WPS6405 Policy Research Working Paper 6405 Public Policy and Industrial Transformation in the Process of Development Pierre-Richard Agénor Hinh T. Dinh The World Bank Office of the Senior Vice President and Chief Economist Operations and Strategy Unit April 2013 Policy Research Working Paper 6405 Abstract This paper studies the role of public policy in promoting learning by doing in the imitation sector. The process industrial transformation from an imitationbased, of industrialization increases the demand for high-skill low-skill economy to an innovation-based, high-skill labor, inducing individuals to invest in education. The economy, where technological progress now occurs model also emphasizes the distinction between basic through the domestic invention of ideas. Industrial or core infrastructure, which promotes imitation, and transformation is measured by changes in an index of advanced infrastructure, which promotes innovation. A industrial structure, defined as the ratio of the variety calibrated version for a low-income country is used to of imitation- to innovation-based intermediate goods. perform several policy experiments, including an increase A key mechanism through which productivity increases in investment in infrastructure, a reduction in the cost of initially in both the imitation and innovation sectors training, and improved enforcement of property rights. is through a knowledge externality associated with This paper is a product of the Operations and Strategy Unit of the Office of the Senior Vice President and Chief Economist. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank. org. The author may be contacted at HDinh@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team PUBLIC POLICY AND INDUSTRIAL TRANSFORMATION IN THE PROCESS OF DEVELOPMENT Pierre-Richard Agénor* Pierre-richard.agenor@manchester.ac.uk Hinh T. Dinh** hdinh@worldbank.org Abstract This paper studies the role of public policy in promoting industrial transformation from an imitation- based, low-skill economy to an innovation-based, high-skill economy, where technological progress now occurs through the domestic invention of ideas. Industrial transformation is measured by changes in an index of industrial structure, defined as the ratio of the variety of imitation- to innovation-based intermediate goods. A key mechanism through which productivity increases initially in both the imitation and innovation sectors is through a knowledge externality associated with learning by doing in the imitation sector. The process of industrialization increases the demand for high-skill labor, inducing individuals to invest in education. The model also emphasizes the distinction between basic or core infrastructure, which promotes imitation, and advanced infrastructure, which promotes innovation. A calibrated version for a low-income country is used to perform several policy experiments, including an increase in investment in infrastructure, a reduction in the cost of training, and improved enforcement of property rights. JEL Classification Numbers: H54, I25, O33, O41 Keywords: industrial transformation; economic growth; public policy Economic Policy (EPOL) __________________________________________________________________________________________ *Hallsworth Professor of International Macroeconomics and Development Economics, University of Manchester, and co-Director, Centre for Growth and Business Cycle Research; and ** Lead Economist, Office of the Senior Vice President and Chief Economist, World Bank. We would like to thank Baris Alpaslan for research assistance, and Doerte Domeland, Zia Qureshi, and David Rosenblatt for helpful discussions. Financial support from Japanese PHRD TF096317 and Dutch BNPP TF09717 is gratefully acknowledged. The Appendices are available upon request. Contents 1 Introduction 3 2 The Model 5 2.1 Consumption and Labor Supply . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Final Good . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Intermediate Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Design Sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 Market-Clearing Conditions . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Dynamics and Steady State 17 4 Calibration 20 5 Public Policy 23 5.1 Provision of Basic Infrastructure . . . . . . . . . . . . . . . . . . . . . . 24 5.2 Training Subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3 Enforcement of Property Rights . . . . . . . . . . . . . . . . . . . . . . 25 5.4 Sequential, Composite Reform Program . . . . . . . . . . . . . . . . . . 26 6 Policy Implications 27 7 Concluding Remarks 29 Appendix A: Dynamics under the Mixed Regime 31 Appendix B: Dynamics under the Imitation and Innovation Regimes 35 References 38 2 1 Introduction During the past decades manufacturing exports have led the economic transformation of many of today’s most successful countries, particularly in East Asia. During a ï¬?rst phase, many of these countries initially competed in international markets by producing labor-intensive, low-cost light manufacturing goods, using technologies imported from abroad. They achieved large productivity gains initially through a reallocation of labor from low-productivity agriculture to high-productivity manufacturing, and from a learning-by-doing effect associated with the use of imported technologies. In many cases, this learning effect helped to boost human capital from initially low levels, setting up the stage later on for a switch to skill-intensive, innovation-based activities, which eventually led to a diversiï¬?cation of manufacturing production and exports. A key aspect of the ongoing debate about economic growth in Sub-Saharan Africa is the extent to which the region can follow a similar path, and capitalize on the factors and advantages that have generated an initial phase of rapid, manufacturing- based development elsewhere–low-cost labor and imitation of foreign technology. So far, however, there has been no large-scale adoption of this strategy in the region. While China’s emergence in the global manufacturing market since the early 1980s has resulted in a broad decline in the market share of all regions, the decline in Sub- Saharan Africa’s share has been longer and deeper than most. Indeed, Sub-Saharan Africa’s share of global light manufacturing has continually declined to less than 1 percent today, and preferential access to U.S. and European Union (EU) markets has made little difference. Manufacturing accounts for only about 9 percent of GDP for Sub-Saharan Africa as a whole, a smaller share than in any region in the world (Dinh et al. (2012a, p. 32)). As a result, many workers have remained trapped in low- productivity jobs in the informal economy. Without a signiï¬?cant transformation of its industrial structure, Sub-Saharan Africa is unlikely to catch up with more prosperous countries like China and Vietnam–which in many regards were not very different from Sub-Saharan Africa when their own transformation process was initiated. This paper contributes to this ongoing debate by studying the role and sequencing of public policy in promoting industrial transformation and economic development. The process that it highlights involves, in a ï¬?rst stage, mostly imitation of foreign technology, using unskilled labor. In that context, technological progress occurs es- sentially by copying foreign ideas. The second stage, which requires wages to be high enough to induce individuals to invest in skills, involves the gradual development of a home-grown innovation sector. Technological progress now occurs mostly by inventing new ideas. The model can replicate a key empirical regularity (see for instance Van- denbussche et al. (2006)): imitation is the main source of productivity growth at early stages of development, whereas innovation can become the main engine of growth as the economy approaches the technology frontier. We measure industrial transforma- tion by changes in an index of industrial structure, deï¬?ned as the ratio of the variety of imitation-based intermediate goods to innovation-based intermediate goods. The key mechanism through which productivity increases initially in both the imitation and in- 3 novation sectors is through a knowledge externality associated with learning by doing in the imitation sector. This tends to raise wages and productivity not only in that sector, but also in the innovation sector, because imitation activities contribute to the stock of knowledge available to all workers. Thus, imitation can serve as a “stepping stoneâ€? for innovation, as for instance in Glass (2010). At the same time, however, this positive externality is not only weaker for skilled workers but it is also subject to di- minishing returns. Therefore, the marginal beneï¬?t of present imitation effort weakens over time. Equally important to our analysis is the fact that the process of industrialization increases the demand for high-skill labor (in both ï¬?nal production and innovation activ- ities), inducing individuals to invest in education. In turn, education stimulates further productivity and technological advancement in the innovation sector. Investment in human capital is therefore not a prerequisite for promoting growth and development in its initial stages.1 Once the process of imitation takes off, it contributes to the accu- mulation of knowledge available to all in the economy, thereby promoting investment in education and an increase in the quality of the labor force. Beyond some point, however, these beneï¬?ts tend to fade, and it becomes crucial to ï¬?nd new ways to in- crease productivity in the innovation sector. Otherwise, a country may become caught in a so-called “middle-income growth trap,â€? with a substantial drop in productivity and slow growth (see Agénor and Canuto (2012)). To conduct our analysis we consider an endogenous growth model, dwelling on Romer (1990), in which designs are produced in two sectors: an imitation sector (which uses only unskilled labor) and an innovation sector (which uses only skilled labor). The production technology in these sectors is crucial to understand the dynamics of development. The acquisition of foreign ideas generates two opposing forces. On the one hand, as a country catches up with the more advanced nations, imitation opportunities gradually decline, thereby reducing growth. On the other, the externality associated with imitation tends to promote innovation activities (as discussed earlier), thereby promoting growth. The strength of this externality determines the speed at which industrial transformation occurs. Another important feature of the model is the distinction between two types of infrastructure: basic infrastructure (which consists of roads, energy, and basic telecom- munications) and advanced infrastructure, which consists of advanced information and communication technologies (ICTs) in general, and high-speed communication net- works in particular. Access to broadband facilitates the buildup of knowledge networks, thereby promoting the dissemination of ideas within and across borders, and fostering innovation (see Romer (2010) and Agénor and Canuto (2012))). Basic infrastructure helps to promote productivity in the imitation sector, whereas advanced infrastructure beneï¬?ts mainly the innovation sector. A low level of productivity in the imitation sector, to begin with, may therefore be due to the lack of access to infrastructure. 1 This is consistent for instance with Iacopetta (2010), where unlike Funke and Strulik (2000) the sequencing between human capital formation and innovation is reversed. 