Nick Bloom Micro-heterogeneity & Macro, general equilibrium
-
Upload
jana-townsend -
Category
Documents
-
view
44 -
download
1
description
Transcript of Nick Bloom Micro-heterogeneity & Macro, general equilibrium
Nick Bloom, Macro Topics, Spring 2007
Do micro distributions matter for macro outcomes
Probably the greatest unanswered question in macro is how to get a tractable micro-to-macro model.
Currently the battleground is in general equilibrium models
First overview the basics, and then discuss a couple of key papers
Nick Bloom, Macro Topics, Spring 2007
The easy life under partial equilibrium
In partial equilibrium models each firms solves its own problem, for example solving for capital and labor:
V(K,L,A)=maxK’,L’{F(A,K’,L’) – wL - C(K’-K,L’-L) + (1/(1+r))*E(V(K’,L’,A’))}
The key assumption is wages (w) and interest rates (r) are fixed.
This allows you to ignore the interaction between firms
Bertola, Caballero, Engel etc.. all do this in their earlier work for numerical simplicity, but is this valid?
Nick Bloom, Macro Topics, Spring 2007
The problem is the curse of dimensionallity
In general equilibrium each firm is still assumed to be solving its own profit maximisation problem.
But now wages and prices are functions of the cross-sectional distribution (m) so that w=f(m), r=g(m):
V(K,L,A,m)=maxK’,L’{F(A,K’,L’) – w(m)L - C(K’-K,L’-L) + (1/(1+r(m)))*E(V(K’,L’,A’,m))}
This problem is now a lot tougher – every firm has to keep track of its own state variables and every other firms state variables.
So if you have 3 states (K,L,A) and N firms, that 3N states!
Nick Bloom, Macro Topics, Spring 2007
Solving models under General Equilibrium
This is called the “Curse” because its exponential in N•If it takes a XGB to solve for 1 firm, it will take XNGB to
solve for N firms.
Hence lots of computing power alone is never going to solve this
So the trick is to somehow approximate this cross-sectional distribution in a way that:
•Reduces it down to something finite and managable•Does not dramatically change the GE flavor of the solution
Anything that does this is also easily defensible under bounded rationality – most individuals/firms also approximate life….
Nick Bloom, Macro Topics, Spring 2007
Per Krusell and Anthony Smith (1998)
“Income and wealth heterogeneity in the macroeconomy”
Journal of Political Economy
Nick Bloom, Macro Topics, Spring 2007
Overview
Undertakes a GE estimation of the effects of wealth distribution on the economy
The fundamental idea was to:•Approximate the cross-sectional distribution using
moments•Use this to operationalize a Recursive Competitive
Equilibrium (to be explained more in a minute)•Also combined different parameters to fit actual data better
An important paper:(i) First paper to undertake this GE approximation(ii) Shares the code for this and provides sufficiently good instructions for others to follow – always do this!
Nick Bloom, Macro Topics, Spring 2007
A Recursive Competitive Equilibrium - Theory
In short this makes sure three sets of conditions are met:
1) Firms and households are optimising given:•Market prices (typically wages and interest rates)•Expectations over evolution of aggregate and cross-section
2) Market prices clear the goods and labor markets
3) Expectations are consistent with outcomes
Nick Bloom, Macro Topics, Spring 2007
A Recursive Competitive Equilibrium - Practice
Numerical solutions assume you can approximate the expectation of distributions. They reformulate using this approximation
This assumes bounded rationality due to computational costs
Important to test this by confirming that the value maximisation for firms and agents is only reduced marginally by the approximation
With this approach you then numerically solve recursively:
Solve for (1, value functions) and (2, market clearing) jointly given an assumption on (3, distributions). Then simulates data for (3, distributions). Then use this simulation to re-solve (1, value functions) and (2, market clearing). Then simulate (3, expectations) again, and continue to loop until you converge
Nick Bloom, Macro Topics, Spring 2007
Solving Recursive Competitive Equilibrium models
Unfortunately there are no results showing that approximate numerical solutions to RCEs with fixed-costs are well behaved:
•A solution exists•This is unique•The RCE solution mechanism outlined earlier will converge
In practice, however, it seems to work. But anyone that can make progress on showing any of the above will have a winning paper…
Nick Bloom, Macro Topics, Spring 2007
The Krusell Smith moments approach to RCEs
They use moments to approximate the distribution – appealing as a statistically standard way to describe any distribution
There are other approaches, for example:
• Cabellero and Engel played around with various Characteristic functions (Taylor, Fourier, Chebyshev etc..)
