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.
We measure how cuts to public procurement propagate through the banking system in a financial crisis. During the European sovereign debt crisis, the Portuguese government cut procurement spending by 4.3 percent of GDP. We find that this cut saddled banks with nonperforming loans from government contractors, which led to a persistent reduction in credit supply to other firms. We estimate a bank-level elasticity of credit supply with respect to procurement demand of 2.5. In a general equilibrium model, our findings point to large effects of fiscal policy on credit supply and output in a crisis. (JEL E23, E44, E62, G01, G21, H57)
