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Proving the Global stability in the Solow Swan Model

Consider a simplified version of the Solow-Swan model in discrete time, where technology is normalized to one and the population size is constant. The Solow equation is given by \begin{equation} ...
Maximilian's user avatar
3 votes
1 answer
96 views

Capital-Output Ratio using Nominal GDP and Nominal GFCF

I have this assignment which asks the following: "Compute the average capital-to-output ratio in Australia from 1960 to 2022. Explain how to compute the average ratio. (Hint: use the nominal GDP ...
Liam Gannaway's user avatar
1 vote
1 answer
63 views

Conceptual question about the zero-inflation steady-state in DSGE-models

As I understand, it is usually common practice, to choose DSGE models in such a way, that the steady-state inflation is freely choose-able and for simplifications it is than usually assumed to be zero....
mindandfields's user avatar
1 vote
0 answers
52 views

Help with the log-linearization of a difficult term

I'm currently trying to retrace a log-linearization done in this paper. I want to log-linearize around the steady-state, as it is commonly done for DSGE models (see here). $\bar{x_t}$ are steady-state ...
mindandfields's user avatar
1 vote
1 answer
66 views

Log-linearizing a second order term around the steady-state

I'm currently trying to retrace a log-linearization done in a paper. I want to log-linearize around the steady-state, as it is commonly done for DSGE models (see here) and I want to disregard all ...
mindandfields's user avatar
3 votes
2 answers
658 views

Solow model with population growth - proof of steady state level of capital per worker

Hello everyone, I am trying to obtain the requested solution as shown in the image (last equation of the image attached), however, after I calculate the law of motion, I only obtain only part of the ...
René González's user avatar
1 vote
1 answer
298 views

The effect of saving rate on steady state

If there is a increase in saving rate and fall back to original level afterwards, what is the effect on steady state in the short run and long run? I am confused about this is because I thought ...
sharonzj f's user avatar
0 votes
0 answers
156 views

Solow Model With Land as Factor

Given the production function: $$Y = K^\alpha (AL)^\beta R^{1-\alpha -\beta}$$. Where $L, A$ grow at exogenously given rates $n, g$ respectively. $R$ is land and is constant in supply and given that $\...
Dayne's user avatar
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1 answer
78 views

Steady state equilibrium in Solow model with a convex production function

Suppose an economy is producing $e^k$ amount of output per capita if it uses $k$ amount of capital per capita. As the production function is strictly convex I am thinking the only steady state is at $...
petearGriffin's user avatar
3 votes
1 answer
337 views

Steady-state savings rate

I'm having trouble with the steady-state savings rate type of problems. Here is the problem I'm stuck on: The production is $Y = 0.5*K^{1/3}(AN)^{2/3}$. If savings is $s$%, what are the steady-state ...
user40459's user avatar
3 votes
0 answers
43 views

Get empirical steady state moments for calibrating a DSGE model

I want to calibrate some parameters of my DSGE model so that in the steady state some variable ratios, that are present in data, are met. My question is, how do I get such ratios from time series ...
manifold's user avatar
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3 votes
1 answer
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Derive the Demographic Structure in the Steady State

I am reading a paper with following description on the demographics in their model: "... each (representative) agent lives for $T$ periods ... We assume that each individual has $e^{f}$ children ...
Alalalalaki's user avatar
  • 2,474
3 votes
1 answer
220 views

Non-trivial steady state

Consider the growth model with inelastic labor supply, full depreciation, log utility and CRS technology with the Bellman equation be defined as follows: $$V(k)=\max(log(k^\alpha-k')+\beta V(k'))$$ st ...
Maybeline Lee's user avatar
1 vote
0 answers
38 views

Problem to find steady state when I assume Y=1

I am trying to do a DSGE model in Matlab, I have all the steady state equations on paper and pencil but I fail to find values for all variables. Indeed, since I have constant return to scale, I have ...
BAL's user avatar
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1 answer
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Constant to the power of t in steady state

