Abstract
This chapter presents a formal “stylised model” in an attempt to pull together the ideas introduced in the introductory chapter into a coherent whole. This is intended to facilitate reasoned discussions on how the environmental, social, and economic influences on individual and community wellbeing interact with each other, as well as the complementarities and tradeoffs between them. In future chapters, this will in turn help us formulate policies towards increasing wellbeing on a sustained basis, while taking into account these complementarities and tradeoffs. Each section of the chapter has three sub-sections. First, a verbal and diagrammatic presentation of the core ideas. Second, a mathematical representation of the verbal and diagrammatic discussion, including the motivations of each of the key actors (such as individual consumers, producers, and the government). Third, a list of references (accompanied by a brief discussion) of the empirical literature that attempts to bring evidence to support or challenge the key assumptions of the theoretical model.
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- 1.
See also Galor and Weil (1999, 2000) on the desirability of building unified models.
- 2.
An alternative model can be based on viability theory (see Krawczyk and Judd 2016; Krawczyk and Kim 2014). In fact, we use such a model to perform numerical policy simulations in Chap. 6 of this book. Yet another potential approach to the problem at hand is provided by overlapping generation models (see De La Croix and Michel 2002).
- 3.
One potential criticism is the absence of stochastic, or probabilistic, uncertainty (or risk) in the model. We return to this point in the second part of the book when we introduce radical uncertainty, and explore its implications for the design and implementation of public policy.
- 4.
We reproduce some key derivations of that paper here to set the generic platform for the more specific (stylised) model to be used in the rest of this chapter.
- 5.
This does not imply that individuals have perfect information. In fact, as we will point out later in Chaps. 5 and 6, extensions of the stylised model recognise the existence of fundamental uncertainty. Rather, what is intended is that individuals behave as if they care about current and future generations into the infinite future.
- 6.
From our perspective, introducing minimum capital requirements and associated costs would be an unnecessary complication (see Jakab and Kumhof 2015).
- 7.
Stiglitz (2015) makes a very compelling case for carefully distinguishing between capital (in the sense of produced assets such as machines) and wealth (including “land or other ownership claims giving rise to rents”). Our broader definition of both wealth and capital assets should hopefully address his concerns.
- 8.
Others, such as Gleeson-White (2015), Sachs (2015) refer to six categories of capital but, depending on how we define them, we are essentially referring to the same types of capital; there are no substantive differences here.
- 9.
Hodgson Geoffrey (2006) offers a wider definition of institutions as systems of established and embedded social rules that structure social interactions. Institutions do not only constrain and influence the choices and actions of individual consumers and businesses, but they also perform a critical enabling function – and their evolution is endogenous (see also Arvanitidis 2004).
- 10.
See also Hamilton and Hepburn (2014), Jones and Vollrath (2018, Chap. 7), and also Savioli and Patuelli (2016), who usefully distinguish between three domains (and associated dimensions) of social capital: cognitive (mental processes, concepts, ideas), relational (trust, norms, identity), structural (organisations, institutions, leadership).
- 11.
We admit that proposing a function like \(\phi (\cdot )\) in (2.9) may amount to social engineering. However, without \(\phi (\cdot )\), obtaining environment-enhancing policies can be difficult in the stylised model of this chapter. As we will argue in Chap. 5, this is not the case in models that include complexity and radical uncertainty.
- 12.
This is an attempt to respond to Gough (2015)’s plea that good policy should be taking into account environmental, economic, and social considerations in an integrated way; and, in the context of the environment, consumption as well as production policies should be considered in a complementary fashion.
- 13.
From now on, we will use the term “scientists” to include engineers as well.
- 14.
The possibility of \(H_{t+1} > 1\) exists and has not been formally ruled out in our model. To ensure the health stock remains \(\in (0, \, 1)\) is a modelling problem. If we are to propose optimal solutions, they have first to be feasible. Mathematically, this condition could be achieved via a Lagrange function. But, it would be messy. This problem concerns other indices as well (e.g., \(\varGamma _t^E\)). We recognise it but, for our purposes in this chapter, we can put it to one side for now.
- 15.
Although the generic production function introduced below does include renewable resources as well, this additional complication would not add value to our analysis. We implicitly capture the presence of renewable resources through allowing for “clean” (new) technology in production, in our stylised model.
- 16.
Note that E does not enter the production function directly. Below, in our stylised model, E affects production, through its effect on the health and therefore the productivity of the labour force. L will be less productive if people’s health is adversely affected because of dirty air (hence our reference to health-adjusted labour).
- 17.
To repeat, the term “dirty technology” is not used in a derogatory sense, but simply as a convenient means of differentiating between two types of technology with significantly different impacts on the accumulation of human capital and the preservation of natural capital.
- 18.
- 19.
“The modern world was made by a revolution in ethical judgments about commercial virtues and vices, in particular by an up-valuation of market-tested betterment – [...] the enrichment of ordinary people, by ordinary people, for ordinary people” (McCloskey 2014, pp. 5–6).
- 20.
What is potentially ignored here is what Antonelli (2016) describes as the “evolutionary complexity approach” to endogenous innovation – based on the interplay between evolution, complexity, and Schumpeter (1947)’s idea of creative responses to significant gaps between actual and expected outcomes. We will return to the implications of complexity and radical uncertainty for public policy in Chap. 5.
- 21.
Sunaga et al. (2015) in turn acknowledges his indebtedness to Acemoglu et al. (2006), Aghion et al. (2005), Michalopoulos et al. (2009).
