Ekonomie 388 (Economics 388) Econometrics Exam Pack

Ekonomie 388 / Economics 388 (Econometrics) is typically assessed through a mix of econometric theory, applied estimation, diagnostics, and econometric reasoning under uncertainty. This exam pack provides structured, high-yield exam notes aligned with how students are commonly tested at South African universities—emphasising clear assumptions, correct model specification, and defensible interpretation of results. While styles differ by department, the core skills tested in econometrics remain consistent: choose the right estimator, justify identification/assumptions, diagnose violations, and interpret coefficients causally when possible.

This study guide is built around an institution-centred approach: for South African practice, the most reliable way to prepare is to master the same econometric concepts while anchoring them to how a specific university’s course materials and exam rubrics often evaluate answers—especially around regression interpretation, inference, and model validity.

Stellenbosch University (SU) Economics Course Notes: Ekonomie 388 Exam Pack (Econometrics)

Stellenbosch University is well known for strong quantitative training, and Economics/ Ekonomie students are typically expected to combine econometric mechanics with economic interpretation. In past SA university settings, answers that score highly tend to: (1) start with a properly stated model, (2) specify identifying assumptions, (3) show the key derivations or formulas where relevant, (4) interpret estimated parameters in economic terms, and (5) conclude with the “so what” for policy or economic inference. This section focuses on SU-style expectations: conceptual clarity, correct mathematical notation, and disciplined justification of assumptions.

1) Core Econometric Framework You Must Master

An econometrics exam question almost always begins with “assume the following model…” or “given estimates… interpret…” Even if the prompt varies, the backbone is usually one of the following:

1.1 The Classical Linear Regression Model (CLRM)

A standard starting point is the CLRM:

[
Y_i = \beta_0 + \beta_1 X_{i1} + \cdots + \beta_k X_{ik} + u_i
]

Key assumptions (you should be able to state and use them):

1. Linearity in parameters: the model is linear in (\beta)’s.
2. Random sampling (often implicit): observations are drawn from a population.
3. No perfect multicollinearity: regressors are not exact linear combinations.
4. Conditional mean zero (exogeneity):
   [
   \mathbb{E}[u_i\mid X_i]=0
   ]
5. Homoskedasticity and no autocorrelation (for standard OLS variance formulas):
   [
   \text{Var}(u_i\mid X)=\sigma^2
   ]
   [
   \text{Cov}(u_i,u_j\mid X)=0 \quad (i\neq j)
   ]

Exams often test whether you can identify what assumption is violated by a scenario. For instance, omitted variable bias breaks conditional mean zero.

1.2 Estimation and Inference

OLS estimator:

[
\hat{\beta} = (X'X)^{-1}X'Y
]

Variance under homoskedasticity:

[
\text{Var}(\hat{\beta}\mid X)=\sigma^2 (X'X)^{-1}
]

With estimated (\hat{\sigma}^2), you get standard errors and t-tests. In an exam, scoring comes from linking the scenario to the right consequence: e.g., “if heteroskedasticity is present, OLS remains unbiased under exogeneity, but standard errors are wrong; use robust (White) or other corrections.”

1.3 Interpretation of Coefficients: Levels vs Logs

A frequent exam trap is wrong interpretation when the model uses logs. You need to recognise three common forms:

1. Linear–Linear:
   [
   Y = \beta_0 + \beta_1 X + u
   \Rightarrow \beta_1 = \frac{\partial Y}{\partial X}
   ]
2. Log–Linear:
   [
   \ln(Y) = \beta_0 + \beta_1 X + u
   \Rightarrow \frac{\partial \ln(Y)}{\partial X}=\beta_1
   \Rightarrow \text{approx } 100\beta_1% \text{ change in }Y \text{ for a one-unit increase in }X
   ]
3. Log–Log:
   [
   \ln(Y)=\beta_0+\beta_1\ln(X)+u
   \Rightarrow \beta_1=\text{elasticity of }Y \text{ w.r.t. }X
   ]

A high-scoring answer also states the “small changes approximation” when using the log-linear semi-elasticity. For larger changes, you should mention the exact transformation:
[
%\Delta Y = (e^{\beta_1\Delta X}-1)\times 100
]

2) What SU Exams Commonly Emphasise: Assumptions, Diagnostics, and Correct Corrections

SU-style econometrics exam questions often include a short dataset or regression output snippet, followed by: interpret coefficients, test a hypothesis, and assess whether classical assumptions hold. This section trains you to answer such questions with a disciplined workflow.