4 From that perspective, to promote imitation activities, which eventually leads to a more diversiï¬?ed production structure, access to high levels of human capital is neither necessary nor sufficient.2 The remainder of the paper is organized as follows. Section 2 presents the model. Its condensed dynamic form is derived in Section 3. Section 4 calibrates the model, assuming an initial situation where the proportion of the labor force consisting of skilled workers is small, the innovation sector is embryonic (so that most the skilled workers, which are in low numbers to begin with, are engaged in the production of ï¬?nal goods), access to basic infrastructure is limited, access to advanced infrastructure is almost inexistent, the cost of acquiring skills is high, and the enforcement of property rights is weak. Section 5 presents a variety of policy experiments, involving an increase in investment in basic infrastructure, a reduction in the cost of training, and improved enforcement of property rights. An illustrative composite reform program, involving a sequential combination of some of these policies, together with investment in advanced infrastructure, is also analyzed. Section 6 draws together the policy implications of the analysis. The ï¬?nal section offers some concluding remarks. 2 The Model The economy that we consider is populated by individuals (grouped into families) with different innate abilities, ï¬?rms, and a government. There are ï¬?ve production sectors: one producing a homogeneous ï¬?nal good, two producing intermediate goods (core and enhanced inputs from now on), and two creating designs, or blueprints used for the production of each of the two categories of intermediate inputs.3 The design sectors are “imitationâ€? and “innovationâ€? sectors, and their relative importance–a measure of industrial diversiï¬?cation, as discussed later–varies in the course of development. The ï¬?nal good is produced by combining both private and public inputs, and is used for consumption, private and public investment, and the production of intermediate goods. Public inputs–basic public infrastructure, which consists of roads, electricity, water and sanitation, and basic telecommunications; and advanced infrastructure, which con- sists essentially of high-speed telecommunications–are provided free of charge but are subject to congestion.4 Production in the design sectors combines public and private (labor) inputs as well, but in different ways. Firms in the ï¬?nal good and design sectors are perfectly competitive whereas those in the intermediate good sectors are monopolistically competitive, each producing (as 2 Contributions focusing on the transition between development regimes and related to our analysis include van Elkan (1996), Walz (1996), Funke and Strulik (2000), Garcia-Castrillo and Sanso (2002), Iacopetta (2010), Gómez (2012), and Chen and Funke (2012). However, none of them addresses the issues of skill distribution and composition of public capital, as we do here. 3 As discussed later, skills are acquired through formal education or training, but we do not explicitly introduce a Lucas-type human capital accumulation sector. 4 We abstract from any direct utility beneï¬?t associated with public capital, as discussed in a number of contributions. 5 in Romer (1990)) a differentiated variety of good. The total number of blueprints existing at a certain point in time coincides with the number of intermediate input varieties and represents the stock of nonrival knowledge available in the economy. The composition of that stock is used later on to measure industrial structure and to study its transformation over time. Knowledge accumulated in the imitation sector creates an externality that promotes productivity in both design sectors, but this beneï¬?t is subject to diminishing marginal returns. Finally, labor (both skilled and unskilled) is perfectly mobile between the ï¬?nal good and design sectors. 2.1 Consumption and Labor Supply There is a continuum of families indexed by ability ï?¡ ∈ (0 1). Ability follows a uniform distribution, with a cumulative distribution function ï?† (ï?¡) = ï?¡ and mean 05. All members of a family have the same ability level, equal to ï?¡. Each family is modeled as a dynastic household whose size grows over time at an exogenously given rate ï?®  0. Each individual member of a family lives forever. With ï?Ž0 denoting the number of members of each family at time ï?´ = 0, the size of the representative family–and, by extension, population size–at time ï?´ is ï?Žï?´ = ï?Ž0 exp(ï?®ï?´). Each family owns a stock of assets, which consists of physical capital and the stock of designs produced in the economy. Income is devoted to the consumption of ï¬?nal goods and the acquisition of new assets. Each family maximizes utility so as to determine the evolution of consumption expenditure over time. Individual members also decide whether to enter the labor force as unskilled workers or (following a training period) skilled workers. In making these decisions, each family takes wages and the interest rate as given. Each individual knows his (her) own ability level ï?¡, as do all the ï¬?rms that might potentially hire him (her). To avoid corner solutions, we will assume that individuals with ability ï?¡ ∈ (0 ï?¡ï?Œ ) never choose to undergo training, whereas individuals with ability ï?¡ ∈ (ï?¡ï?ˆ  1) always choose to do so.5 An individual with ability ï?¡ ∈ (ï?¡ï?Œ  ï?¡ï?ˆ ) can choose to enter the labor force at ï?´ as an unskilled worker and earn from then on the ï?• wage ï?·ï?´ (which is independent of the worker’s ability). Alternatively, he may decide to spend ï¬?rst an exogenously given period of time ï?” in training, incur a cost ï?´ï?£ï?´ during (ï?´ï€» ï?´ + ï?” ), and enter the labor force at ï?´ + ï?” as a skilled worker. From then on a skilled worker with ability ï?¡ earns a wage ï?¡ïƒ‚ ï?·ï?´ ï?“ , where   0 is a productivity parameter (common to all individuals with the same ability) which measures the efficiency of training.6 Thus, skilled workers with higher ability levels earn higher wages, although this may occur with diminishing returns to ability (  1). During training time (ï?´ï€» ï?´ + ï?” ), workers earn no income. Thus, the opportunity cost of becoming skilled 5 Because both skilled and unskilled labor are essential inputs in the production of the ï¬?nal good, and the production function is Cobb-Douglas, these assumptions serve indeed to eliminate the case of zero output. 6 As noted earlier, both categories of labor are perfectly mobile between the ï¬?nal good sector and the design sectors. This implies that there is a single, economy-wide wage for each category of labor. 6 is equal to the discounted value of foregone unskilled wage income. Income is also assumed to be evenly shared within each family (that is, between employed members and trainees) so that, at each point in time, consumption expenditure is the same for each member of a family. The optimization problem of a family with ability ï?¡ and size ï?Ž0 is Z ∞ ï?¡ max ï?•ï?´ = ï?Ž0 ï?µï?¡ ï?´ exp[−( − ï?®)(ï?³ − ï?´)]ï?¤ï?³ï€» (1) ï?´ where   0 is the constant subjective discount rate, and ï?µï?¡ ï?´ is the static utility function of each household member, which is deï¬?ned as 1 − (ï?ƒï?´ï?¡ )1 ï?µï?¡ ï?´ =  (2) 1 − 1 where ï?ƒï?´ï?¡ is consumption by each individual member of the family. With ï?–ï?´ï?¡ denoting the family’s stock of assets, its flow budget constraint is Ë™ ï?´ï?¡ = ï?²ï?´ ï?–ï?´ï?¡ + (1 − ï‚¿ )ï?™ï?´ − ï?Žï?´ ï?ƒï?´ï?¡  ï?– (3) where ï?²ï?´ is the market interest rate, ï?™ï?´ the economy’s output of ï¬?nal goods, and ï‚¿ ∈ (0 1) the tax rate on income. The solution to the family’s dynamic optimization problem yields the standard intertemporal equation, Ë™ ï?´ï?¡ ï?ƒ = (ï?²ï?´ − ) (4) ï?ƒï?´ï?¡ together with the transversality condition limï?´â†’∞ (ï?ƒï?´ï?¡ )− ï?–ï?´ï?¡ exp(−ï?´) = 0. In familiar fashion, equation (4) states that per capita consumption expenditure grows over time if and only if the market interest rate exceeds the subjective discount rate.7 Consider now labor supply decisions.8 As noted earlier, training and employment decisions are made to maximize each family’s discounted wage income, which is equiv- alent to maximizing each member’s discounted wage income. There are two types of costs associated with training. The ï¬?rst is time devoted to training, which depends ï?• on whether the individual member earns the unskilled wage, ï?·ï?´ , or becomes a skilled  ï?“ worker and then earns the wage ï?¡ ï?·ï?´ . The second is the training cost, ï?´ï?£ï?´ . Thus, it is optimal for an individual with ability ï?¡ ∈ (ï?¡ï?Œ  ï?¡ï?ˆ ) to train and become 7 When the market interest rate is relatively high for instance, family members want to save more now and spend more later, resulting in positive growth in per capita consumption expenditure over time. Note that the left-hand side of (4) does not depend on ability, and thus neither on wages earned in production. 8 The discussion here dwells in part on Dinopoulos and Segerstrom (1999) and Agénor and Canuto (2012). See also Hori (2011) and Davis (2013). 7 a skilled worker if and only if9 Z ∞ Z ∞  ï?“ ï?• ï?¡ ï?·ï?³ exp[−(ï?³ − ï?´)]ï?¤ï?³ − ï?´ï?£ï?´ ≥ ï?·ï?³ exp[−(ï?³ − ï?´)]ï?¤ï?³ï€º (5) ï?´+ï?” ï?´ The right-hand side (RHS) of this inequality equals the discounted wage income of ï?• an individual from being employed as an unskilled worker and earning the wage ï?·ï?³ from time ï?³ = ï?´ onward. The left-hand side (LHS) is the lifetime income of a skilled ï?“ worker, who earns zero income during his training period (ï?´ï€» ï?” ) and ï?·ï?³ from time ï?³ = ï?´ + ï?” onward, adjusted for the training cost ï?´ï?£ï?´ occurred during (ï?´ï€» ï?´ + ï?” ). The training cost per unit time ï?³ is assumed to be proportional to the wage that skilled workers make once training is completed and they become employed, so that ï?¡ïƒ‚ ï?·ï?³ï?“ R ∞this cost , with  ∈ (0 1). For simplicity, is taken to incur from that point on until the inï¬?nite future. Thus, ï?´ï?£ï?´ = ï?´+ï?” ï?¡ïƒ‚ ï?·ï?³ ï?“ exp[−(ï?³ − ï?´)]ï?¤ï?³.10 Condition (5) can be readily used to determine the supply of unskilled labor. Indeed, because the LHS of (5) is increasing in ï?¡, whereas the RHS is independent of ï?¡, there exists a threshold level of ability denoted by ï?¡ï?ƒ ï?´ such that (5) holds as an equality. ï?ƒ All individuals with ability lower than ï?¡ï?´  0 (including then with ability lower than ï?¡ï?Œ ) choose to remain unskilled, and all individuals with ability greater than ï?¡ï?ƒ ï?´ ≤ 1 ï?ˆ (including then those with ability greater than ï?¡ ) choose to undergo training and then enter the labor force as skilled workers. Assuming that (5) holds with equality yields Z ∞ Z ∞ ï?ƒ  ï?“ ï?• (ï?¡ï?³ ) (1 − )ï?·ï?³ exp[−(ï?³ − ï?´)]ï?¤ï?³ = ï?·ï?³ exp[−(ï?³ − ï?´)]ï?¤ï?³ï€» ï?´+ï?” ï?´ which simpliï¬?es to exp(−ï?” )(ï?¡ï?ƒ  ï?“ ï?´ ) (1 − )ï?·ï?´ ï?·ï?• = ï?´    Solving this condition for ï?¡ï?ƒ ï?´ yields ï?• ï?·ï?´ 1 ï?¡ï?ƒ ï?´ = [ ï?“ ]1 [exp(ï?” )]  (6) (1 − )ï?·ï?´ which is equal to ï?¡ï?ˆ if the expression on the RHS exceeds ï?¡ï?ˆ . ï?“ Because exp(ï?” ) ≥ 1 and   0, the net wage earned by a skilled worker (1 − )ï?·ï?´ ï?• must be higher than the wage of an unskilled worker ï?·ï?´ for an individual to choose 9 Because each family’s discounted utility is increasing in consumer expenditure and there is no disu- tility associated with training or working, each family maximizes its discounted utility by maximizing its discounted wage income. 10 An alternative assumption would be to assume that the cost is incurred during the training period R ï?´+ï?”  ï?“ (ï?´ï€» ï?