Growth Accounting for a Technology Follower in a World of Ideas: The Case of Singapore

Kong Weng Ho

Hian Teck Hoon

and

Nanyang Technological University

Singapore Management University

December 2008 Abstract: We account for the sources of Singapore’s growth by being explicit about the channels through which Singapore benefits from international R&D spillovers. We find that 61.5 percent of Singapore’s real GDP per worker growth over the 1970-2004 period is due to multifactor productivity growth. More specifically, 52.1 percent of the growth is explained by an increase in the effectiveness of accessing ideas through improvement in Singapore’s educational quality as well as increases in machinery imports and foreign direct investment from the G5 countries. Taking account of technology transfer raises the average rate of return to capital to 12.5 percent. (JEL classification: F43, O33, O47)

Keywords: technological diffusion, idea production function, multifactor productivity growth



Corresponding author: Professor Hian Teck Hoon, School of Economics, Singapore Management University, 90, Stamford Road, Singapore 178903. Tel: (65)-6828-0248; Fax: (65)-6828-0833; Email: [email protected]

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1. Introduction Empirical work by Hall and Jones (1999) and Parente and Prescott (2000) shows that in an international cross-section of countries, the bulk of the huge differences in levels of output per worker is explained by differences in multifactor productivity (MFP). Klenow and Rodríguez-Clare (1997) further shows that differences in multifactor productivity growth rates play an even greater role in explaining differences in the growth rates of income per capita across countries. A theoretical framework that makes both these predictions is one with a group of innovating countries (technology leaders) constantly pushing forward the world technology frontier through its investment in research and development (R&D) with the rest of the world (technology followers) potentially benefiting through international R&D spillovers. Coe, Helpman and Hoffmaister (1997) and Hejazi and Safarian (1999) show empirically that how much any single technology follower benefits from international R&D spillovers depends on its stock of human capital as well as its integration with the technology leaders through trade and foreign direct investment. Nelson and Phelps (1966) is a seminal paper presenting such a theoretical framework while Barro and Sala-i-Martin (1997) provides a more micro-foundation-based treatment of innovation and technological diffusion. Consistent with the empirical findings in these international cross-sectional studies, since Singapore is highly open to the international flow of ideas, Benhabib and Spiegel (2005) find a high multifactor productivity growth rate of 4.31 percent per annum on average from 1960 to 1995 for Singapore, the second fastest-growing economy over the 1960-2000 period in the sample of 112 countries compiled by Barro and Sala-i-Martin (2004, chapter 12). Similarly, Klenow and Rodríguez-Clare (1997) find a large contribution of MFP growth to Singapore’s income growth; they find an average MFP growth rate of 3.3 percent for Singapore from 1960 to 1985. In contrast, growth accounting done by Tsao (1985) and Young (1992, 1995) for Singapore finds a very small contribution of MFP growth to the rapid growth of income per capita. What are the reasons for the differences in the empirical findings on Singapore? What would we find if a more recent updated and revised data series on Singapore, available from the Singapore Department of Statistics, is used in the empirical work? In the following section, we report our empirical results on growth accounting for Singapore using the more recent data series; we find a much higher contribution by MFP growth to per capita income growth compared to what Tsao (1985) and Young (1992, 1995) found. In section 3, we develop a model of how a technology follower like Singapore may benefit from a world of ideas, thus offering a theoretical explanation for our empirical finding of Singapore’s high MFP growth rates. Then in section 4, we conduct a detailed quantitative analysis taking explicit account of the channels for international technology diffusion. In other words, we explain quantitatively the sources of Singapore’s MFP growth---the “residual” in Solow growth accounting. Section 5 concludes.

2. Why Should Singapore’s MFP Growth Rate Be High? Klenow and Rodríguez-Clare (1997) attribute their finding of a high contribution of MFP growth to income growth for Singapore, which contrasts sharply with Young (1995), to the use of a different data source

