77317 THE WORLD BANK ECONOMIC REVIEW, VOL. 14, NO. li 91-109 Vintage Technologies and Skill Constraints: Evidence from U.S. Exports of New and Used Machines Giorgio Barba Navaretti, Isidro Soloaga, and Wendy Takacs When countries import production machinery, they must choose between new and used equipment. This article looks at that choice in the presence of labor-saving technical progress and complementarity between technologies and skills within the firm. It devel- ops a theoretical model of the market for used machines. It then analyzes data on U.S. exports of metalworking machine tools by country of destination, classifying machines according to their vintage and their technological characteristics. The data show that the share of used equipment imported is higher if the importing country has a lower level of development, as measured by income per capita. Econometric estimation of the determi- nants of this share shows that it also is higher the greater is the technological change embodied in the machine or the greater is the change in the skills required to run the machine efficiently. These results indicate that technological factors and skill constraints may be as im- portant as factor prices in determining the choice of technique in developing countries. The policy recommendation emerging from this work—avoid constraints on imports of used equipment—is similar to that in the existing literature. But the reasoning is differ- ent. Instead of emphasizing inappropriate capital-labor ratios for low-wage countries, the results indicate that investment in advanced technologies is effective only if importing countries have the skills to use them. Many developing countries design their trade policies to discriminate against importation of secondhand goods, imposing import bans, licensing requirements, or higher tariff rates. Some industrial countries even discriminate against used products: witness Australia's additional $12,000 tariff on used cars (Wonnacott Giorgio Barba Navaretti is with the Department of Economics at the University degli Studi di Ancona, Centro Studi Luca d'Agliano, and Fondazione Eni Enrico Mattei; Isidro Soloaga u with the Develop- ment Research Group at the World Bank and the Department of Economics at the University of Mary- land, College Park; and Wendy Takacs is with the Department of Economics at the University of Mary- land, Baltimore County. Their e-mail addresses are barba@mailserver.unimi.it, isoloaga9worldbanJt.org, arid wtakacs@umbc.edu. This article was prepared while Mr. Barba Navaretti was a visiting researcher with the Development Research Group at the World Bank. Fondazione Eni Enrico Mattei and Centro Studi Luca d'Agliano partly funded this project. Mr. Anthony M. Bratkovich, engineering director of the U.S. Association for Manufacturing Technology, was extremely patient and helpful in leading the authors through the mysteries of the technological characteristics of metalworking machines. The au- thors appreciate the useful suggestions of Gabriel Castillo, John Nash, Garry Purscll, Maurice Schiff, James Tybout, and the anonymous referees. They also thank Jeff Hayden and Jennifer Ngaine for their assistance. O 2000 The International Bank for Reconstruction and Development / THE WORLD BANK 91 92 THE WORLD BANK ECONOMIC REVIEW, VOL. 14, NO. 1 1994). These policies are motivated by a desire to protect domestic industries against competition from low-priced goods, to avoid becoming a dumping ground for castoffs from high-income countries, to push industries toward the techno- logical frontier, and to avoid the use of obsolete technologies. But trade restrictions on used capital goods appear contrary to the appropri- ate choice of production techniques in developing countries, where low wages and high interest rates call for the use of labor-intensive production processes. Older equipment is likely to be more labor-intensive than new equipment; technological change tends to be labor-saving, and older equipment requires greater maintenance and carries a greater risk of downtime. Moreover, the optimal scale of older machines is smaller, which may be more appropriate for the smaller markets in developing countries, and older machines may be more flexible in their use and less specialized. Thus several authors conclude that firms in low- wage developing countries would find secondhand equipment more profitable than new machines and that developing countries would suffer a welfare loss from import restrictions on used machinery (Sen 1962, Schwartz 1973, James 1974, Thoumi 1975, Mainwaring 1986, and Pack 1977). In this literature some models focus on the impact of greater maintenance costs as machines age (Schwartz 1973 and Thoumi 1975). The literature on vintage capital emphasizes labor-saving technological change (Bardhan 1970, Smith 1976, Gabisch 1975, and Pack and Todaro 1970). And some models in- corporate both phenomena (Mainwaring 1986). Recent contributions on tech- nology transfer link the choice of technique to the skills available in a firm or country. These skills are