Prof. Chitwan Lalji teaches economics at the Indian Institute of Management Kozhikode. The document discusses key concepts in econometrics including: 1) Econometrics uses statistical methods to analyze economic data and test economic theories using real-world data. 2) The main steps in econometrics analysis are developing an economic theory, specifying an econometric model, and conducting hypothesis tests. 3) Econometric models relate an outcome variable like demand or wages to explanatory variables based on economic theory and include an error term for unobserved factors. These models are used to test hypotheses about economic relationships.

1. Prof. Chitwan Lalji
Economics Area
Indian Institute of Management Kozhikode
*Text Books: Wooldridge, J. M. (2016). Introductory econometrics: A modern approach. Nelson Education.
Enders, Walter (2005). Applied Econometric Time Series, 4th ed., Wiley.
Econometric Applications for
Research*

3. What is econometrics..?
• It is the use of statistical methods to analyze economic data
• It is science/art of testing economic theories
• It is the process of fitting mathematical economic models to real-world data
• It is a set of tools used for forecasting future values of economic variables, such as a
firm’s sales, the overall growth of the economy, or stock prices.
• Evaluating and implementing government and business policy
• Science and art of using historical data to make numerical, or quantitative, policy
recommendations in government and business

4. Steps in econometrics analysis?
1. Economic Theory
2. Econometric model
3. Hypothesis Testing

5. Economic Theory
Economic Theory
• Demand Theory – shows the relationship between price and quantity
of a good that consumers are willing to buy at a given price, holding
constant other factors that might affect the quantity demanded.
QD = QD(P)
• Others factors – The quantity that consumers are willing to buy also
depends on their income, price of related goods, etc.
QD = f(Price of good, Income, Price of related goods, etc.)

6. Econometric Model
Economic Theory
QD = f(Price of good, Income, Price of related goods, etc.)
Econometric Model
QD = α + β(Price of good) + γ(Income) + δ(Price of related goods) + ε
Unobserved factors, such
as tastes, habits,
expectations, etc.
Dependent variable,
explained variable,
response variable,…
Independent variable(/s),
explanatory variable(/s),
regressor(/s),…

7. Another example
Model of job training and worker productivity
– What is effect of additional training on worker productivity?
– Formal economic theory not really needed to derive equation:
– Other factors may also be relevant
Hourly wage
Years of formal
education Years of work-
force experience
Weeks spent
in job training

8. Another example
Econometric model of job training and worker productivity
• Most of econometrics deals with the specification of the error
• Econometric models may be used for hypothesis testing
– For example, the parameter represents effect of training on wage
– How large is this effect? Is it different from zero?
Hourly wage Years of formal
education
Years of work-
force experience
Weeks spent
in job training
Unobserved deter-
minants of the wage
e.g. innate ability,
quality of education,
family background …

9. Can you think of any examples….???

10. Econometric analysis requires data
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA DATA
DATA

11. Classification of Data
 Qualitative data and Quantitative data
 Primary data and secondary data
 Cross-sectional, pooled-cross-sectional, time series data and panel data

12. Cross-sectional data
Observation number Hourly wage
Categorical variables
(1=yes, 0=no)

13. Time series data
Unemployment
rate
Average
coverage rate
Average minimum
wage for given year
Gross national
product

14. Pooled cross sections
Number of
bathrooms
Size of house
in square feet
Property tax
Before reform
After reform

15. Panel or longitudinal data
Each city has two time
series observations
Number of
police in 1986
Number of
police in 1990

16. Correlation and Causation
Reference: https://twitter.com/SteveStuWill/status/1309968897391517696/photo/1

17. Correlation and Causation
Reference: https://psychologenie.com/meaning-of-correlation-does-not-imply-causation-explained

18. Correlation and Causation
Reference: https://twitter.com/EUFIC/status/1324667630238814209/photo/1

19. Causation effect
Definition of causal effect of x on y:
"How does variable y change if variable x is changed
but all other relevant factors are held constant“

20. Regression Analysis with
Cross-Sectional Data

21. Simple Linear Regression
Definition of the simple linear regression model
Dependent variable,
explained variable,
response variable,…
Independent variable,
explanatory variable,
regressor,…
Error term,
disturbance,
unobservables,…
Intercept Slope parameter
"Explains variable y in terms of variable x"

22. Simple Linear Regression
• Conditional mean independence assumption
The explanatory variable must not
contain information about the mean
of the unobserved factors

23. Simple Linear Regression
Fitted regression line

24. Simple Linear Regression
Properties of OLS on any sample of data
• Fitted values and residuals
• Algebraic properties of OLS regression
Fitted or predicted values Deviations from regression line (= residuals)
Deviations from
regression line sum up
to zero
Correlation between
deviations and regressors
is zero
Sample averages of y
and x lie on regression
line

25. Simple Linear Regression
Fitted regression line
Fit as good as possible a regression line through the data points:

27. Simple Linear Regression
What does "as good as possible" mean?
• Regression residuals
• Minimize sum of squared regression residuals
• Ordinary Least Squares (OLS) estimates

28. Simple Linear Regression
• Goodness-of-Fit
• Variation
"How well does the explanatory variable explain the dependent variable?"

29. Simple Linear Regression
• Decomposition of total variation
• Goodness-of-fit measure (R-squared)
Total
variation
Explained
part
Unexplained
part
R-squared measures the fraction
of the total variation that is
explained by the regression

30. Assumptions

31. Assumptions

32. Assumptions

34. Assumptions

35. Assumptions

36. Assumptions of CLRM
• Linear in Parameter
• Random Sampling
• Sample variation on the explanatory variable (not all the same value)
• Zero conditional mean: E(u|x) = 0
 Cov(x,u)=0
• Variance of the unobservable (u) conditional on x, is constant
 Homoskedasticity or same variance assumption
The value of the explanatory variable must
contain no information about the
variability of the unobserved factors

38. Log and semi log form
• Incorporating nonlinearities: Semi-logarithmic form
• Regression of log wages on years of eduction
• This changes the interpretation of the regression coefficient:
Natural logarithm of wage
Percentage change of
wage
… if years of education
are increased by one year

39. Log and semi log form
• Incorporating nonlinearities: Log-logarithmic form
• CEO salary and firm sales
• This changes the interpretation of the regression coefficient:
Natural logarithm of CEO salary
Percentage change of salary
… if sales increase by 1 %
Natural logarithm of his/her firm‘s sales
Logarithmic changes are
always percentage changes

40. Example on STATA
Use the following data
• CEOSAL1 data
Please note:
The datasets and do files will be made available in the virtual classroom/moodle.

41. Assumptions of CLRM
• Linear in Parameter
• Random Sampling
• Sample variation on the explanatory variable (not all the same value)
• Zero conditional mean: E(u|x) = 0
 Cov(x,u)=0
• Variance of the unobservable (u) conditional on x, is constant
 Homoskedasticity or same variance assumption
The value of the explanatory variable must
contain no information about the
variability of the unobserved factors

42. Practice Questions
Chapter 1, Wooldridge:
• Problem 1 (pp. 17)
• Computer exercise C4-JTRAIN2 (pp. 18)
Chapter 2, Wooldridge:
• Computer exercise C1-401K (pp. 61)
• Computer exercise C2-CEOSAL2 (pp. 61)
• Computer exercise C4-WAGE2 (pp. 62)
• Computer exercise C5-RDCHEM (pp. 62)

43. Reference
• Chapter 1 and 2, Jeffery M. Wooldridge, (2016). Introductory econometrics: A
modern approach. Fifth Edition, Cengage Learning.

44. Thank you 