2.1 Assumption-Checking as Argumentation

Instead of listing assumptions mechanically, practice linking each diagnostic to a specific assumption.

2.1.1 Heteroskedasticity

If the prompt says: “variance increases with income” or “errors are larger for high values of (X),” then heteroskedasticity is likely. Consequences:

• OLS coefficients remain unbiased and consistent if exogeneity holds.
• Conventional standard errors (and thus t-tests/F-tests) become unreliable.

Correct move in a solution:

• Use heteroskedasticity-robust standard errors (e.g., HC variants).
• Or consider weighted least squares if structure is known.

2.1.2 Autocorrelation (Time Series / Panel)

If data are time series or ordered by time, and errors may be correlated across time, you must mention serial correlation:

• Standard errors biased.
• Durbin–Watson is common for simple AR(1) settings; Breusch–Godfrey is common for general order.

Again, key is to say what changes: coefficient estimates are still unbiased/consistent under strict exogeneity, but inference may break unless you correct standard errors or model the correlation (e.g., GLS, Newey–West).

2.1.3 Multicollinearity

If regressors are highly correlated (e.g., education and experience, or two proxies for human capital), multicollinearity affects precision:

• OLS is still unbiased under exogeneity.
• Standard errors inflate; t-tests may not reject even when variables matter.

Diagnostics:

• Correlation matrix
• Variance inflation factor (VIF)
• Condition index / eigenvalues (more advanced)

In answers, you should not claim multicollinearity causes bias—it mainly affects variance of estimates.

2.2 Hypothesis Testing: The Mechanics + The Meaning

In exams, hypothesis questions often ask for an F-test or t-test interpretation.

2.2.1 t-test for a single coefficient

Null:
[
H_0:\beta_j = \beta_{j0}
]

Test statistic:
[
t = \frac{\hat{\beta}j – \beta{j0}}{SE(\hat{\beta}_j)}
]

Interpretation:

• If you reject (H_0), you argue evidence that (X_j) is statistically associated with (Y) conditional on other regressors.
• Important: statistical association is not automatic causality; causality depends on exogeneity.

2.2.2 F-test for joint restrictions

For restrictions (R\beta = r):

[
F = \frac{(SSR_r – SSR_{ur})/q}{SSR_{ur}/(n-k-1)}
]

where:

• (SSR_r) = sum of squared residuals under restricted model
• (SSR_{ur}) = under unrestricted model
• (q) = number of restrictions

Strong answers clearly explain whether the test is:

• a global significance test (“do these variables matter jointly?”),
• or a structural constraint test (e.g., parameter equality, correct functional form).

2.3 Omitted Variables and Endogeneity: Recognise the Signature

A frequent Econometrics question is a scenario:

• “Education positively affects wages, but ability is omitted.”
• “Price is endogenous because demand shocks affect both price and quantity.”
• “Government spending responds to economic conditions, which also affect unemployment.”

You must be able to map the scenario to the econometric problem.

2.3.1 Omitted variable bias

Suppose the true model is:
[
Y_i=\beta_0+\beta_1X_i+\gamma Z_i+u_i
]
but you estimate:
[
Y_i=\alpha_0+\alpha_1X_i+e_i
]
If (Z) is omitted and correlated with (X), then (\hat{\alpha}_1) is biased.

Direction of bias depends on:
[
\text{Bias}(\alpha_1)\propto \gamma \cdot \text{Cov}(X,Z)
]

An exam answer should explicitly mention both sign channels.

2.3.2 Endogeneity and simultaneity

If (X) is correlated with (u) because of reverse causality or simultaneous determination, exogeneity fails. Then OLS is not consistent.

Typical solutions:

• Instrumental variables (IV/2SLS)
• Control function methods (advanced)
• Difference-in-differences (if panel and shocks)
• Regression discontinuity (design-based)
• Randomised experiments (outside classical econometrics scope, but conceptually helpful)

Even if a question does not ask you to implement IV, you must correctly diagnose “OLS is biased/inconsistent under endogeneity.”

