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\begin{center} {\Large {\bf Notes on    Family Firms }  } \\

 



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7 December 2005 \\


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Andrew Ellul and Eric Rasmusen \\



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{\it Abstract}
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   In many countries even large companies are family firms, closely controlled
by one family but with much of the capital supplied by minority shareholders.
Since close control  allows the owner to operate to the detriment of the
minority shareholders, this is a puzzle, especially in countries where legal
protection of the minority is weak.  We suggest a solution: that by giving the
family a positive but limited opportunity to obtain rents from the firm, this
corporate form causes the family to avoid undesirable risk that a more
responsive directors might accept.

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\noindent {\small
 \hspace*{20pt}Ellul: \\
  \hspace*{20pt}Rasmusen:   Dan R. and Catherine M. Dalton Professor, Department
of Business Economics and Public Policy, Kelley School of Business, Indiana
University,  BU 456, 1309 E. 10th Street, Bloomington, Indiana, 47405-1701.
Office: (812) 855-9219. Fax: 812-855-3354. Erasmuse@indiana.edu. http:
//rasmusen.org. Copies of this paper can be found at\\
  http://rasmusen.org/papers/familyfirm-rasmusen.pdf. JEL Code: D44. }

 {\small We thank   xxx }

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\noindent
  {\bf 1. Introduction} [same as abstract now]

 In many countries even large companies are family firms, closely controlled by
one family but with much of the capital supplied by minority shareholders. Since
close control  allows the owner to operate to the detriment of the minority
shareholders, this is a puzzle, especially in countries where legal protection
of the minority is weak.  We suggest a solution: that by giving the family a
positive but limited opportunity to obtain rents from the firm, this corporate
form causes the family to avoid undesirable risk that a more responsive
directors might accept.
 


 \noindent 
 {\bf 2.  The Model}

  There is a unit length of investors. Fraction $\alpha$ of the investors are  risk-averse passive investors with wealth density $w_p$, and  fraction ($1- \alpha)$ are active risk-neutral investors with wealth density $w_a$. 
    Investors' rate of time preference is $r$. An investor may invest  various portions of his wealth in cash,  in the debt of one or more  individuals, or in the equity of one or more firms.

 There is a  unit interval of  infinitesimal firms (infinitesimal to avoid integer problems).   
Each period a firm undertakes one of two kinds of projects: safe  and risky. The safe  project has a certain return of  $[B-f(X)]V$  per dollar invested, where  $B<1$,  $X$ is the amount of  perks  taken, and $[B-f(0)]V>1$. The risky project  has an $f(X)$ probability of an end value of $0$ per dollar invested   and a ($1-f(X))$ probability of $V$.     The risk is systematic---  if a project with $X=X'$ fails, so will every project with $X \geq X'$. 

    Corporate governance is as follows.   There are two forms of control.   Under open control, the firm is controlled by   one of its active shareholders chosen  randomly  each period with a probability proportionate to his shareholdings.   Under closed control, the firm is controlled permanently by one of its active shareholders   who retains control from period to period. The form of control is decided when the firm is formed and cannot be changed.  The controller makes two decisions: the type of project in which to invest, and the amount $X$ of perks.    Each share gets an equal fraction of the value of the firm  at the end of each  period and   may transfer it to a different firm.  

   
 


 The order of play  is as follows.

1. Investors make loans to each other.

2.   Risk-averse investors invest, either in corporate stock,   individual debt, or cash. 

3.   Risk-neutral investors invest, either in corporate stock,   individual debt, or cash.  

4. The identity of the controller is established in each firm.

5. Firms choose projects according to the desires of their controllers.

6. The project returns are realized.

7. Debt is repaid.

8. Perks are paid out in closely held firms.

9. The  value of the firm  is paid out equally to shareholders.

 I should say, too, that the controller can loot the firm. That affects the project return, though, so it is not good in the long term. That is really a separate idea. 

