Vadim Marmer

Vadim Marmer

Professor of Economics, UBC

Session Notes — Econ 326

Session Notes — Econ 326

2026-03-16

File changes:

  • Created 326_14_dummy.qmd — new lecture converted from LaTeX 326_15_dummy.tex

Conversion details (LaTeX lecture 15 → QMD lecture 14):

  • Title: “Lecture 14: Dummy variables”
  • 18 slides covering: interval/ordinal/categorical variables, dummy variable definitions, single dummy independent variable, intercept shift, log dependent variable, changing the base group, dummy variable trap, slope shift and interactions, multiple categories
  • Slide 3: Female/Male dummy definitions replaced with Married/Unmarried per plan
  • Slide 4: Textbook table image (tab7-1.tif) replaced with R code using wooldridge::wage1
  • Slide 5: Added tenure definition (“number of years at current firm”)
  • Slide 7: Textbook figure (fig7-1.tif) replaced with R-generated intercept shift plot using base R
  • Slide 11: Added binary gender clarification note
  • Slides 12-13: Stata noconstant syntax replaced with R lm(Y ~ X + 0) / lm(Y ~ X - 1)
  • Slide 15: Textbook figure (fig7-2.tif) replaced with R-generated slope shift plot using base R
  • Slides 19-21 (structural breaks / Chow test): dropped entirely per plan
  • Standard conversion applied throughout: TCIMACRO stripped, color markup → bold, eqnarray* → aligned, etc.
  • Estimated equations formatted with \underset{(se)}{coeff} pattern

Post-conversion refinements:

  • Conditioning notation: replaced 4 instances of E\left(...\right) with \E{...} macro for consistency with other lectures
  • Variable names: wrapped all multi-letter variable names (Wage, Female, Male, Educ, Exper, Tenure, Married, Unmarried, Education, Gender) in \text{...} for upright (roman) rendering
  • Missing subscripts: added _i to log model equation (line 234) and Education definition (line 416)
  • Dummy variable trap slide: changed multicollinearity explanation to “In this dataset, Female+Male=1”
  • User manually changed intercept shift superscripts from ^F to ^W (Women), merged intercept shift heading with figure slide, and simplified dummy variable trap text
  • Slope shift plot: redesigned multiple times; final version uses stylized coefficients (β₀=0.8, δ₀=−0.3, β₁=0.10, δ₁=−0.04), dashed guide lines from y-axis intercepts to labels, “Men”/”Women” line labels, and slope annotation labels offset from lines
  • Example slide plot (with actual estimated coefficients) was added then dropped per user request (slope difference too small to see)

Persistent memory updates:

  • Added convention: conditioning expectations must use \E{...} macro
  • Added convention: multi-letter variable names in math must use \text{...} for upright rendering

Verification:

  • All 3 output formats render successfully, 0 KaTeX errors
  • 18 section tags (1 title + 17 content slides)
  • No “Chow” or “structural break” content remains

2026-03-12

File changes:

  • Created 326_12_mreg_testing.qmd — new lecture converted from LaTeX 326_13_mreg_testing.tex

Conversion details (LaTeX lecture 13 → QMD lecture 12):

  • Title: “Lecture 12: Hypothesis testing in multiple regression” (dropped “Part 1”)
  • 15 slides covering: classical normal linear model assumptions, single coefficient tests (two-sided only), linear combination tests, CRS test example with manual calculation, reparameterization approach, and linearHypothesis() in R
  • All Stata code replaced with R equivalents: lm(), summary(), vcov(), qt(), car::linearHypothesis()
  • Simulated data generated with set.seed(123) for reproducibility
  • New slide added: “Testing with linearHypothesis() in R” showing car::linearHypothesis() for both CRS and equal-effects tests
  • Cross-references updated: “Lecture 12” → “Lecture 11”, “Lecture 11” → “Lecture 10”
  • Excluded: entire one-sided alternatives slide (LaTeX lines 367–413) and one-sided bullet (lines 591–593)
  • Spelling fixed: “multicolinearity” → “multicollinearity”
  • Grammar fixed: “Let … are some constants” → “Let … be some constants”
  • Macros used throughout: \E, \Var, \Cov, \Vhat, \se
  • Conditioning on \mathbf{X} applied per project convention

