Questions tagged [difference-equations]

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Signalling Model (How to solve a differential equation?)

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. ...
2
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1answer
69 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 ...
1
vote
1answer
54 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: $$\frac{dp}{dz} = (p+s)/z.$$...
1
vote
1answer
137 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 ...
4
votes
1answer
139 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 ...
4
votes
2answers
187 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})+\...
3
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1answer
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_{...
2
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1answer
76 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}} + ...
3
votes
1answer
66 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 ...
5
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1answer
126 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 ...
3
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1answer
204 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 $&...
4
votes
1answer
247 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 ...