Economic growth in the age of ubiquitous threats: How global risks are reshaping growth theory

Gomes, Orlando Article Economic growth in the age of ubiquitous threats: How global risks are reshaping growth theory Economics: The Open-Access, Open-Assessment Journal Provided in Cooperation with: De Gruyter Brill Suggested Citation: Gomes, Orlando (2024) : Economic growth in the age of ubiquitous threats: How global risks are reshaping growth theory, Economics: The Open-Access, Open-Assessment Journal, ISSN 1864-6042, De Gruyter, Berlin, Vol. 18, Iss. 1, pp. 1-15, https://doi.org/10.1515/econ-2022-0059 This Version is available at: https://hdl.handle.net/10419/306075 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Review Article Orlando Gomes* Economic Growth in the Age of Ubiquitous Threats: How Global Risks are Reshaping Growth Theory https://doi.org/10.1515/econ-2022-0059 received July 13, 2023; accepted November 24, 2023 Abstract: One of the most outstanding accomplishments of the economic science over the last decades is the development of a sound and coherent theory of economic growth. Research in growth theory has demonstrated that significant and systematic increases in well-being are attainable whenever the right formula is implemented. When combined with efficiency, the ingredients of this formula – innovation, the diffusion of ideas, and human capital accumulation –can drive the economy toward a virtuous path of sustained growth. Notwithstanding, this is an overly optimistic view of growth that does not account for the many obstacles that the creation of wealth may encounter. The current essay surveys cutting-edge research on growth theory to conclude in favor of a paradigm shift: the main concern is no longer just with how to correctly combine production inputs, but with how their efficient use is eventually hampered by a large collection of worldwide risks and threats. Global risks come in many shapes (they can be classified as economic, environmental, geopolitical, societal, and technological) but, in any case, they call for a reexamination of growth theory. Keywords: growth theory, growth models, global risks, economic disasters, rare events JEL classification: O41, O33, O43, O44 1 Introduction The World Economic Forum, an independent international organization whose main purpose is to foster public-private cooperation at the highest levels of decision-making, publishes every year, since 2006, the Global Risks Report. The aims and scope of this publication consist of a thorough systematization and assessment of the main and most pressing threats that humanity currently faces. The report defines global risk as “the possibility of the occurrence of an event or condition which, if it occurs, would negatively impact a significant proportion of global GDP, population or natural resources.”(2023 Report, p. 5). As characterized, the notion of risk should be interpreted loosely, to include every danger, menace, and potential disaster that threatens our fragile collective existence. The mentioned report compartmentalizes risks into five broad categories: economic, environmental, geopolitical, societal, and technological. The contents of each category are self-explanatory. On the economic front, macroeconomic risks are highlighted; these include the prospect of economic stagnation and recessions, rising inflation and unemployment, asset bubbles, and debt crises, especially in large economies. Also relevant, regarding the threats posed to the world economy, are the possibility of commodity shocks, the collapse of supply chains, and the proliferation of illicit activities, such as organized crime, trade in counterfeit goods, and tax evasion and fraud. In what concerns the second category, the environment, a long list of threats can also be enunciated, including humanmade environmental damages, overexploitation and mismanagement of critical natural resources, climate change, the loss of biodiversity, extreme weather events, and geophysical disasters. Geopolitical risks encompass terrorism, the threat posed by weapons of mass destruction, geoeconomic and geopolitical confrontations, civil wars, and the dismemberment of multilateral organizations and arrangements. The societal category covers a wide array of risks, from those associated with the spread of infectious diseases  * Corresponding author: Orlando Gomes, Lisbon Accounting and Business School –Lisbon Polytechnic Institute (ISCAL-IPL) and CEFAGE (Univ. Évora –ISCAL) Research Center, ISCAL, Av. Miguel Bombarda, 20, 1069-035 Lisboa, Portugal, e-mail: [email protected], tel: +351 217 984 500 ORCID: Orlando Gomes 0000-0002-7251-8736 Economics 2024; 18: 20220059 Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. (epidemics and pandemics) to many other issues raised by our coexistence in society (e.g., the erosion of public institutions and social cohesion, the deterioration of working conditions and job opportunities, the