Intro

This paper studies subset of intangible capital called organizational capital. The authors define organizational capital as intangible capital embodied in the firm’s key employees

The authors maintain the hypothesis that returns from organizational capital are partly firm specific and partly due to key talent at the firm. Thus, shareholders must split revenues between themselves and key talent to entice them not to take their talents to another firm. This has a number of consequences:

• The share of profits from organizational capital that shareholders can claim is a function of the key talent’s outside option (assumed to be a frontier tech employed by new firms)
• Shareholder’s cash flows from physical and organizational capital have a different risk exposure to shocks to the frontier technology.
• If shareholder’s marginal utility is correlated with the technology shock, heterogeneity in firms’ asset positions leads to differences in risk premia because shareholders demand additional compensation for the risk they are exposed to.

Model

They actually propose two models:

• A simple model they can solve in closed form and use to build up intuitions
• A more complete model that captures all of what they advertised in the beginning and must be solved numerically

Simple model

Continuous time. Infinite horizon

Continuum of firms that produce a common output using physical capital K and organizational capital O.

Output is y_i, t = θ_tK_i + θ_te^ϵ_iO_i, where θ_t is the time t aggregate TFP shock. ϵ_i captures the quality of the match between the firm and key talent.

In this model K, O, and ϵ are fixed.

TFP evolution is

dθ_t = σ_θθ_tdZ_t^θ.

Key has the choice to keep working at same firm with same O, upgrade technology to match the current frontier (restructure), or leave the firm entirely (relocate).

Because relocating is always an option, key talent extracts all surplus from restructuring. Relocating requires capital, which the key talent can buy from their former firm. The price is such that old firms are indifferent between restructuring or relocating. Thus, it doesn’t really matter which one the key talent chooses to do and going forward we just call either of these actions “upgrading to the frontier tech”.

Key talent optimally chooses a stopping time at which to exercise their option to upgrade to the frontier technology. When the upgrade happens (say at time τ) ϵ_i is set to the frontier value of x_τ, and stays there forever. The frontier tech satisfies

dx_t = σ_xdZ_t^x.

The SDF is given by

dπ_t =  − r_fπ_tdt − γ_θπ_tdZ_t^θ − γ_xπ_tdZ_t^x

Value of firm is

V_it = V_it^K + V_it^O

Value of capital satisfies

$$V^K(\theta_t, K_i) = E_t \int_t^{\infty} \frac{\pi_s}{\pi_t} \theta_s K_t ds = \frac{\theta_t}{\bar{r}} K_t,$$

where r̄ = r_f + σ_θγ_θ. The value of organizational capital satisfies

$$V^O(\theta_t, O_i, \epsilon_i, x_t) = Et \int{t}^{\tau} \frac{\pi_s}{\pi_t} \theta_s e^{\epsilon_i} O_i ds + Et \left[\frac{\pi{\tau}}{\pit} \bar{V}^O(\theta{\tau}, O_i, x) \right],$$

where the terminal value is given by

$$\bar{V}^O(\theta_t, O_i, x_t) = E_t \int_t^{\infty} \frac{\pi_s}{\pi_t} \theta_s e^{x_t} O_i ds = \frac{\theta_t}{\bar{r}} e^{x_t} Oi.$$

$$O{it} = (1-\deltaO) O{it-1} + \frac{SGA_{it}}{cpi_t},$$

where δ_O is the depreciation rate of organizational capital (equal to 15% in their calculations – the same number the BEA uses when they apply this method for calculating the stock of R&D capital) and cpi_t is the consumer price index in period t. They also make the assumption that $O_0 = \frac{SGA_1}{g + \delta_O}$ (g chosen to be 10% – growth rate of SG&A expenditures in the sample).

O is scaled by book capital K.

SG&A accounting practices and rules vary by industry. To remove a potential industry bias they collect firms into industries, sort into quintiles based on the O/K ratio within the industry, then construct 5 value weighted portfolios of the firms within each quintile.

The sample includes all Compustat non-financial firms traded on NYSE, AMEX, or NASDAQ that have financial year ending in December and have non-missing industry codes. This leaves them with 5,917 firms from 1970 to 2008.

They do detail their calibration pretty concisely in section III.A.1, so I won’t repeat that here.

Results

Key results:

• In the data, High O/K firms have higher Tobins Q, lower investment rates in K, smaller market cap, higher productivity, higher key talent pay
  • The model matches all these facts qualitatively, and does fairly well quantitatively
  • In the data they also find that high O/K firms are more labor intensive, higher labor expenses per worker, and lower leverage
• Stuff about how the cross-sectional differences in ratio of O/K are related to risk premia
  • In data: High O/K firms have higher returns, lower volatility of returns, and higher sharpe ratio. All same in model
  • TODO: come back here and summarize better

Key testable predictions from the model that are supported in the data are:

• The following are increasing in x
  • Key talent pay
  • Investment in O
  • Reallocation
• Sensitivity of firm earnings to firm output is increasing in O/K, but sensitivity of firms earnings to aggregate output is common for all firms

They do the following robustness checks and confirm that the results hold

• form equal-weighted instead of value-weighted portfolios
• Pool all industries together when making portfolios
• Scale O by property, plant, and equipment instead of book assets
• measure investment in O as SG&A minus advertising