The Dynamics of Resource Allocation in Research Organizations

In firms with research units, two interesting problems arise:

1. Managers that allocate resources are often unsure about the quality of the projects being pursued by research-unit heads

2. Managers are often unsure about the quality of the heads themselves

• Complicating this problem, research units often produce no output for long periods of time; managers have to base their decision of whether to continue a project or keep a unit head on their beliefs

• A unit head who is poorly suited for the unit’s project can lower expected output dramatically

• Given this, it may be difficult to determine whether the head should be replaced or the project should simply be abandoned when a unit performs poorly

Method

• This paper develops and tests a simple decision-theoretic model with the above features

• The unit-level production function has uncertainty, and the head and the project must both be good in order for the unit to have a higher-than-average chance of success

• As managers resolve their uncertainty over time, they shut down under-performing projects and remove heads believed to be of low quality

• The results have implications for resource allocation within the firm

• The paper contributes to the literature by focusing on how selection (shutting down projects and removing heads) and dynamics affect resource allocation within the firm

Testable Hypotheses

1. Holding the stream of output constant, if the managers’ initial beliefs about the project or head are more favorable, the unit gets more resources every period. Thus, indicators of quality that can be observed at the time the head is appointed or the unit is formed have lasting effects on resource allocation.

2. Heads who obtain R&D experience before joining their current unit receive more resources than heads who lack such experience

3. Incumbent heads receive more resources than new heads

4. Older units receive more resources than new units

5. Unassigned heads who are believed to be better are assigned to projects that are believed to be better

Testable Hypotheses, continued

6. If a new head is assigned to a pre-existing project and at some point thereafter the unit’s performance declines, the head is always replaced before the project is abandoned. Similarly, if an experienced head is assigned to a new project and at some point thereafter the units’ performance declines, he will always be assigned a new project if the current one is abandoned

7. Conditional on survival, older units tend to have more resources (as measured, for example, by the number of workers in the unit) and have more variation in size

Survey data on research units in firms is used to test the predictions of the model and to estimate the relative importance of the different effects on the head’s span of control

The Model

• A manager is able to select projects and project heads from a pool and match them up

• Projects are either good or bad; heads are either good or bad

• Assume that the manager cannot directly observe project or head type

• Assume that heads are either incapable of observing project or their own type, or that they are unable to credibly convey this information to the manager

• Projects exist until they are shut down; heads remain until they are removed

• Most of the analysis focuses on manager’s choices that pertain to a single representative research unit (a small group working on a single project)

Formal Structure

In each time period, a unit produces an output with probability

and produces nothing with probability 1

The probability depends on the project type and the head type

If both are good, then ; oth

a

a

a

a a

herwise , where

Only units with good projects and good heads perform better

than others

The unit yields a time series of independent Bernoulli draws

where the probability of success is either

l h l

h

a a a a

a

or

The manager's problem is to try to figure out whether ,

and if it does not, then take the appropriate corrective action

l

h

a

a a

New Heads and New Projects

0

Suppose that the manager has a pool of new heads and a pool of new projects

Suppose that all new heads are identical from the manager's point of view and

are believed to be good with probability ; allp

0

00 0 0

new projects are believed to

be good with probability

If a new head is assigned to a new project, then the initial belief that both

are good is

Consider what happens if the head and the proje

q

p q ct stay together for periods,

where is the number of periods where output occurs and is the number of

periods where output does not occur

s t

s t

Updated Beliefs

00

00 00

0 0 0 0

0 0 0 0

(1 )

(1 ) (1 ) (1 )

Denote the unconditional probability that the head is good by

(1 ) (1 ) (1 )

(1 ) (1 ) (1 )

Denote the unconditio

s th h

st s t s th h l l

s t s th h l l

st s t s th h l l

a a

a a a a

a a p q a a p qp

a a p q a a p q

0 0 0 0

0 0 0 0

nal probability that the unit is good by

(1 ) (1 ) (1 )

(1 ) (1 ) (1 )

Each period, the manager believes that an output will be produced

with probability:

Pr[outpu

s t s th h l l

st s t s th h l l

a a p q a a p qq

a a p q a a p q

t occurs in period ] ( )l st h ls t a a a

Implications for Resource Allocation

• In order to connect the manager’s beliefs to testable predictions about resource allocation, I assume:

The Resources Assumption: Assume that the amount of resources that the manager allocates to the unit is increasing in his belief about the likelihood that output occurs

Formal Results

st 00Result 1: is increasing in . Therefore, any factors that increase the

manager's priors about head or project quality lead to more resources being

allocated in every period as long as the head and

st 00

the project are kept together.

Proof: The derivative of with respect to is positive. QED.

Note that Result 1 also holds for cases in which either the head or the

project is not new; for any init

ial beliefs, future beliefs are increasing in

the initial beliefs

Lemma 1

Since the firm only obtains if both its project and head are good, and

since Result 1 shows that higher values of today are associated with higher

future values of , the manager optimally bases hi

ha

s decisions entirely on

whether it is possible to increase the joint probability that the head and

the project are good. In what follows, I assume that every period the manager

can replace either the head or the project or both:

Lemma 1: If replacements must come from the pool of new heads and projects,

then the manager keeps an incumbent head with his project as long as

(1 ) (1 ) . That is, h l

s t s th la a a a as long as past observations of output are

more likely to come from a good project with a good head than otherwise,

the head and project are kept together

Lemma 1

st 0 0 0 0

st 0

The proof of Lemma 1 simply notes that the manager keeps the head with

his project as long as is at least as large as , , and

The result follows from showing that , etc., as st st

st

p q p q p q

p q

long as

(1 ) (1 )

Lemma 1 is used to prove Results 2-4

s t s th h l la a a a

Results 2 and 4

Result 2: Heads who obtain R&D experience before joining their current unit

receive more resources than heads who lack previous experience, holding

project characteristics constant.

