exercise
Random In-class variable
X= xi
Probability
f(xi) = pi = P(X= xi)
pdf
x1= -1
x2= 0
0.70
0
x3= 1
0.30
= 1
=1
What is the E(X), E(2X-3)?
What is the Var(X), Var(2x-3)?
THE NATURE OF
ECONOMETRICS AND
ECONOMIC DATA
OUTLINE
1.
What is Econometrics?
2.
Steps in Empirical Economic Analysis
3.
Examples
4.
Economic Data
5.
Causality and the notion of Ceteris Paribus
1. WHAT IS ECONOMETRICS?
Combination of statistical methods, economics and data to
answer empirical questions in economics.
There are many different types of empirical questions in
economics. Some examples:
Forecasting:
Use current and past economic data to predict future values
of variables such as inflation, GDP, stock prices, etc.
Testing economic theories:
- Test of the efficiency of the Stock Exchange
- Test the Capital Asset Pricing Model (CAPM)
1. WHAT IS ECONOMETRICS?
Estimation of economic relationships:
- Demand and supply equations;
- Production functions;
- Wage equations, etc.
Evaluating government policies:
- Employment effects of an increase in the minimum wage;
- Effects of monetary policy on inflation.
Evaluating business policies:
- Estimate the optimal price and advertising expenditure for
a new product;
- Compare profits under two pricing policies.
- Evaluate the effectiveness of a job training program.
1. WHAT IS ECONOMETRICS?
Econometrics is relevant in virtually every branch of applied
economics: finance, labor, health, industrial, macro,
development, international, trade, marketing, strategy, etc.
There are two important features which distinguish
Econometrics from other applications of statistics:
1.
Economic data is non-experimental data. We cannot simply
classify individuals or firms in an experimental group and a
control group. Individuals are typically free to self-select
themselves in a group (e.g., education, occupation, product
market, etc).
2.
Economic models (either simple or sophisticated) are key to
interpret the statistical results in econometric applications
2. STEPS IN EMPIRICAL ECONOMIC ANALYSIS
The research process in applied econometrics is not simply
linear, but it has loops. That is, the original question and
model, and even the data collection (e.g., search for
additional information/variables) can be modified after
looking at preliminary econometric results.
Keeping this in mind, it is useful to describe the different
steps of the research process in econometrics:
1. . Formulation of the question(s) of interest.
2a. Formulation of the economic model
2b. Specification of the econometric model
3. Collection of data
4. Estimation, validation, hypotheses testing, prediction
3a. EXAMPLE: economic model of crime
Step 1: Formulate the empirical question(s)
Suppose you want to determine the factors that affect an individuals
participation in criminal activities.
Step 2a: Formulation of the Economic Model
= 1 , 2 , 3 , 4 , 5 , 6 , 7
Where,
y: hours spent in criminal activity
x1: wage for an hour spent in criminal activity
x2: hourly wage in legal employment
x3: income other than from crime or employment
x4: probability of getting caught
x5: probability of being convicted if caught
x6: expected sentence if convicted
x7: age
3a. EXAMPLE: economic model of crime
Step 2b: Specification of the econometric model
There are 2 issues with this:
The form of the function f() must be specified.
Dealing with variables that cannot be reasonably observed.
We can specify an econometric model for the time spent of crime as follows:
= + + + + + + +
Where,
: some measure of the frequency of criminal activity
: the wage that can be earned in legal employment
: the income from other sources
: frequency of arrests for prior crimes (to approximate probability of arrest)
: the frequency of conviction
: average sentence length after conviction
u: error term or disturbance term e.g. family background, moral character.
The s are parameters to be estimated.
3a. EXAMPLE: economic model of crime
Step 2b: Specification of the econometric model
(continued)
Dealing with the unobservable (or error term or
disturbance) u, is one of the most important issues in any
econometric analysis.
Certain conditions on the statistical properties of the error
term are key for the good of properties our estimators of
the parameters of interest.
To a certain extend, we will be able to test for these
conditions. However, the economic interpretation of the
error term (i.e., which are the main factors in it) is very
important to interpret our estimation results.
Step 3: Collection of data
3a. EXAMPLE: economic model of crime
Step 4: Estimation, validation, hypotheses
testing, prediction
We want to estimate the parameters in the
crime model. After estimation, we have to make
specification tests in order to validate some of
the specification assumptions that we have made
for estimation.
The results of these tests may imply a respecification and re-estimation of the model.
Once we have a validated model, we can
interpret the results from an economic point of
view, make tests, and predictions.
3b. EXAMPLE: job training and worker wages
Formulation of the question(s) of interest.- what is impact of job
training on the wages?
Formulation of the economic model
= ( , , )
Specification of the econometric model
= + 1 + 2 + 3 +
Collection of data
Estimation, validation, hypotheses testing, prediction
4. Economic Data
Different types of datasets have their own issues, advantages
and limitations.
Some econometric methods may be valid (i.e., have good
properties) for some types of data but not for others.
We typically distinguish four types of datasets:
1. Cross-Sectional Data
2. Time Series Data
3. Pooled Cross sectional Data
4. Panel Data or Longitudinal Data
4. Economic Data
Cross-Sectional Data
A cross-sectional dataset consists of data on a sample of
individuals, or households, or firms, or cities, or states, or
countries, , taken at a given point in time.
We often assume that these data have been obtained by
random sampling.
Sometimes we do not have a random sample: sample
selection problem; spatial correlation; stratified samples.
4. Economic Data: example of cross-sectional data
4. Economic Data
Time Series Data
A time series dataset consists of data on a variable or several
variables over several periods of time (days, weeks, months,
years).
A key feature of time series data is that, typically, observations are
correlated across time. We do not have a random sample.
This time correlation introduces very important issues in the
estimation and testing of econometric models using time series
data.
Seasonality is other common feature in many weekly, monthly or
quarterly time series data.
4. Economic Data: example of time-series data
4. Economic Data
Pooled cross sections
Suppose we have two cross-sectional household surveys taken in
the U.S., one in year 1985 and the other in 1990. We can form a
pooled cross-sectional data set by combining the two years.
It is useful data to analyze the evolution over time of the crosssectional distribution of variables such as individual wages,
household income, firms investments, etc.
We should distinguish pooled cross-sections from panel data.
In pooled cross sections we do not follow the same individuals
over time. Every period we have a new random sample of
individuals.
4. Economic Data: example of pooled cross-sectional
data
4. Economic Data
Panel Data or Longitudinal Data
In panel data we have a group of individuals (or households,
firms, countries, ) who are observed at several points in
time. That is, we have time series data for each individual
in the sample.
The key feature of panel data that distinguishes them from
pooled cross sections is that the same individuals are
followed over a given period of time.
4. Economic Data: example of pooled cross-sectional
data
5. Causality and the notion of Ceteris Paribus
Most empirical questions in economics are associated
with the identification of CAUSAL EFFECTS.
The notion of ceteris paribus (i.e., other factors being
equal) plays an important role in the analysis of causality.
Consider the wage equation discussed earlier- we might
be interested in the effect of years of education on the
hourly wage, holding all other factors constant.
If we succeed in holding all other relevant factors constant
and then finding a link between education and wage, we
can conclude that education has a causal effect on wages.
= + 1 + 2 + 3 +