Productivity and credibility in industry equilibrium

• Published date: 01 March 2019
• Author: Michael Powell
• Date: 01 March 2019
• DOI: http://doi.org/10.1111/1756-2171.12264

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 121–146

Productivity and credibility in industry

equilibrium

Michael Powell∗

I analyze a model of production in a competitive environment with heterogeneous firms. Efficient

production requiresindividuals within the organization to take noncontractible actions for which

rewards must be informally promised rather than contractually assured. The credibility of such

promises originates from a firm’s future competitive rents. In equilibrium, heterogeneous firms

are heterogeneously constrained, and competitive rents are inefficiently concentrated at the top.

I explore several policy and empirical implications of this result.

1. Introduction

To make a firm more productive, managers have to figure out how to get a given set

of people with a given set of resources to work together more effectively. This can be done

through harder work—asking for more personal sacrifice on the part of the workers. It can

be done through smarter work—putting in place more effective management practices. Also,

it can be done through improving internal resource allocation—ensuring that the right people

have the right resources for the job at hand. Getting people to make sacrifices, getting them

to cooperate with new managerial initiatives, and getting them to use the firm’s resources ap-

propriately requires that they be rewarded for doing so. However, many of these objectives and

whether they have been met are not easily describable to third-party enforcers. Instead, firms

have to rely, at least in part, on informal promises of rewards.1A firm’s ability to improve its

productivity is therefore constrained by its ability to make credible promises. In this article, I

explore the question of why some firms are able to put in place effective practices and others

∗Northwestern University; mike-powell@kellogg.northwestern.edu.

This article is a revised chapter of my MIT PhD. thesis. I am indebted to Robert Gibbons for his advice. This article

has benefitted from the suggestions of Daron Acemoglu, Abhijit Banerjee, Daniel Barron, David Berger, Nick Bloom,

Dan Cao, Ricardo Caballero, Cheng Chen, Sebastian di Tella, Glenn Ellison, Matthias Fahn, Luis Garicano, Jean-Paul

L’Huillier, Hongyi Li, Niko Matouschek, Iuliana Pascu, Michael Peters, Andrea Prat, Luis Rayo, Alp Simsek, Jeroen

Swinkels, Chad Syverson, Steven Tadelis,Heiwai Tang, Eric Van den Steen, Xiao Yu Wang,and seminar par ticipants at

Caltech (2012), Chicago (2013), Columbia (2012), Duke (2012), HKU (2015), LSE (2012), MIT (2012), Northwestern

(2012), NYU (2012), Queen’s (2013), Rochester (2012), Stanford (2012), Toronto (2013), UPenn (2012), and USC

(2012). I am grateful to Mark Armstrong and two anonymous referees for their valuablesuggestions. I thank MIT Sloan’s

Program on Innovation in Markets and Organizationsand the National Science Foundation for financial support.

1See Malcomson (2013) for a survey on the importance of informal agreements for motivating effort; Gibbons and

Henderson (2013) on how productivity-enhancing managerial practices relyon infor mal agreements; and Bloom, Sadun,

and VanReenen (2012) on how lack of trust constrains decentralization and therefore productivity.

C2019, The RAND Corporation. 121

122 / THE RAND JOURNAL OF ECONOMICS

are not by studying how credibility originates in a model of competition among heterogeneous

firms.

I model credibility as self-enforcement in a repeated game (Bull, 1987; MacLeod and

Malcomson, 1989; Levin, 2003) between a firm’s owner and a team of managers. The owner

decentralizes production decisions by allocating resources to each manager. She would like each

manager to utilize those resources appropriately, but formal contracts are unavailable. She can

promise to rewardthe manager for utilizing the resources, b ut she lacks commitment. In a one-shot

game, the owner would neverpay the reward, forward-looking managers will squander the firm’s

resources, and they will not be allocated any resources to begin with. The owner of a long-lived

firm, however, can credibly promise future rewards, as failure to uphold such promises can put

the future of the firm at stake: the firm’s future competitive rents can be used as collateral in the

firm’s promises. Accordingly, a firm with higher future competitive rents can maintain higher

levels of decentralization, in the sense that it can get each of its managers to utilize appropriately

a higher quantity of the firm’s resources in equilibrium.

Explicitly modelling the source of competitive rents is therefore important for understand-

ing the opportunities possessed by individual firms. As in Lucas (1978), output is sold into a

competitive product market, which consists of many firm owners of heterogeneous ability, and

production exhibits decreasing returns to scale. These features imply that firms of different total

factor productivity will coexist in equilibrium. Moreover, firms of different marginal productivity

will coexist in equilibrium, even though all firms face the same factor prices: heterogeneous firms

will be heterogeneously constrained,and therefore there will be misallocation of production. The

credibility necessary to sustain decentralization is determined by each firm’spotential future com-

petitive rents. Competitive rents, credibility, firms’ decentralization levels, and therefore firms’

productivity levels are jointly determined in industry equilibrium. The model offers two sets of

results.

First, by augmenting a standard neoclassical production function with noncontractible

resource-utilization decisions and lack of commitment, the model provides an explanationfor why

firms do not decentralize more, despite the Bloom, Sadun, and Van Reenen (2012) and Aghion

et al. (2017) findings that decentralization improves firm performance. The model highlights the

scarcity of credibility as a barrier to decentralization and illustrates how the firms’ decentralization

levels depend on the underlying environmentsin which they operate. The model delivers patterns

that are consistent with three sets of facts relating to (i) decentralization and firm performance,

(ii) productivity dynamics and firm organization, and (iii) cross-country productivity dispersion

and firm organization.

Second, because competitive rents serve as collateral, their allocation matters for effi-

ciency. In equilibrium, a high-ability owner expects to earn high levels of competitive rents

in the future, which increases her ability to decentralize today. This positive-feedback loop

is limited by decreasing returns to scale, but it nevertheless results in aggregate inefficien-

cies: competitive rents are allocated too progressively. High-ability firms overproduce, impos-

ing first-order pecuniary externality losses on low-ability firms. The competitive equilibrium

is therefore constrained-inefficient, and policies that redistribute profits away from the most

profitable firms, such as an excise tax with an exemption for small firms, may increase overall

welfare.

Related literature. A growing literature explores how models of relational contracts can help

us understand the large and persistent differences in productivity levels we tend to see across

producers. One such article is Board and Meyer-ter-Vehn (2015), which shows that labor-market

competition and on-the-job search can lead to the emergence of wage and productivity dispersion

among ex ante identical firms. This article instead highlights how product-market competition

determines firms’ competitive rents, and therefore constrains firms’ optimal relational incentive

contracts. Heterogeneity in firm ability leads some firms to be more constrained in industry

equilibrium, and I explore the implications of these differences.

C

The RAND Corporation 2019.