We develop a dynamic equilibrium model of a tokenized platform with endogenous decentralized verification. The framework distinguishes miners, who incur mining costs to validate transactions, from non-mining participants, who hold tokens only for transactional benefits. Competition and subsidy-financed mining rewards generate a dual regime: with a small miner base, rents attract all entrants into mining; with a large base, rent dissipation channels entry toward non-mining participation. The model predicts a doubleS shaped adoption trajectory and a discrete upward shift in user-base volatility at the switching point. Using on-chain data, we find robust empirical support that the miner base is the primary fundamental determinant of token adoption and valuation.

Sex-specificity has been reported in a wide range of diseases and complex traits. While sex-specific genetic effects have been documented for certain traits, the genetic mechanisms underlying sex differences in most traits remain largely unexplored. With its large sample size and wide range of diseases and traits, the UK Biobank—a large, prospective cohort study containing health history, phenotypic measurements, and genetic data for over 500,000 individuals—provides an opportunity to explore sexually dimorphic genetic architectures in a large number of traits and diseases. Here, we present a sex-specific analysis of 733 sex-stratified complex trait GWAS for 361,194 white British individuals in the UK Biobank. Among these 733 traits, we detected sex-specific locus in 520 of them. These 520 candidate traits with sex-specific genetic effects were classified to 270 distinct groups. Using a systematic sex-specific discovery-replication analysis, we identify 489 loci showing sex-specific effects on 127 of the candidate trait groups, among which three of them having the most numbers of traits showing replicable signals were further investigated, including fat mass related traits (12 traits), heart disease related traits (7 traits) and body impedance related traits (6 traits). We identify pathways with sex-biased enrichment patterns from exploratory enrichment analyses based on QTL-associated genes. In addition, we present further evidence for significant sex-specific genetic effects in 25 traits by comparing the prediction performance of sex-specific polygenic risk scores (PRS).

With the increasing accessibility of individual-level data from genome wide association studies, it is now common for researchers to have individual-level data of some traits in one specific population. For some traits, we can only access public released summary-level data due to privacy and safety concerns. The current methods to estimate genetic correlation can only be applied when the input data type of the two traits of interest is either both individual-level or both summary-level. When researchers have access to individual-level data for one trait and summary-level data for the other, they have to transform the individual-level data to summary-level data first and then apply summary data-based methods to estimate the genetic correlation. This procedure is computationally and statistically inefficient and introduces information loss. We introduce GENJI (Genetic correlation EstimatioN Jointly using Individual-level and summary data), a method that can estimate within-population or transethnic genetic correlation based on individual-level data for one trait and summary-level data for another trait. Through extensive simulations and analyses of real data on within-population and transethnic genetic correlation estimation, we show that GENJI produces more reliable and efficient estimation than summary data-based methods. Besides, when individual-level data are available for both traits, GENJI can achieve comparable performance than individual-level data-based methods. Downstream applications of genetic correlation can benefit from more accurate estimates. In particular, we show that more accurate genetic correlation estimation facilitates the predictability of cross-population polygenic risk scores.

Genetic risk prediction for non-European populations is hindered by limited Genome-Wide Association Study (GWAS) sample sizes and small tuning datasets. We propose JointPRS, a data-adaptive framework that leverages genetic correlations across multiple populations using GWAS summary statistics. It achieves accurate predictions without individual-level tuning data and remains effective in the presence of a small tuning set thanks to its data-adaptive approach. Through extensive simulations and real data applications to 22 quantitative and four binary traits in five continental populations evaluated using the UK Biobank (UKBB) and All of Us (AoU), JointPRS consistently outperforms six state-of-the-art methods across three data scenarios: no tuning data, same-cohort tuning and testing, and cross-cohort tuning and testing. Notably, in the Admixed American population, JointPRS improves lipid trait prediction in AoU by 6.46%-172.00% compared to the other existing methods.

