Theories and Methods of the Business Cycle. Part 1: Dynamic Stochastic General Equilibrium Models...
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Transcript of Theories and Methods of the Business Cycle. Part 1: Dynamic Stochastic General Equilibrium Models...
Theories and Methods of the Business Cycle.Part 1: Dynamic Stochastic General Equilibrium ModelsIV. A New Neoclassical Synthesis?
Jean-Olivier HAIRAULT, Professeur à Paris I Panthéon-Sorbonne et à l’Ecole d’Economie de Paris (EEP)
1. Introduction
The RBC theory is at odds with the neoclassical synthesis
Real shocks vs. Monetary shocks
Optimal vs. Suboptimal fluctuations
RBC theory has not totally convinced that technology shocks can alone drive the business cycle. The internal mechanisms of the neoclassical growth model does not lead to fluctuations totally consistent with the stylized facts when calibration is seriously done.
The correlation between hours and labor productivity is too high
The response of output does not display a hump-shaped profile
How to reconcile theory with the numerous empirical works which show the non-neutrality of money (in particular in the VAR framework)? Gali [1989], Quarterly Journal of Economics
1. Introduction
Along the development of RBC theory in the 80’s, keynesianism was
looking for micro-foundations
How to get market failures when agents are assumed to optimize?
Imperfect information, imperfect competition, strategic behaviors,…New-
Keynesianism based on real and nominal rigidities. Ball and Romer [1990],
Review of Economic Studies
Non-walrasian features in the good market (monopolistic competition), the
labor market (search frictions), the credit market (adverse selection and
moral hazard)
Mainly theoretical works as new-keynesianism has to address the Lucas’
critique.
What a challenge to overcome RBC theory with their own methodology!
The 90’s was the decade during which a new neoclassical synthesis occurs:
intertemporal choices and strategic behaviors
2. Equilibrium unemployment
Employment volatility represents 70% of total hours
volatility
Hours indivisibility à la Hansen [1985]
Do efficiency wages better explain the relative volatility of
hours to labor productivity? Danthine and Donaldson
[1990], European Economic Review. Employment is not
volatile enough in their model
Efficiency wages are rigid in the sense they do not clear the
labor market, but they are elastic to technology shocks.
Fluctuations generated by the model are essentially the
same as those of the RBC canonical model.
2. Equilibrium unemployment
Equilibrium unemployment, Pissarides [1990], Equilibrium
unemployment theory, Basil Blackwell
Hirings take time as there is imperfect information in the
process of search: search unemployment
Search frictions could explain the persistence of
fluctuations
Merz [1995], Journal of Monetary Economics, Andolfatto
[1996], American Economic Review
2. Equilibrium unemployment
Hirings depend on vacancies (V) and unemployed people (U), but also the
search intensity (e) of these latter.
The participation rate is constant and exogenous.
The probability to have a job is:
The probability to contact a worker:
There are externalities in the search process
p depends positively on the number of vacancies (complementarity) and
negatively on the number of unemployed workers (congestion)
q depends negatively on the number of vacancies and positively on the
number of unemployed workers (congestion)
2. Equilibrium unemployment
The dynamics of employment depends on hirings (a
combination of unemploment and vacancy) and on firings
(a fixed proportion s of the employment stock)
2. Equilibrium unemployment
Representative household (risk-sharing due to the large
scale of the household)
First order conditions are the same as those in the
canonical RBC model, except there is no labor supply, no
partipation decision and hours are negociated between
households and firms (as wage)
2. Equilibrium unemployment
The production function is traditional and combines total
hours and capital.
Firm labor demand is no more static, as they invest in
vacancies. The firm program is now intertemporal.
Labor demand is now determined by the intertemporal
condition:
2. Equilibrium unemployment
Bargaining over hours and wage
Nash criterion
With
is the bargaining power of firms. In Andolfatto [1996], it is equal to the elasticity relative to vacancy in the matching function. In this case, the bargaining leads to the first best allocation as demonstrated by Hosios [1990], Review of Economic Studies.
Given the existence of search frictions, fluctuations are not necessarily sub-optimal. This is why Andolfatto [1996] solves the planner program.
2. Equilibrium unemployment
Stylized facts : standart deviation in the first line, correlation with output in the second line
Andolfatto [1996]
The wage is no longer equal to labor productivity and the labor share is variable and counter-cyclical. The variance of output is obtained without infinite labor elasticity, but results from its higher persistence.
But the correlation between hours and wage is not replicated.
Increasing the volatility of employment by giving more bargaining power to firms as their response to technology shocks will then be more elastic.
2. Equilibrium unemployment
Productivity cycle and Beveridge curve
Stylized facts
Model’s predictions: the productivity cycle is not replicated
contrary to the Beveridge curve
3. Perfect Insurance
Complete markets: perfect risk sharing
B is the amount of insurance whose price is tau.
1-alpha= s for employed workers; 1-alpha = 1-p for
unemployed workers
Two insurance schemes: profit =
The budgetary constraints:
3. Perfect Insurance
First-order conditions:
Risk-sharing condition
For s = n, u
These conditions imply that the capital choices are identical
whatever their employment status. For separable utility fonction,
consumptions are the same, and the unemployed workers are
better off. See Chéron and Langot [2002], Review of Economic
Dynamics for a case where their welfare is lower than that of
employed workers.
