McMahon Flashcards
Equilibrium requires…
- given rt, wt, the allocation satisfies the household problem for each group
- firms maximise profits
- markets clear
OLG pareto improvement
transfers from young to current old
In OLG, which type of technological progress can produce a balanced growth path consistent with Kaldor facts?
Labour-Augmenting: yt=f(Kt,AtLt)
Key is to write the law of motion in terms of Kt+1/At+1 and then not much changes
Kaldor Growth Facts
- Output per worker grows at roughly constant rate (though now seems lower than before but anyway)
- Capital per worker grows over time
- Capital/output ratio roughly constant
- Rate of return on capital constant
- Share of capital and labour in net income roughly constant
- Real wage grows over time
- Constant ratios of consumption to GDP and investment to GDP
Household problem (Ramsey)
Max ∫e^(−(ρ)t)*u(ct)dt
s.t. kdot=wl+rk+profits-c-δk
Hamiltonian
H= u(ct)e^(-pt) + μt(what kdot equals)
FOC: control: …=0
FOC: state: …=−μ ̇t
(These will be good to practice)
Look up TVC
Done this yet?
Features of Ramsey capital driven growth
- Interest rates fall over time as k increases
- Growth rate of output declines (to 0 in the limit)
- Capital to labour ratio grows
(These are not in line with Kaldor facts)
Foreseen shocks in the future
Must get to new saddle path by date the economy changes. Must get there by obeying existing (old) laws of motion
Why is there no growth in typical Ramsey model?
Convergent dynamics caused by decreasing returns to capital
AK model
No steady state but balanced growth path with constant ratio of consumption to capital
(This BGP is not stable as must always have ratio equal to discount rate ρ)
Why is BGP unstable
if g>r, violates the TVC => always growing not discounting so discounted final value of K0 is not 0 => ponzi scheme
if g
Ways of microfounding AK
Knowledge externalities
Learning by doing
Human capital accumulation
Varieties incentives model
Efficient?
Fixed varieties: Profits in intermediate goods, no growth
Endogenous varieties: can create new variety at a cost, growth rate g, depends on scale as profits depend on size of market
Both types are inefficient:
Monopoly supplier produces too few intermediate goods
Growth rate also below optimal
Acyclical macroeconomics variables
wages, government spending, capital stock
Ct and Nt both procyclical only if
wt is procycylical
But wt is modestly procyclical so will need strong substitution way from leisure towards consumption to follow an increase
inter-temporal and intra-temporal FOCs (RBC)
Inter: usual Euler
Intra: 1st derivative wrt C *wt=1st derivative wrt leisure
To get labour to be more variable than output, one needs ? in their RBC model
procyclical savings rates
Problems with special case RBC
Don’t get:
- pro-cyclical savings rates
- pro-cyclical labour effort
- large enough output responses
- enough endogenous persistence
Get head around determinacy in computer model with matrices stuff
Done this yet?
Steps to solve RBC model
- Solve for the non-stochastic BGP
- Rewrite model as log-deviations from the n-S BGP
- Study an alternative model that is log linear and an approximation around the n-S BGP
- Interpretation and calculation (made easier if equations are linear in % deviations from steady state)
Log-linearisation options in order of preference
- exact (just take logs)
- use Yt=Y* x e^yt
- e^x = 1+x for small x
- taylor expansion around steady state
7 log-linear equations
- Production function
- Resource constraint
- Interest rate
- Wage
- Labour-Leisure choice
- Euler equation
- Technology
Just adding incomplete depreciation results in IRFs with
Insufficient (but present) employment response
Too short a business cycle
Insufficient consumption response
Wage too procyclical
Adding persistent shock to depreciation
Not much amplification
Output inherits shock’s persistence
Unrealistic consumption dynamics
Even more procyclical wage
adding very elastic labour supply
Gets desired labour supply response but changes little else
very inelastic labour supply IRFs
No employment response
Huge wage increase
Persistence problem
The stochastic growth model is unable to generate persistent effects from transitory shocks
Amplification problem
Only in extreme cases does y go go up/down more than one-for-one with a change in a
Slower than normal but still positive technological growth can cause output growth to grow slower but not fall (would need negative tech shock)
Hump-shaped response problem
VARs suggest output responses to transitory shocks are hump-shaped but RBC models tend to generate monotonic responses
Blanchard-Kahn Condition
For stability, number of unstable eigenvalues= number of controls
If this is not satisfied we have indeterminacy so model cannot be solved with this technique
What is the problem with labour supply inelasticities in the model compared to the data? How can this possibly be reconciled with the model?
Data estimate elasticity of around 1, model requires around infinity
Either have to argue that the volatility of wages is underestimated or elasticity is underestimated
3 types of model to reconcile labour problem
- Lotteries
- Efficiency wages
- Search
Lotteries results
Hours almost as volatile as output (good)
Hours and wages strongly correlated (bad)
In efficiency wage models, the no-shirking wage increases if
e increases Vu increases q (prob of being caught) decreases discount rate increases b (separation rate) increases
Tobin’s q
Shadow price of installed capital =lambda-mu
investment responds immediately to changes in q
Why is Solow residual probably not an accurate measure of technology?
- Labour hording may happen
- Capacity may not be fully utilised
- TFP growth is predictable by military spending and money supply shocks
- TFP growth -ve a third of the time (do we really forget stuff all the time!?)
Taking this into account, models predict small and countercyclical Solow residuals
