A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we propose prediction intervals for model averaging based on conformal inference. These intervals cover out-of-sample realizations of the outcome variable with a pre-specified probability, providing a way to assess predictive uncertainty beyond point prediction. The framework allows general model misspecification and applies to averaging across multiple models that can be nested, disjoint, overlapping, or any combination thereof, with weights that may depend on the estimation sample. We establish coverage guarantees under two sets of assumptions: exact finite-sample validity under exchangeability, relevant for cross-sectional data, and asymptotic validity under stationarity, relevant for time-series data. We first present a benchmark algorithm and then introduce a locally adaptive refinement and split-sample procedures that broaden applicability. The methods are illustrated with a cross-sectional application to real estate appraisal and a time-series application to equity premium forecasting.

Modern neural networks often encode unwanted concepts alongside task-relevant information, leading to fairness and interpretability concerns. Existing post-hoc approaches can remove undesired concepts but often degrade useful signals. We introduce SPLINCE-Simultaneous Projection for LINear concept removal and Covariance prEservation - which eliminates sensitive concepts from representations while exactly preserving their covariance with a target label. SPLINCE achieves this via an oblique projection that 'splices out' the unwanted direction yet protects important label correlations. Theoretically, it is the unique solution that removes linear concept predictability and maintains target covariance with minimal embedding distortion. Empirically, SPLINCE outperforms baselines on benchmarks such as Bias in Bios and Winobias, removing protected attributes while minimally damaging main-task information.

Stock markets are impacted by a large variety of factors including news and discussions among investors about investment opportunities. With the emergence of social media, new opportunities for having financial discussions arose. The market frenzy surrounding GameStop (GME) on the Reddit subreddit Wallstreetbets, caused financial discussion forums to receive widespread attention and it was established that Wallstreetbets played a leading role in the stock market movements of GME. Here, we present a new data set for exploring the effect of social media discussion forums on the stock market. The dataset consists of posts published on various Reddit subreddits concerning the popular meme stocks GameStop (GME), American Multi-Cinema Entertainment Holdings (AMC), and BlackBerry (BB). We document the data collection and processing steps and show that the posts and comments about these meme stocks are related to their market movements.

We develop a model that captures peer effect heterogeneity by modeling the endogenous spillover to be linear in ordered peer outcomes. Unlike the canonical linear-in-means model, our approach accounts for the distribution of peer outcomes as well as the size of peer groups. Under a minimal condition, our model admits a unique equilibrium and is therefore tractable and identified. Simulations show our estimator has good finite sample performance. Finally, we apply our model to educational data from Norway, finding that higher-performing friends disproportionately drive GPA spillovers. Our framework provides new insights into the structure of peer effects beyond aggregate measures.

A distribution shift between the training and test data can severely harm performance of machine learning models. Importance weighting addresses this issue by assigning different weights to data points during training. We argue that existing heuristics for determining the weights are suboptimal, as they neglect the increase of the variance of the estimated model due to the finite sample size of the training data. We interpret the optimal weights in terms of a bias-variance trade-off, and propose a bi-level optimization procedure in which the weights and model parameters are optimized simultaneously. We apply this optimization to existing importance weighting techniques for last-layer retraining of deep neural networks in the presence of sub-population shifts and show empirically that optimizing weights significantly improves generalization performance.

Social network platforms like Reddit are increasingly impacting real-world economics. Meme stocks are a recent phenomena where price movements are driven by retail investors organizing themselves via social networks. To study the impact of social networks on meme stocks, the first step is to analyze these networks. Going forward, predicting meme stocks' returns would require to predict dynamic interactions first. This is different from conventional link prediction, frequently applied in e.g. recommendation systems. For this task, it is essential to predict more complex interaction dynamics, such as the exact timing. These are crucial for linking the network to meme stock price movements. Dynamic graph embedding (DGE) has recently emerged as a promising approach for modeling dynamic graph-structured data. However, current negative sampling strategies, an important component of DGE, are designed for conventional dynamic link prediction and do not capture the specific patterns present in meme stock-related social networks. This limits the training and evaluation of DGE models in such social networks. To overcome this drawback, we propose novel negative sampling strategies based on the analysis of real meme stock-related social networks and financial knowledge. Our experiments show that the proposed negative sampling strategies can better evaluate and train DGE models targeted at meme stock-related social networks compared to existing baselines.

