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Journal ArticleDOI

Market distortions and local indeterminacy: A general approach

01 May 2014-Journal of Economic Theory (Academic Press)-Vol. 151, pp 216-247

Abstract: We provide a methodology to study the role of market distortions on the emergence of indeterminacy and bifurcations. It consists in introducing general specifications for the elasticities of the crucial functions defining the aggregate equilibrium dynamics of the model. This allows us to study how market distortions influence the range of values for the elasticity of input substitution under which local indeterminacy and bifurcations occur, highlighting the main channels and classes of distortions responsible for indeterminacy. Most of the specific market imperfections considered in the related literature are particular cases of our framework. Comparing them we obtain several equivalence results in terms of local dynamic properties. Applying this methodology to the Woodford [30] framework we find that distortions in the capital market, per se, do not play a major role. We further show that, for empirically plausible values of elasticity of substitution between inputs, indeterminacy requires a minimal degree of distortions. This degree seems to be high under output market distortions, while with labor market distortions the required degree is empirically plausible.

Summary (5 min read)

1 Introduction

  • In this paper the authors develop a methodology to study and fully characterize the role of market distortions on the occurrence of local indeterminacy and bifurcations.
  • These papers provide examples to apply their general methodology (see Section 4).
  • 3Weak values of this elasticity are not empirically relevant (Hamermesh (1993), Duffy and Papageorgiou (2000)).
  • On the other hand, the authors also discuss the degrees of specific market distortions required for the occurrence of indeterminacy under empirically plausible values (i.e. around one) of the elasticity of capital-labor substitution.
  • The authors confirm, focusing on capital income taxation, that distortions on the capital market do not, per se, promote indeterminacy.

2 The model

  • The authors framework extends the perfectly competitive Woodford model to take into account market imperfections.
  • In the cases of productive externalities, imperfect competition in the product market or with consumption, labor or capital taxation, the real interest rate and/or the real wage relevant to consumers’ decisions are no longer equal to the marginal productivities of capital and labor at the firm level.
  • Empirical studies also show that the wage bill is increasing in labor.
  • Hence, the occurrence of indeterminacy and bifurcations in their framework is due to the existence of market distortions, mainly through their effects on αi,j, which are more relevant than βi,j when inputs are not weak substitutes in production.
  • Since θ is small and ε̺,i appears multiplied by θ, distortions on the 10See, for instance, Grandmont and al. (1998), Cazzavillan et. al. (1998), Barinci and Chéron (2001), Lloyd-Braga and Modesto (2007), Dufourt et al. (2008) 11This is not restrictive, since empirical values of θ are rather small (around 0.0123 under most monthly parameterizations).

3 The role of market distortions on local dy-

  • The authors then analyze the occurrence of indeterminacy and bifurcations by studying how T and D evolve in the space (T,D) as some relevant parameters of the model are made to vary continuously in their admissible range, according to the geometrical method developed in Grandmont et al. (1998).
  • To locate these values in the plane (T,D), three lines are relevant .
  • The first condition, necessary for indeterminacy when D′1 (σ) < 0, can only be met with distortions.
  • Take εγ ∈ [1,∞) as the bifurcation parameter with Hopf, flip and transcritical bifurcation values εγH εγF and εγT , respectively given in (23),(24) and (25).18 (a) Consider that αKK takes either nonpositive or positive values.
  • 18Assumptions 3 and 4 are satisfied in all the examples considered in the related literature, and simplify considerably their analysis.

3.1 Discussion of the results

  • By inspection of Tables 1 and 2, the authors see that, when capital and labor are sufficiently substitutable in production, indeterminacy and bifurcations occur in the presence of market distortions.
  • 20 Indeterminacy requires a critical lower bound on the elasticity of substitution between capital and labor (σ), which may be different across configurations.
  • ΣH1 is no longer a necessary condition for indeterminacy, indeterminacy also requires a lower bound for σ.
  • Indeterminacy also requires a critical upper bound (either ǫγH or ǫγT ) on ǫγ, depending on the configuration considered.
  • This is a new interesting result that will be illustrated and further discussed in the economic examples provided in Section 4.

