I. A Model of Endogenous Growth and Restructuring

The model developed here builds on Lucas (1988). Consider a small open economy producing two (baskets of) traded goods, the outputs of which are denoted by Q¹ and Q², and the prices of which are determined in the rest of the world. Initially, for simplicity, abstract from the presence of physical capital.⁹ The population, or labor supply, is assumed to be constant. The two goods are produced by a technology of the Cobb-Douglas type, with diminishing returns to labor

Here, $h_t^i$ is the skill level or human capital specialized in the production of good i, where i = 1,2; N denotes the size of the labor force, and $l_t^i$ is the share of the labor force employed in the production of good i.

The effect of the skill level or human capital, $h_t^i$, is assumed to be entirely external to any of the large numbers of perfectly competitive firms in each industry. This positive externality cannot be captured by any single firm; that is to say, the production of each firm depends on the average skill level in that industry. It is assumed that skills are acquired, according to

and a dot over a variable denotes its derivative with respect to time. The growth of the skill level should be interpreted as occurring due to learning and can be interpreted as learning-by-doing. The rate of growth of skills in equation (2) is a positive function of both the speed of learning, represented by δ_i, and the effort or resources devoted to producing good i, which is assumed to be related to the proportion of the labor force employed in the production of good i. Good 1 will be referred to as the high-technology good and good 2 as the low-technology good. It is posited further that the speed of learning is greater in the high-technology sector than in the low-technology sector, so that δ₁ > δ₂.

Equation (2) implies that the economy’s production possibility frontier shifts out over time, with experience gained by the labor force resulting in an increase in the skill level and, hence, productivity of the labor force. Note that the form of these learning equations implies constant returns to experience. This seems counterintuitive, in that one would expect learning-by-doing or the acquiring of skill in any particular activity to occur rapidly at first, then more slowly, and then not at all. The constant returns to learning in (2) should be interpreted as representing an environment in which innovations are constantly occurring and being adopted, so that learning is interpreted not only as permitting things to be done better, but also results in better things being done. Viewing learning as encompassing the adoption of innovations provides a justification for the assumption of a higher speed of learning in the high-technology sector, since innovations are likely to occur at a relatively more rapid rate in the sector.

It is assumed for simplicity that labor is perfectly homogeneous and mobile across sectors, and that wages are perfectly flexible. Full employment therefore implies

For our purposes it is convenient to allow for a subsidy on wages in sector 1, granted at the rate τ₁, and a tax on wages in sector 2, levied at the rate τ₂. Then combining firms’ first-order conditions for profit maximization, and substituting in the full-employment condition (3), yields

which can then be used to solve for the share of labor in sector 1 as a function of the relative skill level in sector 1 and the exogenous variables of the system, so that

In equation (4b), H_t denotes the ratio of skill levels or human capital; that is, $H_t=h_t^1/h_t^2;$ equals P₂/P₁ and denotes the internationally given relative price of good 2 in terms of the numeraire good 1. Signs underneath arguments in the $l_t^1$ function indicate signs of the partial derivatives, and are straightforward to derive from (4a). The learning or skill accumulation equations can be combined to obtain a relative learning equation and, with substitution of the full-employment condition, yield

