Riccardo Fiorito

Università di Siena

Why Macro Labor Supply Is More

Elastic Than Micro: Theory and

Policy Implications

Brown Bag Lunch Meetings

Dipartimento del Tesoro, Ministero dell’Economia,

Roma, 18 Aprile 2008

Background and Motivation

• This presentation aims at showing that micro and macro labor supply elasticities don’t have to be the same (Fiorito-Zanella, 2008) as it is typically claimed by critics of the RBC model.

• While this is well known in the theoretical literature (Prescott, 2006), we show that the same result can be obtained empirically by using an appropriate aggregation procedure.

Background and Motivation

Estimating and understanding this elasticity is not simply an econometric issue since:

• It involves deep differences in the way of addressing macro-economic modeling.

• It involves also several fiscal policy implications as far as employment and participation decisions are concerned.

Macro Modeling: A Quick Refresher

Macro modeling started after WW2 using:

NIPA definitions (Meade-Stone, 1943; Kuznets, 1946; SNA, 1953 etc.)

Econometric tools (Cowles Commission) for estimating parameters inside large (non-linear) models to be solved (L. Klein, 1950).

A macroeconomic paradigm based on Keynesian income determination (IS/LM), given fiscal and monetary interventions.

Reasons for Crisis

Theory:

The Neo-classical growth model was not used in macroeconomics Business Cycles seen as deviations from an exogenous trend path.

Macroeconomics did not consider individual choices.

Taxation: Lump-sum Taxation ( Expenditure only) rather than distortionary taxation affecting labor, spending and production choices.

Policy: confined to stabilization policies and unable to face supply shocks such as labor and oil shocks in the 70s and later.

Major Remedies

• VAR: None or minimal identification (Sims, 1980, 1986): estimation only matters.

• GMM univariate estimates: More identification is needed (Hansen-Sargent, 1982) to estimate theory-driven parameters.

• Calibration: Prescott (1986), Kydland-Prescott 1982): Deep and other parameters can be obtained by micro estimates, NIPA definitions, theoretical suggestions: nothing has to be estimated!

Calibration and RBC

• In principle, there is no reason that calibration applies to RBC only: it is a wider GE methodology combining NIPA, stylized facts and sound micro-econometric evidence..

• Namely, microeconometric evidence could be used since:

“A fundamental thesis of this line of inquiry is that the measures obtained from aggregate series and those from indivifual panel data must be consistent. After all, the former are just the aggregates of the latter”

(Prescott, 1986, p.22)

• While TFP persistence is widely recognized, labor supply elasticity is much more controversial

Why so important?

• wages reflect labor productivity and affect labor input which enters the production function with a larger share that capital does..

Two Basic Parameters in the RBC model

Technology is the driving force in the economy Impulses

Intertemporal substitution of labor Propagation mechanism

Empirics: • the TFP persistence is widely recognized• the labor supply elasticity is much more controversial.

Microeconomic studies always report a small elasticity (Men: 0 - 0.2; Women: 0 - 1) [Blundell-Macurdy (1999)] .

Macroeconomic evidence: mixed and less widespread because statistically weaker: time-series never are long enough!

Favourable cases: Lucas-Rapping (1969); Alogoskoufis (1987)Non-favourable: Hall (1980); Mankiw-Rothemberg-Summers (1985).

First View: How Reconciling Calibrated and Estimated Parameters?

To account for all business cycle facts in the US, the RBC model requires a much larger labor supply elasticity than it is typically estimated in the micro literature.

Recognizing this gap produced a possible inconsistency or else an incentive to extend the benchmark RBC model.

Reject or Extend the Benchmark RBC model?

Reject: (Summers ’86, Mankiw ’89)

Extend: Nonseparable leisure (Kydland-Prescott ’82) Indivisible labor (Hansen ’85, Rogerson, ‘88) Home-production (Benhabib-Rogerson-Wright ’91) Gov.t consumption (Christiano-Eichenbaum, 1992) Heterogeneous reservation wages (Chang-Kim ’06) Human capital accumulation (Imai-Keane, ‘04) Nonlinearities between labor services and hours

(Rogerson-Wallenius, ‘07)

A Second View

Individual and aggregate labor supply elasticities are conceptually different (Prescott, 2006).

Aggregate elasticity reflects technology too.

Thus, there is no inconsistency if micro and macro elasticity differ.

Different Measures or Different Concepts?

Individual elasticity: % change in individual labor supply (hours per worker) associated with a 1% change in the after-tax real wage, holding wealth constant (Frisch)

h (1-tau)[w/p] (intensive margin)

Aggregate Elasticity Aggregate elasticity: % change in aggregate labor

supply associated with a 1% change in the after-tax real wage, holding wealth constant (Frisch): H (1-tau)[W/P]

Aggregate elasticity is the product of the average hours per worker (h, intensive margin) times the aggregate employment stock N (extensive margin): i.e., it is a product of two different variables, not simply the aggregation of a single variable (intensive margin):

Ht = average( ht )* Nt

Intensive vs. Extensive margin

Hansen (1985):

ttttttt HNHNHNH ln,lncov2lnvarlnvarlnvarlnvar20% :margin intensive55% :margin extensive

Suppose we estimate individual and aggregate elasticities as follows:

∆lnhit = const. + ε∆lnwit + uit , (Micro regression)

∆lnHt = Const. + E∆lnwt + Ut , (Macro regression).

