Endogenous income elasticities

Missio, Fabrizio J. Article Endogenous income elasticities PSL Quarterly Review Provided in Cooperation with: Associazione Economia civile, Rome Suggested Citation: Missio, Fabrizio J. (2025) : Endogenous income elasticities, PSL Quarterly Review, ISSN 2037-3643, Associazione Economia civile, Rome, Vol. 78, Iss. 312, pp. 51-66, https://doi.org/10.13133/2037-3643/18918 This Version is available at: https://hdl.handle.net/10419/324128 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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To view a copy of this license visit http://creativecommons.org/licenses/by-nc-nd/4.0/ vol. 78 n. 312 (March 2025) Endogenous income elasticities FABRICIO J. MISSIO* Abstract: This paper deepens the analysis of the income elasticities of import and export demand in relation to the real exchange rate (RER) within a balance of payments constrained growth framework. It identifies how the RER can affect these elasticities and explores the resulting implications. A key highlight is the RER’s ability to induce structural changes toward more complex and technologyintensive sectors. To illustrate this, a formal multisectoral model is presented, demonstrating the conditions under which a higher RER can alleviate external constraints. Finally, several related considerations are addressed. Federal University of Minas Gerais (CEDEPLAR/UFMG), Belo Horizonte, Brazil, email: fjmis[email protected]mg.br How to cite this article: Missio F.J. (2025), “Endogenous income elasticities”, PSL Quarterly Review, 78 (312), pp. 51-66. DOI: https://doi.org/10.13133/2037-3643/18918 JEL codes: O11, E12, F43 Keywords: balance-of-payments constraint, multi-sectoral Thirlwall’s Law, income elasticities Journal homepage: https://rosa.uniroma1.it/rosa04/psl_quarterly_review The pioneering work of Thirlwall (1979) introduced the standard balance of payments constraint growth model (BPCG). In this model, the only safe way to boost a country's growth rate while maintaining the intertemporal balance of payments equilibrium is through structural changes that increase (reduce) the income elasticities of the demand for exports (imports). The question, therefore, becomes how differences in elasticities cause different growth rates and, above all, what factors determine this. To answer this, researchers have incorporated, into this set of models, functions that try to capture the endogeneity of the income elasticities of international trade (among others: McCombie and Roberts, 2002; Palley, 2003; Botta, 2009). My co-authors 1 and I have argued that the real exchange rate (RER) can affect the productive structure, promoting structural change and altering income elasticities. More specifically, we argue that maintaining a competitive RER incentivizes research and innovation by enhancing selffinancing conditions and access to credit. This, in turn, facilitates the modernization and diversification of productive capacities, ultimately expanding export capacity and reducing * I would like to express my gratitude to the participants of the CNPq project entitled “New Green Developmentalism: Institutions and Public Policies for Reindustrialization with Social Equity” (n. 404978/2023-1) for their valuable contributions and the FAPEMIG (a research-supporting foundation of Minas Gerais state) (APQ-01964-18). 1 I especially mention Frederico G. Jayme Jr, Hugo Carcanholo Iasco Pereira, Luciano Gabriel, José Luis Oreiro, and Ricardo Araújo. Special issue on premature deindustrialization and climate change: global North and South perspectives 52 Endogenous income elasticities PSL Quarterly Review imports in the long run. Furthermore, this environment supports sectors characterized by higher complexity, technological advancement, and productivity, which tends to ease external constraints and foster economic growth in developing countries. However, I believe it is essential to clarify the transmission mechanisms that underlie the hypothesis of income elasticity endogeneity. This is precisely the objective of this article. More specifically, I propose to develop the transmission mechanisms between the RER and income elasticities of international trade further, showing how the RER can affect nonprice competitiveness through structural change and, thus, relax external constraints. Following this, I present a simplified and didactic extension of the multisectoral BPCG framework, integrating the three main transmission mechanisms discussed throughout the article. I then explore the conditions under which the RER can relax external constraints. In summary, the primary theoretical contribution of this paper is to support the hypothesis that the income elasticities of import and export demand are endogenous to RER within a BPCG framework. This work is not intended to be an exhaustive review of the entire literature, as the topic of the effects of the RER on the economy is vast and multifaceted. Readers are encouraged to engage more deeply with the existing literature, including the works of Razmi et al. (2012), Blecker (2016), Rapetti (2020), Demir and Razmi (2022), Palazzo and Rapetti (2023); these offer valuable insights. Additionally, this study can be seen as a complement to previous works developed by myself and co-authors. Naturally, I have benefited greatly from these discussions, and I am grateful to my colleagues for their consistently fruitful contributions. 