A Brief Introduction to Modern Time Series
Definition A time series is a random function xt of an argument t in a set T. In other
words, a time series is a family of random variables ., x t-1, xt, xt+1, . corresponding to
all elements in the set T, where
Test Review:
Discounting
Formula for Net Discounted Benefits (NPV): 9-20 fig1
How discounting affects Cs and Bs: makes them lower over time
Rationale for discounting: time preference people prefer benefits now/costs later
Evidence for choosing a rate:
One-way sensitivity analysis change the value of one parameter holding all others at their basecase values and recalculate the CER or net benefit.
Sinha article uses $ per DALY averted
Vaccine efficacy range from 3% to 16%. When 16%, $/DALY averted roughl
Measure effects, quantify effects, weigh effects
Belestra and Littenberg Initially, boosters up to age 6 and boosters every 10 years.
Whos interested? CDC and Preventative Services Task Force
Recommendations often not followed, but should we emphasize mor
Methods of Cost-Benefit Analysis, Professor Russell
Answers to TEST, October 11, 2012
1. (25 points) Define each term on the right-hand side of the following equation
t
T
Bt
Ct
r
Time period, the units in which time is measured, e.g., one year
Time horizo
1Methods of Cost-Benefit Analysis, Professor Russell
QUIZ, September 27, 2011
1. (25 points) After discounting, a vaccination program for children costs $300
per person and produces 20.1 years of life per person. Not vaccinating costs $100
and produces 20
1. The Likelihood Ratio Test in Small Samples with Known Distribution
Consider the random variable Y~N(
). The unrestricted parameter space for Y
is
. However, on the basis of, say, an
economic model, we have some belief about . We can represent this beli
SAMPLING DISTRIBUTIONS
A. SAMPLE MEAN
1. POPULATION VARIANCE KNOWN
a. NORMAL POPULATION
The mean of , when xi are iid with
expectation is a linear operator
The var of
is found by exploiting the fact that
is found by exploiting the same property
DISTRIBUTI
REVIEW OF LINEAR ALGEBRA*
A.1 ADDITION
Vector addition is defined component wise:
A.2 SCALAR MULTIPLICATION
Scalar multiplication is similar. x is an n component vector, is a scalar.
A.3 INNER PRODUCTS
Let
the inner product of x and y is a number
B.1 INDE
PROPERTIES OF ESTIMATORS
SMALL SAMPLE PROPERTIES
UNBIASEDNESS: An estimator is said to be unbiased if in the long run it takes
on the value of the population parameter. That is, if you were to draw a
sample, compute the statistic, repeat this many, many t
HYPOTHESIS TESTING
As already acknowledged we know little about the values of population
parameters that define the probability distributions of the world. In the
previous section it was our goal to estimate these parameters. Often we may
have some prior
Generalized Least Squares
In this chapter we generalize the results of the previous chapter as the basis for
introducing the pathological diseases of regression analysis. First, we abandon the
assumption of a scalar diagonal variance of the error term, bu
Estimation
6.3.1 Single Equation Methods
6.3.1.1 Instrumental Variables
We begin with Instrumental Variables (IV) estimation for several reasons. First, it is
easy to show that the estimator is consistent. Second, as we shall see, it is easy to
show that
DATA PROBLEMS: Measurement Error
The correct model is y* = x* + but we do not observe or measure the data correctly.
Possibly what we observe is
1
We will consider a few cases, begining with the easiest. Suppose that we can observe
x*, but not y*. Then ou
Asymptotic Theory, Order in Probability
and Laws of Large Numbers
Notation
is the set of all possible outcomes, or the sample space. For example, in flipping
two coins the sample space consists of cfw_H 1 H2, H1 T2, T1 H2, T1 T2, where the
subscripts are
Study Guide for the December 11, 2012 test
The readings covered by this test are: Viscusi; Nichols; Malla et al.; and, if your lecture notes on
indirect valuation methods are not sufficient, Boardman chapter 14, pages 344-57 and 365-68.
No reading was ass