updating lake model mccall function to be consistent with mccall lecture #176

Harveyt47 · 2020-05-05T10:38:30Z

I update the McCall function in the lake model to be consistent with the McCall lecture. The same changes I make in this notebook

I also add a random_state=seed in the markov chain simulation

github-actions · 2020-05-05T10:42:39Z

🚀 Deployed on https://5eb1431c1ab4171097950e4a--practical-lalande-b89631.netlify.app

sayaikegawa · 2020-05-08T11:01:10Z

Thanks @Harveyt47 , that looks good to me.

jstac · 2020-12-29T07:29:32Z

@shlff , are you able to review this pull request?

Does it look OK to you?

shlff · 2020-12-29T21:05:25Z

Thanks @jstac . For the code in QE lectures, as you discussed with me before, we need to make a balance between its efficiency and readability.

I will give my comments on these changes in the following.

(Since this PR is quite old, I will briefly explain the changes in code before comments.)

Let's get started.

shlff

Thanks @jstac . Please find my reviews here.

shlff · 2020-12-29T21:10:28Z

source/rst/lake_model.rst

@@ -63,7 +63,7 @@ Let's start with some imports:
    from scipy.stats import norm
    from scipy.optimize import brentq
    from quantecon.distributions import BetaBinomial
-    from numba import jit
+    from numba import jitclass, float64


Let's call it Change1.

It serves for later newly-adding speedup for the McCallModel class.

Whether we need Change1 depends on whether we want to speed up the McCallModel class with jitclass.

For jitclass, we should use from numba.experimental import jitclass instead.

shlff · 2020-12-29T21:18:53Z

source/rst/lake_model.rst

@@ -644,7 +644,7 @@ Let's plot the path of the sample averages over 5,000 periods
    xbar = lm.rate_steady_state()

    fig, axes = plt.subplots(2, 1, figsize=(10, 8))
-    s_path = mc.simulate(T, init=1)
+    s_path = mc.simulate(T, init=1, random_state=1234)


Let's call it Change2.

It intends to fix the initial random state of random number generator.

From my point of view, it is an unnecessary change for two reasons.

The most important one is that we are not aiming to reproduce the figure. So producing figures with samples won't affect our analysis in the lecture.

Then, adding Change2 might depreciate readability a bit.

shlff · 2020-12-29T21:27:10Z

source/rst/lake_model.rst

+    n = 60                                  # n possible outcomes for w
+    w_default = np.linspace(10, 20, n)      # wages between 10 and 20
+    a, b = 600, 400                         # shape parameters
+    dist = BetaBinomial(n-1, a, b)
+    p_default = dist.pdf()


Let's call it Change3.

It shifts the default wage vector and probabilities outside the class McCallModel.

I think this change is unnecessary since it makes the lecture reading process a bit inconsistency, at least for me. It looks unexpected here. Also, it depreciates both the efficiency and readability of the code.

shlff · 2020-12-29T21:27:29Z

source/rst/lake_model.rst

+    mccall_data = [
+        ('α', float64),          # job separation rate
+        ('β', float64),          # discount factor
+        ('γ', float64),          # Job offer rate
+        ('c', float64),          # unemployment compensation
+        ('σ', float64),          # Utility parameter
+        ('w_vec', float64[:]),   # Possible wage values
+        ('p_vec', float64[:])    # Probabilities over w_vec
+    ]


Let's call it Change4.

For Change4-6, they did three main things:

Change4-5: packing the default utility function and the Bellman updating function into the class McCallModel and speed up the class with classifying parameter's categories and jitclass,

Change6: put function solve_mccall_model into a different code cell and clarify it,

Change6: modify the corresponding parts in the following code to accommodate the new McCallModel class

My comments:

For me, point 2 mentioned above is a relatively good change, which makes the code more readable while keeping its efficiency. But this clarification seems a bit redundant since we have already added comment Iterates to convergence on the Bellman equations in the function. We can actually get rid of this change.

Point 1 seems a bit unnecessary since it makes the code harder to read, though it might enhance its efficiency a bit.

Point 3 depends on the adoption of Point 2.

My suggestion:

get rid of point 2,

whether we should adopt point 1 depends on our aims: readability or efficiency. If we want more efficiency at the cost of the readability, then keep the change. If we want it more readable, then get rid of it.

whether we should to adopt point3 depends on whether we want to adopt point 1

I gave a serious thought to the McCall class added by @Harveyt47 after my last comments.