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for labor inputs and the use of a different value for the output elasticity of capital, . The former paper uses data from the Penn World Tables and assumes an output elasticity of capital of 0.30 while the latter uses data from the Singapore Department of Statistics and an output elasticity of capital of 0.491 in Young (1995) and 0.533 in Young (1992) for the aggregate economy. Like Klenow and Rodríguez-Clare (1997), Benhabib and Spiegel (2005) use data from the Penn World Tables and assumed an output elasticity of capital of 1/3. In this paper, we use the most recently available data series from the Singapore Department of Statistics and compute Singapore’s MFP growth rates from 1970 to 2004 under different assumptions about the value of the output elasticity of capital.1 Detailed documentation of our data sources and data construction is given in Appendix 1. Table 1 shows the average annual growth rates of some key variables for Singapore for the period 1970 to 2004.2 The average growth rate of real GDP per worker was about 4 percent per annum. Human capital and capital-output ratio grew at 1.04 percent and 1.03 percent per annum, respectively, for the same period. For the baseline case with  = 1/3, MFP grew at an average annual rate of 2.43 percent, thus accounting for 61.5 percent of growth in real GDP per worker. As a robustness check, we vary the values of  obtained under different assumptions about product market competition and returns to scale to capital and labor, and re-compute the contribution of MFP growth. (We will discuss the different assumptions and their implications for the values of  shortly.) For all cases of  in Table 1, the growth rate of MFP as a percentage of the growth rate of real GDP per worker was high, ranging from 48.1 to 65.5 percent, suggesting that MFP growth was a major contributor to per capita income growth. It is apparent that using a larger value of  reduces the contribution of MFP growth to Singapore’s per capita income growth, but not entirely.

[Table 1: Average Annual Growth Rates of Key Variables: Singapore, 1970 to 2004]

One possible reason for the difference in our results from Young (1992, 1995) is that our empirical study used the most recent data series from the Singapore Department of Statistics, and the data have been updated and revised since the publication of Young (1992, 1995). A second reason is that we used Mincer’s method to adjust for the educational quality of labor input, a method also used in recent studies such as Hall and Jones (1999), Jones (2002), and Caselli (2005), which is different from Young’s (1992, 1995) approach of using differentiated categories of labor inputs. In our detailed quantitative analysis in section 4, our baseline model uses an output elasticity of capital of  = 1/3, which is consistent with the theoretical foundation of a technology follower growing in a world of ideas. The justification is that  itself is a feature of technology and in a world where technology

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At the time we conducted our empirical analysis for the latest draft (September 2008), the most comprehensive data set available to us (not only for Singapore but also for the G5 countries, which supplied the Research Scientists and Engineers for research that pushed out the technology frontier) was for the period 1970-2004. 2 We start from the year 1970 because this is the earliest year data are available for the stock of foreign direct equity investment from the G5 countries, which we need in order to compute our measure of the effectiveness of technology diffusion.

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followers adopt the ideas created by technology leaders, the value of  should be approximately the same in all countries. (Jones (2005) endogenously derives the shape of the production function and shows that if the distribution of ideas is Pareto, the global production function is Cobb-Douglas.) Empirically, Sarel (1997) assumes that technological factor shares are determined by the industrial structure of the economy and its level of development. His methodology shows that the resulting shares need not be equal to income shares as measured in the national income accounts. In particular, he obtains the estimated output elasticity of capital for Singapore, , of 0.337 on average from 1978 to 1996. Gollin (2002) shows that countries with high measured capital shares in national income might nevertheless have the same  when account is taken of the prevalence of self-employment in these high capital share countries. He argues that, for a number of reasons, the labor income of the self-employed is often treated incorrectly as capital income. Once corrections are made, he argues that  is stable both across time and across countries. Another reason for accepting a lower output elasticity of capital, , than that computed by Young (1992, 1995) is the absence of perfect competition in the product and factor markets. Using a structural regression to estimate productivity growth based on more general production and cost functions, Kee (2004) found that the gross markup in the aggregate economy of Singapore is more than one, implying imperfect competition in the product market, and that the “true”  is lower than the empirically observed capital share in national income. Table 6 in Kee (2004) gives a primal estimate of a gross price-cost markup ratio equal to 1.33 while Table 2 in Kee (2004) estimates an average labor share in total value added of 0.47 for the aggregate economy from 1970 to 2001. Using these estimates, the output elasticity of labor is equal to 0.47 x 1.33 = 0.6251. Given imperfect competition in the product market, the assumption of constant returns to scale to capital and labor implies that the output elasticity of capital, , is equal to 1 - 0.6251 = 0.3749. On the other hand, if the assumption of constant returns to scale to capital and labor is relaxed and a returns to scale coefficient of 0.87, as estimated by Kee (2004), is used instead, the implied  is equal to 0.87 – (0.47 x 1.33) = 0.2449. Kee (2004) obtained a value of  = 0.3749 compared to Young’s (1992)  = 0.53 by taking into account imperfect competition in the product market but retained the assumption of perfect competition in the factor market. However, the existence of monopsony power in the labor market is another theoretical reason why  could be overestimated. Acemolgu and Pischke (1998) argue that the prevalence of general worker training paid for by firms in Germany is evidence of monopsony power in the labor market. In Singapore, the National Trades Union Congress, which is made up of 63 trade unions with a membership of half a million workers making up about 20 percent of the employed workforce, is actively involved in the general training and upgrading of the workforce. The government of Singapore, as a major employer, is equally supportive of general training. Moreover, there is a Skills Development Fund generated from the mandatory contributions of employers that finances workers’ general training. The prevalence of employer-funded general training in Singapore is indicative of a certain degree of monopsony power in the labor market, which would indicate that the true  is probably even lower than Kee’s estimate of 0.3749. However, as robustness tests in our

