i n g p r e s e r v a t i o n of t h e s t a t u s quo; (4) t h e p r a c t i c e of time s e r i e s a n a l y s i s w h i c h d e f a c t o c o n s i d e r s a time series as equivalent to a h o m o g e n e o u s string, o u t of w h i c h a n y piece c a n be c u t a n d a n a l y z e d , t h u s a g a i n limiting o n e s e l f to th e s t a t u s quo of t h e proc e ss studies; (5) t he focus of time series analysis on forecasting growth, e x p a n s i o n , a n d t r e n d s , w h i c h c o n s t i t u t e s a m a s c u l i n i s t methodology, g e a r e d to c o n t i n u o u s existence a n d m a i n t e n a n c e of existing e c o n o m i c society; (6) a distinction b e t w e e n exogenous a n d e n d o g e n o u s va r i a bl e s t h a t relegates marginal, u n p r e d i c t a b l e , a n d u n i m p o r t a n t p h e n o m e n a to t he m a r g i n s of th e s t u d y at h a n d ; (7) d u m m y v a r i a b l e s to d i s t i n g u i s h b e t w e e n categories, r e l e g a t i n g w h o l e g r o u p s (e.g., w o m e n ) to t h e m a r g i n of t h e s t u d y ; (8) s t u b b o r n r e f us a l by e c o n o m e t r i c i a n s to "see" t h a t time series d a t a c a n be "mixed up" in a r e g r e s s i o n model, j u s t as are cro s s -sectio n da t a , t h u s calling into q u e s t i o n all t r a n s f o r m a t i o n s a d d r e s s i n g "bad" D u r b i n - W a t s o n s a n d like s tatistics ; (9) t h e p r a c t i c e of forecasting, w h i c h always f oc u ses on b u s i n e s s activity; a n d (10) p a t r i a r c h a l pr a c t i c e s of a c a d e m e in general a n d economics departm e n t s in p a r t i c u l a r , w h e r e M.A. s t u d e n t s are t a u g h t h o w to do t h i n g s r a t h e r t h a n to q u e s t i o n t h e o r e t i c a l a n d p h i l o s o p h i c a l i m p l i c a t i o n s of t h e i r actions, t h u s leaving u n c h a n g e d the practice of e c o n o m e t r i c s in t h e r e a l m of b u s i n e s s a n d e c o n o m i c d e v e l o p m e n t planning. It will initially be u s e f u l to g ro u p t h e s e p r o b l e m s in t h r e e s e p a r a t e sections. The first deals with the stochastic r e q u i r e m e n t s of s t a t i s t i c a l e s t i m a t i o n a n d testin g a n d w i t h th e types of d a t a g a t h e r e d for u s e in e c o n o m e t r i c models. It also briefly a d d r e s s e s t h e f e m i n i s t c r i t i q u e of f o r e c a s t i n g in a s i m u l t a n e o u s e q u a t i o n f r a m e w o r k . The s e c o n d section deals with time-series a n a l y s i s as t he p o p u l a r a l t e r na t i ve to classical regression models, a n d related i s s u e s s u c h as t h e d i s t i n c t i o n b e t w e e n c r o s s - s e c t i o n a n d times e r i e s d a t a , a n d f o r e c a s t i n g p r a c t i c e s . A s e p a r a t e s e c t i o n is de vot e d to t h e typically m a s c u l i n i s t o r g a n i z a t i o n of a c a d e m e in g e n e r a l a n d of g r a d u a t e p r o g r a m s in e c o n o m i c s in p a r t i c u l a r . F u r t h e r reflections on t he t e n n o n - f e m i n i s t practices of traditional e c o n o m e t r i c s s h o w t h a t t h e y are all r e p r e s e n t a t i o n s of a l a c k of a t t e n t i o n to detail a n d to differences from average b e h a v i o r of th e d o m i n a n t gr oup in society. The p a p e r t h e n t u r n s to a s u m m a r y of guidelines to improve e c o n o m e t r i c practices to t a k e a c c o u n t of the f e m i n i s t critique. While s o m e of t h e s e g u i d e l i n e s are s t r a i g h t 42
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THE CENTRAL LIMIT THEOREM THE REGRESSION MODEL
AND
A s p e c t s of t he i n a d e q u a t e s t o c h a s t i c n a t u r e of econom e t r i c m ode l s , c o m p a r e d to t he r e q u i r e m e n t s imposed by limiting t h e o r e m s t h a t d e s c r i b e p r o p e r t i e s of t h e r e l e v a n t s a m p l i n g distributions, cover m o s t of t he above ten categories, in p a r t i c u l a r t h e r e q u i r e d r a n d o m n e s s of s a m p l e s (1), t h e i n c l u s i v e n e s s of v a r i a b l e s i n c o r p o r a t e d in e c o n o m e t r i c m o d e l s (2 a n d 3), t h e d i s t i n c t i o n b e t w e e n e x o g e n o u s a n d e n d o g e n o u s variables (6), the u s e of d u m m y va r i a bl e s to exclude categories from th e m o d e l s to be e s t i m a t e d (7), a n d t h e e q u i v a l e n c e of t i m e - s e r i e s a n d crosssection s a m p l e s from t he point of view of m a t h e m a t i c a l statistics (8). Probably t h e m o s t s e r i o u s criticism of applied e c o n o m e t r i c s is t he failure of t he m a j o r i t y of applied e c o n o m e t r i c i a n s to realize t h a t statistical e s t i m a t i o n a n d testing t e c h n i q u e s are b a s e d on the C e n t r a l Limit T h e o r e m , w h i c h s t a t e s that, in repeated same-size large r a n d o m samples, t h e s a m p l e m e a n ~ is d i s t r i b u t e d as follows:
~ N(#, a/~[-~, as the n u m b e r of samples - - ~
[11
w h e r e N i n d i c a t e s t h e n o r m a l distribution, n is t h e s a m p l e size, a n d # a n d a are t h e p o p u l a t i o n m e a n a n d s t a n d a r d deviation. While t h e r e q u i r e d large size of n is h a n d l e d p r a g m a t i c a l l y by u s i n g r u l e s of t h u m b , t h e r e are two o t h e r r e q u i r e m e n t s for th e t h e o r e m to hold: s a m p l e s m u s t be b o t h r a n d o m a n d at leas t t h e o r e t i c a l l y r e p e a t a b l e a n infinite n u m b e r of t i m e s . W h e r e l i m i t i n g t h e o r e m s r e q u i r e r a n d o m n e s s , it u s u a l l y is simple randomness, where each population unit has equal non-zero probability of belonging to a n y given sample. While this s a m p l i n g r e q u i r e m e n t is easily v i s u a l i z e d for s a m p l e s t h a t derive from e x p e r i m e n t s , it is m u c h m o r e t e n u o u s in a classical r e g r e s s i o n model e s t i m a t e d on t he basis of s e c o n d a r y n o n - e x p e r i m e n t a l data. We also n e e d to e m p h a s i z e t h a t s i m p l e r a n d o m n e s s of s a m p l e d a t a irrevocably implies t h a t the s a m p l e observations c a n be o r d e r e d in a n y a n d every way, from w h i c h follows t h e e q u i v a l e n c e of t i m e - s e r i e s a n d c r o s s - s e c t i o n data. T h u s , if the
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e x a m i n a t i o n of s e r i a l c o r r e l a t i o n i n c r o s s - s e c t i o n d a t a is d e e m e d "silly" s i n c e w e c a n r e - o r d e r t h e s a m p l e o b s e r v a t i o n s to get rid of it, t h e s a m e c o n c l u s i o n h o l d s for t i m e - s e r i e s s a m p l e d a t a , w h i c h a l s o s h o u l d b e c a p a b l e of b e i n g " m i x e d u p " if t h e y r e s u l t f r o m simple r a n d o m samples. Justification of the Error Term
The typical linear m-equation simultaneous equation m o d e l a n d its t y p i c a l e q u a t i o n a r e listed in e x p r e s s i o n s [2] a n d [3] below: Yt = a + A Y t
+
[21
B Z t + l.tt
w h e r e A is a s u b - d i a g o n a l m a t r i x of coefficients, Z is t h e v e c t o r of the predetermined (including exogenous) variables, and y and u are the vectors summarizing the dependent variables and the stochastic error terms. Y/t = f / ( Y t - 1 , Y t - 2 . . . . ; Xt,
Xt-1 . . . . ) "{-uit
[3l
w h e r e X is t h e v e c t o r of e x o g n e o u s variables. The model's stochastic nature is c a p t u r e d in the disturbances, since each sample observation has a stochastic c o m p o n e n t . E a r l y e c o n o m e t r i c w o r k , n o t a b l y b y Wold (Bentzel a n d W o l d 1946: 1 9 - 3 3 ; W o l d 1967: ch. 1), d e m o n s t r a t e d d e f i n i t e a w a r e n e s s of t h e d i f f e r e n c e s b e t w e e n e x p e r i m e n t a l a n d n o n e x p e r i m e n t a l a n a l y s i s . R e c e n t i n t e r p r e t a t i o n s of t h e e r r o r t e r m allow for a t l e a s t five r o l e s in t h e s p e c i f i c a t i o n of a n e c o n o m e t r i c m o d e l . 2 First, a s a l r e a d y m e n t i o n e d , d a t a for t h e v e c t o r s Y a n d Z i n e q u a t i o n [2] s h o u l d r e s u l t f r o m r a n d o m s a m p l i n g to p e r m i t reliance on limiting theorems about the underlying sampling distributions. Second, the predetermined and exogenous variables a r e g e n e r a l l y m o d e l e d i n s i m p l i f i e d f o r m a s fixed a n d l i n e a r . F o u r t h , t h e Y a n d Z i n c l u d 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 r e o f t e n c o n v e n i e n t m a t e r i a l c o u n t e r - p a r t s , or p r o t o c o l v a r i a b l e s , of t h o s e i n c l u d e d in t h e t h e o r e t i c a l m o d e l f o r m u l a t i o n ; a n d , fifth, Y a n d Z a r e f r a u g h t w i t h m e a s u r e m e n t e r r o r . Wold's i n t e r p r e t a t i o n falls u n d e r t h e s e c o n d a n d t h i r d of t h e s e s o u r c e s of error. T h e f e m i n i s t c r i t i q u e of t h e j u s t i f i c a t i o n of t h e e r r o r t e r m s is f a i r l y o b v i o u s . T h e u s e of s a l i e n t a n d p r o t o c o l v a r i a b l e s to s i m u l t a n e o u s l y j u s t i f y t h e s t o c h a s t i c n a t u r e of t h e e r r o r t e r m a n d t h e o m i s s i o n of a lot of v a r i a b l e s l e a d s to t h e c o n c e r n t h a t t h e i n c l u d e d v a r i a b l e s a r e t h o s e t h a t g e n e r a l l y a r e c o n s i d e r e d to b e
