Growth and International Trade

This chapter is devoted to a simple modeling of the growth of the world economy. To this end a log-linear, CD version of Diamond’s (American Economic Review, 55, 1126–1150, 1965) neoclassical growth model is used as basic overlapping generations (OLG) growth model. This is then extended across several further dimensions in the following chapters. As a simple but complete intertemporal general equilibrium model, it comprises the optimization problems of agents (younger and older households as well as firms) and the market clearing conditions for each model period. The fundamental equation of motion of the efficiency-weighted capital intensity is derived from the first-order conditions for household’s utility and firm’s profit maximization and from labor and capital market clearing conditions. The “golden rule” of capital accumulation ensures that consumption per efficiency capita is maximized over the long run.

This chapter continues the analysis of the basic OLG growth model of the previous chapter. First, the GDP growth rate is defined and related to the growth factor of the (efficiency-weighted) capital intensity. Second, assuming the GDP growth is constant over time and equals the natural growth rate, sufficient conditions for the existence of a unique and globally stable steady state are presented. Third, intergenerational efficiency of the steady state is discussed. Fourth, the comparative dynamics of changes in basic OLG model parameters is illustrated graphically. Fifth, the evolution of the main economic variables, associated with capital intensity along the intertemporal equilibrium path and in steady state, is investigated. Sixth, different concepts of neutral technological progress are compared. Finally, an example of growth accounting is presented in order to demonstrate the empirical significance of technological progress for GDP growth.

This chapter is devoted to the exploration of the relationship between public debt and economic growth in an extended version of the basic OLG growth model described in Chaps. 2 and 3. First, the two-dimensional intertemporal equilibrium dynamics of the debt-to-capital ratio and the efficiency-weighted capital intensity are derived from agents’ FOCs and market-clearing conditions under the assumption of a constant-flow budget policy. Here, in contrast to the basic OLG growth model without public debt, we find multiple steady-state solutions exhibiting both saddle-path and asymptotic stability. Under asymptotic stability there is no unique relationship between public debt and capital accumulation. Starting from a high-debt, low-capital-intensity, and dynamically efficient steady state with a primary budget surplus, the debt-to-GDP ratio can be reduced only by both raising the tax rate and the public expenditure ratio, and it is accompanied by a fall in private capital intensity.

This chapter probes into the pioneering approach of the so-called “new” growth theory, i.e., Romer’s (Journal of Political Economy, 94, 1002–1037, 1986) knowledge externalities in private capital accumulation. After listing the empirical and theoretical shortcomings of the “old” growth theory, the main approaches of the new growth theory are briefly outlined. In Sect. 5.3, knowledge externalities associated with private capital accumulation are introduced into our basic OLG model and the fundamental equation of motion is then derived from the FOCs for utility and profit maximization, and under market clearing. In the subsequent section, the deficiencies of the old growth theory are reconsidered from the perspective of the knowledge externalities of the new growth theory. In Sect. 5.5, public debt is introduced in our new growth model and the effects of variation in the politically fixed net deficit ratio on capital and public debt are investigated. Finally, it is shown that stochastic shocks to total factor productivity in the CD production function, together with investment adjustment costs, can in fact generate GDP time series which resemble empirical evidence.

This chapter presents a neo-Schumpeterian OLG model of self-propelled growth of intermediate-product innovations and over time rising GDP rates. A one-period patent system generates monopoly rents for producers of recently innovated intermediate goods which serve together with competitively produced intermediates as inputs in final good production. The rising variety of intermediates reduces the unit cost and the price of the final good which enables the financing of an ever-increasing rate of intermediate-product innovations by the savings of younger households. Growth in the OLG model of this chapter is attributed to a continuous innovation process driven by rational choices of short-lived agents.

This chapter extends the basic OLG growth model of Chap. 2 by introducing human capital formation and religious participation. In contrast to the R&D models of the new growth theory, the human capital approach based on Lucas’ (Journal of Monetary Economics, 22, 3–42, 1988) seminal contribution helps to explain non-converging GDP per capita across countries despite an unhampered international diffusion of technological knowledge. From the FOCs of households and firms and market-clearing conditions, the fundamental equations of motion for physical capital and the education time per period will be deduced and the existence of non-trivial steady states will be explored. In the model with human capital formation and religious participation, a close relationship between educational attainment and religious participation will be argued and religion will be pointed out as a steady-state phenomenon despite the sociological secularization hypothesis.

