The invariance properties of certain likelihood-based asymptotic tests as well as their extensions for M-estimation, estimating functions and the generalized method of moments have been well studied. The simulation study reported in Crudu and Osorio [Econ. Lett. 187: 108885, 2020] shows that the bilinear form test is not invariant to one-to-one transformations of the parameter space. This paper provides a set of suitable conditions to establish the invariance property under reparametrization of the bilinear form test for linear or nonlinear hypotheses that arise in extremum estimation which leads to a simple modification of the test statistic. Evidence from a Monte Carlo simulation experiment suggests good performance of the proposed methodology.

Despite a large body of theoretical literature on voting mechanisms, there is no documented evidence from real-world panel evaluations about the effect of trimming the extreme votes on sincere voting. We provide the first such evidence by comparing subjective evaluations of experts from different countries in competitive settings with and without a trimming mechanism. In these evaluations, some of the evaluated subjects are experts' compatriots. Using data on 29,383 subjective evaluations, we find that experts assign significantly higher scores to their compatriots in panels without trimming. However, in panels with trimming, this favoritism is generally insignificant.

We consider the standard moral hazard problem with limited liability. The first-order approach (FOA) is the main tool for its solution, but existing sufficient conditions for its validity are restrictive. Our main result shows that the FOA is broadly valid, as long as the agent's reservation utility is sufficiently high. In basic examples, the FOA is valid for almost any positive reservation wage. We establish existence and uniqueness of the optimal contract. We derive closed-form solutions with various functional forms. We show that optimal contracts are either linear or piecewise linear option contracts with log utility and output distributions in an exponential family with linear sufficient statistic (including Gaussian, exponential, binomial, geometric, and Gamma). We provide an algorithm for finding the optimal contracts both in the case where the FOA is valid and in the case where it is not at trivial computational cost.

Capturing nonlinear relationships without sacrificing interpretability remains a persistent challenge in regression modeling. We introduce SplitWise, a novel framework that enhances stepwise regression. It adaptively transforms numeric predictors into threshold-based binary features using shallow decision trees, but only when such transformations improve model fit, as assessed by the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). This approach preserves the transparency of linear models while flexibly capturing nonlinear effects. Implemented as a user-friendly R package, SplitWise is evaluated on both synthetic and real-world datasets. The results show that it consistently produces more parsimonious and generalizable models than traditional stepwise and penalized regression techniques.

We study directed social influence when an influencer chooses from a richer menu than a constrained follower (decision maker, the DM). The DM selects from a feasible set, while the influencer displays a distribution over a superset that includes infeasible alternatives. We propose the Aspiration-Weighted Luce Model (AWLM): the DM forms a convex combination of her idiosyncratic Luce preferences within the feasible set and the influencer's distribution, then renormalizes this attempt target onto the feasible set. This renormalization generates an aspirational dampening effect: holding the influencer's within-feasible composition fixed and shifting exposure toward infeasible alternatives attenuates influence on feasible choices. We provide an axiomatic characterization based on proportional responses to shifts in feasible exposure and a unit-slope leverage restriction across different levels of feasible share. The model allows for point identification of influence strength and idiosyncratic preferences from two exposure regimes, yielding testable overidentifying restrictions for empirical application.

Central banks rely on density forecasts from professional surveys to assess inflation risks and communicate uncertainty. A central challenge in using these surveys is irregular participation: forecasters enter and exit, skip rounds, and reappear after long gaps. In the European Central Bank's Survey of Professional Forecasters, turnover and missingness vary substantially over time, causing the set of submitted predictions to change from quarter to quarter. Standard aggregation rules -- such as equal-weight pooling, renormalization after dropping missing forecasters, or ad hoc imputation -- can generate artificial jumps in combined predictions driven by panel composition rather than economic information, complicating real-time interpretation and obscuring forecaster performance. We develop coherent Bayesian updating rules for forecast combination under sporadic participation that maintain a well-defined latent predictive state for each forecaster even when their forecast is unobserved. Rather than relying on renormalization or imputation, the combined predictive distribution is updated through the implied conditional structure of the panel. This approach isolates genuine performance differences from mechanical participation effects and yields interpretable dynamics in forecaster influence. In the ECB survey, it improves predictive accuracy relative to equal-weight benchmarks and delivers smoother and better-calibrated inflation density forecasts, particularly during periods of high turnover.

Collaboration is expected to play a central role in the transition to a bioeconomy - a central pillar of a green economy. Such collaboration is supposed to connect traditional biomass processing firms with diverse actors in fields where biomass ought to substitute existing or create novel products and processes. This study analyzes the network of technology collaborations among innovating firms in Sweden between 1970 and 2021. The results reveal generally positive associations between direct and indirect ties, with meaningful increases in innovation output for each additional direct collaboration partner. Relationships between brokerage positions and innovation output were statistically insignificant, and cognitive proximity - while following theoretical expectations - materially insignificant. These associations are mostly equal between actors heavily invested in the bioeconomy and those focusing on other innovation areas, indicating that these actors operate under largely similar mechanisms linking collaboration and subsequent innovation output. These results suggest that stimulating collaboration broadly - rather than attempting to optimize collaboration compositions - could result in higher number of significant Swedish innovations, for bioeconomy and other sectors alike.

Randomized Controlled Trials (RCTs), or A/B testing, have become the gold standard for optimizing various operational policies on online platforms. However, RCTs on these platforms typically cover a limited number of discrete treatment levels, while the platforms increasingly face complex operational challenges involving optimizing continuous variables, such as pricing and incentive programs. The current industry practice involves discretizing these continuous decision variables into several treatment levels and selecting the optimal discrete treatment level. This approach, however, often leads to suboptimal decisions as it cannot accurately extrapolate performance for untested treatment levels and fails to account for heterogeneity in treatment effects across user characteristics. This study addresses these limitations by developing a theoretically solid and empirically verified framework to learn personalized continuous policies based on high-dimensional user characteristics, using observations from an RCT with only a discrete set of treatment levels. Specifically, we introduce a deep learning for policy targeting (DLPT) framework that includes both personalized policy value estimation and personalized policy learning. We prove that our policy value estimators are asymptotically unbiased and consistent, and the learned policy achieves a root-n-regret bound. We empirically validate our methods in collaboration with a leading social media platform to optimize incentive levels for content creation. Results demonstrate that our DLPT framework significantly outperforms existing benchmarks, achieving substantial improvements in both evaluating the value of policies for each user group and identifying the optimal personalized policy.

This paper studies AI persuasion by distinguishing between two reasons for disagreement: attention differences, where the AI detects features the decision-maker missed, and comprehension differences, where the AI and the decision-maker interpret observed features differently. We show that AI is more effective in persuading the decision-maker when the disagreement is due to attention differences rather than comprehension differences. We also show that the AI's interpretability shapes how the decision-maker attributes the sources of disagreement and, in turn, whether they follow the AI's recommendation. Our main result is that making AI uninterpretable can actually enhance persuasion and, in the presence of career concerns, improve decision accuracy.

A principal and an agent can launch a project under unanimous consent. Their individual payoffs from the project depend on an underlying state, and the agent privately knows his own preference. The principal can conduct a test to learn about the state and then communicate with the agent, but has limited commitment, as she may misreport her findings. We show that limited commitment makes binary tests optimal. Moreover, when players' preferences are positively aligned, the optimal test is a threshold test. When their preferences are negatively aligned, the optimal test is either an interval test or a tail test, depending on the agent's relative risk attitude. Additionally, the principal can benefit from screening the agent through a menu of tests, which admits a simple structure regardless of the complexity of the agent's type space.