Minor updates

Author: HengchengZhang

lectures/business_cycle.md

@@ -16,7 +16,7 @@ kernelspec:
 
 ## Overview
 
-In this lecture, we review some empirical aspects of business cycles.
+In this lecture we review some empirical aspects of business cycles.
 
 Business cycles are fluctuations in economic activity over time.
 
@@ -94,7 +94,7 @@ wb.series.metadata.get('NY.GDP.MKTP.KD.ZG')
 (gdp_growth)=
 ## GDP growth rate
 
-First, we look at GDP growth. 
+First we look at GDP growth. 
 
 Let's source our data from the World Bank and clean it.
 
@@ -289,7 +289,7 @@ plt.show()
 Greece experienced a very large drop in GDP growth around 2010-2011, during the peak
 of the Greek debt crisis.
 
-Next, let's consider Argentina.
+Next let's consider Argentina.
 
 ```{code-cell} ipython3
 ---
@@ -587,7 +587,7 @@ unempl_rate.columns = unempl_rate.columns.str.replace('YR', '').astype(int)
 fig, ax = plt.subplots()
 
 countries = ['United Kingdom', 'United States', 'Japan', 'France']
-ylabel = 'Unemployment rate (national estimate) (%)'
+ylabel = 'unemployment rate (national estimate) (%)'
 plot_comparison(unempl_rate, countries, 
                 ylabel, 0.05, None, ax, g_params, 
                 b_params, t_params, baseline=None)

lectures/inequality.md

@@ -59,7 +59,7 @@ 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.
 
@@ -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
@@ -274,7 +274,7 @@ 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.
 
 
@@ -345,7 +345,7 @@ lognormal distribution with parameters $\mu$ (mean) and $\sigma$ (standard devia
 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 $\sigma$.