Testing a Goodwin model with general capital accumulation rate

We perform econometric tests on a modified Goodwin model where the capital accumulation rate is constant but not necessarily equal to one as in the original model (Goodwin, 1967). In addition to this modification, we find that addressing the methodological and reporting issues in Harvie (2000) leads to remarkably better results, with near perfect agreement between the estimates of equilibrium employment rates and the corresponding empirical averages, as well as significantly improved estimates of equilibrium wage shares. Despite its simplicity and obvious limitations, the performance of the modified Goodwin model implied by our results show that it can be used as a starting point for more sophisticated models for endogenous growth cycles.Comment: 39 page

Past production constrains current energy demands: persistent scaling in global energy consumption and implications for climate change mitigation

Climate change has become intertwined with the global economy. Here, we describe the importance of inertia to continued growth in energy consumption. Drawing from thermodynamic arguments, and using 38 years of available statistics between 1980 to 2017, we find a persistent time-independent scaling between the historical time integral $W$ of world inflation-adjusted economic production $Y$, or $W\left(t\right) = \int_0^t Y\left(t'\right)dt'$, and current rates of world primary energy consumption $\mathcal E$, such that $\lambda = \mathcal{E}/W = 5.9\pm0.1$ Gigawatts per trillion 2010 US dollars. This empirical result implies that population expansion is a symptom rather than a cause of the current exponential rise in $\mathcal E$ and carbon dioxide emissions $C$, and that it is past innovation of economic production efficiency $Y/\mathcal{E}$ that has been the primary driver of growth, at predicted rates that agree well with data. Options for stabilizing $C$ are then limited to rapid decarbonization of $\mathcal E$ through sustained implementation of over one Gigawatt of renewable or nuclear power capacity per day. Alternatively, assuming continued reliance on fossil fuels, civilization could shift to a steady-state economy that devotes economic production exclusively to maintenance rather than expansion. If this were instituted immediately, continual energy consumption would still be required, so atmospheric carbon dioxide concentrations would not balance natural sinks until concentrations exceeded 500 ppmv, and double pre-industrial levels if the steady-state was attained by 2030

Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing

We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets ${\cal D}_1,\dots,{\cal D}_N$ for the same learning model $f_{\theta}$. Our objective is to minimize the cumulative deviation of the generated parameters $\{\theta_i(t)\}_{t=0}^T$ across all $T$ iterations from the specialized parameters $\theta^\star_{1},\ldots,\theta^\star_N$ obtained for each dataset, while respecting the loss function for the model $f_{\theta(T)}$ produced by the algorithm upon halting. We only allow for continual communication between each of the specialized models (nodes/agents) and the central planner (server), at each iteration (round). For the case where the model $f_{\theta}$ is a finite-rank kernel regression, we derive explicit updates for the regret-optimal algorithm. By leveraging symmetries within the regret-optimal algorithm, we further develop a nearly regret-optimal heuristic that runs with $\mathcal{O}(Np^2)$ fewer elementary operations, where $p$ is the dimension of the parameter space. Additionally, we investigate the adversarial robustness of the regret-optimal algorithm showing that an adversary which perturbs $q$ training pairs by at-most $\varepsilon>0$, across all training sets, cannot reduce the regret-optimal algorithm's regret by more than $\mathcal{O}(\varepsilon q \bar{N}^{1/2})$, where $\bar{N}$ is the aggregate number of training pairs. To validate our theoretical findings, we conduct numerical experiments in the context of American option pricing, utilizing a randomly generated finite-rank kernel.Comment: 54 pages, 3 figure

Estimates of economic and environmental damages from tipping points cannot be reconciled with the scientific literature

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