Questions tagged [recursive-macroeconomics]

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Proof that Inada condition guarantees an interior optima [closed]

In the context of an optimal growth model, how do we prove that the utility function satisfying the Inada condition U'(0) = infinity, is sufficient to say that our optimal policy function g(x) is an ...
6 views

log-linearize a forward looking variable (P/D) with recursive expression

I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, ...
64 views

How does one find values of constants in a value function?

Problem: suppose I have the following maximization problem: \begin{align} &\max_{(c_t)_{t \geq 0}}E_0\left[\sum^{\infty}_{t=0}\beta^{t}\ln c_t\right]\\[2mm] \text{s.t.} \quad & k_{t+1}=A^{1-\...
96 views

More than one Bellman Equation

I'm attending to my first dynamic optimization course, and what I don't fully graps yet is that sometimes we have to use more than one bellman equation. How do you realize that? I mean how do you know ...
46 views

What is a what is meant by a “workhorse” macroeconomic model

A number of times ive seen the Neoclassical Growth Model and Overlapping Generation Model setups referred to as a "workhorse of modern macroeconomics". What does this mean exactly?
147 views

Eating a Cake with Uncertain Preferences

I've been playing around with a lot of cake eating problems and have been messing with how uncertainty could enter the model. One thing that I'm thinking about is whether we can solve a cake eating ...
37 views

Economic interpretation of the given dynamic equations

How do you interpret these equations $$c_{t+1}/c_t=1-\beta [(c_t/w_t)-a]$$ $$w_{t+1}+c_t =kw_t+q$$ where $\beta$ a, k, q are strictly positive parameters. $c$ is consumption and $w$ is wealth. ——...
247 views

The Cake Eating Problem with Depreciation (Modelling difficulties)

How does one go about modelling the cake eating problem with depreciation? (i.e The cake goes bad over time) The problem I have is the following. Lets define a cake eating problem sequentially as: ...
136 views

Do policy functions exist for Finite Horizon Dynamic programming problems?

I've been looking at the cake eating problem over a finite horizion and have been trying to figure out if we can derive a policy function for such a problem. My work is written below. sequence form ...
21 views

Can you recursively forecast one variable using two variables?

My question is probably very elementary but I haven't been able to find an explanation of recursive forecasting that I fully understand. I've read a journal article that seemed to recursively ...
Its known that the Bellman equation in recursive macroeconomics is used for the following problems: $$\sum_{t=1}^\infty\beta^tU(c_t)$$ $$s.t. c_t+k_{t+1}=f(k_t)$$ $$k_0>0$$ Im wondering if we can ...
Let $w_t$ denote a consumer's wealth at time $t$ and $c_t$, the amount she chooses to consume, so her savings exiting this time period are $w_t-c_t$. Given this savings decision, her savings $w_{t+1}$ ...