• Khan and Thomas (2004) used uniform histograms
The choice depends really on the support of the distribution to be approximated
Nick Bloom, Macro Topics, Spring 2007
The Krusell Smith results from using moments
In the paper they report finding that only the 1st moment is required for the solution of the model, with higher moments providing no additional fit.
This is also a result that Thomas (2002), Thomas and Kahn (2004), and Bachman, Caballero and Engel (2006) report
My guess is this is not generally robust – for example with time varying uncertainty distributions compress and expand
Another great paper would be to properly evaluate this across many models
Nick Bloom, Macro Topics, Spring 2007
They find no impact of cross-sectional distribution
The main result from KS is that cross-sectional distribution of wealth has no real effect on – approximate aggregation
This is because their utility function is pretty linear for medium and high levels of wealth, so consumption behaviour is roughly linear.
Since consumption (which is individual weighted by wealth) is mostly in the hands of the rich the average agent is linear
If agents are linear higher order moments don’t matter (next slide)
This had a big impact on macro – suggests that “RAs rule OK”
Nick Bloom, Macro Topics, Spring 2007
Remember our old friend from last time…
Aggregate investment
Adjustment hazard
Distribution of plants
Mandated (desired) investment Year
If the response function (the adjustment hazard for investment and the MPC for consumption) is constant (linear in the gap/wealth) then distributions does not matter
Nick Bloom, Macro Topics, Spring 2007
Message is – at least for consumption - micro-distribution appears not to matter
Good paper – how could you build on this:
•Topic – Look at something more non-linear (labor or investment)
•Technique – Use higher moments, these might matter
•Technical – Provide some more formal proofs for RCEs
Nick Bloom, Macro Topics, Spring 2007
Ruediger Bachmann, Ricardo Caballero and Eduardo Engel (2007)
“Lumpy Investment in Dynamic General Equilibrium”
Yale WP
Nick Bloom, Macro Topics, Spring 2007
Overview
Paper estimates micro-to-macro investment in GE setting. In particular revisits the results from Khan and Thomas, finding lumpiness matters
Contribution is:•Demonstrates the impact of micro-macro GE is sensitive to
parameter choices •Provides alternative methodologies for estimating these
parameters•Quantifies separate impact of PE and GE smoothing
Good paper, shows that key results on GE smoothing are very sensitive to a few parameters, plus new techniques
Nick Bloom, Macro Topics, Spring 2007
They follow basic Khan and Thomas (2005) approach
Generally follow the approach of Khan and Thomas
Main points of departure are over parameter choices, particularly:
• Bigger adjustment costs – more lumps (so micro matters more)• More curvature of the production function – curvature means higher option values, so actions now influence the future• Higher intertemporal elasticity of substitution – higher values mean output moves more over time to save adjustment costs• Inclusion of maintenance investment – reduces drift rate so raises the “memory” of the process
Nick Bloom, Macro Topics, Spring 2007
With these alternative parameters they find a major role for micro smoothing
Nick Bloom, Macro Topics, Spring 2007
Key identifying assumption in there is PE at industry level – which allows you to compare PE to GE
Good idea to try and use additional data to identify paramters
They (like me) believe plant level is already partially aggregated
So use industry level data assuming it is fully aggregated, but PE
Volatility of investment rates
Nick Bloom, Macro Topics, Spring 2007
Our old friend – time varying responsiveness index
If you accept the RI is time varying (which I think I do) then this requires additional assumptions:- Time varying cross-section matters (very possible)- Time varying adjustment costs (less likely)- Other time varying factors in the model (need to introduce these)- Other time varying shocks – uncertainty….
Nick Bloom, Macro Topics, Spring 2007
Message is parameter choices matter a lot in determining micro-macro aggregation effects
Good paper – how could you build on this – similar to earlier, plus:
•Modeling – Include other adjustment costs (quadratic and linear), allow for labor adjustment costs or even technology vintages
•Technique – evaluate impact of using higher moments (is there any way to get them to matter?)
•Identification – robust ways to estimate the underlying parameters
•So what – push beyond time varying RI to look at major shocks (tax credits etc), when this would be really valuable