Questions tagged [difference-equations]

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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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Loss function to State space

I have a quadratic equation and a loss function and need to write then in a state space format according to a model below. My equation is the following below, where T is the degree of a custom index ...
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Dinamic economics, differential equiations [duplicate]

I'm investing for models of system of differential equations, that can be applied in economics. I have to make an analysis of the model, for an exposition. Now I'm trying to choose a model to present, ...
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Model economics with diffential equations [duplicate]

I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have to make an analysis of a model, now I'm in the process of ...
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1 answer
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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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2 votes
1 answer
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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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6 votes
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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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1 answer
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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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4 votes
1 answer
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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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4 votes
2 answers
266 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})+\...
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3 votes
1 answer
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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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1 answer
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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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6 votes
2 answers
190 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 ...
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3 votes
1 answer
349 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 $&...
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4 votes
1 answer
438 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 ...
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