2 An excellent account of the role of the error term in rescuing the classical model from the randomness criticism is found in Darnell and Evans (1990: Ch. 4). 44
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i m p o r t a n t , a n d for w h i c h o b s e r v a t i o n s a r e r e c o r d e d o n a r e g u l a r b a s i s . S a l i e n t v a r i a b l e s t e n d to b e m o n e t a r y in n a t u r e , a n d m e a s u r e b u s i n e s s a c t i v i t y s u c h a s p r o d u c t i o n , a n d i n v e s t m e n t in d u r a b l e s , a n d are, t h e r e f o r e , r e n d e r i n g visible t h e a c t i v i t i e s of t h e " h a v e s " in s o c i e t y , w h i l e o t h e r m o r e m a r g i n a l i z e d g r o u p s a n d t h e i r a c t i v i t i e s a r e n o t c o n s i d e r e d . M o r e o v e r , W o l d ' s first a r g u m e n t - that the error term captures the fact that the model's equations are about individual behavioral units, while average group b e h a v i o r is to b e e x p l a i n e d - - l e a d s f e m i n i s t o r o t h e r c r i t i c s to a r g u e t h a t n o t all i n d i v i d u a l b e h a v i o r a l u n i t s a r e i n c l u d e d . T h a t , a t b e s t , t h e d o m i n a n t g r o u p ' s b e h a v i o r is b e i n g c a p t u r e d , w h i l e non-mainstream g r o u p s of s o c i e t y a r e s u m m a r i l y i g n o r e d , o r d i s s o l v e d in t h e e r r o r t e r m . W h i l e w e c a n d i s c u s s e r r o r t e r m s a n d t h e i r c o m p o n e n t s a t l e n g t h , t h e o n l y t w o w a y s to t r u l y a d d r e s s t h i s r a n d o m n e s s p r o b l e m a r e to i n c r e a s e t h e v a r i a b l e s t h a t a r e i n c l u d e d a s s a l i e n t in e c o n o m e t r i c m o d e l s , a n d to e n h a n c e t h e r a n d o m n e s s of t h e s a m p l e d a t a b y e q u a l i z i n g t h e p r o b a b i l i t y of e a c h m e m b e r of t h e p o p u l a t i o n to b e c o m e a m e m b e r of t h e s a m p l e , i.e., b y p r a c t i c i n g i n c l u s i v e n e s s in our modeling methodology. This conclusion also makes clear that the seemingly a l t e m a t i v e c r i t i q u e s of e c o n o m e t r i c m e t h o d s a n d p a u c i t y or l a c k of d i s a g g r e g a t i o n of s a m p l e d a t a are two s i d e s of t h e s a m e coin. T h e b a s i c m o d e l s h o w n in e q u a t i o n s [2] a n d [3] also calls i n t o question the sharp dichotomy between the Y variable and the X variables. In specifying an econometric model, one often begins by l i s t i n g t h o s e v a r i a b l e s t h a t will b e e n d o g e n o u s . T h e y a r e t h e " i m p o r t a n t " v a r i a b l e s , t h o s e w e a r e e x p e c t e d to m a k e i n f e r e n c e s a b o u t . T h u s , t h e d e c i s i o n b e t w e e n e n d o g e n o u s a n d e x o g e n o u s is n o t a t all i n d e p e n d e n t of d e c i s i o n s r e l a t e d to w h a t n e e d s to b e i n c l u d e d in t h e m o d e l a c c o r d i n g to t h e r e s e a r c h e r or t h e a g e n c y p a y i n g for t h a t r e s e a r c h e r ' s w o r k . S i m i l a r l y , n o n - m a i n s t r e a m g r o u p s a r e o f t e n a c c o u n t e d for b y m e a n s of a d u m m y v a r i a b l e , which essentially formalizes their marginality. A feminist's quest for i n c l u s i v e n e s s w o u l d t r a n s l a t e i n t o t h e q u e s t for e n h a n c e d e n d o g e n e i t y , r e d u c i n g t h e n u m b e r of X v a r i a b l e s a n d i n c r e a s i n g t h e n u m b e r of Y v a r i a b l e s , n o t m e r e l y b y s h i f t i n g Xs i n t o Ys, b u t a l s o b y i n c l u s i o n of n e w v a r i a b l e s in t h e overall d a t a b a s e , t h u s reducing reliance on dummy variables. Forecasting a n d Policy Simulations Forecasting within the classical model has typically b e e n g e a r e d to t h e f o r e c a s t of b u s i n e s s activity. T h e c l o s e s t a m a c r o m o d e l c o m e s to i n c l u d i n g i n d i v i d u a l p e o p l e of all w a l k s of life is to c o n s i d e r a c t i o n s b y c o n s u m e r s . To b e a c o n s u m e r , h o w e v e r , o n e n e e d s a n i n c o m e a n d a b i l i t y to p u r c h a s e , w h i c h l e a v e s o u t all p e o p l e in t h e m a r g i n s w h o do n o t p o s s e s s t h e s e attributes. Moreover, as consumers, the only action considered w o r t h y of i n c l u s i o n in t h e m a c r o m o d e l is t h e i r e x p e n d i t u r e o n
