Questions tagged [difference-equations]

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Nonhomogeneous linear dynamic system exercise

I have the following system of equations: \begin{align*} x_{t+1} & = 3x_t + y_t \\ \\ y_{t+1} & = 2 + 5y_t. \end{align*} I know how to solve it when I do not have a constant, but I couldn't ...
Hypatia's user avatar
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Signalling a relation

I have a very basic, trivial question to ask. (I apologise if it is not a worthy problem) I have been trying to formulate an international Economics model where a larger country is trying to signal a ...
Elina Gilbert's user avatar
2 votes
2 answers
248 views

Solving stochastic difference equation in New Keynesian model (FTPL textbook derivation)

In Cochrane's "Fiscal Theory of the Price Level", I am struggling with the following derivation. Take the first line as given, where $\pi_t$ and $i_t$ are random processes adapted to $\...
Econ's user avatar
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2 votes
1 answer
249 views

Why is there a Walrasian Equilibrium if excess demand goes to infinity as price goes to 0?

In one exercise, we have to argue that a Walrasian Equilibrium exists and the solution says that if we can see that excess demand goes to infinity as price goes to 0, and as price goes to infinity, ...
aliosha karamazov's user avatar
1 vote
0 answers
64 views

How to derive a solution to stochastic difference equation using Blanchard-Kahn method?

Let $z_t =\rho z_{t-1}+\epsilon_t$, where $|\rho|<1$ and $E_t e_{t+1}=0$ I need to solve the stochastic difference equation $E_t[y_{t+2}-2ay_{t+1}+by_t]=z_t$ for $y_t$, $t\geq0$, where $0<b<1$...
OhRoBo's user avatar
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1 vote
0 answers
38 views

Solving separable system of differential equation in three variables

I have the following system of differential equations: $$ m \sqrt{y(x, z)} + \left( \frac{nz}{\sqrt{1-y(x, z)}} + \frac{mx}{\sqrt{y(x, z)}}\right)y_{1}(x,z) = 0 $$ $$ n \sqrt{1-y(x, z)} + \left( \frac{...
Elina Gilbert's user avatar
3 votes
1 answer
89 views

Joint distribution from differential equations

I have the following problem - Z is a random variable which can take any real value in the range [0,1] a and b are independent variables drawn from uniform distribution in the interval [0,1]. Z is a ...
Elina Gilbert's user avatar
1 vote
1 answer
64 views

System of first order partial differential equation

I have following function - $$ \max_{x, y} ~ u(x, y)^{3}x + (1-u(x, y))^{3}y$$ FOC: $$u_{x}(3u(x, y)^{2}x - 3(1-u(x, y))^{2}y) +u(x,y)^{3} = 0$$... (1) $$u_{y}(3u(x, y)^{2}x - 3(1-u(x, y))^{2}y) +(1-u(...
Elina Gilbert's user avatar
0 votes
1 answer
330 views

System of differential equations in economics and areas of interest

More than a question, I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have a research homework and I have to make ...
Pech's user avatar
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4 votes
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98 views

Out-of-Equilibrium Macroeconomic Dynamics using Differential Equations

My OP below asks about the RBC model, but I am actually interested in any out-of-equilibrium macroeconomic model; CGE, DSGE or whatever the correct nomenclature is. The Real Business Cycle model is a ...
LBogaardt's user avatar
  • 281
2 votes
1 answer
67 views

Cross-section experiment with Differences-in-Diffrences estimation [closed]

I am trying to answer the following question related to econometrics: ...
Bazinga's user avatar
  • 155
0 votes
0 answers
52 views

Is it okay to difference data with different time intervals?