3.1.1 Distortions on the ̺ and Ω functions

  • The authors start with the case where distortions affecting only the ̺ and Ω functions are present (αΓ,i = βΓ,i = 0), as it happens, for example, when they only have product or capital market distortions (see Section 4).
  • Then, only configurations (i)− (iv) can be obtained (see (19)), where, as seen above, σ > σH1 is a necessary condition for indeterminacy.
  • Let us now discuss in detail the role of distortions affecting the ̺ function.
  • For αK,K > 0, given the necessary condition αL,L > θαK,K, indeterminacy requires a positive value for αL,L.

3.1.2 Distortions on the Ω and Γ functions

  • The authors consider now distortions that only affect both Ω and Γ, i.e. the intertemporal trade-off condition of workers, as it happens, for instance, when they have labor market imperfections (see Section 4).
  • These last two configurations require that αΓL < α ∗ ΓL as shown in (21).
  • Thus, indeterminacy is possible when the only distortion is an arbitrarily small negative αΓ,L.
  • While general distortions on the real interest rate do not seem to play a major role on the occurrence of indeterminacy, distortions on the generalized offer curve and on the effective consumption seem to help the occurrence of indeterminacy.
  • This would require infinitely large elasticities of private labor supply and of substitution between inputs.

4 Applications

  • The authors now proceed by applying their general methodology and results to several examples that provide microeconomic foundations for the model developed above.
  • The strategy used to analyze each example is the following.
  • The authors start by identifying the ̺(K,L), Ω(K,L) and Γ(K,L) functions.
  • The authors also discuss the minimal degree of distortions required for indeterminacy to occur with an empirically plausible value of the elasticity of capital-labor substitution (around 1).
  • The authors will see in particular that indeterminacy emerges under new configurations (those of Table 1 and Table 2), and that for some sets of distortions’ parameters indeterminacy requires a value for ǫγ bounded away from 1.

4.1 Examples with the same distortion on the real in-

  • In the examples presented below, the same distortion affects both the real interest rate and the real wage, but the generalized offer curve coincides with the competitive one, Γ(K,L) = γ(L).
  • 28They are usually justified by learning by doing or matching problems on labor market.
  • Hence negative externalities illustrate the result, discussed in Section 3, that indeterminacy cannot occur when αK,i and αL,i are all negative.
  • The authors will now emphasize that, for the analysis of local dynamics, many models with imperfect competition on the product market are, in fact, a particular case of the previous framework with positive productive externalities.
  • The same happens when imperfect competition is associated with markup variability or with taste for variety, as the authors now show.

4.2 Examples with different distortions on the real in-

  • L) = γ(L)) so that, as above, D′1 (σ) < 0 and only Table 1 applies.the authors.
  • This will allow us to emphasize that capital market distortions are not, per se, the most relevant ones for indeterminacy.
  • The authors start with the case of capital taxation without public spending externalities in preferences, so that market distortions only appear in the function ̺(K,L).
  • 38Notice that this implies that indeterminacy only occurs when υ > 0, i.e., consumption externalities are of the "keeping-up with the Joneses" type.
  • Indeed, when there is only capital income taxation, the steady state is always a saddle.

4.3 Examples with distortions only on the generalized

  • In the examples presented in this section distortions only affect the generalized offer curve.
  • The authors can easily see that Assumptions 1 and 4 are ensured.
  • This shows that it should be misleading to focus only on the case of an infinitely elastic labor supply when the authors want to fully study the role of some labor market distortions on the occurrence of indeterminacy.
  • Therefore, this last model can be seen as a particular case of not too negative aggregate labor externalities in leisure utility.
  • 44Each worker supplies one unit of labor with a labor desutility that depends on the level of effort.