1. Theoretical aspects In post-Keynesian literature, the RER has been somewhat neglected. In the context of the so-called BPCG models, the long-term equilibrium growth rate depends on the ratio between the income elasticities of exports and imports. Changes in the RER are considered irrelevant for long-term growth, either because of empirical evidence that price elasticities of exports and imports are low (so that the impact of an RER depreciation on the growth rate of exports and imports is limited) or because terms of trade do not show a systematic trend toward appreciation or depreciation in the long run (McCombie and Roberts, 2002, p. 92). According to Thirlwall (2002, p. 69), achieving a higher growth rate over the long term while adhering to the intertemporal balance of payments equilibrium requires structural changes that boost the income elasticity of exports and reduce it for imports. In Thirlwall’s model, the direction of causation flows from elasticities, which reflect the production structure, to growth. As the author points out, this is the basic assumption of all classic core-periphery models, such as those of Prebisch (1950), Myrdal (1957), Seers (1962), and Kaldor (1970). Pasinetti’s (1981, 1993) work on structural economic dynamics advances this discussion. The author demonstrates that changes in the production structure lead to alterations in growth, given the different rates of sectoral demand expansion. In other words, each sector has a particular capacity (a different elasticity) to benefit from increases in output. This idea, along with the operation of an external constraint on growth, was incorporated by Araújo and Lima (2007) into a formal model, analogous to Thirlwall’s, which retains Pasinetti’s multisectoral dynamics. The final result, expressed in the equation known as the Multisectoral Thirlwall’s Law, shows that a country’s per capita income growth rate is directly proportional to the growth rate of its exports (given by the sectoral income elasticity of demand multiplied by the world economy’s growth F.J. Missio 53 PSL Quarterly Review rate) and inversely related to the income elasticity of the sectoral import demand, with both elasticities weighted by the relative shares of the sectors in the trade composition. However, analyses of how variations in exchange rate policy can drive structural changes 2 in economies are still in their early stages. For example, within the BPCG framework, this dimension is often underexplored or insufficiently addressed. In these models, the income elasticities associated with foreign trade serve a dual purpose: they not only determine aggregate demand but also reflect a range of supply-side factors that influence the economy’s structural competitiveness. Then, the external constraint determined by income elasticities can be influenced only by changes in RER levels if the economy undergoes permanent RER depreciation or appreciation. This is valid because the direct effects of exchange rate policy variations on growth are considered, while the potential effects on technological progress, capital accumulation, and productive heterogeneity – and consequently on the elasticities themselves – are overlooked. Therefore, further analysis is needed to deepen the understanding of the connection between the RER and income elasticity. In other words, existing analyses assume that the channels affecting the productive structure operate through the stimuli exerted by RER variations on demand and/or the wage structure. However, while these are important, it is acknowledged that they do not capture the full range of effects. For example, a competitive RER can influence the supply side of the economy by inducing an increase in the industry’s share of the product (see Ottonello et al., 2024). Since this sector exhibits a higher average productivity compared to others, this change tends to enhance the efficiency of the entire economy. Therefore, the starting point for addressing this gap is the understanding that the RER level can influence productivity and the economy’s productive structure, driving changes in patterns of specialization and competitiveness through other mechanisms as well. The hypothesis of endogenous income elasticities of foreign trade expands the analysis by allowing for the examination of additional effects of the exchange rate on growth. Furthermore, it enhances our understanding of the factors that determine these elasticities. 