The Persistence of Diﬀerences in Productivity,Wages, Skill Mixes and Profits Between Firms ina Rapidly Changing Environment
Katsuya Takii
Osaka School of International Public Policy, Osaka University
May 8, 2009
Abstract
In this paper, we construct a dynamic assignment model that can provide a unified explanation of persistent diﬀerences in productivity, wages,skill mixes and profits between firms in a changing and uncertain environment. Large expected organization capital (firm-specific knowledge)
attracts skilled workers, who help to accumulate organization capital. Accumulated large organization capital, in turn, confirms high expectations.
This positive feedback brings about persistent diﬀerences in these variables
even in a changing and uncertain environment. From this feedback mechanism, we identify two sources of persistence: the heterogeneity of skills andthe diﬃculty of measuring organization capital.
To examine the quantitative importance of the two sources, we estimateparameters and simulate the model. Because it is perceived organization
capital that attracts skilled workers who help to accumulate organization
capital, the eﬀect of the perceived value on persistence provides information
about the role of assignment in persistence in our framework. Exploiting
this information, we diﬀerentiate two sources of persistence — positive assortative assignment and noisy information — from others by using an industry
annual dataset from COMPUSTAT covering 1970 to 2004. COMPUSTAT
provides data on an unbalanced panel of publicly traded firms in the US.
It contains information from balance sheets, and information on incomes,
cash flows and financial variables. The value added per worker and theaverage wage rate are constructed for each firm and each year.

1The estimated parameters are all significant and their signs are consistent with theoretical predictions. By using the estimated parameters,
we simulate not only the autocorrelations of relative productivity, relativewages and expected relative profits per worker, but also the correlation
between relative productivity and relative wages; note that, in this paper,“relative” refers to the logarithm of each value relative to industry and year
averages. All simulated autocorrelations replicate the observed autocorrelations quite well. The model is also able to explain the observed highcorrelations between relative productivity and relative wages. That is, ourmodel can quantitatively account for the stylized facts of interest.
We use our model to conduct two counterfactual experiments. Theyshow that if there were no skill diﬀerence between workers and, therefore,
if there were no assignment problem, firms’ relative advantages (disadvantages) would almost disappear in about five years. In addition, the correlation between relative productivity and relative wages would diminish
substantially, while even if output perfectly predicted the level of organization capital, there is only a minor influence on variables’ persistence andthe correlation between relative productivity and relative wages. These exercises consistently suggest that a positive assignment mechanism accounts
for a large part of the observed persistence of variables. The diﬃculty ofestimating organization capital plays only an auxiliary role.
In order to check the robustness of our results, we are currently extending our research into two directions. Firstly, we are extending the model toallowing fixed eﬀects that may still exist without the proposed mechanism.
It permits us to separate the proposed mechanism from other reasons captured by the fixed eﬀect. Secondly, we are reexamining the same modelby using the micro data of the Basic Survey of Japanese Business Structure and Activities by the Ministry of Economy, Trade and Industry from1995 to 2005. It covers all the enterprises with 50 employees or more andgreater than a 30 million yen capitalization that are engaged in mining,
manufacturing, wholesale and retail, or restaurant activities. Hence, wecan examine how diﬀerences in countries and the coverage of firms influence
the importance of proposed mechanism.