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growth accounting exercise in section 4, we use a range of values of  : 0.2449, 0.3749 and 0.53. (Recall that our baseline model uses the value of  =1/3.) In summary, the use of an updated and revised data series and, we would argue, a more appropriate value of , which reflects the high extent of openness to the international flow of ideas into Singapore and the presence of imperfect competition in the product market and monopsony power in the labor market, result in a higher estimated MFP growth rate in our paper compared to Young (1992, 1995). After justifying a high estimated MFP growth rate for Singapore, we want to ask what the determinants of the MFP growth rate are. Our empirical approach is to first obtain values for MFP as a residual in the usual way, and then to proceed to use the residuals in a regression equation to estimate the coefficients in an idea production function. This empirical strategy was originally adopted in an important paper by Griliches (1973). Griliches (1973) made R&D capital the main input in his idea production function whereas Jones (2002) made the number of research scientists and engineers the main input. Our approach builds on the Jones’ formulation but goes on further to incorporate the channels for technology diffusion. To give a preview of our empirical results, we find that, in our baseline model with  = 1/3, 52.1 percent of the growth of Singapore’s real GDP per worker growth rate over the 1970-2004 period is accounted for by an increase in the effectiveness of accessing ideas developed by the technology leaders through improvement in our educational quality and increase in machinery imports and foreign direct investment from the G5 countries. Our finding is consistent with the findings from international crosssectional studies regarding the sources of income growth in a world of ideas. Another finding is that capital accumulation which takes the form of imports of machinery as well as foreign direct investment from the G5 countries enhances the effectiveness of technology transfer thus raising the rate of return to capital. Compared to the rate of return to capital inferred from the traditional Solow growth model with purely exogenous technological progress of 10.7 percent, we find that taking into account the technology transfer channel raises the implied rate of return to capital to 12.5 percent for the period 1971-2004.

3. The Theoretical Model of Technological Diffusion We incorporate the Coe, Helpman, and Hoffmaister’s (1997) technology spillover channels into the Jones (2002) growth accounting framework, with an additional channel via G5 foreign direct investment identified by Hejazi and Safarian (1999) as being empirically important. The goods production function is given by

Yt  At Kt H Yt1 ,

(1)

where  ≡1-, so multifactor productivity is measured in Harrod-neutral terms as in Jones (2002), HYt is the effective workforce, and At is the stock of ideas adopted by the technology follower. Capital Kt accumulates according to

K t  sKt Yt  dKt ,

K0  0 ,

(2)

where sKt is the savings or investment rate, d is the depreciation rate, and K0 is the initial capital stock. Effective workforce HYt is given by

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H Yt  ht LYt ,

(3)

where ht is human capital per worker, and LYt is labor employed in producing output. Human capital of workers is influenced by the amount of time spent accumulating human capital, lht:

ht  e lht ,

 0.

(4)

We assume that the labor force of the technology follower is growing at the rate of n:

N t  N 0 e nt ,

N0  0 .

(5)

The labor resource constraint faced by the technology follower is given by

LAt  LYt  Lt  (1  lht ) N t ,

(6)

where Lt denotes total employment, LAt denotes labor employed in research activities (being Research Scientists and Engineers, RSE’s), l A 

LA L is defined as the research intensity, and lY  Y . L L

Note that the above equations (1) to (6) are also valid for the technology leader (which we take to be the G5 countries in our empirical work). To avoid confusion, we will cap the variables with a tilde  when such variables pertain to the technology leader. For example, the growth rate of the labor force of the technology leader is denoted by n . We define the output per effective worker as

ytE 

Yt . At H Yt

It can be readily shown that the steady-state output per effective worker is given by 

y

E*

  1 sK   ,  g ( AH Y )  d 

where the growth rate of At H Yt is written as g ( At H Yt )  g ( At )  g ( H Yt ) 