´ + ï?” ) as a fraction of the going skilled wage, so that ï?´ï?£ï?´ is instead equal to ï?´ ï?¡ ï?·ï?³ exp[−(ï?³ − ï?´)]ï?¤ï?³. However, because in the calibration presented later we normalize ï?” to zero, this speciï¬?cation is less tractable. 8 to become skilled.11 An increase in the duration of training ï?” , the proportional cost of training , or in the relative wage of unskilled labor, raises the fraction of the population that chooses to remain unskilled. Given (6), the supply of unskilled labor, ï?Žï?´ï?• , equals the number of individuals in the population who choose to remain unskilled: ï?Žï?´ï?• = ï?¡ï?ƒ ï?´ ï?Žï?´  (7) To derive the supply of skilled labor, ï?Žï?´ï?“ , note ï¬?rst that at any time ï?´, (1 − ï?¡ï?ƒ ï?´ )ï?Žï?´ individuals either work as skilled workers or are training to become skilled workers. In this sub-population, those who are actually working as skilled workers are the older individuals, namely, those individuals who were born before ï?´ − ï?” : Z ï?´âˆ’ï?” Z ï?´âˆ’ï?” ï?ƒ ï?ƒ ï?®(1 − ï?¡ï?´ )ï?Žï?³ ï?¤ï?³ = ï?®(1 − ï?¡ï?´ ) ï?Ž0 exp(ï?®ï?³)ï?¤ï?³ = (1 − ï?¡ï?ƒ ï?´ ) exp(−ï?®ï?” )ï?Žï?´  −∞ −∞ The average skill level of workers with ability ï?¡ ∈ (ï?¡ï?ƒ ï?´  1) who have ï¬?nished training equals (ï?¡ï?ƒï?´ + 1)2; thus, the supply of skilled labor at time ï?´, measured in efficiency units of human capital, can be deï¬?ned as (1 + ï?¡ï?ƒ ï?´ ) ï?Žï?´ï?“ = (1 − ï?¡ï?ƒ ï?´ ) exp(−ï?®ï?” )ï?Žï?´  2 or equivalently 1 − (ï?¡ï?ƒ ï?´ ) 2 ï?Žï?´ï?“ = exp(−ï?®ï?” )ï?Žï?´  (8) 2 From equations (6), (7), and (8), it can be seen that a decline in the relative wage of unskilled workers decreases ï?¡ï?ƒ ï?• ï?“ ï?´ and ï?Žï?´ and increases ï?Žï?´ , resulting in a rise in the relative supply of skilled labor, ï?Žï?´ï?“ ï?Žï?´ï?• . 2.2 Final Good Production of the ï¬?nal good, ï?™ï?´ , requires the use of skilled labor, ï?Žï?´ï?“ï?™ , unskilled labor, ï?Žï?´ï?•ï€»ï?™ , private capital, ï?‹ï?´ï?? , basic public infrastructure, ï?‹ï?´ï?‚ , and the combination of core intermediate inputs, ï?¸ï?‰ ï?‰ ï?’ ï?³ï€»ï?´ , where ï?³ ∈ (0 ï??ï?´ ), and enhanced intermediate inputs, ï?¸ï?³ï€»ï?´ , where ï?³ ∈ (0 ï??ï?´ï?’ ):12 ï?‹ï?´ï?‚ ï?“ ï?• ï?™ï?´ = [ ] (ï?Žï?´ï?“ï?™ ) (ï?Žï?´ï?•ï€»ï?™ ) ï?˜ï?´ï‚° (ï?‹ï?´ï?? )ï‚®  (9) ¯ ï?´ï?? ) ï?‹ ï?Žï?´ï‚³ ï?Ž (ï?‹ 11 Recall that all individuals with ability ï?¡ ∈ (ï?¡ï?ˆ  1) always choose to become skilled. 12 In the model advanced public capital does not affect production of the ï¬?nal good, only (as dis- cussed later) productivity in the innovation sector. In general, of course, both the innovation and manufacturing sectors could be assumed to beneï¬?t from access to that type of infrastructure. For instance, it is well documented that in recent years ICTs have helped to integrate supply chains both within and across borders, thereby boosting efficiency in the production of manufactured goods. For the purpose of our analysis, however, what matters is only that the effect of ICTs is relatively stronger on activity in the innovation sector, compared to the ï¬?nal good sector. 9 ¯ ï?´ï?? is the where  ï?“   ï?•   ï‚° ∈ (0 1),   0,  ï?‹   ï?Ž  0, ï‚® = 1 − ( ï?“ +  ï?• ) − ï‚° , ï?‹ aggregate private capital stock, and ï?˜ï?´ is a composite intermediate input deï¬?ned as Z ï??ï?´ï?‰ Z ï??ï?´ï?’ ï?‰ ï‚´  ï?˜ï?´ = [ (ï?¸ï?³ï€»ï?´ ) ï?¤ï?³] · [ (ï?¸ï?’ ï‚´ ï?³ï€»ï?´ ) ï?¤ï?³] (1− )  (10) 0 0 where ï‚´ ∈ (0 1) and 1(1 − ï‚´)  1 is (the absolute value of) the price elasticity of demand for each intermediate good, and  ∈ (0 1). Thus, the composite intermediate input exhibits constant returns to scale with respect to core and enhanced inputs.13 Although coefficient  itself could be made a function of the composition of intermedi- ate goods (falling over time, as the economy’s relative production of enhanced inputs increases), for simplicity it is taken to be constant. Speciï¬?cation (9) implies that there are constant returns in private inputs, and that basic public capital is partially rival and subject to congestion, measured by the aggregate private capital stock and population size. The strength of congestion effects is measured by the parameters  ï?‹ and  ï?Ž . Proï¬?ts of the representative ï¬?rm are given by Z ï??ï?´ï?‰ Z ï??ï?´ï?’ ï?‰ï€»ï?³ ï?‰ ï?™ Πï?´ = ï?™ï?´ − ï??ï?´ ï?¸ï?³ï€»ï?´ ï?¤ï?³ − ï??ï?´ï?’ï?³ ï?¸ï?’ ï?“ ï?“ï?™ ï?³ï€»ï?´ ï?¤ï?³ − ï?·ï?´ ï?Žï?´ ï?• ï?•ï€»ï?™ − ï?·ï?´ ï?Žï?´ − (ï?²ï?´ +  ï?? )ï?‹ï?´ï??  0 0 where ï??ï?´ï?‰ï€»ï?³ (ï??ï?´ï?’ï?³ ) is the price of core (enhanced) intermediate good ï?³, ï?·ï?´ ï?“ ï?• (ï?·ï?´ ) the skilled (unskilled) wage rate, ï?²ï?´ the (net) rental rate of private capital, and  ï?? ∈ (0 1) the rate of depreciation of private capital. The ï¬?nal good is used as the numéraire and its price is normalized to unity. Each producer maximizes proï¬?ts subject to (9)-(10) with respect to labor, private capital, and quantities of all intermediate goods ï?¸ï?ª ï?³ï€»ï?´ , ∀ï?³, taking factor prices and ï??ï?´ ï?ª as given, ï?ª = ï?‰ï€» ï?’. This yields ï?™ï?´ ï?™ï?´ ï?“ ï?·ï?´ = ï?“ , ï?• ï?·ï?´ = ï?•  (11) ï?Žï?´ï?“ï?™ ï?Žï?´ï?•ï€»ï?™ ï?™ï?´ ï?²ï?´ = ï‚® − ï??  (12) ï?‹ï?´ï??  ï?ª ï?šï?´ï?ª 1(1−) ï?¸ï?ª ï?³ï€»ï?´ = ( ï?ªï€»ï?³ )  ï?³ = 1 ï??ï?´ï?ª  (13) ï??ï?´ Z ï??ï?´ï?ª ï?ª ï?šï?´ = ï?™ï?´  (ï?¸ï?ª ï‚´ ï?³ï€»ï?´ ) ï?¤ï?³ï€» (14) 0 13 The Cobb-Douglas form used in (10) is more tractable analytically than an additive form, which would imply that core and enhanced intermediate inputs, as a whole, are perfect substitutes. A more general speciï¬?cation would be to use a CES function with a relatively low–but possibly variable– elasticity of substitution between the two categories of inputs (instead of unity), but this would prevent the derivation of an explicit dynamic form. Alternatively, as in Afonso and Thompson (2011) for instance, intermediate goods could be assumed to be complementary. 10 where ï?ª = ï?‰ï€» ï?’ and  ï?‰ =  ,  ï?’ = 1 −  . The law of motion of private capital is given by Ë™ ï?´ï?? = ï?‰ï?´ + (1 −  ï?? )ï?‹ï?´ï??  ï?‹ (15) where ï?‰ï?´ is private investment. 2.3 Intermediate Goods There are two sets of intermediate goods (IG) producers: those producing core inputs, based on blueprints produced by the imitation sector, and those producing enhanced inputs, based on designs produced by the innovation sector. Each ï¬?rm produces one, and only one, horizontally-differentiated intermediate good. In both cases, production of each unit of intermediate good requires one unit of the ï¬?nal good. Consider ï¬?rst producers of core intermediate goods, ï?¸ï?‰ï€»ï?³ ï?‰ ï?´ , ï?³ = 1 ï??ï?´ . Each pro- ducer must pay a one-off license fee, ï?‘ï?‰ ï?´ , to the ï¬?rm that produced the relevant design in the imitation sector, before producing its own specialized good. Thus, the license fee represents a ï¬?xed entry cost. Once the fee is paid, each producer sets its price to max- imize proï¬?ts, given the perceived demand function for its good (13), which determines marginal revenue. Under a symmetric equilibrium, proï¬?ts are given by Πï?‰ ï?‰ ï?´ = (ï??ï?´ − 1)ï?¸ï?´ ï?‰ or using (13) and (14), Πï?‰ ï?‰ ï?‰ ï?‰ ï?´ = (ï??ï?´ − 1)[ï?™ï?´ ï??ï?´ ï??ï?´ (ï?¸ï?´ ) ] ï?‰ ï‚´ 1(1− ) . The solution yields the optimal price as 1 ï??ï?´ï?‰ï€»ï?³ =  ∀ï?³ = 1 ï??ï?´ï?‰  (16) ï‚´ which indicates, in standard fashion, that ï¬?rms cannot charge a price higher than marginal cost (the price of a unit of the ï¬?nal good), when intermediate goods are perfect substitutes (ï‚´ = 1). Using (13), the quantity demanded at this price is ï?¸ï?‰ ï?³ï€»ï?´ = (ï?šï?´ ) ï?‰ 1(1− ) , ∀ï?³, that R ï??ï?´ï?‰ ï?‰ ï‚´ ï?‰ ï?‰ ï‚´ is, noting that under symmetry 0 (ï?¸ï?³ï€»ï?´ ) ï?¤ï?³ = ï??ï?´ (ï?¸ï?´ ) , ï?™ï?´ ï?¸ï?‰ ï?´ =  ( ) (17) ï??ï?´ï?‰ with maximum proï¬?t given by ï?™ï?´ Πï?‰ ï?´ = (1 − ï‚´ ) ( ) (18) ï??ï?´ï?‰ In equilibrium, the license fee must be set equal to current proï¬?ts:14 ï?‘ï?‰ ï?‰ ï?´ = Πï?´  (19) 14 This assumption that the license fee depends on current proï¬?ts only rather than the present discounted value of all future proï¬?ts (as would be the case with a license of inï¬?nite duration) allows us to eliminate dynamics in terms of ï?‘ï?‰ ï?´ and to focus on price incentives to innovation, as discussed next. 11 Consider now the production of enhanced intermediate goods. Each ï¬?rm must purchase an inï¬?nitely-lived patented design from the innovation sector. Once the patent is paid, each intermediate good producer sets its sale price to maximize proï¬?ts, given the perceived demand function for its good (13). Under a symmetric equilibrium, and using (13) and (14), proï¬?ts are given by Πï?’ ï?’ ï?’ ï?’ ï?’ ï‚´ 1(1− ) ï?´ = (ï??ï?´ − 1)[ï‚° (1 −  )ï?™ï?´ ï??ï?´ ï??ï?´ (ï?¸ï?´ ) ] . The solution yields again the optimal price as 1 ï??ï?´ï?’ =  (20) ï‚´ with quantity demanded as, using (13), ï?™ï?´ ï?¸ï?’ ï?´ = ï‚°ï‚´ (1 −  )( ) (21) ï??ï?´ï?’ and maximum proï¬?t as ï?™ï?´ Πï?’ ï?´ = (1 − ï‚´ )ï‚° (1 −  )( ) (22) ï??ï?´ï?’ If the market for new enhanced designs is competitive, standard arbitrage implies that the price of a patent, ï?‘ï?’ï?´ , must be equal to the present discounted stream of proï¬?ts that the potential producer could make by producing the intermediate input. Thus, Z ∞ ï?‘ï?’ ï?´ = Πï?’ ï?³ exp(−ï?’ï?´ï€»ï?³ )ï?¤ï?³ï€» ï?´ Rï?³ where ï?’ï?´ï€»ï?³ = ï?´ ï?²ïƒ€R Ë™ï?’ ï?¤ïƒ€. Differentiating this expression with respect to time yields ï?‘ï?´ = ∞ ï?’ 15 − exp(ï?’ï?´ï€»ï?´ ) + ï?’ï?´ï€»ï?´ ï?´ Πï?³ exp(−ï?’ï?´ï€»ï?³ )ï?¤ï?³, that is, given that ï?’ï?´ï€»ï?´ = ï?²ï?´ , Ë™ï?’ ï?‘ ï?’ ï?’ ï?´ = ï?²ï?´ ï?‘ï?´ − Πï?´  (23) 2.4 Design Sectors Designs are produced in two sectors: an imitation sector, which employs only unskilled labor, in quantity ï?Žï?´ï?•ï€»ï?‰ , and an innovation sector, which employs only skilled labor, in quantity ï?Žï?´ï?“ï?’ . There is no aggregate uncertainty in either sector. In the imitation sec- tor, local ï¬?rms invest resources in order to absorb and adapt the information needed to replicate new products invented abroad, that is, “reverse engineering.â€? Thus, imitation differs from innovation in that the number of goods that can be copied at any point in time is limited to the rate at which imitable goods are being discovered elsewhere. 15 Equation (23) can be rewritten in the familiar no-arbitrage form ï?²ï?´ = Πï?’ ï?’ Ë™ï?’ ï?’ ï?´ ï??ï?´ + ï??ï?´ ï??ï?´ , which equates the rate of return on private capital to the rate of return on the alternative “assetâ€? (the exclusive right to produce a new design for enhanced intermediate goods), given by the sum of the net revenue (divided by the asset price to give a rate) plus any capital gain associated with a change in that price. 12 Both imitation and innovation create two kinds of knowledge. First, private knowl- edge, which is acquired (for a price) by intermediate goods ï¬?rms to produce a new production input. Second, public knowledge, which spills over to other ï¬?rms in the imitation and innovation sectors–in ways speciï¬?ed later–and increases productivity there. In addition, we also assume that there is an externality from imitation for innovation–as agents learn to imitate, they also develop cognitive skills that help them to innovate. This is consistent with the idea, discussed in the introduction, that imitation can be a “stepping stoneâ€? for true innovation.16 Consider the imitation sector ï¬?rst. The aggregate technology is deï¬?ned as ï?•ï€»ï?‰ Ë™ ï?´ï?‰ = ï??ï?‰ ï?Žï?´ ï?‰ ï?? ï?´( )(1 + ï?§ï?— )ï‚·  (24) ï?Žï?´ where ï??ï?‰ ï?´ is a productivity factor, ï?§ ï?—  0 is the growth rate of the stock of designs available internationally that can be effectively imitated in the country under consider- ation, or equivalently the rate at which the imitation technology frontier changes. We assume that the technology parameter ï‚·ï?