William A. Brock’s research while affiliated with University of Wisconsin–Madison and other places

... Water quality models for river environments based on SDEs have addressed various aspects, including the influence of suspended sediment concentrations on fluvial processes (Jing et al., 2020) [50], dissolved oxygen and biological oxygen demand (Mansour, 2023) [51], antibiotic bacterial dynamics (Gothwal and Thatikonda, 2020) [52], nutrient loads with a focus on regime shifts in river environments (Park and Rao, 2014) [53], and phycocyanin as a pigment indicator of cyanobacteria (Carpenter and Brock, 2024) [54]. Theoretical studies have also explored topics such as the most probable pollution control paths [55] and stochastic differential games for basin-wide carbon and pollution control Song et al., 2024) [56,57]. ...

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Stochastic volatility model with long memory for water quantity-quality dynamics

... Perrin et al. (2022), Cohen et al. (2024)) and some papers in the economics literature that solve continuous time models without complicated distributions or with one-dimensional distribution approximations (e.g. Duarte et al. (2024), Gopalakrishna (2021), Fernández-Villaverde et al. (2023, Sauzet (2021), Achdou et al. (2022b), Barnett et al. (2023)). By contrast, we develop and compare a range of finite dimensional approximations: reducing to finite agents, discretizing the state space, and projection onto a finite set of basis functions. ...

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Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models

... Indeed, they find that the rate of adjustment to equilibrium is realistically slow -that is, if atmospheric CO 2 doubled then Earth would eventually be 2.8 ○ C warmer, noting CO 2 has risen about 50% from 280ppm: see Figure 14.1(a). Brock and Miller (2023) show that moist energy-balance models, which allow for horizontal (latitudinal) net heat transport by way of moisture like those of Langen and Alexeev (2007) and Merlis and Henry (2018) mentioned above are equivalent to a cointegrated system. Although the system is nonlinear in the structural parameters, they can be identified to test for PA and conduct impulse response functions and forecasts that realistically allow for more warming near the poles than near the equator. ...

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Econometric forecasting of climate change

... Arī attiecībā uz stiprām vētrām līdzšinējo datu analīze liecina par nebūtiskām vai teritoriāli atšķirīgām izmaiņām, kamēr nākotnes projekcijas norāda uz iespējamu vētru biežuma pieaugumu Ziemeļeiropā (Ahola et al., 2021;Bednar-Fiedl et al., 2022). Turklāt, vērtējot klimata pārmaiņu ietekmi un turpmāko to izpausmju raksturu pielāgošanās un SEG emisiju samazināšanas politiku kontekstā Eiropas ziemeļu daļā, būtiski ir ņemt vērā arī tā dēvētās polārās pastiprināšanās (polar amplification) ietekmi, kas paredz, ka jebkādas izmaiņas radiācijas bilancē rada lielākas izmaiņas polārajos reģionos nekā vidēji pasaulē (Brock and Xepapadeas, 2020). ...

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Mitigation options for the challenges caused by climate change in the civil protection and disaster management system in Latvia [in Latvian]

... However, this statement must be qualified by emergence of various dialects of English, such as Spanglish spoken by some 40 million of US residents. Moreover, many individuals, especially immigrants, acquire incomplete or partial acquisition of English (Brock et al. 2023). In fact, the number of immigrants to US, UK, and Australia, who do not speak English at all or speak it poorly ranges from 17 to 21 percent. ...

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Patterns of language acquisition: the diffusion of languages

... Dynamic energy prices affect energy structure and energy use decisions. Climate change is modeled to reduce productivity like Cai et al. (2023). Fossil fuel use in the production increases carbon emissions and carbon stocks, leading to global warming (Nordhaus 2010). ...

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Social cost of carbon under endogenous social adaptation

... As a result, decision-makers might favor policies that perform well for a variety of models in the proximity of the benchmark (approximate) model. Robust control is one rigorous way to model this problem; see, for example, Hansen and Sargent (2008), Hansen and Sargent (2010), Anderson et al. (2014), Li et al. (2016), Hansen and Sargent (2022), and Barnett et al. (2022). In this section we introduce model uncertainty regarding the damages resulting from climate change through the variables γ 1 , γ 2 . ...

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An integral transformation approach to differential games: a climate model application

... First, the coefficients of ∆cpu t−1 and ∆cpu t−2 are negative and statistically significant at the 5% level or better, except in the cases in Germany and India, which have opposite signs for either the ∆cpu t−1 or ∆cpu t−2 . The evidence of energy stocks for countries with a negative sign reflects the fact that the NPV < 0, which may be attributed to a spillover of climate uncertainty to business production or household consumption as ∆cpu t causes uncertainty and financial instability (Raza et al. 2024;Kayani et al. 2024) that negatively affect economic activity (Barnett et al. 2022). Under this perspective, a rise in climate uncertainty tends to induce governments to impose taxes on carbon emissions, which raise production costs and, in turn, reduce profits, especially for companies that heavily rely on fossil fuel energy to produce goods. ...

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Effect of Climate Changes, Induced Risks, and Oil Price Appreciation on Energy Stock Returns in World Markets

... Huntingford et al. (2017) approximate pathways using parsimonious statistical models. Miller and Brock (2024) go a step further by locally weighting the parameters of a family of parsimonious statistical models that approximate hundreds of peer-reviewed AR5 pathways. Novel pathways, called quasi-representative concentration pathways, can be created that mimic pathways resulting in similar GHG concentrations in a target year, often 2100, but that were produced by much more complicated models. ...

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Econometric forecasting of climate change

... At best, the selection operating after combining component parts into a technology optimally balances efficiency and production costs (e.g., Bettinger, 2009). However, human behaviour is often far from rational, and, therefore, selective decisions are not optimal in many cases (Bentley & O'Brien, 2015;Bentley et al., 2011;Darley & Kaufmann, 1997;O'Brien et al., 2019;Shennan, 2013;Solée et al., 2013). Declining originality and the extinction of technological designs over time generally correlates with the increasing longevity of surviving models (Gjesfjeld et al., 2016). ...

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Convergent Evolution of Prehistoric Technologies: the Entropy and Diversity of Limited Solutions