4.4 Examples with distortions on the generalized offer

  • L) and Ω(K,L) are affected by market distortions, while the capital market remains perfectly competitive.the authors.
  • This case is new, and is able to illustrate most of the dynamic results exhibited in the general framework.
  • Unions are able to set wages above a reservation wage, with a markup factor µ(K,L) = 1−αs(K/L) 1−s(K/L) ≥ 1, increasing in the bargaining power of unions (1−α) ∈ [0, 1).47 Employment is determined by the equality between the reservation wage and the marginal productivity of labor.
  • 46See Grandmont (2008) for a more detailed discussion.
  • Assuming that government expenditures (Gt) provide services that affect not only workers’ utility for consumption, but also their desutility of labor, the authors will be able to provide an illustration of configuration (vi).

2 further require that −2/ψ − µ < η < s/(1− s − ψ), µ > −s/(1 − s− ψ),

  • For µ > µb, D′1(σ) < 0 and configurations (ii).1, (iii).1 and (iv).1 are the relevant ones.
  • In configurations (ii).1 and (iii).1 indeterminacy emerges for σ > σH1 = s−(1−s−ψ)(η−µ)−θ(1−s)(1+µ) ψ(η−µ) , provided εγ is sufficiently small.
  • 0. So either configuration (v).2 applies54 and indeterminacy occurs under similar conditions than under configuration (iv).1, or configuration (vi).2 is the relevant one and indeterminacy occurs for σS2 < σ < σF when εγF < εγ < εγT , and for σ > σ F when 1 ≤ εγ < min{εγH , εγT }. 55 This example shows that distortions that affect both sides of the intertemporal trade-off of workers, i.e., effective consumption Ω(K,L) and the generalized offer curve Γ(K,L), are able to generate most of the possible dynamic configurations exhibited in their general framework.

5 Concluding remarks

  • With their general analysis of the role of market distortions on local dynamics and the different examples of specific distortions presented above, the authors were able to they emphasize several interesting results, some of them already latent in previous works, but which are here confirmed, generalized and highlighted.
  • 58 further research on this issue is welcome.
  • Second, although the authors only discuss local deterministic indeterminacy and cycles, they may be able to construct stochastic sunspot cycles along indeterminacy and bifurcations 56Some recent works confirm the importance of labor market imperfections in explaining real business cycles data.
  • If the authors estimate the relevant parameters of their general formulation, they will not be able to identify a particular source of specific distortions among those, which belonging to the same class, are observationally equivalent.

6.1 Existence of a steady state

  • A stationary equilibrium of the dynamic system (3)-(4) is a solution (K,L) = (Kt−1, Lt) for all t, that satisfies A̺(K,L) = θ/β and A/B)Ω(K,L)L = Γ(K,L).
  • Substituting this into the second equation the authors then obtain the unique solution for B = [β̺(1, 1)Γ(1, 1)]−1 θΩ(1, 1) > 0.

6.2 Trace T and determinant D of the Jacobian matrix

  • The authors substitute the expressions given in (5) in these two equations, and they assume that the numerator and the denominator 29 of T and D linearly depend on the elasticity of capital-labor substitution σ, i.e. that: Assumption 3 (βL,K + s) = (1−s−βK,K)(s−βL,L) (1−s+βK,L) and βΓ,K = −βΓ,L 1−s−βK,K 1−s+βK,L .
  • This assumption is satisfied in models with no distortion and by all the works considered in the literature and presented here as applications.

6.3 Local stability properties

  • The authors main interest is to understand how the existence of market imperfections change the characterization of local stability properties in terms of the elasticity of substitution between capital and labor, σ, and of the elasticity of the private offer curve, εγ, while keeping s and θ constant at values satisfying Assumption 1.1.
  • Most of the distortions considered in the literature satisfy this condition.

6.4 Configurations

  • Before proceeding let us make a few helpful remarks.
  • Using (20) and (18), configurations (v) and (vi), where D′1(σ) >.

6.4.1 Derivation of Proposition 1

  • The case where D′1 (σ) < 0: Proposition 1 (a) - Table 1 Configuration (i) (S1 ∈ (0, 1)).
  • And the half-line ∆1, that starts on (AC) and points upwards to the left, crosses (AB) above point B. See Figure 4. 61This last case does not appear if σH2 does not exist.
  • With the help of geometrical arguments the authors can see that when σH2 > s−βLL 1+αLL exists, then σH2 > σH3. 69 However σH2 may be higher or lower than σF .
  • To simplify the exposition the authors only present in Table 2 the results for this configuration assuming that σH2 > σF . 70 Configuration (vi) (S1 ∈ (SD, 1)) 71 Define σS2 as the critical value of σ such that the half line ∆ goes through point A.72.
  • All these results are summarized in Table 2.

