ECMT3120 Applied Econometrics
The Complete Exam Bible · Semester 2 2026ECMT3120 Overview
- University of Sydney
- Semester 2 2026
- Paper based final
- Closed book assessment
ECMT3120 Applied Econometrics is a University of Sydney unit about choosing and interpreting empirical methods when ordinary least squares is not enough.
- Assessed by Assignments, an in class test and a formal final examination
- Core skill Match each estimator to the variation and assumption that identify it
- Final preparation Practise model setup, handwritten algebra, diagnostics and economic interpretation
How ECMT3120 is assessed
| Component | Weight | Format |
|---|---|---|
| Assignments 2-4 practice questions | 20% | Eight out of class sets across multiple weeks; AI allowed in the current official outline |
| Mid-semester test In-class, paper-based test | 30% | Week 7, one hour, AI prohibited; current outline date is 15 September 2026 at 14:30 |
| Final exam Paper-based exam | 50% | Formal examination period, two hours, AI prohibited; the captured syllabus states closed book |
What ECMT3120 covers
Applied Econometrics moves from the probability model beneath OLS into designs that address endogeneity and repeated observations. The guide first separates a data generating process from a statistical model, derives matrix least squares, and checks dimensions, rank and residual orthogonality.
It then builds instrumental variables from relevance and exogeneity, develops two stage least squares, and distinguishes first stage strength from validity. The final sequence compares pooled cross sections, difference in differences, first differences, fixed effects and random effects by the variation and assumptions each estimator uses.
Statistical Models and OLS Assumptions
Data generating processes, random sampling, conditional means and interpretationEconometric reasoning begins before estimation. This chapter separates a complete data generating process from a statistical model and an observed sample, then asks what random sampling and conditional mean independence mean in economic terms.
- Data generating processes and parameter indexed statistical models
- Independent and identically distributed sampling as a modelling choice
- Regression equations, structural errors and omitted determinants
- Conditional mean independence and coefficient interpretation
- Descriptive, predictive and causal claims
- Omitted variable bias direction
Matrix OLS from Objective to Inference
Residual geometry, normal equations, rank and sampling varianceMatrix notation turns least squares into a transparent sequence: construct the design matrix, define the residual vector, minimise its squared length, solve the normal equations, and verify dimensions and rank.
- Design matrix, outcome vector and coefficient dimensions
- Residual vectors and sums of squared residuals
- Normal equations and the least squares solution
- Full column rank and perfect collinearity
- Dummy variable base categories
- Residual orthogonality checks
Endogeneity and Instrument Validity
Bias sources, relevance, exclusion and simple instrumental variablesEndogeneity links a regressor to the structural error and makes the OLS slope combine a target effect with omitted influences.
- Endogenous and exogenous regressors
- OLS bias decomposition
- Omitted variables and proxy strategies
- Instrument relevance and first stage evidence
- Instrument exogeneity and exclusion reasoning
- Simple instrumental variable covariance ratio
Two-Stage Least Squares and Weak Instruments
Projection, first stage tests, rank and precisionTwo stage least squares extends simple IV to models with controls, several instruments and several endogenous regressors.
- Included exogenous variables as instruments for themselves
- First stage projection of endogenous regressors
- Second stage structural regression
- Projection matrix and matrix 2SLS
- Joint first stage relevance tests
- Rank with multiple endogenous regressors
IV Diagnostics and Simultaneous Equations
Endogeneity tests, overidentification and structural systemsInstrumental variables analysis does not end when a coefficient appears. A credible answer separates relevance, exogeneity and exclusion, then selects diagnostics that address only the assumptions they can actually test.
- Relevance, exogeneity and exclusion as separate claims
- Exactly identified and overidentified specifications
- Sargan and Hansen overidentification logic
- Interpreting rejection and non-rejection
- Structural and reduced form equations
- Order condition for equation identification
Pooled Cross Sections and Difference-in-Differences
Time effects, interactions, policy comparisons and counterfactual trendsPooled cross sections combine independent samples drawn at different dates and use time indicators to describe aggregate shifts. Difference-in-differences adds a treatment group indicator and a treatment-by-post interaction to recover a relative change.
