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EC339 Applied Econometrics

- Introduction

What is Econometrics?

- Scope of application is large
- Literal definition measurement in economics
- Working definition application of statistical

methods to problems that are of concern to

economists - Econometrics has wide applicationsbeyond the

scope of economics

What is Econometrics?

- Econometrics is primarily interested in
- Quantifying economic relationships
- Testing competing hypothesis
- Forecasting

Quantifying Economic Relationships

- Outcomes of many policies tied to the magnitude

of the slope of supply and demand curves - Often need to know elasticities before we can

begin practical analysis - For example, if the minimum wage is raised,

unemployment may drop as more workers enter the

labor force - However, this depends on the slopes of the labor

supply and labor demand curves - Econometric analysis attempts to determine this

answer - Allows us to quantify causal relationships when

the luxury of a formal experiment is not available

Testing Competing Hypothesis

- Econometrics helps fill the gap between the

theoretical world and the real world - For instance, will a tax cut impact consumer

spending? - Keynesian models relate consumer spending to

annual disposable income, suggesting that a cut

in taxes will change consumer spending - Other theories relate consumer spending to

lifetime income, suggesting a tax cut (especially

a one-shot deal) will have little impact on

consumer spending

Forecasting

- Econometrics attempts to provide the information

needed to forecast future values - Such as inflation, unemployment, stock market

levels, etc.

The Use of Models

- Economists use models to describe real-world

processes - Models are simplified depictions of reality
- Usually an equation or set of equations
- Economic theories are usually deterministic while

the world is characterized by randomness - Empirical models include a random component known

as the error term, or ?i - Typically assume that the mean of the error term

is zero

Types of Data

- Data provide the raw material needed to
- Quantify economic relationships
- Test competing theories
- Construct forecasts
- Data can be described as a set of observations

such as income, age, grade - Each occurrence is called an observation
- Data are in different formats
- Cross-sectional
- Time series
- Panel data

Cross-Sectional Data

- Provide information on a variety of entities at

the same point in time

Time Series Data

- Provides information for the same entity at

different points in time

Panel (or Longitudinal) Data

- Represents a combination of cross-sectional and

time series data - Provides information on a variety of entities at

different periods in time

Conducting an Empirical Project

- How to Write an Empirical Paper
- Select a topic
- Textbooks, JSTOR, News sources (for ideas),

pop-econ - Learn what others have learned about this topic
- Spend time researching what others have done
- Conduct extensive literature review

Conducting an Empirical Project

- Theoretical Foundation
- Have an empirical strategy
- Existing literature may help
- Would apply the methods you learn in this book
- Gather data and apply appropriate econometric

techniques - Interpret your results
- Write it up
- Build like a court case or newspaper article

Where to obtain data

- How to use DataFerrett
- CPS.doc
- Files for course will be stored on datastor
- \\datastor\courses\economic\ec339
- You can download all files from book
- http//caleb.wabash.edu/econometrics/index.htm

Web Links

- Resources for Economists on the Internet are

available at - www.rfe.org
- www.freelunch.com
- www.bea.gov, www.census.gov, www.bls.gov

Math Review

- There is much more to it but these are the

basics you must know

Math Review

- Differentiation expresses the rate at which a

quantity, y, changes with respect to the change

in another quantity, x, on which it has a

functional relationship. Using the symbol ? to

refer to change in a quantity. - Linear Relationship (i.e., a straight line) has a

specific equation. As x changes, how does y

change? - Directly related (x increases, y increases)
- Inversely related (x increases, y decreases)

y

x

x0, y3 or (0,3). x2, y32(2) or (2,7)

Math Review

- Derivatives are essentially the same thing.

Instead of looking at the difference in y as x

goes from 0 to 2, if you look at very small

intervals, say changing x from 0 to 0.0001, the

slope does not change for a straight line - The basic rule for derivatives is that the

distance between the initial x and new x

approches zero (in what is called the limit)

y

x

x0, y3 or (0,3). x.0001, y32(.0001) or

(x,y)(.0001,3.0002)

Math Review

- Derivatives have a slightly different notation

than delta-y/delta-x, namely dy/dx or f(x).

Constants, such as the y-intercept do not change

as x changes, and thus are dropped when taking

derivatives. - Derivatives represent the general formula to find

the slope of a function when evaluated at a

particular point. For straight lines, this value

is fixed.

y

x

x0, y3 or (0,3). x.0001, y32(.0001) or

(x,y)(.0001,3.0002)

Math Review

- Integration (or reverse differentiation) is just

the opposite of a derivative, you have to

remember to add back in C (for constant) since

you may not know the primitive equation. - There are indefinite integrals (over no specified

region) and definite integrals (where the region

of integration is specified). - Also, the result of integration should be the

function you would HAVE TO TAKE the derivative of

to get the initial function.

y

23

3

x

10

Area3(10-0)1/2(10-0)(32(10))130

Basic Definitions

- Random variable
- A function or rule that assigns a real number to

each basic outcome in the sample space - The domain of random variable X is the sample

space - The range of X is the real number line
- Value changes from trial to trial
- Uncertainty prevails in advance of the trail as

to the outcome

Case Study

Weight Data

Introductory Statistics classSpring,

1997 Virginia Commonwealth University

Weight Data

Weight Data Frequency Table

sqrt(53) 7.2, or 8 intervals range

(260?100160) / 8 20 class width

Weight Data Histogram

Number of students

Weight Left endpoint is included in the group,

right endpoint is not.