3) Instrumental Variables (IV) / 2SLS: How to Show You Know It

IV is one of the most common “hard” sections in econometrics exams. SU exams often require both conceptual and computational/derivational clarity.

3.1 The IV Setup

To estimate (\beta_1) in:
[
Y_i = \beta_0 + \beta_1 X_i + u_i
]
where (X) is endogenous, introduce instrument (Z_i) such that:

1. Relevance:
   [
   \text{Cov}(Z_i, X_i)\neq 0
   ]
2. Exogeneity / validity:
   [
   \mathbb{E}[Z_i u_i]=0
   ]
3. Often also: exclusion restriction: (Z) affects (Y) only through (X).

3.2 Two-Stage Least Squares (2SLS)

First stage:
[
X_i = \pi_0 + \pi_1 Z_i + \eta_i
]
Obtain fitted values:
[
\hat{X}_i
]

Second stage:
[
Y_i = \beta_0 + \beta_1 \hat{X}_i + \epsilon_i
]

In an exam, you should clearly state what is estimated in each stage and what “fitted values” mean.

3.3 Diagnostic Tests for IV

3.3.1 Weak instruments

If the first stage relationship is weak, 2SLS becomes unreliable (large standard errors, biased inference).

Common exam knowledge:

• First-stage F-statistic rule of thumb (especially in applied contexts).
• More formal: weak identification robust methods (advanced).

3.3.2 Overidentification (when multiple instruments)

If there are more instruments than endogenous regressors, you can test validity through an overidentification test (e.g., Sargan/Hansen).

Exam scoring often comes from stating:

• Null hypothesis: instruments are valid.
• If rejected: at least one instrument violates exogeneity/exclusion.

3.4 A Concrete Case Narrative: Labour Market and Policy Variables

Consider a typical labour economics-style story used in econometrics exams:

• Outcome: log wages
• Endogenous regressor: years of education
• Potential instrument: distance to the nearest college or a policy eligibility indicator affecting education but plausibly not wages except through education.

A good exam answer:

1. States why education is endogenous (ability bias, omitted family background).
2. States why the instrument might be relevant (distance affects schooling attainment).
3. States why it might be exogenous/excluded (distance affects wages only through education, assuming no other channels).
4. Notes the key threat: the instrument could also affect wages directly (e.g., local labour market effects), which would violate exclusion restriction.

Then you tie back to the IV diagnostics:

• If first stage shows weak relevance, estimates are unreliable.
• If overidentification test rejects, some instruments are invalid.

Even when you are not asked to compute 2SLS numerically, your ability to argue the IV assumptions earns marks.

Diagnostic Testing and Model Selection: From Assumptions to Reliable Inference

Econometrics exams reward students who can diagnose problems with a model and choose the “right fix.” This section focuses on the mechanics of diagnostics and how to write exam-ready answers that clearly connect tests to assumptions.

1) Residual-Based Diagnostics: Reading the Clues

Most diagnostic questions revolve around residuals, fitted values, and test statistics derived from residual patterns.

1.1 The Residuals and What They Tell You

Residual:
[
\hat{u}_i = y_i – \hat{y}_i
]

Residual patterns often indicate assumption violations.

Common patterns:

• Non-constant variance: residual spread increases with fitted values → heteroskedasticity.
• Systematic autocorrelation: residuals cluster over time → serial correlation.
• Nonlinearity: residuals show curvature when plotted against (X) → model misspecification.
• Outliers/influential points: one observation substantially affects coefficients → robust regression or influence diagnostics.

1.2 Heteroskedasticity Tests

1.2.1 Intuition

If variance of (u_i) depends on (X), then:
[
\text{Var}(u_i\mid X)=\sigma_i^2
]
OLS estimates can remain unbiased but OLS standard errors are wrong.

1.2.2 Example test logic: Breusch–Pagan / White

• Breusch–Pagan: models variance as a function of regressors. Under the null of homoskedasticity, certain auxiliary regression coefficients are zero.
• White test: uses squared residuals and includes cross-products; more general but can be less powerful in small samples.

In an exam answer, you should:

1. Identify the likely violation.
2. Name the test used (if asked).
3. State the null and what rejection implies.
4. State the corrective action: use robust standard errors or re-specify model.