Proofreading (proofread-326 agent):

  • Grammar: “satisfies that conditional on” → fronted conditional clause
  • Margin overflow: variance formula split into align*; inline estimated variance moved to display math
  • RevealJS reveal order: 16 code blocks and 2 display math blocks indented under parent bullets

Verification:

  • All 3 output formats render successfully, 0 KaTeX errors
  • 16 section tags (1 title + 15 content slides)
  • No one-sided test material remains

2026-03-05

File changes:

  • Updated 326_10_r2.qmd — R example, reveal order, proofreading
  • Updated 326_11_mreg_properties.qmd — reveal order, proofreading

R example (326_10_r2.qmd):

  • Replaced fabricated numeric example with real data: lm(price ~ sqrft + bdrms + lotsize, data = hprice1) from wooldridge package (n=88, k=3, R²=0.6724, adj R²=0.6607, s=59.83)
  • Shows R code (library(wooldridge), lm(), summary()) and relevant summary() output
  • Second slide recovers SSR, SST, SSE from s and R²

RevealJS reveal-order fixes (verified by 3 agents: opus, codex, gemini):

  • Lecture 11, “Proof of unbiasedness” slide (line 123): converted 3 standalone blocks to bulleted steps for incremental reveal
  • Lecture 11, “Derivation of conditional variance” slide (line 190): indented aligned equation under its introducing bullet

Proofreading fixes (3-agent consensus: opus, codex, gemini):

  • Lecture 11: replaced 7 instances of “regress against” with “regress on”
  • Lecture 10, line 159: added articles before $R^2$ (“the $R^2$ from…”)
  • Lecture 11, line 271: added serial comma, reordered to “$k-1$ additional regressors”
  • Lecture 11, line 345: removed spurious comma before restrictive “if”

Deployment:

  • All 3 output formats render successfully, 0 KaTeX errors
  • Pushed to GitHub, deployment verified

2026-03-04

File changes:

  • Created 326_10_r2.qmd — Lecture 10: R-squared (converted from LaTeX 326_11_r2.tex)
  • Created 326_11_mreg_properties.qmd — Lecture 11: Properties of OLS in multiple regression (converted from LaTeX 326_12_mreg_properties.tex)
  • Updated /_teaching/2026-01-Econ-326.md — added lectures 10 and 11

New content (326_10_r2.qmd, ~300 lines):

  • 15 slides: Fitted values, Sum-of-Squares (SST/SSE/SSR), Proof of SST=SSE+SSR (2 slides), R², R² non-decreasing property, Proof (2 slides), Adjusted R², Estimation of σ², Unbiasedness of s², Stata example (4 slides)
  • Stata output recreated as code block with n=64, k=3, R²=0.5923, adj R²=0.5719

New content (326_11_mreg_properties.qmd, ~370 lines):

  • 16 slides: Multiple regression and OLS (2 slides), OLS estimators are linear, Unbiasedness, Proof of unbiasedness (2 slides), Conditional variance, Derivation of conditional variance, Conditional covariance (2 slides), Normality, Inclusion of irrelevant regressors (2 slides), Proof of variance inequality, Variance and number of regressors, Estimation of variances and covariances
  • Defined \mathbf{X} = \{(X_{1,i}, X_{2,i}, \ldots, X_{k,i}): i = 1, \ldots, n\} for multiple regression
  • Cross-reference to “Lecture 9” (partitioned regression) updated from LaTeX “Lecture 10”

Key results:

  • All conditioning uses \E{\cdot \mid \mathbf{X}}, \Var{\cdot \mid \mathbf{X}}, \Cov{\cdot \mid \mathbf{X}} macros throughout
  • Fixed LaTeX typos: “In n $Y_i$” → “In $Y_i$” (line 1371 of source), summation index in $w_{j,i}$ denominator corrected to use $l$ instead of $i$
  • Proofreading: grammar fixes (“i.e.” → “i.e.,”, removed filler “that”), long equations broken for RevealJS margin overflow, slide titles shortened
  • Reverted proofreader’s \begin{align*} conversion back to $$\begin{aligned}$$ for consistency with all other lectures
  • Both lectures: 0 KaTeX errors, all 3 output formats render successfully
  • Proofreading verified all mathematical derivations correct