This chapter introduces bubbles and financial frictions into the basic OLG growth model of Chap. 2. Contrary to the empirical data supporting the view that bubbles cannot occur in highly developed market economies, in line with Martin and Ventura (Economic growth with bubbles. NBER Working Paper Series, Working Paper 15,870, 2010; Economic growth with bubbles. Mimeo, CREI and Universitat Pompeu Fabra. Accessed on July 28, 2012, from http://​www.​econ.​upf.​edu/​~martin/​EGB.​pdf, 2011a) we now describe sufficient conditions for the existence of rational bubbles in an intertemporal equilibrium in competitive market economies. It turns out that frictions in the financial intermediation between less and highly productive investors are essential not only to establish compatibility between the theory of rational bubbles and empirical evidence, but also to provide a theoretically consistent explanation for the positive correlations between asset price bubbles and capital formation, GDP growth, and aggregate consumption.

Even more than eight decades since the publication of Keynes’ (1936) “General Theory of Employment, Interest, and Money” modern macroeconomists disagree on the notion of “underemployment equilibrium” with so-called “involuntary unemployment.” While the majority of macro theorists trace involuntary unemployment back to frictions and rigidities in the adaptation of wages and product prices to market imbalances, a minority position holds that even under perfectly flexible output prices and wage rates involuntary unemployment might occur. Morishima (Walras’ economics: A pure theory of capital and money. New York: Cambridge University Press, 1977) and more recently Magnani (The Solow growth model revisited. Introducing Keynesian involuntary unemployment, 2015) presume that contrary to the majority view aggregate investment is not perfectly flexible but governed by “animal spirits” of investors. The aim of the present chapter is to integrate the Morishima–Magnani approach into Diamond’s (American Economic Review, 55, 1126–1150, 1965) Overlapping Generations’ (OLG) model with internal public debt subsequently extended by human capital accumulation. It turns out that despite a perfectly flexible real wage and interest rate involuntary unemployment occurs in intertemporal general equilibrium when aggregate investor sentiments are too pessimistic regarding the rentability of investment in real capital. In the model extended by human capital a higher public debt-to-output ratio decreases unambiguously involuntary unemployment, if initially the endogenous output growth rate is higher than the real interest rate.

Intelligent machines (robots) might have vastly destructive consequences for future human welfare and employment. Following Frey and Osborn (The future of employment: How susceptible are jobs to computerization? University of Oxford, 2013), popular media predict that during the next 10 to 20 years, 50% and more of contemporary human jobs will be replaced by robots. Thus, it is natural to ask the question of whether investments in human capital can ameliorate the threatening loss of jobs involving even middle- and high-skilled tasks. Policy advisors mainly recommend public expenditures in order to foster digital competences among the population. However, there might also be an avenue for more traditional human capital investments by individuals and governments. Capital investments in a broader range of human activities than only digital competences might namely ameliorate the rivalry between traditional and digital production in Sachs et al.’s (Robots: Curse or blessing: A basic framework, 2015) overlapping generations (OLG) model. The model focuses on an economy in which final goods are produced by machines without human labor (robots) and by human labor and traditional capital. One key finding is “that an increase in robotic productivity will temporarily raise output, but, by lowering the demand for labor, can lower wages and consumption in the long run. In what we term a paradox of robotic productivity (italics in original), innovations that increase the productivity of robotic investment can, after a generation, lower robotic and total output, and lower the well-being (lifetime utility) of all future generations” (Sachs et al., Robots: Curse or blessing: A basic framework, 2015, 1). Young households in the OLG economy of Sachs et al. (Robots: Curse or blessing: A basic framework, 2015) invest their savings either in robots or traditional capital but nobody invests in human capital. Thus, it remains as the first open question whether Sachs et al.’s (Robots: Curse or blessing: A basic framework, 2015) negative long-run welfare consequences of digitalization also arise when the government as an agent of young households invests in human capital with the aim to counteract the decrease in labor productivity resulting from the substitution of robots for traditional capital. Second. Sachs et al. (Robots: Curse or blessing: A basic framework, 2015) assume full employment while many fear unemployment as a consequence of more productive robots. Thus, the second question is whether robots raise or diminish existing unemployment. The chapter answers both questions by extending the OLG model of Sachs et al. (Robots: Curse or blessing: A basic framework, 2015) through human capital accumulation in line with Glomm and Ravikumar (Journal of Political Economy, 100, 818–834, 1992) and involuntary unemployment in accordance with Magnani (The Solow growth model revisited. Introducing Keynesian involuntary unemployment, 2015). It will be shown which basic model parameters are conducive for beneficial or immiserizing technological change and whether more productive robots will raise or decrease involuntary unemployment.

