Carries The List In Full, And Lessons 5, 6 And 7 Which Are The Ones Being Consulted When A Student Is Working On

1. Core Concept Overview & Intuition

The topic concerns the editorial architecture of a modular econometrics text: which lessons reproduce the module's five-item reference list in full, and which lessons point back to an earlier section instead. The approved course context states that Lesson 1 carries the list in full, and that Lessons 5, 6 and 7 — the lessons consulted when a student is working on estimation — also carry it in full as the module prints it. Lessons 2, 3 and 4, whose lists are identical to the one already given, do not reprint the list; the edition instead points back to the section that carries the full list with ISBNs.

The intuition is one of deliberate redundancy placed where it is needed. A reference list is a working tool: when a student is mid-way through an estimation procedure and needs to consult a source, the list should be immediately at hand rather than requiring a backward search through earlier pages. The module therefore duplicates the list at the front of the estimation block (Lesson 1) and at each of the three estimation lessons (Lessons 5, 6 and 7), while suppressing the duplicate in the intervening theoretical lessons where the list adds nothing new.

A second, equally important structural idea is that the lesson prose is the module's own wording and was not altered. The editorial work is confined to restoring corrupted symbol systems, renumbering misnumbered items, and repairing detached variable keys — never to rewriting the econometric content. This distinction between content (untouched) and presentation (restored) governs how every discrepancy in the module should be read.

The estimation lessons themselves form a coherent methodological sequence. Lesson 5 treats Indirect Least Squares (ILS) for exactly identified systems; Lesson 6 treats Two-Stage Least Squares (2SLS); Lesson 7 treats the Instrumental Variable (IV) method. Because these three lessons are the ones a student consults while working on estimation, they are precisely the lessons that must be self-contained — hence the full reference list at each.

2. Mathematical Formalization & Core Definitions

> Definition (Reference-list placement rule). The module prints the same five-item reference list at the end of every lesson. Where a lesson's list is identical to the one already given, the edition points back to the section carrying the full list with ISBNs rather than reprinting the same page. Lesson 1 carries the list in full; Lessons 5, 6 and 7 carry it in full as the module prints it.

> Definition (Estimation lessons). Lessons 5, 6 and 7 are the lessons consulted when a student is working on estimation. Lesson 5 develops Indirect Least Squares, Lesson 6 develops Two-Stage Least Squares, and Lesson 7 develops the Instrumental Variable method.

> Definition (Structural and reduced forms). A structural equation expresses an endogenous variable in terms of other endogenous variables, predetermined variables and a disturbance. The reduced form expresses each endogenous variable solely in terms of predetermined variables and disturbances. Estimation of a structural equation proceeds through its reduced form.

The ILS procedure, as carried in Lesson 5, is organised as a sequence of steps. The first stage establishes identification of the structural equation; the second derives the reduced form; the third estimates the reduced-form parameters; the fourth solves back from the estimated reduced-form coefficients to the structural coefficients. The essential algebraic relation is that the reduced-form coefficients are functions of the structural coefficients, so that solving the reduced-form system for the structural parameters recovers the structural estimates.

For a two-equation system the reduced form may be written with coefficients $\pi_{ij}$, where $\pi_{ij}$ denotes the coefficient on the $j$-th predetermined variable in the reduced-form equation for the $i$-th endogenous variable. The structural coefficients $\beta$ and $\gamma$ are then recovered from the $\pi$'s by division and substitution, as in the worked solutions of Lesson 5.

The 2SLS procedure of Lesson 6 is organised as five steps: (1) obtain the reduced form of the system; (2) estimate the reduced-form equations by ordinary least squares; (3) form the fitted values of the endogenous regressors; (4) substitute the fitted values into the structural equation of interest; (5) apply ordinary least squares to the resulting equation. The assumptions of the 2SLS method are numbered 1 to 5. Assumption 2 carries sub-items (i)–(vi). Assumption 3 carries sub-items (i)–(vi) for the reduced form. Assumptions 4 and 5 are stated as single items, so the numbering of the 2SLS assumptions runs 1 to 5 with the sub-items nested inside Assumptions 2 and 3.

The IV method of Lesson 7 rests on five assumptions numbered 1 to 5. In the module's printing, Assumption 3 of the IV method carries four sub-items and is then followed by the labels "v) ASSUMPTION 4" and "vi) ASSUMPTION 5"; the edition presents the five assumptions numbered 1 to 5, so that the fourth and fifth assumptions are read as Assumptions 4 and 5 rather than as further sub-items of Assumption 3. The estimator is formed by replacing the endogenous regressor with an instrument that is correlated with it but uncorrelated with the disturbance. In the module's notation the IV estimator of the slope coefficient takes the ratio form

$$
\hat{\beta}{2}^{IV}=\frac{\sum} z_{i} y_{i}}{\sum_{i} z_{i} x_{i}
$$

where $y_{i}$ is the dependent variable, $x_{i}$ is the endogenous regressor and $z_{i}$ is the instrument, each measured in deviation form.