Questions tagged [steady-state]

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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 $\...
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1 answer
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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 $...
3 votes
1 answer
191 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 ...
3 votes
0 answers
31 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 ...
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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 ...
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3 votes
1 answer
93 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 ...
1 vote
0 answers
35 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 ...
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1 vote
1 answer
55 views

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 ...
0 votes
1 answer
70 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 $...
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2 votes
1 answer
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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 ...
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2 votes
1 answer
655 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 ...
-1 votes
1 answer
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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 ...
1 vote
0 answers
167 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 (...
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3 votes
1 answer
192 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-...
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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 ...
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1 vote
1 answer
310 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 ...
7 votes
2 answers
172 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)}...
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7 votes
1 answer
213 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 ...
1 vote
1 answer
573 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, ...
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2 answers
386 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=...
3 votes
1 answer
207 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, ...
1 vote
1 answer
938 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 ...
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1 vote
1 answer
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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}(\...
7 votes
3 answers
909 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 ...
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1 answer
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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 ...
3 votes
1 answer
362 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 $&...
0 votes
2 answers
4k 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 ...
2 votes
1 answer
2k 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 ...
12 votes
2 answers
14k 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 ...
4 votes
1 answer
90 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^{-\...
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1 vote
0 answers
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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 ...
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6 votes
2 answers
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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}...
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6 votes
2 answers
112 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 ...
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10 votes
2 answers
253 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 ...
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