September 1999
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goods and services produced by the business sector (and s o m e t i m e s g o v e r n m e n t ) . T h u s , it is o n l y t h e i r s u p p o r t of t h e s t a t u s q u o of t h e m a r k e t e c o n o m y t h a t is w o r t h y of c o n s i d e r a t i o n . T h i s v e r y a s p e c t of m o d e l i n g a n d f o r e c a s t i n g b e c o m e s a c e n t r a l f e m i n i s t critique. Policy s i m u l a t i o n s w i t h t h e s i m u l t a n e o u s e q u a t i o n m o d e l a r e also d e c e p t i v e . A l t h o u g h s o m e look i n c l u s i v e , t h e r e a l i t y is q u i t e t h e r e v e r s e . C o n s i d e r , for e x a m p l e , t h e s i m u l a t i o n of t h e effect of m i n i m u m w a g e in a s i m u l t a n e o u s e q u a t i o n f r a m e w o r k . 3 O n e will find t h a t t h e m i n i m u m wage h a s a small positive effect on i n f l a t i o n a n d u n e m p l o y m e n t . H o w e v e r , it is u n w i s e to c o n c l u d e from this computation that the minimum wage has a minor d e t r i m e n t a l effect o n t h e e c o n o m y . A m i n i m u m w a g e rise t y p i c a l l y decreases the wage gap between low-wage workers and other w o r k e r s i n t h e e c o n o m y . S p e c i f i c a l l y , t h e g e n d e r w a g e g a p is n a r r o w e d , a n d a m i n i m u m w a g e policy c a n b e a n effective tool to m o v e t o w a r d g e n d e r e q u a l i t y in w a g e s , a n e f f e c t of w a g e e q u a l i z a t i o n n o t c a p t u r e d in m a c r o m o d e l s . E v e n if w a g e e q u a t i o n s a r e d i s a g g r e - g a t e d b y sex, t h e y a r e u n l i k e l y to h a v e t h e r e l e v a n t d e t a i l , s u c h a s t y p e s of w a g e s e a r n e d , g e n d e r i n c i d e n c e of v i o l a t i o n s , etc. M o v i n g b e y o n d t h e w a g e e q u a t i o n , it w o u l d be i m p o s s i b l e to c a r r y t h e e f f e c t of a g e n d e r - d i s a g g r e g a t e d w a g e i n c r e a s e t h r o u g h t h e r e m a i n d e r of t h e e c o n o m y in a s i m u l a t i o n e x e r c i s e , s i n c e o n e l a c k s d a t a to d i s a g g r e g a t e c o n s u m p t i o n a n d o t h e r r e l e v a n t e q u a t i o n s in t h e m o d e l a c c o r d i n g l y . T h e effect of a rise in r e a l m i n i m u m w a g e s a n d a n a r r o w i n g of t h e w a g e g a p in t h e e c o n o m y o n h u m a n dignity, p r o d u c t i v i t y , a n d h a p p i n e s s a r e m i s s i n g a l t o g e t h e r in m o d e l s i m u l a t i o n s . T h e r e m a y b e p r o d u c t i v i t y e q u a t i o n s in t h e m o d e l , b u t p r o d u c t i v i t y is t y p i c a l l y a c o m p u t e d v a r i a b l e , m e a s u r e d a s t h e w a g e bill d i v i d e d b y t h e n u m b e r of w o r k e r s . It d o e s n o t c a p t u r e i n c r e a s e d w o r k effort a n d h i g h e r q u a l i t y w o r k t h a t m a y derive f r o m a n i n c r e a s e d s e n s e of b e l o n g i n g a n d h u m a n dignity. Overall, a m i n i m u m w a g e i n c r e a s e likely h a s a positive effect on the economy. But this c a n n o t b e c a p t u r e d g i v e n t h e c u r r e n t d e t a i l in d a t a g a t h e r e d for the macroeconomy, a n d , t h e r e f o r e , detail i n c o r p o r a t e d in m a c r o e c o n o m i c s i m u l t a n e o u s e q u a t i o n m o d e l s . In criticizing l a c k of i n c l u s i v e n e s s , t h e f e m i n i s t c r i t i q u e a l s o i n c o r p o r a t e s l a c k of c o n c e n t r a t i o n o n a s p e c t s of e c o n o m i c p o l i c i e s in t h e r e a l m of sociology, p s y c h o l o g y , a n d e n v i r o n m e n t a l s t u d i e s , e.g., effects o n h u m a n dignity, s e l f - e s t e e m , a n d air quality.
