6
votes
Accepted
Basic New Keynesian Model: Why variables are defined by integral equations
First of all, this is not something special to "the basic New Keynesian Model". It is a commonly used technique when modeling an economy with competitive environment.
In your case, the author wrote ...
- 196
6
votes
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Intuition for the CES consumption index in New-Keynesian DSGE models
Heuristically, you can think of the integral as just a sum:
$$ \bar{C} = \left( \sum_{i=1}^n C_i^{1-\frac{1}{\epsilon}} \right)^{\frac{\epsilon}{\epsilon - 1}} $$
where $\bar{C}$ is an index of ...
- 2,156
4
votes
Accepted
Log-Linearizing a Dixit-Stiglitz function
Thanks for the hint and the link! I think I now managed to find the solution.
Putting the exponent on the LHS and replacing
$C_t^{1-\gamma}$ with $C+(1-\gamma) C^{1-\gamma}C \tilde{c}$
and
$C_t(...
- 870
3
votes
Accepted
Log linearising EUler equation
As you say the first step is to take log of both sides after that you are just applying the rules for logarithms and rearrange.
For example:
$$\ln (XZ)=\ln X + \ln Z$$
$$\ln X/Z= \ln X - \ln Z$$
$$\...
- 54.4k
3
votes
Accepted
Why solving the model for a benevolent social planner gives an efficient allocation?
I think the general proof is in this paper.
Thinking in a simple exchange Edgeworth Box, a competitive economy involves prices, which mediate the relationship between consumers relative valuation of ...
- 8,581
2
votes
Accepted
Natural real interest rate and output gap
Regarding you first question, the answer is 'yes', at least in your model. For if the real interest rate, $r_t=i_t-E_t\pi_{t+1}$, is equal to its natural level $r^n_t$, then in your model $x_t=E_tx_{t+...
- 973
2
votes
Accepted
Phillips curve and flexible prices
The New Keynesian Philips Curve (NKPC) may be derived using price settings frictions introduced by Guillermo Calvo. The NKPC can under such conditions be written as you write it, i.e. $$\pi_t=\beta ...
- 973
2
votes
Accepted
Taylor rule and optimal monetary policy
I'm not sure I fully understand what you mean by computing it endogenously? The nominal interest rate would be endogenous in the NK framework because the output gap and inflation are endogenous. There'...
- 361
2
votes
Accepted
A general formulation to capture price stickiness
I will answer the first question, I believe the second one can be found in the book's appendix.
"Price stickiness" is defined with respect to the optimal price level for the period (here denoted by a ...
- 33.4k
2
votes
Monetary Transmission in New Keynesian - Euler Equation
Real interest rate = Nominal interest rate - Expected inflation
Reducing the nominal interest rate by more than the decline in the expected inflation, with respect to the inflation target, leads the ...
- 53
2
votes
Long run trade off between inflation and output
Note that if $\pi_t = E_t\pi_{t+1}$ (current and expected future inflation are equal) then
$$\pi_t = E_t\pi_{t+1} + h(y_t-y_t^*) \implies 0 = h(y_t - y_t^*) \implies y_t = y_t^*$$
So as the output ...
- 6,578
2
votes
What does it mean for a technology to have a $|\rho|<1$?
New technology makes past technology obsolete. How many people know these days how to light a fire by rubbing wood together? How many people know the nuts and bolts of tending to the engine of a train ...
- 33.4k
2
votes
Guess and verify?
As Dave Harris commented it depends a bit on the context. I know the guess and verify solution method mainly from solving value functions in differential resource games (more specifically the papers ...
- 2,375
2
votes
Accepted
Keynesian Ethics
If you enjoy ethical and philosophical aspects, you should look into international aid and intervention. Check out "Adaptive Preferences and Women's Empowerment" by Khader and work by Nussbaum in ...
- 141
2
votes
Good paper/article on the mechanisms in RBC vs New Keynesian models
If possible, clarifying what exactly you're most interested in might help answers be more on point and useful. Are you interested in the mechanisms that cause a one-period shock to last (and not just ...
