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Adynamic stochastic general equilibrium model with non-clearing labour markets and imperfect competition is estimated for 21 OECD countries. The model provides for parameters both for preferences and technology and for the degree of structural rigidities on labour and product markets. These parameters are match ed with policy indicators, establishing arela- tionbetweenthe model-based employment adjustment cost parameter and the strictness of employment protection legislation, and between the average size of the mark-upon product markets and the OECD product market regulation indicator. Policy simulations are carried outby modifying the parameters relating to labour and product market rigidities in order to evaluate the impact of a more flexible markets on consumption smoothing. Moreover, the paper establishesa trade-off between more volatile employment and improved consumption smoothing possibilities. Finally, using a standard utilitarian welfare function, the model assesses the optimal stance of structural policies when taking this trade-off into account.

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Resilience, consumption smoothing and structural

policies

Paper prepared for the OECD Workshop

”Structural reforms and economic resilience: evidence and policy

implications”

Ekkehard Ernst

Gang Gong

OECD

Tsinghua University

Economics Department

School of Economics and Management

2, Rue Andr´

e Pascal

Beijing, China

75775 Paris Cedex 16

ekkehard.ernst@oecd.org

Willi Semmler

New School Unversity

Dept. of Economics

Schwartz Center for Economc Policy Analysis

New York

June 2007

Abstract

A dynamic stochastic general equilibrium model with non-clearing labour markets and im-

perfect competition is estimated for 21 OECD countries. The model provides for parameters

both for preferences and technology and for the degree of structural rigidities on labour and

product markets. These parameters are matched with policy indicators, establishing a rela-

tion between the model-based employment adjustment cost parameter and the strictness of

employment protection legislation, and between the average size of the mark-up on product

markets and the OECD product market regulation indicator. Policy simulations are carried

out by modifying the parameters relating to labour and product market rigidities in order

to evaluate the impact of a more ﬂexible markets on consumption smoothing. Moreover, the

paper establishes a trade-oﬀ between more volatile employment and improved consumption

smoothing possibilities. Finally, using a standard utilitarian welfare function, the model

assesses the optimal stance of structural policies when taking this trade-oﬀ into account.

JEL Codes: E32, C61

Keywords: Product market competition, labour market frictions, business cycles, struc-

tural reforms in OECD countries, RBC models

1

Introduction

A rapid recovery after adverse demand shocks and a vigorous adjustment to supply shocks -

in short a country’s resilience - have been identiﬁed as a major policy ﬁeld for many OECD

countries. While traditionally macroeconomic policies play the dominant role in smoothing

the business cycle, the importance of structural policies on labour and product markets has

been recognized in order to understand country diﬀerences in the adjustment dynamics and

the transmission of shocks. In contrast to the analysis of the role of structural reforms in

improving the long-run performance of employment and productivity of OECD countries,

however, research regarding the role of reforms for a country’s resilience has only recently

gained prominence.

In this regard, the speed of adjustment of either prices or quantities to shocks occupies

a prominent place in the literature in explaining the welfare costs of business cycle ﬂuctu-

ations. Nominal rigidities force quantities to adjust to (temporary) demand shocks, with

adverse consequences on disposable income and consumption. Real rigidities, on the other

had, will slow down the adjustment process to (permanent) supply shocks, thereby limiting

the country’s potential to beneﬁt from supply side improvements and protracting the slump

following adverse shocks (Caballero and Hammour, 1998; Caballero, 2007). Policies that

help to raise the adjustment speed to either type of shock will, hence, not only improve the

short-term dynamic behaviour but also raise welfare in the long-run.

A second, less-well research question that arises in the context of policies to increase

resilience concerns a country’s capacity to smooth consumption over the cycle. Consumption

smoothing is a welfare-enhancing reaction of risk-averse households to income shocks. To

the extent that no borrowing constraints are binding the consumer on ﬁnancial market, in

principle all shocks can be absorbed through borrowing or lending on the credit market

and the consumption path becomes a random walk, disconnected from the income stream

(Hall, 1978). However, this result has to be qualiﬁed in an economy where households also

decide upon their labour supply as they have some control over their income stream. With

two decision variables at their disposal, households can control their consumption stream

not only via adjustments to net lending on the ﬁnancial market but also through adjusting

hours worked and labour income. To the extent, however, that structural rigidities on labour

and product markets prevent hours worked to evolve according to the household’s optimal

decisions, the possibilities for consumption smoothing will equally be aﬀected.

In order to address these issues in a coherent way, the following paper presents a dynamic

general equilibrium model with capital accumulation, imperfect competition on product

markets and matching frictions on labour markets. It oﬀers the perspective to estimate

various structural rigidities in a model-coherent and consistent way. In particular, the model

includes a rich structure of the labour market and allows to estimate parameters that reﬂect

employment adjustment costs and wage bargaining power. It also accounts for the degree of

competition on the product market, making use of a sticky information assumption regarding

the price setting process. Moreover, by introducing capital stock dynamics the model allows

1

for shocks to have persistent eﬀects on product and labour markets through the investment

channel.