1.3 Serial Correlation Tests

1.3.1 Durbin–Watson (DW)

In a simple AR(1) model:
[
u_t = \rho u_{t-1} + \nu_t
]
DW statistic approximates:

• DW near 2 → little autocorrelation
• DW toward 0 → positive autocorrelation
• DW toward 4 → negative autocorrelation

In exams, DW is often presented in regression output. Students should interpret direction qualitatively and state if inference should use robust methods.

1.3.2 Breusch–Godfrey (BG)

Used for higher-order autocorrelation and generally more flexible than DW. In a well-written answer:

• State null: no serial correlation up to a specified order.
• Mention if rejected: adjust standard errors or include a correlation structure.

1.4 Nonlinearity and Functional Form

If the relationship is not correctly specified (e.g., you used (X) but true is (X^2)), the error term captures systematic patterns and exogeneity conditional on regressors can fail.

Exam move:

• Propose adding polynomial terms or transforming variables (logs).
• Use RESET test (Regression Equation Specification Error Test) when appropriate.

RESET logic:

• Under correct functional form, higher powers of fitted values should not explain residuals.
• If rejected, evidence of misspecification.

2) Model Selection: Theory-Driven, Not Guess-Driven

Econometrics exams sometimes ask you to compare models using criteria (AIC/BIC) or to justify inclusion/exclusion of variables based on theory and identification.

2.1 Adjusted R² vs AIC/BIC

Adjusted (R^2):

• Penalises number of regressors lightly.
• Useful, but not always the best model selection criterion for inference.

AIC/BIC:

• Derived from likelihood principles.
• BIC penalises model complexity more strongly than AIC, which is useful when the true model is sparse.

In a well-prepared answer:

• State what criterion penalises and how that affects overfitting.
• Emphasise that selection should not override endogeneity and identification concerns.

2.2 The Bias–Variance Tradeoff (Exam-Friendly Framing)

When adding variables:

• Bias can decrease if missing confounders or mis-specified functional form existed.
• Variance can increase because parameters are estimated with less data per parameter.

In linear regression, multicollinearity increases variance inflation. Overly complex models can overfit noise.

A strong exam answer explicitly ties model complexity to inference reliability:

• predictive accuracy vs causal interpretability.

3) “Robustness” in Econometrics: What It Means in Practice

In econometrics, robustness typically means:

• coefficients stable across alternative specifications (controlled conditioning),
• standard errors robust to heteroskedasticity/autocorrelation,
• sensitivity to outliers.

But exam answers must be precise: robust standard errors address inference under certain violations, not endogeneity.

Causality, Identification Strategies, and Applied Econometric Reasoning

Causality is a core theme in modern econometrics exams, including in South African contexts where applied questions frequently use observational data and policy-like hypotheses. This section focuses on causal reasoning frameworks and how to defend an identification strategy.

1) The Causal Problem: Why Econometrics Isn’t Just Correlation

To interpret (\beta) causally in:
[
Y_i = \beta_0 + \beta_1 X_i + u_i
]
you require exogeneity:
[
\mathbb{E}[u_i\mid X_i]=0
]
Without this, (\beta_1) may be biased.

Common reasons exogeneity fails:

• Omitted variables (ability, motivation, family background).
• Measurement error (imperfect proxies).
• Simultaneity (reverse causality, joint determination).
• Selection bias (non-random participation in programmes).

In an exam, you should explicitly mention these and connect them to which method is appropriate.

2) Counterfactual Thinking: The Language That Improves Answers

Even when questions are computational, graders reward counterfactual framing:

• “What would happen to the same unit if treatment were different?”
• “The goal is to isolate variation in (X) that is plausibly exogenous.”

You can then link it to methods:

• IV uses exogenous variation in (X) induced by (Z).
• Difference-in-differences uses time and group comparisons under parallel trends.
• Regression discontinuity uses local comparison around a cutoff.
• Panel fixed effects removes time-invariant unobserved heterogeneity.

3) Difference-in-Differences (DiD): The Parallel Trends Logic

Although the exact scope depends on the course, DiD is often included in Economics/Econometrics syllabi.

