Merge branch 'main' into update_equalizing_difference

Author: HumphreyYang

lectures/equalizing_difference.md

@@ -31,7 +31,7 @@ Our presentation is "incomplete" in the sense that it is based on  a single equa
 
 This ''equalizing difference'' equation  determines  a college-high-school wage ratio that equalizes present values of a high school educated  worker and a college educated worker.
 
-The idea  is that lifetime earnings somehow adjust to make a new high school worker indifferent between going to college and not going to college but instead going to work immmediately.
+The idea  is that lifetime earnings somehow adjust to make a new high school worker indifferent between going to college and not going to college but instead going to work immediately.
 
 (The job of the "other equations" in a more complete model would be to describe what adjusts to bring about this outcome.)
 
@@ -136,7 +136,7 @@ $$
 We suppose that $R, \gamma_h, \gamma_c, T$ and also $w_0^h$  are fixed parameters. 
 
 We start by noting that the pure equalizing difference model asserts that the college-high-school wage gap $\phi$ solves an 
-"equalizing" equation that sets the present value not going to college equal to the present value of going go college:
+"equalizing" equation that sets the present value not going to college equal to the present value of going to college:
 
 
 $$
@@ -257,7 +257,7 @@ plt.ylabel(r'wage gap')
 plt.show()
 ```
 
-Notice how  the intitial wage gap falls when the rate of growth $\gamma_c$ of college wages rises.  
+Notice how  the initial wage gap falls when the rate of growth $\gamma_c$ of college wages rises.  
 
 The wage gap falls to "equalize" the present values of the two types of career, one as a high school worker, the other as a college worker.
 
@@ -347,7 +347,7 @@ Now let's compute $\frac{\partial \phi}{\partial D}$ and then evaluate it at the
 
 Thus, as with our earlier graph, we find that raising $R$ increases the initial college wage premium $\phi$.
 
-Compute $\frac{\partial \phi}{\partial T}$ and evaluate it a default parameters
+Compute $\frac{\partial \phi}{\partial T}$ and evaluate it at default parameters
 
 ```{code-cell} ipython3
 ϕ_T = ϕ(D, γ_h, γ_c, R, T, w_h0).diff(T)

lectures/inflation_history.md

@@ -21,13 +21,15 @@ The `xlrd` package is used by `pandas` to perform operations on Excel files.
 
 ```{code-cell} ipython3
 :tags: [hide-output]
+
 !pip install xlrd
 ```
 
 <!-- Check for pandas>=2.1.4 for Google Collab Compat -->
 
 ```{code-cell} ipython3
 :tags: [hide-cell]
+
 from importlib.metadata import version
 from packaging.version import Version
 
@@ -100,16 +102,16 @@ mystnb:
     caption: Long run time series of the price level
     name: lrpl
 ---
-df_fig5_bef1914 = df_fig5[df_fig5.index <= 1915]
+df_fig5_befe1914 = df_fig5[df_fig5.index <= 1914]
 
 # Create plot
 cols = ['UK', 'US', 'France', 'Castile']
 
-fig, ax = plt.subplots(dpi=200)
+fig, ax = plt.subplots(figsize=(10,6))
 
 for col in cols:
-    ax.plot(df_fig5_bef1914.index, 
-            df_fig5_bef1914[col], label=col, lw=2)
+    ax.plot(df_fig5_befe1914.index, 
+            df_fig5_befe1914[col], label=col, lw=2)
 
 ax.legend()
 ax.set_ylabel('Index  1913 = 100')
@@ -327,11 +329,6 @@ def pr_plot(p_seq, index, ax):
     #  Calculate the difference of log p_seq
     log_diff_p = np.diff(np.log(p_seq))
     
-    # Graph for the difference of log p_seq
-    ax.scatter(index[1:], log_diff_p, 
-               label='Monthly inflation rate', 
-               color='tab:grey')
-    
     # Calculate and plot moving average
     diff_smooth = pd.DataFrame(log_diff_p).rolling(3, center=True).mean()
     ax.plot(index[1:], diff_smooth, label='Moving average (3 period)', alpha=0.5, lw=2)
@@ -345,7 +342,7 @@ def pr_plot(p_seq, index, ax):
     for label in ax.get_xticklabels():
         label.set_rotation(45)
     
-    ax.legend(loc='upper left')
+    ax.legend()
     
     return ax
 ```
@@ -419,7 +416,7 @@ p_seq = df_aus['Retail price index, 52 commodities']
 e_seq = df_aus['Exchange Rate']
 
 lab = ['Retail price index', 
-       '1/cents per Austrian Krone (Crown)']
+       'Austrian Krones (Crowns) per US cent']
 
 # Create plot
 fig, ax = plt.subplots(dpi=200)
@@ -463,12 +460,11 @@ mystnb:
     caption: Price index and exchange rate (Hungary)
     name: pi_xrate_hungary
 ---
-m_seq = df_hun['Notes in circulation']
 p_seq = df_hun['Hungarian index of prices']
 e_seq = 1 / df_hun['Cents per crown in New York']
 
 lab = ['Hungarian index of prices', 
-       '1/cents per Hungarian Korona (Crown)']
+       'Hungarian Koronas (Crowns) per US cent']
 