The model builds, as Uhlig (2004) and Blanchard and Gali (2005), on frictions on the

labour market and allows for price and wage stickiness. We make use of a simpliﬁed search-

and-matching methodology to model the eﬀective level of employment given (sticky) wages.

In this set-up, employment evolves as a result of a match between labour demand and supply.

Moreover, the product market is characterised by imperfect competition that leads to a mark-

up in the retail sector and a socially sub-optimal level of production. (Relative) prices are

set as a result of sticky information whereby ﬁrms update their expectations regarding the

future developments of the market with a lag. Together, these assumptions allow to estimate

the degree of real wage rigidity, employment adjustment costs and the size of the mark-up

on product markets. Despite the limited number of rigidities the model allows to develop

some new insights into potential eﬀects of structural market reforms on the cyclical behavior

of OECD economies, their impact on consumption smoothing, employment volatility and on

households’ overall welfare.

The model’s parameters are estimated for 21 OECD countries. In order to demonstrate

that the estimated parameters properly reﬂect standard wisdom regarding the microeconomic

distortions in OECD economies, they are matched with structural indicators taken from the

OECD International Regulation Database and the OECD Employment Outlook. This allows

to establish a relation between (i) the model-based employment adjustment cost parameter

and the indicator for employment protection legislation, and (ii) the size of the product

market mark-up and the degree of product market regulation.

In the second, policy-oriented part of the paper, the paper presents policy simulations

based on changes in the size of the estimated parameters relating to the degree of labour

market rigidities and the importance of product market imperfections in order to evaluate

the impact more ﬂexible labour and product markets may have on the dynamic properties

of the model. In particular, we are looking at the correlation between consumption and

employment as a measure of consumption smoothing. In the policy simulations, it is shown

that reducing employment protection legislation and hence labour adjustment costs for ﬁrms,

households are able to improve risk sharing over the cycle and experience a decrease in their

consumption volatility by means of adjusting their labour supply (more easily) to its optimal

level. When ﬁrms face high employment adjustment costs, households are precluded from

such a possibility as actual employment will evolve only sluggishly in response to any shock

and employment volatility is low. By way of these policy experiments the paper also assesses

to what extent increasing product market competition can constitute a substitution for a

decrease in employment adjustment costs. The paper shows that product market competi-

tion is less eﬀective in improving consumption smoothing but that it complements labour

market reforms as the joint eﬀect of reforms on both markets exceeds the individual eﬀect of

each reform taken separately. Finally, we assess the trade-oﬀ that arises between improved

consumption smoothing and higher employment volatility following the implementation of

these structural reforms. Using a standard utilitarian welfare function, we show that under

2

certain circumstances, a less ambitious reform package may turn out second-best optimal.

The remainder of this paper is organized as follows. Section 2 presents the structure

of the model, which is calibrated in section 3 for 21 OECD countries. After interpreting

our estimates of structural rigidities, section 4 studies the possible impacts of structural

reforms in the context of such a model by undertaking simulations. Section 5 discusses the

trade-oﬀ between employment volatility and consumption smoothing and the consequences

for welfare-optimizing policies. Section 6 concludes the paper.

2

Sticky information and labour market frictions

2.1

Setting up the model

The economy is characterized by a representative household and monopolistically competitive

intermediate goods producers. Agents enter market exchanges in three markets: the product,

the labour and the capital market. The household owns all factors of production and sells

factor services to ﬁrms and buys (ﬁnal) products for consumption or accumulation of the

capital stock.

The product market is assumed to be imperfectly competitive, with the

individual ﬁrms facing a perceived demand curve and a sticky price (ﬁxed at P = 1).

Wage stickiness.

Following Gong and Semmler (2006) wages are supposed to be sticky,

with wage updating taking place at the pace of labour contract renewal supposed to be ﬁxed

at rate ξ (Calvo wage setting), corresponding to its persistence:

wt = ξwt−1 + (1 − ξ) w∗t

Only a certain fraction of existing contracts will be renewed, for all other labour contracts

the previous wages continue to hold. The optimal bargained wage, on the other hand, is

determined through monopoly union bargaining, where households maximize their utility

against the constraint of ﬁrms’ intertemporal labour demand.

∞

max Et

βiU (ct+i, nt+i)

w∗t

i=0

subject to

kt+i+1 =

1

[(1 − δ) k

1+γ

t+i + f (kt+i, nt+i, At+i) − ct+i]

w∗ =

t

fn(kt+i, nt+i, At+i)

Above, k is the capital stock, c the consumption, n the labour, A the technology; β designates

the intertemporal preference rate; δ the depreciation rate; and γ stands for the stationarity

parameter.

Assuming a constant relative risk aversion (CRRA) utility function for the

household’s instantaneous utility

U (c, n) = ln (c) + θ ln (1 − n)

3

where c: consumption, n: employment and θ the elasticity between consumption and work

eﬀort and let f (kt, nt, At) be the ﬁrm-level production function, the solution to this optimi-

sation problem can be written as:

1−α

1

(θα − 1)

α

w∗ =

α

(1)

t

At α

1 − δ

Implicitly the above optimisation problem may also allow us to derive a sequence of an opti-

mal consumption plan {ct+i}∞ . However, this plan has no feedback eﬀect on the optimum

i=0

wage w∗ but is solved for the given

as expressed in (1), On the other hand, that optimal

t

w∗t

plan may not be carried out since the actual wage wt is not necessary equal to w∗.

t

Factor markets.

Unlike the standard RBC model with competitive markets, factor mar-

kets in this model will be re-opened at the beginning of each period t, necessary to ensure

adjustment in response to a non-clearing labour market. The non-clearing of the market is

related to wage stickiness following the Calvo wage setting and the sequence of bargained

wages {w∗}∞ . The dynamic decision process is an adaptive one. It exhibits two stages: in

t t=0

a ﬁrst step, households determine their consumption and optimal wage pattern (and hence

indirectly their labour supply), in a second step, they re-optimize their consumption plans

following the realized transactions on the labour and product market.

At period t, the representative household expects a series of technology shocks {EtAt+i}∞

0

and real wages and interest rates {Etwt+i, Etrt+i}∞ where i=0,1,2,. . . The decision problem

0

of the household is then to choose a sequence of planned consumption and labour eﬀort

∞

cd

such that

t+i, nst+i 0

∞

max

E

βiU cd

{

t

t+i, nst+i

cd }∞ ,{ns }∞

t+i

=0

t+i

i=0

i=0

subject to

1

ks

=

(1 −

+

t+i+1

δ) ks

f ks

1 + γ

t+i

t+i, nst+i, At+i

− cdt+i

where superscripts d and s stand for “demand” and “supply”. Using standard dynamic

programming techniques, this optimal planning problem can be solved to yield the solution

∞

sequence cd

; however, from each sequence only the ﬁrst tupel

is actually

t+i, nst+i

cd

i=0

t , nst

carried out.

In the ﬁrst period t, the ﬁrm decides upon its inputs kd

given its output constraint

t , nd

t

Eyt related to its perceived demand curve. Standard (one-period) proﬁt maximization yields

the factor demand functions:

kd =

t

fk (rt, wt, At, Eyt)

nd =

t

fn (rt, wt, At, Eyt)

4

As the capital market is supposed to be perfectly competitive, the rental rate of capital, rt,

adjusts in each period such as to clear the market: kt = ks =

. On the labour market,

t

kdt

however, the ﬁxed wage contract does usually not allow to clear the market1.

Wage rigidities introduce frictions on the labour market and force market participations

to carry out transactions oﬀ their optimal supply and demand schedule. Following the spirit

of the search-and-matching literature2, we assume that these rigidities imply that actual

employment (i.e. transactions) corresponds to a weighted average between labour supply

and demand at the current wage:

nt = ωnd + (1 −

t

ω) nst,

where ω measures the degree to which employment is determined by labour demand and will

play a key role in the interpretation of the model and its results. This equation indicates that

actual employment can be a result of a matching process whereby not all desired transactions

are carried out, but where - due to the probabilistic nature of the process - ﬁrms may end

up hiring more than what their current needs are. This may also happen when, for instance,

employment is negotiated, when ﬁrms hoard labour in downturns, employing more than the

proﬁt-maximizing level of workers or when some other real rigidities are present. For the

moment, we leave the interpretation open and only notice that observed employment may

not necessarily correspond to desired levels. We give a more detailed interpretation of the

ω-parameter as soon as we have estimated the model.

Product markets.

The ﬁnal good is produced by combining intermediate goods. This

process is described by the following CES function:

1

1

ρ

Yt =

yρ

(2)

itdi

0

where ρ ∈ (−∞, 1). ρ determines the elasticity of substitution between the various inputs.

The producers in this sector are assumed to behave competitively and to determine their

demand for each good, yit, by maximizing the static proﬁt equation:

1

max

P

P

{

tYt −

ityitdi

yd }

0

it

i∈(0,1)

subject to (2). Given the general price index is supposed to remain constant and normalised

to unity, the demand for intermediate goods depends only on the relative prices of interme-

diate goods, Pit, and the aggregate demand:

1

yd =

ρ−1

it

Pit Yt

1This may nevertheless happen if either the representative ﬁrm has perfect foresight of the sequence of

technology shocks or the wage contract is arranged in the form of a contingency plan. Both will be excluded

here; see Gong and Semmler (2006) for a discussion on this latter point.

2We do not follow the precise set-up here, mainly for reasons of analytical simplicity.

5

The ﬁnal good may be used for consumption and investment purposes.

At the level of the intermediate goods production, each ﬁrm i, i ∈ (0, 1), produces an

intermediate good by means of capital and labour according to a constant returns-to-scale

technology:

yit = Aitk1−α

it

nαit

hence aggregating across all producers yields:

1 yitdi = Atkαtn1−α

t

0

Moreover, from the retail demand for intermediate goods we know that:

1

1

1

1

1

y

ρ−1

ρ−1

itdi =

Pit Ytdi = Yt

Pit di.

