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Holmstrom (1999) - The Firm As A Subeconomy (view source)
Revision as of 22:42, 30 November 2010
, 22:42, 30 November 2010no edit summary
Thus as long as the measure is not collinear with output, it provides additional info and can be used to strengthen incentives. This extends directly to <math>n\;</math> workers.
==Ownership and Incomplete Contracts==
'''Property rights theory''' as embodied originally in Grossman and Hart (1986), and crystalized in Hart and Moore (1990), argues that asset ownership is crucial and central to the theory of the firm. Following [[Williamson (1971) - The Vertical Integration Of Production | Williamson (1971)]] and others, this model argues that the threat of hold-up will lead to underinvestment in relational-specific assets, and so that integration of two assets into a single firm is efficient.
===The Hart-Moore Model===
The simplified model is as follows:
*There are two parties <math>B\;</math> (a buyer) and <math>S\;</math> (a seller).
*There are two dates, 1 and 2.
*There is a set of assets <math>A\;</math>, that can be allocated to either or both parties, or some outsider (which is never optimal)
*At <math>t=1\;</math>, <math>B\;</math> and <math>S\;</math> make private investments <math>b\;</math> and <math>s\;</math>.
*No contract can be written to specify the use (or trades) of the assets at <math>t=2\;</math>
*At <math>t=2\;</math> parties can trade or not. If they trade they split (50-50, see below) <math>v(b,s)\;</math>. If they don't they get their outside options; <math>v_b(b|A_b)\;</math> and <math>v_s(s|A_s)\;</math>.
*It is assumed that <math>v \ge v_s +v_b\;</math>, and these values are exogenously given
The surplus if they trade is:
:<math>v - v_s - v_b\;</math>
Each firm gets half of the surplus (plus the value of their outside option):
:<math>s_b(b,s|A_b,A_s) = \frac{1}{2}\cdot \left ( v(b,s) - v_s(s|A_s) + v_b(b|A_b) \right )\;</math>
The authors assume that with more assets under control, the marginal incentive to invest increases. That is <math>\frac{\partial v_b}{\partial b}\;</math> increases as <math>A_b\;</math> increases, and likewise for <math>s\;</math>. And that there are complementarities in production, that is <math>\frac{\partial v^2}{\partial b \partial s} > 0\;</math>.
Crucially they also assume that the marginal contributions of investment to value are higher when the two parties work together. That is <math>\frac{\partial v}{\partial b} \ge \frac{\partial v_b}{\partial b}\;</math>, and likewise for <math>s\;</math>. This gives us [http://en.wikipedia.org/wiki/Supermodular supermodular] value functions (see also [http://en.wikipedia.org/wiki/Topkis%27s_theorem Topkis's theorem] for the continous case).
===Implications of Hart-Moore===
'''The equilibrium level of investment is at or below the efficient level'''.
From the supermodularity assumption above, we immediately have that:
:<math>\frac{\partial v}{\partial b} \ge \frac{1}{2} \cdot left(\frac{\partial v}{\partial b} + \frac{\partial v_b}{\partial b} \right )\;</math>
As investments are complementary, the less <math>B\;</math> invests, the less <math>S\;</math> will invest (and so forth).
'''It is never optimal to have joint ownership''', as this amounts to two vetos on usage, instead of one. Implicit here is that <math>\frac{\partial v_b}{\partial b}\;</math> increases as '''sole ownership''' of assets counted in <math>A_b\;</math> increases, and likewise for <math>s\;</math>. Thus joint ownership assets could always be reassigned to sole ownership of either party without weakening either parties' incentives to invest, and strengthening at least one party's. Likewise outside ownership is never optimal, at least if [http://en.wikipedia.org/wiki/Shapley_value Shapley value] is the bargaining outcome.
'''Assets that are perfectly complementary should always be owned by the same party''' as otherwise the ownership of one asset by one party renders both assets worthless.
If investments could targetted towards enhancing either inside value <math>v\;</math>, or outside value, <math>v_b\;</math>, then '''there will be a bias towards investing in outside options''', which is a form of rent-seeking - it sacrifices total value in order to get a bigger share.
===Equivalence to Team's Problem===
In the Hart-Moore problem the joint output is <math>y = v(s,b)\;</math>, and the parties provide unobserved inputs <math>e_1 = b\;</math> and <math>e_2 = s\;</math>. The only difference is in the instruments used to motivate the agents: Instead of sharing rules there are asset allocation rules. The asset allocation rules need not be binary (even if there are only two ex-post agreed upon lotteries can expand the payoffs to all linear combinations.
However, there is an important distinction: The payoffs in the property rights model are not only a function of the joint output but also the outside option. In the team's problem, a monitor can break the budget - here the market breaks the budget. It is implicitly assumed that the agents can observe each other's outside options (this may be costly and a friction). If this is the actually the case then unless <math>v_b\;</math> and <math>v_s\;</math> are collinear with with <math>v, they are additional measures as discussed above.
The special case of:
:<math>v = v_b + v_s\; \forall b,s\;</math>
Is a perfectly competitive market for investment - the outside option is the same as the inside option, which gives:
:<math>\frac{\partial s_b}{\partial b} = \frac{\partial v }{\partial b } \quad \mbox \quad \frac{\partial s_s }{\partial s} = \frac{\partial v}{\partial s}\;</math>
And so a socially optimal level of investment. Perfect market monitoring breaks the budget and both sides get the full social return.
The key point is that in this model the market provides to both information and provide the right to exit a relationship, and so the investment incentives. Of course, in reality the generation of the information is not costless, and the bargaining might result in rent seeking.
===Problems with this model===
There are a number of problems, which the paper considers. These include:
*'''Empirical issues''':
**Joint production does occur
**Different bargaining rules can alter the conclusions
**Asset specificity only matters on the margin (adding a constant to the joint surplus makes no difference)
*'''Why Do Firms Own Assets?'''
**The theory is about asset ownership by individuals
**If human capital is used then we have taken the firm as exogenous
**We should be asking what activities do firms do, not what assets do they own
**The model suggests assets should be widely held across individuals, but we observe the opposite - firms own everything!
The paper provides three possible answers to the last point:
#Concentrating assets to ownership by just the firm strengthens the firm's bargaining position with outsiders
#It may influence the terms for financing asset purchases (the firm may be a financial intermediary)
#A firm can then assign workers to assets in 'richer and more varied' manner. This makes the firm more responsive to chamnges that it could not anticipate ex-ante.
In the words of Holmstrom:
My argument is that it allows the firm in internalize many of the externalities
that are associated with incentive design in a world characterized by informational imperfections.
As the theory of second best suggests, an uncoordinated application of the available
incentive instruments will lead to significant externalities. By having access to more instreuments,
the firm can set up a more coherent system of incentives. Often this involves suppressing
excessively strong incentives on individually measured performance for the benefit of enhancing
the effectiveness of more delicate and subtle instruments aimed at encouraging cooperation
and other less easily measured activties...
Let me stress that viewing the firm as a subeconomy, which regulates trade according to
second best principles, does not imply that one firm should own all the assets...
seperate ownership does allow market based bargaining... [and] the very fact that workers can exit
a firm at will... and that consumers and suppliers can do likewise, limits the firm's ability
to exploit these constituents.