disillusionment of the youth, or the emergence of large-scale involuntary migrations). Finally, technological risks are, currently, associated with cybercrime and cyberespionage, digital inequality and digital power concentration, and, among others, the eventual inadvertent or malicious breakdown of critical information infrastructures. Most of the aforementioned risks do not manifest themselves in isolation. Although a global crisis may erupt from a single seed of dystopia, this can spread fast, to other areas of the economy and the society, creating what one might designate as a perfect storm. The COVID-19 pandemic and the recent escalation of geopolitical tensions are two prototypical examples of seeds of dystopia that fueled the uprise of many other meaningful threats (e.g., soaring inflation, increasingly worrisome cyber-security breaches, deeper social fragmentation, massive refugee crises, or the rise of inequalities within and among countries). The substantiation of some of the enunciated threats, and even the mere perception that they might somehow materialize, may seriously hamper economic growth in a variety of ways. The challenge that growth theorists nowadays face is precisely to incorporate these threats into their models and to effectively explain how they might influence the pace of material progress as we know it today. This essay undertakes a selective survey of growth theory (of contributions published from 2020 onward) to clarify that most recent additions to the theory acknowledge and are aware of the main obstacles that worldwide economic growth faces. This contrasts with earlier contributions, which were much more focused on efficiency issues and on how countries should successfully combine the available physical, human, and technological inputs with the objective of maximizing intertemporal utility. Although the aim continues to be the same, i.e., the promotion of material well-being, the focal point is that scholars have, today, a much clearer perception that the existing risks might threaten the efficacy of the conventional formulas leading to sustained economic growth. The remainder of the article is organized as follows. Section 2 highlights the pieces of literature that directly and generically approach the impact of probable significant disasters and rare events on the economy’s growth rate. Special focus is placed on an analytical framework capable of quantifying the growth effects of a disaster and, also, the growth impact of the risk itself. In Section 3, technological risks are addressed. The relevant literature is surveyed, and the typical endogenous growth model is reinterpreted in light of the presence of an additional input: robotic capital and/or artificial intelligence. Section 4 proceeds with a reflection on the interplay between the spread of infectious diseases and economic growth. To share ideas and knowledge, human contact is required; however, with increased human contact comes the possibility of faster dissemination of diseases. The worldwide fast dissemination of the COVID-19 pandemic was the direct consequence of the globalized and interconnected world we live in today, which leads to an undeniable piece of evidence: the closer the globalization process brings us together, the stronger it becomes the risk of catastrophic public health events. In Section 5, environmental risks are highlighted. Environmental concerns are progressively becoming an inseparable part of growth analyses. This is illustrated by exploring an adapted version of a recently proposed model of climate change and growth. In Section 6, geopolitical risks are briefly debated. These may take many forms and they can be associated with growth models in many ways. A typical neoclassical growth model allowing for political instability is characterized to illuminate the impactfulness of this type of risk. In Section 7, a few additional notes on economic risks are added to the survey, and Section 8 concludes. 2 The Accommodation of Risks and Disasters in Growth Models Global economic growth is subject to a wide variety of risks. Although these may be somehow interconnected, they are different in nature, and therefore, as expected, different strands of literature deal with the impact of dissimilar threats in distinct ways, as the sections that follow will highlight. Despite this diversity, there are a few recent studies that address, in a generic and abstract way, the potential impact of menaces and actual disasters on growth. These include Barro and Jin (2021), Douenne (2020), Hao et al. (2020), Jovanovic and Ma (2022), and Krishna et al. (2023). The common point in the mentioned studies is the presence of uncertainty associated with some aspects of the growth process: the outcome of the adoption of new technologies might be uncertain, investment decisions might be unpredictable, or stochastic rare events may cause unforeseeable changes in consumption. The model by