At dl   ht  n . It can also be At dt

shown that

y E g ( ytE )  tE   yt

 E * 1   y   1 ,  y E    t  

where the speed of convergence   (1   )( g ( AH Y )  d ) . A first-order Taylor series expansion around

y E*  1 gives ytE

 y E*  g ( ytE )    E  1 .  yt  Noting that yt 

Yt  At ht ytE for a technology follower, and using the preceding four equations, we Lt

obtain

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dlht ]  (1   )[n  d ] dt   1 dl (1   ) sK1 [n  g ( At )  ht  d ] 1 dt  . yt At ht

g ( yt )   [ g ( At ) 

(7)

We make several ceteris paribus inferences from (7) about the determinants of real GDP per worker growth. First, we observe that an increase in the investment rate sK will raise g(yt). Second, we observe that g(yt) is increasing in the state variables At and ht. Third, we observe that a sufficient though not a necessary condition for an increase in g(At) and/or

dlht to raise g(yt) is that   0.5. Hence to understand the influences dt

on growth of per worker income, it is necessary to understand the determinants of g(At) for the technology follower. Before we identify the determinants of g(At) for a technology follower, we shall take a preliminary look at some key data for Singapore. Figure 1 shows the Hodrick-Prescott filtered real growth rates of per capita GDP and GDP per worker for Singapore from 1961 to 2004. It is useful to differentiate between these two growth rates as population and total employment could be growing at different rates due, say, to changes in labor force participation rate. As a reference point, we have also drawn a line corresponding to a real per capita GDP growth rate of 1.8 percent, which is the mean value for the growth rate of real per capita GDP for the 112 countries with available data from 1960 to 2000 reported in Barro and Sala-i-Martin (2004). Interestingly, 1.8 percent is also the average growth rate of real per capita GDP of the U.S. economy over the past 125 years reported in Jones (2002).

[Figure 1: Hodrick-Prescott Filtered Real Growth Rates of Singapore and U.S. Average Long-Run Growth Rate]

From Figure 1, we observe that, after increasing in the 1960s, Singapore’s growth rates started to decline from about 9 percent at the start of the 1970s. However, the growth rates in the 1980s and the 1990s do not suggest a rapid convergence to that of the U.S. long-run average growth rate. Motivated by (7), we check whether there are increases in the investment rate sK, and change in educational attainment dlh, which would prevent a rapid convergence to the U.S. long-run growth rate. These are depicted in Figure 2.

[Figure 2: Hodrick-Prescott Filtered Investment Rate and Change in Educational Attainment in Singapore]

From Figure 2, we observe that there was an increase in sK from the 1960s to 1970s and a decline from the 1970s down to the early 2000s. Similarly, there was a steady increase in dlh from the 1960s to the early 1990s, after which a slight decline occurred till the early 2000s. According to (7), if   0.5, an increase in average

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educational attainment will unambiguously lead to a steady increase in g(y), holding other things constant. Hence, increases in investment rate and change in educational attainment could have prevented a rapid convergence to the U.S. long-run average growth rate till the 1980s but other factors could be at work as well. Figure 3 shows the natural logarithm of multifactor productivity lnA. The plot of lnA suggests that the growth rate of multifactor productivity is rather stable over the past four decades. We proceed to test whether the growth rate of multifactor productivity, g(A), can statistically be considered a constant in Appendix 2. The results in Appendix 2 show that the hypothesis of constancy of g(A) cannot be rejected using a simple student-t test and that g(A) is stationary using the Dickey-Fuller test for unit root. There is also no problem of serial correlation in the error term. Hence, the augmented version of the Dickey-Fuller test is not required. Based on these statistical tests, we conclude that g(A) can be considered a constant for our empirical analysis in section 4 even though the economy is not necessarily on a balanced growth path. (In deriving the key equations in the theoretical model of this section, we do not need to restrict g(A) to be constant.) We show later that the constancy of g(A) can be explained by the increase in educational quality and increase in imports of machinery and foreign direct investment from the G5 countries, leading to shifts in the steady-state distance to frontier.