Congenital heart disease (CHD) is a leading cause of infant mortality. We analyzed de novo mutations (DNMs) and very rare transmitted/unphased damaging variants in 248 prespecified genes in 11,555 CHD probands. The results identified 60 genes with a significant burden of heterozygous damaging variants. Variants in these genes accounted for CHD in 10.1% of probands with similar contributions from de novo and transmitted variants in parent–offspring trios that showed incomplete penetrance. DNMs in these genes accounted for 58% of the signal from DNMs. Thirty-three genes were linked to a single CHD subtype while 12 genes were associated with 2 to 4 subtypes. Seven genes were only associated with isolated CHD, while 37 were associated with 1 or more extracardiac abnormalities. Genes selectively expressed in the cardiomyocyte lineage were associated with isolated CHD, while those widely expressed in the brain were also associated with neurodevelopmental delay (NDD). Missense variants introducing or removing cysteines in epidermal growth factor (EGF)-like domains of NOTCH1 were enriched in tetralogy of Fallot and conotruncal defects, unlike the broader CHD spectrum seen with loss of function variants. Transmitted damaging missense variants in MYH6 were enriched in multiple CHD phenotypes and account for ~1% of all probands. Probands with characteristic mutations causing syndromic CHD were frequently not diagnosed clinically, often due to missing cardinal phenotypes. CHD genes that were positively or negatively associated with development of NDD suggest clinical value of genetic testing. These findings expand the understanding of CHD genetics and support the use of molecular diagnostics in CHD.

Uncovering environmental factors interacting with genetic factors to influence complex traits is important in genetic epidemiology and disease etiology. We introduce BiVariate Linkage-Disequilibrium Eigenvalue Regression for Gene-Environment interactions (BV-LDER-GE), a statistical method that detects the overall contributions of G × E interactions in the genome using summary statistics of complex traits. In comparison to existing methods which either ignore correlations with additive effects or use partial information of linkage disequilibrium (LD), BV-LDER-GE harnesses correlations with additive genetic effects and full LD information to enhance the statistical power to detect genome-scale G × E interactions.

To construct a stochastic version of [R. J. Barro, J. Polit. Econ. 87, 940-971 (1979)] normative model of tax rates and debt/GDP dynamics, we add risks and markets for trading them along lines suggested by [K. J. Arrow, Rev. Econ. Stud. 31, 91-96 (1964)] and [R. J. Shiller, Creating Institutions for Managing Society's Largest Economic Risks (OUP, Oxford, 1994)]. These modifications preserve Barro's prescriptions that a government should keep its debt-gross domestic product (GDP) ratio and tax rate constant over time and also prescribe that the government insure its primary surplus risk by selling or buying the same number of shares of a Shiller macro security each period.

Lucas and Stokey (1983) motivated future governments to confirm an optimal tax plan by rescheduling government debt appropriately. Debortoli et al. (2021) showed that sometimes that does not work. We show how a Ramsey plan can always be implemented by adding instantaneous debt to Lucas and Stokey’s contractible subspace and requiring that each continuation government preserve that debt’s purchasing power instantaneously. We formulate the Ramsey problem with a Bellman equation and use it to study settings with various initial term debt structures and government spending processes. We extract implications about tax smoothing and effects of fiscal policies on bond markets.

We propose a tractable model of dynamic investment, division sales (spinoffs), financing, and risk management for a multi-division firm that faces costly external finance. The model highlights the importance of considering the intertwined nature of the different policies. Our main results are as follows: (1) risk management considerations prescribe the allocation of resources based not only on the divisions' productivity — as in standard models of ''winner picking'' — but also their risk; (2) firms may choose to voluntarily spin off productive divisions to increase liquidity; (3) diversification can reduce firm value especially in low liquidity states, as it increases the cost of a spinoff and hampers liquidity management; (4) with corporate socialism, liquidity is less valuable since it is less costly to replenish the firm's liquidity through a spinoff; and (5) division-level investment is set such that the ratio between marginal q and the marginal cost of investing in each division equals the marginal value of cash.