0

0

0

Intermediate goods producers face costs to update the relevant information regarding the

developments on their markets (Mankiw and Reis, 2002). To simplify matters, we want to

assume that on average ﬁrms set their optimal prices and quantities according to information

one period earlier, Pit = arg max Et−1πt where πt = Pityit − witnit − ritkit. Firm i, then, sets

its relative optimal price according to the following schedule:

s

wα

P

it−1

itr1−α

it

it =

where s

: real marginal costs.

ρ

it = αα (1 − α)1−α

Given that in equilibrium, all producers are setting the same price Pit = P t > 1, we will

use the following deﬁnition:

1

1

yitdi =

Yt

0

1 − exp (λt)

and call λt the retail margin, measuring the degree of product market competition (via the

eﬀect of ρ on prices). Consequently, the equilibrium on the goods market writes as:

1 yitdi = Atk1−α ⇔

t

nαt

Yt = (1 − exp (λt)) Atk1−α

t

nαt

0

Calibrating the model.

In order to implement the model empirically, certain speciﬁca-

tions regarding the preference function, the technology shock and the stationarity of the

time series have to be made.

As noted above, the economy is represented by a consumer characterized by an instan-

taneous utility function over consumption, c, and leisure, l = 1 − n:

U (c, n) = ln (c) + θ ln (1 − n)

6

with θ the elasticity between consumption and leisure to be estimated with the data.

Moreover, technological shocks are supposed to follow and AR(1) process:

At+1 = a0 + a1At + εt where εt ∼ N 0, σ2ε

The stationarity parameter, γ, can be retrieved by calculating the trend growth rate

of output. Finally, employment, nt, is based on (normalised) hours worked (sample mean

N ), considering that only 1/3 of a day is dedicated to work on average. Box 1 (see above)

summarises the relevant model equations.

Box 1: Summary of the model equations

Consumption:

cd

=

t+1

Et+1 β (1 − δ + rt+1) cdt

Labour supply:

w

β

t

(1 − δ + r

) = 1 − ns

w

t+1) (1 − nst

t+1

t+1

Pre-set wages:

wt = ξwt−1 + (1 − ξ) wopt

t

+ εw

Bargained optimal wage:

1−

1

α

1−

1

α

α

α

A

1−

1−

t

θα α − α α

wopt

t

=

1 − δ

Actual employment:

nt = Et|t−1 ωnd + (1 −

t−1

ω) nst−1

Capital accumulation:

kt+1 = (1 − δ) kt + Yt − cdt

Production function of intermediaries:

yit = f (kit, Aitnit) = Atk1−α

it

nαit

Product market equilibrium:

1

Yt = (1 − λt)

yitdi = cd +

t

it

0

Factor prices:

wt = fn kt, Atndt

rt = fk (kt, Atnt)

7

3

Estimation of the model

3.1

Estimation of structural parameters

In order to estimate the model described in the previous section, several parameters have

to be determined. These include: (i) the parameters describing the process of technological

progress and wage growth; (ii) the preference parameters and the depreciation rate of the

capital stock and (iii) the parameters describing the rigidities on labour and product markets.

While the ﬁrst parameters can be estimated easily on the basis of an AR(1) process

using the TFP residuals that can be derived from a standard growth accounting exercise,

the preference parameters are deeply linked to the ﬁrst-order conditions that result from

solving the above dynamic programming problem. This fact can be used to apply GMM

techniques in order to estimate these parameters. Concretely, the parameters are chosen

such as to match the moments of the model described by the ﬁrst-order conditions of the

above model to those of the underlying data. Notice, moreover, that these parameters can be

established without a concrete knowledge about the underlying labour and product market

rigidities as they are supposed to be unrelated to it.

Given the highly non-linear nature of the optimisation problem, the algorithm used to

pick the right parameters β, δ and θ had to ensure that any local optimum of the GMM

technique is to be avoided. Here, a technique called simulated annealing has been applied,

that combines a grid search procedure with an objective function to assess the size of the

grid jumps. The resulting parameters for our 21 countries can be found in the following

table 1. As to the remaining parameters, the wage share, α, has been taken from country

tables, averaging the values over the corresponding periods for these countries, while the

wage persistence, ξ, has been estimated by OLS.

While the time preference rates are relatively close across countries, corresponding to the

standard interval for these models between 0.95 and 0.99, the country sample displays a large

range of values for the capital depreciation rates, probably reﬂecting some country speciﬁc

trends. In particular the value for Finland seems to be excessively large, implying an annual

depreciation rate of 43%; this may be related to the particular events surrounding the deep

economic crisis in 1993. The two parameters β and θ seems to fall into a reasonable range,

although it must be conceded that no commonly accepted estimates exist regarding the

substitution elasticity between consumption and leisure. Finally, the estimates for the wage

persistence should be taken cum grano salis as OLS estimates of lagged dependent variables

are known to be upward biased; they may nevertheless give a sense of the importance of real

wage persistence across countries with small open economies in general being characterized

by less persistence than bigger, in particular continental European economies. Yet, overall,

as our model in section 2 postulates, our estimates reveal a strong wage persistence, ξ, and

thus a very weak endogeneity of wage determination.