Douenne (2020) is particularly wellsuited to approach the impact of risks on growth. It is a relatively standard optimal growth model where the combination of recursive utility with a stochastic capital 2Orlando Gomes accumulation process allows for the quantification of the effect of disaster risks and of the consequences of actual disasters over the growth rate derived under an endogenous growth setup. In this section, Douenne’s framework is recovered, and its discussion is further extended. Let K t()represent the stock of physical capital at date t. In this setting, the risk is defined as the probability of occurrence of a negative shock affecting the stock of capital. If the shock materializes, K t()falls to ∼=∈ K tωKtω,0,1() () ( ) ; the lower the value of parameter ω , the stronger are the damages caused by the disaster. Although the impact of the disaster on growth is unequivocally negative, the risk that it poses may accelerate or decelerate growth, depending on the effect on consumption and savings. When faced with a risk, therepresentativeagentmayeithertransferconsumption from the present to the future (precautionary savings) or the other way around (precautionary consumption). The key element in this regard is the intertemporal elasticity of substitution: a low elasticity of substitution (lower than 1) stimulates an increase in savings; a high elasticity of substitution (higher than 1) leads to an anticipation of consumption in thefaceoftherisk.Evidently,theprecautionarysavingsscenario is the one leading to faster long-term growth. Douenne’s model is particularly appealing because it allows for a clear distinction between the notions of intertemporal elasticity of substitution and the coefficient of relative risk aversion (CRRA). This separation is feasible if the agent’s preferences are represented through a recursive utility function of the Epstein-Zin type. In this model, the utility function takes the form: =−⎧ ⎨ ⎩+−)+ ⎫ ⎬ ⎭ −− − − − − Ut γCt t e γ Ut t 1 1d1 d . θρt θ γ γ θ 1d 1 1 1 1  () () [( ( )] (1) In expression (1), Ct( ) and Ut()stand for consumption and utility, respectively. The operator  designates the expectation about future utility. The parameters are the following: ≥ρ 0 is the rate of time preference; ∈+∞θ0, \ 1[){ } is the inverse of the intertemporal elasticity of substitution; and ∈+∞γ0, \ 1[){ } is the CRRA; the higher the value of γ ,the stronger is the aversion to risk. The maximization of utility is subject to a constraint on the accumulation of capital. This is a stochastic differential equation, which is represented under the following form: ∑ =− − − ∼ = Kt Yt Ct t Kt Kt qt d dd . i n ii 1 () [ () ()] [ () ()] () (2) In equation (2), Yt()represents output. In order to guarantee the tractability of the model and also an endogenous growth outcome, constant marginal returns are taken, such that =>Yt AKt A,0() () . In the expression, the accumulation of capital can be hit by ndifferent shocks of amplitude −∼=− K tKt ωKt1 ii () () ( )(); the frequency of the shocks is determined by a Poisson process, such that =qt λ t dd ii  () represents the probability of the occurrence of a disaster of type i; λ i is a positive parameter. No other eventual fluctuations besides those triggered by the rare catastrophic events are considered in this setup, as presented. For the characterized dynamics, the average growth of the stock of capital is written as follows: ∑ ⎡ ⎣ ⎢⎤ ⎦ ⎥=− − − = Kt t Kt ACt Kt ωλ d/d 1 . i n ii 1  () () () () () (3) The maximization of utility in (1) subject to capital accumulation constraint (2) requires employing optimal control techniques for stochastic problems. Following the same procedure as in Douenne (2020), the computation of the Hamilton–Jacobi–Bellman equation conducts to an optimal solution in which the consumption–capital ratio is constant. Under the proposed formulation, on the optimal path, the consumption–capital ratio is as follows: ∑ ⎜⎟ =+ −⎛ ⎝−−− ⎞ ⎠ = − Ct Kt ρ θθθAωγλ 11 1 . i niγ i 1 1 () () (4) The impact of risk and risk aversion over the consumption-capital ratio is contingent on the value of the elasticity of intertemporal substitution, − θ 1 .If < − θ 1 1, then the consumption-capital ratio decreases with risk (with a higher probability of disasters –higher λ i –and with a higher intensity of disasters –lower ωi), and with risk aversion (higher γ ). The opposite results are obtained for > − θ 1 1.If =θ 1 , then the consumption–capital ratio is equal to the rate of time preference. When < − θ 1 1, people increase savings in the face of a given risk; this is a scenario of precautionary savings. When > − θ 1 1, people prefer to increase consumption when confronted with higher uncertainty, a phenomenon that can be designated as precautionary consumption. Substituting the optimal consumption–capital ratio in (4) into (3), one obtains the expected growth rate or the average long-run growth rate (of capital, consumption, and