Questions tagged [difference-equations]
The difference-equations tag has no usage guidance.
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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 ...
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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 $\...
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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, ...
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What does differentiability of Utility function at an optimal solution x* mean?
I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other ...
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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 $0<b<1$...
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Solving separable system of differential equation in three variables
I have the following system of differential equations:
$$ m \sqrt{y(x, z)} + \left( \frac{nz}{\sqrt{1-y(x, z)}} + \frac{mx}{\sqrt{y(x, z)}}\right)y_{1}(x,z) = 0 $$
$$ n \sqrt{1-y(x, z)} + \left( \frac{...
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Joint distribution from differential equations
I have the following problem -
Z is a random variable which can take any real value in the range [0,1]
a and b are independent variables drawn from uniform distribution in the interval [0,1].
Z is a ...
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System of first order partial differential equation
I have following function -
$$ \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(...
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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 ...
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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 ...
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Cross-section experiment with Differences-in-Diffrences estimation [closed]
I am trying to answer the following question related to econometrics:
...
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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, ...
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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 ...
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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.
...
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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 ...
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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:
$$\frac{dp}{dz} = (p+s)/z.$$...
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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 ...
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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 ...
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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})+\...
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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:
$$\frac{B_{t}-B_{t-1}}{p_{t}} + \frac{M_{...
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Difference equation in OLG framework
This question is also regarding Aiyagari and Gertler (1985). We have the governments flow budget contraint:
$\frac{B_{t-1}}{p_{t}} + \bar{g}w = \tau_{y}(t)+\tau_{o}(t) + \frac{M_{t}-M_{t-1}}{p_{t}} + ...
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Looking for discussion on equilibrium vs dynamic models in econometrics
I'm a statistician/machine learning scientist more familiar with molecular bio than economics. Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling.
A common ...
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Rigorous proof needed: Acemoglu (Intro Growth) Corollary $2.1.2$
I am reading Acemoglu's intro to modern economic growth. But I am having trouble understanding his proof to a theorem related with stability. Here is the theorem:
And here are some related ...
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Prove the uniqueness of steady state
I have a difference equation
$$
p_t^{1-\alpha}=\alpha\sigma \left(y-p_t-\frac{(\sigma p_{t-1}^\alpha+b)p_t^{1-\alpha}}{\alpha\sigma} \right)
$$
where $\alpha \in [0,1]$ and everything else is $&...
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How to linearize the following difference equation?
I'm doing economic modelling where $x_t$ is the intertemporal cash-flow variable. I need to solve the following recurrence relation
$$x_{t+1}=\frac{x_{t+8}}{x_{t+1}}$$
My problem is that I don't ...
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