\bigskip

\noindent
 {\bf What Happens without Family Firms?}

   If there were no family firms, the equilibrium will be for the risk-neutral
investors to invest in stock in   firms which would invest in the risky
project and for the risk-averse investors to hold  mostly cash and to hold a
small amount of stock.

 The reason all firms will invest in risky projects is simply that the active investors are all risk-neutral, and they make the decisions. 

 Whoever is the controller will choose $X$ based on his shareholdings, but it will be very high, because  control is reassigned in the next   period.  

    Active investors will invest evenly across firms, because the probability of becoming the controller is greatest in a firm with the fewest active investors. 

Here is the controller's payoff: 
\begin{equation} \label{e2}
\pi (x, safe)  = \left( \frac{1}{1+r} \right)  \left(  x +    w_a (B - f(x))V \right) 
\end{equation}
or 
\begin{equation} \label{e2}
\pi (x, risky)  =\left( \frac{1}{1+r} \right)  \left(  x +    w_a (1-f(x)) V\right) 
\end{equation}

 The first order conditions are 
\begin{equation} \label{e2}
\frac{ d\pi (x, safe) }{dx} = \left( \frac{1}{1+r} \right)  \left(  1 +    w_a (  - f'(x))V \right) =0
\end{equation}
or 
\begin{equation} \label{e2}
\frac{ d \pi (x, risky)  }{dx} =\left( \frac{1}{1+r} \right)  \left(  1 +    w_a ( -f'(x)) V\right) =0
\end{equation}
 Thus, $x^*$ is the same for both types of investment. The  controller will choose the risky project, since its expected return is higher because $B<1$. 

 Consider what happens if one of the risk-averse investors only has a choice
between cash and the risky project. If his initial wealth is $g$ and he  invests
$z$ in the risky project, his utility will be
\begin{equation} \label{e2}
 .5 U(g-z) + .5 U(g+[1-C](2)(S+K)z)  
\end{equation}
Maximizing yields
\begin{equation} \label{e2}
 -.5 U'(g-z) + .5 [1-C](2)(S+K) U'(g+[1-C](2)(S+K)z)=0   
\end{equation}
 and  there exists some $z$ sufficiently small to make this first order
condition true.  This result that  risk-averse investors would put some of their
wealth in a risky asset  is a
basic result in portfolio theory, and uninteresting in this context. 


What is more interesting is why the
risk-averse investor is restricted to either cash or the risky  project,  rather
than debt,  or equity in a firm which invests in the safe project.

First, consider debt. Risk-neutral individuals would like to borrow, so they
could leverage themselves and buy more equity. Risk-averse investors, however,
would not lend, knowing that the borrower   would invest in equity and if he
were leveraged enough would be unable in the bad state to repay. Firms would
like to borrow too, for leverage, but risk- averse investors would not lend to
them either, for the same reason.

Second, consider equity in a safe firm. Risk-averse investors would like to own shares in a firm that would invest just in the safe project. If they were the controlling shareholders, that is what they would do.  But they are assigned to firms randomly  before they know how many risk-neutral investors will buy shares in the firm.  There is a risk-- or even a certainty-- that more than 51\% of the shares of a firm will be owned by risk-neutral investors, in which case the risky project will be chosen.

There are multiple equilibria. The certainty (actually near certainty here) of firms being controlled by risk-neutral investors is the equilibrium described above: all risk-averse investors choose to invest very little in equity.

 The other extreme is an equilibrium in which all the risk-neutral investors do invest everything in equity. They are more willing to do this, knowing that since they are all investing in equity, some firm will happen to be controlled by them and will choose safe projects. This equilibrium can exist if enough firms end up being controlled by risk-averse investors.  The percentage of firms so controlled is a function of $\theta$ that we will denote as $h(\theta)$. This kind of equilibrium will exist if for both $w=g$ and $w=f$,
\begin{equation} \label{e1}
   h(\theta)  U([1+S]w) + [1-h(\theta)][ .5 U(0) + .5 U(  [1-C](2)(S+K) w)] \geq
U(w).
\end{equation}
  Otherwise, the only equilibrium is that in which all firms invest in risky
projects.