3 Some studies have incorporated functions into BPCG models to capture the endogeneity of elasticities. McCombie and Roberts (2002) integrate structural change into Thirlwall’s Law by introducing hysteresis in the parameters that determine the economy’s long-term growth rate. In this scenario, the ratio of the income elasticities of demand for exports and imports is specified as a nonlinear function of past growth rates. Palley (2003) suggests that the income elasticity of import demand is a negative function of excess capacity. The rationale behind this approach is that imports are related to economic “bottlenecks”. As excess capacity and unemployment decrease, these bottlenecks become more significant, thereby increasing the share of imports in income growth. Botta (2009) argues that, in developing countries, the income elasticities of export (import) demand are a positive (negative) function of the share of manufacturing in domestic output. It is also acknowledged that the income elasticities of import and export demand are endogenous to the RER level (Barbosa-Filho, 2006; Missio and Jayme Jr., 2012; Ferrari et al., 2013; Oreiro et al., 2015; Missio et al., 2017). According to Missio and Jayme Jr. (2012), the starting point is to observe that there are other mechanisms (not explored by the literature) through which the RER level influences productivity 2 Structural change is understood as the reorganization of the productive structure, reflected in a country’s trade specialization pattern. 3 In summary, it is assumed that changes in the productive structure, which reflect modifications in elasticities, alter the external constraints and, therefore, that policies that promote such structural changes have effects on growth. 54 Endogenous income elasticities PSL Quarterly Review and the productive structure of the economy, thereby altering the pattern of specialization and competitiveness. These “new” mechanisms are associated with the possibility that maintaining a competitive RER 4 can establish incentives for, for example, technological progress. More specifically, currency depreciation – increasing firms’ profits and their capacity for self-financing – affects the funds that are available to these firms to undertake investment projects related to research and innovation. 5 RER appreciation promotes a redistribution of income from profits to wages, which implies a reduction in firms’ ability to self-finance. This leads to decreased availability of internal funds for acquiring new technologies. Additionally, firms face increased difficulties in accessing external financing due to information asymmetries in financial markets, resulting in credit rationing. Consequently, even with the potential to acquire inexpensive technology from abroad, various productive sectors may remain unable to invest in modernizing their productive capacity. On the other hand, with a competitive RER, it is expected that firms will undertake innovative activities, leading to greater productive heterogeneity (for example, a larger variety of goods produced) and structural homogenization, as technological progress is now attained by sectors not traditionally linked to external markets. In the more backward sectors, where the returns on innovative activities are higher, it is expected that discontinuities will be swiftly overcome. 6 An increase in productive heterogeneity, especially in tradable sectors, underscores the Kaldorian insights from “Verdoorn’s Law”, which highlights a positive link between industrial output growth and productivity. This growth leads to transformative changes in productive structures and demand composition, which, in turn, promote new processes and product innovations in the industrial sector. Such growth supports the expansion of business operations and the adoption of modern technology, enhancing productivity. This shift not only drives internal sectoral innovation but also lays the groundwork for increased external economic interactions. Additionally, a competitive RER boosts external demand, fostering output growth and cumulative productivity gains, particularly through dynamic economies of scale, where technological changes become irreversible. This cycle of growth and increasing returns accelerates productivity and technological advancement, enhancing competitiveness in external markets through mechanisms such as learning by doing, using, interacting, and exporting. 