‰ ∈ (0 1) is less than unity, to capture the fact that the growth in imitable goods worldwide entails diminishing marginal beneï¬?ts for domestic imitation–perhaps because some technical speciï¬?cations involved in foreign ideas are fairly complex, or that adaptation costs are large, thereby constraining (at the margin) the country’s ability to imitate. We also assume, as in Chen and Funke (2012) for instance, that the international knowledge pool available for copying, grows at an exogenous rate.17 We also assume, to eliminate scale effects, that it is the ratio of unskilled workers to total population that affects activity in that sector.18 Productivity in imitation activities depends on the economy’s stock of imitated designs and access to basic infrastructure: ï?‰ ï?‰ ï??ï?‰ ï?‚ ïƒ?1 ï?‰ ïƒ?2 ï?‰ ï?´ = (ï?«ï?´ ) (ï?­ï?´ ) ï??ï?´  (25) ï?‚ ï?‰ ï?‰ where ï?«ï?´ = ï?‹ï?´ï?‚ ï?‹ï?´ï?? , ï?­ï?‰ ï?‰ ï?? ï?´ = ï??ï?´ ï?‹ï?´ , ïƒ?1  0, and ïƒ?2 ≥ 0. Thus, as in Romer (1990), each design creates a positive externality for future imitation activities. In addition, as in Agénor and Canuto (2012), we account for the fact that–at least temporarily– productivity may exhibit increasing marginal returns (ïƒ?ï?‰2  0) with respect to imitative knowledge, as a result of strong learning-by-doing effects. We also assume that access 16 As in Perez-Sebastian (2007), we could also assume that the beneï¬?t of imitation diminishes as the country gets closer to the world technological frontier for imitated goods. However, doing so directly would add further analytical complications. Instead, we capture this effect indirectly, as discussed later. 17 The exogeneity of the law of motion of the international pool of ideas implies that we abstract from the fact that domestic innovation (under the relevant regime) might yield new goods that will add up to the international pool of imitable designs. We do so for simplicity. Notice, however, that this effect will be small at low levels of economic development because then the production of innovative designs is low or inexistent. 18 This speciï¬?cation is consistent with the “dilution effectâ€? discussed by Dinopoulos and Segerstrom (1999). See also Grossmann and Thomas (2007). 13 to basic public capital is subject to (proportional) congestion, measured by the private capital stock. ï?‰ Ë™ ï?‰ Firms in the imitation sector choose labor so as to maximize proï¬?ts, Πï?‰ ï?´ = ï?‘ï?´ ï??ï?´ − ï?• ï?•ï€»ï?‰ ï?·ï?´ ï?Žï?´ , subject to (24), and taking the wage rate, the license fee, ï?‘ï?‰ ï?´ , and productivity ï??ï?´ , as given. The ï¬?rst-order condition with strictly positive employment (ï?Žï?´ï?•ï€»ï?‰  0) is ï?‰ given by ï?‘ï?‰ ï??ï?‰ ï?‰ ï?·ï?´ï?• = ( ï?´ ï?´ )(1 + ï?§ï?— )ï‚·  (26) ï?Žï?´ Consider now the innovation sector. The aggregate technology is deï¬?ned as ï?“ï?’ Ë™ ï?´ï?’ = ï??ï?’ ï?Žï?´ ï?? ï?´ ( ) (27) ï?Žï?´ where ï??ï?’ï?´ is productivity, which depends on access to advanced infrastructure and both stocks of technological knowledge–with innovation creating a stronger spillover effect than imitation:: ï?? ïƒ?ï?’ ï?’ ïƒ?ï?’ ï?’ ï??ï?’ 1 2 ï?’ ï?´ = (ï?«ï?´ ) (ï?­ï?´ ) (ï??ï?´ + ïƒ?3 ï??ï?´ ) ï?‰ (28) ï?? ï?’ ï?’ ï?’ where ï?«ï?´ = ï?‹ï?´ï?? ï?‹ï?´ï?? , ï?­ï?’ ï?’ ï?? ï?´ = ï??ï?´ ï?‹ï?´ , ïƒ?1  0, ïƒ?2 ≥ 0 and 0 ≤ ïƒ?3  1. This speciï¬?cation accounts again for the possibility of increasing marginal returns associated with innovative knowledge (ïƒ?ï?’ 2  0), if only for a temporary period, as in Agénor and Canuto (2012). For tractability, access to advanced infrastructure is again congested by the private capital stock.19 We also assume that imitation enhances productivity in the innovation sector. This speciï¬?cation accounts for an efficiency gain associated with imitation–if only during a transitory phase: the more a country engages initially in copying, the more its workers become familiar with existing innovations made abroad, and the easier it is to engage in original innovation. However, we also assume that the knowledge created as a by-product of imitation creates (marginal) efficiency gains that are less signiï¬?cant than those associated with home-grown innovation, so that ïƒ?ï?’ 3  1. Our speciï¬?cation also accounts for the possibility that imitation may not create any spillover at all for innovation (ïƒ?ï?’ ï?‰ 3 = 0), or that the spillover may weaken over time if the ratio ï??ï?´ ï??ï?´ ï?’ itself decreases over time, which may well occur if the development of the innovation sector is sufficiently rapid. Firms in the innovation sector choose labor so as to maximize proï¬?ts, ï?’ Ë™ ï?’ ï?“ ï?“ï?’ Πï?’ ï?´ = (1 − )ï?‘ï?´ ï??ï?´ − ï?·ï?´ ï?Žï?´  subject to (27), and taking the wage rate, the patent price, ï?‘ï?’ ï?´ , and productivity as given. In this expression, the coefficient  ∈ (0 1) measures the deadweight loss associated with a poorly functioning system to enforce property rights (administration 19 This assumption makes the treatment of congestion in the design sectors symmetric and is conve- nient analytically. Alternatively, congestion could be measured by the level of activity in the innovation sector, that is, the stock of innovative blueprints. 14 of patents, etc.). The view is that these inefficiencies translate into a lower ability of ï¬?rms in the innovation sector to appropriate the rents created by their activity–that is, the proï¬?ts of the intermediate good ï¬?rm using their design. Put differently, even though the price of the patent paid by each intermediate good producer is ï?‘ï?’ ï?´ , due to inefficiencies in enforcing property rights the producer receives only a fraction 1 −  of that price.20 The ï¬?rst-order condition is given by ï?“ (1 − )ï?‘ï?’ ï?’ ï?´ ï??ï?´ ï?·ï?´ ≥  (29) ï?Žï?´ with equality if ï?Žï?´ï?“ï?’  0. Thus, innovation takes place only if skilled wages are not too low. In addition, improved enforcement of property rights translates into higher wages, which tends to draw more labor into the innovation sector and to promote activity there. 2.5 Government The government levies a tax on ï¬?nal good output at the rate ï‚¿ , invests a total of ï?‡ï?‚ ï?? ï?• ï?´ and ï?‡ï?´ on basic and advanced infrastructure, and spends ï?‡ï?´ on other items. Its services are provided free of charge. It cannot issue bonds and must therefore run a balanced budget: X ï?‡ï?´ = ï?‡ï?¨ï?´ = ï‚¿ ï?™ï?´  (30) Shares of public spending are all assumed to be constant fractions of government revenues: ï?‡ï?¨ï?´ =  ï?¨ ï‚¿ ï?™ï?´  ï?¨ = ï?? ï?‚ ï?• (31) Combining (30) and (31) therefore yields X  ï?¨ = 1 (32) ï?¨ Stocks of public capital evolve according to Ë™ ï?´ï?ª = ï?‡ ï?‡ï?ª ï?‹ ï?ª ï?´ + (1 −  ï?‡ )ï?‹ï?´  ï?ª = ï?? ï?‚ (33) where  ï?‡ ∈ (0 1) is a depreciation rate and ï?‡ ∈ (0 1) an efficiency parameter, which measures the extent to which investment flows translate into actual accumulation of public capital. As in Agénor (2010, 2012), we interpret this parameter as an indicator of the quality of public sector management. For simplicity, both  ï?‡ and ï?‡ are assumed to be the same for the two types of public capital. 20 See Eicher and García-Peñalosa (2008) and Lorenczik and Newiak (2012) for a more formal analy- sis of property rights in an innovation-based model of economic growth. 15 2.6 Market-Clearing Conditions To close the model requires specifying the equilibrium conditions between supply and demand in the goods market, and the labor markets for skilled and unskilled labor. The equilibrium condition of the ï¬?nal good market is Z ï?‰ ï??ï?´ Z ï?’ ï??ï?´ ï?™ï?´ − ï?¸ï?‰ ï?³ï€»ï?´ ï?¤ï?³ − ï?¸ï?’ ï?¡ ï?³ï€»ï?´ ï?¤ï?³ = ï?Žï?´ ï?ƒï?´ + ï?‰ï?´ + ï?‡ï?´  (34) 0 0 with the left-hand side representing value added. R ï??ï?ª Under symmetry, 0 ï?´ ï?¸ï?ª ï?ª ï?ª ï?ª ï?ª ï?ª ï?³ï€»ï?´ ï?¤ï?³ = ï??ï?´ ï?¸ï?´ , and as shown earlier, ï?¸ï?´ =  ï?™ï?´ ï??ï?´ , ï?ª = ï?‰ï€» ï?’. Thus, equation (34) becomes (1 − ï‚°ï‚´ )ï?™ï?´ = ï?Žï?´ ï?ƒï?´ï?¡ + ï?‰ï?´ + ï?‡ï?´  that is, using (30), (1 − ï‚°ï‚´ − ï‚¿ )ï?™ï?´ = ï?Žï?´ ï?ƒï?´ï?¡ + ï?‰ï?´  (35) This equation can be solved for private investment, ï?‰ï?´ . Equilibrium of the market for unskilled labor implies that workers are employed either in the production of the ï¬?nal good or in the imitation sector, that is, ï?Žï?´ï?•ï€»ï?™ + ï?Žï?´ï?•ï€»ï?‰ = ï?Žï?´ï?• , or equivalently, in terms of ratios, ï?•ï€»ï?™ ï?´ + ï?•ï€»ï?‰ ï?´ = ï?• ï?´  (36) where ï?• ï?• ï?´ = ï?Žï?´ ï?Žï?´ is the total supply of unskilled labor in proportion of the total population, which from (7) is equal to ï?¡ï?ƒ ï?´ . Similarly, equilibrium of the market for skilled labor implies that workers are em- ployed either in the production of the ï¬?nal good or in the innovation sector, that is, ï?Žï?´ï?“ï?™ + ï?Žï?´ï?“ï?‰ = ï?Žï?´ï?“ , or equivalently, in relative terms, ï?“ï?™ ï?´ + ï?“ï?’ ï?´ = ï?“ ï?´ï€» (37) where ï?“ ï?“ ï?´ = ï?Žï?´ ï?Žï?´ is the supply of skilled labor, measured in efficiency units, in proportion of the total population, which from (8) is equal to 05[1 − (ï?¡ï?ƒ 2 ï?´ ) ] exp(−ï?®ï?” ). 21 ï?•ï€»ï?™ ï?“ï?™ With the marginal product conditions (11) solved for ï?´ and ï?´ , (26) and (29), ï?• the latter holding with equality, solved for ï?·ï?´ and ï?·ï?´ ï?“ , and ï?• ï?“ ï?´ and  ï?´ determined as indicated earlier from (7) and (8), conditions (36) and (37) can be solved for ï?•ï€»ï?‰ ï?´ and ï?“ï?’ ï?´ residually. Figure 1 summarizes the production structure of the model and the distribution of labor across sectors. 21 Note that, because the supply of skilled labor is measured in efficient units of human capital, the equality ï?“ ï?• ï?ƒ ï?´ +  ï?´ = 1 does not hold. This is because the number of skilled workers (1 − ï?¡ï?´ )ï?Žï?´ is adjusted for average ability, as measured by(ï?¡ï?ƒ ï?´ + 1) 2. 16 3 Dynamics and Steady State Consider now the dynamics of the economy, under a “mixedâ€? regime where both imi- tation and innovation activities coexist (ï?? Ë™ ï?´ï?‰  0 and ï?? Ë™ ï?´ï?’  0). In general, there are two margins to consider: a ) the decision to acquire skills for individuals with ability ï?¡ ∈ (ï?¡ï?Œ  ï?¡ï?ˆ ), which depends on whether the unskilled wage is lower or higher than the skilled wage, ï?·ï?´ ï?• ≶ ï?“ ï?·ï?´ ; b ) whether employment in the innovation sector is positive, that is, ï?“ï?’ ï?´  0, which depends on whether (29) holds with equality. ï?“ï?’ In the mixed regime, where both ï?“ ï?ƒ ï?ˆ ï?´  0 (with ï?¡ï?´ ≤ 1 − ï?¡ ) and  ï?´  0, equations (28) and (29) yield22 ï?“ ï?‘ï?’ ï?´ ï?? ïƒ?ï?’ ïƒ?ï?’ ï?’ ï?­ï?´ ï?‰ ï?·ï?´ =( )(ï?«ï?´ ) 1 (ï?­ï?’ 2 ï?’ ï?´ ) [1 + ïƒ?3 ( ï?’ )]ï??ï?´  (38) ï?Žï?´ ï?­ï?´ To determine the growth rate, the ï¬?rst step is to derive the restrictions on the congestion parameters in (9). In a symmetric equilibrium, ï?˜ï?´ = [(ï??ï?´ï?‰ )1 ï?¸ï?‰  ï?’ 1 ï?’ 1− ï?´ ] [(ï??ï?´ ) ï?¸ï?´ ]  (39) From (17) and (21), ï?¸ï?ª ï?ª ï?ª ï?´ =  (ï?™ï?´ ï??ï?´ ), for ï?ª = ï?‰ï€» ï?’. Substituting these results in (39) yields ï?˜ï?´ =   (1 −  )1− [(ï??ï?´ï?‰ ) (1−) (ï??ï?´ï?’ )(1− )(1−) ]ï?™ï?´  or equivalently,23 ï?™ï?´ ï?˜ï?´ = Λ1 (ï?­ï?‰ ï?´)  (1− ) (ï?­ï?’ ï?´ ) (1− )(1− ) ( )(ï?‹ï?´ï?? )1  ï?‹ï?´ï?? where ï?­ï?ª ï?ª ï??  ï?´ = ï??ï?´ ï?‹ï?´ , ï?ª = ï?‰ï€» ï?’ and Λ1 =  (1 −  ) 1− . Substituting this expression in (9) yields  ï?“ ï?•ï€»ï?™  ï?•  ï?“ + ï?• − ï?Ž ï?™ï?´ = (ï?“ï?™ ï?´ ) ( ï?´ ) ï?Žï?´ (40) ½ ¾ ï?‚  (1− )(1− ) ï?™ï?´ ×(ï?«ï?´ ) Λ1 (ï?­ï?‰ ï?´)  (1−) (ï?­ï?’ ï?´ ) ( ï?? ) (ï?‹ï?´ï?? )ï‚®++(1− ï?‹ )  ï?‹ï?´ The following restrictions on the congestion parameters  ï?‹ and  ï?Ž are imposed: Assumptions:  ï?“ +  ï?• −  ï?Ž = 0, ï‚® +  +  (1 −  ï?‹ ) = 1. 22 ï?• ï?“ Given the assumptions made earlier, even if ï?