This chapter extends the basic OLG growth model of Chap. 2 into a two-country OLG model with free trade of two commodities and government bonds but internationally immobile labor and capital. In the original version of the model set-up, young households in both countries hold national fiat money for transaction purposes. The intertemporal choice problem of young households is split into two parts: first, the determination of utility-maximizing asset holding and consumption expenditures and second, the expenditure minimizing allocation of the consumption basket on the two commodities produced domestically and abroad. From the latter, the purchasing power parity in its absolute and relative version is derived, while from the former the uncovered interest parity condition is obtained. Finally, the basic neoclassical (Heckscher–Ohlin) model of inter-sectoral trade is presented as a special case of the general two-country model.

This chapter is devoted to work out the main propositions of neoclassical trade theory in a temporary equilibrium of the two-country OLG model of the previous chapter. Mathematically spoken, the neoclassical trade theory consists of three lemmas and one proposition: the Stolper-Samuelson Theorem, the Rybczynski Theorem, the Heckscher–Ohlin–Samuelson Theorem, and the Heckscher–Ohlin Theorem. We prove all these theorems by using the log-linear utility functions and the Cobb–Douglas production functions of our basic two-country OLG model without money and government bonds. We illustrate the main claims graphically and provide intuitive explanations for them. We also point out empirical limitations of the factor proportion theory (Leontief paradox) and present theoretical advancements like the neo-factor proportion theory and the product-cycle hypothesis to cope with the restrictions of the basic theory.

This chapter leaves (neo-) classical trade theory in order to be able to address the astonishing phenomenon of enormous international trade among similarly developed industrialized countries. The traditional assumptions of perfect competition in all markets, of trade with standardized homogeneous goods and of constant returns to scale are replaced by monopolistic competition in output markets, product differentiation, and decreasing average production costs. This change in the market and cost structure enables us to address intra-industry (intra-sectoral) trade among highly developed countries. In formalizing Linder’s (An essay on trade and transformation. New York: Wiley, 1961) pioneering work on a demand-oriented trade theory in line with the already classic Dixit-Stiglitz (American Economic Review, 67, 297–308, 1977) approach, we present a full-fledged monopolistic equilibrium solution with a 100% of intra-sectoral trade.

This chapter is devoted to developing elements of an economic theory of globalization. At the beginning, different aspects of the globalization of markets and production are considered and the main causes of the globalization process since the early 1970s are enumerated. To entangle the economic consequences of two of these main causes a comparative-static analysis is used first. Since the integration of populous developing countries into the world market economy changes their factor proportions, the simultaneous dynamics of region-specific factor proportions and terms of trade are analyzed in an inter-temporal equilibrium of the Heckscher–Ohlin two-country model. In view of rather high savings rates of Asian economies, a terms of trade improvement for these emerging economies can be foreseen. To check this rather optimistic long-run result Krugman and Venables’ (Quartely Journal of Economics, 110, 857–880, 1995) medium-run core-periphery globalization model is finally analyzed.

While international trade in produced commodities and services raise national welfare by exploiting comparative cost advantages and increasing the number of intermediate products, it is by no means clear how international trade raises the GDP growth rate, a conjecture widely held among laypersons. It is the objective of this chapter to introduce trade in intermediate goods into a two-country version of the OLG model of Chap. 6 in order to be able to analyze the growth-enhancing effects of international trade. It turns out that due to the cost-saving effect of a larger number of intermediate product variants the price of final products steadily decreases and the growth rate of the final product rises compared to the autarky situation.

The Euro crisis 2012 had caused concerns both with respect to public debt sustainability and the stability of exchange rates of highly indebted countries. This chapter investigates these concerns in a two-good, two-country OLG model of the world economy with country-specific saving rates to mimic also Asian economies. We find that the concerns with respect to debt sustainability are warranted since limits for national debt levels do exist. The concerns regarding exchange rate stability are not warranted since unilateral debt expansion does not impact the real exchange rate at all or the impacts are independent of the external balance of the debt-expanding country.

Financial crises associated with banking crises or the recent Pandemic-related lockdowns leave heavy fiscal legacies. For the USA, e.g., an increase in the gross government debt-to-GDP ratio toward nearly 150% is predicted by 2021. Due to its unsustainability, a significant reduction of public debt in the USA and in other advanced countries seems to be indispensable. However, as shown in this chapter, the long-run welfare effects of debt reduction in advanced countries at home as well as on emerging countries are not in accordance with debt reduction necessities. In particular, we show that domestic and foreign welfare decrease when the domestic country (USA) reduces public debt, given that this country has a negative external balance and a lower capital production share than the other country (China) and that dynamic inefficiency holds.