The disparity in genetic risk prediction accuracy between European and non-European individuals highlights a critical challenge in health inequality. To bridge this gap, we introduce JointPRS, a novel method that models multiple populations jointly to improve genetic risk predictions for non-European individuals. JointPRS has three key features. First, it encompasses all diverse populations to improve prediction accuracy, rather than relying solely on the target population with a singular auxiliary European group. Second, it autonomously estimates and leverages chromosome-wise cross-population genetic correlations to infer the effect sizes of genetic variants. Lastly, it provides an auto version that has comparable performance to the tuning version to accommodate the situation with no validation dataset. Through extensive simulations and real data applications to 22 quantitative traits and four binary traits in East Asian populations, nine quantitative traits and one binary trait in African populations, and four quantitative traits in South Asian populations, we demonstrate that JointPRS outperforms state-of-art methods, improving the prediction accuracy for both quantitative and binary traits in non-European populations.

We study the high-dimensional asymptotic behavior of inferences based on summary statistics that are widely used in genome-wide association studies (GWAS) under model misspecification. The high dimensionality is in the sense that the number of single-nucleotide polymorphisms (SNPs) under consideration may be much larger than the sample size. The model misspecification is in the sense that the number of causal SNPs may be much smaller than the total number of SNPs under consideration. Specifically, we establish two parameters of genetic interest, namely, the consistency and asymptotic normality of the estimators of the heritability and genetic covariance. Our theoretical results are supported by the findings of empirical studies involving simulated and real data.

Predicting genetic risks for common diseases may improve their prevention and early treatment. In recent years, various additive-model-based polygenic risk scores (PRS) methods have been proposed to combine the estimated effects of single nucleotide polymorphisms (SNPs) using data collected from genome-wide association studies (GWAS). Some of these methods require access to another external individual-level GWAS dataset to tune the hyperparameters, which can be difficult because of privacy and security-related concerns. Additionally, leaving out partial data for hyperparameter tuning can reduce the predictive accuracy of the constructed PRS model. In this article, we propose a novel method, called PRStuning, to automatically tune hyperparameters for different PRS methods using only GWAS summary statistics from the training data. The core idea is to first predict the performance of the PRS method with different parameter values, and then select the parameters with the best prediction performance. Because directly using the effects observed from the training data tends to overestimate the performance in the testing data (a phenomenon known as overfitting), we adopt an empirical Bayes approach to shrinking the predicted performance in accordance with the estimated genetic architecture of the disease. Results from extensive simulations and real data applications demonstrate that PRStuning can accurately predict the PRS performance across PRS methods and parameters, and it can help select the best-performing parameters.

We propose a stochastic control model to study corporate investment with generalized investment frictions, including investment lags and various of adjustment costs. We find that the dominance of the ``good news principle'' or ``bad news principle'' is determined by the joint effect of investment lags and adjustment costs, reconciling the results in Bernanke (1983) and Bar-Ilan and Strange (1996). Meanwhile, we resolve disputes between the net present value rule and the real option method of making investment decisions, and we find that the accuracy of the NPV rule depends on both investment lags and the opportunity cost of adjustment. Moreover, we calibrate our model with aggregated firm data and show that the co-existence of investment lags and the opportunity cost of adjustment is the key to explaining the correlation between investment and lagged profit.

We consider a long-term portfolio choice problem with two illiquid and correlated assets and formulate it as an eigenvalue problem in the form of a variational inequality. The eigenvalue is associated with the portfolio’s optimal long-term growth rate, and the free boundaries implied by the variational inequality correspond to the optimal trading strategy. After proving the existence and uniqueness of viscosity solutions for the eigenvalue problem, we perform an asymptotic expansion in terms of small correlations and obtain semi-analytical approximations of the free boundaries and the optimal growth rate. Our leading order expansion implies that the free boundaries are orthogonal to each other at four corners and have C1 regularity. We propose an efficient numerical algorithm based on the expansion, which proves to be accurate even for large correlations and transaction costs. Moreover, following the approximate trading strategy, the resulting growth rate is very close to the optimal one.

Using the Panel Study of Income Dynamics Survey, we reveal the non-linear dependence, between-squares correlation, between stock returns and earning risk exists. To understand how this non-linear dependence affects household life-cycle profile, we develop a life-cycle model that incorporates between-squares correlation and shows that this non-linear dependence can explain low participation rate and moderate risky asset shares. Empirical studies support the model’s predictions that households with higher between-squares correlations are less likely to participate in the stock market and lower their risky asset holdings conditional on participation.