·ï?´  ï?·ï?´ , there is always some supply of skilled labor ï?ˆ in the economy–those with ability ï?¡ ∈ (ï?¡  1); that is, ï?¡ï?ƒ ï?ˆ ï?´ = 1 − ï?¡ . Even so, however, this does not imply that an innovation sector will emerge; in addition, condition (38) must hold. Put differently, having skilled labor in the economy is a necessary, but not sufficient, condition for innovation activity to take place. 23 ï?? (1− ) ï??  (1− ) ï?? (1− )(1− ) ï?? 1 ï?? Note that (ï?‹ï?´ ) = (ï?‹ï?´ ) (ï?‹ï?´ ) = (ï?‹ï?´ ) ï?‹ï?´ . 17 Thus, the level of output becomes: ï?‚ (1− ) (ï?«ï?´ ) Λ2 © ï?‰  (1−) ï?’ (1− )(1−) ª(1− ) ï?? ï?™ï?´ = ï?“ï?™ ï?“ ï?•ï€»ï?™ ï?• (ï?­ï?´ ) (ï?­ï?´ ) ï?‹ï?´  (41) [(ï?´ ) (ï?´ ) ]−1(1− ) (1− ) where Λ2 = Λ1 . Equation (41) is thus linear in the private capital stock. To simplify notations, suppose for the moment that training occurs instantaneously, so that ï?” = 0.24 Thus, equations (6), (7), and (8) become ½ ï?• ï?“ ï?ƒ ï?• max[ï?¡ï?Œ  [ï?·ï?´ (1 − )ï?·ï?´ï?“ 1 ] ] if ï?·ï?´  (1 − )ï?·ï?´ ï?¡ï?´ = ï?ˆ ï?• ï?“  (42) 1−ï?¡ if ï?·ï?´ ≥ (1 − )ï?·ï?´ ï?Žï?´ï?• ï?Žï?´ï?“ 1 − (ï?¡ï?ƒ ï?´ ) 2 ï?• ï?´ = = ï?¡ï?ƒ ï?´  ï?“ ï?´ = =  (43) ï?Žï?´ ï?Žï?´ 2 From the ï¬?rst-order conditions (11), ï?·ï?´ ï?• ï?·ï?´ï?“ =  (ï?Žï?´ï?“ï?™ ï?Žï?´ï?•ï€»ï?™ ), where  =  ï?•  ï?“ . This expression is equivalent to ï?·ï?´ ï?• ï?“ ï?·ï?´ ï?“ï?™ =  (ï?´ ï?•ï€»ï?™ ï?´ ). Thus, the unskilled-skilled wage ratio varies inversely with the relative supplies of skilled and unskilled labor in the ï¬?nal good sector. Using this result, Appendix A shows that the dynamic system ï?• ï?“ that drives the economy when ï?·ï?´  (1 − )ï?·ï?´ (which we consider to be the “normalâ€? case) consists of six ï¬?rst-order differential equations and ï¬?ve static equations: Ë™ï?´ ï?« ï?ª © ï?ª −1 ª ï?™ï?´ ï?ƒ ï?ª =  ï?ª ï?‡ ï‚¿ (ï?«ï?´ ) − (1 − ï‚°ï‚´ − ï‚¿ ) ( ï?? ) + ï?ºï?´ + ï?? − ï?‡ï€» (44) ï?«ï?´ ï?‹ï?´ ï?ƒ Ë™ï?´ ï?º ï?™ï?´ ï?ƒ ï?ƒ = ï?® + [ − (1 − ï‚°ï‚´ − ï‚¿ )]( ï?? ) + ï?ºï?´ −  ( +  ï?? ) − (1 −  ï?? ) (45) ï?ºï?´ ï?‹ï?´ Ë™ï?’ ï?­ï?´ ï?? ïƒ?ï?’ ï?’ 1 (ï?­ï?’ )ïƒ?2 [1 + ïƒ?ï?’ ( ï?­ï?‰ ï?´ ï?“ï?™ ï?™ï?´ ï?’ = (ï?«ï?´ ) ï?´ 3 ï?’ )](ï?“ ï?ƒ ï?´ −  ï?´ ) − (1 − ï‚°ï‚´ − ï‚¿ )( ï?? ) + ï?ºï?´ − (1 −  ï?? ) (46) ï?­ï?´ ï?­ï?´ ï?‹ï?´ Ë™ï?‰ ï?­ï?´ ï?‚ ïƒ?ï?‰ ïƒ?ï?‰ ï?— ï‚·ï?‰ ï?• ï?•ï€»ï?™ ï?™ï?´ ï?‰ = (ï?«ï?´ ) 1 (ï?­ï?‰ ï?´ ) (1 + ï?§ ) ( ï?´ −  ï?´ 2 ï?ƒ ) − (1 − ï‚°ï‚´ − ï‚¿ )( ï?? ) + ï?ºï?´ − (1 −  ï?? ) (47) ï?­ï?´ ï?‹ï?´ Ë™ï?’ ï?™ï?´ ï?’ ï?™ï?´ ï?’ −1 ï?‘ï?´ = [ï‚®( ï?? ) −  ï?? ]ï?‘ï?´ − (1 − ï‚´ )ï‚° (1 −  )( ï?? )(ï?­ï?´ )  (48) ï?‹ï?´ ï?‹ï?´ ï?™ï?´ (ï?«ï?´ ï?‚ (1− ) ) Λ2 © ï?‰  (1−) ï?’ (1− )(1−) ª(1− ) = (ï?­ï?´ ) (ï?­ï?´ )  (49) ï?‹ï?´ï?? [(ï?“ï?™  ï?“ ï?•ï€»ï?™ ) ï?• ]−1(1− ) ï?´ ) ( ï?´ ï?’ ï?“ ï?™ï?´ (ï?«ï?? )−ïƒ?1 ï?­ï?‰ ï?“ï?™ ï?´ = ( ï?? ) ï?’ ï?´ ï?’ (1+ïƒ?ï?’ ) [1 + ïƒ?ï?’ 3 ( ï?´ −1 ï?’ )]  (50) 1 −  ï?‹ï?´ ï?‘ï?´ (ï?­ï?´ ) 2 ï?­ï?´ 24 Eicher and García-Peñalosa (2001) and Howitt and Mayer-Foulkes (2005) make a similar assump- tion to facilitate the theoretical analysis of their models. However, given our focus on numerical results, we reintroduce later inertia in the acquisition of skills–albeit in a different way. 18 ï?• ï?‚ −ïƒ?ï?‰ −ïƒ?ï?‰ ï?‰ ï?•ï€»ï?™ ï?´ = (ï?«ï?´ ) 1 (ï?­ï?‰ ï?´) 2 (1 + ï?§ ï?— )−  (51) (1 − ï‚´) ( ) ï?“ï?™   ï?• ï?´ = max ï?¡  [ ï?Œ ( ï?´ )]1  (52) 1 −  ï?•ï€»ï?™ï?´ ½ ¾ ï?“ 1 − (ï?¡ ) 1 − (ï?• ï?ˆ 2 ï?´ ) 2 ï?´ = min   (53) 2 2 for ï?ª = ï?? ï?‚ . ï?? ï?‚ ï?ƒ These equations determine the dynamics of the system in terms of ï?«ï?´ , ï?«ï?´ , ï?ºï?´ , ï?­ï?‰ï?´, ï?­ï?’ , and ï?‘ ï?’ . In the steady state, ï?«Ë™ï?? = ï?«Ë™ï?‚ = ï?ºË™ ï?ƒ = ï?­Ë™ ï?‰ = ï?­Ë™ ï?’ = ï?‘Ë™ ï?’ = 0. Variables ï?´ ï?´ ï?´ ï?´ ï?´ ï?´ ï?´ ï?´ ï?ƒ ï?ºï?´ and ï?‘ï?’ ï?´ are jump variables, whereas the others are backward-looking variables. Given the complexity of the model, saddlepath stability (which requires the Jacobian of the system to have two positive eigenvalues) cannot be established analytically; however, given the range of parameter values that we consider later, and the numerical simulations that we perform, the model turns out to be saddlepath stable. In the steady state, the growth rates of the private and public capital stocks, the growth rate of consumption, the growth rate of imitation- and innovation-based knowl- edge, are all equal, whereas the license fee and the price of patents are constant. From the static conditions (49)-(53), ï?™ï?´ ï?‹ï?´ï?? , ï?“ï?™ ï?•ï€»ï?™ ï?´ , ï?´ , ï?• ï?“ ï?´ , and  ï?´ are also constant. Thus, the steady-state growth rate of output is the same as the growth rate of the private capital stock. The constancy of ï?• ï?“ ï?´ and  ï?´ (which is related to the constancy of ï?¡ï?´ ) ï?ƒ implies that in the steady state factor supplies grow at the same rate as the population, that is, ï?Ž Ë™ ï?´ï?“ ï?Žï?´ï?“ = ï?Ž Ë™ ï?´ï?• ï?Žï?´ï?• = ï?ŽË™ ï?´ ï?Žï?´ = ï?®. The long-run growth rate, γ , can be written in several equivalent ways. In partic- ular, as shown in Appendix A, ï?‰ Ëœï?? )ïƒ?ï?’ ï?’ Ëœ ï?­ Ëœï?“ Ëœï?“ï?™ ) γ = (ï?« Ëœ ï?’ )ïƒ?2 [1 + ïƒ?ï?’ 1 (ï?­ 3 ( ï?’ )]( −  (54) Ëœ ï?­ ï?“ where Ëœ  ≤ 1 − ï?¡ï?Œ . During the transition process, the stock of imitative knowledge increases, which through the learning by doing effect, raises productivity of unskilled labor in the imi- tation sector–possibly at a very rapid rate initially (see (25)). This helps to increase productivity of both types of labor in the production of the ï¬?nal good as well, and therefore wages for both categories of workers. If the skilled wage increases faster than the unskilled wage, the proportion of the labor force willing to invest in the acquisition of skills will also increase (see (8)), which in turn will dampen the rise in wages in the ï¬?nal good sector. At the same time, as the skilled wage given in (38) increases, ï?“ï?’ ï?´ will also increase, thereby promoting activity in the innovation sector. Thus, learning through the imitation sector may indeed help to accelerate the transition toward an innovation-based economy. The model can also produce alternative development regimes, depending on the wage conditions that determine individual occupational choices and the emergence of 19 an innovation sector. The two main cases that may arise (pure imitation and pure innovation), and the associated dynamic systems, are discussed in Appendix B. In what follows, we maintain our focus on a mixed regime, but one in which the innovation sector is very small (rather than inexistent) to begin with, and calibrate the model to study the transitional dynamics and the long-run effects of policy shocks. Before we do so it is worth noting that two variables that summarize the different phases of development highlighted above are the effective supply of skilled workers, ï?“ ï?´, and more importantly the relative ratio of the stocks of imitative to total knowledge, ï?­ï?´ = ï?­ï?‰ ï?‰ ï?’ ï?‰ ï?‰ ï?’ 25 ï?´ (ï?­ï?´ + ï?­ï?´ ) = ï??ï?´ (ï??ï?´ + ï??ï?´ ). During the transition, ï?“ ï?´ is increasing if the relative skilled wage is increasing, whereas ï?­ï?´ tends to fall if the economy is converging toward an innovation-based regime; the “modernâ€? or “innovation-basedâ€? economy is achieved when the imitation sector becomes a residual, so that ï?­ï?´ takes a relatively small value.26 Alternatively, the economy may be “stuckâ€? in an imitation-based regime, in the sense that ï?­ï?´ , although falling, remains positive in the steady state.27 Important considerations to assess the behavior of ï?“ ï?´ and ï?­ï?´ are the actual length of the transition to a mature economy and the role of public policy in affecting the nature of, and most importantly the speed at which, skills are acquired and industrial transformation occurs. We now turn to these issues, using a calibrated version of the model. 4 Calibration To study the transitional dynamics of the model and the steady-state effects of public policy, we calibrate it as follows. On the household side, the annual discount rate is set at 004, a fairly conventional choice. The elasticity of intertemporal substitution  is set at 03, in line with the evidence for developing countries reviewed in Agénor and Montiel (2008). The parameter that measures the efficiency of training, , is set initially at 05 and sensitivity analysis is conducted later. We normalize ï?Ž0 to unity (thus, each family starts with one member) and set the growth rate of the population, ï?®, at 21 percent. We assume that the cost of acquiring an education is quite high 25 Note that, because of the assumption that ï‚´ is the same for both types of intermediate goods, their prices–as can be seen in (16) and (20)–are the same. The index ï?­ï?´ can thus be measured directly in terms of quantities. 26 A third indicator could be the relative cost of innovation, ï?¸ï?´ = ï?£ï?’ ï?‰ ï?’ ï?´ (ï?£ï?´ + ï?£ï?´ ), deï¬?ned as the ratio ï?’ ï?“ ï?’ ï?‰ ï?• ï?‰ of the cost of innovation, ï?£ï?´ = ï?·ï?´ ï??ï?´ , to the cost of imitation, ï?£ï?´ = ï?·ï?´ ï??ï?´ (with innovation being more costly if ï?£ï?’ ï?‰ ï?´  ï?£ï?´ ). Note also that n the present setting, both design sectors grow at the same rate in the steady state, even though (as shown numerically) the relative size of the imitation sector shrinks over time. 27 The model also has implications for the nature of the ï¬?nal good produced in the economy, even though we have considered only one (aggregate) ï¬?nal good. In the early stages of development, where imitation activities predominate, the ï¬?nal good can be viewed essentially as a light manufactured good. As innovation activities develop, it can be viewed as a more advanced manufacturing good, for instance an equipment good. A more advanced treatment would of course consist in modeling the “lightâ€? and “heavyâ€? manufacturing sectors separately. 20 and initially set  at 015 of the skilled wage. We also maintain the normalization of ï?” to zero (which was imposed in the previous section); but to introduce inertia in the transformation of unskilled labor into skilled labor, we impose a partial adjustment on ï?• ï?´ to its equilibrium value as given in (52). 28 By implication, the share of skilled ï?“ workers in the labor force, ï?´ , also adjusts gradually. This speciï¬?cation therefore captures indirectly the fact that training is a process that takes time. In the ï¬?nal good sector, the elasticity of production with respect to basic public capital,  , is set at 014, the average value reported by Bom and Ligthart (2011).29 The elasticity of production with respect to unskilled labor,  ï?• , is set at 02, the elasticity with respect to skilled labor,  ï?“ , at 035, and the elasticity of production with respect to private capital, ï‚®, at 03, a fairly standard choice (see Agénor (2011)). By implication, the elasticity of output with respect to enhanced intermediate goods, ï‚° , is equal to 015. This is substantially lower than the value of 036 used by Funke and Strulik (2000) and Sequeira (2011) for instance, but it is more appropriate for a low- income country where, to begin with, the share of intermediate goods is relatively small, compared to capital and especially labor. We also assume that the relative share of imitated goods in the composite intermediate good ï?˜ï?´ , as measured by  (which, when multiplied by ï‚° , measures the relative share of that input in ï¬?nal production), is set at 09.30 The depreciation rate for private capital is set at 0068, which corresponds to the average value estimated by Bu (2006, Table 8) for three African countries (Ghana, Kenya, and Zimbabwe). In the intermediate goods sectors, the parameter ï‚´ (which determines the price elasticity of the demand for intermediate goods) is set to 061, similar to the value set by Chen and Funke (2012, Table 1).31 This implies an elasticity of substitution of about 26, which corresponds also to the value found by Acemoglu and Ventura (2002). In the imitation sector, the growth rate of the international pool of blueprints ï?