7 In short, sustaining a competitive RER fosters greater productive heterogeneity, advances technological progress, enhances the capacity to finance investments, and increases overall labour productivity. This ensures, over time, a higher income elasticity of demand for exports. Similarly, the income elasticity of demand for imports decreases as domestic manufacturing diversifies and 4 Discussing a competitive RER requires considering its level. Achieving a competitive rate requires implementing policies over a certain period that lead to a significant and sustained devaluation. The impact of the RER on the productive structure is partly due to this change in its level. Therefore, the terms competitive RER, RER devaluation, and RER undervaluation are often used interchangeably. 5 The empirical literature shows that the main determinants of R&D spending and physical capital investment are cash flow and sales volume (Hall, 1992; Himmelberg and Petersen, 1994; Bond et al., 1999). These are two variables that are positively affected by depreciations in the RER level. See also Dao et al. (2021). 6 It is implicitly assumed that technology is one of the essential elements in long-term growth, as improvements in production techniques lead to increases in productivity and an acceleration of the growth rate, allowing for the incorporation of excess labour and a reduction in structural heterogeneity. Moreover, it is acknowledged that structural change can be promoted by the very accumulation of capital, which leads to a reduction in the technological gap, as new technologies are typically embodied in new machinery and equipment (Fagerberg, 1994). Thus, since both capital accumulation and technological innovation are influenced by the level of the RER, it is evident that the RER also has effects on growth from the supply side of the economy. 7 The increase in productive heterogeneity in a “dual” economy à la Lewis allows for an increase in labour productivity through the reallocation of labour from lagging nontradable sectors to advanced tradable sectors. F.J. Missio 55 PSL Quarterly Review the technology incorporated in these products advances. Therefore, a depreciated RER enhances productive diversity and the technological sophistication of domestic goods, reducing reliance on imports and subsequently lowering the income elasticity of demand for imports. 2. RER, structural change, and the endogenous income elasticities The main argument in support of the hypothesis of endogenous income elasticities of foreign trade, relative to the RER level, is that the exchange rate can induce structural change and, consequently, modify a region’s or country’s economic structure, thereby improving its performance in international trade in a sustained manner over time (Missio and Jayme Jr., 2012; Bresser-Pereira et al., 2015; Marconi et al., 2021). Thus, to clarify these points, it is assumed that structural change occurs because the RER level influences the productive structure in three dimensions: i) the share of each sector/product in total imports and exports (composition effect); ii) the number of sectors (products) existing (produced) in the economy (specialization effect); and iii) the attractiveness of products and/or the intensity of technological progress embodied in the products (sophistication effect). The key question now is to identify the mechanisms through which the RER can generate composition, specialization, and sophistication effects (which are not necessarily independent of one another). In general, these mechanisms can be identified as follows: a) Composition effect: the RER is a crucial tool for promoting growth through temporary, yet sufficiently prolonged, changes in the relative prices of tradable and nontradable goods. Sustaining a stable and competitive RER can realign the productive structure towards technologically advanced tradable goods, enabling short-term impacts on aggregate demand from international trade to facilitate long-term economic growth. The facilitation of access to international markets stimulates production in export sectors, generating positive dynamic externalities across the economy, such as learning from competition in external markets and attracting foreign direct investment. This enhances the productivity and competitiveness of domestic products. For developing countries that have progressed in their industrialization, maintaining a competitive RER particularly benefits the industrial sector by facilitating the acceptance of the Kaldorian implications of Verdoorn’s Law, which links industrial output growth to productivity growth. As industrial production expands, new processes are adopted, new businesses emerge, and existing firms grow, enabling the adoption of modern equipment and thus increasing overall economic productivity. Some studies in the literature that address these links are Barbosa-Filho (2006), Cimoli et al. (2013), Ferrari et al. (2013), Missio et al. (2017), Libman et al. (2019) and Palazzo (2024a, 2024b). b) Diversification effect: this refers to