8

policies

Paper prepared for the OECD Workshop

”Structural reforms and economic resilience: evidence and policy

implications”

Ekkehard Ernst

Gang Gong

OECD

Tsinghua University

Economics Department

School of Economics and Management

2, Rue Andr´

e Pascal

Beijing, China

75775 Paris Cedex 16

ekkehard.ernst@oecd.org

Willi Semmler

New School Unversity

Dept. of Economics

Schwartz Center for Economc Policy Analysis

New York

June 2007

Abstract

A dynamic stochastic general equilibrium model with non-clearing labour markets and im-

perfect competition is estimated for 21 OECD countries. The model provides for parameters

both for preferences and technology and for the degree of structural rigidities on labour and

product markets. These parameters are matched with policy indicators, establishing a rela-

tion between the model-based employment adjustment cost parameter and the strictness of

employment protection legislation, and between the average size of the mark-up on product

markets and the OECD product market regulation indicator. Policy simulations are carried

out by modifying the parameters relating to labour and product market rigidities in order

to evaluate the impact of a more ﬂexible markets on consumption smoothing. Moreover, the

paper establishes a trade-oﬀ between more volatile employment and improved consumption

smoothing possibilities. Finally, using a standard utilitarian welfare function, the model

assesses the optimal stance of structural policies when taking this trade-oﬀ into account.

JEL Codes: E32, C61

Keywords: Product market competition, labour market frictions, business cycles, struc-

tural reforms in OECD countries, RBC models

1

Introduction

A rapid recovery after adverse demand shocks and a vigorous adjustment to supply shocks -

in short a country’s resilience - have been identiﬁed as a major policy ﬁeld for many OECD

countries. While traditionally macroeconomic policies play the dominant role in smoothing

the business cycle, the importance of structural policies on labour and product markets has

been recognized in order to understand country diﬀerences in the adjustment dynamics and

the transmission of shocks. In contrast to the analysis of the role of structural reforms in

improving the long-run performance of employment and productivity of OECD countries,

however, research regarding the role of reforms for a country’s resilience has only recently

gained prominence.

In this regard, the speed of adjustment of either prices or quantities to shocks occupies

a prominent place in the literature in explaining the welfare costs of business cycle ﬂuctu-

ations. Nominal rigidities force quantities to adjust to (temporary) demand shocks, with

adverse consequences on disposable income and consumption. Real rigidities, on the other

had, will slow down the adjustment process to (permanent) supply shocks, thereby limiting

the country’s potential to beneﬁt from supply side improvements and protracting the slump

following adverse shocks (Caballero and Hammour, 1998; Caballero, 2007). Policies that

help to raise the adjustment speed to either type of shock will, hence, not only improve the

short-term dynamic behaviour but also raise welfare in the long-run.

A second, less-well research question that arises in the context of policies to increase

resilience concerns a country’s capacity to smooth consumption over the cycle. Consumption

smoothing is a welfare-enhancing reaction of risk-averse households to income shocks. To

the extent that no borrowing constraints are binding the consumer on ﬁnancial market, in

principle all shocks can be absorbed through borrowing or lending on the credit market

and the consumption path becomes a random walk, disconnected from the income stream

(Hall, 1978). However, this result has to be qualiﬁed in an economy where households also

decide upon their labour supply as they have some control over their income stream. With

two decision variables at their disposal, households can control their consumption stream

not only via adjustments to net lending on the ﬁnancial market but also through adjusting

hours worked and labour income. To the extent, however, that structural rigidities on labour

and product markets prevent hours worked to evolve according to the household’s optimal

decisions, the possibilities for consumption smoothing will equally be aﬀected.

In order to address these issues in a coherent way, the following paper presents a dynamic

general equilibrium model with capital accumulation, imperfect competition on product

markets and matching frictions on labour markets. It oﬀers the perspective to estimate

various structural rigidities in a model-coherent and consistent way. In particular, the model

includes a rich structure of the labour market and allows to estimate parameters that reﬂect

employment adjustment costs and wage bargaining power. It also accounts for the degree of

competition on the product market, making use of a sticky information assumption regarding

the price setting process. Moreover, by introducing capital stock dynamics the model allows

1

for shocks to have persistent eﬀects on product and labour markets through the investment

channel.

The model builds, as Uhlig (2004) and Blanchard and Gali (2005), on frictions on the

labour market and allows for price and wage stickiness. We make use of a simpliﬁed search-

and-matching methodology to model the eﬀective level of employment given (sticky) wages.

In this set-up, employment evolves as a result of a match between labour demand and supply.

Moreover, the product market is characterised by imperfect competition that leads to a mark-

up in the retail sector and a socially sub-optimal level of production. (Relative) prices are

set as a result of sticky information whereby ﬁrms update their expectations regarding the

future developments of the market with a lag. Together, these assumptions allow to estimate

the degree of real wage rigidity, employment adjustment costs and the size of the mark-up

on product markets. Despite the limited number of rigidities the model allows to develop

some new insights into potential eﬀects of structural market reforms on the cyclical behavior

of OECD economies, their impact on consumption smoothing, employment volatility and on

households’ overall welfare.

The model’s parameters are estimated for 21 OECD countries. In order to demonstrate

that the estimated parameters properly reﬂect standard wisdom regarding the microeconomic

distortions in OECD economies, they are matched with structural indicators taken from the

OECD International Regulation Database and the OECD Employment Outlook. This allows

to establish a relation between (i) the model-based employment adjustment cost parameter

and the indicator for employment protection legislation, and (ii) the size of the product

market mark-up and the degree of product market regulation.

In the second, policy-oriented part of the paper, the paper presents policy simulations

based on changes in the size of the estimated parameters relating to the degree of labour

market rigidities and the importance of product market imperfections in order to evaluate

the impact more ﬂexible labour and product markets may have on the dynamic properties

of the model. In particular, we are looking at the correlation between consumption and

employment as a measure of consumption smoothing. In the policy simulations, it is shown

that reducing employment protection legislation and hence labour adjustment costs for ﬁrms,

households are able to improve risk sharing over the cycle and experience a decrease in their

consumption volatility by means of adjusting their labour supply (more easily) to its optimal

level. When ﬁrms face high employment adjustment costs, households are precluded from

such a possibility as actual employment will evolve only sluggishly in response to any shock

and employment volatility is low. By way of these policy experiments the paper also assesses

to what extent increasing product market competition can constitute a substitution for a

decrease in employment adjustment costs. The paper shows that product market competi-

tion is less eﬀective in improving consumption smoothing but that it complements labour

market reforms as the joint eﬀect of reforms on both markets exceeds the individual eﬀect of

each reform taken separately. Finally, we assess the trade-oﬀ that arises between improved

consumption smoothing and higher employment volatility following the implementation of

these structural reforms. Using a standard utilitarian welfare function, we show that under

2

certain circumstances, a less ambitious reform package may turn out second-best optimal.

The remainder of this paper is organized as follows. Section 2 presents the structure

of the model, which is calibrated in section 3 for 21 OECD countries. After interpreting

our estimates of structural rigidities, section 4 studies the possible impacts of structural

reforms in the context of such a model by undertaking simulations. Section 5 discusses the

trade-oﬀ between employment volatility and consumption smoothing and the consequences

for welfare-optimizing policies. Section 6 concludes the paper.

2

Sticky information and labour market frictions

2.1

Setting up the model

The economy is characterized by a representative household and monopolistically competitive

intermediate goods producers. Agents enter market exchanges in three markets: the product,

the labour and the capital market. The household owns all factors of production and sells

factor services to ﬁrms and buys (ﬁnal) products for consumption or accumulation of the

capital stock.

The product market is assumed to be imperfectly competitive, with the

individual ﬁrms facing a perceived demand curve and a sticky price (ﬁxed at P = 1).

Wage stickiness.

Following Gong and Semmler (2006) wages are supposed to be sticky,

with wage updating taking place at the pace of labour contract renewal supposed to be ﬁxed

at rate ξ (Calvo wage setting), corresponding to its persistence:

wt = ξwt−1 + (1 − ξ) w∗t

Only a certain fraction of existing contracts will be renewed, for all other labour contracts

the previous wages continue to hold. The optimal bargained wage, on the other hand, is

determined through monopoly union bargaining, where households maximize their utility

against the constraint of ﬁrms’ intertemporal labour demand.

∞

max Et

βiU (ct+i, nt+i)

w∗t

i=0

subject to

kt+i+1 =

1

[(1 − δ) k

1+γ

t+i + f (kt+i, nt+i, At+i) − ct+i]

w∗ =

t

fn(kt+i, nt+i, At+i)

Above, k is the capital stock, c the consumption, n the labour, A the technology; β designates

the intertemporal preference rate; δ the depreciation rate; and γ stands for the stationarity

parameter.

Assuming a constant relative risk aversion (CRRA) utility function for the

household’s instantaneous utility

U (c, n) = ln (c) + θ ln (1 − n)

3

where c: consumption, n: employment and θ the elasticity between consumption and work

eﬀort and let f (kt, nt, At) be the ﬁrm-level production function, the solution to this optimi-

sation problem can be written as:

1−α

1

(θα − 1)

α

w∗ =

α

(1)

t

At α

1 − δ

Implicitly the above optimisation problem may also allow us to derive a sequence of an opti-

mal consumption plan {ct+i}∞ . However, this plan has no feedback eﬀect on the optimum

i=0

wage w∗ but is solved for the given

as expressed in (1), On the other hand, that optimal

t

w∗t

plan may not be carried out since the actual wage wt is not necessary equal to w∗.

t

Factor markets.

