Dynamic Agency and the q Theory of Investment

DeMarzo, Peter M., Michael J. Fishman, Zhiguo He, and Neng Wang, 2012, “Dynamic Agency and the q Theory of Investment,” The Journal of Finance, Vol. 67, No. 6 (2012), 2295-2340.

Purpose:  To introduce an agency problem into the standard q theory of investment; to show that cash flow is not the best predictor of investment.

Motivation:  A large body of literature uses cash flow to predict firm investment levels.  This paper argues that a better proxy is “financial slack,” which is directly related to the agency problem.

Model:

  • Productivity is a Brownian motion, and the agent controls the drift but not the volatility.
  • w = W/K is the agent’s total expected payoff per unit of capital, and must be high enough to incentivize the agent to maximize productivity.
  • The level of w depends on λ, σ, and historical firm profitability.
    • λ is a measure of the extent of the agency problem.
    • σ is the volatility of firm productivity.
    • Past productivity raises or lowers w, and the agent loses his job when w = 0.
    • A portion of w is deferred, giving the agent a stake in continued firm success.
  • Investor’s expected payoff per unit of capital, p(w), is a function of how much they pay the agent.
  • Average q is total firm value per unit of capital stock, or qa = p(w) + w.
  • Marginal q, or qm = p(w)wp’(w).
    • Firms invest when marginal q is less than 1, so investment is a function of w. It follows that investment depends upon λ, σ, and past firm performance.
  • “Financial slack” equals w/λ, and is the largest productivity shock the firm can suffer without changing agents.
  • The agent accumulates cash and available credit equal to the firm’s “financial slack,” then distributes excess income to shareholders.

Conclusions:

  • Financial slack is a better predictor of investment than cash flow.
  • Average q is higher than marginal q because an increase in capital stock K reduces w, and hence reduces the agent’s [historically determined] incentives to maximize productivity.
  • Financial slack and profitability are substitutes in determining average q.
  • When the firm is profitable, w rises, the agent’s incentives grow, and return on investment increases.
    • Investment is serially correlated.
  • The cost of incentivizing the agent leads to underinvestment in every state of the world.