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Econ-269 · economics · Economics

Contracting frictions in global sourcing

LLM status Open unverified

Statement

Original subject group: Trade, globalization and geoeconomics

Audit classification: Background; proposed extension. The NBER primary indexed abstract and metadata verify this real 2025 paper. Full text was inaccessible during this audit, and no exact open passage was verified. Its conditional quantitative question should not be relabeled an unresolved general theorem.

Definitions and precise research target

Fix heterogeneous firms choosing domestic or foreign suppliers and whether to own production stages. Contracts are incomplete in a specified sense: a declared subset of investment or quality actions cannot be enforced by courts. Let $\kappa_{ab}$ measure enforcement costs or noncontractible exposure for transactions between jurisdictions $a,b$. Firms choose organization, sourcing and relationship-specific investment optimally, with wages and prices clearing. Let $W(\kappa)$ be discounted household welfare and $Q(\kappa)$ trade volumes. The task is to identify losses from these frictions relative to a defined counterfactual $\kappa=0$: \[\Delta W=W(0)-W(\kappa),\qquad\Delta Q=Q(0)-Q(\kappa).\] Specify which institutional change implements friction removal and which technologies, preferences and trade policies remain fixed. Separate enforcement frictions from search, transport and financing costs using a stated exclusion or structural restriction. Establish whether organizational choices and sourcing patterns uniquely identify $\kappa$ or only composite wedges. Include endogenous multinational ownership, entry and supplier investment in welfare comparisons. Report sensitivity to bargaining rules and cross-country institutional measurement. A model matching observed sourcing shares can estimate a conditional counterfactual without proving that its enforcement mechanism is uniquely identified or that the broader research question was first stated in that paper.

Additional formal definitions and scope (editorial). Specify a complete contracting model: the nonverifiable action set, feasible enforceable contract terms, outside options, allocation of ownership/control rights and any bargaining rule. Noncontractibility is not simply a proportional transaction cost; if $\kappa_{ab}$ is used, define whether it changes enforcement probability, investment appropriability, or a resource wedge and identify each component separately. The intervention $\kappa=0$ must say whether it makes all actions verifiable or only removes enforcement costs; ownership responses and transfers may differ. Define trade volume in physical quantities or a common-price real index, and welfare by discounted household utility with fiscal and contractual resource costs. Even if enforcement improves, $\Delta Q$ need not be positive for every trade flow; no sign theorem is assumed. A structural conditional estimate and unique causal identification of legal institutions are different claims.

For the identification part, declare an admissible class $\Theta$ of structural models, including preferences, technologies, shock laws, measurement/sampling rules and any equilibrium selector. If $O$ denotes the complete observable history and $T(\theta)$ the target defined above, the identified set is $\mathcal I_T=\{T(\theta):\theta\in\Theta,\ \mathcal L_\theta(O)=\mathcal L_{\rm obs}(O)\}$; point identification means this set is a singleton. A $do(a)$ comparison replaces stated policy/technology equations while fixing the declared exogenous law and re-solving the remaining equations. These definitions do not assert that an identification theorem holds without further restrictions.

Variants and assumption changes

  1. Fixed contracting model (source subcase). Estimate its declared enforcement/appropriability wedge and compute the model-specific welfare and trade counterfactuals; this conditional task already has published working-paper estimates.
  2. Institutional mechanism identification (editorial). Separate enforcement, nonverifiability, search and finance using independently justified variation, allowing endogenous ownership and supplier investment.

References and source audit

  1. NBER indexed primary record verifies Chor and Ma, 2025 WP 34044 and DOI; no invented priority claim. Locator: Indexed abstract; exact full-text introduction locator unverified. Support: Conditional contracting welfare/trade study. Original author PDF and NBER direct PDF/page fetches failed; primary indexed abstract/metadata inspected. URL: https://www.nber.org/papers/w34044.
  1. Davin Chor; Lin Ma. 2025. The Aggregate Welfare and Trade Implications of Contracting Frictions in Global Sourcing. Indexed abstract; exact full-text introduction locator unverified. https://www.nber.org/papers/w34044. DOI: https://doi.org/10.3386/w34044.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-269-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-269

Enforcement, investment and sourcing: welfare gains without monotone trade

Catalogue problem: F12-265. Status: Unresolved. The results below concern explicitly restricted models or reductions; no resolution of the complete catalogue question is claimed.

