ECMT6002 Econometric Applications
The Complete Exam Bible · S2 2026ECMT6002 Overview
- Postgraduate
- University of Sydney
- Semester 2 2026
- Econometrics
- Applied modelling
ECMT6002 Econometric Applications is a postgraduate University of Sydney unit about choosing, estimating, diagnosing and interpreting econometric models. The opening part of the course builds the classical linear regression model carefully.
- Match Choose the estimator for the data structure and identifying assumptions.
- Interpret Separate coefficient calculation from statistical and economic meaning.
- Diagnose Use diagnostics to decide which conclusion or standard error is defensible.
- Identify Treat instruments as an identification argument, not merely an extra regression.
- Translate Convert nonlinear model coefficients into the quantity the question actually asks for.
How ECMT6002 is assessed
| Component | Weight | Format |
|---|---|---|
| Final exam | 55% | Written exam in the formal exam period, lasting 2 hours. It covers all content, with greater weight on material from Weeks 7 to 13. |
| In-semester test | 35% | One hour written test in Week 8 with short answer questions covering material from Weeks 1 to 6. |
| Applied Project | 10% | Data analysis group assignment and numerical exercise due in Week 11, with an indicative duration of approximately 4 weeks. |
These are the published Semester 2 2026 settings. Confirm live submission controls and the final exam timetable in Canvas.
Current ECMT6002 dates
| Date | Item | Control |
|---|---|---|
| 24 September 2026, 18:30 | In-semester test | Week 8, one hour |
| 25 October 2026, 23:59 | Applied Project | Week 11 due and closing time |
| Formal exam period | Final exam | Check the official timetable for the exact sitting |
Dates are as published in the official Semester 2 2026 University of Sydney unit outline. Confirm exact deadlines and submission settings in the live LMS.
What ECMT6002 covers
The course moves from linear regression and inference through diagnostics, asymptotics and instrumental variables, then develops time series, specification testing, panel estimators, likelihood and binary choice. The guide follows that progression and makes the assumptions, calculations and diagnostic decisions explicit.
Regression Setup and OLS
Population models, least squares and interpretationThe opening chapter turns a verbal economic relationship into a population regression, a sample regression and a residual.
- Population regression and disturbance
- Sample regression and residual
- Least squares objective
- Slope and intercept interpretation
- Levels and logarithms
- Goodness of fit versus causal credibility
Multiple Regression and Joint Tests
Partial effects, fit measures and joint inferenceMultiple regression adds controls so that each slope describes a partial relationship. This chapter uses the partialling out interpretation to explain omitted variable bias, then develops individual and joint hypothesis tests.
- Partial effects and controls
- Omitted variable bias
- Individual t tests
- Joint F tests
- R squared and adjusted R squared
- Statistical versus economic significance
Diagnostics and Robust Inference
Heteroskedasticity, serial correlation and robust errorsThis chapter diagnoses what happens when the disturbance variance is not constant or disturbances are correlated over time. OLS coefficients can remain centred on the target under suitable exogeneity conditions while conventional standard errors fail.
- Heteroskedasticity
- Serial correlation
- Residual diagnostics
- Heteroskedasticity robust errors
- Autocorrelation consistent errors
- Efficiency and feasible GLS
Asymptotic Reasoning
Probability limits, consistency and large sample inferenceAsymptotic theory replaces exact finite sample claims with approximations that improve as information accumulates. The law of large numbers supports probability limits and consistency, while a central limit theorem supports approximate normal inference.
- Random samples and sample moments
- Probability limits
- Law of large numbers
- Consistency
- Central limit theorem
- Asymptotic normality and standard errors
Stochastic Regressors and Instruments
Endogeneity, relevance, exogeneity and IVStochastic regressors become a problem when their sample variation is connected to the structural disturbance.
- Random regressors and exogeneity
- Sources of endogeneity
- Instrument relevance
- Instrument exogeneity
- Reduced form and first stage
- Single instrument IV estimator
Two Stage Least Squares and Systems
Multiple instruments, 2SLS and simultaneous equationsTwo stage least squares extends the IV idea to multiple instruments and endogenous regressors.
- First stage projections
- Second stage structural equation
- Included and excluded instruments
- Order and rank identification
- Simultaneous equations
- Overidentification and inference
Time Series Models and Forecasting
Dynamic models, stationarity and forecast evaluationTime series methods use the ordering of observations rather than treating rows as exchangeable. This chapter develops autoregressive and distributed lag models, stability and stationarity, one step and multi step forecasts, and forecast errors.
- Lag operators and dynamic equations
- Autoregressive models
- Stability and stationarity
- Dynamic multipliers
- Recursive forecasting
- Forecast errors and loss
Specification Tests and Prediction
Functional form, model selection and prediction intervalsA regression can be estimated perfectly and still answer the wrong question because its functional form, regressor set or disturbance assumptions are misspecified.