human capital or other technological capabilities ac- quired through deliberate learning or learning by doing (Benhabib and Rustichini 1991, Chan and Hopenhayn 1991, Keller 1994, Jovanovic and MacDonald 1993, and Jovanovic and Nyarko 1995, 1998). The more skills that are specific to a particular technique, the more costly it is to switch to that technique. The skill factor is likely to affect the choice between new and used machines when new machines embody technical change. In this article we model a firm's choice between new and used machines. We test the predictions emerging from the modeling exercise using data on U.S. exports of new and used metalworking machinery, disaggregated by type of machine and by country of destination. The model incorporates three factors: greater downtime as machines age, labor-saving technical progress, and the greater skill requirements of more technologically sophisticated machinery. Most of the literature on trade in used machinery focuses on heterogeneity between countries based on the stylized fact that developing countries have lower wages and higher capital costs than industrial countries (Sen 1962, Smith 1974, and Mainwaring 1986). We adopt a slightly different model based on heteroge- neity among firms (as in Bond 1983). Our model takes into account that if labor and capital markets are imperfect or distorted by sectoral labor regulations or subsidized directed credit, firms in the same country may face different wage rates and capital costs. Barba Navaretti, Soloaga, and Takacs 93 Firms also can differ in the technical and managerial skills available to them. Heterogeneity among firms located in different countries provides the underlying motive for international trade in new and used capital equipment. Models that do not take firm heterogeneity into account predict fairly extreme patterns of trade in used machinery. For example, several models predict that firms in devel- oping countries would import only the oldest machinery available. The assump- tion that firms within developing countries may face different wage structures and interest rates is reasonable, given imperfections in capital markets, the coex- istence of multinationals and purely domestic firms, and the dichotomy between the formal and informal sectors. I. THE FIRM'S CHOICE BETWEEN NEW AND USED MACHINERY This section develops a model that is a version of Bond (1983), modified to include international trade of machinery. Differences between New and Used Machinery New and used machinery can differ in three important ways: risk of break- down, productivity of embodied technology, and required technical skills. Used machinery normally requires more maintenance and is more likely to break down than new machinery. Maintenance demands high labor input. In addition, if employees are paid for a regular work schedule, machine downtime means that workers are idle, implicitly increasing the labor intensity of the production pro- cess. We capture the impact of breakdowns and the maintenance requirements of used machines by adjusting output for downtime using the factor a, defined as the ratio of a used machine's output to that of an identical new machine, that is, one not yet operated (0 < a < 1). Machinery of a given vintage embodies the technology available when it was produced. Labor-saving technical progress is captured by distinguishing between output per worker with a machine newly produced in the current pe- riod (an) and output per worker with a machine embodying last period's tech- nology, when that machine was new (au). Thus the ratio au I aH captures the rate of labor-saving technical progress, independent of the downtime effect, a, with (*„/*„) £ 1 . To identify the independent impacts of technical progress and the aging pro- cess in the context of metalworking machines, we distinguish between low-tech and high-tech machines. From a technological point of view machine tools (es- pecially metal-cutting tools) can be divided into two broad categories. Numeri- cally controlled machines have a high rate of technological upgrading, linked to the development of electronics. These are "high-tech" machines. Manual ma- chines may improve in terms of design and safety, but they have no or a very low rate of technical progress. These are "low-tech" machines. The difference in la- bor productivity between new and used low-tech machines is attributable only to increases in maintenance and longer downtime. The difference in labor produc- 94 THE WORLD BANK ECONOMIC REVIEW, VOL. 14, NO. 1 rivity between new and used high-tech machines is attributable to technical progress as well as to increases in maintenance and longer downtime. For low-tech (manual) machines output per worker varies with age because of the downtime (a) effect (figure 1). For high-tech (numerically controlled) ma- chines labor productivity declines with the age of the machine because of the combined effect of downtime and the lower technological sophistication embod- ied in older machines (figure 1). There are two key features of the relationships