income), ∑∑ ≡⎡ ⎣ ⎢⎤ ⎦ ⎥=⎡ ⎣ ⎢⎤ ⎦ ⎥=⎡ ⎣ ⎢⎤ ⎦ ⎥ =−+ −− −−− = − = g Kt t Kt Ct t Ct Yt t Yt θAρ θθωγλωλ d/d d/d d/d 111 11 . i niγ ii n ii 1 1 1  () () () () () () () () (5) The growth rate in expression (5) involves three terms with different meanings. The first term corresponds to the Economic Growth in the Age of Ubiquitous Threats 3 no-risk outcome, the well-known Euler equation result, according to which the pace of growth is essentially determined by the difference between the marginal return on capital and the rate of time preference. The second term represents the impact of risks on growth; the risk may increase the pace of growth if < − θ 1 1(precautionary savings trigger higher long-term growth). The third term is the impact of the actual occurrence of the disaster, which is necessarily negative. Hence, the proposed framework has the merit of separating the consequences of the threat from those of the disaster itself; they will both negatively influence welfare, but their joint effectongrowthmightnotbenegative if the risk induces, to a large extent, precautionary savings. The above reasoning considers multiple risks (nrisks, to be precise) but no association between them. As mentioned in the introduction, the threat of a large-scale nefarious event (e.g., a pandemic or a war) is just a probable seed of dystopia that easily spreads to many other areas of society or the economy. Hence, one may conceive a scenario in which an initial high-probability–high-intensity risk is just the first step in a chain of foreseeable events with progressively lower intensity and probability of occurring. A stylized form of representing the above reasoning consists of taking a firstriskofprobability = λλ 1 and intensity =ω ω 1 , and a series of subsequent risks obeying conditions =∈ + λ ϕλ ϕ,0,1 ii1( ) and =∈ + ωδωδ,0,1 ii1() . Taking →∞ n (i.e., an infinite series of progressively lower probability –lower intensity potential disasters), the growth rate in expression (5)ispresentableasafunctionoftheeight relevant parameters of the model (Aρθγλωϕ δ ,,,,,,,): =−+ −− −−− −− −−−− −− −− − g θAρ θθλγϕδ ϕ ω ϕϕδ λϕδ ϕ ω ϕϕδ 11 111 11 11 11 . γγ γ 11 1 () () ()( ) () ()() (6) If risks following the initial threat are of some significance, meaning that the values of ϕ and δ are relatively high, then the initial effect of the seed of dystopia is prolonged in time. This effect is clearly negative in respect to the impact of the disaster. However, as remarked earlier, it can be either positive or negative regarding the risk itself, given the value of parameter θ . Douenne (2020) introduces an additional relevant topic, namely the possibility of deliberate risk mitigation. In what respects global risks, the effort to lower them requires an international coordination of efforts, because the large majority of the already highlighted risks are associated with global commons (e.g., the preservation of the environment, peacekeeping, or the prevention of infectious diseases). Because free riding is unavoidable, the international community should at least guarantee a coalition of the willing. Analytically, in the context of the model, risk mitigation consists of diverting a share of income, ∈ τ 0,1( ) ,to reduce the probability of the disaster. Under risk alleviation, the probability of a disaster falls from λ to − λ τ1α ( ) , <<α0 1 . Solving the model in this scenario yields an optimal result for share τ , =⎡ ⎣ ⎢−−⎤ ⎦ ⎥ −− τ ωλα Aγ 11 . γα 11 1 () () (7) One considers that the risk reduction effort is exerted only upon the first risk (the seed of dystopia). Because all other risks depend on the first, the risk reduction spreads over all potential subsequent disasters. In this case, the optimal consumption–capital ratio is =+ −⎡ ⎣ ⎢− −− − −−− −− ⎤ ⎦ ⎥ −− − Ct Kt ρ θθθτA τλγϕδ ϕ ω ϕϕδ 11 1111 11 , αγγ γ 11 1 () () () () () ()( )(8) and the expected growth rate comes, =−−+ − −− −−− −− −− −−− −− −− − g θτA ρ θθ τλγϕδ ϕ ω ϕϕδ λτ ϕδ ϕ ω ϕϕδ 1111 111 11 111 11 . αγγ γ α 11 1 [( ) ] ( )() ()( ) () () ()() (9) The prevention of disasters has a negative direct impact on growth because it diverts resources from capital accumulation, but it has a positive effect via disaster avoidance. The growth effect via risk is, again, dependent on the intertemporal elasticity of substitution. The characterized model is general enough to be applicable to any kind of global risk. However, different types of risks have specificities, concerning growth, that are worth exploring. This exploration begins in the following section, with a discussion about threats of a technological nature. 