6.5 Expressions for critical values of εγ

  • Hence, if this condition is not met, then εγT > εγF for all σ > s−βLL 1+αLL .
  • ΑK,LβΓ,L 1−s−βK,K 1−s+βK,L ] αL,L − αΓ,L − θ[αK,K(1 + αΓ,L)− αΓ,KαK,L] σH2 is a critical value of σ such that the half-line ∆ goes through the point (T,D) = (2, 1), i.e., goes through point C.74 Note that εγT = εγH for σ = σH2 .
  • ΣH3 is the critical value of σ such that the half line ∆ goes through the point (T,D) = (−2, 1), i.e., goes through point B.75 Note that εγF = εγH for σ = σH3 .
  • The authors show conditions for its existence and uniqueness.

6.8 Existence of σH2

  • To discuss the existence and uniqueness of σH2 , the authors consider first the configurations where S1 ∈ (0, 1), and then the remaining ones.
  • Note that the equation ǫγH = ǫγT is a polynomial of degree 2, i.e. has at most two solutions.
  • Since S(+∞) ∈ (0, 1), the authors can see geometrically that a solution σH2 ∈ (σH1 ,+∞) must exist and the number of these solutions is odd.
  • Note that in this particular case, ǫγT does not depend on σ.

6.9 Existence of σH3

  • Here the authors limit their analysis to configurations (iv), (v) and (vi) since σH3 is only relevant under these configurations.
  • Consider now configurations (v) and (vi).

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Market distortions and local indeterminacy:
a general approach
Teresa Lloyd-Braga
1
, Leonor Modesto
2
and Thomas Seegmuller
3
1
Universidade Católica Portuguesa (UCP-FCEE) and CEPR
2
Universidade Católica Portuguesa (UCP-FCEE) and IZA
3
Paris School of Economics and CNRS
May 13, 2009
Abstract
We provide a general methodology to study the role of market
distortions on local indeterminacy and bifurcations. We extend the
well-known Woodford (1986) model to account for market distortions,
introducing general specifications for three crucial functions: the real
interest rate, the real wage and the workers’ offer curve. The elastic-
ities of these three functions play a key role on local dynamics and
allow us to identify which types of distortions are the most powerful
for indeterminacy.
Most of the specific market imperfections considered in the related
literature are particular cases of our general framework. Comparing
them we obtain several equivalence results in terms of indeterminacy
mechanisms. We also provide examples of distortions that illustrate
new results. Furthermore we show that, for an elasticity of substitu-
tion between inputs around unity, indeterminacy requires a minimal
degree of distortions. However, the degree of labor market distortions
compatible with that requirement is empirically plausible.
JEL classification: C62, E32.
Keywords: Indeterminacy, endogenous fluctuations, market imperfections,
externalities, imperfect competition, taxation.
Corresponding Author: correspondence should be sent to Leonor Modesto, Univer-
sidade Católica Portuguesa, FCEE, Palma de Cima, 1649-023 Lisboa, Portugal. e-mail:
lrm@fcee.ucp.pt.
1