between labor productivity and the two types of machines. First, output per worker is always lower for low-tech than for high-tech machines. Second, at any point in time, the decline in labor productivity with age is larger for high-tech machines than for low-tech machines. The third way in which new and used technologies may differ is in the skills required to operate the machines. The literature on vintage technology empha- sizes the role of technology-specific skills (Evenson and Westphal 1994 and Keller 1994). Metalworking machine tools provide a good example. Manual machines (low-tech) require sophisticated craftsmen to operate them. Numerically con- trolled (high-tech) machines require electronic technicians. Accumulated learn- ing by doing could be lost when a firm switches to a new technology (Chari and Hopenhayn 1991, Dasgupta and Stiglitz 1988, Jovanovie and MacDonald 1993, and Jovanovic and Nyarko 1995, 1996). Complementarities between workers with different skills may constrain the choice of technology (Chari and Hopenhayn 1991). Linking the educational level of the people using the machines (craftspeople, technicians, engineers) to the technology embodied in the machines is essential, Figure 1. Labor Productivity and Machine Age with and without Technical Progress Output per worker High-tech machines Low-tech machines Age of machine Barba Navaretti, Soloaga, and Takacs 95 but not sufficient. Technological knowledge is often tacit and not transmittable in codified form (David 1993), and technological capabilities are related to the performance of many different technological functions (Lall 1987). Skills, then, should refer to the absorptive capacity of a firm or a country, that is, the ability to master a given technology (Evenson and Westphal 1994 and Keller 1994). Absorptive capacity is affected by the physical, social, and economic characteris- tics of a firm or country. Firms therefore may be reluctant to move to high-tech machines because they do not have the skills to use them or because building up such skills would be more costly than continuing to use low-tech machines. In our simplified setting we assume that if a firm adopts a new high-tech machine that it does not have the appropriate skills to run it suffers a loss in productivity. The firm's current level of productivity is captured by y, the proportion of full-capacity output achievable with new machines, given current skills (where 0 S y£ 1). We refer to Y as the "inability coefficient," since y is lower the less able is the firm. The skill factor may constrain the choice between new and used machines to the extent that new machines embody an increasing level of technological sophistication. Trade Policy Different trade policy instruments influence the choice between new and used machines in different ways. An equal ad valorem tariff rate, t, on all imported machines raises the domestic price of new and used machines proportionally. Restrictions discriminating against used equipment through either higher tariffs or licensing requirements increase the cost of used equipment disproportionately, discouraging its use. Relative Prices We assume that machines last for two periods. A firm buying a new machine can sell it at the end of the period for the going price of a used machine, but used machines will have zero scrap value at the end of the second period of use. The analysis assumes that machines are paid for at the beginning of the period and that wages are paid out at the end of the period. At the end of the period the firm's (net) cost of using a new machine embodying the current period's technol- ogy would be: (1) CH=Pn(l + r)(l + t)-Pu(l + t) + — q. a n The firm's (net) cost of using a machine embodying the previous period's tech- nology (if the machine had never been used) would be: (2) Cu = PJl + r)(l + t) + — q 96 THE WORLD BANK ECONOMIC REVIEW, VOL. 14, NO. 1 where C, is the total cost of production using machinery i {i = n for new machines, and i = u for used machines), P,is the price of machine i, a, is the labor productivity of machine i (ty = q I L<) when it is (was) unused, L, is the labor input per time period with machine i, w is the wage rate per time period, r is the interest rate, t is the ad valorem tariff rate on machinery imports, and q is the full-capacity output of a machine when it is new.1 If the machine embodying last period's technology is used in that period, it yields only a of the output it did when new. If the productivity of the new ma- chine is constrained because of the lack of skill in the labor force, the new ma- chine yields only y times the designed output.2 More precisely, a is the propor- tion of the hill-capacity output of a new machine that can be produced when the machine has been used for one period, and y is the proportion of full-capacity output that can be produced using die new machine with current skills. A firm will be indifferent between new and used machinery if unit costs are the same with the two types of equipment: (3) yq aq Thus a firm will be indifferent between new and used equipment when: Pu(l + t) + — q PJl + r)(l + t) + — q 5 fi a Solving for PH yields U, the price of used equipment at which the firm is indiffer- ent between using new and used equipment: where p = 1 / (1 + r) and 6 = 1 / (1 + t). If the market price of used machinery (Pu) is less than a firm's indifference price (17), the firm will buy used equipment; if the market price is greater (Pu > U), the firm will buy new equipment. Given the market price, Pu, an increase in 17 makes it more likely that a firm will buy used equipment, and a decrease in 17 raises the chance that it will buy new equipment. 