— available for imitation, ï?§ï?‰ , is set at 002, in Chen and Funke (2012, Table 1). The elasticity with respect to the growth rate of imitable goods worldwide, ï‚·ï?‰ , is set initially at 035, in line again with Chen and Funke (2012, Table 1). The elasticity with respect to basic infrastructure ïƒ?ï?‰ ï?‰ 1 is set initially at 02, whereas the externality coefficient ïƒ?2 is set at 0. In the innovation sector, parameter ïƒ?ï?’ 1 , which measures the response to advanced infrastructure, is set initially at 02. Parameter ïƒ?ï?’ 2 is set initially at 00. The parameter 28 This assumption prevents large, and unrealistic, jumps in the composition of the labor force from contaminating the overall dynamics. Conceptually, given the assumption of inï¬?nite-horizon households, a partial adjustment process is also more appealing than ï¬?xing ï?” arbitrarily. 29 Note that other studies, based on simultaneous equation methods, obtain substantially higher values; see Agénor and Neanidis (2010). 30 In preliminary experiments, an alternative value of  = 05 was also used; the results did not prove very sensitive to this change. 31 By comparison, Funke and Strulik (2000) use a value of 054, whereas Sequeira (2011) uses alter- native values of 04 and 094. The latter value implies a fairly high elasticity of substitution between intermediate goods and captures market conditions that are close to competitive, given that it implies a low price markup. 21 measuring the externality associated with the stock of imitative knowledge, ïƒ?ï?’ 3 , is set initially equal to a very low value 004. The results turn out to be quite sensitive to the magnitude of the learning-by-doing effect of imitative knowledge, and sensitivity analysis is also reported later on. We assume that initially enforcement of property rights is poor and set the parameter  at 08. Thus, the “effectiveâ€? patent price is only 20 percent of the actual price. Regarding the government, the tax rate on ï¬?nal output, ï‚¿ , is set equal to 0151, which corresponds to the average ratio of tax revenues to GDP for low-income countries calculated by Baldacci et al. (2004, p. 530). By deï¬?nition, because the model does not consider deï¬?cit ï¬?nancing, this is also the share of government spending in output. The share of government investment in basic infrastructure,  ï?‚ , is set equal initially to 45 percent (or 07 percent of GDP), and the share of investment in advanced infrastructure to 05 percent. Thus, we consider the case of a country where initially much of public investment in infrastructure–which is low to begin with–is devoted to “coreâ€? infrastructure, roads, basic phone lines, and so on. This is a natural assumption for a low-income country. The depreciation rate for public capital,  ï?‡ , is set at 003, as in Agénor et al. (2008).32 To estimate the efficiency parameter of public spending, ï?‡ , we use the median value estimated by Dabla-Norris et al. (2011) for a sample of 71 developing countries, that is, 04.33 Thus, we assume that initially 60 percent of both types of investment is “wastedâ€?, in the sense that it does not transform into public capital. This creates, prima facie, a strong case for governance reform. Parameter values are summarized in Table 1. In the actual solution for the growth rate, a multiplicative constant is introduced in order to yield an initial annual growth rate of ï¬?nal output equal to 24 percent per annum, which corresponds to the average growth rate in Sub-Saharan Africa over the period 1990-2010. We also set initial values for several other variables. The initial proportion of the population that is unskilled, ï?• , is set at 095; using formula (43), this gives ï?“ = 0049. The absolute share of the unskilled labor force in ï¬?nal good production, ï?•ï€»ï?™ , is set at 07, which implies that the share of that type of labor in the imitation sector is 025. Similarly, the share of the (effective) skilled labor force in the ï¬?nal good sector, ï?“ï?™ , is set at 004, which implies that the share of that type of labor in the innovation sector is 0009. The core infrastructure-private capital ratio is set initially at ï?«ï?‚ = 02, whereas the advanced infrastructure-private capital ratio is set initially at ï?«ï?? = 005. The ratio of imitation-based goods to private capital is set equal to ï?­ï?‰ = 04, whereas the ratio of innovation-based goods to private capital is set equal to ï?­ï?’ = 005. By implication, our index of industrial structure, ï?­ = ï?­ï?‰ (ï?­ï?‰ + ï?­ï?’ ), is initially equal to 089. In sum, the low-income economy that we calibrate is characterized initially by a ) a 32 By way of comparison, Cubas (2011) uses a uniform value of 004 in compiling his estimates of public capital stocks across countries. 33 An alternative approach is to use the governance index deï¬?ned in Baldacci et al. (2008, Table 1), which once normalized to be between 0 and one, gives a value of 05. However, the results are not highly sensitive to that change. 22 positive but low growth rate in income per capita; b ) an embryonic innovation sector and a relatively more developed imitation sector; c ) a high cost of acquiring skills; d ) a large unskilled labor force, employed in both the imitation sector and ï¬?nal good pro- duction (and more so in the latter); e ) a small fraction of skilled workers in the labor force, employed almost entirely in ï¬?nal good production (in line with the assump- tion that the innovation sector is negligible in size); f ) limited availability of basic infrastructure and almost nonexistent advanced infrastructure; and g ) correspondingly a relatively low share of public investment in basic infrastructure and a much lower one on advanced infrastructure. At the same time, both stocks of public capital are relatively small in proportion to the private capital stock. Figure 2 shows the evolution of the economy’s industrial structure, based on the above initial conditions.34 The results are displayed for three different values of para- meter, ïƒ?ï?’ 3 , which measures the strength of the knowledge externality associated with imitation activities for the innovation sector: the benchmark case with a calibrated value of 004, and higher values of 02 and 05. In the base case, the relative size of the imitation sector increases slightly at ï¬?rst and comes down fairly slowly, dropping to close to zero after about 80 years. During the same time frame, the share of the unskilled labor force, ï?• , falls from 095 to 063 (with an increase in the proportion of unskilled workers in the ï¬?nal good sector from 070 to 074), whereas the share of the (effective) skilled labor force, ï?“ , grows from 0049 to 031.35 By contrast, in the other cases, the relative size of the imitation sector falls at a faster pace; in particular, with ïƒ?ï?’3 = 05, the index of industrial structure drops to close to zero in about 50 years. Thus, the benchmark case that we consider is still a rather mixed picture. The learning effect associated with imitation activities does have a substantial impact on industrial structure and the economy does become eventually a mature, innovation-based econ- omy. However, left on its own, this process would take decades to occur. The question then is to what extent public policy can help to accelerate the transition. As noted earlier, this is the sense in which we deï¬?ne industrial policy. 5 Public Policy We now consider a variety of public policies aimed at promoting growth and industrial transformation. Speciï¬?cally, we consider a policy aimed at promoting access to basic infrastructure; a training subsidy aimed at reducing the cost of acquiring skills; and 34 In all the simulations reported in this paper, we assume that the min and max functions in (52) and (53) do not bind. Because of difficulties with solving numerically the continuous-time version of the model, it is solved as a discrete time approximation using the Extended Path algorithm of Fair and Taylor (1983). The discrete-time approximation is actually more appropriate for implementing the sequential, composite reform program discussed later. 35 The growth rate of ï¬?nal output converges to the benchmark value of 24 percent per annum. Note that the fact that ï?­ï?´ tends to zero does not mean that the imitation sector disappears; rather, it implies that it becomes small in relative terms, compared to the size of the innovation sector. In the steady state, both sectors grow at the same rate, as discussed earlier. 23 a policy aimed at improving enforcement of intellectual property rights. To highlight the role of policy complementarities, we also consider a sequential, composite program which involves combining some of these policies, together with investment in advanced infrastructure. 5.1 Provision of Basic Infrastructure Consider ï¬?rst a permanent, budget-neutral increase in the share of spending on ba- sic infrastructure,  ï?‚ , from an initial value of 0045 to 0085, ï¬?nanced by a cut in unproductive spending, ï?• .36 The ï¬?rst impact of this policy is to promote activity in both the ï¬?nal good sector and the imitation sector. Both effects tend to increase the marginal product of unskilled labor and therefore the economy-wide wage for that category of workers. In the initial phase, this tends to reduce incentives for workers to acquire skills, and therefore to reduce the (effective) supply of skilled labor. However, the increase in activity in the imitation sector enlarges the pool of knowledge accessible to all workers and generates two types of externalities: it raises productivity not only in the imitation sector but also in the innovation sector. In turn, this puts upward pressure on skilled wages, which mitigates the initial adverse effect on individual incentives to invest in education. The net effect on economic growth depends on the extent to which these opposite effects on skilled labor supply offset each other or not. Note also that because public capital in basic infrastructure raises labor productiv- ity in both the ï¬?nal good and the imitation sectors, the extent to which the allocation of the unskilled labor force is affected depends on the parameters characterizing the production technology. Under some parameter conï¬?gurations, it is possible that there may be no change in the sectoral distribution of the unskilled labor force, with the ad- justment of the labor market operating essentially through a redistribution of workers across skill categories. Figure 3 shows the impact of this policy on industrial transformation for three different values of the ïƒ?ï?’ 3 , the parameter that measures the strength of the externality associated with imitation activities for the innovation sector, These values are the same as those used in Figure 2.37 The results show that, as can be expected, the relative size of the imitation sector increases at ï¬?rst; however, as the spillover effect of imitation- related knowledge for innovation begins to matter, this increase is reversed–the larger the effect of ïƒ?ï?’3 , the faster this reversal occurs. 36 In what follows, when considering shifts in productive spending, we only consider offsetting cuts in unproductive spending. The trade-offs involved otherwise are not well known. Note also that the very assumption that the government can reduce unproductive spending to ï¬?nance investment implies that there may be far-reaching governance reforms involved. 