Lecture 1 - Introduction and Fundamentals
Topics in Econometrics - M2 ENS Lyon
Vincent Bagilet
2026-09-15
Introduction
Why this class?
How would you define economics research?
To me, de facto delineated by:
A subject: The study of socio-economic phenomena …
A framework: … through the lens of economic theory …
A set of methods (specifically for applied economics): … using econometrics tools
Produces theoretical models and confronts them to data
Applied economics is concerned with taking theory to the data (and then informing theory)
Why do we need econometrics?
First, how would you define metrics?
Originally, the application of statistical methods to economic data, through the prism of economic theory
Now, to me, also a set of specific methods and approaches, very much geared towards causal inference
Metrics is somehow the core of applied economics
Think of it as a toolbox
Steps of Applied Economics Analyses (1/2)
Define question/topic
Find, get, wrangle and clean data
- Choose proxy variables for our theoretical quantities
- Collect a sample of observations
Exploratory data analysis and summary statistics
Define an identification strategy
Build a regression model
- Assume a functional form for the empirical model
…
Steps of Applied Economics Analyses (2/2)
Estimate your model
- Fit the model to a sample of observations
Specification checks and additional inference
Robustness checks
Communication
- Interpret the sign and magnitude of the estimated parameters and draw conclusions
A More Structured Version
Design: decisions of data collection and measurement
- eg, decisions related to sample size and ensuring exogeneity of the treatment
Modeling: define statistical models
- In between design and analysis
Analysis: estimation and questions of statistical inference
- eg standard errors, hypothesis tests, and estimator properties
Objectives of the class
Form more intuition on what econometric tools actually do to our data
Discuss practical hurdles and challenges we may face when doing applied economics:
Help us be aware of some of them
Provide us with some tools to be able to spot others by ourself
Side quest: help you get started with your masters thesis
Topics class: will not cover everything but instead pick points within topics
Logistics
Website
https://vincentbagilet.github.io/metrics_m2/
A typical lecture
I introduce concepts and intuition
We discuss a paper together (when reading assigned)
Some R coding together and on your own
Grading and assignments
| Assignment | Percentage of final grade | Due date |
|---|---|---|
| Participation | 10 % | - |
| Homework | 20 % | See below |
| Replication | 20 % | October 22, 9:00am |
| Final report | 30 % | November 9, 8pm |
| Final presentation | 20 % | November 6, 8:45am |
Final project
In pairs
Build a simulation to replicate an analysis you may do in your master thesis
Generate realistic fake-data, run your analysis and discuss your results
Project proposal, short report, presentation
Structure of the final project
Structure it as short research paper (pitch):
Quick motivation and context
Research question
Data section: describe how you generate your data. Start very simple, complexify later
Modeling and analysis: describe your model, your choices and the outputs of your regressions
Discussion: what did you learn with this exercise
Hurdles to accurate estimates
The need for accurate estimates
“Accurate” estimates have:
The same sign as the “true” underlying effect
A comparable magnitude as the “true” underlying effect
That are precise enough
Assumes that there is a “true” underlying effect, a true DGP
They can:
- Help with our understanding of the world and inform our theories
- Even inform policy
Improving our understanding of the world
Accurate estimates tell us:
Is there an effect?
In which direction?