Proof: Consider a project of arbitrary quality . There are two candidate heads.

One has previous experience for periods and was not removed; the other

is new. Expected output is higher with the experienced head as long

q

s t

0

as

. Sub in for and simplify to show that this holds as long as

the condition in Lemma 1 holds. Thus, as long as the experienced head

was not removed, he is believed to be better than a ne

s t s tp q p q p

0

w head. QED

Result 4 states that older units receive more resources than new units, holding

head characteristics constant; the proof is similar (compare to )s tq q

Result 3

Incumbent heads receive more resources than new heads, holding other things

constant.

Proof: Suppose the manager has the same unconditional beliefs about two

researchers and there is a project the mastp

nager believes to be good with

probability . Assume one of the researchers has been head of the project

for periods while the other has not; note that this is the only difference

between the two r

stq

s tesearchers. In this case, the manager allocates more

resources to the unit when the incumbent is in charge as long as .

Simple algebra shows that this inequality holds as long as the head was

n

st st stp q

ot removed (which implies that the condition in Lemma 1 holds). QED

Result 5

If there are two heads and two projects, none of which have been together

before, and the manager believes that one head is better than the other and

one project is better than the other, the better head is matched with the

better project.

Proof: Suppose the worse head and project are believed to be good with

probabilities and , and that the better head and project are believed to be

good with probab

p q

ilities and , where 1 and 1. Since 1 and

1, (1 )(1 ) 0, which can be expanded and rearranged as

1 . Now multiply both sides by to see that

( )( ) ( ) ( ). QED

p q

pq

p q pq p q p q

Result 6

If a new head joins an established project and the unit later performs poorly,

the head will always be replaced before the project is shut down, if shut-down

occurs.

Proof: Denote the manager's initial b

0

elief about the project quality at the time

the head and project are matched by ', where ' must be at least

(otherwise the project would have been shut down). The proof shows that the

project is al

q q q

0

ways kept as long as the condition in Lemma 1 holds and will

be kept if that condition fails as long as ' exceeds . We know that if the

condition in Lemma 1 fails the manager takes some action; thus

q q

the action must

be to remove the head. QED

Additional Implications for Cross-Sectional Data

• The data is a cross-section of research units

• Given this, it is important to determine the model’s additional implications for cross-sectional data

• I identify a research unit in the data with a “project” in the model; thus, the empirical counterpart of a “project” is simply whatever activities the unit undertakes

• The main additional implication is that older units should be larger on average and the variance in size should be larger among older units

• To see this, suppose a group of new units start today and experience shocks over time; initially all receive the same resources but as shocks occur some are shut down while others grow

• Conditional on survival, size grows and becomes more variable

Data

• The data is from the International Comparative Study on the Management, Productivity, and Effectiveness of Research Teams and Institutions, an international study of research units conducted by UNESCO during 1971-89

• I consider only research units that belong to firms involved in either agriculture, chemistry, physics, or the technical sciences

• The countries represented are Austria, Belgium, Brazil, Egypt, Finland, Hungary, South Korea, Nigeria, and Spain

• I control for field-country fixed effects in the econometric analysis• Summary statistics suggest that some type of selection process is

operating: the distributions of “unit age” and “years as head” are both skewed to the right, and heads are not identified with the unit (they can come and go while the unit lives on)

Econometric Model

• Results 1-4 predict that the amount of resources allocated to the head of a research unit depends on indicators of head quality that can be observed at the time he becomes head, his R&D experience, his length of tenure as head, and the age of the unit

• Result 5 establishes that unit size is correlated with head quality for another reason – heads who are believed to be better are assigned to units that are believed to be better

• To evaluate these claims, I need a measure of the resources allocated to the head; I use the number of scientists in the unit:

Sci = f(age, education, experience, years as head, field-country dummies)

Specification

Two key factors determine the econometric specification:

1. The dependent variable is integer-valued. Thus, a count data model is appropriate

2. Since the theoretical model predicts that unit size is more variable in cohorts that have older units and more experienced heads, it is important to allow for cross-section heterogeneity (overdispersion in the number of scientists)

The negative binomial count data model is appropriate in this case; it extends the Poisson model to allow for overdispersion

The Negative Binomial Model

( ) exp( ' )

where represents the variables of interest, exp( ' ) and exp( ).

Under the assumption that has a gamma distribution with mean 1 and variance

, the density of

i i i i i

i i i i i

i

i

E sci x u

x x u

u

sci

conditional on has conditional mean and conditional

variance (1 ), where measures overdispersion relative to the Poisson

distribution (the Poission model restricts 0).

I report results fo

i i

i i

x

r OLS, Poisson, and the negative binomial model.

In three country/unit type cases, unit size is perfectly predicted by the

country/unit type fixed effect; I exclude these cases from the estimation

routines.

Results

• The results in all three cases (OLS, Poisson, and negative binomial) are similar, and all three sets of results suggest that there is a positive relationship between the unit size and the four variables of interest, as the model suggests

• The overdispersion parameter of the negative binomial model is statistically significant at the 1% level, which suggests that there is substantial cross-sectional heterogeneity (as the model suggests), and that the restriction to Poisson is rejected

• The results are robust to the exclusion of outliers (a few of the units are quite large relative to the others)

Marginal Effects

• I report the marginal effects (computed at the mean values) from the negative binomial model; the effect of an additional year of education has the largest effect on expected unit size, followed by an additional year as head of the unit

• Roughly, on average, one extra scientist is added if either the head has four additional years of education, seven additional years as head of the unit, nine additional years of experience before joining the unit, or if the unit is 17 years older