RBC Flashcards
What is the fisher elasticity
The formula is given by
dn/dw w/n = (1-n)/n
or
e_nw = (1-n)/n
and is derived from the trade of condition.
The elasticity tells us how the labor supply changes on the margin when we change the wage just a little bit. That is the change in working hours due to a change in wage. Empirically, this elasticity should be about 0 - 0,5.
What is the pros and cons of the RBC model
The model produces a good account of US economic activity, especially for macro quantities
It produces an economy nearly as volatile as in the data. More precisely, In Kydland and Prescott original computations, it accounts for 77% of business cycles fluctuations.
It is consistent with the observed large variability of investment relative to output and lower volatility of consumption relative to output.
It captures the observed comovement between macro variables.
Some other features are less good (especially true for prices):
Consumption and hours much less volatile than in the data. Not enough
volatilities in prices.
It does not generate enough persistence nor amplification. The only amplification mechanism here is labor supply, and it is
fairly weak. The only persistence mechanism in the model is capital accumulation, but this is weak as well.
What is the RBC-model and how does it stand empirically?
An infinite horizon DSGE Representative agent model with leisure, a production sector, and technology shocks.
It is an stochastic (supply side factor are source of fluctuations in b-cycles) infinite horizon model.
The model’s empirical performance is anchored to three main ingredients:
- highly persistent and sufficiently volatile technology shock
- a sufficiently elastic labor supply
- empirically reasonable steady-state shares of consumption and investment in output.
This simple model performs surprisingly well, even though it does not generate enough persistence or amplification.
What do we mean by amplification and persistence in the RBC?
Amplification denotes a model’s ability to have output react by substantially more than the exogenous shock, i.e. “small” shocks can generate “large” fluctuations. The only amplification mechanism here is labor supply, and it is fairly weak.
Persistence denotes a model’s ability to make shocks have persistent effects. The only persistence mechanism in the model is capital accumulation, but
this is weak as well.
What are the choice variables in the RBC model?
Consumption, leisure (1 - labor) and capital next period.
How do agents derive utility for labor in the RBC model?
work (n) provides indirect utility by generating income for consumption.
What is the basic setup in the RBC model? I.e., what actors do we have, and what do they want to do?
HH that choose between consumption and leisure.
Firms choose inputs of production to maximize profit.
We assume that HH owns capital and firms rent it from them, i.e., the firms maximisation problem is static.
Productivity is stochastic and cycles are supply driven.
How do we theoreticly solve the decentralized and the centralized version of the RBC model?
Are the solutions different?
In the decentralized equilibrium, we should solve households’ and firms’ decision problems separately and then impose the mkt clearing conditions.
In the centralized equilibrium, a benevolent social planner, chooses allocations to maximize agents welfare. The social planner is subject to the resource constraint.
▶ In absence of distortions, solving the decentralized problem or the problem of a benevolent social planner yields the same solution (First Welfare Theorem).
What is HH BC in the RBC that we have used in class?
k_(t+1) + c_t = w_t n_t + (1+r_t)k_t
Where n is the labor supply.
k_(t+1) is the investment in capital.
What is the impact of an increase in wages on labor supply in the RBC-model?
Conditionally on (the marginal utility of ) consumption, an increase in the wage reduces leisure and raises labor supply (see later how this is measured by the ”Frisch elasticity”)
▶ However, higher labor supply increases income and thus consumption. Two forces play a role:
- Substitution effect. An increase in w induces an incentive to increase labor supply since this factor is better remunerated. (+)
- Wealth/Income effect. At the same time, there is an opportunity to consume the same quantity of goods by working less.(-)
The total effect is ambiguous and depends on the utility function.
With log-utility, SE and IE cancels.
Det är så enkelt som att det är det klassiska med SE och IE. Detta är ju det mest klassiska som vi alltid pratar om vid labor supply.
What is the replication argument? How can it be used to rule our DRS in a production function?
We can rule out decreasing returns to scale using a replication argument, i.e. if a certain output level can be produced from given inputs, it should be possible to double all inputs and obtain at least double output by just doing the same thing all over once more.
“The standard replication argument is a fundamental justification for constant returns to scale in production. If we wish to double the production of computers from a factory, one feasible way to do it is to build an equivalent factory across the street and populate it with equivalent workers, materials and so on.” Paul Romer.
What is the firms problem in the RBC?
Max profit.
Max PY - C(k,n)
Max_k,n F(k,n) - (r+δ)k - wn
Where Y = F(k,n) and we output-normalize price to one.
What nice feature do we derive in a competetative market with CRS technology?
F = F_k k + F_n n
How do we derive the recourse constraint in the RBC model?
With HH BC:
K_t{+1} + c_t = w_t n_t + (1+rt)k_t
F_k = r+δ
F_n = w
First, remember that with CRS
F=F_k k + F_n n
Then
kt+1 + ct = wtnt + (1 + rt) kt ⇒
kt+1 + ct = Fnnt + (1 + Fk − δ) kt ⇒
ct + kt+1-(1-δ)kt = F (kt , nt)
Where ct + kt+1-(1-δ)kt = It
ct + It = F (kt , nt)
How do we compute the soliw residual z_t in the RBC model with CD-technology?
Take log of the production function and re arrange to have log(z) alone on the LHS.
Log zt = log yt − α log kt − (1 − α) log nt
