Update inequality.md

Author: DiaPorntipa

lectures/inequality.md

@@ -35,10 +35,10 @@ periods, diminishing their wealth.
 The resulting growth in inequality caused political turmoil that shook the
 foundations of the republic. 
 
-Eventually the Roman Republic gave way to a series of dictatorships, starting
+Eventually, the Roman Republic gave way to a series of dictatorships, starting
 with Octavian (Augustus) in 27 BCE.
 
-This history is fascinating in its own right, and also because we can see some
+This history is fascinating in its own right, and we can see some
 parallels with certain countries in the modern world.
 
 Many recent political debates revolve around inequality.
@@ -59,9 +59,9 @@ shape our findings reduces objectivity.
 To bring a truly scientific perspective to the topic of inequality we must
 start with careful definitions.
 
-In this lecture we discuss standard measures of inequality used in economic research.
+In this lecture, we discuss standard measures of inequality used in economic research.
 
-For each of these measures we will look at both simulated and real data.
+For each of these measures, we will look at both simulated and real data.
 
 We will install the following libraries.
 
@@ -86,7 +86,7 @@ from interpolation import interp
 
 One popular measure of inequality is the Lorenz curve.
 
-In this section we define the Lorenz curve and examine its properties.
+In this section, we define the Lorenz curve and examine its properties.
 
 
 ### Definition
@@ -208,7 +208,7 @@ years = df.year.unique()
 F_vals, L_vals = [], []
 
 for var in varlist:
-    # create lists to store Lorenz, Ginis
+    # create lists to store Lorenz curve data
     f_vals = []
     l_vals = []
     for year in years:
@@ -274,15 +274,15 @@ Another popular measure of income and wealth inequality is the Gini coefficient.
 
 The Gini coefficient is just a number, rather than a curve.
 
-In this section we discuss the Gini coefficient and its relationship to the
+In this section, we discuss the Gini coefficient and its relationship to the
 Lorenz curve.
 
 
 ### Definition
 
 
 As before, suppose that the sample $w_1, \ldots, w_n$ has been sorted from
-smallest to largest
+smallest to largest.
 
 The Gini coefficient is defined for the sample above as 
 
@@ -340,12 +340,12 @@ The following code computes the Gini coefficients for five different
 populations.
 
 Each of these populations is generated by drawing from a 
-lognormal distribution with parameters $\mu$ and $\sigma$.
+lognormal distribution with parameters $\mu$ (mean) and $\sigma$ (standard deviation).
 
 To create the five populations, we vary $\sigma$ over a grid of length $5$
 between $0.2$ and $4$.
 
-In each case we set $\mu = - \sigma^2 / 2$.
+In each case, we set $\mu = - \sigma^2 / 2$.
 
 This implies that the mean of the distribution does not change with $\sigma$. 
 
@@ -416,12 +416,12 @@ varlist = ['n_wealth',   # net wealth
 
 df = df_income_wealth  
 
-# create lists to store Lorenz, Gini for each inequality measure
+# create lists to store Gini for each inequality measure
 
 Ginis = []
 
 for var in varlist:
-    # create lists to store Lorenz, Ginis
+    # create lists to store Gini
     ginis = []
     
     for year in years:
@@ -432,7 +432,7 @@ for var in varlist:
         
         rd.shuffle(y)    # shuffle the sequence
         
-        # calculate and store ginis
+        # calculate and store Gini
         gini = qe.gini_coefficient(y)
         ginis.append(gini)
         
@@ -515,7 +515,7 @@ In this section we show how to compute top shares.
 ### Definition
 
 
-As before, suppose that the sample $w_1, \ldots, w_n$ has been sorted from smallest to largest
+As before, suppose that the sample $w_1, \ldots, w_n$ has been sorted from smallest to largest.
 
 Given the Lorenz curve $y = L(x)$ defined above, the top $100 \times p \%$
 share is defined as