3. Perfect Insurance
Given these optimal choices, the budgetary constraints can
be rewritten as follows:
It can be noticed that:
The representative household program is then:
4. Monopolistic competition and nominal rigidities
Considering VAR studies (following the seminal article of Sims [1980], Econometrica), money supply shocks would impact the output. J. Gali [1992], Quarterly Journal of Economics, Bec and Hairault [1993], Annales d’Economie et Statistiques [1993]
Taking into account money supply shock in DSGE models implies to have money demand theoretical foundations: Why do we hold money ? Old issue in economics…
Money reduces transaction or search costs in the good market: Kiyotaki and Wright [1989], Journal of Political Economy
More tractable in DSGE models, cash-in-advance constraint can be added in the household program, Cooley and Hansen [1989], American Economic Review:
Without any nominal rigidities, this approach fails to generate a positive and strong response of output after a positive monetary (supply) shock. Only the inflation tax propagation mechanism which is a negative wealth effect: positive response of labour supply and output, but very weak effects.
4. Monopolistic competition and nominal rigidities
(Inflation tax +) nominal rigidities: prices are rigid due to
menu costs (New-Keynesian approach) (an alternative:
rigidity of the nominal wage due to the existence of wage
contracts)
This implies to consider imperfect competition in the good
market: monopolistic competition in the line of Blanchard
and Kiyotacki [1897], American Economic Review
Nominal rigidities + monopolistic competition in DSGE:
Hairault and Portier [1993], European Economic Review
4. Monopolistic competition and nominal rigidities
Firms have monopoly power due to good differentiation.
Prices include a mark-up over the marginal cost.
Firms maximize profit by taking into account the effect of
prices on the good demand.
The demand for good j is a proportion of the total demand
which depends on the relative price of good j:
The total demand for good j is then:
4. Monopolistic competition and nominal rigidities
The nominal profit of firm j is:
Due to the presence of adjustment costs on prices, firm
choices are now intertemporal:
4. Monopolistic competition and nominal rigidities
The first-order conditions are :
Prices are not equalized to marginal costs:
4. Monopolistic competition and nominal rigidities
The first-order conditions are:
The money supply process is:
4. Monopolistic competition and nominal rigidities
The Solow Residual is no longer a pure measure of
technology. The factor elasticities are not consistently
measured by factor shares in total revenues due to the
existence of markups.
The naive SR is contamined by money supply shocks as
these latter make markups counter-cyclical in the business
cycle
After a money supply shock, firms want to increase prices
in order to leave unchanged their mark-up. As there exist
adjustment costs on prices, prices do not increase as much
as invariant mark-up would imply. Markups are weaker than
at the steady state.
5. Financial imperfections
Limited participation and money supply shocks
Fuerst [1992], Journal of Monetary Economics, Christiano
and Eichenbaum [1992], American Economic Review
The nominal and real interest rates decline after a positive
monetary shock in empirical studies
5. Financial imperfections
The nominal and real interest rates decline after a positive
monetary shock since the supply of deposits is pre-
determined
Firms rent wages
R
Dd, Ds
5. Financial imperfections
Financial Accelerator, Carlstrom and Fuerst [1997],
American Economic Review, Bernanke, Gertler and
Gilchrist, Handbook of Macroeconomics
Entrepreneurs have access to a risky project. Lenders have
no information about the ex-post return. They have to pay a
verification cost.
The optimal contract is then a debt contract. The debtor
interest rate depends on the entrepreneur’s wealth.
Serial correlation of output growth depends on the agency
costs:
6. Sunspot and fluctuations
Self-fulfilling propheties, Farmer and Guo [1994], Journal of
Economic Theory
Animal spirits at the heart of the business cycle
Extrinsic shocks vs. Shocks on fundamentals
Indeterminacy of the equilibrium: too many eigenvalues inferior to
1 (more than the number of pre-determined variables).
Sunspot equilibria can arise in this case.
This approach must be distinguished from news about the future
of some fundamentals, see Hairault, Langot and Portier [1997],
Journal of Economic, Dynamics and Control, Beaudry and Portier
[2006], American Economic Review
6. Sunspot and fluctuations
Final good is produced by using intermediated inputs
Production of these inputs under increasing return to scale
and monopolistic competition
The reduced form of the model is :
with
6. Sunspot and fluctuations
If the labor elasticity is small enough relative to a, ie the
labor demande curve is increasing with a slop superior to
that of the labor supply curve, the eigenvalues are strictly
inferior to one and sunspot equilibria exist
7. Business cycle costs
Stabilization of business cycle? What does it mean in the DSGE framework?
Welfare criterion must be considered, and not volatility criterion, especially the output volatility
Business cycle costs are very small in terms of stationary consumption; eliminating all fluctuations is equivalent in welfare units to 0.008% of the steady state consumption, Lucas [1987], Models of Business Cycles, Basil Blackwell.
This implies that the distorsions introduced by the stabilization policy must be very small too.
Harberger triangles could be much more important than Okun gaps, Greenwood and Huffman [1991], Journal of Monetary Economics.
« I argue in the end that, based on what we know now, it is unrealistic to hope for gains larger than a tenth of a percent from better countercyclical policy » Lucas [2003], American Economic Review