I am wondering how to get the steady-state for the following Euler equation. I know that we can get rid of time in subscripts. However, here I have a constant (a) to the power of $t$. Does anyone know ...
Giordano's user avatar
0 votes
1 answer
102 views

Question on overlapping generations

My question is from over lapping generations Question is as follows I found that $$k(t+1)= \frac{\beta(1-\alpha)}{(1+\beta)(1+n)}A(t)k(t)^{\alpha}$$ How can I deal with A(t) to find the steady state $...
studentp's user avatar
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2 votes
1 answer
96 views

Difference between long run coefficient and non stochastic steady state coefficient ARDL model

I am a little bit confused on the definition of long run equilibrium coefficient. Suppose I have an ARDL model as: $y_t = \rho_1 y_{t-1} + \rho_2 y_{t-2} + \beta_1x_{t-1} + \beta_2x_{t-2} $ The steady ...
Giorgetto's user avatar
  • 223
2 votes
1 answer
2k views

Log linearising EUler equation

I am trying to solve a problem that asks to log linearise following Euler equation of the New Keynesian model: $$C^{-\sigma}_t=\beta E_tC^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1}).$$ The solution is ...
randomname's user avatar
-1 votes
1 answer
54 views

Would a zero-growth economy with zero-growth population still have the same GDP?

If a country was to turn to a steady-state economy (or circular economy) where there is neither economic nor population growth with time, and there is no natural resources being added to the system ...
Abanob Ebrahim's user avatar
1 vote
0 answers
382 views

Proving the existence of a steady state

I am trying to prove the existence of at least one stable steady state in a situation where I am given properties of the production function but not an explicit functional form. I have the following (...
Julia B's user avatar
  • 76
3 votes
1 answer
457 views

Overlapping Generations model: Social Planner solution

Assume we have a model of OVG where there are 2 overlapping generations, youngs and olds, the agents are two period living. The utility function is logaritmic, and the production function is Cobb-...
Chaos's user avatar
  • 148
1 vote
2 answers
2k views

What does steady state mean?

I am reading a book on business cycle models, and it keep using the word "steady state". It never defined what that actually means. Obviously it is the idea that some key variables reach constant ...
Damnew's user avatar
  • 11
1 vote
1 answer
450 views

Solow model golden rule with my exact answer

In a perfectly competitive Solow economy with physical capital accumulation, population growth and a Cobb-Douglas production function, show that the “golden rule” steady-state would be reached if at ...
Enjoyecon's user avatar
7 votes
2 answers
208 views

"If $\lambda$ is greater than than 1, the system explodes." Why does the system explode?

David Romer in his textbook Advanced Macroeconomics (Third Edition) writes regarding the speed of convergence of the Diamond model the following: (Pg. 83) Equation (2.60) [$k_{t+1}={1\over{(1+n)(1+g)}...
Bensstats's user avatar
  • 889
7 votes
1 answer
286 views

An Optimal Control Model: A Ridiculous Result for a Steady State

I was experimenting with a seemingly simple optimal control problem that generates a system of differential equations. When I calculate the values of the steady state of the system I get some very ...
Artem Kochnev's user avatar
1 vote
1 answer
766 views

Taylor Series Approximation around steady state in Solow

In my Advanced Macro script, the professor says take TSA1 of the following equation: $(1+g)(1+n)k_{t+1} = sk^\alpha_{t+1} + (1-\delta)k_t$ where $g$ is technological progress, $n$ population growth, ...
Karel's user avatar
  • 21
1 vote
2 answers
430 views

Solow model, time and steady state

Suppose we have a Solow model: $$ Y(t)=C(t)+I(t) $$ $$ I(t)=sY(t) $$ $$ \dot K=I(t)-δK(t) $$ With a given Cobb-Douglas: $$ Y(t)=Z(t)K^aL^{1-a} $$ $$ y(t)=Y(t)/L(t) $$ $$ k(t)=K(t)/L(t) $$ $$ y=...
inquirius's user avatar
3 votes
1 answer
225 views

What conditions must we demand for the economy to be always on the saddle path?

