Resilience, consumption smoothing and structural policies

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Resilience, consumption smoothing and structural
Paper prepared for the OECD Workshop
”Structural reforms and economic resilience: evidence and policy
Ekkehard Ernst
Gang Gong
Tsinghua University
Economics Department
School of Economics and Management
2, Rue Andr´
e Pascal
Beijing, China
75775 Paris Cedex 16
[email protected]
Willi Semmler
New School Unversity
Dept. of Economics
Schwartz Center for Economc Policy Analysis
New York
June 2007

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

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

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

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.
Sticky information and labour market frictions
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)
subject to
kt+i+1 =
[(1 − δ) k
t+i + f (kt+i, nt+i, At+i) − ct+i]
w∗ =
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
Assuming a constant relative risk aversion (CRRA) utility function for the
household’s instantaneous utility
U (c, n) = ln (c) + θ ln (1 − n)

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:
(θα − 1)
w∗ =
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
wage w∗ but is solved for the given
as expressed in (1), On the other hand, that optimal
plan may not be carried out since the actual wage wt is not necessary equal to w∗.
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}∞
and real wages and interest rates {Etwt+i, Etrt+i}∞ where i=0,1,2,. . . The decision problem
of the household is then to choose a sequence of planned consumption and labour effort

such that
t+i, nst+i 0

βiU cd
t+i, nst+i
cd }∞ ,{ns }∞
subject to
(1 −
δ) ks
f ks
1 + γ
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
t , nst
carried out.
In the first period t, the firm decides upon its inputs kd
given its output constraint
t , nd
Eyt related to its perceived demand curve. Standard (one-period) profit maximization yields
the factor demand functions:
kd =
fk (rt, wt, At, Eyt)
nd =
fn (rt, wt, At, Eyt)

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,
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 −
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:
Yt =

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:
tYt −
yd }
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:
yd =
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.

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
yit = Aitk1−α
hence aggregating across all producers yields:
1 yitdi = Atkαtn1−α
Moreover, from the retail demand for intermediate goods we know that:
itdi =
Pit Ytdi = Yt
Pit di.
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:

it =
where s
: real marginal costs.
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:
yitdi =
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 ⇔
Yt = (1 − exp (λt)) Atk1−α
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)

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
Et+1 β (1 − δ + rt+1) cdt
Labour supply:
(1 − δ + r
) = 1 − ns
t+1) (1 − nst
Pre-set wages:
wt = ξwt−1 + (1 − ξ) wopt
+ εw
Bargained optimal wage:

 α
θα α − α α 
= 

1 − δ
Actual employment:
nt = Et|t−1 ωnd + (1 −
ω) nst−1
Capital accumulation:
kt+1 = (1 − δ) kt + Yt − cdt
Production function of intermediaries:
yit = f (kit, Aitnit) = Atk1−α
Product market equilibrium:
Yt = (1 − λt)
yitdi = cd +
Factor prices:
wt = fn kt, Atndt
rt = fk (kt, Atnt)

Estimation of the model
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.