3 The Wonders of Automation and Artificial Intelligence: What Can Go Wrong? The progress associated with computational capabilities and artificial intelligence opens new significant promising prospects regarding long-term growth. In this respect, a pertinent question is raised by Nordhaus (2021): are we 4Orlando Gomes heading toward a singularity point, i.e., toward a moment in history in which, without much human intervention, growth could accelerate further and further? This idyllic scenario is rapidly discarded by the author, based on empirical estimates and the use of a few logical arguments. The strong idea is that technological wonders are necessarily accompanied by relevant technological risks that must be accounted for in order to prevent major technological disasters. Technological risks are an unavoidable side effect of the progressive sophistication of digital tools and other technical novelties. Such tools rely on increasingly high levels of connectivity and integration, which is necessarily accompanied by rising vulnerabilities. One must not forget that the technologies that foster growth are the same technologies that can be used for criminal activities, espionage, and other fraudulent and destructive activities. Moreover, the eventual path toward the creation of super-intelligent machines can be a threat on its own, because with intelligence comes the ability to reason and to create and frame moral norms. For these reasons, and others (namely, the scarcity and non-renewable nature of most physical resources), it is safe to assert that we are not heading toward a singularity. Most of the endogenous growth literature that equates the role of automation and artificial intelligence is a little bit more down to earth than what the above paragraphs might suggest. The main concern that transpires from such literature respects to the shortand medium-term impact of the new technologies on employment and income distribution. These new technologies support a new form of capital that, unlike physical capital, is a substitute and not a complement to labor. Recent studies addressing automation and growth include Acemoglu and Restrepo (2022), Abeliansky and Prettner (2023), Gasteiger and Prettner (2022), Hémous and Olsen (2022), Klarl (2022), Lu (2021, 2022), Moll et al. (2022), Irmen (2021), Prettner and Strulik (2020), Ray and Mookherjee (2022), and Sasaki (2023). The above-mentioned research proposes a wide variety of models and frameworks that are distinct in their structure and approach, but that share some common ground: in any of the cases, automation replaces labor (at least low-skilled labor), and it allows for enhanced productivity. At the end of the day, the new production capabilities are likely to foster growth, but one should not jump immediately to this conclusion. With automation comes the polarization of jobs and wages and the concomitant increase in income inequality (low-skilled workers lose for high-skilled workers and capital owners). As a significant part of the population loses income, two potentially damaging consequences emerge: a fall in aggregate demand and an increase in social discontentment. These collateral effects might overcome the productivity gains from automation, in what respects growth and, most evidently, in what concerns social welfare. Accounting for automation in standard growth analysis requires adding a new input to the short list of production factors that are typically assumed. This new input is robotic capital (automated machines and processes, and artificial intelligence algorithms). As highlighted by Abeliansky and Prettner (2023), robotic capital mixes features of both traditional inputs: it is like labor, becauseitoccupiesthesameroleas human labor in the production process, and it is like capital, because it can be accumulated and it represents the non-human contribution to production. In the study by Lu (2021), the automation input is directly interpreted as artificial intelligence. This is a special form of capital, with singular and non-trivial properties. It has similarities with human capital, because it can learn and accumulate knowledge by itself; it has similarities with ideas, because they are both nonrival. In the study by Bloom et al. (2023), the distinction between industrial robots and artificial intelligence is made analytically explicit. These are interpreted as two separate inputs in production. Roughly speaking, while robots are a replacement for low-skilled workers in the development of routine tasks, artificial intelligence substitutes for high-skilled workers, who perform non-routine creative tasks. This distinction is important and has consequences for the organization of work, income distribution and, ultimately, growth. While conventional automation processes place downward pressure on the wages of low-skilled workers, thus increasing the skill premium (i.e., the value of the ratio between the wages of high-skilledworkersandlowskilled workers), ChatGPT and related technologies that replicate human thinking and creativity predominantly influence the wages of high-skilled labor (although these cutting-edge technologies may put pressure as well on the subsistence of low-skilled jobs). Consequently, artificial intelligence is likely to contribute to a