Note that this is an adverse selection problem, exacerbated by the greater
awareness of the risk-neutral investors. Under our assumptions, no risk-neutral
investors are caught as minority shareholders in safe firms. Rather, they
withdraw and reinvest in risky firms-- further increasing the chances (if we fix
the model--flaw here) that firms are risky. The safe firms will be 100\% owned
by risk-averse shareholders.

(xxx If we had more classes of risk, we could get more extreme adverse selection
in a more complicated model. Once  the most active risk-averse invetors left a
firm, it woudl adtop riskier policies, and the next most risk-averse acive
investors would leave, and so forth. Maybe this is the way to go--- a firm
chooses a risk level based on its median shareholder. But then the risk-neutal
ones would elave too.... )
 
\bigskip

\noindent
 {\bf What Happens with Family Firms?}

Can you re-start a family firm? 

There are two reasons why the family firm will do better. First, it has a longer time horizon, so it will make $x$ less.  

I don't yet have a reason why it chooses the safe project. 


What if we introduce family firms? 

 The family firms are risk-neutral, so for their investment return, they prefer the risky project. That might bankrtupt hte firm, though, in whcih case they lose their future perks. Also, they will choose the perks to be lower. 

 It may be that they can only attract investors if they invest enough of their wealth, too. 





Suppose  first that the family owns an
infinitesimal amount of the firm's assets. That means the family's payoff is its
perks, $M$, minus the  effort cost $C$ if it picks the risky project. As a
result, the family has two motives for avoiding the risky project: the direct
cost $C$ and the possbility of failure and not getting $M$. So the family firm
will only invest in teh safe project.

 As a result, risk-neutral investors will not want to invest in the family
firm.\footnote{MOdified model: make the safe project somewhat risky too. Then
the risk-neutral investors will be willing to invest in the family firm with teh
safe project because of the leverage: the firms as a whole bears little risk,
but the equity will bear a lot of risk. This will generate an endogenous
debt/equity ratio. }  They will stick to shareholder-controlled firms. Risk-
averse investors, however, will happily invest in a family firm if it is big
enough. If it has $A$ in assets, they will invest if $(1+R)A-M > A$. They won't
care whether they are holding equity or bonds.

 Thus, in equilibirum there will be $\theta$ shareholder-controlled firms and
$(1-\theta)$ family firms.

 In this model, the family does not have to own a significant number of shares
in the firm. A modification would be to say that family control requires a
significant amount of ownership. That does not alter things if the family is
risk averse, adn knwon to be. If hte family is risk-neutral, then the family's
incentive to switch to the risky project for its higher return must be balanced
against its liking for the safe project because of the perks and effort.

 

 

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 {\bf References} 
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Ellul, Andrew 


Rasmusen, Eric (1988)  ``Stock Banks and Mutual Banks,''   Journal of Law and
Economics, 31: 395-422 (October 1988).  http:
//rasmusen.org/pacioli/published/Rasmusen\_88JLEC.mutual.pdf.


 

"A Theory of Trustees, and Other Thoughts," in  Public Debt and its Finance in a
Model of a Macroeconomic Policy Game: Papers Presented at a Workshop held in
Antalya, Turkey on October 10-11, 1997,   ed. by Tahire Akder.
 http://rasmusen.org/pacioli/published/Rasmusen\_98.BOOK.trustees.NEW.pdf 



 Measuring Judicial Independence: The Political Economy of Judging in Japan,
University of Chicago Press,   2003 (with J. Mark Ramseyer).
 http://rasmusen.org/published/Rasmusen-03-5ps-japan.txt

``An Income-Satiation Model of Efficiency Wages,''   Economic Inquiry (July
1992) 30: 467- 478.  
(http://rasmusen.org/pacioli/published/Rasmusen\_92ECINQ.effwages.pdf) .
 

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