The transformation of macroeconomic policy and research prize Lecture, December 8, 2004 by

381

Previously, others had effectively endogenized the savings decision by ana-

lyzing the optimal growth path because, by the second welfare theorem, the

optimal path is the competitive equilibrium path for this model.

5

But in order

for the model to be used to study business cycle fluctuations, the labor supply

decision must be endogenized as well.

6

Step 2: Modify the National Accounts to Be Consistent with the Theory

Prior to our work, macroeconomics was concerned with developing a theory

of the national accounts statistics. Preferences and technology are the given,

not the national accounts statistics. This means that we had to modify the 

national accounts to be consistent with the theoretical abstraction or model

we used. The most important modification when studying business cycles is to

treat consumer durable expenditures as an investment in the same way that

expenditures on new housing and home improvement are treated as invest-

ments in the national accounts. Once this is done, services of consumer 

durables and consumer durable rental income must be imputed, in much the 

same way as is currently done for owner-occupied housing. This increases 

investment share of output and has consequences for the cyclical behavior of the

economy. What led us to think about this issue is that consumer durable expen-

ditures are highly variable, behaving very similarly to producer durable invest-

ments and not like consumer expenditures on nondurable goods and services.

Step 3: Restrict the Model to Be Consistent with the Growth Facts

The growth facts are that consumption and investment shares of output are

roughly constant, as are labor and capital cost shares. All the variables and

the real wage grow over time except for labor supply and the return on capi-

tal, which are roughly constant. This leads to a Cobb–Douglas production

function. These facts also imply the constancy of the capital-output ratio and

of the rental price of capital.

Two key growth facts are that the real wage and consumption grow at the

same secular rate as does real output per capita, while labor supply displays

no secular trend. This restricts the period utility function to be of the form

(4)

u(c,1–h) =                                 .

5 

Cass (1965) and Koopmans (1965) in deterministic situations establish the existence of an 

optimal path and characterize properties of this optimal path. Diamond (1965) studies the com-

petitive equilibrium path in an economy with capital accumulation. In his economy, people live two

periods. Brock and Mirman (1972) deal with the problem of optimal growth when there are 

stochastic shocks to the technology. These studies are in the nonquantitative theory tradition.

Danthine and Donaldson (1981) compute the equilibrium process for the Brock and Mirman

(1972) stochastic growth model.

6

Auerbach, Kotlikoff, and Skinner (1983) carry out a deterministic dynamic applied general 

equilibrium analysis with endogenous labor supply in which they evaluate tax policies.

(c g (1 – l ))

1– 

␴

–1

1 – 

␴

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We set 

␴ 

= 1. This parameter was not calibrated to growth observations. We

made this choice based on a variety of evidence. The principal evidence used

is comparisons of the return on capital for fast- and slow-growing economies.

Fortunately, it turned out that our findings are not sensitive to this parameter,

because at the time of our work, this key economic parameter had not been

tightly tied down.

With 

␴ 

= 1, the above utility function is

(5)

log c + g(1– l ).

The nature of the g function matters. The growth facts do not tie down the

elasticity of substitution between consumption and leisure, and this parameter

turned out to be key for deriving the predictions of the growth model for 

business cycle fluctuations. Subsequently, this key parameter has been tied

down.

Step 4: Introduce a Markovian Shock Process

We wanted something in our model economy that led to labor supply errors

and something to propagate these errors. Here, by “labor supply errors” I mean

the difference between the optimal labor supply decision given individuals’

information set and the decision that they would make if they observed the

state of the economy without observation error. We introduced a total factor

productivity shock that is independent over time and assumes that agents see

the value of total factor productivity (TFP) with noise prior to making their

labor supply decisions. We also introduced a second highly persistent autore-

gressive TFP shock. We introduced this shock because it is simple to do and

we were curious to see what its consequences are. In order to use the Kalman

filter, the two shocks and measurement errors are all normally distributed.

Step 5: Make a Linear Quadratic Approximation

The next step is to determine the steady state of the economy when the 

variances of the TFP shocks are zero. Then a linear quadratic economy is

constructed, which has the same first two derivatives at the steady state. This 

linear quadratic economy displays the growth facts, and its equilibrium is easily

computed. The behavior of this economy will be arbitrarily close to the 

economy we began with for sufficiently small variances of the two TFP shocks

and the measurement errors. It turned out that it was extremely close even

for variances far bigger than the ones we introduced.

7

Step 6: Compute the Competitive Equilibrium Process

The next step is to compute the recursive competitive equilibrium stochastic

process.

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7 

Danthine and Donaldson (1981), who computed the exact equilibrium for the stochastic model

using computationally intensive techniques, found this to be the case.

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