ch 10

markdown/Ch10. Basic Regression Analysis with Time Series Data.md

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+---
+jupyter:
+  jupytext:
+    formats: notebooks//ipynb,markdown//md,scripts//py
+    text_representation:
+      extension: .md
+      format_name: markdown
+      format_version: '1.3'
+      jupytext_version: 1.16.4
+  kernelspec:
+    display_name: merino
+    language: python
+    name: python3
+---
+
+# 10. Basic Regression Analysis with Time Series Data
+
+```python
+%pip install matplotlib numpy pandas statsmodels wooldridge -q
+```
+
+```python
+import matplotlib.pyplot as plt
+import numpy as np  # noqa
+import pandas as pd
+import statsmodels.formula.api as smf
+import wooldridge as wool
+```
+
+## 10.1 Static Time Series Models
+
+$$ y_t = \beta_0 + \beta_1 z_{1t} + \beta_2 z_{2t} + \cdots + \beta_k z_{kt} + u_t $$
+
+### Example 10.2 Effects of Inflation and Deficits on Interest Rates
+
+```python
+intdef = wool.dataWoo("intdef")
+
+# linear regression of static model (Q function avoids conflicts with keywords):
+reg = smf.ols(formula='i3 ~ Q("inf") + Q("def")', data=intdef)
+results = reg.fit()
+
+# print regression table:
+table = pd.DataFrame(
+    {
+        "b": round(results.params, 4),
+        "se": round(results.bse, 4),
+        "t": round(results.tvalues, 4),
+        "pval": round(results.pvalues, 4),
+    },
+)
+print(f"table: \n{table}\n")
+```
+
+## 10.2 Time Series Data Types in Python
+
+### 10.2.1 Equispaced Time Series in Python
+
+```python
+barium = wool.dataWoo("barium")
+T = len(barium)
+
+# monthly time series starting Feb. 1978:
+barium.index = pd.date_range(start="1978-02", periods=T, freq="ME")
+print(f'barium["chnimp"].head(): \n{barium["chnimp"].head()}\n')
+```
+
+```python
+# plot chnimp (default: index on the x-axis):
+plt.plot("chnimp", data=barium, color="black", linestyle="-")
+plt.ylabel("chnimp")
+plt.xlabel("time")
+```
+
+## 10.3 Other Time Series Models
+
+### 10.3.1 Finite Distributed Lag Models
+
+$$ y_t = \alpha_0 + \delta_0 z_t + \delta_1 z_{t-1} + \cdots + \delta_k z_{t-k} + u_t $$
+
+### Example 10.4 Effects of Personal Exemption on Fertility Rates
+
+```python
+fertil3 = wool.dataWoo("fertil3")
+T = len(fertil3)
+
+# define yearly time series beginning in 1913:
+fertil3.index = pd.date_range(start="1913", periods=T, freq="YE").year
+
+# add all lags of 'pe' up to order 2:
+fertil3["pe_lag1"] = fertil3["pe"].shift(1)
+fertil3["pe_lag2"] = fertil3["pe"].shift(2)
+
+# linear regression of model with lags:
+reg = smf.ols(formula="gfr ~ pe + pe_lag1 + pe_lag2 + ww2 + pill", data=fertil3)
+results = reg.fit()
+
+# print regression table:
+table = pd.DataFrame(
+    {
+        "b": round(results.params, 4),
+        "se": round(results.bse, 4),
+        "t": round(results.tvalues, 4),
+        "pval": round(results.pvalues, 4),
+    },
+)
+print(f"table: \n{table}\n")
+```
+
+### Eample 10.4 (continued)
+
+```python
+fertil3 = wool.dataWoo("fertil3")
+T = len(fertil3)
+
+# define yearly time series beginning in 1913:
+fertil3.index = pd.date_range(start="1913", periods=T, freq="YE").year
+
+# add all lags of 'pe' up to order 2:
+fertil3["pe_lag1"] = fertil3["pe"].shift(1)
+fertil3["pe_lag2"] = fertil3["pe"].shift(2)
+
+# linear regression of model with lags:
+reg = smf.ols(formula="gfr ~ pe + pe_lag1 + pe_lag2 + ww2 + pill", data=fertil3)
+results = reg.fit()
+
+# F test (H0: all pe coefficients are=0):
+hypotheses1 = ["pe = 0", "pe_lag1 = 0", "pe_lag2 = 0"]
+ftest1 = results.f_test(hypotheses1)
+fstat1 = ftest1.statistic
+fpval1 = ftest1.pvalue
+
+print(f"fstat1: {fstat1}\n")
+print(f"fpval1: {fpval1}\n")
+```
+
+```python
+# calculating the LRP:
+b = results.params
+b_pe_tot = b["pe"] + b["pe_lag1"] + b["pe_lag2"]
+print(f"b_pe_tot: {b_pe_tot}\n")
+```
+
+```python
+# F test (H0: LRP=0):
+hypotheses2 = ["pe + pe_lag1 + pe_lag2 = 0"]
+ftest2 = results.f_test(hypotheses2)
+fstat2 = ftest2.statistic
+fpval2 = ftest2.pvalue
+
+print(f"fstat2: {fstat2}\n")
+print(f"fpval2: {fpval2}\n")
+```
+
+### 10.3.2 Trends
+
+### Example 10.7 Housing Investment and Prices
+
+```python
+hseinv = wool.dataWoo("hseinv")
+
+# linear regression without time trend:
+reg_wot = smf.ols(formula="np.log(invpc) ~ np.log(price)", data=hseinv)
+results_wot = reg_wot.fit()
+
+# print regression table:
+table_wot = pd.DataFrame(
+    {
+        "b": round(results_wot.params, 4),
+        "se": round(results_wot.bse, 4),
+        "t": round(results_wot.tvalues, 4),
+        "pval": round(results_wot.pvalues, 4),
+    },
+)
+print(f"table_wot: \n{table_wot}\n")
+```
+
+```python
+# linear regression with time trend (data set includes a time variable t):
+reg_wt = smf.ols(formula="np.log(invpc) ~ np.log(price) + t", data=hseinv)
+results_wt = reg_wt.fit()
+
+# print regression table:
+table_wt = pd.DataFrame(
+    {
+        "b": round(results_wt.params, 4),
+        "se": round(results_wt.bse, 4),
+        "t": round(results_wt.tvalues, 4),
+        "pval": round(results_wt.pvalues, 4),
+    },
+)
+print(f"table_wt: \n{table_wt}\n")
+```
+
+### 10.3.3 Seasonality
+
+### Example 10.11 Effects of Antidumping Filings
+
+```python
+barium = wool.dataWoo("barium")
+
+# linear regression with seasonal effects:
+reg = smf.ols(
+    formula="np.log(chnimp) ~ np.log(chempi) + np.log(gas) +"
+    "np.log(rtwex) + befile6 + affile6 + afdec6 +"
+    "feb + mar + apr + may + jun + jul +"
+    "aug + sep + oct + nov + dec",
+    data=barium,
+)
+results = reg.fit()
+
+# print regression table:
+table = pd.DataFrame(
+    {
+        "b": round(results.params, 4),
+        "se": round(results.bse, 4),
+        "t": round(results.tvalues, 4),
+        "pval": round(results.pvalues, 4),
+    },
+)
+print(f"table: \n{table}\n")
+```

