Lecture 6
Numerical Optimization Techniques
Want to maximize or minimize the (possibly nonlinear) objective function F ( ) , which
is usually log likelihood function.
3 parts to numerical search algorithms:
(1) obtaining initial starting values for the pa
LECTURE 1
Some Examples of Maximum Likelihood Estimation
Maximum Likelihood Estimation is a statistical estimation technique that chooses
as estimates of the parameters of a statistical model the parameter values that, given the
data, maximize the likelih
Lecture 2
Examining the efficiency of estimators vis-vis the Cramer-Rao Lower Bound.
Hessian for N ( , 2 ) model:
N
2
H=
N ( xi )
i =1
4
H11 =
i =1( xi )
2 l ( x; , 2 )
2
4
=
2
2
N
( x ) 2 l ( x; , )
N
i =1 i
2
6
2 4
N
2 l ( x; , 2 )
2
2
Lecture 5
Three ML Test Procedures: LR, W and LM
Likelihood Ratio Test
Let be the parameter vector, be the ML estimator, and R be the restricted ML
estimator.
L( R )
The likelihood ratio is =
L( )
where L(.) denotes the likelihood function.
Then -2ln ~ 2J
Lecture 7
Two-Step Estimation Methods that are Asymptotically Equivalent to MLE
(Linearized Maximum Likelihood Procedures)
See A.C. Harvey EATS, Chapter 4 Section 5
For proof that linearized ML estimators are asymptotically equivalent to MLE see
A.C. Harv
CHAPTER 6
Growth and Ideas
OVERVIEW
KEY CONCEPTS
As a subsequent development to the Solow growth model,
the Romer growth model expands macroeconomists ability
to address one of the most important questions about an
economys growth experience; namely, how
The rising costs of complying with supervisory demands have brought the issue of regulatory burden to the attention of both lawmakers and bank regulators. But one relatively
underappreciated aspect of regulatory burden is
the potential for the supervisory
Lecture 4
Estimating the Asymptotic Covariance Matrices of
Maximum Likelihood Estimators
The asymptotic variance-covariance matrix of MLEs can be estimated by
1
[I ( )]
1
~ | =
~
~ ML
2 ln L
= E
.
~ ~ | =
~
~ ML
However, this estimator may not be av
Lecture 3
Maximum Likelihood Estimation for the Classical Normal Linear Regression
Model, Examination of MVU Efficiency of Estimators, and the Super Theorem of
Maximum Likelihood Estimation
; ~ N (0, 2 I )
y = X +
~
~
~
~
1
L( y X , , ) =
2
~
~
~
N
2
* ex
INSTRUCTIONS: Select the @ response to each question or statement and bubble in the
corresponding letter on your scantron. You may write on this exam, but only answers marked on the
scantron are graded. Each correct response is worth 5 points out of 200.
2008 Financial Crisis Breakdown
The 2008 financial crisis was a contribution of a number of factors that
created a meltdown in many financial markets. The financial crisis has been
proclaimed to be one of the worst economic disasters since the Great Depre
Trade has been a practice that has been used since the beginning of time. Throughout
history as countries began to separate, countries exchanged their abundant resource for
a necessary resource for their survival that was scarce in their country. This sys
Bell Curve and Equations
Individuals who are high and low skilled are the individuals that tend to
migrate to destination countries by leaving their host country. The migration
patterns for a designated range of skills demonstrates that individuals that a
November 11, 2016
Illicit Markets Markets where it is hard or illegal to sell a product
- For example, you cannot own a tank
Supply is restricted because it is against the law to have it so possessing something
from the illicit markets is illegal as well
Specialization and Human Capital
Where do the gains from labor market specialization arise according to the author?
Incentives for specialization, trade, and the production of comparative advantage
through investment are shown to arise from increasing ret
Heterogenous Human Capital and Migration
What is heterogeneous human capital? Heterogeneous human capital means that
each individual is endowed with different levels of human capital.
What does the author mean by a U-shaped relationship between education
Declining Bee Population: Causes, Impacts, and Solutions
I.
Importance of bees in the ecosystem
Bees play a larger role in the Ecosystem than we know. These insects are easily
overlooked for how vital their functions really are. Their pollination practice
International Parity conditions
Purchasing Power Parity
In todays context, it is entirely useless to study this
Why?
Outsourcing and PPP both cannot be true at the
same time
Well, almost
Do you know why?
Other reasons for not wanting to study PPP
It
Basic concepts and principles in
Econometrics
The material in this PPT is based on CFA-2013, Level II, Book 1
unless otherwise stated
Econometrics
Econometrics is the application of mathematics, statistical
methods, and computer science, to economic data
Global Crisis Causes
V. Anantha Nageswaran
January 2016
The many causes of the crisis
Meta Cause:
The inherent instability of finance
Low volatility before crisis: a sign of
complacency and overconfidence
4
History repeats itself? VIX chart extended
up to
Global Financial Crisis Responses
and Consequences Part 2
V. Anantha Nageswaran
October 2016
The only game in town
Source: IIF Capital Markets Monitor July/August 2016
China Peoples Bank of China assets
China: Monetary Authority: Total Assets
2002=100
Chi
Money Illusion
Concept
Refers to the tendency of people to think of currency in nominal, rather than real, terms. In other words, the
numerical/face value (nominal value) of money is mistaken for its purchasing power (real value) at a previous
point in t
Setting the stage
What separates the two periods?
Source: http:/nakedkeynesianism.blogspot.sg/2014/05/on-why-golden-age-of-capitalism-was.html
Dr. Subbarao contrasts physics and
economics
The laws of physics are universal in space and time. The laws of
ec
Asian Crisis and EMU
Convergence
Dr. V. Anantha Nageswaran
October 2015
Did REER (post-2010) decline help Japan?
Source: IMF World Economic Outlook Database, October 2015
Pre-Asian crisis: Current account balances
Source: IMF World Economic Outlook Databa
The Gold Standard
Source: http:/www.visualcapitalist.com/12-stunning-visualizations-of-gold-bars-show-its-rarity/
This is 400 oz. of gold
Source: http:/www.visualcapitalist.com/12-stunning-visualizations-of-gold-bars-show-its-rarity/
Beginnings
The gold s
Homework 4c (Principles Type Practice Questions on Cost and Production)
1. If MPK = 10, MPL = 20, PK = 2 and PL = 4 then in the long run the rm should
a. shut down
b. use more labor and less capital
0. use the same amount of labor and capital
(1. use less
Homework 4b
1. Let the short run production function be given by q = LiKiand K = 16.
a. Express L as a function of q and nd %.
b. Differentiate q = LiKi, K = 16 to nd the MPL (= (11%) and use (a) to show %
c. Use 1a and PK = 5 and PL = 16 to complete the