A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary choice literature, it presents significant challenges for other models as well and is not as well understood in more general settings. These challenges are only magnified for models that feature many fixed effects and other high-dimensional parameters. We address the current ambiguity surrounding this topic by studying the conditions that govern the existence of estimates for (pseudo-)maximum likelihood estimators used to estimate a wide class of generalized linear models (GLMs). We show that some, but not all, of these GLM estimators can still deliver consistent estimates of at least some of the linear parameters when these conditions fail to hold. We also demonstrate how to verify these conditions in models with high-dimensional parameters, such as panel data models with multiple levels of fixed effects.
After a period of stable prices in advanced economies, inflation surged in 2022, largely driven by substantial increases in international food and energy prices. Using electronic payments data to estimate a demand system, we derive expenditure and price elasticities and evaluate the welfare effects of these relative price changes for Portuguese consumers. Our results indicate an average welfare loss of approximately 10% of total expenditure, disproportionately affecting lower-spending consumers. Furthermore, we observe that lower-expenditure consumers generally have larger price elasticities than their higher-spending counterparts. These results reinforce the evidence of the unequal welfare costs of inflation on consumers.
We study the effects of trade liberalization on the full wage distribution, exploiting Spain's 1993 entry into the European Single Market. Using employer-employee data, we identify the causal effects of trade across the entire wage distribution, using a novel shift-share instrument embedded in an unconditional quantile regression. We find that the liberalization reduced wage inequality, leading to wage compression through earnings gains at the bottom of the distribution and wage losses at the top. We trace this compression to two asymmetric channels: import competition disproportionately harmed high earners, while export opportunities benefited low earners. The key mechanism is an import-driven "skill-downgrading." A multi-region multi-sector model shows that the key insight for understanding these empirical results is that trade's distributional effects depend on the skill intensity of a country's tradable sector, and Spain's was relatively low-skill intensive back then.
While a growing body of research has examined the economic and social consequences of extreme weather, few attempts have been made to collate this evidence into a coherent map. This scoping review addresses this gap by providing the first systematic mapping of research on the socio-economic sensitivity of European regions to short-run weather shocks. Following a PRISMA-ScR protocol, we search Scopus and Web of Science, identifying 77 eligible articles published between 2000 and 2025. We analyse how studies define and measure weather shocks and socio-economic outcomes, the data and methods they employ, the sectors and regions they cover, as well as the associated impacts across sectors and the channels they operate through. Our review finds that weather shocks are consistently associated with reduced output growth, increased heat-related mortality, rising inflationary pressures, and greater inequality, with effects varying by region, sector, and income level. However, we also identify significant gaps in spatial resolution, sectoral coverage, and methodological diversity. By mapping the existing evidence and its limitations, this review provides a structured foundation for future research on weather-related socio-economic risk in Europe.
This paper examines the functioning of the European Single Market through the experience of Spain and Portugal, two economies whose geographical proximity, shared border and joint EU membership since 1986 make them a particularly informative case study. Organizing the analysis around the Single Market’s four freedoms, the paper combines descriptive indicators, structural-gravity estimates, a multi-country general-equilibrium trade model, price-convergence and electricity-coupling measures, administrative labour-market data, survival analysis and granular investment and banking data to assess integration in trade, energy, labour mobility and capital markets. The findings show that Iberian integration is substantial but markedly uneven across dimensions. Trade in goods and production network linkages have deepened considerably since accession, and wholesale electricity markets are exceptionally well integrated, reflecting strong complementarities between Spanish solar and Portuguese hydropower generation. By contrast, services trade, labour mobility and non-bank financial investment remain comparatively underdeveloped. These results show that the legal framework of the Single Market has generated deep integration in some markets while leaving others fragmented, and that closing the remaining gaps requires more effective implementation, regulatory cooperation and mutual recognition, supported by infrastructure investment and interoperable administrative systems.