This chapter investigates the domestic and foreign welfare effects of unilateral and multilateral permit policies in a two-country overlapping generations model with producer carbon emissions. We show that the welfare effects of a more stringent cap on emissions depend on the external balance of the policy-implementing country, the dynamic (in)efficiency of the world economy, and the preference for environmental quality. Under dynamic efficiency, the global welfare loss of policy implementation in the net foreign creditor country is lower than of a policy implementation in the net foreign debtor country. Moreover, although the country which has unilaterally implemented a permit policy would gain from a multilateral policy, the associated welfare loss for the other country is larger than that of a unilateral policy abroad.

This chapter compares nationally optimal (Nash equilibrium) to internationally optimal (Pareto efficient) emission permit levels in a two-country overlapping generations model with national emission permit systems and the environment as a global public good. When each government maximizes its steady-state economic and environmental welfare and one country is a net foreign creditor and the other one a net foreign debtor, it is nationally optimal for the creditor country with sufficiently high environmental preferences to choose a stricter permit level than the debtor country. However, the resulting Nash equilibrium permit levels are not Pareto efficient. Depending on the direction and strength of the countries’ differences in external balances and environmental preferences, Pareto efficiency mandates that their permit levels are either adjusted in opposite directions or reduced both.

In spite of the insightful diagnose of the late Milton Friedman that the single currency of the European Economic and Monetary Union (EMU) would not survive the first major economic crisis, the Euro exists since more than two decades. This is all the more surprising as after Euro inception severe external imbalances between Northern and Southern Euro zone countries popped up which brought prominent US economists (Stiglitz 2012; Rodrik 2012) to forecast the collapse of the EMU. In order to understand why these economists feared EMU’s break-up it seems to be expedient to explore the extent to which the external debt accumulation of Southern EMU countries can be attributed to Euro-related capital market integration. We suggest that basically differences in economic fundamentals, associated with the political and cultural heterogeneity of Northern and Southern Euro zone countries, were transformed into the observed external imbalances when interest rates converged.

A dramatic decline of European Monetary Union (EMU) periphery’s and the US saving rate, house price booms and huge global and intra-EMU trade imbalances characterize the evolution of the world economy since Euro-related intra-EMU and global financial integration after the East-Asian currency crisis up to the onset of the global financial crisis 2007/2008. While the intra-EMU and global trade imbalances and the huge level differences between Asian and US saving rates can be explained by means of Farmer and Mihaiescu’s (Credit constraints and differential growth in equilibrium modeling of EMU and global trade imbalances, 2016) three-country, three-good OLG model with financial constraints and growth rate differentials, the pronounced decline in EMU periphery’s and in the US saving rate cannot. It is natural to suggest that house price booms in EMU periphery and in the USA. boosted consumption and reduced savings. Thus, this chapter introduces house price dynamics à la Arce and López-Salido (American Economic Journal: Macroeconomics, 3:212–241, 2011) and Basco (Journal of International Economics, 92:78–94) into Farmer and Ban’s (Progress in economic research, Nova Science, New York, 2015) inter-temporal equilibrium model, and finds that house price increases let EMU periphery’s and US saving rates indeed decline more quickly—in line with empirical facts.

In contrast to the sociological secularization hypothesis, there is not much disputed evidence that religion stubbornly refused to disappear. In fact, although organized (Christian) religion continues to decline in the Western part of the world there is a religious revival in Africa, Asia, and Latin America. Focusing on Europe and Northern America from an economist’s point of view one is tempted to ask whether Christianity might persist in the long-run of a globalized market economy. The present chapter provides a specific answer to this broad question by using a dynamic economic modeling approach, e.g., an overlapping generations’ (OLG) model of the global market economy wherein economic development (rise in per capita income) is driven by physical and human capital accumulation. Religion is part of social capital and affects children’s educational attainment positively as substantial empirical evidence shows (e.g., Ewing 2000). Based on this and other empirical observations, Fan (2008) constructed an overlapping generations’ model of a closed economy in which an individual’s religious participation is due to the concern for her children’s human capital formation as well as her religious beliefs. However, the present stage of economic globalization is better represented by a multi-country, open-economy model with internationally mobile capital than by a closed-economy model. Thus, we extend Fan’s (2008) invaluable closed economy towards a two-country open-economy OLG model a la Michel and Vidal (2000) with country-specific human capital accumulation and religious participation. In this model framework, it will be shown why religion might be thriving in developing Africa, Asia, and Latin America and be an everlasting social phenomenon even in the economically advanced West in spite of the decline in Western religious participation (as measured by church attendance).