In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive a consistent estimator of the integrated volatility, which converges stably to a mixed Gaussian distribution at the optimal rate $n^{1/4}$. To refine the finite sample performance, we propose a two-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our two-step estimators. In an empirical study, we characterize the dependence structures of microstructure noise in several popular sampling schemes and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating integrated volatility.

It is customary to estimate error-in-variables models using higher-order moments of observables. This moments-based estimator is consistent only when the coefficient of the latent regressor is assumed to be non-zero. We develop a new estimator based on the divide-and-conquer principle that is consistent for any value of the coefficient of the latent regressor. In an application on the relation between investment, (mismeasured) Tobin's $q$ and cash flow, we find time periods in which the effect of Tobin's $q$ is not statistically different from zero. The implausibly large higher-order moment estimates in these periods disappear when using the proposed estimator.

This paper contributes to the limited literature on the temperature sensitivity of residential energy demand on a global scale. Using a Bayesian Partial Pooling model, we estimate country-specific intercepts and slopes, focusing on non-linear temperature response functions. The results, based on data for up to 126 countries spanning from 1978 to 2023, indicate a higher demand for residential electricity and natural gas at temperatures below -5 degrees Celsius and a higher demand for electricity at temperatures above 30 degrees Celsius. For temperatures above 23.5 degrees Celsius, the relationship between power demand and temperature steepens. Demand in developed countries is more sensitive to high temperatures than in less developed countries, possibly due to an inability to meet cooling demands in the latter.

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. The practical relevance of the theory is highlighted in a set of empirical examples. We further obtain an asymptotic test and confidence bounds for the unfeasible " true " invertibility region of the parameter space.

The social cost of carbon is the damage avoided by slightly reducing carbon dioxide emissions. It is a measure of the desired intensity of climate policy. The social cost of carbon is highly uncertain because of the long and complex cause-effect chain, and because it quantifies and aggregates impacts over a long period of time, affecting all people in a wide range of possible futures. Recent estimates are around \$80/tCO$_2$.

This paper provides a unified framework for bounding policy relevant treatment effects using instrumental variables. In this framework, the treatment selection may depend on multidimensional unobserved heterogeneity. We derive bilinear constraints on the target parameter by extracting information from identifiable estimands. We apply a convex relaxation method to these bilinear constraints and provide conservative yet computationally simple bounds. Our convex-relaxation bounds extend and robustify the bounds by Mogstad, Santos, and Torgovitsky (2018) which require the threshold-crossing structure for the treatment: if this condition holds, our bounds are simplified to theirs for a large class of target parameters; even if it does not, our bounds include the true parameter value whereas theirs may not and are sometimes empty. Linear shape restrictions can be easily incorporated to narrow the proposed bounds. Numerical and simulation results illustrate the informativeness of our convex-relaxation bounds.

To address the dual environmental challenges of pollution and climate change, China has established multiple environmental markets, including pollution emissions trading, carbon emissions trading, energy-use rights trading, and green electricity trading. Previous empirical studies suffer from known biases arising from time-varying treatment and multiple treatments. To address these limitations, this study adopts a dynamic control group design and combines Difference-in-Difference (DiD) and Artificial Counterfactual (ArCo) empirical strategies. Using panel data on A-share listed companies from 2000 to 2024, this study investigates the marginal effects and interactive impacts of multiple environmental markets implemented in staggered and overlapping phases. Existing pollution emissions trading mitigates the negative effects of carbon emission trading. Carbon trading suppresses (improves) financial performance (if implemented alongside energy-use rights trading). The addition of energy-use rights or green electricity trading in regions already covered by carbon or pollution markets has no significant effects.