I think it is a good idea to make the class consistent here, but we should modify the class a bit to capture all features from the origin code.

shlff · 2020-12-29T21:28:15Z

source/rst/lake_model.rst

+    @jitclass(mccall_data)
    class McCallModel:
        """
        Stores the parameters and functions associated with a given model.
        """

-        def __init__(self, 
-                    α=0.2,       # Job separation rate
-                    β=0.98,      # Discount rate
-                    γ=0.7,       # Job offer rate
-                    c=6.0,       # Unemployment compensation
-                    σ=2.0,       # Utility parameter
-                    w_vec=None,  # Possible wage values
-                    p_vec=None): # Probabilities over w_vec
+        def __init__(self,
+                    α=0.2,       
+                    β=0.98,      
+                    γ=1.0,       
+                    c=6.0,       
+                    σ=2.0,       
+                    w_vec=w_default, 
+                    p_vec=p_default): 

            self.α, self.β, self.γ, self.c = α, β, γ, c
            self.σ = σ
+            self.w_vec = w_vec
+            self.p_vec = p_vec

-            # Add a default wage vector and probabilities over the vector using
-            # the beta-binomial distribution
-            if w_vec is None:
-                n = 60  # Number of possible outcomes for wage
-                # Wages between 10 and 20
-                self.w_vec = np.linspace(10, 20, n)
-                a, b = 600, 400  # Shape parameters
-                dist = BetaBinomial(n-1, a, b)
-                self.p_vec = dist.pdf()  
+
+        def u(self, c):
+            σ = self.σ
+            if c > 0:
+                return (c**(1 - σ) - 1) / (1 - σ)
            else:
-                self.w_vec = w_vec
-                self.p_vec = p_vec
-
-    @jit
-    def _update_bellman(α, β, γ, c, σ, w_vec, p_vec, V, V_new, U):
-        """
-        A jitted function to update the Bellman equations.  Note that V_new is
-        modified in place (i.e, modified by this function).  The new value of U
-        is returned.
+                return -10e6
+
+        def update_bellman(self, V, V_new, U):
+            α, β, γ, c = self.α, self.β, self.γ, self.c
+            w_vec, p_vec, u = self.w_vec, self.p_vec, self.u
+
+
+            for w_idx, w in enumerate(w_vec):
+                # w_idx indexes the vector of possible wages
+                V_new[w_idx] = u(w) + β * ((1 - α) * V[w_idx] + α * U)

-        """
-        for w_idx, w in enumerate(w_vec):
-            # w_idx indexes the vector of possible wages
-            V_new[w_idx] = u(w, σ) + β * ((1 - α) * V[w_idx] + α * U)
+            U_new = u(c) + β * (1 - γ) * U + \
+                            β * γ * np.sum(np.maximum(U, V) * p_vec)

-        U_new = u(c, σ) + β * (1 - γ) * U + \
-                        β * γ * np.sum(np.maximum(U, V) * p_vec)
+            return U_new


Let's call it Change5.

shlff · 2020-12-29T21:30:07Z

source/rst/lake_model.rst


-        return U_new
+We will create a function ``solve_mccall_model`` to iterate with the Bellman operator.


Let's call the remaining Change6.

updating lake model mccall function to be consistant with mccall lecture

da14dbc

Harveyt47 requested a review from sayaikegawa May 5, 2020 10:38

Harveyt47 added the in-work label May 5, 2020

shlff self-requested a review December 29, 2020 11:04

shlff reviewed Dec 29, 2020

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mmcky requested review from shlff and jstac February 9, 2021 00:08

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updating lake model mccall function to be consistent with mccall lecture #176

updating lake model mccall function to be consistent with mccall lecture #176

Harveyt47 commented May 5, 2020

github-actions bot commented May 5, 2020

sayaikegawa commented May 8, 2020

jstac commented Dec 29, 2020

shlff commented Dec 29, 2020 •

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		return U_new
		We will create a function ``solve_mccall_model`` to iterate with the Bellman operator.

updating lake model mccall function to be consistent with mccall lecture #176

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updating lake model mccall function to be consistent with mccall lecture #176

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Harveyt47 commented May 5, 2020

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shlff commented Dec 29, 2020 •

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