- Functional form diagnostics
- Added powers and RESET logic
- Nested and nonnested comparison
- Information criteria
- Point prediction
- Confidence and prediction intervals
Fixed Effects Panel Models
Within transformations and time invariant heterogeneityPanel data observe the same units repeatedly, allowing estimators to separate persistent unit differences from within unit change. The fixed effects model permits the time invariant unit effect to be correlated with regressors.
- Panel data structure
- Unit effects and correlation
- Within transformation
- First difference comparison
- Time fixed effects
- Cluster robust inference
Random Effects and Maximum Likelihood
Variance components, GLS and likelihood logicRandom effects models the unit component as part of a structured composite disturbance and requires it to be uncorrelated with the regressors. Generalised least squares uses partial demeaning rather than removing all between unit information.
- Random effects assumptions
- Composite error covariance
- GLS and partial demeaning
- Fixed versus random effects
- Likelihood and log likelihood
- Score, information and curvature
Binary Choice Models
Linear probability, probit, logit and marginal effectsBinary outcomes require a model for probabilities rather than an unrestricted conditional mean. The linear probability model is simple but can predict outside the unit interval and has heteroskedastic disturbances.
- Linear probability model
- Latent index representation
- Probit probability
- Logit probability and odds
- Maximum likelihood estimation
- Marginal effects and classification
You learn what a population regression says, how ordinary least squares chooses coefficients, how multiple regression isolates a partial effect, and why a standard error is inseparable from the assumptions used to construct it. The course then turns to situations in which those assumptions fail.
Heteroskedasticity and serial correlation motivate robust inference, while asymptotic reasoning explains why large sample approximations can remain useful even when exact small sample results do not apply. Endogeneity is the major identification problem.
The instrumental variables chapters distinguish instrument relevance from instrument exogeneity, show the reduced form and first stage logic, and extend the single instrument estimator to two stage least squares and simultaneous equation systems. Later material changes the data structure. Dynamic time series models require attention to stationarity, persistence and forecast evaluation.
Specification tests ask whether the chosen functional form and regressor set are credible. Panel data methods exploit repeated observations to remove time invariant unobserved heterogeneity, then compare fixed effects with random effects assumptions.
The final part develops maximum likelihood as an estimation principle and applies it to probit and logit models, where coefficients must be translated into probabilities or marginal effects. Assessment in the current Semester 2 outline consists of a written final exam, an in-semester test and a data analysis group project.
The guide therefore combines derivations, short calculations, diagnostic decision rules and interpretation prompts. It does not assume that a formula alone is an answer: every method is tied to its identifying assumptions, the data structure it suits, and the claim it can support.
Worked example · free
Forecasting from an autoregressive model
- +1Insert the latest observed value into the conditional mean: 1.2 + 0.6 times 5 = 4.2.
- +1Check stability: the autoregressive coefficient has absolute value below one, so a finite long run mean exists.
- +1Compute the long run mean as 1.2 divided by 1 minus 0.6, which equals 3.
- +1Use observed minus forecast for the forecast error: 4.5 minus 4.2 equals 0.3.
Key terms
- Conditional mean
- The expected value of an outcome given a stated information set or collection of regressors.
- Ordinary least squares
- An estimator that selects coefficients to minimise the sum of squared sample residuals.
- Exogeneity
- A condition linking regressors or instruments to the disturbance. Its exact form depends on the estimator and data structure.
- Heteroskedasticity
- Variation in the conditional variance of the disturbance across observations.
- Serial correlation
- Dependence between disturbances from different time periods after conditioning on the model regressors.
- Consistency
- Convergence in probability of an estimator to the parameter as the sample size grows.
- Endogeneity
- Correlation between an explanatory variable and the structural disturbance, which generally invalidates OLS causal interpretation.
- Instrument relevance
- The requirement that an instrument predicts the endogenous regressor after accounting for included exogenous variables.
- Instrument exogeneity
- The requirement that an instrument is uncorrelated with the structural disturbance.
- Stationarity
- Stability of the probabilistic behaviour of a time series over time, under the stationarity concept being used.
- Fixed effects
- A panel estimator that removes time invariant unit effects through within unit variation.
- Random effects
- A panel model that treats the unit effect as a random component uncorrelated with the regressors.
- Maximum likelihood
- An estimation principle that chooses parameters making the observed sample most probable under a specified model.
- Marginal effect
- The change in a predicted outcome or probability associated with a small change in a regressor, holding specified quantities fixed.
ECMT6002 FAQ
What is the assessment structure?
The current Semester 2 outline assigns 55% to a two hour written final exam, 35% to a one hour in-semester written test, and 10% to an applied data analysis group project. The test covers the early regression and inference material, while the final covers the whole course with more weight on later weeks.
What should I write after calculating an estimate?
State what the number estimates, the units of the effect, what is being held fixed, and the assumptions needed for the interpretation. For nonlinear and dynamic models, also identify the evaluation point or information set. A correct number without that translation is an incomplete econometric answer.
How do I distinguish relevance from exogeneity?