37 Note that in Figure 3, as well as in Figures 4 to 6, the index of industrial structure converges back to its baseline value. Recall that in the baseline value the index drops to zero in ï¬?nite time; what this implies therefore is that the fundamental role of the permanennt policy shocks that we consider is only to speed up the transition to an innovation-based economy. 24 5.2 Training Subsidy Consider now a policy aimed at reducing training costs. As discussed earlier, this cost is assumed to be proportional to the skilled wage, at the rate  = 015 initially. We assume that the policy involves a permanent reduction in this rate to 005, and is ï¬?nanced through a reallocation among components of unproductive spending. Thus, this policy is also budget neutral. Naturally enough, the reduction in the training cost induces more workers to invest in education. The increase in skilled labor supply, at ï¬?rst, tends to lower wages in that sector; however, because the increase in skilled employment occurs both in the ï¬?nal good sector and in the innovation sector, promoting activity there, a secondary, indirect effect is also at play: the increase in the variety of innovation-based (or enhanced) intermediate goods helps to promote activity in the ï¬?nal good sector. In addition, because the shift toward innovation raises the productivity of labor in that sector, the initial effect is magniï¬?ed. At the same time, however, the increase in the supply of skilled labor in the ï¬?nal good sector tends to raise the marginal product of unskilled workers, which tends to raise the unskilled wage–thereby mitigating the initial effect on incentives to acquire skills. Figure 4 shows the impact of this policy on the country’s industrial structure, for two values of the parameter , 04 (the benchmark case) and a lower value of 02, which measures the strength of ability’s effect on wages; the smaller  is, the weaker this effect, which means that individuals with lower abilities would earn less. Even though the quantitative effect of the training subsidy on the industrial structure is relatively small, the net effect of the training subsidy is a higher supply of skilled labor and higher activity in the innovation sector, thereby explaining the initial increase in the relative size of that sector. The smaller the parameter  is, the stronger these effects are. 5.3 Enforcement of Property Rights Consider a reform of property rights that is designed to promote innovation activities– such as improved functioning of the bureau of patents, for instance. This is captured by considering a drop in the coefficient , from an initial value of 08, to ï¬?rst 04, and then to 00. In the second scenario, therefore, ï¬?rms in the innovation sector earn the full patent price. The economic effects of this shock are fairly intuitive. By increasing the ability of ï¬?rms engaged in innovation to secure the return to their activity, improved protection of property rights tends also to raise labor demand in that sector–and thus wages as well. The increase in skilled wages induces more workers to invest in skills, thereby promoting growth. Thus, the growth effect is unambiguously positive. Figure 5 shows the impact of this policy on industrial structure. It shows that securing property rights may play an important role in accelerating the process of industrial transformation. These reforms have sizable effects not only because they increase the direct return 25 to innovation, but also because they provide greater incentives for workers to acquire skills. It is worth noting that a key reason why the growth effect of this policy is unam- biguous is, of course, the fact that in the model poor enforcement of property rights creates a deadweight loss; no one really beneï¬?ts from intellectual piracy. However, in a more general setting with multiple ï¬?nal goods, piracy could generate signiï¬?cant beneï¬?ts for some producers; if so the net effect of improving the protection of property rights on growth could be mitigated–and, in some extreme cases, possibly reversed. 5.4 Sequential, Composite Reform Program We now consider a sequential program, characterized by the following components: during an initial period of 8 years, the share of spending on basic infrastructure,  ï?‚ , is increased from 0045 to 0085; it is then reduced gradually by one percentage point every year, to 0025 over 6 years, and kept at that level permanently. During an initial period of 7 years, the share of spending on advanced infrastructure, ï?? , is kept at the benchmark level of 0005; it is then increased to 0045 for a subsequent period of 7 years, reduced over the following two years by one percentage point each year to 0025, and kept at that level permanently. There is no training subsidy for the ï¬?rst 4 years, so that  remains equal to its benchmark value of 015; then the subsidy reduces  to 010 for the following 5 years, and to 005 permanently thereafter. For the ï¬?rst seven years there are no efforts to improve the enforcement of property rights, so that  remains at its benchmark value of 08; then, through appropriate reforms,  is reduced to 06 over a period of 4 years; 03 over another period of 4 years; and ï¬?nally to 0, permanently from then on. Of course, there is a signiï¬?cant element of arbitrariness in this timing. But what we are trying to capture is a policy focusing ï¬?rst on improving access to basic infrastructure (through a “Big Pushâ€? in public investment) and imitation activities; next, an effort to promote human capital accumulation through training subsidies and enforcement of property rights; and, soon after, access to advanced infrastructure, to promote innovation. Figure 6 shows the impact of this reform program on industrial structure. As the parameter that measures the strength of the externality associated with imitation activities for the innovation sector, ïƒ?ï?’ 3 , increases from its benchmark value of 004 to higher values of 02 and 05, the magnitude of the transitory drop in the index of industrial structure becomes larger. Thus, if indeed external learning effects are associated with imitation, a sequential reform program that is front-loaded on access to basic infrastructure can speed up the transition process to a mature economy. Put differently, in a low-income economy where to begin with unskilled labor is in abundant supply, the imitation sector is relatively small, and the innovation sector embryonic, public investment in basic infrastructure yields higher marginal growth beneï¬?ts than investment in advanced infrastructure. The key reason is that expansion of activity in that sector would remain constrained by the lack of skilled workers in the labor force. In a second stage, higher investment in advanced infrastructure, if preceded 26 by a policy that induces more individuals to acquire skills, and if accompanied by a policy that helps to promote the enforcement of property rights, would generate higher marginal growth beneï¬?ts than investment in basic infrastructure. The learning externality associated with imitation activity in a ï¬?rst stage can help magnify the beneï¬?ts that can be generated in this second stage. 6 Policy Implications The foregoing discussion has important implications both for growth-promoting policies in today’s poor countries in Sub-Saharan Africa and, more generally, for understanding the industrial transformation process whereby countries can move from imitation to innovation. During the past decade, the region’s GDP grew at an average of over 5.2 percent a year between 2001 to 2010, compared with an average of -0.4 percent in the 1990s (see Dinh et al. (2012b )).38 However, to a large extent, this outcome was the result of booming commodity prices, rather than the result of a deep transformation of the industrial structure. Yet, as noted in the introduction, such transformation is essential to generate sustained growth in output and employment–as illustrated by the expe- rience of East Asian countries during the 1960s, and more recently China’s during the 1980s. Indeed, these countries followed initially a growth strategy that relied heavily on the development of light manufacturing, taking advantage of relatively cheap labor and their ability to imitate foreign goods. The lesson from East Asia’s experience in transiting from low- to middle-income status is clear: a sustainable growth strategy in Sub-Saharan Africa should focus, in a ï¬?rst stage, on increasing the productivity of medium and large formal ï¬?rms and on alleviating the key constraints that they face, namely, in terms of access to basic infrastructure (most importantly electricity, see Andersen and Dalgaard (2013)). As noted by Dinh et al. (2012b ), as local producers increase the scale of their operations, improve the quality of their products, and accu- mulate experience with technology, management, and marketing, they become better positioned to take advantage of emerging export opportunities. As China’s competitive edge in the global export market in light manufactures continues to erode–as a result of steeply rising costs of land, regulatory compliance, and especially labor (including both wages and beneï¬?ts) in the country’s coastal export manufacturing centers–the redistribution of cost advantages in labor-intensive manufacturing presents an oppor- tunity for Sub-Saharan Africa to start producing and exporting a wide range of light manufacturing goods.39 38 These numbers may actually underestimate the region’s performance in recent years. According to Young (2012), measures of real consumption based on a variety of nonstandard indicators suggest that living standards in Sub-Saharan Africa have grown 3 to 4 four times faster than the rates indicated in conventional data sets. 39 The possibility for Sub-Saharan Africa to becoming competitive in light manufacturing worldwide may well occur despite the fact that new entrants (Bangladesh, Cambodia, and China’s interior provinces) have already begun to line up; see UNIDO (2009) and Chandra et al. (2012). 27 This strategy is feasible because Sub-Saharan Africa has two major potential ad- vantages that could help promote competitiveness in light manufacturing. The ï¬?rst is a labor cost advantage. The second is an abundance of natural resources that supply raw materials, such as skins for the footwear industry, hard and soft timber for the fur- niture industry, land for the agribusiness industry, and so on. Even with its relatively low-skill workforce, Sub-Saharan Africa could become competitive in a broad range of light manufacturing sectors. In the apparel sector, for instance, small numbers of man- agers and technicians can guide hundreds of workers.40 For the longer term, upgrading to more complex production will undoubtedly require a better-trained workforce than is currently available. But the expansion of light industry need not await higher school enrollment and better-quality schooling. Industrial transformation can begin rapidly by targeting promising sectors with modest skill requirements and then adopting pol- icy measures–such as industry-speciï¬?c vocational training programs–that may con- tribute to lowering the cost of acquiring skills and promote learning-by-doing effects.41 This approach would help to channel scarce resources for infrastructure services to speciï¬?c locations or industries, thereby mitigating the adverse effect that the lack of access to these services has had on production costs and labor productivity. As docu- mented by Eifert et al. (2008) and Foster and Briceño-Garmendia (2010) for instance, indirect costs related to infrastructure services continue to account for a relatively high share of the costs of ï¬?rms in poor African countries.42 If indeed the lack of access to infrastructure is the most signiï¬?cant constraint on the expansion of labor-intensive light manufacturing industries, then it is important for African governments to focus their scarce resources in that area, making sure that economies of scale are properly exploited.43 Our model, and the simulation results that it produced, provide much support for this strategy. The key features of our calibration capture fairly well some of the characteristics of a “typicalâ€? low-income economy in Sub-Saharan Africa: an embryonic innovation sector and a relatively more developed imitation sector (yet small in terms of the size of the economy); a high cost of acquiring skills, possibly due to a lack of tangible collateral for securing loans to ï¬?nance human capital accumulation; a small fraction of skilled workers in the labor force, and correspondingly a large unskilled labor force, operating partly in the imitation sector; limited availability of basic infrastructure and almost nonexistent advanced infrastructure. The simulations help to emphasize the fact 40 As noted by Dinh et al. (2012a ) for instance, specialists report that inexperienced workers can learn to operate sewing machines in no more than two weeks. 