Econometrics
June 19, 2025
1
,Econometrics
Contents
1 Lecture 1: Introduction 4
1.1 Global data lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 what is econometrics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 from theory to empirics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 how we structure data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Types of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Causality and ceteris paribus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 why is data analysis an important policy tool? . . . . . . . . . . . . . . . . . . . . 6
1.6 example 1: achievement and hours spent studying . . . . . . . . . . . . . . . . . 6
1.7 basic maths and statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.8 simple regression: two variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Lecture 2: Regression Analysis 11
2.1 steps to be taken in regression analysis . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Classical assumptions OLS regression model . . . . . . . . . . . . . . . . . . . . . 11
2.3 Multivariate linear regression model . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.1 F-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Credible standard errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Credible standard errors with R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 lecture 3: Dummies, interactions, etc. 16
3.1 Interpretation of coefficient estimates . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Sums of squares and R 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Dummy variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 dummy’s in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.2 Dummy variables with more than 2 categories . . . . . . . . . . . . . . . . 19
3.4 Interaction terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Nonlinearities and missing variables . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Lecture 4: Time series I 21
4.1 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 t-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Confidence intervals for β1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.3 p-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Lecture 5: Time series II 26
5.1 autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1 Consequences of pure autocorrelation . . . . . . . . . . . . . . . . . . . . 27
5.2 Detection of Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
,Econometrics
5.3 correction for autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4 granger causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6 Lecture 6: Panel Data I 29
6.1 types of panel data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.2 Omitted variable bias/Confounders . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.3 Panel data models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 Lecture 7: Panel Data II 33
7.1 techniques of panel data estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.1.1 Pooled OLS with panel data . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.1.2 Between estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.3 first differences estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.4 Least squares dummy variables . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.5 Fixed effects (within) estimator . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.1.6 comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.2 Time fixed effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3 Unit and time fixed effects (two way fixed effects) . . . . . . . . . . . . . . . . . . 37
7.4 Randem effects (RE) estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.5 Violated OLS assumption and Serial correlation: clustered standard errors (SE) 38
7.6 Which estimator is appropriate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8 summary 40
3
, Econometrics
1 Lecture 1: Introduction
1.1 Global data lab
Gobal data lab: performing researh and developing instruments for measuring and analysing
progress of societies.
The instruments include indicators, specialied databases, and web-based tools for translat-
ing data into understandable and usable knowledge.
At the heart of the data lab is the area database, a big data infrastructure with information
on over 35 milion individuals in 130+ countries.
Development indicators for 1300+ sub-national regions (provinces) within countries.
1.2 what is econometrics?
Econometrics is Theory/model, data and statistics all in 1.
Practical approach:
Economic theory → Mathematical model of theory → Econometric model of theory → Data
→ Estimation of econometric model → Hypothesis testing → Forecasting or prediction →
Using the model for control or policy purposes.
Statistical tools are used to estimate economic relationships, test economic theories and
evaluate policies.
Application of economic theory to real world data; formal economic models can be tested:
utility maximisation, supply and demand.
Theory may be ambiguous as to the effect of some policy change → program evaluation.
Rare in economics to have experimental data! Need to use nonexperimental, or observa-
tional data to make inferences, i.e. to draw conclusions.
Examples:
• Evaluation of a government policy
• Returns to schooling
• Returns to different investment funds
• Impact of conflict on sustainable development
1.2.1 from theory to empirics
Observations of real world relationships
• Systematic discription = Economic model simplifies, leaves out some factors, often
there are no functional form assumptions)
• Application of economic model to the real world: Econometric/Empirical model (impose
functional form, some factors cannot be observed
4
June 19, 2025
1
,Econometrics
Contents
1 Lecture 1: Introduction 4
1.1 Global data lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 what is econometrics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 from theory to empirics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 how we structure data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Types of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Causality and ceteris paribus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 why is data analysis an important policy tool? . . . . . . . . . . . . . . . . . . . . 6
1.6 example 1: achievement and hours spent studying . . . . . . . . . . . . . . . . . 6
1.7 basic maths and statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.8 simple regression: two variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Lecture 2: Regression Analysis 11
2.1 steps to be taken in regression analysis . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Classical assumptions OLS regression model . . . . . . . . . . . . . . . . . . . . . 11
2.3 Multivariate linear regression model . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.1 F-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Credible standard errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Credible standard errors with R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 lecture 3: Dummies, interactions, etc. 16
3.1 Interpretation of coefficient estimates . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Sums of squares and R 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Dummy variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 dummy’s in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.2 Dummy variables with more than 2 categories . . . . . . . . . . . . . . . . 19
3.4 Interaction terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Nonlinearities and missing variables . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Lecture 4: Time series I 21
4.1 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 t-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Confidence intervals for β1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.3 p-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Lecture 5: Time series II 26
5.1 autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1 Consequences of pure autocorrelation . . . . . . . . . . . . . . . . . . . . 27
5.2 Detection of Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
,Econometrics
5.3 correction for autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4 granger causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6 Lecture 6: Panel Data I 29
6.1 types of panel data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.2 Omitted variable bias/Confounders . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.3 Panel data models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 Lecture 7: Panel Data II 33
7.1 techniques of panel data estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.1.1 Pooled OLS with panel data . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.1.2 Between estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.3 first differences estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.4 Least squares dummy variables . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1.5 Fixed effects (within) estimator . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.1.6 comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.2 Time fixed effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3 Unit and time fixed effects (two way fixed effects) . . . . . . . . . . . . . . . . . . 37
7.4 Randem effects (RE) estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.5 Violated OLS assumption and Serial correlation: clustered standard errors (SE) 38
7.6 Which estimator is appropriate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
8 summary 40
3
, Econometrics
1 Lecture 1: Introduction
1.1 Global data lab
Gobal data lab: performing researh and developing instruments for measuring and analysing
progress of societies.
The instruments include indicators, specialied databases, and web-based tools for translat-
ing data into understandable and usable knowledge.
At the heart of the data lab is the area database, a big data infrastructure with information
on over 35 milion individuals in 130+ countries.
Development indicators for 1300+ sub-national regions (provinces) within countries.
1.2 what is econometrics?
Econometrics is Theory/model, data and statistics all in 1.
Practical approach:
Economic theory → Mathematical model of theory → Econometric model of theory → Data
→ Estimation of econometric model → Hypothesis testing → Forecasting or prediction →
Using the model for control or policy purposes.
Statistical tools are used to estimate economic relationships, test economic theories and
evaluate policies.
Application of economic theory to real world data; formal economic models can be tested:
utility maximisation, supply and demand.
Theory may be ambiguous as to the effect of some policy change → program evaluation.
Rare in economics to have experimental data! Need to use nonexperimental, or observa-
tional data to make inferences, i.e. to draw conclusions.
Examples:
• Evaluation of a government policy
• Returns to schooling
• Returns to different investment funds
• Impact of conflict on sustainable development
1.2.1 from theory to empirics
Observations of real world relationships
• Systematic discription = Economic model simplifies, leaves out some factors, often
there are no functional form assumptions)
• Application of economic model to the real world: Econometric/Empirical model (impose
functional form, some factors cannot be observed
4
