whether reservation wage data are available to the analyst. The 2SLS
approach pioneered by L-C (1984) uses recorded reservation wage data, which
are available in the ALS data set, and is based on particular functional forms
of the reservation wage and hazard functions. These functional specifications
a r e c o n f o r m a b l e w i t h t h e reduced f o r m r e p r e s e n t a t i o n of t h e Weibull h a z a r d f u n c t i o n used in C h a p t e r 4. T h i s allows us t o m a k e direct c o m p a r i s o n s , especially w i t h r e g a r d t o t h e d u r a t i o n d e p e n d e n c e effect of u n e m p l o y m e n t . W e h a v e been able t o secure i d e n t i f i c a t i o n of b o t h s t r u c t u r a l e q u a t i o n s by c o m b i n i n g t h e r e s t r i c t i o n s f o u n d in K-N (1979, 1981b) a n d L-C (1984). W e h a v e also r e - e s t i m a t e d t h e s t r u c t u r a l e q u a t i o n s using modified 2SLS a n d m a x i m u m likelihood p r o c e d u r e s which allow for selectivity bias.
T h e e s t i m a t e d results concur w i t h m o s t of t h e p r e d i c t i o n s of t h e t h e o r e t i c a l j o b search model. R e s e r v a t i o n w a g e is f o u n d t o be declining w i t h e l a p s e d u n e m p l o y m e n t , albeit a t a d e c r e a s i n g r a t e . T h e e s t i m a t e d coefficient ( = 0 . 0 4 6 ) of elapsed d u r a t i o n in t h e r e s e r v a t i o n w a g e e q u a t i o n implies t h a t a p e r s o n w h o h a s been u n e m p l o y e d for 3 m o n t h s h a s a r e s e r v a t i o n w a g e which is 11% lower t h a n w h e n he first b e c a m e u n e m p l o y e d a n d in a n o t h e r 3 m o n t h s t h e c o r r e s p o n d i n g v a l u e will be 14%. T h e s e figures a r e c o m p a r a b l e w i t h t h o s e f o u n d in K-N (1979) w h e r e t h e r a t e of decline is c o m p u t e d a s 2.5% per m o n t h . O u r r e s u l t s also p r o v i d e evidence of positive d u r a t i o n d e p e n d e n c e , t h e m a g n i t u d e of which is c o n s i s t e n t w i t h , a n d gives renewed c o n f i d e n c e in t h e reduced f o r m e s t i m a t e s f o u n d in C h a p t e r 4.
No c l a i m s however will be m a d e t o suggest t h a t t h e j o b search model p r o v i d e s a c o m p l e t e a n d a d e q u a t e e x p l a n a t i o n of u n e m p l o y m e n t b e h a v i o u r . T h e r e is evidence in our results which suggest t h a t q u a n t i t y c o n s t r a i n t s m a y play a role in d e t e r m i n i n g u n e m p l o y m e n t . T h i s is implied f r o m t h e s t r u c t u r a l e s t i m a t e s which show u n e m p l o y e d females h a v i n g significantly lower r e s e r v a t i o n w a g e s a n d yet e x p e r i e n c i n g longer spells of u n e m p l o y m e n t a t t h e s a m e t i m e . T h e absence of significant selectivity bias in t h e e s t i m a t e s also s u p p o r t this h y p o t h e s i s . T h e reason is t h a t a d j u s t m e n t s for selectivity bias is b a s e d on t h e p r e m i s e t h a t exit f r o m u n e m p l o y m e n t is d i c t a t e d by supply b e h a v i o u r i.e. w h e n t h e r e s e r v a t i o n wage, w , is exceeded by t h e offered wage, w . H o w e v e r , if q u a n t i t y c o n s t r a i n t s in t h e f o r m of deficient d e m a n d a r e o p e r a t i v e a n d p r e v e n t exit f r o m u n e m p l o y m e n t even if w < w , t h e n it is likely t h a t t h e e x t e n t of selectivity bias in t h e s a m p l e will n o t be a s serious.
APPENDIX G
EFFECT OF CHANGE IN WAGE OFFER DISTRIBUTION
i-w dG(w)
W e w a n t t o s h o w t h a t [ dw > 0. 0 2
dq
F i r s t w e need t o p r o v e t h a t if t h e m e a n s of t w o d i s t r i b u t i o n s F and G are e q u a l , t h a t is, /Xp = and if t h e v a r i a n c e s < oJ^, then
[ G{x) dx > [ F(x] dx V 2 G l0,oo). Jo Jo In o t h e r w o r d s , t h e d i s t r i b u t i o n F s t o c h a s t i c a l l y d o m i n a t e s G in the second d e g r e e . P r o o f : f^F = /- oc r CO = / xf(x) d x = 1 - F(x) dx Jo Jo Since /Xp = f i ^ , /• oo roo - / 1 - F ( x ) d x = 1 - G ( i ) dx Jo Jo r OC rOO ^ / F{x) dx = / G ( z ) dx. Jo Jo L e t X j be t h e p o i n t w h e r e F ( x ^ ) = G ( X j ) . W e k n o w t h a t G ( y ) > F ( y ) V z e [ 0 , X j ) . B u t since F(x) dx = f ^ G(x) dx, a n d F ( x ) > 0, G ( x ) > V x , / G(x] dx > [ F(x) dx V z e [0,oo) Jo Jo Q . E . D . F o r finite w ' < oo, it m u s t be t r u e t h a t * r G(x) - F(x) > 0. Jo
If we consider a small change in a ^ ' to a^^ where = V ' + then » w y ^ dG(w)