Is it large enough to matter? (practical significance)
They help:
Test, form and compare theories
Calibrate models
Build future research on solid ground
Informing policy: air pollution in the US
Clean Air Act:
The EPA (Environmental protection agency) sets air quality standards
Based on the costs and benefits of various standards
States implement the standards
Health benefits: \(\Delta Y \approx Pop \times Y_0 \times \hat{\beta} \times \Delta AQ\)
\(\hat{\beta}\): health effect estimated in the literature
Benefits proportional to \(\hat{\beta}\)
Example: in 2024, change in PM2.5 standard (12 → 9 µg/m³):
Health benefits computed from literature estimates: $22-46B per year
Costs: $0.6B per year
Typical sources of inaccurate estimates
At the design stage:
- eg, measurement error, low statistical power
At the identification stage:
- eg, reverse causality, confounders, SUTVA violations, (implicit) sample selection
At the modeling stage:
- eg, misspecification, bad controls, negative weights and implicit weighting,
At the inference stage:
- eg, incorrect standard errors, weak instruments
Selective publication and generalization:
- eg, specification search, publication bias, external validity
Order of concern
There is some chronology in hurdles: each only matters to the extent that the previous one are addressed
We need to have, in that order of concern:
A good research question, grounded in theory
A good design: enough data, well measured, etc
A good identification strategy to avoid some fundamental hurdles (reverse causality, confounders, etc)
An adequate specification that allows us to estimate the quantity we want to estimate
Make reliable inference based on well-constructed standard errors for instance
Reliable communication: make sure the audience receive what we intend to share
In this class we will explore
Common hurdles and challenges in empirical work
How regression works “under the hood”
Causal identification strategies and their assumptions
How design, modeling, and analysis choices shape empirical results
How to use simulations to explore estimator behavior and diagnose potential problems specific to your own cases
Existing references and where to find additional information on a specific topic
Outline of the class
Introduction and Fundamentals
Simulations
Linear regression and causal inference
Design: Fixed Effects
Design: IV
Modelling
Analysis
Communication
Research questions
What is a good research question?
It can be answered
- There is some sort of objective answer
It should improve our understanding of the world
Should inform theory in some way
Takes us from theory to an hypothesis (statement about what we will observe in the world)
A solid econometric analysis only matters to the extent that you have a good research question (but the opposite might be true as well)
Example
Impact of the size of motors of boats in Norway and cod catch under a catch cap
Not that interesting in itself, is it? Would be more interesting if, for instance:
Look at this from a game theory and forced technological adoption perspective
Find a way to use this case to say something new or different on management of renewable natural resources
Can produce radically different papers on the same topic and setting
Use theory to put light on your specific case and your specific case to inform theory
Identifying a research question
Can start with a research question/hypothesis or from theory
Or can find a natural experiment and come up with a question
Know your literature to identify gaps
We are interested in why and not what
Avoid data mining: it can help but to identify questions to test on other data sets
Is your research question good?
Relevance: is it interesting, important or policy relevant ?
Potential results: what would any result tell you about your theory?
Feasibility: is the right data available?
Scale: how much resources would you need?
Research design: is there a good one that would allow you to answer your question?
Keep it simple: avoid building several questions into one
Avoiding hurdles
How to avoid hurdles?
Learn, understand metrics and applied research
The Barque of Dante by Manet, after a painting by Delacroix
Replication, a helpful learning tool
How to avoid hurdles?
Derive the maths
Sometimes relatively straightforward and very illuminating
eg drivers of the variance of your estimator: \(\mathbb{V}_{\hat{\beta}} = \dfrac{\sigma_u^2}{n \sigma_x^2}\)
Deriving the maths can be more complex and time consuming
How to avoid hurdles?
Simulations can help
Super easy to implement simple simulations
Can be informative of what does not work
Can help you identify where the issue comes from
We will discuss that with an example in a second
How to avoid hurdles?
Implement checks
Check if the model seems to represent the DGP
Check if our identification hypotheses seem to hold
Check if the hypotheses for estimation seem to hold
Look at the consequences if this does not hold
Robustness checks
Evaluate the design retrospectively
Objectives for this class
Build a mindful mindset
Help you be aware of some of them
Provide you with some tools to be able to spot others by yourself
Learn how to implement simulations
Simulations: usefulness through an example
A simple example: OVB
- How does an omitted variable affect our point estimate of interest? Why?
Under which condition is an omitted variable an issue
How does it affect the point estimate? The s.e.?
How does that vary with various parameters? eg correlation between variable (sign and magnitude)
Start very simple and complexify the process
Let’s move to R
Lecture summary
What did we do today?
Discussed the pervasiveness of econometrics in applied research and therefore the usefulness of studying it
Browsed logistics
Reviewed some common hurdles encountered in applied research
Explored how to implement a simple simulation to understand the impact of an omitted variable depending on the value of various parameters
A few random take-away points
A great econometrics analysis only matters to the extent that you have a good research question
Get inspiration from papers you like: structure, methods, questions, graphs and tables, etc
Attend seminars! You can always grab something (at worst in terms of form)
There are many reasons for our estimation to yield incorrect results:
Learn how to spot and understand them
Simulations can help!