RBC Flashcards
Formulate the competitive EQ
See L1. p.34
Set of allocation {choice variables}
and prices {w,R}
such that given
{prices}, {choice} solves the HH problem
and {prices}, {choice} solves the firm problem
given
Market clearing conditions.
What is the law of motion of capital
I_t = k_{t+1}-(1-δ)k_t
What does and dosen’t the RBC model get right when compared to data?
From Macro 1:
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.
How does a TFP shock affect the RBC economy?
TFP goes up, output jumps:
When output jumps, it creates an wealth effect with makes consumption increase.
With consumption smoothing, savings increase, i.e., investment jumps.
when TFP increases, wages and current interest rates jumps.
As Wages jumps, hours worked increase (the is the only amplification).
Then as expected returns to savings decline, HH like to decrease savings, this has an dampening effect.
What is Business cycle accounting?
Business cycle accounting is an accounting procedure used in macroeconomics to decompose business cycle fluctuations into contributing factors.
The underlying premise of the procedure is that the economy has a long-run trajectory that is perturbed by various frictions. These are called wedges and the earliest version of the procedure includes a productivity wedge, a labor wedge, an investment wedge, and a government consumption wedge. Business cycle accounting decomposes fluctuations in macroeconomic variables, such as GDP or employment, into fluctuations of each of these wedges (and their combinations).
The method rests on the insight that many models are equivalent to a prototype growth
model with time-varying wedges which resemble productivity, labor and investment taxes, and government consumption. Wedges corresponding to these variables efficiency, labor, investment, and government consumption wedges–are measured and then fed back into the model in order to assess the fraction of various fluctuations they account for.
Give an example of BCA and the Solow residual in terms of output, consumption and labor supply?
We have this model
$$
\hat y_t =\hat c_t\gamma(1+\hat n_t)
$$
But this does not fit the date. Then we say that the $\psi^N_t$ is the wedge (Solow residual).
$$
\hat y_t =\hat c_t\gamma(1+\hat n_t)+\psi_t^N
$$
That is, we try to explain the volatility, but this volatility does not fit the model. Thus, by e.g., adjusting the Frisch elasticity $\gamma$, we might reduce the wedge/residual.
Remember that the Solow residual isthe portion of an economy’s output growth that cannot be attributed to the accumulation of capital and labor, the factors of production. The Solow residual represents output growth that happens beyond the simple growth of inputs.
In the RBC framework, what is meant by “capacity utilization”?
Firms don’t utilize all their capital and labor at all times. That is, they adjust the usage of their predetermined factors of production over the business cycle. Low utilization = low TFP.
Thus we can measure (input data or electricity usage) capacity utilization and use it as a proxy for TFP. We can also study how much inputs the firms are buying.
In the RBC framework, what is meant by “Misallocation”
Market frictions which makes it hard for production to move where production is most efficient.
A standard calibration of the vanilla RBC model with a reasonable technology shock process has quite a few problems with matching the data. The lack of empirical fit is manifested in large fluctuations in the labor wedge and the efficiency wedge (and also the government consumption wedge):
- Relatedly, too little amplification and lack of persistence
- Does not produce reasonable fluctuations in hours worked
What following two extensions help to improve the fit of the model?
Employment lotteries (RBC extension)
Variable capacity utilization (RBC extension)
What is the easiest way to increase the amplification and flucturation due to “hours worked” in the RBC model? Why is this no a reasonable method?
This is easy to do by increasing the labor supply elasticity (Frisch elasticity ). However, the literature suggest that the intensive margin labor supply elasticity only is about $\eta\in(0,0.5)$.
Therefor we instead use the “employment lotteries extension” which is one which incorporate labour supply at the extensive margin.
Describe the Employment lotteries (RBC extension)
This is an extension of the RBC model that serves the purpose to increase the amplification due to “hours worked”.
The “employment lotteries extension” is one which incorporate labour supply at the extensive margin. That is, households choose to work or not (or full time vs half time).
We have N_t = {0,\bar{N}} rather than
We have N_t \in [0,\bar{N}] rather than
This is basically a way to motivate using a frinch elasticity = infinity (\phivar = 0). That is, infinity elasticity is that you rejact by working the maximum level or not work at all.
Apparently, in complete markets, households would be better off if they where to collude and entered a lottery with other households on wether to work or not. Therefor, this extension incorporates a work lottery where households work and get the disutility of this with prob $\alpha$ or not work with prob $(1-\alpha)$.
Apparently, the key thing with employment setup is that we go from having convex disutility to linear disutility.
That labor markets are organized through lotteries is of course a bit hard to swallow,
but the lottery part is not really fundamental, it is rather the indivisibility.
The lottery convexifies the choice set ⇒ we can proceed with our F.O.C.s as usual. Because, otherwise it is super-complicated to solve the model.
This extension then help us explain the data with the RBC model
What are the problem with the Employment lotterie-approace?
If we observe that someone doesn’t work in a recession, should we interpret that as a voluntary choice? Isn’t involuntary unemployment the main reason we are concerned with recessions?
Explain the variable capacity utilization (RBC extension)?
The Volatility of our TFP shock process should be lowered due to variations in capacity utilization. In this extension, we add capacity utilization in to the model. This will affect the level of output holding production factors constant ⇒ speaks directly to the efficiency wedge.
The fact that firms do not always operate at full capacity indicates that marginal cost is increasing in utilization.
The key in this model is that we say that capital depreciation is a function of capital utilization. That is $\delta = \delta(U_t)$ and that households utilization level of their renting out capital is $K^*_t = U_tK_t$.
This yields more variation in the capacity utilization and thus more 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 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.
