Gomes and Livdan (2004)

• The authors use a formal dynamic model of a value maximizing firm to show that the main empirical findings about firm diversification and performance are consistent with value maximization

• In the model, diversification allows a firm to explore better productive opportunities while taking advantage of synergies; a “diversification discount” is observed even though diversification itself does not destroy value

• The main competing explanations for the facts are based on agency theory, but the authors point out that agency-based explanations lack solid theoretical foundations (why do owners tolerate such obvious value-reducing actions?) and are difficult to test directly; support for the agency view typically comes from the perceived failure of alternatives

The Model

In the model, firms diversify for two reasons:1. Diversification allows firms to exploit economies of scope by

eliminating redundancies across activities and reducing fixed costs

2. Diversification allows a mature slow-growing firm to explore attractive new productive opportunities

• Using numerical computations, the model generates an artificial cross sectional distribution of firms; the authors compare results obtained from this artificial data to real data

• The model predicts that diversified firms have, on average, a lower Tobin’s q than focused firms, as documented by Lang and Stulz (1994)

• The intuition is that firms diversify only when they become relatively unproductive in their current activities

Contributions to the Literature

• Some other recent work such as Matsusaka (2001) and Maksimovic and Phillips (2002) also analyzes diversification using models of profit maximizing firms

• However, conglomerate firms in these models are still endowed with lower profit opportunities than specialized firms; Matsusaka models diversification as an intermediate less productive search stage and Maksimovic and Phillips assume that firms must incur extra costs when they produce in more than one industry

• In the authors’ model conglomerates are not assumed to be ex ante less efficient

• The model endogenously links productivity, size, and valuations to diversification strategies in a fully specified general equilibrium environment and generates artificial data; a key strength is this close relation to observable facts

Formal Structure

• Real firms differ in several ways: size, growth, investment, diversification; the model must produce such a cross section of firms

• The economy consists of households and firms, but the model focuses on the firms, who produce a consumption good

• Households are summarized by a single representative consumer making optimal consumption and portfolio decisions

• Time is discrete and the horizon is infinite• There are two separate industries; each period firms can either be

focused in sector 1 or 2 or operate in both (which is denoted by 3)• Firms who are focused in period t cannot simply switch industries in

period t + 1; they must either remain as they are or diversify• Diversified firms can remain diversified or become focused in either

industry

Production

The outcome of production in sector in period is

Goods are perfect substitutes; the relative price of both goods is 1

Production in each sector requires capital, labor, and is

subject to a shock

sts t y

Labor is hired at a competitive wage rate ; capacity is

owned by the firm

The production function for a firm in sector s is

, where 0 1

The restriction on th

st k l

st

t

zst t t k l

z

W

y e k l e coefficients guarantees that production

exhibits decreasing returns to scale, so returns fall as the firm grows

Productivity and Capacity

1

Productivity levels are firm specific and cannot be traded

Productivity in each sector follows an AR(1) process:

where each is a normal random variable w

s s st t t

st

z z

2

1 2

1

ith mean zero and

variance ; sector shocks are independent from each other

Denote ( , )

Total firm capacity follows

(1 )

where denotes gross investment

t t t

t t t

t

z z z

k k i

i

and is the depreciation rate

Timing

1. Every firm arrives at period t with its capacity and immediately observes its productivity levels in both sectors

2. Then the firm decides which sectors to operate in

3. Then the firm allocates capital and labor across its activities

4. Then the firm decides how much to invest, which determines its capacity the following period

Profits

1 2

,

If the firm focuses in one sector:

( , , ; ) max[ ]

where is a fixed cost

If the firm chooses to be diversified:

(3, , ; ) max[ ( ) ( ) ((1 ) )

st k l

t

t k l t

t t

zt t t t t t t t

l

z zt t t t t t t t t

l

s k z W e k l W l f

f

k z W e k l e k

((1 ) )

