employed  in  exporting  firms.  This  finding  stands  in  sharp  contrast  to  results  obtained  using average  firm  level  wages  instead.  One  reason  for  this  difference  is  simply  that  the  use  of detailed  worker  level  data  allows  us  to  take  into  full  account  any  changes  in  the  composition of  the  workforce  (by  controlling  for  both  observable  and  time-­‐invariant  unobservable worker  characteristics)  following  trade  policy.  Furthermore,  by  taking  worker-­‐firm  match effects  into  account,  we  are  able  to  control  for  changes  in  the  composition  of  firms’  match quality  following  trade  policy  changes.  If,  following  trade  liberalization,  exporting  firms improve  their  average  match  quality  by  hiring  workers  with  better  match  quality,  the estimates  of  the  coefficient !!" without  controlling  for  match  effects  would  mistakenly  be estimated  as  significant  even  in  the  absence  of  any  true  effect.

Table  4.3,  which  compares  the  changes  in  the  distribution  of  estimated  match  effects  in exporting  firms  relative  to  non-­‐exporting  firms,  confirms  this  point.<sup>38</sup> Comparing  the  period 1998  to  1990,  we  see  an  increase  in  both  the  mean  and  the  median  match  effect  in  exporting firms,  while  the  mean  and  median  match  effect  both  fall  in  non-­‐exporting  firms.  As  we  have noted  earlier,  match  fixed  effects  in  equation  (3)  absorb  both  worker  and  firm  fixed  effects in  addition  to  time-­‐invariant  match  quality  of  a  given  employment  spell.  Consequently,  our finding  of  an  improvement  in  average  match  effect  in  exporting  firms  between  1990  and 1998  summarizes  the  combined  effect  of  a  change  in  workforce  composition  in  these  firms in  terms  of  improvement  in  worker  quality  in  time  invariant  worker  specific  characteristics, such  as  innate  ability  (captured  by  worker  fixed  effects)  and  improvement  in  the  quality  of the  worker-­‐firm  matches  (captured  by  match-­‐fixed  effects).<sup>39</sup> The  improvement  in  the distribution  of  match-­‐specific  ability  in  exporting  firms  is  consistent  with  the  Helpman, Itskhoki,  Redding  (2010)  model  which  predicts  that  with  trade  liberalization,   exporting firms  will  screen  more  intensively  and  set  a  higher  ability  threshold  for  employment.  It  is also  roughly  in  line  with  the  prediction  of  Davidson,  Matusz,  and  Shevchenko  (2008)  that greater  openness  leads  to  better  labor  market  sorting  of  higher  ability  workers  into  higher technology  firms.  This  finding  serves  to  explain  the  difference  between  the  results  at  the firm  level  and  those  at  the  worker  level:  If  average  quality  of  the  workforce  (in  terms  of match  specific  ability  or  innate  (time-­‐invariant)  ability)  improves  systematically  in

> 38   Table   4.3   is   for   a   group   of   firms,   which   were   included   in   our   sample   in   both   1990   and   1998   and   did not   switch   export   status   during   this   period. 39   Note   that   firm-­‐fixed   effect   for   a   given   firm   is   constant   across   time   and   cannot   account   for   the improvement   in   match   quality   between   1990   and   1998.

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