Figure 2 graphs the possible dynamic paths of the economy represented by equations (4b) and (5). The growth of skills in each activity is determined by both the speed of learning and the effort or resources—that is, proportion of the labor force—devoted to each activity. Since the speeds of learning are posited to be different in the two sectors, there will exist distributions of the labor force between the two sectors such that the ratio of skill levels remains exactly constant over time: where, for example, the effect on the growth of the relative skill level of a smaller share of labor devoted to producing the high-technology good is offset exactly by the higher speed of learning in that activity. In Figure 2 the ${\dot{H}}_t=0$ line denotes such a locus of points where relative skill levels remain constant. The arrows indicate the direction of movement of the relative skill level, H_t, when the economy is off the ${\dot{H}}_t=0$ line. The curve OL represents the general equilibrium employment share in sector 1, $l_t^1$, as given by equation (4b). Under the assumptions here the economy is always on this curve, and the double arrows on the curve thus indicate the actual path of the economy at any relative skill level H_t. The two curves intersect at a critical relative skill level, $H_t^c$, in the production of the high-technology good. Given an initial ratio of human capital in the two sectors, H₀, and in the absence of exogenous shocks to the system, the future path of production is completely determined. Unless the economy is initially endowed with a relative human capital ratio of exactly $H_t^c$ the economy will, over time, naturally traverse either up the OL ray, eventually specializing in the production of the high-technology good 1, or it will move in the opposite direction, specializing eventually in good 2. If the economy specializes in good 1, the growth rate of aggregate output is, from equations (1) and (2), δ₁, which is, by assumption, greater than δ₂, the growth rate if the economy specializes in good 2. Thus, movements in Figure 2 toward L can be identified as converging to a high-growth path, and movements toward O as converging to a low-growth path. It can be shown that at any point in time along a transition path—that is, at any point on the OL curve—the rate of growth of output increases monotonically from δ₂ at O to δ₁ at L.

Dynamic Path of Economy

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Dynamic Path of Economy

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Dynamic Path of Economy

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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The production possibility frontier (PPF) shifts out, over time, proportionately in favor of the good that the country has an initial comparative advantage in producing—that is, the good it produces relatively more of—since its skill level will grow relatively more in the activity to which it devotes larger resources. Thus, at unchanged relative prices, except by pure chance, in the case where resources are initially apportioned in the production of each good such that relative skill levels remain constant, the economy will end up specializing in the production of one of the two goods over time. Initial comparative advantage is thus magnified over time. Since the speed of learning is posited to be greater in the high-technology good, eventual specialization in that good implies a higher steady-state growth rate.

The analysis presents a manifestation of popular notions of bottle necks to growth.¹⁰ There are no forces in the system just discussed that would necessarily place the economy on a path converging to the high-growth path. Whether the economy ends up on the high-growth path or the low-growth path will depend upon its initial relative skill levels and internationally given relative prices. Since the learning effects are assumed to be external, agents do not take them into account, and the high-technology good is thus underproduced, and production and trade are determined by temporal or historical comparative advantage. The market, left to itself, will not necessarily pick the high-growth path, except by historical accident. There is thus a clear role for government intervention. In particular, allocating labor toward the high-technology good, relative to the free market solution, would result over time in the acquisition of comparative advantage in the production of the high-technology good and a higher growth rate.

An alternative reason for the existence of differential potentials for productivity increases that are external to any single firm is different rates of technology transfer from the rest of the world to the two sectors.¹¹ Imagine, for simplicity, that “available” technological progress occurs globally at a faster rate in the high-technology sector. Now suppose that the (relative) speed of adoption of these innovations—that is, the actual transfer of the technology—is a function of the (relative) resources devoted to the production of each good. The analysis of different rates of technology transfer from abroad is then equivalent to that described above for endogenous productivity increases.

The role of skills upgrading is transparent in the framework of Figure 2. An exogenous increase in the relative skill level in the production of the high-technology good would move the economy to the right along the curve OL. Thus, a relatively skill-scarce economy can, by increasing its skill level, cross the threshold value of $H_t^c$, and put itself on a self-sustaining path of restructuring toward the high-technology good, leading eventually to complete specialization in the good, and a higher steady-state growth rate.