markdown/Ch2. The Simple Regression Model.md

@@ -75,6 +75,7 @@ b = results.params
 print(f"b: \n{b}")
 ```
 
+
 ```python
 def plot_regression(x, y, data, results, title):
     # scatter plot and fitted values:

markdown/Ch6. MRA - Further Issues.md

@@ -73,6 +73,9 @@ $$z_y = \frac{y - \bar{y}}{\text{sd}(y)}  \qquad \text{and} \qquad z_{x_1} = \fr
 
 $$\text{price\_sc} = \beta_0 + \beta_1 \cdot \text{nox\_sc} + \beta_2 \cdot \text{crime\_sc} + \beta_3 \cdot \text{rooms\_sc} + \beta_4 \cdot \text{dist\_sc} + \beta_5 \cdot \text{stratio\_sc} + u$$
 
+
+
+
 ```python
 # define a function for the standardization:
 def scale(x):

notebooks/Ch2. The Simple Regression Model.ipynb

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+   "metadata": {
+    "lines_to_next_cell": 2
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notebooks/Ch6. MRA - Further Issues.ipynb

@@ -109,7 +109,9 @@
     "\n",
     "### Example 6.1: Effects of Pollution on Housing Prices\n",
     "\n",
-    "$$\\text{price\\_sc} = \\beta_0 + \\beta_1 \\cdot \\text{nox\\_sc} + \\beta_2 \\cdot \\text{crime\\_sc} + \\beta_3 \\cdot \\text{rooms\\_sc} + \\beta_4 \\cdot \\text{dist\\_sc} + \\beta_5 \\cdot \\text{stratio\\_sc} + u$$"
+    "$$\\text{price\\_sc} = \\beta_0 + \\beta_1 \\cdot \\text{nox\\_sc} + \\beta_2 \\cdot \\text{crime\\_sc} + \\beta_3 \\cdot \\text{rooms\\_sc} + \\beta_4 \\cdot \\text{dist\\_sc} + \\beta_5 \\cdot \\text{stratio\\_sc} + u$$\n",
+    "\n",
+    "\n"
    ]
   },
   {