[Figure 3: Logarithm of Multifactor Productivity in Singapore, 1960-2004]

Now we proceed to endogenize the evolution of At. We begin by defining the effective world research effort H At as M

H At   LAit ,

(8)

i 1

where i indexes each of the G5 economies. The number of RSE’s in a technology follower such as that of Singapore is insignificant compared to the combined number in G5 economies and hence makes a negligible contribution to the effective world research effort.3 The stock of ideas adopted by the technology follower advances according to 

 G 5MTt G 5FDI t  At   H At At Et    , Kt   Yt

A0  0 ,

(9)

where H At is effective world research effort, which is given by the sum of research scientists and engineers in G5,  > 0, 0    1 ,  < 1,  > 0,  > 0, G5MTt is imports of machinery and transport equipment from G5,

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For example, in 2005, Singapore had 21,338 RSE’s, about 0.84 percent of the combined number in G5 economies. Data on patent grants by country of origin, obtained from the website of the World Intellectual Property Organization, http://wipo.int, show that in 2006, ratio of patent grants originated in Singapore to those from the G5 was 0.21 percent. Expenditure on R&D in Singapore was only 0.52 percent of the total expenditure on R&D in G5 countries in 2005, based on data from http://stats.oecd.org and Yearbook of Statistics 2008, published by the Singapore Department of Statistics. Based on these statistics, Singapore’s contribution to the effective world research effort is negligible and it may be considered a technology follower in a world of ideas.

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G5FDIt is the stock of foreign direct investment from G5, Et is tertiary enrollment to employment ratio, and A0 is the initial level of technology. As in Jones (2002),  varies between zero and one, implying possible duplication of research findings by research scientists. A positive (negative)  will imply that past research increases (decreases) the current flow of new ideas. The symbol ~ is used to cap variables pertaining to the combined G5 economies. We have introduced three channels of improving At in the technology follower: the quality of learning captured by Et, the linkage to advanced imported technology through machinery import captured by

G 5MTt G 5FDI t , and the quality of capital stock captured by . When a multinational corporation Yt Kt

set up by a G5 country in Singapore imports machinery from its home country, it is empirically difficult to disentangle the separate knowledge transmission effects of machinery imports and foreign direct investment. Thus, we assume the same elasticity parameter  for both channels, as given in (9). Figure 4 shows time plots of these three channels of idea transmission for the case of Singapore.

[Figure 4: Hodrick-Prescott Filtered Channels of Idea Transmission for Singapore]

From Figure 4, we observe that the linkage to advanced technology through machinery import from G5 countries has steadily increased from the 1960s till the late 1990s, followed by a downturn in the early 2000s. The channel via foreign direct investment from G5 countries has steadily increased and accelerated beginning in the late 1990s. The quality of learning began to increase more significantly in the 1980s and the 1990s. The quantitative contribution of these three channels of idea transmission to Singapore’s growth will be presented in section 4. These three channels apply to technology followers, and determine how effectively ideas created at the world technology frontier by the technology leaders are transmitted to and adopted by the followers. The evolution of the frontier stock of ideas Tt is described by

Tt   H At Tt ,

T0  0 ,

which is the form of the idea production function given in Jones (2002) for a technology leader. Hence, the growth rate of ideas of the technology leader at the frontier is given by

g (Tt ) 

Tt   H At Tt 1 . Tt

(10)

Using (10), we re-write (9) to get

g ( At ) 

1  T   G 5MTt G 5FDIt  At  g (Tt )  t  Et    , At Kt   At   Yt

A0  0 .

(11)

In this set-up, the stock of ideas adopted by the technology follower grows faster when the frontier stock of ideas is growing faster, when the technology follower is further away from the frontier4, and when the three

Recall that  < 1, as assumed earlier. In fact, later in the empirical studies, we will find that  < 0, which is also the case found in Jones (2002). 4

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channels of idea transmission are stronger. As the technology follower advances toward the frontier, reflected in a smaller distance to frontier,

Tt , its growth rate of multifactor productivity diminishes, holding other At

things constant. It is important to note that while the average years of schooling lh affects human capital accumulation and hence output, it is the quality of learning captured by the tertiary enrollment to employment ratio E which influences the growth rate of adopted ideas.

Definition 1 The steady-state distance to frontier is defined as the stock of ideas in the technology leader relative to the stock of ideas adopted by the technology follower when g(At) = g(Tt) (which are not necessarily constant), and when E,

G 5MT G 5FDI , and are held constant, and it is given by Y K 



*

G5 FDI 1 T  1  G 5MT  .   E   K   A  Y

(12)

Hence, the steady-state distance to frontier is negatively related to the quality of learning as well as the linkage to imported technology through capital imports and foreign direct investment from the technology leader. In the convergence to the steady-state distance to frontier, the growth rate of ideas adopted in the technology follower will slow down; however, the pace of decline may be offset if there are increases in the strength of the three channels of idea transmission as such increases effectively reduce the steady-state *

T  distance to frontier   . Figure 4 shows that the tertiary enrollment to employment ratio, the share of  A capital imports from G5 countries as a ratio to GDP, and the share of G5 foreign direct investment stock to total capital stock have all been rising especially in the past two decades thus reducing the steady-state *

G 5MT G 5FDI T  distance to frontier   . Using (11) and (12) and holding E, , and constant, we obtain Y K  A   Tt     g ( At )   At    g (Tt )   T *       A  

1

, or

  Tt   T *       g ( At )   At   A    1 *  g (Tt )  T         A

1

.

