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ECON2515 · Intermediate Applied Econometrics Ii

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Intermediate Applied Econometrics II

— Master OLS, inference and model specification in R — the applied econometrics toolkit for real-world causal questions.

ECON 2515 Intermediate Applied Econometrics is the University of Adelaide's second-year course on using real-world observational data to answer economic questions — does more education raise income, does a subsidy change behaviour — not just to spot patterns. You learn to estimate and interpret regression models in R, moving from the simple OLS estimator to multiple regression, then to inference (t-tests, confidence intervals, p-values and F-tests) and the specification problems that break it (omitted-variable bias, multicollinearity, heteroskedasticity). The recurring theme is that regression is not causation: a significant coefficient is only causal if the key exogeneity assumption holds. The closed-book final rewards interpretation and judgement over formula recall — you must read the R output, defend the test you chose, and diagnose the model, so practising worked interpretations matters far more than memorising derivations.

ECON 2515 · University of Adelaide
Contents · the whole subject, one map

What ECON 2515 covers

ECON 2515 runs across ten teaching topics that build from what econometrics is, through the OLS estimator and multiple regression, into the full inference toolkit (t-tests, p-values, F-tests) and the model-specification problems of multicollinearity and heteroskedasticity, closing with an applied model-critique review.

01Foundations of EconometricsWhat econometrics is · types of economic data · probability, derivatives & graphing review · R and RStudio setup02Simple Linear Regression and the OLS Estimatorpopulation vs sample regression function · deriving OLS · assumptions SLR.1-SLR.5 · unbiasedness & variance03Goodness of Fit and Functional FormsSST/SSE/SSR decomposition · R-squared · log-linear, linear-log, log-log & quadratic forms · elasticity interpretation04The Multiple Linear Regression Modeladding regressors · partialling-out / ceteris paribus · omitted variable bias · MLR assumptions · adjusted R-squared05Inference: Testing a Single Population Parametersampling distribution of OLS · the t-test · one- vs two-sided tests · confidence intervals · write-up steps06Hypothesis Testing Using p-valuesp-value definition & logic · relation to significance levels · decision rules · reading regression output07Testing More Than One Parameter: the F-testjoint hypotheses · restricted vs unrestricted models · F-statistic · testing linear combinations · overall significance08Multicollinearity, Indicator Variables and Interactionsdetecting multicollinearity · dummy variables · base/reference category · interaction terms · slope shifters09Heteroskedasticity: Detection and Correctionconsequences for OLS & inference · detecting heteroskedasticity · robust standard errors · WLS/GLS correction10Course Review and Applied Model Critiquesynthesising OLS · inference & specification · interpreting R output · diagnosing & defending an empirical model · exam prep
Assessment

How ECON 2515 is assessed

ComponentWeightFormat
Quizzes (Quiz 1-4, online timed)subject to confirmationOnline Canvas quizzes, MCQ + short numeric, timed 20-50 min, due across the term (raw 10 pts each)
Group Assignment 1 - Written Reportsubject to confirmationGroup empirical written report using real data in R (raw 80 pts), due ~Week 5
Group Assignment 2 - Video Presentationsubject to confirmationGroup video presentation of an empirical analysis (raw 80 pts), due ~Week 10
Final Examinationsubject to confirmation2 hr face-to-face closed-book: Part A 15 MCQ x2 marks + Part B 2 worked-answer questions (40 marks)
Worked example · free

Multiple regression: interpret a coefficient, find the marginal effect and the turning point

Q [10 marks]. Using data on 1,500 workers, weekly earnings ($) are modelled as EARN = β₁ + β₂EDUC + β₃EXPER + β₄EXPER² + u, with OLS estimates β̂₂ = 28.5 (EDUC), β̂₃ = 11.2 (EXPER), β̂₄ = −0.160 (EXPER²) and β̂₁ = −150. (a) Interpret the coefficient on EDUC. (b) Derive the marginal effect of experience and evaluate it at EXPER = 6 years. (c) After how many years of experience do earnings start to decline?
  • +3(a) EDUC enters linearly, so β̂₂ is a level-level effect: holding experience (and its square) constant, one more year of education is associated with about $28.50 more in weekly earnings. State 'ceteris paribus' explicitly — in multiple regression every slope is a partialled-out, other-things-equal effect.
  • +2(b) Because experience appears as EXPER and EXPER², its effect is not constant. Differentiate: ∂EARN/∂EXPER = β̂₃ + 2β̂₄·EXPER = 11.2 + 2(−0.160)·EXPER = 11.2 − 0.32·EXPER.
  • +2(b, cont.) Evaluate at EXPER = 6: 11.2 − 0.32(6) = 11.2 − 1.92 = $9.28 of extra weekly earnings per additional year of experience at that point.
  • +3(c) Earnings peak where the marginal effect is zero: 11.2 − 0.32·EXPER = 0, so EXPER* = 11.2 / 0.32 = 35 years. Beyond 35 years, extra experience is associated with lower earnings (β̂₄ < 0 gives a hump shape).
EDUC: +$28.50 per year, ceteris paribus; marginal effect of experience at 6 years = $9.28/year; earnings turn down after EXPER* = −β̂₃/(2β̂₄) = 35 years.
Sia tip — For any β₃x + β₄x² pair, the marginal effect is β₃ + 2β₄x (never just β₃ — always plug in the stated x) and the turning point is −β₃/(2β₄). A negative squared-term coefficient means a rise-then-fall hump; a positive one means a U-shape.
Glossary

