modeling and measuring organization capitalmkredler/readgr/gonzalezonatkesonkehoe05.pdf · the life...

Modeling and Measuring Organization CapitalAndrew Atkeson and Patrick J. KehoeJournal of Political Economy (2005)

Presented by Beatriz Gonzalez

June 2015

Presented by Beatriz Gonzalez (UC3M) Modeling and Measuring Organization Capital June 2015 1 / 25

Outline

1 Motivation

2 The ModelDecreasing Returns to ScaleAdding Imperfect Competition

3 Calibration and Measurement

4 Industry Evolution in the Steady State

5 Measuring Organizational Capital

6 Conclusion


MotivationThe life cycle of plants

Data shows that manufacturing plants have a clear life cycle: they areborn small, grow with age, and die.

Figure: Average Employment over the Life Cycle. Source: Hsieh and Klenow (2014)

What is the driving force of this behaviour?


MotivationOrganizational capital and organization rents

Some economist have defended that this is driven by the so-calledorganizational capital, or plant-specific knowledge.

Theory suggests that where plants are in the life cycle determines thesize of the payments, or organization rents.

I It is a ’compensation’ for the interest cost to plant owners of waitingfor their plants to grow.

I Young plants tend to have low organization rents and older plantshigher ones, since they have built more organizational capital.


MotivationAim

Aim

Use a quantitative growth model of the life cycle of plants, along withU.S. data, to infer the overall size of these organization rents.

How? Use a model of heterogeneous firms in age (s) and specificproductivity (A), whose improvements are idiosyncratic andage-dependent.


Outline

1 Motivation





6 Conclusion


The ModelHouseholds

Continuum of size 1 of households: each one consists of a worker(who supply inelastically for wt) and a manager( who supplyinelastically for wmt)

max{ct}∞t=0

∞∑t=0

βt log(ct) (1)

s.t.∞∑t=0

ptct ≤∞∑t=0

pt(wt + wmt) + k0 + a0 (2)

k0, a0 given


The ModelPlants

Plants are characterized by its specific productivity A and its age s:organization capital (A,s).

Start at t wih organizational capital (A, s)1 Decide whether or not to operate.2 If operate

F Hire one managerF Hire kt , lt and produce yt = ztA

1−νF (k, l)ν

3 Draw an independent innovation to specific productivity ε, withprobability from an age-dependent distribution πs

Start at t+1 wih organizational capital (Aε, s + 1)


The ModelPlants

Given rt , wt and wmt , plants maximize:

maxk,l

ztA1−νF (k, l)ν − rtk − wt l − wmt (3)

zt is the economywide productivity.

If plants decide to operate, they hire one manager, l workers and kcapital.

Plant owners earn variable dividends:

ztA1−νF (kt(A), lt(A))ν − rtkt(A)− wt lt(A)︸︷︷︸

dt(A)

−wmt (4)


The ModelPlants

Free entry condition

N∑s=0

(1

1 + i

)s

(ds − wm) = 0 (5)

Free exit: Stay-exit decision given by the Bellman equation:

Vt(A, s) = max{x}

[0, dt(A)− wmt +

pt+1

pt

∫εVt+1(Aε, s + 1)πs+1(dε)

](6)

→ xt(A, s) gives us the exit decision.


The ModelPlants

New plants can adopt a blueprint the period before entering (at t-1):organizational capital at t would be (A,s)= (τt ,0)

τt evolves exogenously.

Decision of whether or not to hire a manager to prepare a blueprintfor a new plant is also dynamic:

V 0t = −wmt +

pt+1

ptVt+1(τt+1, 0) (7)

Managers hired iff V 0t ≥ 0

In equilibrium, V 0t φt = 0


The ModelDistribution of plants

µt(A, s) is the distribution of plants at time t of age s withproductivity lower or equal than A.

φt ≥ 0 is the mass of managers preparing blueprints for new plants int.