41 Mathews (2006) for instance discusses the techonological learning gains that occurred in Taiwan, China through its electronics sector. 42 Although the survey results reported in Dinh and Clarke (2012) suggest that ï¬?rm managers in the region are most concerned about electricity, other areas of infrastructure may also constrain ï¬?rm performance in Africa. Eifert et al. (2008) show that, in particular, transportation and communication costs are high in Sub-Saharan Africa. 43 The successful experience of East Asia with industrial parks is an example in that regard. Instead of waiting to solve the infrastructure problem for the whole country, they focused instead on providing infrastructure for enterprises located inside the parks. 28 that learning through imitation may enable ï¬?rms to improve productivity signiï¬?cantly in a ï¬?rst stage, and that this may eventually beneï¬?t innovation activity as well. Put differently, imitation contributes to create the knowledge base necessary for fostering innovation; by doing so, it helps to increase labor productivity and to create incentives for workers to invest in higher education. The experience of East Asian countries in transitioning from middle- to high-income status provides also important lessons for Sub-Saharan Africa. As noted earlier, these countries successfully relied on a growth strategy based on low wages and technology imitation. However, once the pool of underemployed rural workers started to shrink and wages began to rise, competitiveness deteriorated, and the productivity gains asso- ciated with sectoral reallocation and technology catch-up began to disappear in many of them. Rising wages made labor-intensive manufacturing exports less competitive on world markets (Chandra and Kolavalli (2006)). At that point, some countries (most importantly Korea) were able to switch from imitation as the main source of pro- ductivity growth to broad-based, home-grown innovation.44 Others, however, were unable to make that switch and ended up as a result in a so-called “middle-income growth trap,â€? with a substantial reduction in growth and total factor productivity. As discussed by Agénor and Canuto (2012, 2013), avoiding this trap requires timely im- plementation of public policies aimed at improving access to advanced infrastructure, enhancing the protection of property rights, reforming labor markets, and promoting access to ï¬?nance. These policies have proved central to fostering technological learning, attracting talented individuals into R&D activities, and allowing inventors to ï¬?nance the development of their ideas. The lesson from that experience for today’s poor coun- tries in Sub-Saharan Africa is again very clear: governments in the region should act early–rather than late, when the beneï¬?ts of cheap labor and the gains from imitating foreign technology are all but exhausted–and decisively to promote innovation and boost productivity. Our numerical results also support the view that, following a ï¬?rst stage where countries should invest signiï¬?cantly in basic infrastructure, policies aimed at promoting innovation must be put in place without much delay; these include institutional reforms aimed at promoting property rights related to research activities, and the provision of advanced infrastructure, which is essential to encourage the buildup of national and international knowledge networks. This second stage should begin well before the beneï¬?ts of low wages and imitation of foreign technology yield diminishing returns or are completely exhausted. 7 Concluding Remarks The purpose of this paper was to study the role of public policy in promoting indus- trial transformation from an imitation-based, low-skill economy, where technological 44 Crespi and Zuniga (2012) also provide evidence for six Latin American countries that ï¬?rms that innovate have higher labor productivity. 29 progress results mainly from copying and adapting foreign ideas, to an innovation- based, high-skill economy, where technological progress now occurs mostly by inventing new ideas domestically. Using a model of endogenous growth, industrial transforma- tion was measured by changes in an index of industrial structure, deï¬?ned as the ratio of the variety of imitation- to innovation-based intermediate goods. In the model, a key mechanism through which productivity increases initially in both the imitation and innovation sectors is through a knowledge externality associated with learning by do- ing in the imitation sector. The process of industrialization was shown to increase the demand for high-skill labor, inducing individuals to invest in education. In turn, edu- cation stimulates further productivity and technological advancement in the innovation sector. The model also emphasized the distinction between basic or core infrastructure, which promotes imitation, and advanced infrastructure, which promotes innovation. In this setting, investment in human capital is not a prerequisite for promoting growth and development in its initial stages. The model was calibrated for a “typicalâ€? low-income country and used to perform a variety of policy experiments, involving an increase in investment in basic infrastruc- ture, a reduction in the cost of training, and improved enforcement of property rights. An illustrative composite reform program, combining these policies sequentially, to- gether with investment in advanced infrastructure, was also analyzed. The results showed the importance of improved access to basic infrastructure to initiate a growth and development process based on imitation, in a ï¬?rst stage, and higher investment in advanced infrastructure to promote a shift to an innovation-based process, at a later stage. The broader policy implications of the analysis were also discussed. A key point of our analysis (largely corroborated by the evidence) is that the lack of skills is not a binding constraint for launching a two-pronged growth strategy, aimed in a ï¬?rst phase at promoting the development of labor-intensive manufacturing industries and, in a second phase, at promoting skill-intensive domestic innovation. At the same time, our analysis helps to emphasize the importance of access to advanced infrastructure and enforcement of intellectual property rights to achieve that second phase. An important extension of our framework would be to introduce explicitly ï¬?nancing constraints, both at the level of the production of goods and the production of ideas. The evidence collected in Dinh and Clarke (2012) shows that in Sub-Saharan Africa, while start-up ï¬?rms can survive and grow without access to bank loans or other support from the formal ï¬?nancial sector, for them to grow bigger they need access to ï¬?nance. Beck et al. 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Journal of Political Economy, 120 (August 2012), 696-739. 33 Table 1 Calibrated Parameter Values: Benchmark Case Parameter Value Description Households  004 Annual discount rate  03 Elasticity of intertemporal substitution ï?® 0021 Growth rate of population  05 Productivity parameter (efficiency of training)  015 Training cost (in proportion of skilled wage) Final Goods  014 Elasticity wrt to public-private capital ratio ï?• 02 Elasticity with respect to unskilled labor ï?“ 035 Elasticity with respect to skilled labor ï‚® 03 Elasticity with respect to private capital ï‚° 015 Elasticity with respect to composite intermediate input  09 Share of core inputs in composite intermediate input ï?? 0068 Rate of depreciation, private capital Intermediate goods ï‚´ 061 Substitution parameter, intermediate goods Imitation sector ï‚·ï?‰ 035 Elasticity wrt distance from technology frontier ïƒ?ï?‰1 02 Elasticity wrt basic public infrastructure ïƒ?ï?‰2 00 Productivity parameter, stock of imitated goods ï?§ï?— 002 Growth rate of world stock of imitable goods Innovation sector ïƒ?ï?’1 02 Elasticity wrt advanced public infrastructure ïƒ?ï?’2 00 Productivity parameter, stock of innovative goods ïƒ?ï?’3 004 Learning effect, stock of imitated goods  08 Proportion of patent price lost due to poor property rights Government ï‚¿ 0151 Tax rate on output of ï¬?nal good ï?? 0005 Share of spending on advanced infrastructure ï?‚ 0045 Share of spending on basic infrastructure ï?‡ 04 Efficiency parameter, public investment ï?‡ 003 Rate of depreciation, public capital 34 Figure 1 Production Structure and Labor Supply Imitation Sector Innovation sector License fee Patents Designs Designs Unskilled Core Enhanced Skilled labor intermediate intermediate labor goods goods Advanced infrastructure Basic Final good Infrastructure Private capital Relative wages Labor supply decisions Figure 2 Baseline Scenario: Index of Industrial Structure for Different Parameter Values 1 0.9 0.8 0.7 R 0.6 ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€°ï€´ 3 0.5 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€µ 3 0.4 0.3 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€² 3 0.2 0.1 0 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 Time Figure 3 Higher Share of Investment in Basic Infrastructure (Absolute deviations from baseline) 0.15 R G ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€°ï€´ï€¬ï€ ï?ªï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€¸ 3 0.1 R 0.05 ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€°ï€´ 3 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€³ï€®ï€µ 3 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€µ 3 0 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 Time Figure 4 Reduction in the Cost of Acquiring Skills (Absolute deviations from baseline) 0 -0.01 ï?£ï€ ï€½ï€ ï€°ï€®ï€´ -0.02 -0.03 ï?£ï€ ï€½ï€ ï€°ï€®ï€² -0.04 -0.05 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 Time Figure 5 Improved Enforcement of Property Rights (Absolute deviations from baseline) 0 -0.1 ï?¬ï€ ï€½ï€ ï€°ï€®ï€´ -0.2 -0.3 ï?¬ï€ ï€½ï€ ï€°ï€®ï€° -0.4 -0.5 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 Time Figure 6 Sequential, Composite Reform Program (Absolute deviations from baseline) 0 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€°ï€´ 3 -0.1 R -0.2 ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€µ 3 R ï?¦ï€ ï€ ï€ ï€½ï€ ï€°ï€®ï€² 3 -0.3 -0.4 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 Time