- Independent cross sections pooled across time
- Time indicators and changing intercepts
- Group indicators and baseline gaps
- Treatment by post interaction
- Four cell mean difference-in-differences
- Parallel trends and counterfactual change
First Differences and Panel Identification
Within unit changes, time invariant effects and panel policy modelsPanel data follow the same units through time, allowing a researcher to remove stable unobserved heterogeneity rather than hoping it is uncorrelated with regressors.
- Panel structure and unit-time indexing
- Time-invariant unobserved effects
- First-difference transformation
- Identification from within-unit changes
- Strict exogeneity after transformation
- Time effects and common shocks
Fixed Effects, Random Effects and Model Choice
Demeaning, covariance structure, Hausman logic and estimator selectionFixed effects and random effects use panel structure in different ways.
- Within transformation for fixed effects
- Identification from deviations around unit means
- Loss of time-invariant regressors under fixed effects
- Composite error structure in random effects
- Quasi-demeaning and the transformation parameter
- Random effects orthogonality assumption
The captured Semester 2 2026 materials begin with data generating processes, statistical models and matrix OLS, then devote three teaching blocks to instrumental variables and two blocks to panel data. The central habit is to separate an estimator from the assumptions that give it meaning. For OLS, this means examining the conditional mean and the contents of the error term.
For instrumental variables, it means establishing predictive relevance while defending instrument exogeneity through economic reasoning. For panel estimators, it means deciding whether identification comes from changes within the same unit, differences between units, or a weighted combination of both.
The official assessment has three components: assignments worth 20 percent, a paper based in class test worth 30 percent, and a paper based final examination worth 50 percent. The final lasts two hours in the formal examination period, and the syllabus describes it as closed book.
The source does not publish a question count, section structure, calculator rule or formula sheet permission, so this guide does not invent those details. Instead, each chapter rehearses the reasoning moves evidenced by the university practice solutions: define the model, show the transformation or estimator, state the null or identifying assumption, calculate transparently, and interpret the result in economic units.
The source pack includes detailed material through fixed and random effects. Later syllabus topics are not expanded into unsupported chapters. Every worked problem here uses original contexts and values while retaining the genuine course methods and marking cues.
Worked example · free
Recover a difference in differences estimate
- +1The treated corridor change is 35 minus 42, which equals minus 7 minutes.
- +1The comparison corridor change is 36 minus 38, which equals minus 2 minutes.
- +1Subtract the comparison change from the treated change: minus 7 minus minus 2 equals minus 5 minutes.
- +1Interpret the sign through the outcome: the lane is associated with an additional 5 minute reduction in travel time relative to the comparison trend.
- +1A causal reading requires the comparison trend to represent the treated corridor without the lane and no simultaneous corridor specific intervention.
Key terms
- Data generating process
- A complete probability mechanism that generates the variables and dependence in a population.
- Statistical model
- A collection of possible data generating processes indexed by unknown parameters or features.
- Conditional mean independence
- The identifying condition that the structural error has mean zero after conditioning on included regressors.
- Full column rank
- The requirement that design matrix columns contain distinct information so the least squares solution is unique.
- Endogeneity
- Correlation between a regressor and the structural error, often created by omitted factors, simultaneity or measurement error.
- Instrument relevance
- The requirement that an excluded instrument predicts the endogenous regressor after included controls.
- Instrument exogeneity
- The requirement that an instrument remains unrelated to the structural error and affects the outcome only through the endogenous regressor.
- Two stage least squares
- An estimator that projects endogenous regressors onto instruments and uses the fitted variation in the structural equation.
- Overidentification
- A setting with more excluded instruments than endogenous regressors, creating extra restrictions that can be tested jointly.
- Difference in differences
- A design that subtracts the control group change from the treated group change to remove a shared time movement.
- Fixed effects
- A within unit estimator that removes stable unobserved effects by subtracting each unit's time average.
- Random effects
- A feasible GLS estimator that uses partial demeaning under the stronger assumption that unit effects are uncorrelated with regressors.
ECMT3120 FAQ
How is the unit assessed?
The current official outline lists assignments worth 20 percent, a paper based in class test worth 30 percent, and a paper based final examination worth 50 percent. The numeric weights total 100 percent. Check current unit notices for operational dates and instructions.
What is published about the final format?
The official outline states that the final is paper based, lasts two hours, and sits in the formal examination period. The captured syllabus states that it is closed book. A section count, question count, calculator rule and formula sheet rule are not published in these materials.
What makes an instrument valid?
