6

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 that there is a continuum of differentiated goods represented by the interval [0,1] and each firm is producing one of the goods. You can imagine that there are ...


6

Gali's Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework, provides an advanced undergraduate / first-year graduate student introduction to these models, and I'd recommend it for self studies. According to chapter 1, available online, which offers an overview of the New Keynesian Model, the key elements are: ...


5

Check out the following: Jordi Gali; Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework David Romer; Advanced Macroeconomics Michael Woodford; Interest and Prices: Foundations of a Theory of Monetary Policy The first two will ground you in the theory of nominal rigidities and the business cycle. Woodford's ...


5

Michael Woodford's book Interest and Prices, while it may not be explicitly New Keynesian, may have some of the rigor you're looking for applied to this class of models. A more direct alternative would be New Keynesian Economics edited by Mankiw and Romer. While it's a collection of papers not a textbook, if you're looking for underpinnings of New Keynesian ...


5

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 aggregate consumption, and utility is given by $u \left( \bar{C} \right)$. It's easy to check that the marginal rate of substitution between goods $j$ and $k$ is ...


4

This journal article (Oct 29-2011,) has parts from a telephone conversation of the journalist with Sargent: http://www.nytimes.com/2011/10/30/your-money/thomas-sargent-nobel-winner-rejects-philosophical-slogans.html Although none of it mentions "New-Keynsian", there are some interesting points, like "Professor Sargent said he felt insulted by people who ...


4

Drago Bergholt has all math steps for Gali's book: The Basic New Keynesian Model


3

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 goods - the marginal rate of substitution. A (benevolent) social planner does not need those prices, as goods will not be traded in the market, but simply ...


3

Yes. In the core New Keynesian model in Galí, it is possible for the aggregate profits of intermediate good producers to be zero or negative; and it is even more likely that the profits of individual intermediate good producers, who may be stuck at prices far from the optimum, will be negative. Since it's easier to characterize the aggregate, I'll discuss ...


3

One book which I have used and which has an excellent chapter on NK-DSGE models is Monetary Theory and Policy by Carl E. Walsh. Even though he only has one chapter on NK-DSGE models (50 pages or so) the chapters before discuss staggered price and wage setting models used in the NK-DSGE models. He also has chapters discussing the Sidrauski MIU model and the ...


3

I've just found Michael Wickens' Book and George Mccandless' ABC of RBC. Wickens leaves the stochastic element of the DSGE's model out of the picture, so I'm not sure if it's a good book. McCandless book has great reviews. I took a peek and it seems to be really good pedagogical tool. It may really be a good buy.


3

I will try to answer this question although it is rather hard using only one paragraph, if not impossible. A paragraph explaining what New-Keynesian Economics is: Models explaining price and wage stickiness using rational expectations and utility maximizing behaviour. See Gordon, R.J, 1990 for more details. For a defining equation the New-Keynesian ...


3

Mathematically speaking, we are not sure. The infinite sums mentioned is of the form $$E_t\sum_{k=0}^{\infty}\gamma^kX_{t+k},\;\; 0<\gamma<1$$ The fact that there is the declining factor, $\gamma^k$, provides some comfort that the sum converges, but from examples like the harmonic series we know that even if $\lim_{k\rightarrow \infty}\gamma^kE_tX_{t+...


3

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 $C_t(i)^{1-\gamma}$ with $C(i)+(1-\gamma)C(i)^{1-\gamma}\tilde{c}_t(i)$ i get (subtracting Steady State values): $(1-\gamma) C^{1-\gamma}C \tilde{c}=\int_0^1 (1-\...


3

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: $$\ln (XZ)=\ln X + \ln Z$$ $$\ln X/Z= \ln X - \ln Z$$ $$\ln X^a = a \ln X$$ $$\ln 1 = 0$$ Also an important approximations that hold close to zero are applied here as well these are: $\ln(1+x) \approx x $ for $x$ ...


2

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'd be feedback between nominal interest rates and inflation, which both feed into each other for example. So in that sense I'd consider the approximation of ...


2

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 star) or equivalently in inflation terms. We do not have price stickiness if the current inflation equals the optimal inflation: $$\pi_t = \pi^*_t$$ Looking ...


2

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 real interest rate to go down. When the real interest rate goes down, the real exchange rate depreciates, both lead real monetary conditions to loosen. [Real ...


2

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 gap tends to zero in the long run, inflation will perfectly determine next period's inflation, so monetary policy that affects inflation in the short run cannot ...


2

$$(\sum_{k=0}^\infty \theta^k E_k(Q_{t,t+k} Y_{t+k|t} (P_t^*/P_{t-1} - \alpha MC_{t,t+k} \beta_{t-1,t+k}))) = 0 $$ Log linearize around the zero inflation steady state. $$p_t^* - p_{t-1} = (1 - \beta\theta) \sum_{k=0}^\infty (\beta\theta)^k E_t(\widehat{mc}_{t+k|t} + p_{t+k} - p_{t-1}) $$ Where $$\widehat{mc}_{t+k|t} \equiv {mc}_{t+k|t} - mc$$ In other ...


2

I often dip into "advanced undergrad" texts when I really want something broken down. Sometimes they deliver, sometimes not. With that beaming endorsement, I'll offer this suggestion: pair Romer's Advanced Macroeconomics, with Jeffery Parker's Coursebook (for Romer) for Macro Theory at Reed College. His coursebook takes the time to really work through some ...


2

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 powered by coal? Heck, how many coal-trains are still operational? So yes, we do forget our past discoveries and technologies, as they are replaced by new ...


2

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 on fish wars), although I have also seen it used for value functions when there is no strategic interaction. In such problems one is typically looking for a ...


2

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 regards to social justice. These are some great texts coming off of reading Hayek. If you aren't familiar with the concept of adaptive preferences, it is the idea ...


2

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 $x_t=E_tx_{t+1}$ and $x_t=0$ for all $t$ is a solution which is consistent with the dynamic equation. (Note that other solutions are consistent with the dynamic equation in ...


2

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. $$\pi_t=\beta E_t\pi_{t+1}+\kappa x_t,$$ and where $\kappa=0$ if no firm change their prices, and $\kappa=\infty$ if all firms change their prices. (Technical note: Here I ...


2

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-degenerate price level (nominal!) is compatible with such model structure, as its system is written down in growth rates, as that's what loglinearised variables ...


2

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 level. Neoclassical economics: Steady state output is achieved when capital-labour ratio is stable or constant. In steady state, economy is not growing and also ...


2

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 just use the following: $$s_t=\ln(S_t)$$ And use the well known fact that for small values of $i$ the following approximation holds: $$\ln(1+i)\approx i$$ And ...


1

At least in environmental and resource economics it is because it internalizes all externalities. If there is only a single person to consider (and the payoff of this person is "made up" of the sum of individual welfare) than by maximizing the sum all externalities get accounted for.


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