3 I have done this elsewhere (Sellekaerts 1982) in the context of a modified version of the MPS model, in which new equations for wages, prices, and productivity were incorporated to model the effect of the minimum wage. 46
September 1999
The Practice of Econometrics: A Feminist Critique
T I M E - S E R I E S A N A L Y S I S TO T H E R E S C U E ? W h i l e t h e r e a r e s o l u t i o n s to a d d r e s s t h e f e m i n i s t c r i t i q u e w i t h i n c l a s s i c a l r e g r e s s i o n m o d e l s , t h e r e is m u c h l e s s h o p e for m o d e l s in t h e c a t e g o r y of t i m e - s e r i e s a n a l y s i s . To t h e n o n - f e m i n i s t p r a c t i c e s a l r e a d y m e n t i o n e d in r e l a t i o n to r e g r e s s i o n a n a l y s i s , we m u s t n o w a d d p r a c t i c e s [4], [5], a n d [6]. Briefly, VAR (vector a u t o r e g r e s s i o n ) h a s b e c o m e p o p u l a r s i n c e t h e d e v e l o p m e n t of B o x - J e n k i n s a n a l y s i s , a u g m e n t e d w i t h T.C. L i u ' s ( 1 9 6 0 ) c r i t i c i s m of t h e p a u c i t y of v a r i a b l e s in e c o n o m e t r i c e q u a t i o n s , in l i g h t of t h e o m i s s i o n of v a r i a b l e s a s t h e s t a n d a r d w a y of a c h i e v i n g i d e n t i f i c a t i o n , a n d w i t h t h e i n t r o d u c t i o n of c a u s a l i t y a n a l y s i s for e c o n o m e t r i c m o d e l s . R e l e v a n t a r t i c l e s d e v e l o p i n g t h i s field a r e t h o s e of G r a n g e r (1969) a n d S i m s (1972, 1982). A b a s i c VAR m o d e l is p r e s e n t e d by e q u a t i o n [4] below:
AY, + y_ CY,_, : u t
[4]
w h e r e t h e s u m m a t i o n r u n s f r o m l t h r o u g h k, w h i c h is t h e m a x i mum allowable by the data, and where the matrices A and C have d i m e n s i o n k x n . T h e t i m e s e r i e s a r e t h e n t r a n s f o r m e d to g u a r a n t e e s t a t i o n a r i t y . T h i s y i e l d s t r a n s f o r m e d v a r i a b l e s , so t h a t the model's specification becomes:
Yt = ~ B y t - i + et
[51
w h e r e t h e Ys a r e n o w v a r i a b l e s r e p r e s e n t e d b y a s t a t i o n a r y p r o c e s s , all t h e a v a i l a b l e l a g s of all t h e Ys a r e i n c l u d e d o n t h e r i g h t - h a n d s i d e , a n d w h e r e t h e "error" v e c t o r is v i e w e d a s a n " i n n o v a t i o n " to t h e p r o c e s s . F o l l o w i n g t h e c h o i c e of t h e l o n g e s t l e n g t h of "/4' p o s s i b l e , c o n s i d e r i n g t h e a v a i l a b l e d e g r e e s of f r e e d o m , a d d i t i o n a l " s m o o t h n e s s " r e s t r i c t i o n s a r e a p p l i e d to f u r t h e r s i m p l i f y t h e m o d e l . Finally, p r e d i c t i o n s c a n b e m a d e , o n e p e r i o d a h e a d a t a t i m e . S i n c e n o o t h e r s o u r c e of "error" is allowed, a n d t h e b e h a v i o r of t h e s y s t e m is c o n s i d e r e d to b e u n c h a n g e d , government economic policies simply become "innovation shocks" to a n o t h e r w i s e d e t e r m i n i s t i c s y s t e m . I n its B a y e s i a n v e r s i o n (BVAR) t h e m e t h o d a l l o w s for t i m e v a r y i n g p a r a m e t e r s , in t h e s e n s e t h a t t h e c o e f f i c i e n t m a t r i c e s of t h e m o d e l follow a r a n d o m w a l k ( S i m s 1982: 140). E s t i m a t e s of t h e c o e f f i c i e n t s for t h e s t a r t of t h e s a m p l e p e r i o d a r e m o d i f i e d w i t h e a c h n e w o b s e r v a t i o n , u s i n g a K a l m a n filtering a p p r o a c h . A n o t h e r logical p r o g r e s s i o n in v e c t o r a u t o r e g r e s s i v e m o d e l i n g t a k e s u s to c o i n t e g r a t i o n ( H e n d r y 1 9 8 6 ) . T w o v a r i a b l e s a r e s a i d to b e cointegrated if t h e i r d i f f e r e n c e is s t a t i o n a r y , a p a r t f r o m a m u l t i p l i c a t i v e c o n s t a n t . T h i s b r i n g s u s b a c k to t h e b a s i c r e q u i r e m e n t for u n d e r l y i n g s t a t i o n a r i t y . September 1999
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Review of Radical Political Economics