I have a question that is from an old project and that I want to clarify purely for future research. The question is, if you have a time-series that occurs at intermittent intervals, say once ever 4, ...
John Sonnino's user avatar
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0 answers
76 views

Dynamic programming and Difference equations applications

I'm asked by my teacher to prepare a presentation with economic applications of Dynamic Programing (Bellman Equation) and Difference equations. I'm not sure what this things are used for in economics ...
Juan Sebastian's user avatar
6 votes
1 answer
141 views

Signalling Model (Rearranging the FOCs of UMP)

I'm currently reading "SAVING RATES AND POVERTY: THE ROLE OF CONSPICUOUS CONSUMPTION AND HUMAN CAPITAL" by Omer Moav and Zvika Neeman, and I encounter some problem deriving one of the equations. ...
Estee L's user avatar
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2 votes
1 answer
581 views

What am I doing wrong in the derivation of Bass diffusion model?

I've been deriving Bass diffusion model and keep consistently finding a different result than Bass' original answer. To make things worse, every single link in the Google results page just copies the ...
Ravshan S.K.'s user avatar
1 vote
1 answer
86 views

Solving differential equation in The Economics of Superstar (by Rosen)

I am currently reading "The Economics of Superstar" written by Rosen (1981). I don't understand one differential equation he used in the paper. The equation is as follows: $$\frac{dp}{dz} = (p+s)/z.$$...
shk910's user avatar
  • 495
1 vote
1 answer
219 views

Samuelson Acceleration Model Question

I first posted my question in the wrong forum (I did not know that there was an economic forum now) so I want to apologise for that by User Ben Bolker and User Robert. Also special thanks to User ...
4lfr3d's user avatar
  • 11
6 votes
1 answer
339 views

Solving Leeper (1991) model

I am attempting to solve a variation of Leeper's (1991) model, which deals with the FTPL. This is what I have done so far: The utility function is $\log(c_t)+\delta\log⁡(M_t/p_t)$. I obtain two ...
sageofspades's user avatar
4 votes
2 answers
324 views

Solving rational expectations model - Sims form

I am trying to solve my first ratex model and make some impulse response functions using Dynare. I am following Leeper (1991). This is what I have done so far: The utility function is $\log(c_{t})+\...
user11767's user avatar
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3 votes
1 answer
1k views

Deriving intertemporal budget constraint from flow constraint

I am trying to learn how to solve difference equations in order to derive intertemporal budget constraints. Consider the government's flow budget constraint: $$\frac{B_{t}-B_{t-1}}{p_{t}} + \frac{M_{...
user11767's user avatar
  • 661
2 votes
1 answer
108 views

Difference equation in OLG framework

This question is also regarding Aiyagari and Gertler (1985). We have the governments flow budget contraint: $\frac{B_{t-1}}{p_{t}} + \bar{g}w = \tau_{y}(t)+\tau_{o}(t) + \frac{M_{t}-M_{t-1}}{p_{t}} + ...
user11767's user avatar
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3 votes
1 answer
100 views

Looking for discussion on equilibrium vs dynamic models in econometrics

I'm a statistician/machine learning scientist more familiar with molecular bio than economics. Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling. A common ...
Count Zero's user avatar
6 votes
2 answers
233 views

Rigorous proof needed: Acemoglu (Intro Growth) Corollary $2.1.2$

I am reading Acemoglu's intro to modern economic growth. But I am having trouble understanding his proof to a theorem related with stability. Here is the theorem: And here are some related ...
ask's user avatar
  • 295
3 votes
1 answer
497 views

Prove the uniqueness of steady state

I have a difference equation $$ p_t^{1-\alpha}=\alpha\sigma \left(y-p_t-\frac{(\sigma p_{t-1}^\alpha+b)p_t^{1-\alpha}}{\alpha\sigma} \right) $$ where $\alpha \in [0,1]$ and everything else is $&...
Sher Afghan's user avatar
4 votes
1 answer
534 views

How to linearize the following difference equation?

I'm doing economic modelling where $x_t$ is the intertemporal cash-flow variable. I need to solve the following recurrence relation $$x_{t+1}=\frac{x_{t+8}}{x_{t+1}}$$ My problem is that I don't ...
Übel Yildmar's user avatar