A credible instrument must predict the endogenous regressor after controls and remain unrelated to the structural error. Relevance can be investigated in the first stage. Exogeneity needs a substantive argument ruling out direct effects, shared omitted causes and behavioural responses.
Why can two stage least squares be less precise than OLS?
OLS uses all observed variation in a regressor, including variation that may be endogenous. Two stage least squares deliberately uses the portion predicted by instruments. When that fitted portion is limited or collinear with controls, standard errors can grow even when the design is more credible.
How should I choose between fixed and random effects?
Start with whether stable unit heterogeneity is likely correlated with the regressors. Fixed effects permits that correlation and uses within unit changes, but drops time invariant regressors. Random effects retains between unit information under a stronger orthogonality assumption and can be more efficient when that assumption is credible.
Are past papers included?
The captured folder contains assignment solutions and weekly practice solutions, but no past exam, sample final or practice final. This guide therefore offers original questions modelled on the documented reasoning tasks and mark allocations without presenting them as past paper content.
Questions students ask in each ECMT3120 chapter
- Why is a regression equation not a complete econometric model?
- An equation names variables and parameters but does not state how observations are sampled, how the error behaves, whether units are dependent, or how regressors relate to omitted determinants. Those assumptions determine whether an estimator has a sampling distribution and whether its coefficient receives a descriptive or causal interpretation. Chapter 01 · Statistical Models and OLS Assumptions
- Why does full column rank matter for OLS?
- Full column rank makes the design cross product invertible and gives a unique coefficient vector. If an intercept accompanies an indicator for every category, the design contains perfect linear dependence. Omitting a base category restores rank and defines the coefficient comparisons. Chapter 02 · Matrix OLS from Objective to Inference
- Why does endogeneity break ordinary least squares?
- When a regressor covaries with the structural error, the OLS slope combines the target effect with the influence of omitted factors associated with the regressor. The problem is identification, so a smaller standard error or larger sample does not remove the contaminated comparison. Chapter 03 · Endogeneity and Instrument Validity
- Why do included controls appear in both stages?
- An included control is exogenous and therefore instruments its own coefficient. The first stage asks whether excluded instruments predict the endogenous regressor after conditioning on those controls. The second stage retains the original controls so the structural comparison matches the stated model. Chapter 04 · Two-Stage Least Squares and Weak Instruments
- Does passing an overidentification test prove every instrument is valid?
- No. The test evaluates joint compatibility with the maintained model and has limited power in finite samples. Instruments can share the same violation, or the test may simply fail to detect a modest violation. Defend each exclusion restriction substantively even after non-rejection. Chapter 05 · IV Diagnostics and Simultaneous Equations
- Is difference-in-differences just a before and after comparison?
- No. A before and after comparison mixes the treatment effect with any common time shock. Difference-in-differences subtracts the comparison group's change, using it to estimate the counterfactual change for the treated group. Chapter 06 · Pooled Cross Sections and Difference-in-Differences
- What exactly disappears after first differencing?
- Any additive characteristic that is constant through time for a unit disappears, whether observed or unobserved. Variables that do not change over time also disappear, so their separate coefficients cannot be estimated in the differenced equation. Chapter 07 · First Differences and Panel Identification
- Why can fixed effects include a time effect but not a unit-constant regressor?
- A common time indicator changes across periods and survives unit demeaning. A unit-constant regressor equals its own unit mean in every period, so its within-transformed value is zero and its separate coefficient cannot be recovered. Chapter 08 · Fixed Effects, Random Effects and Model Choice
How to study for the exam
Build revision around identification stories rather than a formula list. For each method, write the economic question, the source of endogeneity or dependence, the variation the estimator uses, and the assumption that turns that variation into an effect. Rework matrix OLS until dimensions and residual checks are automatic.
For instrumental variables, keep relevance, endogeneity and overidentification as three different diagnostic questions with three different nulls. For difference in differences, calculate the four cell means before discussing the counterfactual trend. For panel data, compare pooled OLS, first differences, fixed effects and random effects by what each removes and what each still assumes.
Practise by hand because the final is paper based and closed book in the captured syllabus. End every solution with units, direction, comparison population and one specific remaining threat. If a result relies on an exclusion restriction, parallel trends, strict exogeneity or random effects orthogonality, write that condition beside the number rather than leaving it implicit.
Check the current official timetable and unit notices for the final date, venue and permitted items.
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