(13)

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*

T  Jones (2002) found g(Tt) to have been approximately constant from 1950 to 1993 so if   is also  A declining steadily due to a steady increase in educational quality and linkage to the G5 through capital imports and foreign direct investment (see (12)), g(At) would be approximately constant and above g(Tt). A linearization of (13) around the steady state gives

  Tt      A g ( At )  g (Tt )  (1   )   t *  1 g (Tt ) .  T        A  

(14)

Proposition 1 Given  < 1, the growth rate of ideas in a technology follower g(At) (i) is positively related to the growth rate of ideas in the technology leader g(Tt), (ii) is positively related to its distance to frontier

Tt , At *

T  (iii) is negatively related to its steady-state distance to frontier   ,  A (iv) is positively related to the three channels of idea transmission, namely the quality of learning E, the linkage to imported technology through capital import

G 5MT G 5FDI , and the quality of capital stock , Y K

through their influence on the steady-state distance to frontier, and (v) is higher than the technology leader if its current distance to frontier is further than its steadystate distance to frontier.

Rewriting (1) in terms of output per worker gives

yt 

 Yt K   ( t )1 lYt ht At1 . Lt Yt

(15)

Using (2) and (9), (15) can be rewritten as

yt  ( where k 

 sKt      G 5MTt G 5FDI t   )1 lYt ht ( ) H At [ Et (  ) ] , nt  g (kt )  d g ( At ) Yt Kt

(16)

K   , and   . Note that in the derivation of (16), we do not have to restrict the growth L 1 1

rates g(kt) and g(At ) to be constant.5 Along a steady-state balanced-growth path where the capital-output ratio

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Jones (2002) assumes that the stocks K and A grow at constant rates as his focus is on the constant growth path of the U.S. economy. The derivation of (10) in Jones (2002) actually does not require constant growth rates in K and A. Our derivation of (16) without such restrictions is provided in Appendix 3.

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( Kt / Yt ), lYt, ht, g(At), Et,

G 5MTt G 5FDI t , , and G5 research intensity lAt are all constant, the growth rate of Yt Kt

output per worker is

g ( y )   n ,

(17)

where n is the exogenous growth rate of the combined labor force of the G5 economies. In a world of ideas, the technology follower’s balanced-growth path is driven by the labor force growth in the G5 economies from where ideas spread out. However, its growth outside the balanced-growth path will be influenced by its capital intensity, distance to frontier, and the three channels facilitating the spillover of ideas, namely, the quality of learning and the linkage to advanced imported technology through capital import and foreign direct investment from G5.

4. Quantitative Analysis Based on the theoretical model developed in section 3, we are now equipped to conduct a growth accounting exercise for a technology follower in a world of ideas. We will use the data for Singapore and examine whether the three channels of idea transmission are important in explaining the growth rate of the stock of adopted ideas, or equivalently, multifactor productivity. In the first sub-section, we report results for our baseline case where the output elasticity of capital,  , is equal to 1/3 as well as the results with different values of  = 0.2449, 0.3749, and 0.53, the last being the value used by Young (1992). In the second subsection, we conduct a quantitative analysis of the implied rates of return to capital. Data sources and the construction of data series are documented in Appendix 1.6

4.1. Growth Accounting in a Framework of Idea Transmission This sub-section will conduct a growth accounting exercise for Singapore, incorporating the channels of idea transmission. We use (2) and (4) to rewrite (16) as 

 K 1      G 5MTt G 5FDIt   yt   t  lYt e lht ( ) H At [ Et (  ) ] . g ( At ) Yt Kt  Yt 

(18)

Taking natural logarithm and differentiating with respect to time, and using (8), we have

g ( yt ) 

K   g ( t )  g (lYt )  g ( g ( At )) lht   g (lAt )   n 1   Yt  G5MTt G 5FDI t     g ( Et )  g( ) g( ). 1 1 Yt 1 Kt

(19)

For Singapore, the share of employed workers engaged in R&D is less than one percent in 2004 so lY > 0.99. Our analysis will proceed under the approximation that lA = 0 and lY = 1. As pointed out before, we tested whether g(A) can statistically be considered a constant in Appendix 2. The test results confirm that g(A) is stationary and that g(g(At)) is not statistically different from zero. Therefore, in the growth accounting

6

The data set used in our empirical work is available at http://www3.ntu.edu.sg/home/kwho.