Unlike the standard RBC model with competitive markets, factor mar-

kets in this model will be re-opened at the beginning of each period t, necessary to ensure

adjustment in response to a non-clearing labour market. The non-clearing of the market is

related to wage stickiness following the Calvo wage setting and the sequence of bargained

wages {w∗}∞ . The dynamic decision process is an adaptive one. It exhibits two stages: in

t t=0

a ﬁrst step, households determine their consumption and optimal wage pattern (and hence

indirectly their labour supply), in a second step, they re-optimize their consumption plans

following the realized transactions on the labour and product market.

At period t, the representative household expects a series of technology shocks {EtAt+i}∞

0

and real wages and interest rates {Etwt+i, Etrt+i}∞ where i=0,1,2,. . . The decision problem

0

of the household is then to choose a sequence of planned consumption and labour eﬀort

∞

cd

such that

t+i, nst+i 0

∞

max

E

βiU cd

{

t

t+i, nst+i

cd }∞ ,{ns }∞

t+i

=0

t+i

i=0

i=0

subject to

1

ks

=

(1 −

+

t+i+1

δ) ks

f ks

1 + γ

t+i

t+i, nst+i, At+i

− cdt+i

where superscripts d and s stand for “demand” and “supply”. Using standard dynamic

programming techniques, this optimal planning problem can be solved to yield the solution

∞

sequence cd

; however, from each sequence only the ﬁrst tupel

is actually

t+i, nst+i

cd

i=0

t , nst

carried out.

In the ﬁrst period t, the ﬁrm decides upon its inputs kd

given its output constraint

t , nd

t

Eyt related to its perceived demand curve. Standard (one-period) proﬁt maximization yields

the factor demand functions:

kd =

t

fk (rt, wt, At, Eyt)

nd =

t

fn (rt, wt, At, Eyt)

4

As the capital market is supposed to be perfectly competitive, the rental rate of capital, rt,

adjusts in each period such as to clear the market: kt = ks =

. On the labour market,

t

kdt

however, the ﬁxed wage contract does usually not allow to clear the market1.

Wage rigidities introduce frictions on the labour market and force market participations

to carry out transactions oﬀ their optimal supply and demand schedule. Following the spirit

of the search-and-matching literature2, we assume that these rigidities imply that actual

employment (i.e. transactions) corresponds to a weighted average between labour supply

and demand at the current wage:

nt = ωnd + (1 −

t

ω) nst,

where ω measures the degree to which employment is determined by labour demand and will

play a key role in the interpretation of the model and its results. This equation indicates that

actual employment can be a result of a matching process whereby not all desired transactions

are carried out, but where - due to the probabilistic nature of the process - ﬁrms may end

up hiring more than what their current needs are. This may also happen when, for instance,

employment is negotiated, when ﬁrms hoard labour in downturns, employing more than the

proﬁt-maximizing level of workers or when some other real rigidities are present. For the

moment, we leave the interpretation open and only notice that observed employment may

not necessarily correspond to desired levels. We give a more detailed interpretation of the

ω-parameter as soon as we have estimated the model.

Product markets.

The ﬁnal good is produced by combining intermediate goods. This

process is described by the following CES function:

1

1

ρ

Yt =

yρ

(2)

itdi

0

where ρ ∈ (−∞, 1). ρ determines the elasticity of substitution between the various inputs.

The producers in this sector are assumed to behave competitively and to determine their

demand for each good, yit, by maximizing the static proﬁt equation:

1

max

P

P

{

tYt −

ityitdi

yd }

0

it

i∈(0,1)

subject to (2). Given the general price index is supposed to remain constant and normalised

to unity, the demand for intermediate goods depends only on the relative prices of interme-

diate goods, Pit, and the aggregate demand:

1

yd =

ρ−1

it

Pit Yt

1This may nevertheless happen if either the representative ﬁrm has perfect foresight of the sequence of

technology shocks or the wage contract is arranged in the form of a contingency plan. Both will be excluded

here; see Gong and Semmler (2006) for a discussion on this latter point.

2We do not follow the precise set-up here, mainly for reasons of analytical simplicity.

5

The ﬁnal good may be used for consumption and investment purposes.

At the level of the intermediate goods production, each ﬁrm i, i ∈ (0, 1), produces an

intermediate good by means of capital and labour according to a constant returns-to-scale

technology:

yit = Aitk1−α

it

nαit

hence aggregating across all producers yields:

1 yitdi = Atkαtn1−α

t

0

Moreover, from the retail demand for intermediate goods we know that:

1

1

1

1

1

y

ρ−1

ρ−1

itdi =

Pit Ytdi = Yt

Pit di.

