Skip to main content
4 votes

Looking for discussion on equilibrium vs dynamic models in econometrics

Economists (most of them) build their models assuming most of the time stochastic dynamic equilibrium. So Economics does not contrast "dynamic" with "equilibrium" - it synthesizes them. It is ...
Alecos Papadopoulos's user avatar
4 votes
Accepted

System of differential equations in economics and areas of interest

One of the most fundamental distinctions in economics is that between stocks, measured at a point in time, and flows, measured over a period of time or as instantaneous rates. The construction of ...
Adam Bailey's user avatar
  • 8,529
4 votes
Accepted

Cross-section experiment with Differences-in-Diffrences estimation

Dif-in-dif (DiD) strategy relies on the identifying assumption of parallel trend. This essentially means that in the absence of the treatment, the control group and the supposedly treatment group ...
Rei's user avatar
  • 153
3 votes
Accepted

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

You are missing an integration constant $$ \log\left(\frac{p + qF(t)}{1 - F(t)}\right) = (p + q)t + \color{red}{\tilde{C}} $$ This constant you can name it whatever you want, I'm going to name it as ...
caverac's user avatar
  • 1,216
3 votes
Accepted

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

Let $z_j(p)$ be the excess demand function for good $j$, where $p := \frac{p_2}{p_1}$ is the relative price between the two goods. Note it is possible to express the excess demand functions as single ...
Nicolas Torres's user avatar
3 votes

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

Here is a revised derivation. Thanks! This is much clearer, I hope. \begin{equation} E_{t}\left[ (1-\lambda_{1}^{-1}L)(1-\lambda_{2}L^{-1})\pi_{t+1}\right] =\sigma\kappa\lambda_{1}^{-1}i_{t}. \label{...
John Cochrane's user avatar
3 votes

Solving Leeper (1991) model

You have the government's flow budget constraint (re-written in real terms): $b_{t} + m_{t} + \tau_{t} = g + \frac{m_{t-1}}{\pi_{t}} + R_{t-1}\frac{b_{t-1}}{\pi_{t}}$ (1) Now all you need to do is ...
user11767's user avatar
  • 661
2 votes

System of first order partial differential equation

I don't think your reasoning is correct. Some remarks: If you have an optimization problem, then you assume that you know the objective function, which in your case contains the function $u(x,y)$. As ...
tdm's user avatar
  • 12.4k
2 votes
Accepted

Nonhomogeneous linear dynamic system exercise

Preamble This answer does not provide a step-by-step solution to the above exercise. It shows how if you can solve a linear dynamic system without the constants (a homogeneous linear dynamic system) ...
Giskard's user avatar
  • 29.4k
2 votes

Nonhomogeneous linear dynamic system exercise

Hi: Using the lag operator, L, for $y_t$, you can write $y_{t+1}(1- 5L) = 2 \longrightarrow y_{t+1} = \frac{2}{(1-5L)}$. But you cannot write that an an infinite series because the thing multiplying ...
mark leeds's user avatar
2 votes
Accepted

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

The OP correctly identified a mistake here. Since the author claims monotonicity for a general function, let's disprove it for the simple linear case. Consider $$x_{t+1} = g(x_t) = -0.5x_t$$ This ...
Alecos Papadopoulos's user avatar
2 votes
Accepted

Deriving intertemporal budget constraint from flow constraint

Take your second equation, move it forward one period, and rearrange. You get: $$ B_t = \frac{p_{t+1} s_{t+1} + \Delta M_{t+1}}{R_{t+1}} + \frac{B_{t+1}}{R_{t+1}} $$ Then, define the nominal ...
luchonacho's user avatar
  • 8,591
2 votes
Accepted

Difference equation in OLG framework

The following approach seems to work in this case: look for the stead state formula of $T_t$. You can do this by taking (2.8) and the formula for $T_t$, and combine them. Then, get rid of all $t$ ...
luchonacho's user avatar
  • 8,591
1 vote

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

I'll assume throughout that $|\lambda_1| > 1$ and $|\lambda_2| < 1$, since otherwise the sums would diverge. Start from $$ \mathrm{E}_t \left[(1 - \lambda_1^{-1} L)(1 - \lambda_2L^{-1})\pi_{t + ...
Wittgenstein's Poker's user avatar
1 vote

Joint distribution from differential equations

From the fundamental theorem of calculus it follows that the relationship between a function and its partial derivative is given by: $$ Z(a,b)= \int_0^a \frac{\partial Z}{\partial a}(x,b) dx + Z(0,b), ...
Bertrand's user avatar
  • 3,371
1 vote
Accepted

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

The differential equation is of the form $$y' + f(x)y = q(x)$$ The correct answer in our case is $$p = -s$$ so that you know what you are targeting. Namely, it does not depend on $z$. You can ...
Alecos Papadopoulos's user avatar
1 vote

Samuelson Acceleration Model Question

There is nothing more to it than the equation $$Y_t - (c_y+v)Y_{t-1} = C^a + I^a$$ This is a linear non-homogeneous first-order difference equation, and it is non-homogeneous because there is a non-...
Alecos Papadopoulos's user avatar
1 vote

Solving rational expectations model - Sims form

If you are planning on using Dynare, you do not need to "solve" the model using Sim's method. Dynare takes care of the solution algorithm for you. If you want to get to IRFs quickly, I suggest ...
James Graham's user avatar
1 vote

Solving rational expectations model - Sims form

I think I have managed to solve it. However, not the way I was initially hoping. I simplified the stacked matrices using the given conditions and some assumptions. Here is my solution: Eq. (3) I ...
user11767's user avatar
  • 661
1 vote

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

Since the OP asked for a rigorous proof, here is one. By Acemoglu's inequality in the first part of his proof, we can separate $\{x(t)\}_{t=0}^{\infty}$ into two subsequences, an increasing ...
Louis Becker's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible