From 7917a8f7faf88995762dee4936e6cc100c901ed1 Mon Sep 17 00:00:00 2001 From: Miles Tiley Date: Thu, 28 Nov 2019 14:55:32 +1100 Subject: [PATCH 1/2] Proofread and typo fix in heavy_tails --- source/rst/heavy_tails.rst | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/source/rst/heavy_tails.rst b/source/rst/heavy_tails.rst index 576fd346..50f3b8ef 100644 --- a/source/rst/heavy_tails.rst +++ b/source/rst/heavy_tails.rst @@ -64,7 +64,7 @@ It matters for taxation and redistribution policies, as well as for flow-on effects for productivity growth, business cycles, and political economy -* see, e.g., :cite:`acemoglu2002political`, :cite:`glaeser2003injustice`, :cite:`bhandari2018inequality` or :cite:`ahn2018inequality`). +* see, e.g., :cite:`acemoglu2002political`, :cite:`glaeser2003injustice`, :cite:`bhandari2018inequality` or :cite:`ahn2018inequality`. This lecture formalizes some of the concepts introduced above and reviews the key ideas. @@ -123,7 +123,7 @@ Heavy Tails in Asset Returns Next let's look at some financial data. Our aim is to plot the daily change in the price of Amazon (AMZN) stock for -the period 1st January 2015 to 1st November 2019, +the period from 1st January 2015 to 1st November 2019. This equates to daily returns if we set dividends aside. @@ -172,7 +172,7 @@ One impact of heavy tails is that sample averages can be poor estimators of the underlying mean of the distribution. To understand this point better, recall :doc:`our earlier discussion -` of the Law of Large Numbers, which considered iid :math:`X_1, +` of the Law of Large Numbers, which considered IID :math:`X_1, \ldots, X_n` with common distribution :math:`F` If :math:`\mathbb E |X_i|` is finite, then @@ -395,7 +395,7 @@ Prove: If :math:`X` has a Pareto tail with tail index :math:`\alpha`, then Exercise 3 ---------- -Repeat exercise 1, but replacing the three distributions (two normal, one +Repeat exercise 1, but replace the three distributions (two normal, one Cauchy) with three Pareto distributions using different choices of :math:`\alpha`. @@ -425,7 +425,7 @@ phenomena. To illustrate this fact in a simple way, let us consider an economy with 100,000 firms, an interest rate of ``r = 0.05`` and a corporate tax rate of -15%. +15\%. Your task is to estimate the present discounted value of projected corporate tax revenue over the next 10 years. From 05f1caadc2c51fe1ebabbc37b669de8f63a2a181 Mon Sep 17 00:00:00 2001 From: Miles Tiley Date: Thu, 28 Nov 2019 15:43:24 +1100 Subject: [PATCH 2/2] Fix typos in kesten_processes.rst --- source/rst/kesten_processes.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/rst/kesten_processes.rst b/source/rst/kesten_processes.rst index 2b8e447e..344b3157 100644 --- a/source/rst/kesten_processes.rst +++ b/source/rst/kesten_processes.rst @@ -55,7 +55,7 @@ Kesten Processes single: Kesten processes; heavy tails -A **Kesten process** is a stochastic processes of the form +A **Kesten process** is a stochastic process of the form .. math:: :label: kesproc @@ -230,7 +230,7 @@ Since :math:`F^*` is stationary for the wealth process, this is just Hence the fraction of households with wealth in :math:`[0, y]` is the same next period as it is this period. -Since :math:`y` was chosen arbitrarily, the distribution is inchanged. +Since :math:`y` was chosen arbitrarily, the distribution is unchanged. Conditions for Stationarity