An optimal tax and government borrowing plan in a setting with tax distortions (Barro, 1979) locally pin down the marginal cost of servicing government debt, called marginal p. An option to default determines the government’s debt capacity and its optimal state-contingent risk management policies make its debt risk-free. Optimal debt-GDP ratio dynamics are driven not only by three widely discussed forces, 1.) a primary deficit, 2.) interest payments, and 3.) GDP growth, but also by 4.) hedging costs. Hedging fundamentally alters debt transition dynamics and equilibrium debt-capacity, which are at the center of the recent 'r-g' and debt sustainability discussions. We calibrate our model and make comparative dynamic quantitative statements about the debt-GDP ratio transition dynamics, equilibrium debt capacity, and how long it will take the US to attain debt capacity.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

We propose a unified dynamic framework to study the economics of the supply side of bitcoin mining, such as endogenous transaction fees, the miners' liquidation policies, and endogenous inventory holdings, in the face of declining system block rewards and stochastic demand. The model yields two economic insights: First, high jump risk and transaction fees income can be major forces driving miners to significantly reduce their inventory even when bitcoin prices are relatively low. Second, the model explains the observed co-movements of average transaction fees, average block sizes, and Bitcoin prices.

BACKGROUND:Both lifestyle and genetic factors confer risk for cardiovascular diseases, type 2 diabetes, and dyslipidemia. However, the interactions between these 2 groups of risk factors were not comprehensively understood due to previous poor estimation of genetic risk. Here we set out to develop enhanced polygenic risk scores (PRS) and systematically investigate multiplicative and additive interactions between PRS and lifestyle for coronary artery disease, atrial fibrillation, type 2 diabetes, total cholesterol, triglyceride, and LDL-cholesterol. METHODS:Our study included 276 096 unrelated White British participants from the UK Biobank. We investigated several PRS methods (P+T, LDpred, PRS continuous shrinkage, and AnnoPred) and showed that AnnoPred achieved consistently improved prediction accuracy for all 6 diseases/traits. With enhanced PRS and combined lifestyle status categorized by smoking, body mass index, physical activity, and diet, we investigated both multiplicative and additive interactions between PRS and lifestyle using regression models. RESULTS:We observed that healthy lifestyle reduced disease incidence by similar multiplicative magnitude across different PRS groups. The absolute risk reduction from lifestyle adherence was, however, significantly greater in individuals with higher PRS. Specifically, for type 2 diabetes, the absolute risk reduction from lifestyle adherence was 12.4% (95% CI, 10.0%-14.9%) in the top 1% PRS versus 2.8% (95% CI, 2.3%-3.3%) in the bottom PRS decile, leading to a ratio of >4.4. We also observed a significant interaction effect between PRS and lifestyle on triglyceride level. CONCLUSIONS:By leveraging functional annotations, AnnoPred outperforms state-of-the-art methods on quantifying genetic risk through PRS. Our analyses based on enhanced PRS suggest that individuals with high genetic risk may derive similar relative but greater absolute benefit from lifestyle adherence.

Recently polygenetic risk score (PRS) has been successfully used in the risk prediction of complex human diseases. Many studies incorporated internal information, such as effect size distribution, or external information, such as linkage disequilibrium, functional annotation, and pleiotropy among multiple diseases, to optimize the performance of PRS. To leverage on multiomics datasets, we developed a novel flexible transcriptional risk score (TRS), in which messenger RNA expression levels were imputed and weighted for risk prediction. In simulation studies, we demonstrated that single‐tissue TRS has greater prediction power than LDpred, especially when there is a large effect of gene expression on the phenotype. Multitissue TRS improves prediction accuracy when there are multiple tissues with independent contributions to disease risk. We applied our method to complex traits, including Crohn's disease, type 2 diabetes, and so on. The single‐tissue TRS method outperformed LDpred and AnnoPred across the tested traits. The performance of multitissue TRS is trait‐dependent. Moreover, our method can easily incorporate information from epigenomic and proteomic data upon the availability of reference datasets.