Question and restrictions

The catalogue asks for the welfare and trade consequences of eliminating incomplete-contracting frictions while ownership, sourcing and entry adjust, and for identification of the underlying enforcement primitives. Chor and Ma [cm] already provide a structural general-equilibrium analysis and quantitative counterfactuals under their model. This attempt does not treat those conditional estimates as an unresolved theorem. It studies a transparent small-open-economy limit in which the hold-up channel, organizational selection and an identification failure can all be proved explicitly.

An enforcement mechanism rather than a transport wedge

There is a finite nonempty set $J$ of sourcing--ownership modes. A mode records domestic or foreign location and, if desired, arm's-length or integrated ownership. Mode $j$ has investment productivity $A_j>0$, resource-cost coefficient $c_j>0$, setup resource cost $F_j\geq0$, enforcement-failure probability $\kappa_j\in[0,1]$, and supplier bargaining share $b_j\in(0,1]$ in the failure state. Both states occur after the supplier's relationship-specific investment $x\geq0$. If enforcement succeeds, an enforceable revenue entitlement gives the supplier marginal revenue $A_j$; if it fails, ex post bargaining gives marginal revenue $b_jA_j$. Expected marginal appropriation is therefore \[ \beta_j A_j,\qquad \beta_j=1-\kappa_j(1-b_j)\in(0,1]. \] Gross real surplus before investment cost and setup is $A_jx$, investment costs $c_jx^2/2$, and setup costs $F_j$. Investment cannot be specified in the ex ante contract. An enforceable fixed transfer between buyer and supplier is available before investment. It does not depend on $x$ or on subsequent enforcement. Both parties have sufficient wealth, are risk neutral, and have outside payoff zero. A buyer with take-it-or-leave-it bargaining power sets this transfer, chooses a mode or nonentry, and pays setup costs. Transfers may have either sign.

For an explicit price closure, this is a small open economy with numeraire price one and an outside constant-returns sector fixing the resource wage at one. Resource supplies are large enough for all displayed activities. Surplus is measured for the union of buyer and supplier owners, including foreign owners if the supplier is foreign. Thus it is joint/global surplus, not a claim about the buyer country's welfare after international rent transfers. There are no endogenous terms of trade in this benchmark.

Lemma (Investment and fixed-transfer extraction): In mode $j$, investment and maximal buyer profit after the participation-preserving fixed transfer are \[ x_j=\frac{\beta_jA_j}{c_j},\qquad S_j=\frac{A_j^2}{c_j}\left(\beta_j-\frac{\beta_j^2}{2}\right)-F_j. \] The chosen mode maximizes $S_j$ whenever this maximum is positive; nonentry has surplus zero. Fix a deterministic tie-breaking rule including entry at a zero maximum.
Proof: Writing $T$ for a transfer from supplier to buyer, the supplier maximizes $\beta_jA_jx-c_jx^2/2-T$. Strict concavity gives the unique investment $x_j$. Its pre-transfer payoff is $\beta_j^2A_j^2/(2c_j)$, so the buyer can set $T$ equal to that amount and satisfy participation with equality. Buyer operating receipts before this transfer are $(1-\beta_j)A_jx_j$. Subtracting setup cost and adding $T$ gives the displayed $S_j$. Equivalently, total joint surplus at the induced investment is $A_jx_j-c_jx_j^2/2-F_j=S_j$. The transfer does not change the marginal investment return, so rent extraction does not repair the hold-up distortion. Maximization over the finite modes and outside option gives the selection statement. ∎

A welfare theorem with endogenous organizational selection

Write $S_j^0=A_j^2/(2c_j)-F_j$ for the fully enforced value, and let \[ W_\kappa=\max\{0,\max_jS_j\},\qquad W_0=\max\{0,\max_jS_j^0\}. \] All other primitives, the resource-price closure, and the mode menu are held fixed in the counterfactual.
Theorem (Exact within-mode loss and selection bounds): For each mode, \[ S_j^0-S_j=L_j:=\frac{A_j^2}{2c_j}(1-\beta_j)^2. \] Consequently $W_0\geq W_\kappa$. Include a dummy outside mode with $S_{\varnothing}=S_{\varnothing}^0=L_{\varnothing}=0$. If $j_\kappa$ and $j_0$ are selected baseline and full-enforcement maximizers, then \[ L_{j_\kappa}\leq W_0-W_\kappa\leq L_{j_0}\leq\max_{j\in J\cup\{\varnothing\}}L_j. \] The same conclusions hold if independent opportunities are summed, with their own finite mode sets and no common resource constraint.
Proof: Complete the square: \[ \frac{A_j^2}{2c_j}-\frac{A_j^2}{c_j} (\beta_j-\beta_j^2/2) =\frac{A_j^2}{2c_j}(1-\beta_j)^2\geq0. \] Taking maxima proves monotonicity. Since $S_{j_\kappa}=W_\kappa$ and $S_{j_\kappa}^0\leq W_0$, their difference gives the lower bound. Similarly $S_{j_0}\leq W_\kappa$ and $S_{j_0}^0=W_0$ give the upper bound. The dummy mode makes both arguments valid with entry or exit at the boundary. Summing independent inequalities proves the final claim. ∎