12

exercise to follow, we will take g(g(At)) = 0. Hence, the growth accounting equation for Singapore can be simplified to

g ( yt ) 

K  g ( t )  lht   g (lAt )   n 1   Yt G5MTt G5 FDI t    g ( Et )  g( . ). 1 1 Yt Kt

(20)

In our growth accounting exercise, we take  = 1/3 to be our baseline case. We take the return to schooling parameter  = 0.07, the same value used in Jones (2002), based on evidence from the literature of the labor market. To conduct the growth accounting exercise, we will need to empirically estimate three parameter values: ,

  and . (Since Jones (2002) assumed immediate dissemination of ideas, he 1 1

only had to econometrically estimate one parameter, namely, .) The detailed regression results are given in Appendix 4. As mentioned earlier, the approach adopted here of first obtaining values for multifactor productivity as a residual in the usual way, and then proceeding to use the residuals in a regression equation to estimate the coefficients in an idea production function was first used in an important paper by Griliches (1973). Griliches (1973) made R&D capital the main input in his idea production function whereas Jones (2002) made the number of research scientists and engineers the main input. Our approach builds on the Jones’ formulation but goes on further to incorporate the channels for technological diffusion. We point out that as we go from the baseline case of  = 1/3 to robustness checks using  = 0.2449, 0.3749, and 0.53, we re-calculate multifactor productivity as the residual in (15), and econometrically re-estimate γ,

 and 1

 accordingly. 1 Assuming  = 1/3, our baseline case, Table 2 provides the breakdown in contributions to growth. The sample period starts from 1970 since foreign direct investment data are available from 1970 onwards. [Table 2: Accounting for Singapore’s Growth with Transmission Channels: Baseline Case  = 1/3]

From Table 2, we see that the portion of unexplained growth is 1.21 percent for the period 1970 to 2004. The fact that the portion of unexplained growth is positive means that there is an under-explanation of per worker income growth based upon the contributions of all the terms appearing on the right-hand-side of (20). We can, however, be more precise. Standard growth accounting treats the contributions of physical capital and labor inputs (represented by the first two terms on the right-hand side of (20)) as precisely measured, and treats the algebraic difference between the value of the left-hand side term of (20), g(yt), and the sum of the first two terms on the right-hand side of (20) as a Solow residual, following Solow (1957). What our approach, building upon Griliches (1973) and Jones (2002), does is to quantitatively “explain” the Solow residual. It turns out that, based upon our theory of how technological diffusion occurs for a

13

technology follower in a world of ideas, we under-explain the Solow residual by about one percent. From Table 2, we may say that the idea transmission channels help to account for 52.13 (41.71 + 10.42) percent of g(y) for the period 1970 to 2004. As a robustness check, we use other values for  as discussed earlier. Table 3 reports the results.

[Table 3: Accounting for Singapore’s Growth with Transmission Channels: Robustness Check with

 = 0.2449, 0.3749, and 0.53]

From Table 3, we observe that while growth of capital intensity contributes more to the growth of real GDP per worker with a larger value of , the contribution of the idea transmission channels remains strong and robust, especially the learning effect captured by the growth of tertiary enrollment to employment ratio. The G5 machinery imports and FDI transmission effect is positive for  = 0.2449 and 0.3749 but negative for  = 0.53 as for the latter case, the estimated  is negative. We have argued earlier that the value of  should be much lower than 0.53 for a technology follower in a world of ideas and the estimated negative  when  = 0.53 may reflect an inappropriate choice of a large . Interestingly, when  = 0.3749, the case with imperfect competition in the product market with constant returns to scale in capital and labor, the portion of unexplained real GDP per worker growth was 0.00 percent, just like a perfect fit! The other values of  give an over-explanation of 8.71 to 9.87 percent. When  = 0.2449, the idea transmission channels jointly explain up to 36.96 + 31.75 = 68.71 percent of the growth rate in real GDP per worker. When  = 0.3779, 42.87 + 7.70 = 50.57 percent of the growth of real GDP per worker is explained. Even with  = 0.53, the idea transmission channels explain up to 50.46 – 4.95 = 45.51 percent of the growth of real GDP per worker. In summary, the findings in Table 3 and Table 2 confirm that transmission channels account significantly for the growth of real GDP per worker in Singapore, a technology follower in a world of ideas, for the period from 1970 to 2004.