the changes produced by RER on the variety of goods (sectors) that make up the export and import baskets. From the perspective of exports, the argument has two main points. i) A competitive RER encourages export-oriented investments by facilitating domestic firms’ access to external markets. This suggests that economic development is shaped by the investment rate, which is, in turn, influenced by the exchange rate, especially concerning export-driven investments. These investments result in diversification of production. ii) Given that technological progress largely stems from capital accumulation – where new technologies are typically embedded in new machinery and 56 Endogenous income elasticities PSL Quarterly Review equipment – it is reasonable to expect the addition of new products to the export basket (Missio and Jayme Jr., 2012; Oreiro et al., 2015). Furthermore, a variant of this effect can be observed in how the RER influences the functional distribution of income. Specifically, changes in income distribution, which are impacted by variations in the RER, affect the productive structure, ultimately determining the degree of specialization in production (Dosi et al., 1990; Missio and Jayme Jr., 2012). Regarding imports, the competitive RER reduces the variety of imported goods, concentrating imports on essential goods necessary for the functioning of the economy. As the level of economic development increases, the reliance on these goods diminishes, as domestic production begins to meet local market demand. c) Sophistication effect: the RER can substantially impact technological progress embedded in products. Specifically, currency devaluation boosts corporate profits and enhances firms’ capacity for self-financing, thereby increasing available funds for investment in research and innovation projects. This leads to a greater availability of internal funds for acquiring new technologies, and it reduces firms’ reliance on external financing, particularly since credit markets often face rationing due to information asymmetries. Consequently, under a competitive exchange rate, companies are more likely to engage in innovative activities that incorporate higher levels of technology into their products, enhancing their quality and appeal in international markets. 8 See Missio and Jayme Jr. (2012), Caglayan and Demir (2019) and Marconi et al. (2020). Identifying these mechanisms is crucial; however, that alone does not clearly demonstrate their effects on income elasticities. To progress in this area, applying sectoral models can be an effective approach. To illustrate this, we note that the aggregate income elasticities of exports can be viewed as a weighted average of sectoral elasticities. Formally, this can be expressed as: 𝜀 =∑𝜔𝑋𝑖𝜀𝑖 𝑘 𝑖=1 (1) where 𝜀 is the aggregate income elasticity, 𝜔𝑋𝑖 represents the share of sector 𝑖 in the export basket, 𝜀𝑖 is the income elasticity of sector 𝑖, and 𝑘 is the number of products/sectors exported. This weighted formula captures the influence of sectoral elasticities on the aggregate elasticity, reflecting the different contributions of each sector. Equation (1) formalizes the idea that a country’s export profile is composed of 𝑘 goods, each with a specific income elasticity 𝜀𝑖, whose contribution to the determination of 𝜀 depends on its share in that profile, 𝜔𝑋𝑖. By using equation (1) and simplifying it under the assumption that the effects are independent, we can demonstrate the effect of the RER on the aggregate elasticity of the exports by considering each of the three main effects discussed above. i) Considering the composition effect, we have: 𝜀(𝜃)=∑𝜔𝑋𝑖(𝜃).𝜀𝑖 𝑘 𝑖=1 (1.1) 8 The increase in R&D activities (sophistication effect), combined with the emergence of new business units (composition effect), leads to the introduction of new products, reinforcing the specialization effect. Furthermore, it is important to emphasize that the sectoral sophistication effect has implications for other sectors of the productive structure, as structural homogenization is expected, since technological progress is now also incorporated in sectors that are not linked to the external market. Given that the returns on innovative activities are higher in the lagging sectors, it is expected that the discontinuities will be quickly overcome. F.J. Missio 57 PSL Quarterly Review where 𝜃 is the RER level. A competitive RER promotes a change in the productive structure in favour of high-tech tradable goods, which have a higher income elasticity of demand. It is important to note that, while the values of the elasticities remain unchanged, the share of the sectors associated with higher elasticities does change. This implies that the aggregate value of 𝜀 will increase. ii) Considering the diversification effect, we argue that modifications in the long-term RER level impact the quantity of goods (sectors) that make up the export import profile. In formal terms, k is a function of the RER level. 