update to rng keys

Author: HumphreyYang

lectures/doubts_or_variability.md

@@ -194,6 +194,16 @@ Setting $y_{t+1} = 1$ (a risk-free bond) in {eq}`bhs_pricing_eq` yields the reci
 
 ### Hansen--Jagannathan bounds
 
+```{note}
+The derivation here uses the Cauchy-Schwarz inequality, which yields the bound
+directly from the pricing equation for excess returns.
+
+{doc}`hansen_jagannathan_1991` derives the same
+bound by projecting $m$ onto the space of traded payoffs, which additionally
+yields the duality with the mean-variance frontier and the tighter
+positivity-restricted bound.
+```
+
 Let $R_{t+1}^e$ denote the gross return on a risky asset (e.g., the market portfolio) and $R_{t+1}^f$ the gross return on a one-period risk-free bond.
 
 The **excess return** is

lectures/dovis_accounting_mf.md

@@ -1323,19 +1323,19 @@ def particle_filter(y_data, key, N_particles,
 We demonstrate the particle filter on synthetic data that mimics an institutional disinflation: inflation declines from roughly 30% to 5% while debt rises from 20% to 45% of GDP.
 
 ```{code-cell} ipython3
-np.random.seed(0)
+rng = np.random.default_rng(0)
 T_sim = 60
 t_reform = 25
 
 inflation_data = np.concatenate([
-    25 + 5 * np.random.randn(t_reform),
-    np.linspace(25, 5, 10) + 2 * np.random.randn(10),
-    5 + 2 * np.random.randn(T_sim - t_reform - 10)
+    25 + 5 * rng.standard_normal(t_reform),
+    np.linspace(25, 5, 10) + 2 * rng.standard_normal(10),
+    5 + 2 * rng.standard_normal(T_sim - t_reform - 10)
 ])
 debt_data = np.concatenate([
-    20 + 2 * np.random.randn(t_reform),
-    np.linspace(20, 40, 10) + 3 * np.random.randn(10),
-    40 + 3 * np.random.randn(T_sim - t_reform - 10)
+    20 + 2 * rng.standard_normal(t_reform),
+    np.linspace(20, 40, 10) + 3 * rng.standard_normal(10),
+    40 + 3 * rng.standard_normal(T_sim - t_reform - 10)
 ])
 
 y_data = jnp.column_stack([inflation_data, debt_data])

lectures/gorman_heterogeneous_households.md

@@ -1685,7 +1685,7 @@ We use the same technology and preference parameters.
 We set household-specific parameters below and impose $\sum_j \phi_j = 1$.
 
 ```{code-cell} ipython3
-np.random.seed(42)
+rng = np.random.default_rng(42)
 N = 100
 
 # Aggregate endowment process parameters
@@ -1695,8 +1695,8 @@ N = 100
 
 
 # Mean endowments α_j and aggregate exposure φ_j
-αs = np.random.uniform(3.0, 5.0, N)
-φs_raw = np.random.uniform(0.5, 1.5, N)
+αs = rng.uniform(3.0, 5.0, N)
+φs_raw = rng.uniform(0.5, 1.5, N)
 φs = φs_raw / np.sum(φs_raw)  # normalize so Σ φ_j = 1
 
 # Rank households by mean endowment to assign idiosyncratic risk

lectures/hansen_richard_1987.md

@@ -97,7 +97,6 @@ from scipy.optimize import minimize
 from scipy import stats
 import pandas as pd
 
-np.random.seed(42)
 ```
 
 ## Data generation

lectures/rob_markov_perf.md

@@ -568,12 +568,13 @@ def nnash_robust(A, C, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2,
     k_1 = B1.shape[1]
     k_2 = B2.shape[1]
 
+    rng = np.random.default_rng(0)
     v1 = np.eye(k_1)
     v2 = np.eye(k_2)
     P1 = np.eye(n) * 1e-5
     P2 = np.eye(n) * 1e-5
-    F1 = np.random.randn(k_1, n)
-    F2 = np.random.randn(k_2, n)
+    F1 = rng.standard_normal((k_1, n))
+    F2 = rng.standard_normal((k_2, n))
 
 
     for it in range(max_iter):