Income and emotional well-being: Evidence for well-being plateauing around $200,000 per year

Is emotional well-being monotonically increasing in the level of income or does it reach a plateau at some income threshold, whereafter additional income does not contribute to further well-being? Conflicting answers to this question has been suggested in the academic literature. In a recent paper, using an income threshold of $100,000 per year, Killingsworth et al. (2023) appears to have resolved these conflicts, concluding that emotional well-being is monotonically increasing in income for all but the unhappiest individuals. In this paper, we show that this conclusion is sensitive to the placement of the income threshold at which the relationship between emotional well-being and income is allowed to plateau. Using standard econometric methods, we propose a data-driven approach to detect the placement of the threshold. Using this data-driven income threshold, a flat relationship between household income and emotional well-being above a threshold around$200,000 per year is found. While our analysis relaxes the assumption of a pre-specified income threshold, it relies on a number of other assumptions, which we briefly discuss. We conclude that although the analysis of this paper provides some evidence for well-being plateauing around $200,000 per year, more research is needed before any definite conclusions about the relationship between emotional well-being and income can be drawn

Hybrid scheme for Brownian semistationary processes

We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. [Quant. Finance 16(6), 887-904, 2016], respectively.Comment: 33 pages, 4 figures, v4: minor revision, in particular we have derived a new expression (3.5), equivalent to the previous one but numerically more convenient, for the off-diagonal elements of the covariance matrix Sigm

The Local Fractional Bootstrap

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method to two empirical data sets: we assess the roughness of a time series of high-frequency asset prices and we test the validity of Kolmogorov's scaling law in atmospheric turbulence data

Energy, economy, and emissions: A non-linear state space approach to projections

We propose a non-linear state-space model to examine the relationship between CO$_2$ emissions, energy sources, and macroeconomic activity, using data from 1971 to 2019. CO$_2$ emissions are modeled as a weighted sum of fossil fuel use, with emission conversion factors that evolve over time to reflect technological changes. GDP is expressed as the outcome of linearly increasing energy efficiency and total energy consumption. The model is estimated using CO$_2$ data from the Global Carbon Budget, GDP statistics from the World Bank, and energy data from the International Energy Agency (IEA). Projections for CO$_2$ emissions and GDP from 2020 to 2100 from the model are based on energy scenarios from the Shared Socioeconomic Pathways (SSP) and the IEA's Net Zero roadmap. Emissions projections from the model are consistent with these scenarios but predict lower GDP growth. An alternative model version, assuming exponential energy efficiency improvement, produces GDP growth rates more in line with the benchmark projections. Our results imply that if internationally agreed net-zero objectives are to be fulfilled and economic growth is to follow SSP or IEA scenarios, then drastic changes in energy efficiency, not consistent with historical trends, are needed

Inference and forecasting for continuous-time integer-valued trawl processes and their use in financial economics

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and asymptotic normality of this estimator. The same methods allow us to develop probabilistic forecasting methods, which can be used to construct the predictive distribution of integer-valued time series. In a simulation study, we document good finite sample performance of the likelihood-based estimator and the associated model selection procedure. Lastly, the methods are illustrated in an application to modelling and forecasting financial bid-ask spread data, where we find that it is beneficial to carefully model both the marginal distribution and the autocorrelation structure of the data. We argue that integer-valued trawl processes are especially well-suited in such situations

Composite likelihood estimation of stationary Gaussian processes with a view toward stochastic volatility

We develop a framework for composite likelihood inference of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that has been proposed to describe the random log-spot variance of financial asset returns. A simulation study shows that it delivers good performance in these settings and improves upon a method-of-moments estimation. In an application, we inspect the dynamic of an intraday measure of spot variance computed with high-frequency data from the cryptocurrency market. The empirical evidence supports a mechanism, where the short- and long-term correlation structure of stochastic volatility are decoupled in order to capture its properties at different time scales

Modeling, forecasting, and nowcasting U.S. CO₂ emissions using many macroeconomic predictors

We propose a structural augmented dynamic factor model for U.S. CO2 emissions. Variable selection techniques applied to a large set of annual macroeconomic time series indicate that CO2 emissions are best explained by industrial production indices covering manufacturing and residential utilities. We employ a dynamic factor structure to explain, forecast, and nowcast the industrial production indices and thus, by way of the structural equation, emissions. We show that our model has good in-sample properties and out-of-sample performance in comparison with univariate and multivariate competitor models. Based on data through September 2019, our model nowcasts a reduction of about 2.6% in U.S. per capita CO2 emissions in 2019 compared to 2018 as the result of a reduction in industrial production in residential utilities

Trend analysis of the airborne fraction and sink rate of anthropogenically released CO2

Is the fraction of anthropogenically released CO2 that remains in the atmosphere (the airborne fraction) increasing? Is the rate at which the ocean and land sinks take up CO2 from the atmosphere decreasing? We analyse these questions by means of a statistical dynamic multivariate model from which we estimate the unobserved trend processes together with the parameters that govern them. We show how the concept of a global carbon budget can be used to obtain two separate data series measuring the same physical object of interest, such as the airborne fraction. Incorporating these additional data into the dynamic multivariate model increases the number of available observations, thus improving the reliability of trend and parameter estimates. We find no statistical evidence of an increasing airborne fraction, but we do find statistical evidence of a decreasing sink rate. We infer that the efficiency of the sinks in absorbing CO2 from the atmosphere is decreasing at approximately 0:54%yr-1