Key terms

Econometrics
Using statistical methods on real-world (usually observational) economic data to quantify relationships, test theories, forecast and evaluate policy — with a focus on causal, not merely predictive, questions.
Ceteris paribus
'All else equal.' The thought experiment that defines a causal effect: how y changes when one x changes while all other relevant factors are held constant.
OLS estimator
Ordinary least squares — the rule that picks the intercept and slopes to minimise the sum of squared residuals Σ(yᵢ − ŷᵢ)²; unbiased and BLUE under the Gauss-Markov assumptions.
Zero conditional mean (exogeneity)
The assumption E[u|x] = 0 (SLR.4 / MLR.4). It is what makes OLS unbiased and the estimate causal; it fails under omitted variables, reverse causality or measurement error.
Omitted variable bias (OVB)
The bias in an OLS coefficient when a variable that belongs in the model and is correlated with an included regressor is left out; direction = sign(effect on y) × sign(correlation with the included x).
R-squared / adjusted R-squared
R² = SSE/SST is the share of variation in y explained by the model; it only rises as regressors are added, so adjusted R² penalises extra variables and is used to compare models of different size.
Functional form
How variables enter the (still linear-in-parameters) model — level-level, log-linear, linear-log, log-log or quadratic — which fixes how the slope and elasticity are interpreted.
Elasticity
The percentage change in y for a 1% change in x, (∂y/∂x)·(x/y); read directly as β₁ in a log-log model.
t-statistic
t = (β̂ − c)/se(β̂) ~ t(n−k−1), measuring how many standard errors the estimate sits from the null value c; the basis of single-parameter hypothesis tests and confidence intervals.
p-value
The probability of a test statistic at least as extreme as the one observed, assuming H₀ is true; reject H₀ when p ≤ α. It measures evidence against the null, not the probability the null is true.
F-test
A joint test of several restrictions at once, F = [(SSR_R − SSR_U)/q] / [SSR_U/(n−k−1)] ~ F(q, n−k−1); one-tailed, and equal to t² for a single restriction.
Multicollinearity
High (but not perfect) correlation among regressors; it inflates standard errors and makes individual t-stats insignificant (VIF > 10 flags it) but does not bias the coefficients.
Heteroskedasticity
Non-constant error variance, Var(u|x) ≠ σ² (violates MLR.5); OLS stays unbiased but the usual standard errors are wrong, so inference needs robust (White) standard errors or WLS/GLS.
FAQ

ECON 2515 FAQ

How is ECON 2515 assessed?

Assessment combines online timed Canvas quizzes (Quiz 1-4, MCQ + short numeric), two group tasks (a written empirical report in R around Week 5 and a video presentation around Week 10), and a 2-hour face-to-face closed-book final exam. Exact weightings are set by the course profile each offering and are subject to confirmation, so check your official Canvas page.

Is there a final exam, and what does it look like?

Yes — a 2-hour, face-to-face, closed-book final. Part A is 15 multiple-choice questions worth 2 marks each (30 marks); Part B is 2 worked-answer questions with parts (40 marks) where you must show all steps. You may bring one A4 cheat sheet (both sides) and a calculator; statistical tables (t, F, normal) are provided.

What is the hardest part of the course?

Most students find the interpretation and inference judgement calls harder than the algebra: getting the log/linear/log-log/quadratic/interaction interpretation direction right, computing marginal effects and turning points, choosing one- vs two-sided tests with the correct degrees of freedom, and telling apart the three specification problems (OVB biases coefficients, while multicollinearity and heteroskedasticity affect only precision or the standard errors).

How should I prepare for the exam?

The exam rewards application, not recall, so practise reading R/STATA output and writing full worked answers: interpret every coefficient type, run the 6-step hypothesis-test template, compute t, F, CIs and marginal effects from given numbers, and always separate statistical significance from economic magnitude and from causal validity. Build your one-page A4 sheet early around the formula list, the assumption table and the functional-form interpretations.

Do I need to know R for this course?

Yes. Workshops, quizzes and the group assignments use R / RStudio to estimate models and run diagnostics (e.g. VIFs, Breusch-Pagan and White tests, robust standard errors). The exam itself is closed-book on paper but tests your ability to read and interpret the kind of R output you produced during the term.

What maths background do I need?

The course assumes comfort with basic probability (expectation, variance, covariance, conditional distributions) and single-variable calculus (power, exp and log rules; the chain and product rules) so you can derive OLS and compute marginal effects. Week 1 reviews these, but revisit them early if they are rusty.

Is this page official or affiliated with the University of Adelaide?

No. This is an independent AskSia study guide built to help you revise ECON 2515. It is not produced, endorsed by, or affiliated with the University of Adelaide, and it does not reproduce official course materials. Always confirm assessment details, dates and weightings on your official Canvas course profile.

Study strategy

How to study for the exam

Treat ECON 2515 as a skills course, not a memory course: keep pace with the pre-workshop videos and slides each week so the 3-hour workshop is spent practising in R rather than catching up, and do every quiz and worked problem by hand at least once so you can reproduce a t-stat, an F-stat, a confidence interval, a marginal effect and a turning point without the software. As the term builds, maintain a running one-page A4 sheet — OLS variance, R²/adjusted R², t/F/CI formulas, the MLR.1-6 assumption list and what each one buys, the functional-form interpretation table, and the 6-step test write-up — because that same sheet is your allowed exam aid. In the final weeks, drill past-style Part B questions end to end: read the output, interpret each coefficient with the correct log/dummy/quadratic/interaction rule, run the test with the right degrees of freedom and tail, then finish with a sentence on economic magnitude and whether the estimate can be called causal.

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