Is it enough to assume that agents have perfect foresight, or have 'rational' expectations for the economy to always - except in few cases - be in the stable saddle path? With rational expectations, ...
An old man in the sea.'s user avatar
1 vote
1 answer
1k views

How to determine the Steady State of this model?

Consider the system of two equations: $$y_t=\beta\mathbb{E}_t[y_{t+1}+\gamma\cdot z_{t+1}]$$ $$x_t=\rho x_{t+1}+y_t$$ $$z_t=(z_0-Z_t)e^{-at}+z_T$$ Determine the steady state. The solution manual ...
Holograph's user avatar
  • 121
1 vote
1 answer
178 views

Evaluation around steady state for a specific DSGE Model

The following equations are taken from Ravenna, walsh: "Optimal Monetary Policy with Unemployment and Sticky Prices" (2011). (i)$$\frac{Z_{t}}{\mu_{t}} = w_t + \frac{\kappa}{q_{t}} - (1-\rho)E_{t}(\...
Ralle Kalle's user avatar
7 votes
3 answers
1k views

Solution Method for Infinite-Horizon Maximization Problem

Full disclosure: this problem was part of a final exam that none of our class could really solve definitively. Below the general form is a specific utility function we worked with that I'll try to ...
Kitsune Cavalry's user avatar
  • 6,648
0 votes
1 answer
803 views

Solow Growth Model. Steady State. Can someone explain please?

my lecturer is doing a rather poor job explaining what he's written down, so I'm wondering if someone would be able to explain the following graph for me? This is a part of the Solow-Swann Growth ...
Schteeb's user avatar
3 votes
1 answer
508 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 $&...
Sher Afghan's user avatar
0 votes
2 answers
5k views

Marginal Product of Capital in the Solow Model

In the classic form of the Solow Model: $$ Y=K^\alpha (AL)^{1-\alpha } $$ Describe circumstances in which the marginal product of capital could rise over time, at least for a temporary period. I've ...
James Baker's user avatar
2 votes
1 answer
3k views

Solow Model, Growth rate of K/L and Y/L in steady state

I have been given the following setup: $$ Y=K^\theta (AL)^{1-\theta }$$ Where Y = Output, K = Capital, L = Labour and A = Productivity. $$ \frac{\dot{L}}{L} = n $$ $$ \frac{\dot{A}}{A} = g $$ The ...
James Baker's user avatar
13 votes
2 answers
16k views

Solow Model: Steady State v Balanced Growth Path

Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model: $$ Y = K^\beta (AL)^{1-\beta} $$ I have been asked to derive the steady ...
James Baker's user avatar
4 votes
1 answer
96 views

Conjecture Steady State from limit properties

The question is related to this thread. I'd like to derive a unique steady state for an optimal control problem. Consider the following programm \begin{align} &V(x_0) := \max_u \int^\infty_0 e^{-\...
clueless's user avatar
  • 1,579
1 vote
0 answers
171 views

Log linearization

Consider some time series data $X=\{x_t:t\in[0,\infty)\}$. Define a steady state by \begin{align} x\in X:x_{t+1} - x_t = 0 \end{align} and the log deviation from steady state with \begin{align} \hat ...
clueless's user avatar
  • 1,579
6 votes
2 answers
238 views

Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
clueless's user avatar
  • 1,579
6 votes
2 answers
125 views

Real Positive Eigenvalue, but Stable Dynamics

UPDATE I was not thinking straight anymore and got totally confused after working hours on my equations. The point is, I have an unstable system, but I force it on the stable path. After realizing ...
clueless's user avatar
  • 1,579
10 votes
2 answers
282 views

Optimality of Zero Capital Taxation

The Chamley-Judd result of zero optimal capital taxation says that 0 capital taxation are required in order to maximize welfare at the steady state. The result is 30 years old. Still assuming that ...
FooBar's user avatar
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