Feministl Critique of VAR, BVAR, and Cointegration E c o n o m e t r i c m e t h o d o l o g y h a s f o c u s e d its c r i t i c i s m of t h e m e t h o d s a r o u n d t h e t h e m e t h a t t h e y a r e e q u i v a l e n t to m e a s u r e m e n t w i t h o u t t h e o r y . M o r e specifically, t h e i n c l u s i o n of o n l y a l i m i t e d n u m b e r of v a r i a b l e s , t h e c h o i c e of lag l e n g t h s o n t h e b a s i s of d e g r e e s of f r e e d o m , a n d p a r t i c u l a r l y t h e i m p o s i t i o n of s t a t i o n a r i t y of t h e t i m e s e r i e s h a v e b e e n s u b j e c t to f r e q u e n t c r i t i c i s m (see D a r n e l l a n d E v a n s 1 9 9 1 : 1 2 8 - 2 9 for a s u m m a r y ) . F u r t h e r m o r e , s i n c e VAR m o d e l s c a n in a s e n s e be s e e n a s r e d u c e d f o r m s of a s t r u c t u r a l m o d e l t h a t h a s b e e n explicitly s p e c i f i e d , a l a r g e n u m b e r of a l t e r n a t i v e s t r u c t u r a l f o r m s or e c o n o m i c t h e o r i e s c o u l d h a v e p r o d u c e d t h e r e d u c e d f o r m at h a n d , a n n i h i l a t i n g t h e p o t e n t i a l of VAR m e t h o d s to t e s t e c o n o m i c t h e o r i e s (Cooley a n d LeRoy 1985). To t h i s list, we c a n a d d t h r e e f e m i n i s t c r i t i q u e s . First, w h e n VAR f o r e c a s t s a r e c o m p a r e d w i t h t h o s e o b t a i n e d by other methods, such comparisons invariably focus on commercial f o r e c a s t s , w h i c h a r e t y p i c a l l y n o t r e p r e s e n t a t i v e of t h e b e s t results that can be obtained with traditional model simulations. Feminist criticism would also focus on the emphasis on c o m m e r c i a l f o r e c a s t s a n d activity, i.e., t h e e x c l u s i v e m a s c u l i n i s t n a t u r e of f o r e c a s t i n g in g e n e r a l . Second, e c o n o m i s t s a r e r e a l i z i n g m o r e a n d m o r e t h a t t h e e c o n o m i c p e r f o r m a n c e of a n a t i o n a n d t h e w e l l b e i n g of its p e o p l e a r e n o t well d e s c r i b e d b y m o v e m e n t s in t h e i r GNP, m o n e y s t o c k , a n d e x c h a n g e r a t e s . "Aggregates" reflect t h e t r a d i t i o n a l m a s c u l i n i s t v i e w s of e c o n o m i s t s of t h e 1 9 2 0 s . To g a t h e r i n f o r m a t i o n a b o u t t h e w e l l b e i n g of a n a t i o n ' s i n h a b i t a n t s , we m u s t m e a s u r e a n d e x p l a i n d a t a a b o u t e d u c a t i o n levels, h e a l t h c a r e a c c e s s , o w n e r s h i p p a t t e r n s , a n d so on, n o n e of w h i c h a r e f o c u s e d o n in t i m e - s e r i e s a n a l y s i s . Third, b y t h e i r v e r y n a t u r e , VAR m o d e l s m u s t v i e w t h e f u t u r e a s r e a s o n a b l y s i m i l a r to t h e p a s t . T h e r e f o r e , f u n d a m e n t a l c h a n g e s in s o c i e t y to e n h a n c e t h e lives of p e o p l e in t h e m a r g i n s a r e d i s c a r d e d a pr/or/. THE ROLE OF ACADEME ECONOMICS PROGRAMS
AND
T h e p r o l i f e r a t i o n of M a s t e r of A r t s in E c o n o m i c s p r o g r a m s , a n effort to t a p t h e i n t e r n a t i o n a l a n d d o m e s t i c m a r k e t s of g r a d u a t e s t u d e n t s w h o s e e k g r a d u a t e d e g r e e s b u t l a c k i n t e r e s t , skill, or f u n d s to e n t e r a P h . D . p r o g r a m , h a s c o n t r i b u t e d to t h e p r a c t i c e of b a d t r a d i t i o n a l m a s c u l i n i s t e c o n o m e t r i c s ( n u m b e r 10 of t h e n o n - f e m i n i s t p r a c t i c e s in t r a d i t i o n a l e c o n o m e t r i c s l i s t e d in t h e i n t r o d u c t i o n above), for five r e a s o n s . F i r s t , a c a d e m e is b y d e s i g n s l o w in a c c e p t i n g c h a n g e . As Liz S t a n l e y w r i t e s (1997: 181), " A c a d e m i c r e p r o d u c t i o n is in e s s e n c e a
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h o m o s o c i a l o n e i n w h i c h o l d e r m e n offer p a t r o n a g e to y o u n g e r m e n w h o i n r e t u r n offer t h e a p p e a r a n c e of h o m a g e . T h e s e a r e r e l a t i o n s of s u p e r - a n d s u b o r d i n a t i o n d e p e n d e n t o n t h o s e p o w e r relations that exist between teachers and taught, initiates and neophytes." This academic reproductive system maintains the s t a t u s q u o o v e r s c a r c e a c a d e m i c r e s o u r c e s , w h i c h is r e f l e c t e d in promotions, grant evaluations, required courses on college c u r r i c u l a , a n d f u n d i n g of h i g h e r e d u c a t i o n b y t h e l e g i s l a t u r e . 4 S e c o n d , f e m i n i s t e c o n o m e t r i c s , w h i c h r e q u i r e s a t t e n t i o n to b e t t e r data, more inclusive data, and more careful evaluation than usual of s t a t i s t i c a l t e s t s a p p l i e d , r e q u i r e s t h e level of s c h o l a r l y w o r k t h a t is g e n e r a l l y a s s o c i a t e d w i t h P h . D . s t u d y a n d d i s s e r t a t i o n r e s e a r c h . T h i r d , M.A. p r o g r a m s a r e o f t e n s p e c i a l i z e d in b u s i n e s s e c o n o m i c s or i n t e r n a t i o n a l e c o n o m i c s , a n d f o c u s o n a p p l i e d e c o n o m e t r i c s to t h e e x t e n t t h a t e s t i m a t e s or f o r e c a s t s a r e m a d e of o u t p u t , profits, i n v e s t m e n t s , etc., t h a t is, v a r i a b l e s t h a t e x p r e s s c o n c e r n s of t h e b u s i n e s s w o r l d . T h e r e is n o i n t e r e s t , n o r t i m e , for t h e s e s t u d e n t s to l e a r n a b o u t t h e pitfalls of t h e m e t h o d s t h e y a p p l y . F o u r t h , M.A. p r o g r a m s h a v e f a l l e n v i c t i m to t h e f o c u s o n f a s t t r a c k e d u c a t i o n , w h e r e g r a d u a t i o n is b a r e l y a y e a r after e n r o l l m e n t in t h e p r o g r a m . To t h e e x t e n t t h a t s t a t i s t i c s a n d e c o n o m e t r i c s r e m a i n p a r t of s u c h p r o g r a m s , t h e y b e c o m e a t o o l k i t , w h e r e s t u d e n t s l e a r n h o w to m a k e a c a n n e d p r o g r a m "work" a n d p r o d u c e " r e s u l t s " r a t h e r t h a n learning when the formulas that can be computed with such p r o g r a m s a r e v a l i d . F i n a l l y , t h e p r o l i f e r a t i o n of m i c r o c o m p u t e r s and the internet have rendered data gathering and tedious c o m p u t a t i o n s o b s o l e t e for s t u d e n t s . E a s e of a c c e s s to d a t a m a k e s t h e u s e r c o m p l a c e n t a n d l e s s critical t h a n w h e n d a t a c o l l e c t i o n is t h e r e s u l t of a t e d i o u s e x p e r i m e n t or s u r v e y . W h i l e t h e M.A. t r a c k in e c o n o m i c s p r o g r a m s f o s t e r s t h e n o n feminist practice of econometrics, t h e r e is a n a d d i t i o n a l d e t r i m e n t a l s p i l l o v e r effect. M a n y s t u d e n t s in s u c h p r o g r a m s a r e non-U.S, students, and some eventually become involved with p o l i c y m a k i n g i n t h e i r h o m e c o u n t r y . T h u s , t h e y c o n t i n u e to practice maintenance of t h e p a t r i a r c h a l status quo, and s o m e t i m e s fall p r e y to " S a c h s - i s t " a d v i s o r s f r o m U.S. i n s t i t u t i o n s .
WHAT THEN MUST WE DO? T h e f e m i n i s t s o l u t i o n is n o t to d i s c a r d e c o n o m e t r i c s , b u t to u s e t h e s e t o o l s m o r e c a r e f u l l y a n d w i t h m o r e a t t e n t i o n to data gathering. While bulky and seemingly detailed simultaneous equation macromodels as well as VAR models have major s h o r t c o m i n g s i n t e n t h s of i n c l u s i v e n e s s , a n d t h e b a s i c c l a s s i c a l
4 This was the central argument of Virginia Woolf in Three Guineas (1937). September 1999
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Review of Radical Political Economics r e g r e s s i o n m o d e l is l a c k i n g in s t o c h a s t i c q u a l i t i e s r e q u i r e d to a p p l y l i m i t i n g t h e o r e m s , all is n o t lost. S e v e n g e n e r a l g u i d e l i n e s t h a t go in t h e d i r e c t i o n of a d d r e s s i n g t h e f e m i n i s t c r i t i q u e follow. It is i m p o r t a n t to r e a l i z e t h a t all of t h e s e g u i d e l i n e s m u s t b e f o l l o w e d s i m u l t a n e o u s l y , b e c a u s e a d e t a i l e d , w e l l - w e i g h t e d s e t of data, cranked into a simultaneous equation model that loses this d e t a i l i n t h e i n t e r a c t i o n w i t h o t h e r e q u a t i o n s , is to n o avail. F u r t h e r , t h e g u i d e l i n e s t h a t follow h a v e n o p a r t i c u l a r o r d e r of i m p o r t a n c e a t t a c h e d . T h e o r d e r l i s t e d is o n e of c o n v e n i e n c e , n o t of e m p h a s i s . W i t h t h e s e q u a l i f y i n g r e m a r k s , I offer t h e following list of f e m i n i s t e c o n o m e t r i c h a b i t s . 