Questions tagged [difference-equations]
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12
questions
5
votes
0answers
64 views
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
votes
1answer
77 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
58 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
148 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
142 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
193 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
votes
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:
$$\frac{B_{t}-B_{t-1}}{p_{t}} + \frac{M_{...
2
votes
1answer
79 views
Difference equation in OLG framework
This question is also regarding Aiyagari and Gertler (1985). We have the governments flow budget contraint:
$\frac{B_{t-1}}{p_{t}} + \bar{g}w = \tau_{y}(t)+\tau_{o}(t) + \frac{M_{t}-M_{t-1}}{p_{t}} + ...
3
votes
1answer
67 views
Looking for discussion on equilibrium vs dynamic models in econometrics
I'm a statistician/machine learning scientist more familiar with molecular bio than economics. Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling.
A common ...
5
votes
1answer
127 views
Rigorous proof needed: Acemoglu (Intro Growth) Corollary $2.1.2$
I am reading Acemoglu's intro to modern economic growth. But I am having trouble understanding his proof to a theorem related with stability. Here is the theorem:
And here are some related ...
3
votes
1answer
223 views
Prove the uniqueness of steady state
I have a difference equation
$$
p_t^{1-\alpha}=\alpha\sigma \left(y-p_t-\frac{(\sigma p_{t-1}^\alpha+b)p_t^{1-\alpha}}{\alpha\sigma} \right)
$$
where $\alpha \in [0,1]$ and everything else is $&...
4
votes
1answer
258 views
How to linearize the following difference equation?
I'm doing economic modelling where $x_t$ is the intertemporal cash-flow variable. I need to solve the following recurrence relation
$$x_{t+1}=\frac{x_{t+8}}{x_{t+1}}$$
My problem is that I don't ...