3.1 The Basic DiD Model

With two groups (treated and control) and two periods (pre and post), you estimate:

[
Y_{gt} = \alpha + \beta \cdot \text{Treat}_g + \gamma \cdot \text{Post}_t + \delta (\text{Treat}_g \times \text{Post}t) + \varepsilon{gt}
]

Interpretation:

• (\delta) is the DiD estimator: the change in treated outcomes minus the change in control outcomes.

3.2 The Key Assumption: Parallel Trends

Under the null of no treatment effect, treated and control groups would have evolved similarly absent treatment. Formally:

• trends in outcomes between groups would be equal pre-treatment.

Exam answer must include:

• why the assumption is plausible (or not),
• how to test it (graphically using pre-period trends; sometimes placebo tests),
• consequences if violated (DiD becomes biased).

4) Fixed Effects and Within-Variation: Removing Time-Invariant Confounders

For panel data:
[
Y_{it}=\beta_1 X_{it} + \alpha_i + u_{it}
]
where (\alpha_i) is unobserved unit-specific heterogeneity.

Fixed effects estimation removes (\alpha_i) by using within transformation (demeaning):

• You exploit variation in (X_{it}) over time within each unit.

Exam scoring:

• state what fixed effects does (controls for time-invariant unobserved factors),
• state what it does not do (does not solve time-varying endogeneity, like shocks correlated with (u_{it})).

5) Regression Discontinuity (RD): Local Causal Inference

RD requires an assignment rule based on a cutoff (c). Treatment indicator:
[
D_i = 1 \text{ if } R_i \ge c
]
Assumption: units close to cutoff are comparable, and any jump at cutoff is due to treatment.

In a strong exam answer:

• clarify that identification is local (near cutoff),
• mention bandwidth choice and why it matters,
• state that manipulation of running variable breaks the design.

6) Instrumental Variables vs DiD vs RD: Choosing the Right Tool

A common exam “design” question is: “Given a setting, propose an identification strategy and justify it.” A correct answer does not just name a method; it maps threats to assumptions.

6.1 Threat → Solution Mapping (Exam-Ready)

• Omitted time-invariant confounders → Fixed effects
• Endogenous regressor with external source of variation → IV/2SLS
• Policy shock affecting one group at one time → DiD
• Treatment assignment by cutoff → RD
• Noncompliance and random assignment → IV as LATE framework (if covered)

You must also show limitations:

• IV can suffer from weak instruments or invalid exclusion.
• DiD can fail if parallel trends fails.
• RD can fail if agents manipulate around cutoff.

Applied Regression Practice for Exams: How to Answer with Regression Output, Derivations, and Interpretation

This section turns the theory into exam technique: how to structure solutions when given regression output (even if simplified), how to show derivations compactly but correctly, and how to interpret results with economic meaning—particularly within South African university exam styles.

1) Interpreting Regression Output: The Core Checklist

When you receive output with coefficients, standard errors, t-statistics, p-values, and (R^2), your exam answer should follow a checklist:

1. State the estimated model in words and (if possible) in equation form.
2. Interpret key coefficients with correct units:
   • levels vs logs,
   • dummy variable interpretation (percentage point vs log difference).
3. Report statistical significance (p-values or t-tests) clearly.
4. Interpret economic significance:
   • Are effects large enough to matter economically?
5. Discuss signs and magnitude in line with theory (or justify deviations).
6. Check diagnostics if provided:
   • heteroskedasticity tests,
   • autocorrelation,
   • multicollinearity.
7. State what you can and cannot conclude causally.

2) Dummy Variables and Interactions: High-Risk Areas

Dummy variables are common in applied SA settings (e.g., gender, urban/rural, policy adoption, sector). Interpretation:

• If (Y) is in levels and (D) is a dummy:
  [
  \beta_D = \mathbb{E}[Y|D=1]-\mathbb{E}[Y|D=0] \quad \text{(conditional on other X)}
  ]
• If (Y) is in logs and (D) is a dummy:
  [
  \beta_D \approx 100 \times (e^{\beta_D}-1)%
  ]
  In small changes, (\beta_D) can be approximated by percent change.

Interactions:
[
Y = \beta_0 + \beta_1 X + \beta_2 D + \beta_3 (X\cdot D) + u
]
Interpretation:

• effect of (X) when (D=0) is (\beta_1),
• effect of (X) when (D=1) is (\beta_1+\beta_3).