Role of Wage Differentials in Economic Restructuring

A simple and convenient way to analyze the effect of an exogenous decline in the relative wages paid in the high-technology sector is to examine the effect of a tax on wages in the labor-intensive, low-technology sector, or the effect of a subsidy on wages in the high-technology sector.¹² Consider the effect of an increase in the tax rate on wages in sector 2, τ₂. Recalling equation (4b), an increase in τ₂ results in an upward shift of the OL curve, as depicted in Figure 3, to OL′, so that, as would be expected, an increasing proportion of the labor force is employed in the high-technology sector at any skill level. It now intersects the ${\dot{H}}_t=0$ line at a lower relative skill level, $H_t^{c^{\prime }}$. This implies that if the economy initially had a relative skill level between $H_t^{c^{\prime }}$ and $H_t^c$, it would have been on a path converging to the low-growth path; after the shift in the OL curve, skill levels between $H_t^{c^{\prime }}$ and $H_t^c$ become points converging to the high-growth path. The mechanism by which this occurs is straightforward. A decline in the relative wage paid by producers of good 1 shifts employment in favor of good 1, increasing the proportion of the labor force devoted to producing the high-technology good. Increasing the proportion of resources devoted to producing the high-technology good increases the scope for learning or acquiring comparative advantage in that activity. The locus of initial conditions converging to eventual specialization in the high-technology good thus increases.

Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector 2

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector 2

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector 2

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Role of Investment

The rate of investment in physical capital plays an important role in the restructuring of output.¹⁵ An increase in the stock of physical capital would increase by relatively more the output of the capital-intensive sector. Thus, in the above setting, where the capital-intensive good is the high-technology good, an increase in the stock of physical capital will shift the composition of output and employment in favor of the high-technology good. Hence, an increase in the rate of investment can be viewed as an alternative engine for the restructuring of output, while additionally providing an independent source of economic growth.

In introducing physical capital accumulation into the model above, some simplifying assumptions are made to keep the analysis tractable. The case of interest is one where the high-technology sector is relatively capital intensive, and productivity increases at a faster rate because the speed of learning and, hence, the rate of skill accumulation is greater. A simple and tractable way to maintain these assumptions is to take the extreme case: capital is employed only in the high-technology sector; and whereas, as before, in the high-technology sector skills are accumulated by learning, the skill level in the low-technology good is constant and normalized to equal unity. Production functions can then be written as

$\begin{array}{ccc}{Q}_t^1=H_t{\left[l_t^{1}N\right]}^{\mathrm{\alpha }}{K}_t^{1-\mathrm{\alpha }}& & \\ Q_t^2={\left[l_t^{2}N\right]}^{\mathrm{\beta }},\hfill & 0<\mathrm{\alpha }<\mathrm{\beta }<1,& \left(6\right)\end{array}$

where K_t represents the stock of physical capital. Note the slight change in notation: the skill level in the high-technology sector is now denoted by H_t. This is to highlight the fact that while formally H_t now represents only the absolute skill level in sector 1, it can still be interpreted as the relative skill level in that sector. As before, it is assumed that the rate of growth of the skill level in sector 1, H_t, increases with the proportion of the labor force, $l_t^1$, devoted to producing good 1. Specifically

$\begin{array}{cc}\frac{{\dot{H}}_t}{H_t}={\mathrm{\delta }}_1{l}_t^1-{\mathrm{\delta }}_2,& \begin{array}{cc}{\mathrm{\delta }}_1>{\mathrm{\delta }}_2\mathrm{.}& \left(7\right)\end{array}\end{array}$

It is assumed along with Kouri (1979) that for a small open economy, net investment at home is an increasing function of the discrepancy between the actual rate of return to capital, r_t, adjusted for any taxes levied at the rate Φ, and the exogenously given rate of return, r^*, in the international capital market:¹⁶

$\begin{array}{cc}{\dot{K}}_t=\mathrm{\gamma }\left[(1-\mathrm{\Phi })r_t-r^{*}\right]\mathrm{.}& \left(8\right)\end{array}$

Assuming a competitive market for capital, the rate of return (rental) to capital at home is given at any point in time by the marginal product of capital in sector 1:

$\begin{array}{cc}{r}_t=(1-\mathrm{\alpha })H_t{\left[l_t^{1}N\right]}^{\mathrm{\alpha }}{K}_t^{-\mathrm{\alpha }}\mathrm{.}& \left(9\right)\end{array}$

As in the previous subsection, first-order conditions for profit maximization can be combined with the full-employment condition to yield

$\begin{array}{cc}\frac{{\begin{array}{c}(1-l_t^1)\end{array}}^{1-\mathrm{\beta }}}{{\left(l_t^1\right)}^{1-\mathrm{\alpha }}}=\frac{\mathrm{\beta }P{N}^{\mathrm{\beta }-\mathrm{\alpha }}(1-{\mathrm{\tau }}_1)}{\mathrm{\alpha }{H}_t{K}_t^{1-\mathrm{\alpha }}(1+{\mathrm{\tau }}_2)},& \left(10\text{a}\right)\end{array}$

so that

$\begin{array}{cc}{l}_t^1\text{\hspace{0.5em}=}{l}_t^1(H_t,{\mathit{\text{K}}}_t\text{;}\mathit{\text{P}}\text{,}{\text{N}}^{\mathrm{\beta }-\mathrm{\alpha }},{\tau }_1\text{,}{\tau }_2)\mathrm{.}\hfill & \left(10\text{b}\right)\\ (+)(+)(-)(-)(+)(+)& \end{array}$

Substituting (10b) into (7), combining (8) and (9), and again substituting in (10b), yields a pair of dynamic equations in the skills level and the stock of physical capital:

$\begin{array}{cc}\frac{{\dot{H}}_t}{H_t}={\mathrm{\delta }}_1{l}_t^1(H_t,K_t;P,N^{\mathrm{\beta }-\mathrm{\alpha }},{\mathrm{\tau }}_1,{\mathrm{\tau }}_2)-{\mathrm{\delta }}_2& \left(11\right)\\ (+)(+)\hfill & \end{array}$

$\begin{array}{cc}{\dot{K}}_t=\mathrm{\gamma }\left[(1-\mathrm{\Phi })(1-\mathrm{\alpha })H_t\right[l_t^1(H_t,K_t;P,N^{\mathrm{\beta }-\mathrm{\alpha }},{\mathrm{\tau }}_1,{\mathrm{\tau }}_2)N{]}^{\mathrm{\alpha }}{K}_t^{-\mathrm{\alpha }}-r^{*}]\mathrm{.}& \left(12\right)\\ (+)(+)\hfill & \end{array}$

It follows that

$\begin{array}{cc}\frac{\partial {\dot{H}}_t}{\partial H_t},\frac{\partial {\dot{H}}_t}{\partial K_t},\frac{\partial {\dot{K}}_t}{\partial H_t}>0,& \left(13\text{a}\right)\end{array}$

and it can be established that

$\begin{array}{cc}\frac{\partial {\dot{K}}_t}{\partial K_t}<0.& \left(13\mathrm{b}\right)\end{array}$

To establish (13b), differentiate (12) with respect to the capital stock, and rearrange, so that

$\begin{array}{cc}\frac{\partial {\dot{K}}_t}{\partial K_t}=\mathrm{\gamma }(1-\mathrm{\Phi })(1-\mathrm{\alpha })H_t{N}^{\mathrm{\alpha }}\mathrm{\alpha }{\left(l^1\right)}^{\mathrm{\alpha }}{K}_t^{-\mathrm{\alpha }-1}[\frac{K}{l^1}\frac{\partial l^1}{\partial K}-1],& \left(14\right)\end{array}$

and, therefore,

$\begin{array}{cc}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left[\frac{\partial {\dot{K}}_t}{\partial K_t}\right]=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}[\frac{K}{l^1}\frac{\partial l^1}{\partial K}-1]\mathrm{.}& \left(15\right)\end{array}$

