The m+e+c methodological signature

 

The m+e+c method keeps mathematics, economics, and computation close enough that each can check the other two. A mathematical object is not left as a formal construction: it is interpreted inside an economic model and implemented explicitly. Conversely, code is not treated as a black box: its variables, dimensions, constraints, and numerical output remain traceable to the mathematics and to the economic question.

This proximity is the project’s methodological signature. It makes the notebooks useful not only as demonstrations, but as research instruments whose arguments can be inspected, reproduced, and extended.

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Mathematics, economics, and computation

Each central object is developed in three registers. The mathematics identifies the structure of the problem; the economics explains what the objects and restrictions mean; and the implementation makes every step operational. None of the three is an appendix to the others.

Optimization and duality

Whenever possible, a problem is organized around an explicit optimization formulation. Primal and dual problems are written side by side, with feasibility, optimality, and complementary slackness stated clearly. This gives a common language for linear programming, optimal transport, matching, discrete choice, dynamic programming, and related models.

Economic interpretation of multipliers

Multipliers are treated as economic objects rather than merely algebraic devices. Their units, signs, and normalization are made explicit, and they are interpreted as prices, shadow values, marginal welfare effects, or equilibrium adjustments whenever the model permits. Comparative statics should be readable directly from this interpretation.

Matrix-first formulations

Indexed equations establish meaning; vector and matrix formulations establish structure. The passage from one to the other is shown explicitly, including dimensions and stacking conventions. The resulting matrix representation should align closely with the implementation and make sparsity, separability, and computational scale visible.

Classical problems and data

New techniques are anchored in canonical problems, models, and datasets. Classical examples make conventions comparable across notebooks and provide benchmarks against which an implementation can be checked. The point is not nostalgia, but cumulative understanding: a familiar problem lets the reader see exactly what a new method changes.

Verification

Numerical output is part of the argument. Implementations report the checks appropriate to the problem—constraint residuals, objective values, primal–dual gaps, first-order conditions, or agreement with a small instance that can be solved independently. From-scratch algorithms are used where they clarify the mechanism; library routines are introduced with their mathematical inputs and outputs exposed.

Interlocking notebooks

The notebooks form a connected body of work. Objects introduced in one series reappear in another, notation is kept stable where possible, and cross-links make dependencies visible. A reader should be able to move from a simple formulation to a more advanced application without relearning the project’s basic language.

Economics as the conclusion

The endpoint is an economic conclusion, not merely a successful computation. A notebook closes the loop by returning to identification, equilibrium, welfare, comparative statics, institutional interpretation, or the empirical question that motivated the model.

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Mathematical notation

Indices, sets, dimensions, and domains are declared before use. Scalars, vectors, and matrices are visually distinguishable; objective functions and constraint maps retain consistent names across primal and dual formulations. Normalizations and sign conventions are stated where they first matter.

 

Code names mirror the mathematical objects closely enough to be recognized. Shapes and stacking orders are documented, intermediate quantities remain inspectable, and compact abstractions are introduced only after the underlying operation has been shown.

 

Vectorization begins from indexed relations. The stacking order is specified before a vectorized expression is used, and Kronecker products are accompanied by their dimensions and role in the assembled system. Small cases are constructed explicitly to verify that the vectorized implementation matches the intended equations.

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A finished m+e+c notebook should allow the reader to reconstruct the mathematical argument, understand its economic content, reproduce the numerical result, and modify the implementation without losing the link among the three. That is the standard by which the method is meant to be judged.