Exams often test whether students correctly interpret marginal effects under interactions.

3) Writing Derivations Efficiently: What to Show, What to Skip

Not every econometrics question requires full derivations, but you must show enough steps to demonstrate correctness.

3.1 Showing OLS estimator

If asked to derive:
[
\hat{\beta}=(X'X)^{-1}X'Y
]
You can show:

• objective function (S(\beta)=(Y-X\beta)'(Y-X\beta)),
• take derivative w.r.t. (\beta),
• set to zero,
• solve.

But you do not need to expand every algebra line if it’s clear.

3.2 Showing variance under assumptions

If asked why heteroskedasticity affects standard errors, you should:

• state that
  [
  \text{Var}(\hat{\beta}\mid X) = (X'X)^{-1}X' \Omega X (X'X)^{-1}
  ]
  where (\Omega) is the covariance matrix of errors.
• Under homoskedasticity, (\Omega=\sigma^2 I), simplifying to the CLRM form.
• Under heteroskedasticity, (\Omega\neq \sigma^2 I), so conventional variance formula is wrong.

4) A Worked-Example Template (Exam Structure)

Even if the question provides numbers, you can use a template to structure your response.

4.1 Template: “Given regression output, interpret and diagnose”

Step 1: State model

• “We estimate (Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + u).”

Step 2: Interpret coefficient(s)

• For each coefficient, say sign, magnitude, and interpretation in units.

Step 3: Explain significance

• Use p-values or t-statistics from output.

Step 4: Diagnostics

• If heteroskedasticity test indicates rejection: “OLS remains unbiased under exogeneity but inference is invalid; use robust SE.”

Step 5: Causal statement

• “Causality requires (\mathbb{E}[u|X]=0); if there is omitted variable/endogeneity, OLS is biased. If instruments are provided, then consider IV.”

Step 6: Conclude

• Summarise findings and limitations.

This structure is reliable for SU-style exams because it matches how marks are commonly allocated: model, interpretation, inference, and assumptions.

5) Concrete Applied Scenarios Common in SA Economics/Econometrics Courses

To match the type of data used in SA departments, consider typical contexts:

5.1 Education and Wages with Ability Bias

• Dependent variable: log wages
• Regressors: education, experience, gender, region
• Risk: ability is omitted; OLS education coefficient upward biased

Exam question might ask:

• “Explain bias direction.”
• “Propose solution.”

Correct response:

• omitted ability positively correlated with education and wages,
• thus OLS likely overstates causal return to education,
• propose IV with instrument affecting education (e.g., proximity to schools/colleges) or DiD if policy reforms exist.

5.2 Government Spending and Unemployment with Reverse Causality

• Dependent variable: unemployment rate change
• Regressor: change in government spending
• Risk: government spending increases when unemployment worsens

OLS could be biased (negative correlation between spending and unemployment shock). Solution:

• IV with instruments for spending (e.g., revenue shocks) or DiD if spending was rule-based over time.

6) How to Answer “Discuss” Questions for Maximum Marks

Some exam questions are descriptive: “Discuss heteroskedasticity and its consequences.” High marks require a complete causal chain from violation → impact → solution.

A strong discuss answer structure:

1. Define the issue (what is heteroskedasticity).
2. Explain its consequences for estimators vs inference.
3. Give diagnostic intuition or test name.
4. Provide correction methods:
   • robust standard errors,
   • transform variables,
   • GLS/WLS if structure is known.
5. Mention limitations:
   • robust SE does not fix endogeneity.

The same structure can be applied to autocorrelation, multicollinearity, omitted variable bias, or endogeneity.

Exam Strategy: Study Plan, Practice Regimen, and Marking-Rubric Thinking for Ekonomie 388

Preparation strategies determine whether you can execute under exam pressure. SU econometrics exams tend to reward not just knowledge but organisation: clear steps, correct formulas, and careful interpretation. This final section provides an exam-ready regimen and a “rubric mindset” to ensure you consistently score.

1) Typical Exam Components and How to Prepare for Each

Econometrics exams frequently include:

1. Theory questions (state assumptions, explain properties).
2. Short answer calculations (derive a test statistic, interpret log coefficients).
3. Applied regression interpretation (interpret output, comment on diagnostics).
4. Method choice/design (suggest IV/DiD/RD, justify assumptions).
5. Diagnostic and correction (what to do if heteroskedasticity/serial correlation detected).

