Papers

When a local housing market receives a population shock, the shock is absorbed by new construction, by conversion of the existing stock, by households consuming less space and by the movement of other residents, and prices move until these margins exhaust it. I develop a spatial-equilibrium framework in which these shares have a closed form and sum to one, and I estimate it for Spain’s two immigration waves with a 2003–2024 panel of 50 provinces and a shift-share instrument based on settlement by country of birth. In 2003–2008 each unit of inflow was matched by about 0.7 units of new housing. In 2015–2024 the construction margin closed: the dwelling-stock response is zero, and administrative starts and completions respond to inflows only in provinces that came out of the 2008 bust with little unsold new housing. The current wave has been absorbed by squeezing instead. In the population register, persons per household rise by 0.84% for each 1% of population arriving, and each 1% raises rents by about 1% and house prices by about 4% cumulatively. Natives move towards receiving provinces, which amplifies the shock; with that reallocation the model matches the rent response only if space per household is about four times as elastic as standard calibrations assume. Neither topography nor vacant urban land predicts the response across provinces, so the paper reads the collapse between waves as a fall in effective supply elasticity without identifying a single cause. The rent burden falls mainly on the bottom income deciles and on households headed by people under 45.

AI agents can perform tasks, but unlike workers they can be copied at the price of compute. This paper asks what that does to the economics of production. In a task-based model, a firm can let agents perform a task only after implementing it: integrating the agent, redesigning the workflow and preparing the data. Implementation uses a distinct kind of labor and is a fixed cost per task, independent of scale. Five results follow. Automation depends on market size relative to organizational frictions, so AI-native entrants can out-automate larger incumbents. Cheaper agents raise the demand for implementation labor: the technology substitutes for the workers who perform tasks and complements those who deploy it. When implementation capacity is inelastic, a fall in the price of AI raises the implementation wage rather than the number of automated tasks, and its effect on unit costs is bounded by the current automation share, the Hulten term that existing macroeconomic estimates take as given. Finally, the same bottleneck shields production workers: displacement is triggered by the expansion of implementation capacity, not by the falling price of AI. If AI lowers its own implementation cost, the bottleneck persists only while that rate stays below a threshold the paper derives. Read through the model, the ten-year productivity estimate of Acemoglu (2025) presumes implementation capacity growing at roughly 8–22% a year. Agents are abundant; what is scarce is the organization able to deploy them.

Does generative AI widen or compress productivity differences between workers? This paper develops a microeconomic model in which an AI tool has two separate margins: a frontier, the problems it can solve for anyone, and leverage, the extra work it lets a person get through. The gain from adoption is V-shaped in ability, with its minimum at the worker whose knowledge equals the AI’s frontier. Frontier advances are equalising and leverage is skill-biased. The V survives leverage that rises with ability up to a stated bound, and when the frontier is a distribution the kink becomes a smooth valley with an observable floor. The average AI×skill complementarity therefore changes sign as the frontier moves through the ability distribution. This offers an account of conflicting experimental findings that differs from the autonomy-based account of Ide and Talamàs (2025) and can be tested against it: tools whose main effect is speed rather than knowledge should favour the able even when they act only as co-pilots. Relative inequality never rises with ability-neutral leverage, but inequality in levels can. When the frontier is jagged, the ability to judge AI output becomes the skill-biased margin, and over-trusting workers can lose. Adoption is two-tailed, so the sign of selection bias depends on the vintage of the technology. Workers capture a share of the gain that rises with diffusion across employers. The return to ability falls to zero below the frontier, which removes the incentive for juniors to climb rungs the AI already occupies. The paper closes with seven testable predictions, the implied sign of selection in each existing study, and the designs needed to test them.

Generative AI changes the production function of software: every answer, document or completed task consumes inference compute, so software acquires a positive marginal cost that scales with how intensively each customer uses it. I derive the consequences in three steps. First, flat access breaks. Heavy users become the least profitable, flat pricing’s share of attainable profit falls monotonically with inference cost, and it collapses once a unit of inference costs half the value of the first unit of use. Second, and centrally, the unit of sale follows control of compute. When the customer controls usage, as with copilots, usage pricing disciplines consumption and pass-through of inference cost exceeds Borch’s risk-sharing benchmark. When the provider controls the process, as with agents, usage pricing is cost-plus, and the efficient contract moves towards paying for outcomes. Outcome pricing is worth its verification cost when the compute bill per task is large. Third, with constant inference cost scale economies vanish; they survive only through firm-specific learning in inference. Common falls in compute prices raise margins without raising gross profit, and because AI also lowers the cost of building software, free entry pushes the gross profit of the typical firm towards its entry cost; this is a benchmark for the typical firm, not a prediction about the most successful ones. Financial statements of 307 US-listed software firms are consistent with these predictions. Early generative-AI adopters saw gross margins fall four to five points relative to other firms after 2023, a result that rests on 32 early adopters, survives a “machine learning” placebo, controls for mean reversion and a matched comparison at about three quarters of its size and marginal significance, and weakens among larger firms. Market value tracks gross profit more closely than revenue. The learning rate in inference cannot be identified from public accounts.

With heterogeneous firms, trade raises wage inequality where few firms export and lowers it where most do. I show that the variance of log wages in a local labour market is hump-shaped in the employment share of exporters for any productivity distribution, and that the shape of the hump carries information about the tail of the productivity distribution that can be read from wage data alone: with a Pareto tail, wage dispersion among exporters does not vary with the exporter share, and the peak lies between 1/e and 1/2. Foreign demand raises inequality up to and beyond that peak. Using five waves of Spain’s Wage Structure Survey (2006–2022), which record whether each worker’s employer sells mainly abroad, I find the hump across region–sector cells, with a peak at 0.35 (95% interval 0.29–0.43). Within-exporter wage dispersion does not vary with the exporter share, as a Pareto tail implies. Most Spanish employment lies on the rising side of the hump. Three instruments (EU demand for each sector’s products, the regional product mix and exposure to the construction bust) have weak first stages, so the causal effect of exporting is not identified. Model-based counterfactuals bound it: a five-point rise in the exporter share raises the variance of log wages by about 2 points (×1000) according to within-cell estimates and an exact accounting, and by 13 according to the cross-section, against an observed fall of 34 points over 2006–2022. The 2008 bust raised measured inequality through the loss of mid-wage construction jobs but compressed the wage structure more. The 2019 minimum-wage increase compressed the lower tail in proportion to its regional bite.

The data and code released with Working Paper 001. A balanced panel of Spain’s 50 provinces for 2002–2026 with population by place of birth, house prices, rents, the dwelling stock and households; the settlement shares and national shifts needed to build a leave-one-out shift-share instrument for foreign-born inflows from 1998, 2001 or 2011 settlement patterns; geographic and planning measures of supply constraints; the stock of unsold new housing by province for 2015–2024, assembled from the Ministry of Housing’s annual reports; and persons per household rebuilt from about 36,000 census sections of the population register for 2015–2023. Every series is public and every step is scripted. Data are released under CC BY 4.0 and code under the MIT licence.