0

0

0

Intermediate goods producers face costs to update the relevant information regarding the

developments on their markets (Mankiw and Reis, 2002). To simplify matters, we want to

assume that on average ﬁrms set their optimal prices and quantities according to information

one period earlier, Pit = arg max Et−1πt where πt = Pityit − witnit − ritkit. Firm i, then, sets

its relative optimal price according to the following schedule:

s

wα

P

it−1

itr1−α

it

it =

where s

: real marginal costs.

ρ

it = αα (1 − α)1−α

Given that in equilibrium, all producers are setting the same price Pit = P t > 1, we will

use the following deﬁnition:

1

1

yitdi =

Yt

0

1 − exp (λt)

and call λt the retail margin, measuring the degree of product market competition (via the

eﬀect of ρ on prices). Consequently, the equilibrium on the goods market writes as:

1 yitdi = Atk1−α ⇔

t

nαt

Yt = (1 − exp (λt)) Atk1−α

t

nαt

0

Calibrating the model.

In order to implement the model empirically, certain speciﬁca-

tions regarding the preference function, the technology shock and the stationarity of the

time series have to be made.

As noted above, the economy is represented by a consumer characterized by an instan-

taneous utility function over consumption, c, and leisure, l = 1 − n:

U (c, n) = ln (c) + θ ln (1 − n)

6

with θ the elasticity between consumption and leisure to be estimated with the data.

Moreover, technological shocks are supposed to follow and AR(1) process:

At+1 = a0 + a1At + εt where εt ∼ N 0, σ2ε

The stationarity parameter, γ, can be retrieved by calculating the trend growth rate

of output. Finally, employment, nt, is based on (normalised) hours worked (sample mean

N ), considering that only 1/3 of a day is dedicated to work on average. Box 1 (see above)

summarises the relevant model equations.

Box 1: Summary of the model equations

Consumption:

cd

=

t+1

Et+1 β (1 − δ + rt+1) cdt

Labour supply:

w

β

t

(1 − δ + r

) = 1 − ns

w

t+1) (1 − nst

t+1

t+1

Pre-set wages:

wt = ξwt−1 + (1 − ξ) wopt

t

+ εw

Bargained optimal wage:

1−

1

α

1−

1

α

α

α

A

1−

1−

t

θα α − α α

wopt

t

=

1 − δ

Actual employment:

nt = Et|t−1 ωnd + (1 −

t−1

ω) nst−1

Capital accumulation:

kt+1 = (1 − δ) kt + Yt − cdt

Production function of intermediaries:

yit = f (kit, Aitnit) = Atk1−α

it

nαit

Product market equilibrium:

1

Yt = (1 − λt)

yitdi = cd +

t

it

0

Factor prices:

wt = fn kt, Atndt

rt = fk (kt, Atnt)

7

3

Estimation of the model

3.1

Estimation of structural parameters

In order to estimate the model described in the previous section, several parameters have

to be determined. These include: (i) the parameters describing the process of technological

progress and wage growth; (ii) the preference parameters and the depreciation rate of the

capital stock and (iii) the parameters describing the rigidities on labour and product markets.

While the ﬁrst parameters can be estimated easily on the basis of an AR(1) process

using the TFP residuals that can be derived from a standard growth accounting exercise,

the preference parameters are deeply linked to the ﬁrst-order conditions that result from

solving the above dynamic programming problem. This fact can be used to apply GMM

techniques in order to estimate these parameters. Concretely, the parameters are chosen

such as to match the moments of the model described by the ﬁrst-order conditions of the

above model to those of the underlying data. Notice, moreover, that these parameters can be

established without a concrete knowledge about the underlying labour and product market

rigidities as they are supposed to be unrelated to it.

Given the highly non-linear nature of the optimisation problem, the algorithm used to

pick the right parameters β, δ and θ had to ensure that any local optimum of the GMM

technique is to be avoided. Here, a technique called simulated annealing has been applied,

that combines a grid search procedure with an objective function to assess the size of the

grid jumps. The resulting parameters for our 21 countries can be found in the following

table 1. As to the remaining parameters, the wage share, α, has been taken from country

tables, averaging the values over the corresponding periods for these countries, while the

wage persistence, ξ, has been estimated by OLS.

While the time preference rates are relatively close across countries, corresponding to the

standard interval for these models between 0.95 and 0.99, the country sample displays a large

range of values for the capital depreciation rates, probably reﬂecting some country speciﬁc

trends. In particular the value for Finland seems to be excessively large, implying an annual

depreciation rate of 43%; this may be related to the particular events surrounding the deep

economic crisis in 1993. The two parameters β and θ seems to fall into a reasonable range,

although it must be conceded that no commonly accepted estimates exist regarding the

substitution elasticity between consumption and leisure. Finally, the estimates for the wage

persistence should be taken cum grano salis as OLS estimates of lagged dependent variables

are known to be upward biased; they may nevertheless give a sense of the importance of real

wage persistence across countries with small open economies in general being characterized

by less persistence than bigger, in particular continental European economies. Yet, overall,

as our model in section 2 postulates, our estimates reveal a strong wage persistence, ξ, and

thus a very weak endogeneity of wage determination.

8

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