The measure of plants that operate at t is

λt(A, s) =

∫ A

0xt(a, s)µt(da, s) (8)

The law of motion of the plants’ distribution is

µt+1(A′, s + 1) =

∫Aπs+1

A′

Aλt(dA, s) for s > 0 (9)

µt+1(τt+1, 0) = φt for s = 0 (10)


Linking Plant Size and Organizational Rents

The size of the plant is given by

nt(A) =A

A(11)

where

A =∑s

∫AAλt(dA, s)

The equilibrium allocations are

kt(A) = nt(A)kt

lt(A) = nt(A)lt

yt(A) = nt(A)yt

Variable profits are

dt(A) = (1− ν)yt(A) = (1− ν)nt(A)yt


Steady State Growth Path

At grows at (1 + gτ ).

zt grows at (1 + gz).

Aggregate variables yt , ct , kt ,wt and wmt grow at

1 + g =[(1 + gz) (1 + gτ )1−ν

]1/(1−να)

φt ,V0t and rt are constant.

∀t, s,A, distributions evolve

µt+1(A, s) = µt+1(A/(1 + gτ ), s)

λt+1(A, s) = λt+1(A/(1 + gτ ), s)


Outline

1 Motivation





6 Conclusion


Adding Imperfect Competition

Add imperfect competition: plants face downward-sloping demandI It scales up the amount of variable profits in the economy.

Each plant produces a differentiated product, which a competitivefirm aggregates to produce a homogeneous final good:

yt =

[∑s

∫Ayt(A)θλt(dA, s)

]1/θ

The static maximization problem is the same as before, with ν = γθ,where θ is the inverse of the equilibrium markup of price overmarginal cost.


CalibrationFollowing McGrattan and Prescott (2005), introduce a corporateprofit tax τc , and compute δ, k/y , τc , να.The shock to productivity follows an age-dependent normaldistribution

logεs ∼ N(ms , σ2s )

wherems = κ1 + κ2 [(S − s)/S ]2 if s ≤ S , 0ms = κ1

σs = κ3 + κ4 [(S − s)/S ]2 if s ≤ S , σs = κ3 ow

Figure: Calibration of shockPresented by Beatriz Gonzalez (UC3M) Modeling and Measuring Organization Capital June 2015 17 / 25

Calibration

→Calibrated to match data from 1988 panel of the U.S. Census BureausLongitudinal Research Database:

Fraction of the labor force employed in plants of different age groups.Employment at t is (lt + lt−1)/2

Job creation rate: lt − lt−1 if lt ≥ lt−1, 0 otherwise.

Job destruction rate: lt−1 − lt if lt ≤ lt−1, 0 otherwise.


Calibration Targets: the Model and the Data

(a) % of labor employedby age of plants.

(b) Job creation by ageof the plant.

(c) Job destruction byage of the plant.

→ Model’s outcomes are within one standard deviation of the observedtime-series fluctuations.


Implications of the calibrated model

Does the model perform well in other features of US data?

Figure: Job destruction in failing plants by age of plant.

→ Total job destruction in plants that fail is 3.1 % in the model and 2.2%in the data


Implications of the calibrated model

Does the model perform well in other features of US data?

Figure: Distribution of job creation and destruction


Implications of the calibrated modelMeasures of productivity of labor and capital across plants areconstant.

yt(A)

lt(A)=

ytlt

andyt(A)

kt(A)=

ytkt

Although there aresubstantial variations in average productivity acrossindividual plants in the data, there is no systematic relation betweenthe average productivity of a plant and its age (Bartelsman andDhrymes (1998))

Figure: Average productivity of plants by age in U.S. data for 197286. Source:Bartelsman and Dhrymes (1998).


Measuring Organizational Capital

Aggregate output is distributed among four factors:1 Physical capital: να2 Workers: ν(1− α)3 Managers: wm/y4 Owners of organizational capital: the rest.


Conclusion

They have built a quantitative model of the life cycle of plants.

Starting a new plant: project of investing in organization capital thattypically yields a back-loaded life cycle pattern of organization rents→ aggregate payments to owners of plants for compensation for theinvestment in organization capital are positive

Used to measure the payments to owners of a specific form ofintangible capital directly, rather than as a residual.


Thank you!!


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