reduction in the skill premium, as the performance of high-skilled tasks becomes no longer exclusive to imaginative human minds. In either case (i.e., whether machines and algorithms replace humans in the completion of routine activities or cognitive demanding tasks), the phenomenal increase in the efficiency of technologies that replace human participation and effort in production threatens jobs, welfare, and also growth, as it concentrates the means of production in the hands of a few capital owners in detriment of the large army of workers that populate society. Besides industrial robots and ChatGPT-like technologies, yet another novel input might be considered to compose the aggregate production function that underlies growth analyses. This input is big data (Cong et al., 2022), Economic Growth in the Age of Ubiquitous Threats 5 and it differs from robotic capital/artificial intelligence in the sense that it is not a substitute for labor. However, these factors also share some properties: they are nonrival and, unlike human capital, they can be detached from people and concentrated in the hands of a few, thus contributing to strong levels of income and wealth inequality. Besides this, the use of data raises another critical risk for people, namely the risk associated with their privacy. Based on the mentioned literature, a synthesis model can be compiled. Start by assuming a Cobb–Douglas production function, with robotic capital denoted by R t( ) , =+>∈ − Yt AKt Lt Rt A α,0, 0,1 . αα1 () ()[() ()] ( ) (10) In equation (1), standard notation is adopted: Yt Kt, , () () and L(t) represent, respectively, output, physical capital, and labor (for the sake of the exposition let this last variable be constant over time, L(t)=L); Ais the productivity index and α the output–capital elasticity. The substitutability between labor and robotic capital is evident from the expression; in the limit, if all labor is replaced by machines, production is still possible. Define ≡tRt Lϱ /() () and assume the commonly used notations for per capita income and capital. Equation (10) is equivalent to its intensive form counterpart, =+ − y tAkt t1ϱ . αα1 () ()[ ()] (11) In a competitive economy, factor returns correspond with their respective marginal products. In the devised scenario, the wage rate is identical to the rate of return on robotic capital, ==− ⎡ ⎣ ⎢+⎤ ⎦ ⎥ wt r t αA ktt 11ϱ . R α () () ( ) () () (12) The rate of return on physical capital is: =⎡ ⎣ ⎢+⎤ ⎦ ⎥ − rt αA t kt 1ϱ . α1 () () () (13) Under this simple formulation, it is straightforward to observe that the labor income share falls with an increase in the employment of robotic capital: =− + wt yt αt 1 1ϱ . () () () (14) In contrast, if one defines capitalists as the agents who hold any form of capital (physical and robotic), their income share is: +=+ + rtkt r t t yt αt t ϱϱ 1ϱ . R ()() ()() () () () (15) From expression (15), one concludes that as the participation of robotic capital in production increases, the income share of capitalists increases as well. The above logical argumentation can be extended to include the separation between industrial robots and artificial intelligence (Bloom et al., 2023). In this case, production function (10) can be augmented by splitting the human workforce into unskilled labor ( L u ) and skilled labor ( Ls ), and by distinguishing between robotic capital, R t( ) , and artificial intelligence, R t AI(). As remarked earlier, R t( ) is a direct replacement for L u , while R t AI()is a direct replacement for Ls . A conceivable enlarged production function is, then, =+++ >∈ − Yt AKt L Rt L R t Aαβ , 0, , 0,1 . αuβsβαβ AI 1/ () (){[ ()] [ ()]} () () (16) In intensive form, =+++ − y tAktl t lςtϱ . αuβsβαβ1/ () (){[ ()] [ ()]} () (17) In equation (17), lu and l s represent, respectively, the shares of unskilled and skilled labor (their sum is equal to 1); t ϱ () is defined as before (per capita robotic capital) and ≡ ς tRt L AI () ()(per capita artificial intelligence). In the current case, wages and returns from different forms of capital are, respectively, == − +++ + − wt rt αyt ltltlςt 1 ϱϱ , uRuu βsβ1 () () ()() () [ ()] [ ()] (18) == − +++ + − wt r t αyt lςt l tlςt 1ϱ, ssu βsβ RAI 1 () () ()() () [ ()][ ()] (19) =rt αy t kt . () () () (20) The skill premium is straightforward to display, given expressions (18) and (19), =+++ + +++ + − − wt wt ltltlςt lςt l tlςt ϱϱ ϱ . s u uu βsβ su βsβ 1 1 () () () [ ()] [ ()] () [ ()][ ()] (21) The computation of derivative ∂⎛ ⎝⎞ ⎠ ∂ςt wst wut () () () allows us to verify what is the impact of an increase in artificial intelligence technologies over the difference in income between non-skilled and high-skilled workers. For the proposed technology of production, the derivative has a negative sign under condition +>+ l ςt l tϱ su () ( ) , i.e., whenever the number of skilled tasks surpasses the volume of unskilled tasks developed in the economy, the increase in the use of