Intensive and Extensive Margin

Then the elasticities are:

)lnvar(

)ln,lncov(

)lnvar(

)ln,lncov(

)lnvar(

)ln,lncov(

)lnvar(

)ln,lncov(

)lnvar(

)ln,lncov(

t

tt

t

t

t

ttt

t

tt

it

itit

W

WN

W

WH

W

WHN

W

WH

w

wh

So the aggregate elasticity is the sum of the intensive margin and the extensive margin.

Our Contribution (Fiorito-Zanella, 2008)

• We derive a standard, life-cycle, labor supply equation (Macurdy, 1981) which is aggregated via home production. The latter accounts for changes in the extensive margin.

• Empirically, we use the PSID data to aggregate, each year, the individual units entering the labor supply equation.

Since the micro (panel) and the macro labor supply (time series) are estimated exactly in the same way, we interpret differences in the estimated Frisch elasticity as reflecting aggregation only.

• In the labor supply case, aggregation means the product of the intensive and extensive margins, i.e. a different variable from micro.

• Aggregate labor supply is conceptually different from the individual one: thus, there is no inconsistency in finding - or assuming - that aggregate labor supply is much more elastic.

Data

• The PSID is long enough (1968-2005) to apply our procedure. We use, however, all of the annual waves (1968-1997) to avoid interpolation of the missing years.

Disadvantages: no info on assets, tax rates, real interest rate and other important variables.

Need to control for r “anomalous” years using appropriate dummies.

How do our ‘artificial’ series compares with the real ones?

Data: PSID vs. USA

-0.24

-0.12

0

0.12

0.2419

69

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

Variation ln(employment) PSID Variation ln(employment) USA

Data: PSID vs. USA

-0.06

-0.03

0

0.03

0.0619

67

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1998

2000

2002

Variation ln(hours) USA Variation ln(hours) PSID

The Underlying Model

An economy with a single consumption good that can be provided by market or home-production. Labor is the only input, tax rate constant. Profit maximization with CRS technology implies

0

,lim

1

1

:subject to ,,:max

1

1

00

,,, 1

iTiT

iTiTT

T

itHitit

ititHit

Hititititit

titit

t

ahhc

ac

lcu

lhh

yarhhwac

lcuEit

Hititit

ititw

The Model: Who Works on the Market?

Obviously, in equilibrium:

So is individual i’s reservation wage,

Hitit

Hitit

Hitit

Hitit

whh

whh

if 0 and 0

if 0 and 0

Hit itw

~

The Model: NFOC’s

Under CRRA specification,

NFOC’s of individuals who work on the market can be written as

1

1

1,

11itit

itit

lclcu

1ln1lnln

ln1

ln1

ln1

ln

ln1

ln

ittit

ititit

itit

Er

wh

c

The Model: Deriving the Micro Regression

Using standard procedures (Blundell and MaCurdy, 1999), the Euler equation for labor supply is:

This is the micro regression where 1/η is the labor supply elasticity.

ititit uwh ln1

ln

The Model: Deriving the Macro regression

We obtain the macroregression aggregating the first-order conditions and using the home production as shown in the paper:

Individual elasticity is:

Aggregate elasticity is:

The extensive margin is reflected by zt.

For feasibility reasons we treat zt as constant since employment does not change too much.

ttt

t UWz

H lnln

/1

/tz

Implementation

We have two structural equations:

We do not correct for selection in order to precisely isolate intensive and extensive margins. However, when correcting for the selection bias, the micro estimate change is negligible.

We will also add non-labor income as control in both.

Consistency requires instruments. RE impose using lags because of econometric exogeneity. Lags of levels work better than lags of first differences.

ttt

ititit

UWCONSTH

uwconsth

ln.ln

ln.ln

Overall Results

We find an individual elasticity of about 0.1, a low value that is standard in the literature.

We find an aggregate elasticity of about 0.9, a much larger value not far from available calibration studies.

75% of the difference is due to the “extensive margin” i.e. participation/employment.

Main conclusion: in the labor supply case, microeconometric parameters are not a good source for calibrating aggregate models

Results 1

Results 2: decomposition of aggregate elasticity

Conclusions

We do not aim at providing a new estimates of the micro regression: we evaluate only the effect of aggregation. However, our micro elasticity is standard.

When the individual and the aggregate Frisch elasticities are consistently estimated, the former is magnified by a factor of about 9.

About 75% of this effect is due to the movements along the extensive margin.

In this case, the micro parameter is not a good source for calibrating the aggregate because micro and macro labor supply are different concepts.

Policy implications

While we cannot include tax rates, our results have also fiscal implications if tax rates don’t change too much. Combining previous studies (Fiorito-Padrini, 2001) with stylized facts evidence, the ratio between the deviations from the smooth trend of the effective labor tax rate is always smaller than the corresponding volatility in real GDP: the volatility ratio ranges for the G7 from about .5 for Canada and France to about .3 for the US, Italy and Germany.

Further Policy Implications.. If the aggregate elasticity is close to 1 and if women

elasticity is surely higher, reducing tax rates can have a significant effect on labor supply and, eventually, on the overall growth rate.

• This has several implications for government spending, including the incentive to provide services helping female participation. Likewise, transfers serving the opposite purpose should be reduced.

• Since the extensive margin dominates the intensive one, current proposals for de-taxing overtime work, seem to be less effective than general tax rate cuts acting on the most important, extensive, margin.