Ian Helfrich · Working handbook
Econometrics Across Disciplines
Measurement, models, and decisions.
Mathematics gives us a way to describe a question carefully, investigate it, and explain what an answer means. This book begins with economic objects we can picture and builds the tools needed to reason about them. Concrete examples lead into algebra, probability, geometry, calculus, and econometric inference.
Pictures and applications accompany complete mathematical arguments. A result names its assumptions, explains each consequential step, and links to the definition or earlier result it uses. Python, Julia, and R implement the same declared calculations independently.
This working edition contains three foundation chapters: economic questions, measurement, and observation clocks. Each has complete proofs, original figures, worked exercises, and Python, Julia, and R programs that reproduce its calculations. The fifteen-lecture time-series course is published separately.
Reading levels
Each symbol appears with a text label. The levels identify what a passage requires; they do not rank readers.
- ○ Orientation
- Concrete questions, pictures, arithmetic, and explanations of unfamiliar terms. A reader can begin here before studying advanced mathematics.
- ◇ Core
- The algebra, calculus, probability, and linear algebra needed to carry an econometric argument through an application. Assumptions remain beside the claims they support.
- ◆ Theory
- Precise definitions and complete proofs, such as the identification limits in chapter 1, classical attenuation in chapter 2, and prefix invariance and the information-gain identity in chapter 3.
- ✦ Workshop
- A bounded investigation, diagnostic exercise, or research extension. Each passage states whether it is worked practice, an executed finding, or a proposed question.
The introductory route supplies the conditions and meaning of each result. A technical passage can be skipped without turning its conclusion into an unconditional promise. Chapter 1's Theory section uses a finite example so its identification proof can be followed before measure-theoretic probability.
Available chapters
- 01Economic questions, useful predictions, and interventions
Six possible days explain how a good forecast can leave the effect of an intervention unresolved. Complete finite proofs and independent Python, Julia, and R calculations.
Objects and foundations · Written and numerically checked - 02Constructing a measured world
Units, imperfect readings, calibration, repeated measurements, and changing denominators, with complete proofs and independent calculations.
Objects and foundations · Written and numerically checked - 03Observation clocks, releases, vintages, and provenance
Reconstructing what was knowable, joining by availability, and proving that future revisions cannot change an earlier forecast.
Objects and foundations · Written and numerically checked
The handbook is the derivation-level companion to the twelve-chapter Econometric Argument: the course develops applied designs at a compact pace, and the handbook works through their foundations in finite examples, with complete proofs and calculations checked in three languages. The course's continuous training example develops the same identification principle as this handbook's finite utility example.