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[lqramsey] Fix calculation of H #288

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Merged
merged 3 commits into from
Oct 30, 2025
Merged

[lqramsey] Fix calculation of H #288

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4fbfa40
Fix calculation of H in lqramsey.md
sudayuga Oct 27, 2025
0b09889
Fix variable in risk-free rate and summation notation
sudayuga Oct 27, 2025
d3845d4
Merge branch 'main' into lqramsey
HumphreyYang Oct 30, 2025
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6 changes: 3 additions & 3 deletions lectures/lqramsey.md
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Original file line number Diff line number Diff line change
Expand Up @@ -510,7 +510,7 @@ Define
```{math}
:label: lq_rfr

R^{-1}_{t} := \mathbb E_t \beta^j p^t_{t+1}
R^{-1}_{t} := \mathbb E_t \beta p^t_{t+1}
```

$R_{t}$ is the gross $1$-period risk-free rate for loans
Expand All @@ -527,7 +527,7 @@ $$
and the cumulation of $\pi_t$

$$
\Pi_t := \sum_{s=0}^t \pi_t
\Pi_t := \sum_{s=0}^t \pi_s
$$

The term $\pi_{t+1}$ is the difference between two quantities:
Expand Down Expand Up @@ -693,7 +693,7 @@ def compute_paths(T, econ):
ns = P.shape[0]
F = scipy.linalg.inv(eye(ns) - β * P)
a0 = 0.5 * (F @ (x_vals.T @ Sm.T)**2)[0]
H = ((Sb - Sd + Sg) @ x_vals) * ((Sg - Ss) @ x_vals)
H = ((Sb - Sd + Sg) @ x_vals) * ((Sg + Ss) @ x_vals)
b0 = 0.5 * (F @ H.T)[0]
a0, b0 = float(a0[0]), float(b0[0])
else:
Expand Down
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