Relevance concerns whether the instrument moves the endogenous regressor, usually examined through the first stage. Exogeneity concerns whether the instrument is excluded from the structural disturbance. Strong first stage prediction cannot prove exogeneity, so the economic exclusion argument must be stated separately.
When should I use fixed effects?
Fixed effects is useful when repeated observations are available and unobserved unit characteristics may be correlated with the regressors. It removes time invariant unit effects, so identification comes from within unit changes. It cannot separately estimate coefficients on regressors that never change within a unit.
How should I revise time series models?
Practise a fixed sequence: write the dynamic equation, identify the information set, check stability, compute the requested forecast, and define the forecast error convention. Then compare models using out of sample loss rather than in sample fit alone. Keeping those steps explicit prevents most indexing mistakes.
What is the main binary choice trap?
A logit or probit coefficient is not generally a direct probability change. Translate it through a marginal effect or compare predicted probabilities at stated covariate values. Also check whether the question asks about a latent index, odds, probability, or classification because those are distinct objects.
Are past exam papers included?
No past exam paper or official sample paper was present in the supplied course source. The practice material in this guide is newly written from the documented concepts and assessment format. Use it to rehearse methods, then confirm any current exam instructions and permitted materials in Canvas.
Questions students ask in each ECMT6002 chapter
- Why does the fitted line pass through the means?
- With an intercept, the first order condition makes the sample residuals sum to zero. Rearranging the average fitted equation therefore gives mean y equal to the intercept plus the slope times mean x. Chapter 01 · Regression Setup and OLS
- Why can two insignificant t tests produce a significant F test?
- The joint test accounts for the covariance between coefficient estimates and asks whether restrictions hold together. Separate t tests answer different marginal questions and do not control the same joint rejection event. Chapter 02 · Multiple Regression and Joint Tests
- Do robust errors fix endogeneity?
- No. They change estimated sampling uncertainty under variance misspecification. If a regressor is correlated with the structural disturbance, the coefficient target itself is compromised and a different identification strategy is needed. Chapter 03 · Diagnostics and Robust Inference
- Does consistency imply unbiasedness?
- No. Consistency is a limiting property, while unbiasedness is an exact expectation statement at a given sample size. An estimator can be biased in finite samples and still have bias that vanishes asymptotically. Chapter 04 · Asymptotic Reasoning
- Can relevance be tested directly?
- The first stage provides evidence about sample relevance and instrument strength. It does not establish population exogeneity, and weak instrument diagnostics must be interpreted in the setting of the chosen estimator and test. Chapter 05 · Stochastic Regressors and Instruments
- Can I manually run two regressions?
- The fitted value intuition is useful, but ordinary standard errors from a manually run second regression are generally wrong. Use a 2SLS routine or the correct matrix covariance calculation for inference. Chapter 06 · Two Stage Least Squares and Systems
- Why do forecasts converge to the long run mean?
- In a stable autoregression, repeated powers of the autoregressive coefficient shrink toward zero. The influence of the current deviation therefore fades while the intercept accumulation approaches the unconditional mean. Chapter 07 · Time Series Models and Forecasting
- What does rejection of RESET prove?
- It indicates that the maintained conditional mean is inadequate against the added function alternatives. It does not identify a unique missing variable or guarantee that one particular nonlinear replacement is correct. Chapter 08 · Specification Tests and Prediction
- Why do time invariant regressors disappear?
- Their value equals their unit mean in every period. Subtracting the unit mean therefore creates a column of zeros, leaving no within unit variation from which to estimate a separate slope. Chapter 09 · Fixed Effects Panel Models
- What is the key random effects restriction?
- The time invariant unit effect must be uncorrelated with the regressors under the maintained model. If that restriction fails, random effects combines contaminated between variation with within variation and becomes inconsistent. Chapter 10 · Random Effects and Maximum Likelihood
- Why not interpret a logit coefficient as a probability change?
- The coefficient changes the linear index and log odds. The derivative of probability multiplies that coefficient by the logistic density, so the probability effect varies with the covariate values. Chapter 11 · Binary Choice Models
How to study for the exam
Revise by estimator decision rather than by formula list. For every method, keep a compact card with the target parameter, the variation that identifies it, the assumptions, the estimator, the standard error choice, one diagnostic and the correct interpretation. Begin with OLS because later methods are responses to a particular OLS failure.
When you reach instruments, draw the causal story and keep relevance separate from exogeneity before doing any algebra. For time series, always label time indexes and the information set used by a forecast. For panel data, ask whether the useful variation is between units or within a unit over time and whether the unit effect may be correlated with regressors.
For likelihood and binary choice, practise moving among the index, the probability, the log likelihood and a marginal effect. Use the current assessment split to pace practice: short derivations and diagnostic explanations suit the in-semester test, while later model comparison and interpretation deserve extra attention for the final exam.
Complete problems without notes, mark the first line where the reasoning failed, and then redo the same problem from a blank page. Keep a separate error log for algebra, assumptions, data structure and interpretation because each category needs a different remedy. Finally, check the live Canvas page for exact assessment controls and the final examination timetable.
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