Numerical Summaries

- Center of the data
- mean
- median
- Variation
- range
- quartiles (interquartile range)
- variance
- standard deviation

Mean or Average

- Traditional measure of center
- Sum the values and divide by the number of values

Median (M)

- A resistant measure of the datas center
- At least half of the ordered values are less than

or equal to the median value - At least half of the ordered values are greater

than or equal to the median value - If n is odd, the median is the middle ordered

value - If n is even, the median is the average of the

two middle ordered values

Median (M)

- Location of the median L(M) (n1)/2 ,where n

sample size. - Example If 25 data values are recorded, the

Median would be the (251)/2 13th ordered

value.

Median

- Example 1 data 2 4 6
- Median (M) 4
- Example 2 data 2 4 6 8
- Median 5 (ave. of 4

and 6) - Example 3 data 6 2 4
- Median ? 2
- (order the values 2 4 6 , so Median 4)

Comparing the Mean Median

- The mean and median of data from a symmetric

distribution should be close together. The

actual (true) mean and median of a symmetric

distribution are exactly the same. - In a skewed distribution, the mean is farther out

in the long tail than is the median the mean is

pulled in the direction of the possible

outlier(s).

Quartiles

- Three numbers which divide the ordered data into

four equal sized groups. - Q1 has 25 of the data below it.
- Q2 has 50 of the data below it. (Median)
- Q3 has 75 of the data below it.

Weight Data Sorted

L(M)(531)/227

L(Q1)(261)/213.5

Variance and Standard Deviation

- Recall that variability exists when some values

are different from (above or below) the mean. - Each data value has an associated deviation from

the mean

Deviations

- what is a typical deviation from the mean?

(standard deviation) - small values of this typical deviation indicate

small variability in the data - large values of this typical deviation indicate

large variability in the data

Variance

- Find the mean
- Find the deviation of each value from the mean
- Square the deviations
- Sum the squared deviations
- Divide the sum by n-1
- (gives typical squared deviation from mean)

Variance Formula

Remember that you must find the deviations of

EACH x, square the deviations, THEN add them up!

Standard Deviation Formulatypical deviation from

the mean

standard deviation square root of the

variance

Variance and Standard DeviationExample from Text

- Metabolic rates of 7 men (cal./24hr.)
- 1792 1666 1362 1614 1460 1867 1439

Variance and Standard DeviationExample

Observations Deviations Squared deviations

1792 1792?1600 192 (192)2 36,864

1666 1666 ?1600 66 (66)2 4,356

1362 1362 ?1600 -238 (-238)2 56,644

1614 1614 ?1600 14 (14)2 196

1460 1460 ?1600 -140 (-140)2 19,600

1867 1867 ?1600 267 (267)2 71,289

1439 1439 ?1600 -161 (-161)2 25,921

sum 0 sum 214,870

Notice the deviations add to zero, so each

deviation must be squared

Variance versus Standard Deviation

Note Standard deviation is in the same units as

the original data (cal/24 hours) while variance

is in those units squared (cal/24 hours)2. Thus

variance is not easily comparable to the original

data.

Density Curves

- Example here is a histogram of vocabulary

scores of 947 seventh graders.

The smooth curve drawn over the histogram is a

mathematical model for the distribution. This is

typically written as f(x), also known as the

PROBABILITY DISTRIBUTION FUNCTION (PDF)

Density Curves

- Example the areas of the shaded bars in this

histogram represent the proportion of scores in

the observed data that are less than or equal to

6.0. This proportion is equal to 0.303. The area

underneath the curve, is called the CUMULATIVE

DENSITY FUNCTION (CDF) denoted F(x)

Density Curves

- Example now the area under the smooth curve to

the left of 6.0 is shaded. If the scale is

adjusted so the total area under the curve is

exactly 1, then this curve is called a density

curve. The proportion of the area to the left of

6.0 is now equal to 0.293.

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Density Curves

- Always on or above the horizontal axis
- Have area exactly 1 underneath curve
- Area under the curve and above any range of

values is the proportion of all observations that

fall in that range

Density Curves

- The median of a density curve is the equal-areas

point, the point that divides the area under the

curve in half - The mean of a density curve is the balance point,

at which the curve would balance if made of solid

material

Density Curves

- The mean and standard deviation computed from

actual observations (data) are denoted by and

s, respectively.

- The mean and standard deviation of the actual

distribution represented by the density curve are

denoted by µ (mu) and ? (sigma), respectively.

Question

Data sets consisting of physical measurements

(heights, weights, lengths of bones, and so on)

for adults of the same species and sex tend to

follow a similar pattern. The pattern is that

most individuals are clumped around the average,

with numbers decreasing the farther values are

from the average in either direction. Describe

what shape a histogram (or density curve) of such

measurements would have.

Bell-Shaped CurveThe Normal Distribution

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The Normal Distribution

- Knowing the mean (µ) and standard deviation (?)

allows us to make various conclusions about

Normal distributions. Notation N(µ,?).

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68-95-99.7 Rule forAny Normal Curve

- 68 of the observations fall within (meaning

above and below) one standard deviation of the

mean - 95 of the observations fall within two standard

deviations (actually 1.96) of the mean - 99.7 of the observations fall within three

standard deviations of the mean

68-95-99.7 Rule for Approximates for any Normal

Curve

68-95-99.7 Rule forAny Normal Curve

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