Econometrics 341
What is Econometrics?
Econometrics is an economic subject that uses theory and develops statistical methods to:
- Build and/or estimate economic relationships (models): 𝑄" = 𝑓 (𝑃, 𝑃( , 𝑃)* )
- uses data to provide economic measurement of impact
- estimation provides magnitudes for parameters of variables determining the
phenomenon under study. E.g., effect of advert on sales.
Purpose of econometrics is to use econometric analysis to
- test economic theories (e.g., theory predicts 0<MPC<1)
- evaluate policy (for govt/business)
- forecast/predict key (macro) variables (or phenomenon of interest).
Model Variables
- Important feature of modern approach to econometrics is that regressors (along with
regressand) are random variables. For social sciences, this approach is more realistic
than the usual approach of non-random (fixed) regressors.
STEPS IN EMPIRICAL ECONOMIC ANALYSIS - DETAILS
Empirical analysis relates to the use of actual data to estimate an econ relationship.
1. Formulate the question of interest.
This entails clearly stating what phenomenon is to be investigated.
2. Formulate economic model
- In general, an economic model represents relationships between variables
mathematically.
Example 1– Individual Consumer Demand
In the case of testing consumer theory in microeconomics;
-the framework is that individuals maximise utility by choosing quantities of goods to
consume subject to a budget constraint => two equations.
-the outcome is a demand equation where quantity demanded depends on price of the good,
price of related goods, income and individual characteristics that affect taste.
Assume the goal is to study effect of change in price of product, X, on demand for X.
Then economic model is:
𝐷- = 𝑓.𝑃- , 𝑃/ , 𝐼, 𝑧2
(1)
Where
𝐷- = quantity demanded of good X.
𝑃- = price of good X.
𝑃/ = price of related good Y.
𝐼 = income.
𝑧 = factors influencing the consumer’s tastes and/or preferences.
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Observations on the Economic Model
i. Economic theory is used to determine variables used to explain qty of X and direction
of influence.
ii. Occam’s razor principle is used. Other factors affect the demand for good X, but they
are left out.
iii. Model (1) is not specific about the functional form 𝑓(∙) of the model.
3. Formulate Econometric Model
After specifying an economic model, we derive an econometric model from it.
To specify an econometric model, four things must be resolved:
(i)
Specify a specific form of the function 𝑓(∙).
(ii)
How to deal with model variables that cannot be observed – e.g., tastes of
consumers, ability of worker, quality of education, etc.
(iii) Account for many other variables that affect the dependent variable but which are
not included in the model.
(iv)
We need to ensure that the model captures a ceteris paribus relationship between
the variable we are explaining and its primary determinant.
Econometric model of demand for qty demanded of a commodity
An econometric model relating to the economic model in (1) might be
•
•
•
•
𝐷- = 𝛽7 + 𝛽9 𝑃- + 𝛽: 𝑃/ + 𝛽; 𝐼 + 𝑢
(2)
Econometric model assumes linear relationship
Where u is a stochastic variable called the error term. It contains factors that influence
𝐷- but not included in the model.
Causal effect of 𝑃- is ensured by inclusion of other variables - 𝑃/ and 𝐼.
Generally we use the plus sign in specifying the model. This does not imply direction
of effect. The sign of coefficient is determined by theory/intuition.
4. Stating Hypothesis/Hypotheses of Interest
Following the specification of econometric model, we state the hypothesis of interest.
• Since we intend to examine the effect of price of X on 𝐷- , then 𝑃- is the variable of
interest.
• Hence, we state the hypothesis of interest in terms coefficient of 𝑃- . For example state
the hypothesis that price of X has no effect on 𝐷- as
𝛽9 = 0.
5. Collecting Data and Estimating the Model
The last step involves collecting relevant data and using econometric method to estimate the
model and formally testing the hypothesis of interest.
- Often we use a sample instead of the population values.
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Example 2 – The Case of Relationship between Job Training and Worker Productivity
The question of interest is to examine the effect of on-the-job training on worker
productivity.
Economic reasoning suggests that worker productivity is affected by training, education and
experience.
Also, micro says workers are paid a wage commensurate to their productivity. So wage can
be used to proxy for productivity.
From this the economic model is:
wage = f (educ, exper, tra)
(3)
where
wage =hourly wage,
educ =years of formal education,
exper= years of workforce experience, and
tra =weeks spent in job training.
Observations
i. Other factors generally affect worker’s wage rate, but they are left out.
ii. The functional form of model (3) is not specified.
iii. Theory is used to determine regressors.
Formulating econometric model
- Econometric model formulated from equ (3) becomes:
𝑤𝑎𝑔𝑒 = 𝛽7 + 𝛽9 𝑒𝑑𝑢𝑐 + 𝛽: 𝑒𝑥𝑝𝑒𝑟 + 𝛽; 𝑡𝑟𝑎 + 𝑢
(4)
Deterministic Vs Stochastic Regression Model
Deterministic models assume an exact relationship between 𝑦 and 𝑥. Explicit forms of
economic models are deterministic.