The theorem explicitly allows switching location or ownership and the activation of previously unprofitable opportunities. Its monotonicity uses extraction and the fixed-price closure. It need not hold for national welfare when enforcement shifts foreign rents, for financially constrained suppliers, or for an economy with endogenous wages and congestion.

Proposition (Trade can fall to zero when enforcement improves): There is a two-mode economy satisfying all preceding assumptions in which eliminating contracting frictions strictly raises joint welfare and strictly lowers foreign sourcing from a positive quantity to zero.
Proof: Take one domestic mode $D$ and one foreign mode $F$, with zero setup costs and \[ (A_D,c_D,\beta_D)=(2,1,1/5),\qquad (A_F,c_F,\beta_F)=(1,1/2,4/5). \] Both appropriation shares can arise with common bargaining share $b=1/10$: use $\kappa_D=8/9$ and $\kappa_F=2/9$. Baseline surpluses are \[ S_D=4(1/5-1/50)=18/25,\qquad S_F=2(4/5-8/25)=24/25. \] Hence foreign sourcing is uniquely chosen with investment $x_F=8/5$ and real delivered quantity $A_Fx_F=8/5$. Define the trade measure as this foreign delivered quantity, with domestic sourcing contributing zero. With full enforcement, $S_D^0=2>S_F^0=1$, so domestic sourcing is uniquely chosen, welfare rises from $24/25$ to $2$, and trade falls to zero. No nominal exchange-rate or price-index change produces this reversal; the organizational/location margin does. ∎

What quantity data fail to identify

The previous mechanism also separates observed investment from an enforcement primitive.
Proposition (A specified observational equivalence): Suppose the observable law consists only of the selected mode, its deterministic investment $x$, and output $Ax$. Even if $A=1$, $F=0$ and bargaining share $b=1/4$ are known, these observations do not identify the gain from full enforcement when $c$ is unknown. In contrast, if $c$ is known and the selected mode has $b<1$, then its enforcement probability is identified from positive investment by \[ \kappa=\frac{1-cx/A}{1-b}, \] provided the resulting parameter belongs to $[0,1]$.
Proof: Use a single available mode. In economy one let $(\beta,c)=(1/2,1/2)$; in economy two let $(\beta,c)=(3/4,3/4)$. Both have $x=\beta A/c=1$, output one, and positive entry surplus. The common known $b=1/4$ gives admissible failure probabilities $2/3$ and $1/3$. Yet the full-enforcement gains are, respectively, \[ \frac{1}{2(1/2)}(1-1/2)^2=\frac14, \qquad \frac{1}{2(3/4)}(1-3/4)^2=\frac1{24}. \] Thus the observable laws coincide while the target differs. These economies need not have the same observed costs or profits; the proposition does not include those variables in the data. If $c$ is known, the investment first-order condition identifies $\beta=cx/A$; solving $\beta=1-\kappa(1-b)$ proves the converse formula. For $b=1$, enforcement has no marginal investment effect and $\kappa$ cannot be recovered this way. ∎

Remaining gap and empirical interpretation

Ownership is a genuine discrete option in this model only insofar as its primitive bargaining shares, costs or failure risks differ. Estimating those differences, rather than labeling every low investment ratio an enforcement wedge, is essential. The identification proposition concerns a narrow data set; it is not a criticism of structural identification using richer moments in [cm]. An empirical application would need investment-cost information, enforcement variation, ownership and sourcing outcomes, fixed entry costs and an explicit market closure.

The results establish a hold-up mechanism, endogenous selection bounds, a real-trade reversal and a concrete nonidentification example. They leave endogenous wages, prices, multisector input demand, external financing and country-specific welfare distribution unresolved. Those are central components of the catalogue's general-equilibrium quantitative task.

Completion Estimate

35%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt proves hold-up welfare-loss bounds with endogenous mode selection, constructs a trade reversal and demonstrates enforcement nonidentification from narrow sourcing data. General-equilibrium welfare and trade counterfactuals still require endogenous wages and prices, richer institutional identification, financing and country-specific ownership and rent effects.

References

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