1 Introduction
In this paper we develop a methodology to study and fully characterize the
role of market distortions on the occurrence of local indeterminacy and bi-
furcations. Several papers have been studying the effects of certain specific
market distortions (linked to externalities, imperfectly competitive markets,
or government intervention) on local dynamics,
1
but a systematic analysis
within a general unified framework, able to compare the importance of dif-
ferent types of distortions as a route to indeterminacy and bifurcations, is
still missing. In order to do that we introduce a general framework, able to
account for market distortions without specifying a priori their source, and
highlight the main channels through which indeterminacy occurs.
Although our methodology can be applied to any dynamic general equi-
librium model, the dynamic framework considered in this paper is based on
the perfectly competitive one sector model of a segmented asset economy of
Woodford (1986) and Grandmont et al. (1998).
2
Market distortions play a
role on the local stability properties of the steady state because they modify
the elasticities of three crucial functions that characterize our two dimen-
sional equilibrium dynamic system: the real interest rate, the real wage or
equivalently effective consumption per unit of labor, and the generalized offer
curve. We introduce general specifications for these elasticities that allow us
to recover most of the distortions on product, capital and labor markets, and
admit perfect competition as a particular case.
Focusing on not too weak values of the elasticity of capital-labor sub-
stitution,
3
we show that, in contrast to the perfectly competitive economy,
4
when there are market distortions, indeterminacy and bifurcations may oc-
cur in the presence of sufficiently high capital-labor substitution and labor
supply elasticities. However, in some cases, indeterminacy is ruled out if the
individual labor supply elasticity becomes arbitrarily large, implying that,
by imposing an infinitely elastic labor supply, one may obtain a wrong idea
of the dynamic implications of some distortions. We find that distortions
affecting the real interest rate do not play a major role. On the contray, even
(arbitrarily) small distortions on the offer curve and/or effective consumption
1
See the survey by Benhabib and Farmer (1999) and the bibliographic references in
Section 4.
2
This is a suitable framework for our purpose, since several papers have introduced
specific market distortons on product and factor markets in this model. These papers
provide examples to apply our general methodology (see Section 4).
3
Weak values of this elasticity are not empirically relevant (Hamermesh (1993), Duffy
and Papageorgiou (2000)).
4
Indeterminacy only occurs under perfect competition (Woodford (1986), Grandmont
et al. (1998)) for a weak capital-labor substitution.
2

promote the occurrence of indeterminacy. However, indeterminacy can only
prevail for values of the elasticity of capital-labor substitution around one
(those considered empirically plausible), under a minimal level of distortions
in the offer curve and/or in effective consumption. Furthermore, distortions
modifying the offer curve affect significantly the emergence of indeterminacy,
leading to new results.
To clarify these findings, we apply our general method to examples of spe-
cific distortions on the product, capital and labor markets, focusing on two
types of results. On one hand, we obtain several equivalence results in terms
of local dynamics and indeterminacy mechanisms. We find that labor and
consumption taxation with a balanced budget are equivalent to consumption
externalities, sharing the same indeterminacy mechanism. Product market
imperfections (due to mark-up variability and taste for variety) can be seen
as particular cases of the framework with positive externalities in produc-
tion, and unemployment benefits with efficiency wages can be recovered as
a particular case of an economy where the desutility of labor is negatively
affected by labor externalities. On the other hand, we also discuss the de-
grees of specific market distortions required for the occurrence of indetermi-
nacy under empirically plausible values (i.e. around one) of the elasticity of
capital-labor substitution. We confirm, focusing on capital income taxation,
that distortions on the capital market do not, per se, promote indeterminacy.
Under output market distortions, indeterminacy may emerge, but requires
parameters configurations at odds with empirical evidence, i.e., too strong
positive externalities in production or high markups. On the contrary, under
labor market distortions (unions, efficiency wages, unemployment benefits,
externalities in preferences), indeterminacy and bifurcations emerge for em-
pirically plausible distortions. Hence, labor market distortions are the most
relevant for indeterminacy.
The rest of the paper is organized as follows. We present our general
framework in Section 2, study the role of distortions on local dynamics in
Section 3, and apply our results to examples with specific market distortions
in Section 4. Section 5 provides concluding remarks. Proofs and technical
details are provided in the Appendix.
2 The model
Our framework extends the perfectly competitive Woodford model to take
into account market imperfections. To ease the presentation we begin with
a brief exposition of this model.
According to the perfectly competitive economy studied by Woodford
3