Example:
𝑦 = 𝛽7 + 𝛽9 𝑥
Specific example of Consumption Function:
Let 𝑦=consumption expenditures, denoted by cons; 𝑥=income, denoted by inc. Then model is
𝑐𝑜𝑛𝑠 = 𝛽7 + 𝛽9 𝑖𝑛𝑐
Stochastic models assume an inexact relationship between 𝑦 and 𝑥. Econometric models are
stochastic.
.
Example:
𝑦 = 𝛽7 + 𝛽9 𝑥 + 𝑢
Specific example of Consumption Function:
Then model becomes
𝑐𝑜𝑛𝑠 = 𝛽7 + 𝛽9 𝑖𝑛𝑐 + 𝑢
ð Not all changes in 𝑐𝑜𝑛𝑠 are explained by changes in 𝑖𝑛𝑐.
Graphical illustrations of the two types of model using Consumption Function.
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Figure: Exact Relationship
y
x
Note: all the y-x points fall exactly along the line.
Figure: Inexact Relationship
y
.
.
.
.
.
.
.
x
Note: all the y-x points lie close around the scatter line (indicating high correlation), but not all the
points fall on the line.
STRUCTURE OF ECONOMIC DATA
There are different types of data.
1. Cross-Sectional (CS) Data
A cross-sectional data refers to observations on a set of economic units/entities e.g.
households (HHs) taken at a given time period.
E.g., income of various HHs in December 2016.
-
Sometimes the time period is not exactly the same for all the units in the sample.
Then we ignore these small timing differences and view the data as cross-sectional
data collected in a given month.
Key Features of CS Data
(i)
That cross-sectional data can often be assumed to have been obtained by random
sampling from an underlying population.
(ii)
Another feature is that the ordering of the data is not important for econometric
analysis.
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For example, if we get info on 300 workers’ wages, experience, etc in a particular month by
randomly drawing them from total working people, then we really have a random sample
from the population of all workers.
Table showing (Hypothetical) Cross-Sectional Data
Obsno
Wage rate/day (pula)
1
6.10
2
6.24
3
6.00
:
:
225
22.56
:
:
300
6.50
Exper
2
22
3
:
6
:
5
Note: that all the 300 wage data (and also experience data) were collected from various
workers at a given time period – e.g., a week/month.
2. Time Series (TS) Data
Time series data refers to observations collected on a variable(s) over time.
Examples: include CPI/inflation series, GDP series, credit series etc.
Ordering of data is important for econometric analysis in time series data.
Reasons
- Past events can influence future events.
- Lags in behaviour are common in social sciences.
Key Features of TS Data
(a) Dependency in data
-is that economic observations can rarely be taken as independent across time.
-an observation in one period tends to be similar to the observation in the immediate next
period.
Consequences
- this phenomenon makes the econometric analysis of TS data difficult.
- standard econometric methods of analysis are often not applied directly to TS data.
(b) Data frequency
This refers to the time interval at which the observations are collected. For Botswana, some
data are recorded
- daily (e.g., exchange rates) => frequency is daily
- monthly (e.g., inflation)
=> frequency is monthly
- quarterly (e.g., GDP).
=> frequency is quarterly
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Minimum Wage and Unemployment
obsno year
1
1950
2
1951
3
1952
:
:
37
1986
avgmin
0.20
0.21
0.23
:
3.35
unemp
15.4
16.0
14.8
:
18.9
3. Pooled Cross Sections
This refers to observations where cross-sectional data for different time periods have been put
together.
-
The dataset has both cross-sectional and time series features simultaneously.
This putting together of cross-sectional data is called pooling.
Reason for pooling
Pooling CS data often provides a useful way to analyse the effect of a new govt policy.
- Accomplished by putting together data from before and after the policy change.
Example of pooled Cross Sections for data on 120 houses for 2001 and on 165 houses for
2004.
Table Showing Pooled CS Data
Obsno
Year
1
2001
2
2001
3
2001
:
:
120
2001
121
2004
:
:
285
2004
hprice
500,500
850,000
470,500
:
960,000
485,000
:
350,000
Bdrms
3
4
2
:
4
2
:
2
Note that the houses whose data were collected in 2001 are not necessarily the same houses
whose data were collected in 2004 – e.g., the 2 bedroom houses are different.
4. Panel or Longitudinal Data
Panel data pools together time series data on a set of cross-sectional units.
For example, investment data on the same set of firms over a period of 3 years.
Crucial difference between a panel dataset and a pooled CS dataset is that in a panel dataset,
data is recorded for the same observation units over time, but observation units differ in
pooled CS.
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Example of panel data on firms’ investment (Inv), income (Inc), and interest (ir) for 3 years
(2000 - 2002).
Hypothetical
Firm
1
1
1
2
2
2
3
3
3
year
2000
2001
2002
2000
2001
2002
2000
2001
2002
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Inv
6.0
4.6
9.4
9.1
8.3
0.6
9.1
4.8
9.1
Inc
5.8
7.9
5.4
6.7
6.6
0.4
2.6
3.2
6.9
ir
1.3
7.8
1.1
4.1
5.0
7.2
6.4
6.4
2.1