 # Create plot
 fig, ax = plt.subplots(dpi=200)
@@ -537,7 +533,7 @@ e_seq[e_seq.index > '05-01-1924'] = np.nan
 
 ```{code-cell} ipython3
 lab = ['Wholesale price index', 
-       '1/cents per polish mark']
+       'Polish marks per US cent']
 
 # Create plot
 fig, ax = plt.subplots(dpi=200)
@@ -579,7 +575,7 @@ p_seq = df_deu['Price index (on basis of marks before July 1924,'
 e_seq = 1/df_deu['Cents per mark']
 
 lab = ['Price index', 
-       '1/cents per mark']
+       'Marks per US cent']
 
 # Create plot
 fig, ax = plt.subplots(dpi=200)
@@ -606,7 +602,7 @@ e_seq[e_seq.index > '12-01-1923'] = e_seq[e_seq.index
                                           > '12-01-1923'] * 1e12
 
 lab = ['Price index (marks or converted to marks)', 
-       '1/cents per mark (or reichsmark converted to mark)']
+       'Marks per US cent(or reichsmark converted to mark)']
 
 # Create plot
 fig, ax = plt.subplots(dpi=200)

lectures/prob_dist.md

@@ -124,6 +124,8 @@ S = np.arange(1, n+1)
 ax.plot(S, u.pmf(S), linestyle='', marker='o', alpha=0.8, ms=4)
 ax.vlines(S, 0, u.pmf(S), lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('PMF')
 plt.show()
 ```
 
@@ -136,6 +138,8 @@ S = np.arange(1, n+1)
 ax.step(S, u.cdf(S))
 ax.vlines(S, 0, u.cdf(S), lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('CDF')
 plt.show()
 ```
 
@@ -232,6 +236,8 @@ S = np.arange(1, n+1)
 ax.plot(S, u.pmf(S), linestyle='', marker='o', alpha=0.8, ms=4)
 ax.vlines(S, 0, u.pmf(S), lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('PMF')
 plt.show()
 ```
 
@@ -244,6 +250,8 @@ S = np.arange(1, n+1)
 ax.step(S, u.cdf(S))
 ax.vlines(S, 0, u.cdf(S), lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('CDF')
 plt.show()
 ```
 
@@ -267,6 +275,8 @@ u_sum = np.cumsum(u.pmf(S))
 ax.step(S, u_sum)
 ax.vlines(S, 0, u_sum, lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('CDF')
 plt.show()
 ```
 
@@ -289,21 +299,13 @@ The mean and variance are:
 ```{code-cell} ipython3
 λ = 2
 u = scipy.stats.poisson(λ)
-```
-    
-```{code-cell} ipython3
 u.mean(), u.var()
 ```
-
-The the expectation of Poisson distribution is $\lambda$ and the variance is also $\lambda$.
+    
+The expectation of the Poisson distribution is $\lambda$ and the variance is also $\lambda$.
 
 Here's the PMF:
 