- 22.
In our model, “banks” are both financial intermediaries between savers and investors, and financiers of loans to investors: “In the real world, the key function of banks is the provision of financing, or the creation of new monetary purchasing power through loans [...] The bank therefore creates its own funding, deposits, in the act of lending” (Jakab and Kumhof 2015, p. 3). While, for simplicity, we conceptualise “banks” as playing both roles, in fact the latter is the distinctive role of banks among all financial intermediaries.
- 23.
This section is substantially based on Jakab and Kumhof (2015), and represents a simplified version of their model to suit our purposes. It also borrows ideas from Sunaga et al. (2015).
- 24.
There is also another cost that we should be allowing for, namely the penalty banks have to pay if they do not meet their minimum capital requirements (see Jakab and Kumhof 2015), but that level of detail is not required for our purposes.
- 25.
See Jakab and Kumhof (2015) for an articulation of the micro-foundations of Eq. (2.57).
- 26.
\(Z_{t}\equiv c_{\varOmega _{w}}(\varOmega _{w})+c_{\varOmega _{y}}(\varOmega _{y})+c_{B}(B)\) as in Eq. (2.103) (see Acemoglu et al. 2016).
- 27.
Given the purpose of this chapter, complicating the model by adding final products that can also be imported, or switching to importing the final product but exporting the machines, does not add anything of value to our analysis.
- 28.
For a recent empirical study of the determinants, and population-distribution and heterogeneity, of resilience (in terms of total psychological response) at the individual level, to ten major adverse life events, as well as a useful survey of this literature, see Etilé et al. (2017).
- 29.
The closely related critical question, faced with numerous potential catastrophes, with uncertainties surrounding occurrences and timings, which should society attempt to avert, is carefully analysed by Martin and Pindyck (2015).
- 30.
We want to specifically thank Ken Warren at the New Zealand Treasury for his insights on risk management as resilience-enhancement, particularly in the context of dealing with systemic risks from a policy perspective.
- 31.
In a similar vein, Acemoglu and Robinson (2015) emphasise that, “[...] inequality should not be thought of as always summarized by a single index, such as the Gini index or the top 1% share. Rather, the economic and political factors stressed here determine the distribution of resources more generally [...]” (p. 16).
- 32.
Toledo et al. (2016) provides a very useful summary of the literature on multi-dimensional poverty, as well as alternative measures to capture poverty as exclusion and deprivation. Eiffe (2010) summarises Smith’s and Sen’s work on poverty and notes that they both have emphasised both the multi-dimensional and absolute nature of poverty, and therefore poverty as exclusion and a source of shame has to be conceptualised and measured relative to the society in which it occurs.
- 33.
Strictly speaking \(u(\cdot , \cdots )\) here is different from that in (2.9) and from the subsequent utility functions in the next sections. However, for simplicity, we call all such functions \(u(\cdot , \cdots )\).
- 34.
So are the arguments of \(\varOmega ^{y}(\cdot ,\cdots )\) in Eq. (2.90). In general, it is difficult to assure that these index numbers, which satisfy the respective stock Eqs. (2.84)–(2.87) (and (2.91)–(2.93)) remain in \([0,\, 1]\). An appropriate calibration of the parameters \(\xi ^{\cdot , \cdot }, \delta _t^{\cdot }, \gamma ^{\,\,\cdot }\), etc. can assure this condition for a range of values of \(E_t, S_t,\) etc. Another possibility would be to model the stock equations using the function \(arctan(\cdot )\). E.g., Eq. (2.86) could be modelled as follows:
$$ \varGamma _{t+1}^{E} =\frac{2}{\pi }\arctan \left( (1+\delta ^{\varGamma _{E}})\varGamma _{t}^{E} + \gamma ^{\varGamma _{E}} E_{t}\right) \, $$The right hand side of this equation has the property of decreasing returns and remains between 0 and 1 for positive arguments.
- 35.
Strictly speaking, the same symbol suggests, if not implies, that the expressions are identical. So, by way of example, we should be careful to note, when we use Y in Eq. (2.89) and then again in (2.31), that we are not referring to “the same” Y. However, for our purposes, in both cases we are referring to the single final output produced in our small economy.
- 36.
See comments in footnote 34, Sect. 2.8.2.
- 37.
This section draws heavily on Turnovsky (2013) and Turnovsky and Mitra (2013).
- 38.
In the stylised model, successful scientists become entrepreneurs; and unsuccessful ones generate income as skilled labour.
- 39.
In fact overall wellbeing reflects access to both the private and public components of comprehensive wealth. We are implicitly assuming here that there is equity of access to public components of comprehensive wealth.
- 40.
The corresponding evidence regarding unemployment is presented in Di Tella et al. (2001).
- 41.
The parallel references to unemployment are from Frey and Stutzer (2002).
- 42.
“Most of the radical, revolutionary innovations that have fuelled the dynamics of capitalism – from railroads to the Internet, to modern-day nanotechnology and pharmaceuticals – trace the most courageous, early and capital-intensive ‘entrepreneurial’ investments back to the State.” Mazzucato (2015, p. 2).
- 43.
See also Cowen (2007).
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Karacaoglu, G., Krawczyk, J.B., King, A. (2019). Stylised Model. In: Intergenerational Wellbeing and Public Policy. Springer, Singapore. https://doi.org/10.1007/978-981-13-6104-3_2
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