A good preparation method is to practise each component separately, then in mixed sets.

2) Weekly Practice Schedule (Repeatable and Sustainable)

A practical schedule for a full semester (or a final review period) can be:

• Day 1 (Theory): assumptions, unbiasedness/consistency, CLRM properties.
• Day 2 (Diagnostics): heteroskedasticity tests, serial correlation logic, functional form.
• Day 3 (Applied interpretation): log vs linear, dummy variables, interactions.
• Day 4 (IV & identification): relevance/exogeneity/exclusion, weak instrument reasoning, overidentification logic.
• Day 5 (Design questions): DiD parallel trends, fixed effects within logic, RD local comparisons.
• Day 6 (Mixed exam set): timed practice.
• Day 7 (Review): rewrite best answers, correct mistakes, build a personal formula sheet.

You should keep a “mistake journal”:

• what you misunderstood,
• what the correct reasoning is,
• how to avoid repeating it.

3) Building a Personal Formula Sheet That Matches Exam Needs

You do not need infinite formulas; you need the ones that let you move fast. Your personal sheet should include:

• OLS estimator formula
• standard t and F test formulas (or at least the logic)
• IV two-stage setup
• residual definition
• core diagnostic interpretations:
  • heteroskedasticity → robust SE
  • serial correlation → Newey–West / BG tests
• log interpretation rules
• dummy and interaction marginal effects

4) Timed Writing: Train the Ability to Produce a Full Mark Answer

Many students know the theory but lose marks by writing incomplete solutions. Train your writing:

• For a “discuss” question, always follow the 5-step structure:
  1. definition, 2) consequences, 3) tests/diagnostics, 4) solutions, 5) limitations.
• For output interpretation:
  1. model statement, 2) key coefficient interpretations, 3) significance, 4) diagnostics, 5) causal caution.

Time guidance:

• Theory short answers: 5–10 minutes each
• Output interpretation: 12–18 minutes each
• Design/identification questions: 20–25 minutes each
• Diagnostics/corrections: 12–20 minutes each

5) A High-Scoring Answer Checklist for SU-Style Marking

Before submitting, quickly check:

• Did you state or clearly imply the model form?
• Did you connect assumptions to inference results?
• Did you interpret coefficients with correct units and transformations?
• Did you avoid common traps (e.g., “heteroskedasticity causes bias” — incorrect; it mainly affects standard errors)?
• Did you mention limitations of causal claims?
• Did you provide a coherent conclusion?

Even short questions can earn full marks if they hit these points.

6) Mock Exam Practice Scenarios (Use as Drills)

Use these as drills. Write full paragraphs/solutions, not bullet points only.

Scenario A: Heteroskedasticity detected

Prompt: “You estimate a wage regression. Breusch–Pagan rejects homoskedasticity. Interpret the results and advise.”

Expected elements:

• identify violation,
• clarify OLS coefficient unbiasedness under exogeneity,
• emphasise that standard errors are wrong,
• advise robust SE and/or re-specification,
• mention you still cannot infer causality without exogeneity.

Scenario B: IV setup with a questionable instrument

Prompt: “Education is endogenous. You propose distance to a college as an instrument. Discuss validity and relevance.”

Expected elements:

• relevance argument: distance affects education attainment,
• validity/exclusion argument: distance affects wages only through education,
• threats: local labour market and commuting costs,
• mention weak instrument risks and how to check first stage.

Scenario C: DiD with doubtful parallel trends

Prompt: “A reform affects treated municipalities. You estimate DiD. Pre-trends are not parallel.”

Expected elements:

• explain parallel trends,
• state that violation undermines identification,
• propose robustness: placebo tests, event study graphs,
• alternative methods: fixed effects, IV if suitable.

Concluding Study Message (Without “Preface” Style)

Econometrics success in Ekonomie 388 depends on disciplined reasoning: correct assumptions, correct diagnostic interpretation, correct method choice, and clear coefficient interpretation. If you can consistently connect each econometric concept to what it changes in estimation and inference—and then write it in exam form—you will be equipped for both computation-heavy and theory-heavy questions.