-```{code-cell} ipython3
-λ = 2
-u = scipy.stats.poisson(λ)
-```
-
 ```{code-cell} ipython3
 u.pmf(1)
 ```
@@ -314,6 +316,8 @@ S = np.arange(1, n+1)
 ax.plot(S, u.pmf(S), linestyle='', marker='o', alpha=0.8, ms=4)
 ax.vlines(S, 0, u.pmf(S), lw=0.2)
 ax.set_xticks(S)
+ax.set_xlabel('S')
+ax.set_ylabel('PMF')
 plt.show()
 ```
 
@@ -386,7 +390,8 @@ for μ, σ in zip(μ_vals, σ_vals):
     ax.plot(x_grid, u.pdf(x_grid),
     alpha=0.5, lw=2,
     label=f'$\mu={μ}, \sigma={σ}$')
-
+ax.set_xlabel('x')
+ax.set_ylabel('PDF')
 plt.legend()
 plt.show()
 ```
@@ -402,6 +407,8 @@ for μ, σ in zip(μ_vals, σ_vals):
     alpha=0.5, lw=2,
     label=f'$\mu={μ}, \sigma={σ}$')
     ax.set_ylim(0, 1)
+ax.set_xlabel('x')
+ax.set_ylabel('CDF')
 plt.legend()
 plt.show()
 ```
@@ -446,7 +453,8 @@ for μ, σ in zip(μ_vals, σ_vals):
     ax.plot(x_grid, u.pdf(x_grid),
     alpha=0.5, lw=2,
     label=f'$\mu={μ}, \sigma={σ}$')
-
+ax.set_xlabel('x')
+ax.set_ylabel('PDF')
 plt.legend()
 plt.show()
 ```
@@ -461,6 +469,8 @@ for σ in σ_vals:
     label=f'$\mu={μ}, \sigma={σ}$')
     ax.set_ylim(0, 1)
     ax.set_xlim(0, 3)
+ax.set_xlabel('x')
+ax.set_ylabel('CDF')
 plt.legend()
 plt.show()
 ```
@@ -500,6 +510,8 @@ for λ in λ_vals:
     ax.plot(x_grid, u.pdf(x_grid),
     alpha=0.5, lw=2,
     label=f'$\lambda={λ}$')
+ax.set_xlabel('x')
+ax.set_ylabel('PDF')
 plt.legend()
 plt.show()
 ```
@@ -512,6 +524,8 @@ for λ in λ_vals:
     alpha=0.5, lw=2,
     label=f'$\lambda={λ}$')
     ax.set_ylim(0, 1)
+ax.set_xlabel('x')
+ax.set_ylabel('CDF')
 plt.legend()
 plt.show()
 ```
@@ -557,6 +571,8 @@ for α, β in zip(α_vals, β_vals):
     ax.plot(x_grid, u.pdf(x_grid),
     alpha=0.5, lw=2,
     label=fr'$\alpha={α}, \beta={β}$')
+ax.set_xlabel('x')
+ax.set_ylabel('PDF')
 plt.legend()
 plt.show()
 ```
@@ -569,6 +585,8 @@ for α, β in zip(α_vals, β_vals):
     alpha=0.5, lw=2,
     label=fr'$\alpha={α}, \beta={β}$')
     ax.set_ylim(0, 1)
+ax.set_xlabel('x')
+ax.set_ylabel('CDF')
 plt.legend()
 plt.show()
 ```
@@ -614,6 +632,8 @@ for α, β in zip(α_vals, β_vals):
     ax.plot(x_grid, u.pdf(x_grid),
     alpha=0.5, lw=2,
     label=fr'$\alpha={α}, \beta={β}$')
+ax.set_xlabel('x')
+ax.set_ylabel('PDF')
 plt.legend()
 plt.show()
 ```
@@ -626,6 +646,8 @@ for α, β in zip(α_vals, β_vals):
     alpha=0.5, lw=2,
     label=fr'$\alpha={α}, \beta={β}$')
     ax.set_ylim(0, 1)
+ax.set_xlabel('x')
+ax.set_ylabel('CDF')
 plt.legend()
 plt.show()
 ```
@@ -720,6 +742,8 @@ We can histogram the income distribution we just constructed as follows
 x = df['income']
 fig, ax = plt.subplots()
 ax.hist(x, bins=5, density=True, histtype='bar')
+ax.set_xlabel('income')
+ax.set_ylabel('density')
 plt.show()
 ```
 
@@ -760,6 +784,8 @@ x_amazon = np.asarray(data)
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 ax.hist(x_amazon, bins=20)
+ax.set_xlabel('monthly return (percent change)')
+ax.set_ylabel('density')
 plt.show()
 ```
 
@@ -774,6 +800,8 @@ KDE will generate a smooth curve that approximates the PDF.
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 sns.kdeplot(x_amazon, ax=ax)
+ax.set_xlabel('monthly return (percent change)')
+ax.set_ylabel('KDE')
 plt.show()
 ```
 
@@ -784,6 +812,8 @@ fig, ax = plt.subplots()
 sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.1, alpha=0.5, label="bw=0.1")
 sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.5, alpha=0.5, label="bw=0.5")
 sns.kdeplot(x_amazon, ax=ax, bw_adjust=1, alpha=0.5, label="bw=1")
+ax.set_xlabel('monthly return (percent change)')
+ax.set_ylabel('KDE')
 plt.legend()
 plt.show()
 ```
@@ -802,6 +832,8 @@ Yet another way to display an observed distribution is via a violin plot.
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 ax.violinplot(x_amazon)
+ax.set_ylabel('monthly return (percent change)')
+ax.set_xlabel('KDE')
 plt.show()
 ```
 
@@ -822,6 +854,8 @@ x_apple = np.asarray(data)
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 ax.violinplot([x_amazon, x_apple])
+ax.set_ylabel('monthly return (percent change)')
+ax.set_xlabel('KDE')
 plt.show()
 ```
 
@@ -855,6 +889,8 @@ x_grid = np.linspace(-50, 65, 200)
 fig, ax = plt.subplots()
 ax.plot(x_grid, u.pdf(x_grid))
 ax.hist(x_amazon, density=True, bins=40)
+ax.set_xlabel('monthly return (percent change)')
+ax.set_ylabel('density')
 plt.show()
 ```
 
@@ -882,6 +918,8 @@ x_grid = np.linspace(-4, 4, 200)
 fig, ax = plt.subplots()
 ax.plot(x_grid, u.pdf(x_grid))
 ax.hist(x_draws, density=True, bins=40)
+ax.set_xlabel('x')
+ax.set_ylabel('density')
 plt.show()
 ```