(1986) and Grandmont et al. (1998), in each period t N
, a final good is
produced under a constant returns to scale technology AF (K
t1
, L
t
), where
A > 0 is a scaling parameter, F (K, L) is a strictly increasing function, con-
cave and homogeneous of degree one in capital, K > 0, and labor, L > 0.
From profit maximization, the real interest rate ρ
t
and the real wage ω
t
are re-
spectively equal to the marginal productivities of capital and labor, i.e. ρ
t
=
AF
K
(K
t1
, L
t
) (K
t1
/L
t
) and ω
t
= AF
L
(K
t1
, L
t
) (K
t1
/L
t
).
There are two types of infinitely-lived consumers, workers and capitalists.
Both can save through two assets, money and productive capital. However,
capitalits are less impatient than workers and do not supply labor, whereas
workers face a finance constraint which prevents them from borrowing against
their wage earnings. Focusing on equilibria where the finance constraint is
binding and capital is the asset with the greatest return, it follows that
only workers hold money (they save all their wage income in money), and
capitalists hold the entire stock of capital. As in Woodford (1986), the be-
haviour of the representative worker can be summarized by the maximization
of U
C
w
t+1
/B
V (L
t
) subject to the budget constraint P
t+1
C
t+1
= w
t
L
t
,
where P
t
is the price of the final good and w
t
the nominal wage at period t,
C
w
t+1
0 the worker’s consumption at period t + 1, B > 0 a scaling para-
meter, V (L) the desutility of labor in L [0, L
] and U(C
w
/B) the utility
of consumption.
5
The solution of this problem is given by the intertemporal
trade-off between future consumption and leisure:
ω
t+1
L
t+1
/B = γ(L
t
) (1)
where γ(L) is the usual offer curve and C
w
t+1
= ω
t+1
L
t+1
at the monetary
equilibrium, with a fixed constant amount of money in the economy.
The representative capitalist maximizes the log-linear lifetime utility func-
tion
t=1
β
t
ln C
c
t
subject to the budget constraint C
c
t
+ K
t
= (1 δ +
r
t
/P
t
)K
t1
, where C
c
t
represents his consumption at period t, β (0, 1) his
subjective discount factor, r
t
the nominal interest rate and δ (0, 1) the
depreciation rate of capital. Solving the capitalist’s problem we obtain the
capital accumulation equation
K
t
= β [1 δ + ρ
t
] K
t1
(2)
A perfectly competitive intertemporal equilibrium is a sequence (K
t1
, L
t
)
5
It is assumed that U
C
w
t+1
/B
is a continuous function of C
w
t+1
0, and C
r
, with
r high enough, U
> 0, U
′′
0 for C
w
t+1
> 0 , and xU
′′
(x)/U
(x) < 1. Also, V (l) is a
continuous function for [0, L
], and C
r
, with r high enough, V
> 0, V
′′
0 for (0, L
).
We also assume that lim
LL
V
(L) = +, with L
(the worker’s endowment) possibly
infinite.
4

R
2
++
, t = 1, 2, ..., , given K
0
> 0, satisfying (1) and (2), where ω
t
=
(K
t1
/L
t
) and ρ
t
= (K
t1
/L
t
).
6
We now present our general framework with market distortions, explain-
ing in a second step the main differences with respect to the perfectly com-
petitive case. We propose a more general equilibrium dynamic system, given
by (3)-(4) in Definition 1 below, where
t
represents the real interest rate rel-
evant to capitalists’ decisions, Γ
t
a generalized offer curve, and
t
L
t
effective
consumption. In what follows, we denote by ε
X,y
the elasticity, evaluated at
the steady state, of the function X = {, , Γ} with respect to the argument
y = {K, L}, while ε
γ
1 0 is the inverse of the elasticity of labor supply
of the representative worker with respect to labor, s (0, 1) the elasticity of
the production function with respect to capital, and σ > 0 is the elasticity
of capital-labor substitution of the representative firm, all evaluated at the
private level and at the steady state.
7
Definition 1 A perfect foresight intertemporal equilibrium of the economy
with market distortions is a sequence (K
t1
, L
t
) R
2
++
, t = 1, 2, ..., , that
for a given K
0
> 0 satisfies:
K
t
= β [1 δ +
t
] K
t1
(3)
(1/B)Ω
t+1
L
t+1
= Γ
t
(4)
where
t
A(K
t1
, L
t
),
t
AΩ(K
t1
, L
t
) and Γ
t
Γ(K
t1
, L
t
). The
functions (K, L), Ω(K, L) and Γ(K, L) are positively valued and differen-
tiable as many times as needed for (K, L) R
2
++
, such that
ε
,K
= α
K,K
+
β
K,K
σ
1 s
σ
, ε
,L
= α
K,L
+
β
K,L
σ
+
1 s
σ
ε
,K
= α
L,K
+
β
L,K
σ
+
s
σ
, ε
,L
= α
L,L
+
β
L,L
σ
s
σ
ε
Γ,K
= α
Γ,K
+
β
Γ,K
σ
, ε
Γ,L
= α
Γ,L
+
β
Γ,L
σ
+ ε
γ
,
(5)
where α
i,j
R and β
i,j
R, for i = K, L, Γ and j = K, L, are parameters
independent of ε
γ
and σ
As under perfect competition, the dynamics of the economy with market
distortions are governed by a two dimensional system in capital and labor,
where the first equation represents capital accumulation and the second one
6
See Grandmont et al. (1998) and Woodford (1986) for more details.
7
We consider the normalized steady state (K, L) = (1, 1) of the dynamic system (3)-(4),
whose existence is shown in Proposition 2 of Appendix 6.1.
5

