5

In theoretical modeling the consistency is applied in the same way as in philosophy/logic. Internal consistency simply means that the argument is consistent with itself and has no contradiction within itself (as opposed to external consistency where its not enough for argument to be valid on its own but it should also not contradict other facts). A simple ...


5

I think you're referring to the decoy effect. A popular example of this is the Economist subscription puzzle, popularized in Dan Ariely's TED Talk (starting at 12:22).


4

Yes the $z(t)$ column vector, as it appears in $(4)$ is written upside-down in the translation. Also the first equation in $(2)$ is translated lagged once, i.e. the translated system describes the $w(t-1)$ equation. Finally there is a typo in the $\Gamma_1$ matrix, there is a void 6th column that should be ignored, and $\theta$ should be in the 4th column ...


3

Two notes. A. "Conditioning on information" has always been applied in economics without much attention to probability theory-rigor, because it has (indeed) such a strong intuitive sense: "based on the information I have (where "information" here means data, processing algorithms, psychological makeup, almost anything) I somehow form ...


2

Suppose you have a dynamic system $$ x_{t+1} = Ax_{t} $$ with a stationary point (or steady state as used in growth or RBC literature), say, $x^*$, i.e. $x^{*} = Ax^{*}$. Now, consider the following question. Starting from an initial value $x_0$, how many paths are there leading to the stationary point $x^*$? If there is an unique path going from $x_{0}$ ...


2

You have the government's flow budget constraint (re-written in real terms): $b_{t} + m_{t} + \tau_{t} = g + \frac{m_{t-1}}{\pi_{t}} + R_{t-1}\frac{b_{t-1}}{\pi_{t}}$ (1) Now all you need to do is substitute (2) and the policy rules (also, I don't think Leeper's utility function had a $\delta$ but that's not important) and linearise. I.e linearise: $b_{t} ...


2

The idea of a rational expectations equilibrium is more general than BNE. It simply means that the belief system of agents is consistent with the model and incorporates all available information. This abstract idea can be applied for games, markets or other types of interactions. BNE is a solution concept for non-cooperative games. The expectations being ...


2

The two approaches specify the linear rational expectations problem somewhat differently, but one can reconcile the solutions they produce. In addition to the difference in the equation system specification, KW use the "predetermined variables" concept while AM does not. King and Watson (KW) address a model of the form $$ A E_t y_{t+1} = B y_t + C_0E_t ...


2

Depends on what exactly you mean by backward looking component. When people talk about agents being 'backward looking' they often mean adaptive expectations, if that is what you have in mind then answer would be no. However, rational expectations really just require agents to have model consistent expectations (see Snowdon, Vane, & Wynarczyk,(1994). A ...


2

Yes. In general not. Let's say the individual has initial wealth $W$ and the gamble $g$ has payouts $0$ and $G$, each with probability $1/2$. As you say, the certainty equivalent $C$ of the gamble is the amount $C$ with $$u(W+C)=(u(W)+u(W+G))/2.$$ Now the same individual would be willing to pay at most $P$ to enter the gamble, where $$u(W)=(u(W-P)+u(W+G-P))/...


2

This is due to the famous Lucas critique. To make long story short, in the past in the heyday of Keynesian macroeconomics it was quite normal for macroeconomists to just postulate some relationships based on relatively casual empirical observations like for example the Philips curve which says that there is positive relationship between inflation and ...


2

This is not a formal definition, but a useful piece of intuition. I think that the best way to think about it is that when there is uncertainty in a model it arises mainly in two forms either there is information that some agents have, but not every agent has it (private information), or there are truly random events that no one knows (in game theory jargon,...


1

These are many questions. O.k., so let's go step by step: (Q1) What is a mapping actually? A map is just another term for a function. Here, every "law of motion", the actual one (ALM) and the perceived one (PLM), is characterized by its parameters $a$ and $b$. The ALM depends on the PLM, and the function mapping the PLM-parameters to the ALM-parameters is ...


1

$\newcommand{\vect}[1]{{\bf #1}}$ Note that you can write the system in the form $$ \dot{\vect{x}} = A \vect{x} + \vect{b} $$ where $$ \vect{x} = \left(\begin{array}{c} x \\ y\end{array}\right), ~~~~ A = \left(\begin{array}{cc} 1 & 1 \\ 2 & -1\end{array}\right), ~~~~~ \vect{b} = \left(\begin{array}{c} 1 \\ 5\end{array}\right) $$ A fixed point $\...


1

If you are planning on using Dynare, you do not need to "solve" the model using Sim's method. Dynare takes care of the solution algorithm for you. If you want to get to IRFs quickly, I suggest writing up the linearized version of your model in a .mod file, then from Matlab, simply run dynare model.mod. Here are some example .mod files for you to work ...


1

I think I have managed to solve it. However, not the way I was initially hoping. I simplified the stacked matrices using the given conditions and some assumptions. Here is my solution: Eq. (3) I write as $\pi_{t+1} = \alpha \beta \pi_{t} + \beta \theta_{t} + \eta_{t+1}$ Forwarding equation (4) one period and arranging it in terms on $b_{t+1} = -\varphi_{1} ...


1

In fact, saddle path equilibrium is one of the most common equilibrium in canonical growth models, mainly in dynamic optimization problems. It is possible that he makes a reference to a decentralized equilibrium without cycles around steady state. Otherwise, if there are cycles around a steady-state equilibrium. It means that there are oscillations (see ...


1

To stick to the simpler deterministic case, it is perfect foresight and the Transvarsality condition (TVC)that guarantees that an optimizing agent will stay on the saddle-path, because all other paths lead to the violation of TVC (corner solutions violate the TVC). In a deterministic environment and with perfect foresight the agent knows this and so he ...


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