- 1,370
2
votes
Accepted
Basic New Keynesian Model - Price and Wage Level after shock
Try to give a look at what happens to inflation's IRF. If it stays positive for the whole horizon of the IRF then simply prices have increased over time at the inflation rate. I guess that any non-...
- 106
2
votes
What are the assumptions of real business cycle theory and Keynesian theory?
The distinction is between "nominal" and "real" recessions and booms.
Real business cycle theory was developed to point out the fact that variations in employment and hours could occur even in an ...
- 691
2
votes
Log-linear version of the uncovered interest rate parity
It’s derived as follows. First start with original equation.
$$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$
Take natural logs of both sides:
$$\ln(1+i_t)=\ln(1+i^*_t)+\ln(S_{t+1}) -\ln(S_t)$$
Now you ...
- 54.4k
2
votes
Accepted
How to interpret the difference between natural level and steady state in Macroeconomic theory
Natural level of output is equivalent to full employment output. This does not mean full employment of all resources, there is always a natural level of unemployment even in full employment output ...
- 1,990
2
votes
Accepted
Why is Keynes attacking the (neo)classical theory of interest rates on the grounds that it is indeterminate?
You can use some some initial $Y_0$ to find an interest rate, but this is precisely the indeterminacy problem. We would like to be able to derive the equilibrium interest rate without assuming some ...
- 54.4k
2
votes
Accepted
Max of a profit function: partial derivative of an integral function?
You are really asking about the marginal product of a CES production function.
The LHS of your second equation is $P * dY/dY(i)$ where $Y_t$ is a CES aggregator of the $Y_t(i)$.
Let's define $\rho = \...
- 216
2
votes
Intuition for effect of interest rate changes in New Keynesian model
Yes the 'standard story' you reference is the correct intuition here. Lower nominal interest rate encourage consumption which puts pressure on both output and prices.
Household can actually save and ...
- 54.4k
2
votes
Accepted
The new Keynesian IS curve: What determines output?
The solution to your question is price stickiness, or as the author calls it staggered pricing. Let's assume a typical question in the Basic New Kenesian DSGE Model: What happens when a technological ...
- 520
2
votes
About marginal cost setting on Jordi Gali's work
The equation is in logs. Thus,
$$MC_{t}=\frac{W_{t}/P_{t}}{MPN_{t}}$$
$$mc_{t} = w_{t}-p_{t}-mpn_{t}$$
And after that use
$$MPN_{t} = (1-\alpha)\frac{Y_{t}}{N_{t}} = (1-\alpha)A_{t}N_{t}^{-\alpha}$$
...
- 21
2
votes
Basic New Keynesian model with flexible price
I think what you are looking for is a standard RBC-model. Because the main step, going from RBC to New Keynesian, is to include Calvo pricing among other things. This is covered in many textbooks like ...
- 61
2
votes
Accepted
Deriving optimality conditions in the New Keynesian model framework with an undefined consumption function
I'm not quite sure what $Z$ stands for in this model (looks like some kind of multiplier over the standard utility) but I can generally guess the rest. $C$ stands for consumption, $L$ for real money ...
- 153
2
votes
What are the major flaws of the RBC model and how does the New Keynesian model address them?
Following Galí (2015, p.3) the RBC model rests in three major assumptions: i) the efficiency of business cycle, ii) technology shocks as source of economic fluctuations, iii) the limited role of ...
- 821
1
vote
How were unit labor costs estimated by Gali and Gertler (1999)?
In Galı́ & Gertler (1999) the authors state that marginal costs is given by:
$$MC_t = \frac{S_t}{\alpha}$$ where $\alpha$ is the labor elasticity (from the Cobb-Douglas prod. function), and $S_t$ ...
- 54.4k
1
vote
Accepted
Why Keynesians prefer short run measures despite straight long-run Phillips curve?
Actually both New Keynesians, Keynesians and Monetarists are advocating for short-run government activism, just the underlying mechanisms are different and Monetarists stress monetary over fiscal ...
- 54.4k
1
vote
Accepted
Why consumption is defined as $ C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}} $
For some reason Ubiquitous edited this information into the question, rather posting it as an answer:
$i$ indexes the goods available for consumption
Integrals are just sums with a lot of ...
- 28.6k
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