The paper presents the professor-student network of Nobel laureates in economics. 74 of the 79 Nobelists belong to one family tree. The remaining 5 belong to 3 separate trees. There are 350 men in the graph, and 4 women. Karl Knies is the central-most professor, followed by Wassily Leontief. No classical and few neo-classical economists have left notable descendants. Harvard is the central-most university, followed by Chicago and Berlin. Most candidates for the Nobel prize belong to the main family tree, but new trees may arise for the students of Terence Gorman and Denis Sargan.

We study the quality of secondary school track assignment decisions in the Netherlands, using a regression discontinuity design. In 6th grade, primary school teachers assign each student to a secondary school track. If a student scores above a track-specific cutoff on the standardized end-of-primary education test, the teacher can upwardly revise this assignment. By comparing students just left and right of these cutoffs, we find that between 50-90% of the students are "trapped in track": these students are on the high track after four years, only if they started on the high track in first year. The remaining (minority of) students are "always low": they are always on the low track after four years, independently of where they started. These proportions hold for students near the cutoffs that shift from the low to the high track in first year by scoring above the cutoff. Hence, for a majority of these students the initial (unrevised) track assignment decision is too low. The results replicate across most of the secondary school tracks, from the vocational to the academic tracks, and stand out against an education system with a lot of upward and downward track mobility.

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low sample size settings, such as genetic microarrays. Second, it improves interpretability as components are regularized to zero. However, over-regularization of sparse singular vectors can cause them to deviate greatly from the population singular vectors, potentially misrepresenting the data structure. Additionally, sparse singular vectors are often not orthogonal, resulting in shared information between components, which complicates the calculation of variance explained. To address these challenges, we propose a methodology for sparse PCA that reflects the inherent structure of the data matrix. Specifically, we identify uncorrelated submatrices of the data matrix, meaning that the covariance matrix exhibits a sparse block diagonal structure. Such sparse matrices commonly occur in high-dimensional settings. The singular vectors of such a data matrix are inherently sparse, which improves interpretability while capturing the underlying data structure. Furthermore, these singular vectors are orthogonal by construction, ensuring that they do not share information. We demonstrate the effectiveness of our method through simulations and provide real data applications. Supplementary materials for this article are available online.

In finance, durations between successive transactions are usually modeled by the autoregressive conditional duration model based on a continuous distribution omitting zero values. Zero or close-to-zero durations can be caused by either split transactions or independent transactions. We propose a discrete model allowing for excessive zero values based on the zero-inflated negative binomial distribution with score dynamics. This model allows to distinguish between the processes generating split and standard transactions. We use the existing theory on score models to establish the invertibility of the score filter and verify that sufficient conditions hold for the consistency and asymptotic normality of the maximum likelihood of the model parameters. In an empirical study, we find that split transactions cause between 92 and 98 percent of zero and close-to-zero values. Furthermore, the loss of decimal places in the proposed approach is less severe than the incorrect treatment of zero values in continuous models.

Empirical researchers often estimate spillover effects by fitting linear or non-linear regression models to sampled network data. Here, we show that common sampling schemes induce dependence between observed and unobserved spillovers. Due to this dependence, spillover estimates are biased, often upwards. We then show how researchers can construct unbiased estimates of spillover effects by rescaling using aggregate network statistics. Our results can be used to bound true effect sizes, determine robustness of estimates to missingness, and construct estimates when missingness depends on treatment. We apply our results to re-estimate the propagation of idiosyncratic shocks between US public firms, and peer effects amongst USAFA cadets.

We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on random rather than deterministic time scales. This enables us to convert the original problem into an equivalent discrete-time optimal stopping problem with $\mathbb{N}_{0}$-valued stopping times and a possibly infinite horizon. To numerically solve this problem, we design a random times least squares Monte Carlo method. We also analyze an iterative policy improvement procedure in this setting. We illustrate the efficiency of our methods and the relevance of randomly arriving opportunities in a few examples.