(2 ) ], s.t. [0,1]

where denotes the fraction of resources that the diversified firm

allocates to sector 1 in period

The parameter indicate

k lt t

t t t

t

l

W l f

t

s fixed cost savings from eliminating

redundancies

Discussion

• In reality, synergies are created through the elimination of redundancies across business lines, such as overhead

• In the model, “synergies” are captured by the savings parameter lambda, which generates a form of economies of scope and creates a benefit to diversification that cannot be replicated by shareholders

• This is a key departure from the literature: in this model conglomerates create value for investors, and the diversification discount is driven entirely by the endogenous nature of the diversification decision

• The model assumes decreasing returns to scale in each sector; as the firm grows in size, marginal productivities fall and it becomes unprofitable for the firm to continue to invest in its existing activities

• Instead, the firm explores new opportunities• Thus, large firms are more likely to become diversified, as in reality

Discussion

Conglomerates also benefit from two other features in the model:

1. They have more options than focused firms because focused firms cannot simply switch industries

2. Since the productivity shocks are not perfectly correlated, diversification allows a firm to explore alternative profit opportunities and lower exposure to cash flow risk. However, this feature is not valued by investors in general equilibrium because they can diversify their portfolio

Thus, in the author’s model, production is more efficient and resources are saved when operations are combined into a conglomerate

This ensures that the model does not generate a diversification discount directly from its assumptions; the discount is generated endogenously from self-selection

Optimality

Let ( , , ) denote the state for a firm that was active in sector

in period 1, has units of capacity at the beginning of

period , and faces a vector of shocks

Optimal firm behavior can be summar

s k z

s t k

t z

', '

ized by the value function:

( , , ; ) max{ ( ', , ; ) (1 ) '

( ', ', '; ') ( ' | )}

subject to the constraint that focused firms cannot switch sectors,

where the

k sv s k z W s k z W k k

v s k z W N dz z

superscript ' denotes the value of the state variables at

the beginning of next period, is the discount factor, and

( ' | ) is the cdf of ' conditional on N dz z z z

Propositions

Proposition 1: There exists a unique function ( , , ) that solves the

dynamic program. This function is continuous and increasing in both and

Proposition 2: The optimal diversification decision can

v s k z

k z

~^ ~

be characterized by

a threshold value k( , ) that is increasing in and decreasing in , .

At values of k above this threshold it is optimal to diversify.

The endogenous shock-dependent selecti

s ss z z z s s

on emphasized in Proposition 2

drives the results; as several recent empirical studies have emphasized,

conglomerates are not a random subsample of the cross section of firms

Corollaries

Corollary 1: If there are no fixed costs ( 0), diversification is

always optimal

Corollary 2: Suppose 0. Diversification is always optimal if 1

(i.e., if synergies are sufficiently large).

Without fi

f

f

xed costs, profits are always positive in both sectors and

the firm would have no incentive to focus, given the assumption of

decreasing returns to scale

Similarly, if synergies are sufficiently large, firms never focus

Aggregation

To construct an artificial panel of firms, individual decisions

must be aggregated

Since each firm can be described by its ( , , ), the cross-sectional

distribution of firms is completely summarized by a

s k z

measure

( , , ) defined over this state space

For empirical purposes the authors are interested in the properties

of a stationary equilibrium where the distribution does not depend

on initial conditions

s k z

, so '

Demand, Labor Supply, and General Equilibrium

They summarize the household sector with a single representative

agent deriving utility from leisure and consumption , with

income from wages and dividends (which are given by

each firm's current

L C

W D

,

cash flows)

There are no aggregate shocks, so all aggregate quantities and

prices are constant and the consumer problem collapses to the

static representation:

max ln( )

C LU C AL

. .