1. We assume th*t full-capacity output of a new machine is always the same (q) independent of the type of machine, whereas the labor input necessary to achieve full-capacity output changes (thus affecting labor productivity a,). 2. Labor input doe* not change if the machine is used at less than full-capacity output. Either worken are paid on a fixed schedule, or they use their idle time to maintain machines. Barba Navaretti, Soloaga, and Takacs 97 Equation 5 implies the following: • The indifference price of used machines equals the price of new machines with production capacity equal to that of used machines (the first term in the numerator on the right side of equation 5), net of the higher labor costs of used compared with new machines (the second term in the numerator on the right side of equation 5). • Other things being equal, the smaller is a (the more the use of equipment generates a loss in productivity) and the smaller is aj an (the greater is the rate of labor-saving technical progress), the lower is the indifference price (the less desirable are used machines). • The indifference price of used machines increases as y falls, other things being equal, so firms that do not have the technical skills required to run new machinery will be more likely to opt for used equipment. The impact of the wage rate, interest rate, and machinery tariff rate on the indifference price of used machinery is more complicated to assess and depends crucially on the firm's skill level, y. Unless the firm lacks most of the skills needed to use higher-technology equipment, the productivity of new machines is greater than that of used machines for the firm, that is, aajyan < 1. In this case U declines when w and (3 increase, so firms facing high wages and low capital costs are more likely to prefer new machines (because it is more likely that U < Pu). Also, U decreases as 9 increases, implying that higher tariffs raise the indifference price of used machines, making their purchase more likely. Indeed, tariff increases push the indifference price downward in the same way as do increases in the cost of capital (r). But lack of skills to make use of higher- technology equipment (a sufficiently low y) could eliminate or reverse the influ- ence of wages, interest rates, and tariff levels on the indifference price. The Market for Used Machines We assume that there are two regions, North and South. Firms in the North (N) are homogeneous (all have the same y) and face the same factor prices. Firms in the South are either large (L) or small (S). Large southern firms have more technical skills (higher y) and face more expensive labor and cheaper capital than small southern firms.3 Given the homogeneity of northern firms, used machines are supplied at their indifference price (UN), therefore, Pu = UN. Northern firms are indifferent be- tween purchasing used or new machines.4 The South is a price taker because it is 3. This assumption is consistent with widespread evidence that labor and capital markets in developing countries are fraught with imperfections and often are segmented, so that small and large firms face different wage and interest rates. These differences are a result of credit rationing, labor regulations, dichotomies between formal and informal sectors, and the coexistence of multinational and indigenous firms. In addition, small and large firms Hiffrr in ^i n^ of tyrhriral skills and th*r*fnr* may have widely different values of y. 4. The northern indifference price is the equilibrium price of used machines even if northern firms only 98 THE WORLD BANK ECONOMIC REVIEW, VOL 14, NO. 1 small in machinery markets compared with the North. New and used machinery prices are determined in northern machinery markets, and both large and small southern firms face an infinitely elastic supply of new and used machines at those prices. In the South large firms have sufficient skills to absorb new technology (high y). They face sufficiently high wages and low interest rates so that, at the prices of new and used machines determined in the North, large southern firms would opt for new machines, as UL < UN. Small southern firms, in contrast, have relatively low y and face high interest rates and low wages. Thus the indifference price of small southern firms exceeds that of northern firms (from equation 5), and small firms buy only used machines. With heterogeneous firms in the South and homogeneous firms buying at the indifference price in the