Skip to content

Commit

Permalink
Remove time subscript on PermGroFac
Browse files Browse the repository at this point in the history
The code and the earlier model assumes $\Gamma_t$ to be a constant, so changed the notation in the later model as well
  • Loading branch information
sidd3888 authored Nov 6, 2023
1 parent 77dbbf5 commit cb66d46
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions examples/Gentle-Intro/Gentle-Intro-To-HARK.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -387,10 +387,10 @@
"Specifically, our new type of consumer receives two income shocks at the beginning of each period: a completely transitory shock $\\theta_t$ and a completely permanent shock $\\psi_t$. Moreover, lenders will not let the agent borrow money such that his ratio of end-of-period assets $A_t$ to permanent income $P_t$ is less than $\\underline{a}$. As with the perfect foresight problem, this model can be framed in terms of __normalized__ variables, e.g. $m_t \\equiv M_t/P_t$. (See [here](https://www.econ2.jhu.edu/people/ccarroll/papers/BufferStockTheory/) for all the theory). Accordingly the normalized utility and continuation value are $u$ and $v_t$.\n",
"\n",
"\\begin{align*}\n",
"v_t(m_t) &= \\max_{c_t} u(c_t) + \\aleph\\beta \\mathbb{E} [(\\Gamma_{t+1}\\psi_{t+1})^{1-\\rho} v_{t+1}(m_{t+1}) ] \\\\\n",
"v_t(m_t) &= \\max_{c_t} u(c_t) + \\aleph\\beta \\mathbb{E} [(\\Gamma\\psi_{t+1})^{1-\\rho} v_{t+1}(m_{t+1}) ] \\\\\n",
"a_t &= m_t - c_t \\\\\n",
"a_t &\\geq \\underline{a} \\\\\n",
"m_{t+1} &= R/(\\Gamma_{t+1} \\psi_{t+1}) a_t + \\theta_{t+1} \\\\\n",
"m_{t+1} &= R/(\\Gamma \\psi_{t+1}) a_t + \\theta_{t+1} \\\\\n",
"\\mathbb{E}[\\psi_t]&=\\mathbb{E}[\\theta_t] = 1 \\\\\n",
"u(c) &= \\frac{c^{1-\\rho}}{1-\\rho}\n",
"\\end{align*}\n",
Expand Down

0 comments on commit cb66d46

Please sign in to comment.