Now, differentiating (10a) and rearranging

$\begin{array}{cc}\left[\frac{K}{l^1}\frac{\partial l^1}{\partial K}\right]=\frac{1}{\frac{(1-\mathrm{\beta })}{(1-\mathrm{\alpha })}\frac{l^1}{(1-l^1)}+1}<1,& \left(16\right)\end{array}$

so that $\partial \dot{K}/\partial K<0.$ Given (13a) and (13b)

$\begin{array}{cc}\frac{dH}{dK}{|}_{\dot{K}=0}>0,& \\ \frac{dH}{dK}{|}_{\dot{H}=0}<0,& \left(\begin{array}{c}17\end{array}\right)\end{array}$

so that a phase diagram describing the possible dynamic paths of the economy can be drawn, as in Figure 4.

Dynamic Path of Economy with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Dynamic Path of Economy with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Dynamic Path of Economy with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Note that both the skill level, H_t, and the stock of capital, K_t, are predetermined variables given by history at any point in time. As the arrows indicate, there exists a locus of initial H, K combinations, labeled CC in Figure 4, which places the economy on a path converging to a steady-state combination of $\overline{H}$, $\overline{K}$¹⁷ The curve CC corresponds in this setting to the point $H_t^c$, in the previous subsection. Again, the initial combination of skill level and capital stock determines the entire future path of production, and there are three possibilities: if the initial H, K endowment places the economy above CC, then the economy will, over time, tend toward specialization in the capital-intensive, high-technology good; if below CC, the economy will tend toward specialization in the labor-intensive, low-technology good; if exactly on CC, the economy will remain diversified, converging over time to $\overline{H}$, $\overline{K}$ Note that CC is downward-sloping in Figure 4. This implies that a high stock of capital can offset a low-skill level as a bottleneck, and vice versa, in attaining a self-sustaining path to restructuring toward the capital-intensive, high-technology good.

This expanded framework allows consideration of the two main components of the wage-correction policy: a change in relative wages and an increase in the overall level of wages. Consider first the relative wage effect. As before, consider the effect of an increase in the rate of tax, τ₂, on employment in the labor-intensive, low-technology sector 2. Given the signs of the partial derivatives in equation (10b), it follows that both the ${\dot{H}}_t=0$ curve and the ${\dot{K}}_t=0$ curve shift down in the H, K plane, as shown in Figure 5 where the original curves are depicted by dashed lines. This implies that the CC curve, which separates initial conditions converging to eventual specialization in the high-technology good from those converging to specialization in the low-technology good, also shifts down from CC¹ to CC². The shaded area in Figure 5 denotes the set of points that originally would have resulted in the economy continuously expanding its share of labor-intensive, low-technology goods, but now become points leading to eventual specialization in the high-technology good.

Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effect of an Increase in the Tax Rate on Wages in the Low-Technology Sector with Endogenous Capital Accumulation

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Consider now the effect of an increase in average real wages in excess of productivity growth. Since such an increase would reduce the rate of return to capital, a convenient way to model it is to examine the effect of an increase in the tax, Φ, on the return to capital.¹⁸ In this case there is no effect on the ${\dot{H}}_t=0$ curve, since Φ does not enter equation (11). From equation (12), however, the ${\dot{K}}_t=0$ curve shifts up or to the left in the H, K plane as shown in Figure 6. Thus at each skill level, the rate of investment is zero at a smaller level of the capital stock. Each point on the original ${\dot{K}}_t=0$ curve represents a pair of skill and physical capital levels, such that the tax-adjusted rate of return to capital was just equal to that in the rest of the world. An increase in the tax rate thus requires, for any skill level, a lower level of capital, so that the marginal product of capital rises sufficiently to equate the domestic tax-adjusted rate of return to that given exogenously in the rest of the world. The upward shift of the ${\dot{K}}_t=0$ curve implies a consequent upward shift of the CC curve in Figure 6 from CC¹ to CC². In this case the shaded area denotes a set of points that originally would have resulted in production converging to specialization in the high-technology good but, as a result of the decline in the rate of return to capital, become points converging to specialization in the labor-intensive, low-technology good.

