ETF2100 Chap.3 OLS Assumptions, Properties and Causal Boundaries

OLS Assumptions, Properties and Causal Boundaries

Fix scale, actor and purpose

The overview treats the error term as fundamental rather than as leftover noise. In its training example, ability, education quality and family background can affect wages without being explicitly measured. A ceteris-paribus coefficient asks how the conditional mean changes when one regressor changes while the other represented regressors are fixed. That interpretation is algebraic.

To elevate it to a causal effect, the relevant unobserved determinants must not move systematically with the regressor after the controls and design are considered. Linearity alone does not deliver that separation.

The chapter objective is to connect an OLS interpretation to the data-generating assumptions that make it credible. Begin by defining error term at the scale used in the question.

Record whom or what error term describes, its period or operating state, and evidence that distinguishes error term from omitted-variable bias. Without that discipline, error term can quietly change meaning between the opening claim and the final recommendation.

Next, make ceteris paribus do explanatory work.

State the direction of ceteris paribus, the process it carries and the condition that keeps its link with error term credible. A useful ceteris paribus note does not merely say that the relationship matters.

It identifies which observation establishes error term, which observation tests ceteris paribus and which value of omitted-variable bias would force a different account.

Use omitted-variable bias as the chapter's discriminating lens. Compare at least two feasible cases and decide whether omitted-variable bias strengthens, narrows or reverses the preferred result.

If it cannot alter any conclusion, it is functioning as decoration. Attach the comparison to the same unit, population or system boundary used for error term and ceteris paribus.

Connect evidence to the outcome

A complete application of error term has an actor, evidence, relationship and decision.

The actor has responsibility; evidence identifies the error term state; ceteris paribus explains why action may work; and omitted-variable bias supplies a review signal. This error term–ceteris paribus–omitted-variable bias structure makes ETF2100 reasoning auditable without turning one definition into a universal rule.

A regression of wages on participation in a voluntary training program finds a positive coefficient.

Write the causal threat before celebrating the estimate: employees who volunteer may also have stronger motivation, and motivation belongs in the error term if unmeasured. If motivation raises wages and raises participation, the training coefficient combines the program relationship with selection. Adding experience can reduce one source of confounding but does not guarantee that the remaining error is unrelated to training.

Evidence from assignment rules, timing, comparable groups or a credible design matters more than a longer regressor list.

Now change one condition: Now suppose training places were randomly allocated among eligible applicants. Identify which selection path is weakened and which problems, such as attrition or non-compliance, remain. Predict the direction of the result before consulting an example.

Explain whether the change affects the definition of error term, the mechanism carried by ceteris paribus, the comparison represented by omitted-variable bias, or only the confidence attached to the conclusion.

Keep the controlling limit visible: Calling a coefficient partial does not make it causal; it only states which included variables are held fixed in the equation.

This omitted-variable bias limit is not ceremonial.

It specifies the observation, design feature or operating condition that separates a careful use of error term from a claim that outruns ceteris paribus evidence.

Check what the claim cannot carry

For retrieval, close the explanation and reconstruct error term, ceteris paribus and omitted-variable bias in three different sentences: a definition, a relationship and a counter-case.

Then attach one concrete ETF2100 example to each. Reopen the omitted-variable bias material only to correct the first missing error term–ceteris paribus link; copying everything hides which analytical role failed.

For written or oral assessment, put the omitted-variable bias conclusion after the reasoning.

Start with the requested decision, use error term to establish the object and trace ceteris paribus before allowing omitted-variable bias to challenge the preferred position. Report omitted-variable bias at the scale earned by error term evidence, preserving uncertainty and implementation constraints around ceteris paribus.

Create an error log specific to error term.

Record the triggering fact, mistaken error term inference, repaired relationship involving ceteris paribus, and evidence from omitted-variable bias that distinguishes the two. Repeat the repaired ceteris paribus move on a different omitted-variable bias case so feedback becomes a transferable diagnostic for error term.

A strong final check asks four questions. Is error term defined consistently?

Does ceteris paribus explain a process rather than repeat the outcome? Can omitted-variable bias genuinely contradict the preferred answer? Does the last sentence remain inside this limit: Calling a coefficient partial does not make it causal; it only states which included variables are held fixed in the equation.

If any error term–ceteris paribus–omitted-variable bias answer is no, revise that defective relationship rather than adding more description.

What this chapter covers

• 01

  error term

• 02

  ceteris paribus

• 03

  omitted-variable bias

• 04

  connect an OLS interpretation to the data-generating assumptions that make it credible

• 05

  Calling a coefficient partial does not make it causal; it only states which included variables are held fixed in the equation.

Changed error term case

Key terms

error term

The collection of unobserved factors affecting the response but omitted from the stated equation.

ceteris paribus

A comparison that changes one factor while holding the other relevant factors fixed.

omitted-variable bias

Systematic distortion that can arise when an excluded cause of the response is related to an included regressor.

OLS Assumptions, Properties and Causal Boundaries FAQ

Exam move

Retrieve error term, ceteris paribus and omitted-variable bias; explain their relationship; apply them to the changed case; then test the result against the stated boundary.

Working through OLS Assumptions, Properties and Causal Boundaries in ETF2100? Sia is AskSia’s AI Econometrics tutor — ask any ETF2100 OLS Assumptions, Properties and Causal Boundaries question and get a clear, step-by-step explanation grounded in how ETF2100 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.