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For simple classification tasks, we show that users can benefit from the advantages of using small, local, generative language models instead of large commercial models without a trade-off in performance or introducing extra labelling costs. These advantages, including those around privacy, availability, cost, and explainability, are important both in commercial applications and in the broader democratisation of AI. Through experiments on 17 sentence classification tasks (2-4 classes), we show that penalised logistic regression on the embeddings from a small LLM equals (and usually betters) the performance of a large LLM in the "tens-of-shot" regime. This requires no more labelled instances than are needed to validate the performance of the large LLM. Finally, we extract stable and sensible explanations for classification decisions.

We present a novel framework for estimation and inference with the broad class of universal approximators. Estimation is based on the decomposition of model predictions into Shapley values. Inference relies on analyzing the bias and variance properties of individual Shapley components. We show that Shapley value estimation is asymptotically unbiased, and we introduce Shapley regressions as a tool to uncover the true data generating process from noisy data alone. The well-known case of the linear regression is the special case in our framework if the model is linear in parameters. We present theoretical, numerical, and empirical results for the estimation of heterogeneous treatment effects as our guiding example.

How does the monetary and fiscal policy mix alter households' saving incentives? To answer these questions, we build a heterogenous agents New Keynesian model where three different types of agents can save in assets with different liquidity profiles to insure against idiosyncratic risk. Policy mixes affect saving incentives differently according to their effect on the liquidity premium -- the return difference between less liquid assets and public debt. We derive an intuitive analytical expression linking the liquidity premium with consumption differentials amongst different types of agents. This underscores the presence of a transmission mechanism through which the interaction of monetary and fiscal policy shapes economic stability via its effect on the portfolio choice of private agents. We call it the 'self-insurance demand channel', which moves the liquidity premium in the opposite direction to the standard 'policy-driven supply channel'. Our analysis thus reveals the presence of two competing forces driving the liquidity premium. We show that the relative strength of the two is tightly linked to the policy mix in place and the type of business cycle shock hitting the economy. This implies that to stabilize the economy, monetary policy should consider the impact of the 'self-insurance' on the liquidity premium.

The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We argue that this is not a conceptually sound approach and suggest an alternative based on the new law of total odds. We quantify the bias of the total probability estimator of the unconditional class probabilities and show that the total odds estimator is unbiased. The sample version of the total odds estimator is shown to coincide with a maximum-likelihood estimator known from the literature. The law of total odds can also be used for transforming the conditional class probabilities if independent estimates of the unconditional class probabilities of the population are available. Keywords: Total probability, likelihood ratio, Bayes' formula, binary classification, relative odds, unbiased estimator, supervised learning, dataset shift.

University rankings are increasingly adopted for academic comparison and success quantification, even to establish performance-based criteria for funding assignment. However, rankings are not neutral tools, and their use frequently overlooks disparities in the starting conditions of institutions. In this research, we detect and measure structural biases that affect in inhomogeneous ways the ranking outcomes of universities from diversified territorial and educational contexts. Moreover, we develop a fairer rating system based on a fully data-driven debiasing strategy that returns an equity-oriented redefinition of the achieved scores. The key idea consists in partitioning universities in similarity groups, determined from multifaceted data using complex network analysis, and referring the performance of each institution to an expectation based on its peers. Significant evidence of territorial biases emerges for official rankings concerning both the OECD and Italian university systems, hence debiasing provides relevant insights suggesting the design of fairer strategies for performance-based funding allocations.

Economies are fundamentally complex and becoming more so, but the new discipline of data science-which combines programming, statistics, and domain knowledge-can help cut through that complexity, potentially with productivity benefits to boot. This chapter looks at examples of where innovations from data science are cutting through the complexities faced by policymakers in measurement, allocating resources, monitoring the natural world, making predictions, and more. These examples show the promise and potential of data science to aid policymakers, and point to where actions may be taken that would support further progress in this space.

Central banks increasingly use social media to communicate beyond financial markets, yet evidence on public engagement effectiveness remains limited. Despite 113 central banks joining Twitter between 2008 and 2018, we lack understanding of what drives audience interaction with their content. To examine engagement determinants, we analyzed 3.13 million tweets mentioning the Bank of England from 2007 to 2022, including 9,810 official posts. We investigate posting patterns, measure engagement elasticity, and identify content characteristics predicting higher interaction. The Bank's posting schedule misaligns with peak audience engagement times, with evening hours generating the highest interaction despite minimal posting. Cultural content, such as the Alan Turing 50 pound note, achieved 1,300 times higher engagement than routine policy communications. Engagement elasticity averaged 1.095 with substantial volatility during events like Brexit, contrasting with the Federal Reserve's stability. Media content dramatically increased engagement: videos by 1,700 percent, photos by 126 percent, while monetary policy announcements and readability significantly enhanced all metrics. Content quality and timing matter more than posting frequency for effective central bank communication. These findings suggest central banks should prioritize accessible, media-rich content during high-attention periods rather than increasing volume, with implications for digital communication strategies in fulfilling public transparency mandates.

How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year's portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year's conditional default rates will always be located between last year's portfolio-wide default rate and the ML forecast for next year. As an application example, then cost quantification is discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.