Effects of an Increase in the Tax Rate on the Return to Capital

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effects of an Increase in the Tax Rate on the Return to Capital

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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Effects of an Increase in the Tax Rate on the Return to Capital

Citation: IMF Staff Papers 1991, 004; 10.5089/9781451956917.024.A003

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The questions raised at the end of the last section on restructuring can now be answered. First, in the framework developed above, government intervention can play a pivotal role in providing an initial impetus for restructuring, which market forces may not naturally generate due to the presence of external learning effects. A second question was whether restructuring would simply raise the level of output or could influence long-run growth potential. The framework developed here clearly suggests scope for the latter if the high-technology and knowledge-and-skill-intensive sectors have the inherent potential for higher productivity growth. Finally, on the third issue—the effect of the wage-correction policy on economic restructuring—the analysis suggests that there were probably two opposing influences. The decline of relative wages in the higher-paid occupations, on the one hand, tended to shift employment in favor of these occupations, thus moving the economy onto, or further along, a path to self-sustaining restructuring toward capital-intensive, high-technology and knowledge-and-skill-intensive activities. The rapid increase in real wages across the board, on the other hand, lowered the rate of return to capital and thus lowered investment, which tended to move the economy away from such a path.¹⁹

II. Conclusion

This paper has examined a particular phase in the growth experience of Singapore—that of economic restructuring. To examine the process of restructuring in general, a model of endogenous growth and restructuring for a small open economy incorporating learning-by-doing was developed. A broad conclusion from this framework is that impediments to restructuring may exist because of the potential importance of external learning effects, the benefits of which redound not to individual firms but to a sector as a whole. Such externalities present bottlenecks to market-driven restructuring and create a role for government intervention. In particular, it was shown that a diversion of resources, even temporary, can induce an acquisition of comparative advantage and hence permanently affect the pattern of trade and growth. The framework thus suggests that if high-technology and knowledge-and-skill-intensive sectors inherently have the potential for higher productivity growth, economic restructuring would not simply raise the level of output but could permanently raise the rate of long-run growth.

The framework was employed to analyze the effects of, among other things, the wage-correction policy on the direction and pace of economic restructuring in Singapore. The results indicate that there were probably two opposing influences. The decline of relative wages in the higher-paid occupations, on the one hand, tended to shift employment in favor of these occupations, thus moving the economy onto, or further along, a path of self-sustaining restructuring toward higher-technology and knowledge-and-skill-intensive activities. The absolute increase in average real labor costs across the board in excess of productivity growth, on the other hand, lowered the rate of return to capital and thus lowered investment, tending to move the economy away from such a path. However, note that in Singapore restructuring did not hinge on the net effect of these two opposing forces alone, since it was boosted in addition by the upgrading of skills and the promotion of investment in relatively labor-saving and knowledge-and-skill-intensive activities. Indications are that initial bottlenecks to restructuring in Singapore have been overcome—a basic level of skills and trained manpower now exists, and a critical mass of high-technology and knowledge-and-skill-intensive activities has been established—and comparative advantage in these activities is likely to grow naturally.

It is worth emphasizing that the framework developed here for examining alternative growth strategies was for a small and highly open labor-constrained economy. The policy conclusions reached, therefore, may not be applicable for all countries, and it should be noted that a shift toward production of high-technology goods is not sustainable for the world as a whole. Two crucial assumptions were made. First, the analysis was carried out on the assumption of a fully employed and constant labor force. This seems accurate for Singapore at the end of the 1970s. For a labor-surplus economy, however, a shift toward labor-saving means of production may clearly not be appropriate in the presence of a large pool of unemployed labor. Second, for a small open economy, world demand was assumed to be infinite. A global shift in production toward any one good would, in the absence of any change in tastes, undoubtedly shift the terms of trade against the good, making its production less profitable and limit the scope for growth.²⁰