artificial intelligence reduces income inequality (lowers the skill premium). Other meaningful results are attached to the weight of wages and capital returns on income. Equations (18) and (19) directly indicate that the higher the values of ϱ(t) and ς(t), the lower will be the wage income share; 6Orlando Gomes i.e., additional automation, via robotic capital and artificial intelligence, contributes to a decline of the relative income of workers. Consequently, as the values of ϱ(t) and ς(t) rise, reflecting the stronger relative presence of automated processes in production, the more income will be concentrated in the hands of capital owners, which poses a real and concrete danger for social and political stability. To associate all the above reasoning to a growth model, one would need to consider a standard physical capital accumulation equation and an intertemporal felicity function. Then, it would be necessary to add one (or more) robotic capital sector(s) to the analysis: the self-replicating features of robots and, essentially, of artificial intelligence make it reasonable to consider that no other input is required for its generation and that, probably, in the current stage of development, this input would escape the prevalence of diminishing marginal returns. As a result, in this framework, robotic capital and ChatGPT-like technologies become the drivers of endogenous growth. However, this is adifferent type of growth; it is a growth process that largely amplifies inequalities and that changes the structure of demand in the economy. Hence, the analysis of growth in the automated economy clearly requires a modeling framework with heterogeneous agents: by separating workers from capital owners, one will be able to discern how the ongoing unconstrained evolution of technology represents a risk, not only for those who directly suffer with the loss of jobs, but to all people that may end up living in a dystopian world populated by an ever-increasing army of excluded. 4 Lessons from the Pandemic The ravaging global pandemic of the early 2020s raised disquieting interrogations about the reality that we had taken for granted concerning world prosperity and growth. It revealed how a low-risk, huge-impact event may suddenly affect the lives of everyone on this planet. It also showed that accounting for growth is not just an exercise of measuring the quantity and quality of inputs and the efficiency in their use; there are relevant societal issues, in this case about public health, that must be accounted for. As it is evident, the COVID pandemic led to a rethinking of growth theory in the presence of health emergencies and disasters. Meaningful recent work on the macroeconomic consequences of the spread of infectious diseases comprehends the works of Carmona and León (2023), Fogli and Veldkamp (2021), Hao et al. (2023), Lu (2023), and Shi (2023). The most common strategy in assessing the growth implications of the propagation of infectious diseases, followed by most of the above-mentioned literature, consists of merging benchmark optimal growth models with standard epidemiological analytical frameworks of the SIR (susceptible–infectious–recovered) type. As individuals pass from each epidemiological state to the next, the economy also evolves from one growth stage to another. Evidently, periods in which a significant percentage of the population is in an infectious state are periods of slower growth. The channels from disease to growth are essentially three: labor productivity, human capital accumulation, and population growth. Combined, the various negative effects might have devastating consequences for the world economy and the living standards of people around the world. Some of the work on the impact of infectious diseases on growth, most noticeably that of Fogli and Veldkamp (2021), establish a link between the spread of diseases and the diffusion of ideas and technology. The argument is that interaction among people diffuses both ideas and diseases. Therefore, given their health conditions and systems, countries must choose an adequate balance between knowledge diffusion and the risk of the transmission of infirmities. Knowledge and infectious pathogens have one characteristic in common: they are both nonrival; however, they have an antagonistic nature in the sense that the first is a global good, while the second is a global bad. The assessment of externalities must be pondered: the positive externalities originating in knowledge diffusion must be weighed against the negative externalities that the diffusion of virus and germs brings. As an illustration of the growth implications of disease propagation, consider the following straightforward reasoning. Imagine a standard growth model, with physical and human capital as production inputs. In this setup, the driver of growth is human capital accumulation; thus, let us concentrate on the motion of this input, represented in time ( ) 0.5 Figure 1: Double-logistic epidemic diffusion. Economic Growth in the Age of Ubiquitous Threats 7 what follows by variable H t(). Human capital is subject to obsolescence at rate ∈δ0,1 , h() and its production is subject to constant returns; however, there is a productivity loss in the education sector directly attributable to illness. Let variable ϕ t( ) represent the prevalence of an infectious disease, and let x t( ) be the productivity loss directly attributable to the disease. With the above information, one can display the growth rate of human capital (which will also be the growth rate of the economy under a trivial two-sector optimal growth setup) in the following terms: =− − > Ht Ht BϕtxtδB 1,0 . h () () [()()] (22) Assume that x t( ) is time-invariant and that the prevalence rate evolves, as in the study by Hao et al. (2023), following a double-logistic rule, i.e., =⎛ ⎝+−+⎞ ⎠ −− ϕ tϕ ee 1 11 1 . at at 012 () (23) All parameters in equation (23) are positive values. Figure 1 illustrates the evolution of the infection rate for == = ϕ aa2.5, 1, and 0.4 012 . After a first phase of fast increase in the share of infected in the population, this value gradually falls to zero. In this simple framework, given equation (22), in the absence of the disease, the economy grows at a constant rate. The effect of the epidemic is to provoke a transient fall in the growth rate. Figure 2 illustrates this effect for the spreading mechanism displayed in Figure 1 and characterized through equation (23). The above reasoning directly applies to the dissemination of a disease but, in fact, it is adaptable to many other societal threats. Any event leading to social distrust or the breakdown of social ties (e.g., the growing youth disillusionment mentioned in the introduction) may cause a negative impact on the accumulation of human capital. In the sketched framework, the impact is transitory, in the sense that it is expected that the health issue will be resolved sooner or later. Some societal problems might be more profound and eventually trigger a growth slowdown of a more permanent nature. 5 The Greatest of Them All: The Environmental Externality As remarked in the latest editions of the Global Risks Report, environmental threats (climate change, extreme weather episodes, biodiversity losses, depletion of natural resources, and man-made disasters) occupy the first place in the ranking of global risks, in terms of both likelihood and expected damaging impact. Due to their catastrophic nature, environmental risks are hard to reconcile with economic theory and, in particular, with growth theory, which privileges “business as usual.”Nonetheless, there is a voluminous new literature searching for a coherent integration between the two. It is safe to say that environmental concerns have become an increasingly relevant part of the theory of economic growth. Contributions are dispersed and approach diverse aspects of the environmental menace. One of the most prominent topics concerns the impact of pollution or, more precisely, carbon emissions (Oliveira & Lima, 2022; Olijslagers et al., 2023; van den Bremer & van der Ploeg, 2021). Measuring the social cost of carbon is a complicated task, given the inherent long-term uncertainty that makes it unfeasible to compute undisputable discount rates to quantify the current value of future damages. In growth models, the environment is frequently added to the analysis through the exploration of the pollution-growth trade-off: pollution is a by-product of production, while environmental quality is an argument of the utility function. The solution for the underlying conundrum consists of promoting the transition to clean production technologies (Hart, 2020). Casey (2024) and Hassler et al. (2021) develop growth models in which technical change endogenously evolves to increase energy efficiency and to adapt to environmental changes. Energy dependence will then determine the structure of production and the pace of growth. Fabozzi et al. (2022) look at the economy from the perspective of green growth. Green growth is associated with the notion of putting science and technology at the service of environmental preservation, at the same time they facilitate time () ( ) Figure 2: Transitional path implied by the spread of an infectious disease. 8Orlando Gomes Sasaki, H. (2023). Growth with automation capital and declining population. Economics Letters,222(January), 110958. Shi, S. (2023). Knowledge, germs, and output. Review of Economic Dynamics,48(April), 297–319. Sriket, H., & Suen, R. M. (2022). Sources of economic growth in models with non-renewable resources. Journal of Macroeconomics,72(June), 103416. Thies, C. F., & Baum, C. F. (2020). The effect of war on economic growth. Cato Journal,40(1), 199–212. Tohmé, F., Caraballo, M. A., & Dabús, C. (2022). Instability, political regimes and economic growth. 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