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16 citations


Journal ArticleDOI
Abstract: We develop a new multistep monotone map approach to characterize minimal state-space recursive equilibrium for a broad class of infinite horizon dynamic general equilibrium models with positive externalities, dynamic complementarities, public policy, equilibrium indeterminacy, and sunspots. This new approach is global, defined in the equilibrium version of the household’s Euler equation, applies to economies for which there are no known existence results, and existing methods are inapplicable. Our methods are able to distinguish different structural properties of recursive equilibria. In stark contrast to the extensive body of existing work on these models, our methods make no appeal to the theory of smooth dynamical systems that are commonly applied in the literature. Actually, sufficient smoothness to apply such methods cannot be established relative to the set of recursive equilibria. Our partial ordering methods also provide a qualitative theory of equilibrium comparative statics in the presence of multiple equilibrium. These robust equilibrium comparison results are shown to be computable via successive approximations from subsolutions and supersolutions in sets of candidate equilibrium function spaces. We provide applications to an extensive literature on local indeterminacy of dynamic equilibrium.

9 citations


Journal ArticleDOI
TL;DR: It is found that a strong social norm to work destabilizes conventional wisdom by reversing the negative effects of social security on employment, and destabilizes the economy by facilitating the emergence of endogenous fluctuations.
Abstract: We study employment dynamics in an OLG model with unemployment benefits financed by taxing wages, and with a defined contribution plan. The novelty with respect to recent studies of the effects of social security in this context is that we introduce a social norm to work, shaping the worker’s participation decision, and hence affecting the reservation wage. We find that a strong social norm to work destabilizes conventional wisdom by reversing the negative effects of social security on employment, and destabilizes the economy by facilitating the emergence of endogenous fluctuations.

4 citations


Journal ArticleDOI
Yang Gao1, Gang Gong1, Gang Gong2Institutions (2)
Abstract: Economists believe that economic fluctuations can be smoothed by stabilization mechanisms, such as price adjustment, embedded in the economy. While price adjustment can be seen as a stabilization mechanism, are there mechanisms that can destabilize an economy? We find that as early as 1939, Harrod discussed a destabilization mechanism, the firm's investment adjustment, illustrated in his knife-edge puzzle. We build a macro-dynamic model with investment and price as the core macroeconomic variables. Our analysis shows that the interaction between the stabilization mechanism (price adjustment) and the destabilization mechanism (investment adjustment) generates fluctuations and cycles. However, due to price stickiness, the price adjustment mechanism may not be enough to stabilize the economy. In this case, a government stabilization policy is necessary for further stabilization. As this paper also addresses the microfoundations of Keynesian quantity theory, including the choice of output and investment in optimization, it can be related to traditional Keynesian economics, with a new perspective to understand business cycles.

