Exercises 303
sizes between 20 and 25, and then jumps again for class sizes greater than 25.
To model these threshold effects, define the binary variables
S TRsmall = 1 if S TR < 20, and STRsmall = 00therwise:
S TRmoderate = 1 if 20 s S TR 5 25, and S T
Department of Economics
Boston University
Spring 2017
EC304: Empirical Economic Analysis II
Class hours:
Monday and Wednesday 10:10-11:25
Class location:
CAS 226
Instructor:
Prof. Zhongjun Qu, [email protected]
O ce hours:
Wednesday 2:00-3:30, Thursday 9:3011:00
CAS EC 501 Microeconomics
Assignment 1
Solutions
1. 3.4
Solution: a) convex preferences; b) concave preferences; c) both convex and concave
(linear) preferences
2. 3.6
Solution: a) u = p + b; b) @ 2 u(c; y)[email protected]@y > 0; c) u(1; y) < u(0; y) < u(p; y) where
p
Boston University, Department of Economics
ECON 304: Empirical Economics (II)
Spring 2017
Problem Set 1
(Due: Monday, Feb 13)
Note: the page numbers correspond to those of Stock and Watson: "Introduction to
Econometrics" (Third Edition).
1. P135, 4.2.
2.
Chapter 12
Instrumental Variables Regression
1
Instrumental Variables Regression the Basic Idea
Recall three important threats to internal validity are:
omitted variable bias;
simultaneous causality bias (X causes Y, Y causes X);
errors-in-variables bi
Chapter 8
Nonlinear Regression Functions
1
Preview
Everything so far has been linear in the Xs
But the linear approximation is not always a good one
The multiple regression framework can be extended to handle
regression functions that are nonlinear in one
Chapter 9: Assessing Studies Based on Multiple Regression
1
Assessing Studies Based on Multiple Regression
Lets step back and take a broader look at regression:
Is there a systematic way to assess (critique) regression
studies? What makes a study based on
Chapter 4: Linear Regression with One Regressor
1
The model to study
Yi = 0 + 1Xi + ui, i = 1, n
where,
X is the independent variable or regressor
Y is the dependent variable
0 = intercept
1 = slope
ui = the regression error
ui consists of omitted factors
Chapter 6
Introduction to Multiple Regression
1
Outline
Omitted variable bias
2. Multiple regression and OLS
3. Measures of fit
4. Sampling distribution of the OLS estimator
1.
2
Omitted Variable Bias (SW Section 6.1)
The error u arises because of factors
Chapter 7
Hypothesis Tests and Confidence Intervals in
Multiple Regression
1
The Outline
Hypothesis tests and confidence intervals for a single coefficient
Joint hypothesis tests on multiple coefficients
Other types of hypotheses involving multiple coeffi
Discussion: Regression toward the Mean
Spring 2013
()
Discussion: Regression toward the Mean
Spring 2013
1 / 10
Three examples
Example
(Standardized educational tests in Massachusetts) In 1999, schools were given
improvement goals. For each school, the De
Chapter 1: Economic Questions and Data
1.
2.
3.
Econometrics?
Econometrics uses data to provide quantitative answers to
economic questions.
In this chapter, we will
examine some economics questions,
discuss the types of data that are available to answer s
Chapter 2. Review of Concepts in Statistics
Spring 2017
()
Chapter 2. Review of Concepts in Statistics
Spring 2017
1 / 10
Sample and population
Denition
A population is a set of entities about which statistical inferences are to be drawn. A
sample is part
EC304. Midterm #2 outline.
General info:
1. Bring a simple calculator and the printouts of the statistical tables for normal, t-, and chi-square-distributions
(will be also distributed in class).
2. An extra pen/penc
GDP:
1. Three ways of measuring GDP:
a) expenditure approach: Y = C + G + I +Nx
b) income approach: all income earned in the economy
c) production approach: limitation: no doubling the value of production; only new
production counts
2. GDP limitations:
a)
Shuangqi Tian
Hw.4
1. a) The second is correct because price should be the response variable and sales should be the
explanatory variable in order to be economically correct.
b) R^2 = rxy^2 which is the square of the correlation coefficient between depend
Shuangqi Tian
EC 304
Hw. 2
4. a)
b) mean = 201334, there is no standard deviation because only 1 variable exists.
c)
coefficient of variability = standard deviation/ mean = 146983.4/ 271178.2 0.542
Standard deviation is more intuitive to represent the sam
Lecture: Continuous Time Models with
Investment Applications
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Brownian Motion
Brownian motion (Wiener process): Continous time stochastic
process with three properties:
Markov process: probability
Lecture 6: Recursive Preferences
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Basics
Epstein and Zin (1989 JPE, 1991 Ecta) following work by Kreps
and Porteus introduced a class of preferences which allow to
break the link between risk aver
Lecture 8: Two period corporate debt model
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
A two-period model with investment
At time 1, the firm buys capital k, using equity issuance s and
debt: the firm issues a debt with face value b, at un
Lecture 7: Term Structure Models
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Bond basics
A zero-coupon n period bond is a claim to a sure payoff of 1 at
(n)
time t + n. The price is denoted Pt and it satisfies the
recursion:
(n)
(n1)
Pt
=
Lecture 1: Asset pricing and the equity premium
puzzle
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Overview
Some basic facts.
Study the asset pricing implications of household portfolio
choice.
Consider the quantitative implications of a s
Lecture 4: Campbell-Shiller Decomposition
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Campbell and Shiller decomposition
Introduce a log-linear approximation to the present-value
identity (prices = Present Discounted Value [PDV] of dividen
Lecture 2: Stochastic Discount Factor
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Stochastic Discount Factor (SDF)
A stochastic discount factor is a stochastic process cfw_Mt,t+s
such that for any security with payoff xt+1 at time t + 1 t
Lecture 3: Euler-Equation Estimation
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Euler equation tests
This lecture considers some further implications and tests of the
standard asset pricing model: for any gross return Rt+1 , we
have the e
Some notes on continuous time finance
Basics:
Instantaneous total return:
dpt
Dt
+
dt
pt
pt
where pt is price and Dt is instantaneous rate of dividend.
Model price as a diffusion:
dpt
= () dt + () dz
pt
Risk free security can be modeled as a security w
Lecture 5: Asset Pricing Model with Habit
Formation
Simon Gilchrist
Boston Univerity and NBER
EC 745
Fall, 2013
Habit model:
Assume:
U =E
X
t u (ct , ht )
t=0
,with u given, for instance, by the formula
u(c, h) =
(c h)1
,
1
where > 0 is a parameter and h