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Based on what the book "Microeconometrics using Stata" covers, below is a topologically sorted reorganization where:

  • earlier items = prerequisites, reusable primitives, or broadly independent
  • later items = dependent, composite, or specialized capabilities
  • each layer builds cleanly on previous ones

🧠 Topologically Sorted Capability Graph (Microeconometrics System)

Layer 0 — Core Infrastructure (must exist first)

These are non-negotiable primitives everything else depends on.

Data & Execution Engine

  • Data frame abstraction (columns, labels, missing values)
  • Type system (numeric, categorical, panel indexing)
  • Vectorized operations
  • Group-by / aggregation
  • Merge / reshape (wide ↔ long)

Reproducibility & Workflow

  • Script execution (do-files equivalent)
  • Logging + output capture
  • Random number seeding

Programming Primitives

  • Macros / variables
  • Control flow (loops, conditionals)
  • Functions / modular code

Layer 1 — Mathematical & Statistical Primitives

These enable any estimator.

Linear Algebra Core

  • Matrix operations (multiply, invert, decompose)
  • Sparse support (optional but valuable)

Probability & Statistics

  • Distributions (normal, binomial, Poisson, etc.)
  • Sampling and random number generation
  • Moments (mean, variance, covariance)

Optimization Engine

  • Objective function abstraction
  • Gradient / Hessian support
  • Solvers (Newton, quasi-Newton, BFGS)

Layer 2 — Simulation & Resampling

Independent of specific models, widely reused.

  • Monte Carlo simulation framework
  • Bootstrap (nonparametric, parametric)
  • Resampling utilities
  • Performance evaluation tools

Layer 3 — Baseline Estimation Frameworks

These define the general estimation paradigms.

Least Squares Framework

  • Ordinary Least Squares (OLS)
  • Weighted least squares
  • Residual computation + diagnostics hooks

Maximum Likelihood Framework

  • Log-likelihood specification
  • Generic MLE solver interface
  • Score and information matrix

Method of Moments / GMM

  • Moment condition abstraction
  • Weighting matrix estimation
  • Two-step GMM

Layer 4 — Core Linear Models

Built directly on Layer 3.

Linear Regression

  • OLS estimation + inference
  • Prediction and fitted values

Robust Inference

  • Heteroskedasticity-robust SEs
  • Cluster-robust SEs

Generalized Least Squares

  • Feasible GLS
  • Variance structure modeling

Diagnostics

  • Residual analysis
  • Specification tests
  • Multicollinearity detection

Layer 5 — Endogeneity & Identification Tools

Depend on linear model + inference infrastructure.

Instrumental Variables

  • Two-stage least squares (2SLS)
  • Weak instrument diagnostics
  • Overidentification tests

Control Function Methods

  • Residual inclusion approaches
  • Endogeneity correction workflows

Layer 6 — Panel Data Foundations

Requires linear models + IV + data structure support.

Panel Data Handling

  • Indexing (entity, time)
  • Within/between transformations

Panel Estimators

  • Fixed effects (FE)
  • Random effects (RE)
  • Hausman test

Layer 7 — Nonlinear Estimation Core

Requires MLE + optimization.

Binary Choice Models

  • Logit / probit estimation
  • Marginal effects

General Nonlinear Models

  • Nonlinear regression
  • Prediction and interpretation tools

Layer 8 — Limited Dependent Variable Models

Built on nonlinear estimation.

  • Tobit (censoring)
  • Truncated regression
  • Sample selection (Heckman)

Layer 9 — Discrete Choice Systems

Depend on nonlinear + likelihood framework.

  • Multinomial logit
  • Conditional logit
  • Nested logit
  • IIA diagnostics

Layer 10 — Count Data Models

Parallel branch from nonlinear MLE.

  • Poisson regression
  • Negative binomial
  • Overdispersion handling

Layer 11 — Mixture & Zero-Inflated Models

Depend on count + latent structure + MLE.

  • Zero-inflated models
  • Hurdle models
  • Finite mixture models
  • EM algorithm

Layer 12 — Duration / Survival Models

Require likelihood + specialized distributions.

  • Hazard and survival functions
  • Parametric survival models
  • Cox proportional hazards

Layer 13 — Dynamic & Advanced Panel Models

Depend on panel + GMM + nonlinear.

  • Dynamic panel (Arellano–Bond)
  • GMM for panels
  • Endogenous regressors in panels

Layer 14 — Nonlinear Panel Models

Depend on nonlinear + panel structure.

  • Fixed-effects logit
  • Random-effects nonlinear models
  • Incidental parameters problem

Layer 15 — Flexible / Distributional Methods

More independent but require core estimation.

  • Quantile regression
  • Robust distributional analysis

Layer 16 — Semiparametric & Nonparametric Methods

Require strong statistical primitives.

  • Kernel regression
  • Local polynomial regression
  • Bandwidth selection
  • Partially linear models

Layer 17 — Causal Inference Framework

Cross-cutting but depends on many earlier tools.

Treatment Effects

  • Potential outcomes framework
  • ATE / ATT estimation

Matching & Weighting

  • Propensity scores
  • Matching estimators

Endogenous Treatment

  • IV treatment effects
  • Selection correction

Layer 18 — Modern / Extended Capabilities

Built last due to broad dependencies.

Machine Learning Integration

  • Lasso / Ridge
  • Cross-validation
  • Post-selection inference

Bayesian Methods

  • Prior/posterior computation
  • MCMC (Gibbs, Metropolis-Hastings)

Spatial Models

  • Spatial lag / error models
  • Spatial weight matrices

🧩 Key Design Insights

1. Separate Estimation Engines from Models

  • OLS, MLE, GMM = reusable cores
  • Everything else = thin wrappers

2. Treat Panel, Nonlinear, and Causal as Orthogonal Axes

  • Panel ≠ nonlinear ≠ causal

  • Your architecture should allow combinations:

  • nonlinear + panel

  • panel + IV
  • nonlinear + causal

3. Build Around Composable Primitives

  • likelihood()
  • moments()
  • transform(panel)
  • simulate()