Q2. What are the future works in "Market distortions and local indeterminacy: a general approach" ?
Empirical analysis on this issue is therefore an important direction for further research. 56 A possible explanation for these results may be linked to the fact that future expectations, which open the room for fluctuations driven by selffulfilling expectations, only affect the current decisions of consumers/workers, thus rendering distortions that affect the intertemporal trade-off of consumers/workers more important than those affecting the capital accumulation equation. Although some works have already considered some of these aspects,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.
Q3. What is the reason for the indeterminacy and bifurcations in their framework?
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.
Q4. What is the role of market distortions on the local stability properties of the steady state?
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 their two dimensional equilibrium dynamic system: the real interest rate, the real wage or equivalently effective consumption per unit of labor, and the generalized offer curve.
Q5. In what configurations does indeterminacy emerge for > h1?
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 εγis sufficiently small.
Q6. How do the authors obtain the local dynamics of the system?
By loglinearizing the system (3)-(4) around the normalized steady state,we obtain the local dynamics for K̂t = (Kt −K) /K and L̂t+1 = (Lt+1 − L) /L given by following equations:[ K̂t L̂t+1 ] = [ (1 + θε̺,K) θε̺,L ǫΓ,K−εΩ,K(1+θε̺,K)1+εΩ,LεΓ,L−θεΩ,Kε̺,L 1+εΩ,L ][ K̂t−1 L̂t ] ≡ [J ] [ Kt−1−K K Lt−L L ](6) Market distortions influence the local dynamics of the model, relatively to the perfectly competititive case, by modifying the elasticities εΩ,i, ε̺,i and εΓ,i.
Q7. What is the methodology used in this paper?
Although their methodology can be applied to any dynamic general equilibrium 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).
Q8. What is the significance of bifurcations in the case of a steady state?
Note also that bifurcations are quite relevant in explaining persistency of business fluctuations, since they appear when at least one eigenvalue crosses the unit circle.
Q9. What is the first example of a perfectly competitive economy?
In the first example presented the authors consider a perfectly competitive economy where public expenditures, financed by variable taxation under a balanced budget rule, are introduced.
Q10. What is the elasticity of the production function with respect to labor?
In what follows, the authors denote by εX,y the elasticity, evaluated at the steady state, of the function X = {̺,Ω,Γ} with respect to the argument y = {K,L}, while εγ − 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.
Q11. What is the effect of distortions on the offer curve?
As seen above, indeterminacy is possible in the presence of arbitrarily small distortions affecting either effective consumption or the offer curve.
Q12. What are the relevant factors for indeterminacy?
On the contrary, under labor market distortions (unions, efficiency wages, unemployment benefits, externalities in preferences), indeterminacy and bifurcations emerge for empirically plausible distortions.
Q13. What is the definition of a perfect foresight intertemporal equilibrium?
A perfect foresight intertemporal equilibrium of the economy with market distortions is a sequence (Kt−1, Lt) ∈ R 2 ++, t = 1, 2, ...,∞, that for a given K0 > 0 satisfies:Kt = β [1− δ + ̺t]Kt−1 (3)(1/B)Ωt+1Lt+1 = Γt (4)where ̺t ≡ A̺(Kt−1, Lt), Ωt ≡ AΩ(Kt−1, Lt) and Γt ≡ Γ(Kt−1, Lt).
Q14. What is the first example of a financial constrained framework?
The first example is based on Dufourt et al. (2008), where the Woodford finance constrained framework is extended to take into account the existence of involuntary unemployment (see also Lloyd-Braga and Modesto (2007)).