North, firms in both the South and the North purchase new and used machines. In the South small firms' demand for used machines and large firms' demand for new machines depend on the demand for their output. Suppose that small and large firms' products (Xs and XL, respectively) are imperfect substitutes, are nontradable, and have downward-sloping demand functions P(X{). The demand for used machines by small southern firms must be consistent with the zero- profit condition: (6) where X s is the quantity of the final product produced and sold by small south- ern firms, P(XS) is the price of Xs, and subscript S designates the value of the variables for small southern firms. The production function for small southern firms is given by: (7) Xs=aqQtt, where Qu is the quantity of used machines employed by small southern firms. The demand function for good X s is given by: (8) P(Xs) = b-cXs. Substituting equation 7 into equation 8, and equation 8 into equation 6, yields the demand function for used machines by small southern firms: (9) Pu When Pu > Us, that is, when the price of used equipment is greater than the indifference price of southern firms, they will not buy any used machines.5 Thus 5. Technology and the cost parameters of large and small firms are assumed to be such that large southern firms strictly prefer new machines and small southern firms strictly prefer used machines at the northern supply price, U^. The indifference price of small firms, Us, is the price of used machines at which small firms are indifferent between producing and not producing. We use a somewhat different notation to disfingiiith this concept. We thank an anonymous referee for pointing out this subtkty. Barba Navaretti, Soloaga, and Takacs 99 the inverse demand function (equation 9) must be consistent with the following condition: Pu £ U s when Qu = 0. Therefore, the demand for used machines among small southern firms is given by: (10) Pu=Us-«*VWQ?S- In equilibrium, because the North is large and pins down the price for used equipment, UN = ?„, and the quantity of used equipment demanded by the South will be the quantity demanded at the North's indifference price (UN). Thus the equilibrium quantity of used machines demanded by small southern firms is given by: (11) ca. Equation 11 shows that the quantity of used machines demanded in the South is greater the larger is the gap between the indifference prices of small southern and northern firms. Similarly, the demand for new machines by large southern firms must be consistent with their zero-profit condition: (12) PH = J where subscript L designates the value of the variables for large southern firms. Their production function is given by: (13) XL=YL<7Q B > where Qn is the quantity of new machines employed by large southern firms. The demand function for good XL is given by: (14) P(XL) = e-gXL. Substituting equation 13 into equation 14, and equation 14 into equation 12, yields large southern firms' demand for new machines as a function of the price of used machines: (15) Pu =PB(1- When Pu < UL, that is, when the price of used equipment is less than the indif- ference price of large southern firms, large southern firms will not buy new ma- chines. Thus the inverse demand function (equation 15) must be consistent with the following condition: Pu <, UL when Q^- = 0. Therefore, (16) K=VL+gilc?SQ?L. 200 THE WORLD BANK ECONOMIC REVIEW, VOL 14, NO. 1 Again, the equilibrium price of used equipment is the northern indifference price (UN). Thus the equilibrium quantity of new machines demanded by large south- ern firms is given by: (17) In the South large firms keep new machines for one year and then sell them to small firms. Small firms can buy used machines from large firms or import them. In the steady state, large firms' demand for new machines (Q^t) will equal their supply of used machines ( Q ^ ) , and the domestic market for used machines in each soudiern firm will be in equilibrium when: (18) MU=Q™-QSHL, where Mu is the quantity of used machines imported. The equilibrium quantity of used machines imported by the South will be determined by the interaction between the northern indifference price, U^ which defines foreign supply (NN in figure 2), large southern firms' supply of used machines (equation 17 and LL in figure 2), and small southern firms' demand for used machines (equation 10 and SS in figure 2). Given equation 1$, the quan- tity of imports of used machines is the horizontal distance between LL and SS at height NN. 6 When the gap between small southern firms' indifference price and the world price of used machines increases, the shifts in SS and NN generate an increase in the quantity of used machines demanded by small southern firms. When the gap between the world price of used machines and large southern firms' indifference price increases, the shifts in LL and NN generate an increase in the domestic supply of used machines. The ratio Oy of used machines imported to total machines imported (esti- mated empirically in the following section) will then be Therefore, (19) *„=!-•