2 citations


Journal ArticleDOI
Abstract: Nous etudions une economie multi-branches a generations imbriquees, ou les entreprises de chaque branche vivent deux periodes, investissant strategiquement en premiere et produisant sous regime de concurrence cournotienne en seconde periode. Les equilibres des jeux en deux etapes, ainsi que sur les marches des produits, du travail et du capital, determinent le nombre d’entreprises a chaque periode et un systeme dynamique a deux equations. L’emergence de fluctuations endogenes robustes comme consequence de l’investissement strategique est mise en lumiere par contraste avec un modele sans investissement strategique et avec libre entree.

2 citations


References
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Journal ArticleDOI
Susanto Basu1, Susanto Basu2, John G. Fernald3Institutions (3)
Abstract: A typical (roughly) two‐digit industry in the United States appears to have constant or slightly decreasing returns to scale. Three puzzles emerge, however. First, estimates often rise at higher levels of aggregation. Second, apparent decreasing returns contradicts evidence of only small economic profits. Third, estimates with value added differ substantially from those with gross output. A representative‐firm paradigm cannot explain these puzzles, but a simple story of aggregation over heterogeneous units can. Theory and evidence on aggregation invalidate the common use of demand‐side instruments. Finally, we discuss implications of heterogencity for macroeconomic modeling: A one‐sector macroeconomic model that ignores heterogeneity may sometimes require firm‐level parameters, but at other times the model may require the “biased” aggregate parameters.

1,261 citations


Journal ArticleDOI
Enrique G. Mendoza1, Assaf Razin2, Assaf Razin3, Linda L. Tesar4  +1 moreInstitutions (4)
Abstract: This paper proposes a method for computing tax rates using national accounts and revenue statistics. Using this method we construct time series of tax rates for large industrial countries. The method identifies the revenue raised by different taxes at the general government level and defines aggregate measures of the corresponding tax bases. This method yields estimates of effective tax rates on factor incomes and consumption consistent with the tax distortions faced by a representative agent in a general equilibrium framework. These tax rates compare favorably with existing estimates of marginal tax rates, and highlight important international differences in tax policy.

971 citations


Journal ArticleDOI
Abstract: We investigate properties of the one-sector growth model with increasing returns under two organizational structures capable of reconciling the existence of aggregate increasing returns with competitive behavior by firms. The first involves input externalities; the second involves monopolistic competition. We show, for parameters in close accord with recent literature on real business cycles, that the model displays an indeterminate steady state that can be exploited to generate a model of business fluctuations driven by self-fulfilling beliefs. In our first class of models, growth is generated by exogenous increases in factor productivity. In the second class the marginal product of capital is large enough for endogenous growth. Journal of Economic Literature Classification Numbers: E00, E3, O40.

820 citations


Journal ArticleDOI
Abstract: We propose a simple method to help researchers develop quantitative models of economic fluctuations. The method rests on the insight that many models are equivalent to a prototype growth model with time-varying wedges which resemble productivity, labor and investment taxes, and government consumption. Wedges corresponding to these variables–efficiency, labor, investment, and government consumption wedges–are measured and then fed back into the model in order to assess the fraction of variousfluctuations they account for. Applying this method to U.S. data for the Great Depression and the 1982 recession reveals that the efficiency and labor wedges together account for essentially all of the fluctuations; the investment wedge plays a decidedly tertiary role, and the government consumption wedge, none. Analyses of the entire postwar period and alternative model specifications support these results. Models with frictions manifested primarily as investment wedges are thus not promising for the study of business cycles.

635 citations


Journal ArticleDOI
Abstract: The author studies the implications for optimal portfolio decisions and equilibrium asset prices of the hypothesis that agents care about other agents' consumption level (in addition to their own). That hypothesis is introduced in two settings: (1) a one-period CAPM model and (2) a multiperiod asset pricing model. The presence of externalities is shown to affect the optimal risky share, as well as the size of adjustments in the latter in response to exogenous changes in the risk-adjusted equity premium. In equilibrium, the equity premium is also affected by the sign and the intensity of the externalities. Copyright 1994 by Ohio State University Press.

633 citations


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No. of citations received by the Paper in previous years
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20153