The optimality conditions yield a demand for final goods and an

infinitely elastic labor supply, which pins down the wage:

s t C WL D

W A

Calibration

• Computing the stationary equilibrium requires parameter values that must be selected to be consistent with either long-run properties of the data (unconditional first moments) or with prior empirical evidence

• Since most data is available at an annual frequency, they assume that a time period in the model corresponds to one year

• They use independent evidence on the degree of returns to scale to set the output elasticities at .65 (labor) and .3 (capital)

• The rate of depreciation of the capital stock is set to .1

• The four remaining parameters cannot be individually identified from the available data; they are chosen so that the model is able to approximate the unconditional moments from the panel studied by Lang and Stulz (1994) (cross-sectional mean and dispersion of Tobin’s q, the fraction of diversified firms, the average level of q for conglomerates; the main stylized facts are conditional moments, or regressions, from this panel)

Numerical Method

• Computing requires a numerical algorithm capable of approximating the stationary equilibrium

• The algorithm includes three steps:

1. Solving the firm’s problem and compute the optimal firm decision rules

2. Use the optimal decision rules and iterate to compute the stationary distribution

3. Compute aggregate quantities and use the market clearing condition to determine the equilibrium levels of consumption and labor

The first step employs value function iteration on a discrete state space; the authors specify a grid with a finite number of points for the capital stock as well as a finite approximation to the normal random vector z

The Stationary Distribution

*To compute , take the optimal value function ( , , ) and

the decision rules ( , , ) and ( , , ) as well as the stochastic

process for the shocks and proceed as follows:

1. Define the size of the p

v s k z

k s k z s s k z

z

anel by specifying the number of

firms and the length of time

2. Simulate a sequence of exogenous shocks for each firm in

every period

3. For the initial period, initiate each firm's capital stock at

an initial value and randomly allocate firms to either sector

1 or 2

Iterations

For all other periods:

1. Given the current state for each firm, use the optimal policy functions

to determine the next period's capital stock and sectoral decision

2. Using the value function, compute the current market value of the firm

3. Using the stochastic process for the shocks, compute next period's shock

4. Construct the cross-sectional distribution of firms ( , , )

5. Continue the sit it it its k z

1

*

imulation until || ||

Use the stationary distribution and the goods market equilibrium

condition to obtain aggregate consumption

it it

Diversification Discount

0 1 2

The authors focus on the relationship between diversification and firm value

Previous empirical papers estimate equations like

ln( )

where is the value of Tobiit it it it

it

q b b DIV b k

q

n's for firm at the beginning of period ,

is the beginning period size of the firm, and is a dummy variable

that takes the value 1 if the firm is diversified in period

The authors estima

it it

q i t

k DIV

t

te such an equation using their artificial panel by

constructing the variables

( ', , ) and {1 if ' 3; 0 else}

where ( ', , ) denotes the value of the firm of size that choos

p s k zq DIV s

kp s k z k

es to

operate in sector ' in period s t

Results

• The authors compare the results of estimating the regression using their model’s data to the empirical results of Lang and Stulz (1994)

• They report the means across 100 simulations for both their coefficients and t-statistics

• As in the real data, the model’s results show that diversified firms are discounted and the discount is statistically significant

• The model predicts a diversification discount that is quantitatively similar to that found in the real data

• The results are robust to excluding outliers with q greater than 5• The results suggest that selection is sufficient to explain the

“diversification discount”; diversification in this model is optimal for those firms that diversify and breaking them up would destroy shareholder value

• If synergies are large enough, the discount can disappear; this may explain evidence that suggests that the magnitude of the discount varies with the level of synergies

Source of the Discount

• Following Lang and Stulz (1994), the authors report the results of several additional comparisons using their artificial data

• Estimating the regression for the subsample of firms that do not change the number of segments in which they operate (which excludes newly diversified and refocused firms) does not eliminate the observed discount (as in the data)

• There is some suggestion in the model and the data that diversifying firms experience drops in q and refocusing firms experience increases in q

• Recent empirical work suggests finds that firm spin-offs and divestitures tend to raise value while improving the quality of investment, and the model explains why this occurs: firms refocus when productivity shocks become more asymmetric, so divestitures are associated with increased productivity and investment in ongoing activities