5 First, in c l a s s i c a l m o d e l s , w e m u s t l o o k for h i g h e r t - v a l u e s rather than borderline o n e s . Second, r e l i a n c e o n l i m i t e d d e p e n d e n t v a r i a b l e m e t h o d s h e l p s a d d r e s s t h e s t o c h a s t i c limitat i o n s of s a m p l e d a t a . T h e s e m e t h o d s a r e f a i r l y s t a n d a r d for researchers doing detailed work in labor market studies and p o p u l a t i o n s s t u d i e s . Third, t e c h n i c a l c o r r e c t i o n s f o r s e r i a l correlation should be avoided, since they hide misspecification r a t h e r t h a n a d d r e s s i n g it. S u c h c o r r e c t i o n s i n c l u d e t h e m e t h o d s u s e d in t i m e - s e r i e s a n a l y s i s to o b t a i n s t a t i o n a r i t y . Fourth, t h e u s e of d u m m y v a r i a b l e s h a s t h e effect of excluding g r o u p s f r o m t h e main model specification, rather than including them. This inclusion must ideally take a different form, which includes gathering data and specifying verifyable theories based on these d a t a . Fifth, s u r v e y m e t h o d s a n d e x p e r i m e n t a l m e t h o d s c a n a d d r e s s b o t h t h e p a u c i t y of d a t a a n d t h e s t o c h a s t i c n a t u r e r e q u i r e d for c l a s s i c a l s t a t i s t i c a l i n f e r e n c e . Sixth, e c o n o m e t r i c s c a n n o t b e d o n e in a v i r t u a l i n f o r m a t i o n void. E c o n o m i c s a n d , hence, econometrics must be ideally conducted in an i n t e r d i s c i p l i n a r y e n v i r o n m e n t , r e l y i n g o n f i n d i n g s in o t h e r s o c i a l sciences, behavioral sciences, and environmental studies. Seventh, a c a d e m e s h o u l d i d e a l l y b e c o m e a p l a c e for c h a n g e , i n n o v a t i o n , a n d i n c l u s i v e n e s s , n o t a m a i n b a s t i o n of t h e s t a t u s quo. Eight, c o n s i d e r i n g the confinements of mainstream theories--their data and their verification in the deductive framework of hypothesis testing--econometricians should rely m o r e o n i n d u c t i v e m e t h o d s of a n a l y s i s . I n d u c t i o n is o n e of t h e m e t h o d s i d e n t i f i e d w i t h t h e d i s c i p l i n e of d e m o g r a p h y ( P r e s t o n 1993), a n d i n d u c t i v e p r o o f s a r e c o m m o n in m a t h e m a t i c a l a n a l y s i s w h e n e v e r a n i n t e g e r c o u n t e r is p r e s e n t . It is p u z z l i n g to s e e t h a t the powerful proof by induction, which is a s t a n d a r d m a t h e m a t i c a l tool, is h a r d l y e v e r u s e d b y e c o n o m e t r i c i a n s . Yet, every time we address sample data and population data that can b e n u m b e r e d c o n s e c u t i v e l y f r o m 1 to n or N , w e o p e n t h e
5 Several of these are consistent with the five propositions to improve the study of discrimination, advocated by D. Figart (1997). 50
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The Practice of Econometrics: A Feminist Critique p o s s i b i l i t y for a p p l y i n g i n d u c t i v e p r o o f s . A m a t h e m a t i c a l p r o o f u s i n g i n d u c t i o n u s e s t h r e e s t e p s : (a) p r o v e t h e p r o p o s i t i o n at h a n d for t h e f i r s t e l e m e n t , (b) p r o v e it for c o n s e c u t i v e r e p r e s e n t a t i v e e l e m e n t s "k" a n d " k + l , " a n d (c) d r a w t h e c o n c l u s i o n t h a t it h o l d s for all e l e m e n t s i n t h e s a m p l e or p o p u l a t i o n u n d e r c o n s i d e r a t i o n . N o t e t h a t it is, b y d e s i g n , a n i n c l u s i v e p r o o f . W h e n i n d u c t i o n is u s e d a s a g e n e r a l tool of e c o n o m i c a n a l y s i s , we a t t a c h a n o t h e r m e a n i n g to t h e w o r d , i.e., t h e f a c t t h a t w e do n o t h a v e r e a d y t h e o r i e s a v a i l a b l e , a n d m a y h a v e to t r e a t d a t a we h a v e a v a i l a b l e w i t h s o m e m i s t r u s t , w h i c h e n c o u r a g e s u s to d r a w i n f e r e n c e s t h a t a r e r o o t e d i n t h e t o t a l i t y of a v a i l a b l e e v i d e n c e f r o m d i f f e r e n t m e t h o d s . A g a i n , i n d u c t i o n is s e e n to b e m o r e i n c l u s i v e t h a n is deduction.
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