𝜀(𝜃)=∑𝜔𝑋𝑖.𝜀𝑖 𝑘(𝜃) 𝑖=1 (1.2) iii) In the case of the sophistication effect, since there is a change in the degree of technology incorporated into the products, the income elasticity associated with each product changes: 𝜀(𝜃)=∑𝜔𝑋𝑖.𝜀𝑖 𝑘 𝑖=1 (𝜃) (1.3) It is assumed that the first two effects influence the aggregate elasticity of imports in opposite directions. Specifically, a competitive RER tends to decrease the share of goods with a higher degree of technological intensity in the import portfolio and to reduce the number of imported products. The sophistication effect does not apply. 3. Endogeneity in the multisectoral model This section aims to present a formal argument that integrates the key issues discussed. Specifically, the proposed formalization seeks to account for the effects of variations in the RER on the productive structure (structural change) in the three dimensions outlined in the previous section, while also considering the hypothesis of the endogeneity of elasticities. In formal terms, this implies adopting a modified version of Thirlwall’s multisectoral law, that is: 𝑦𝑑=(∑𝜌𝑖(𝜃)𝜀𝑖(𝜃) 𝑘(𝜃) 𝑖=1 )/(∑𝜑𝑖(𝜃)𝜋𝑖 𝑛(𝜃) 𝑖=1 )𝑦𝐸 (2) where 𝑦𝑑 is the domestic income; 𝑦𝐸 is the external income, 𝜌𝑖 (𝜑𝑖) represents the share of sector i in exports (imports), 𝜀𝑖 (𝜋𝑖) is the income elasticity of demand for exports (imports), 𝑘 (𝑛) is the number of sectors/products that make up the exports (imports), and 𝜃 is the RER level. Equation (2) specifically incorporates the idea that structural change is endogenous to the RER. 9 Even if the number of sectors remains constant and the elasticities do not change, variations in the RER can still affect the participation of each sector in the productive structure and, consequently, can influence the growth rate (composition effect). Additionally, equation (2) 9 Equation (2) supports the findings of the multisectoral model discussed by Araújo and Lima (2007), indicating that, even when elasticities remain constant, structural changes can impact the overall growth rate. These changes often result from shifts in demand composition – due not to changes in elasticities but rather to the varying participation of each sector in aggregate exports or imports – driven by evolving tastes or preferences, as suggested by Engel’s law. Additionally, it aligns with the results of Missio et al. (2017), demonstrating how RERs affect technological progress through the mechanism of cumulative causation, known as the sophistication effect. 58 Endogenous income elasticities PSL Quarterly Review incorporates the idea that the RER can influence the number of sectors in the economy (diversification effect), particularly those linked to the international market (where sophistication effect is most prominent). From equation (2), we can demonstrate that (see appendix): 𝑑𝑦𝑑/𝑑𝜃 =[(∑(𝜌𝑖′(𝜃)𝜀𝑖(𝜃)+𝜌𝑖(𝜃)𝜀𝑖′(𝜃)) 𝑘(𝜃) 𝑖=1 )(∑𝜑𝑖(𝜃)𝜋𝑖 𝑛(𝜃) 𝑖=1 )− (∑𝜌𝑖(𝜃)𝜀𝑖(𝜃) 𝑘(𝜃) 𝑖=1 )(∑𝜑𝑖 ′(𝜃)𝜋𝑖 𝑛(𝜃) 𝑖=1 )]/[(∑𝜑𝑖(𝜃)𝜋𝑖 𝑛(𝜃) 𝑖=1 )2]𝑦𝐸 (3) To advance the analysis of the sign of this derivative, we note that: i) 𝑑 𝑘 𝑑 θ >0 – Currency devaluations increase the number of export sectors connected to international trade. According to Bresser-Pereira (2012), the RER acts as a kind of switch that either “turns on” or “turns off” firms that are technologically and administratively competent in relation to global demand. ii) 𝑑 𝑛 𝑑 θ <0 – A competitive RER tends to decrease the diversity of imported products and the involvement of foreign sectors in the national economy. This happens for two main reasons: first, it enables the domestic economy to focus on producing goods with higher technological intensity (the sophistication effect); second, the price effect redirects demand towards imports. As a result, domestically manufactured goods progressively cater to the demand for technologically advanced products, whereas imports become concentrated on less technologically intensive, more cost-effective goods. iii) 𝑑 𝑘 𝑑 θ >𝑑 𝑛 𝑑 θ – Tastes, preferences and habits, along with investments in advertising, marketing, and the establishment of distribution channels, create a certain rigidity in the declining demand for imported goods. As a result, the presence of international sectors in the domestic economy contracts more slowly than the expansion of domestic firms into international markets. Additionally, we can consider that 𝜌𝑖(𝜃), 𝜀𝑖(𝜃), and 𝜑𝑖(𝜃) are linear in 𝜃, that is: i) 𝜌𝑖(𝜃)=𝑎𝑖(𝜃)+𝑏𝑖 (4) ii) 𝜑𝑖(𝜃)=−𝑒𝑖(𝜃)+𝑓𝑖 (5) iii) 𝜀𝑖(𝜃)=𝑐𝑖(𝜃)+𝑑𝑖 (6) Equation (4) illustrates the “composition effect” on exports. A competitive RER fosters exports, investment, and industrialization, thus enhancing the participation of more technologyintensive sectors. 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