Cross-references:

  • LaTeX 11 → QMD 10 (R²), LaTeX 12 → QMD 11 (properties)
  • Course page updated with lectures 10–11

2026-02-26

File changes:

  • Created /Users/vmarmer/GitHub/vadimmarmer.github.io/files/Econ_326/326_09_mreg.qmd — Lecture 9: Multiple regression (converted from LaTeX 326_10_mreg.tex)

New content (326_09_mreg.qmd):

  • 17 sections covering: motivation for multiple regression, omitted variable bias (2 slides), multiple linear regression model, interpretation of coefficients, changing multiple regressors simultaneously, modelling nonlinear effects, OLS estimation, normal equations (2 slides), partitioned regression, proof of partitioned regression result (5 slides), “partialling out”
  • YAML frontmatter for 3-format output (HTML, PDF, RevealJS)
  • Hidden macro div with \E, \Var, \Cov, \Vhat, \se

Key results:

  • Fixed known typo from LaTeX source line 1296: $X_{4}$ → $X_{k}$ in step 3 of the partitioned regression proof
  • Math review verified all derivations correct (omitted variable bias, OLS FOCs, normal equations, partitioned regression proof steps 1-4)
  • Flagged: line 143 equation $\Delta Y = \beta_0 + \beta_1 \Delta X_1 + \beta_2 X_2 + \ldots$ inherited from original LaTeX source is mathematically incorrect as a “change” equation (should be $\Delta Y = \beta_1 \Delta X_1$)
  • 18 prose edits applied (unanimous/majority agreement from 3-agent polishing): “regress against” → “regress on” throughout, missing articles, “and etc.” → “etc.”, “squared errors function” → “sum of squared errors”, commas before nonrestrictive “which”, and other grammar fixes
  • Adopted \E{\cdot \mid \mathbf{X}} notation throughout: converted bare E\left(...\right) to \E{...} macro, changed assumption to \E{U_i \mid \mathbf{X}} = 0, added \mathbf{X} definition in OVB slide
  • Removed $ wrapping from \gdef macros in hidden div (caused visible $ in PDF output)
  • Fixed reveal order on 5 slides (Partitioned regression, Proof slides, “Partialling out”): indented standalone text/equations under bullet points for proper incremental reveal
  • Added lecture 9 entry to course page (_teaching/2026-01-Econ-326.md)
  • All 3 output formats render successfully, 0 KaTeX errors

Cross-references:

  • LaTeX source: /Users/vmarmer/Documents/teaching/Econ 326/326_10_mreg.tex
  • YAML template: 326_08_htesting.qmd
  • Numbering: LaTeX lecture 10 → QMD lecture 09 (shift by 1 for N ≥ 10)

2026-02-15

File changes:

  • Created /Users/vmarmer/Documents/teaching/Econ 326/326_ps_05.tex — Assignment 5 (2 pages)
  • Updated /Users/vmarmer/Documents/teaching/Econ 326/TODO.md — all items marked completed

New content (326_ps_05.tex):

  • Q1: Intercept-only model Y_i = beta_0 + U_i — interpret beta_0, derive E[sum hat_U_i^2] = (n-1)sigma^2, propose unbiased estimator of sigma^2
  • Q2: Derive Var(beta_1_WLSX) under classical assumptions for simple regression with arbitrary positive weights w_i(X_i); includes hint showing WLS estimator formula with weighted means
  • Q3: R output (rent ~ income, n=26) with missing entries A-D (SE, CI bounds); interpret 95% CI; construct 90% CI and compare widths
  • Q4: Propose one-sided CI (-inf, U] for beta_1 using t critical values; prove coverage = 1-alpha under normality

Config changes:

  • Added “Session notes” and “TODO list” sections to project CLAUDE.md (chezmoi source)
  • Added user preferences (session notes, TODO tracking) to project MEMORY.md