4.2. Implications for the Rate of Return to Capital This sub-section will discuss the implications for the rate of return to capital for a technology follower in a world of ideas, and provide a quantitative breakdown of the components of the rate of return to capital. We take  = 1/3 to be the baseline case but will also present results for  = 0.2449, 0.3749, and 0.53, as robustness tests. The rate of return to capital is not just the direct marginal product of capital (MPK) in our model because an additional unit of capital will also affect the accumulation of the stock of ideas for the technology follower through two idea transmission channels: linkage to advanced technology via machinery imports, and quality of capital stock via foreign direct investment from G5 countries. The channel of quality of learning is assumed not to be associated with a change in K. Differentiating the goods production function (1) with respect to K, we have

14

dY  Y (1   )Y dA   , or, dK K A dK

dY  Y (1   )Y    dK K K     ln A 1  ln A 1     ln K  ln K  G 5MT   G 5FDI   ln    ln     Y   ln  G 5MT   K   ln  G5FDI     Y     K

  .       

(21)

From (21), we see that the association of an increase in K with imports of machinery and transport equipment from the G5 countries and with G5 foreign direct investment will facilitate the transmission of ideas, raising A and consequently the return to capital. This indirect effect will be added on to the direct MPK effect. Note that this indirect effect may diminish as K increases further as the term in squared brackets in (21) is multiplied by Y/K, which could be decreasing in K. In other words, for a technology follower, the extra lift to the rate of return to capital provided by the two idea transmission channels could be temporary and not permanent. How do we break down the components of the rate of return to capital quantitatively using (21)? Note that using the definition of g(A), we may rewrite (9) as

ln At 

G 5MTt G5FDI t 1      ln  ln H At  ln Et  ln  ln . 1   g ( At ) 1   1 1 Yt 1 Kt

Hence,

 ln A  , and   G 5MT  1    ln    Y   ln A  .  G 5 FDI   1  ln    K  In our empirical studies, we have an estimate for

change in K corresponding to the percentage change in

 . Next, we need to compute the percentage 1

G 5MT G 5FDI and , respectively, for each year. The Y K

empirical version of (21) is then given by

dY  Y (1   )Y    . [ dK K K 1

1 1  ]. G5MT G 5FDI ( ) ( ) K K Y K / / G 5MT G 5FDI K K Y K

(22)

To abstract from business cycle movements, we apply Hodrick-Prescott filters to the empirical components of (22). Figure 5 shows the Hodrick-Prescott filtered MPK’s: the first term of (22), which is

15

without transmission channels, and the entire right-hand side of (22) with transmission channels, for the baseline case of  = 1/3. We observe that the rate of return to capital did diminish in the 1970s; however, with the influence of idea transmission channels incorporated, the rate of return to capital was higher than the conventionally calculated rate of return to capital based on exogenous technological progress throughout the period under study. Furthermore, in more recent years the influence of idea transmission channels has strengthened. [Figure 5: Hodrick-Prescott Filtered Rate of Return to Capital (Baseline Case  = 1/3)]

Table 4 shows a breakdown of the various components of the rate of return to capital for the 1970s, 1980s, 1990s and for the whole period 1971-2004. We see that the idea transmission effect accounted for 10.34 percent of the total rate of return to capital in the 1970s. Their contribution was smaller in the 1990s, 5.91 percent. For the entire period, it is 14.90 percent. Equivalently, for the period 1971-2004, including the idea transmission mechanism raises the rate of return to capital by about 0.0187/0.1067 = 17.53 percent. Compared to the rate of return to capital inferred from the traditional Solow growth model with purely exogenous technological progress of 10.67 percent, we find that taking into account the technology transfer channel raises the implied rate of return to capital to 12.54 percent for the period 1971-2004. [Table 4: Components of Rate of Return to Capital: Singapore, 1971-2004 (Baseline Case  =1/3)] Next, we consider the robustness checks with different values of , as discussed earlier. Table 5 reports the results for the entire period from 1971 to 2004. The transmission effect accounts for 45.13 percent of the rate of return to capital when  = 0.2449. When  = 0.3749, the transmission effect explains 9.74 percent of the rate of return to capital. For the case of  = 0.53, the transmission effect was negative as the estimated  was negative. Observe from Table 4 and Table 5 that as  increases, the direct MPK, given by the first part of the right-hand side of (22), increases. However, the rate of return to capital with incorporation of the transmission channels is not necessarily positively related to . For example, the direct MPK of 0.0784 when  = 0.2449 is much smaller than that of 0.1200 when  = 0.3749. However, after incorporating the transmission channels, the rate of return to capital is 0.1429 when  = 0.2449, which is higher than that of 0.1329 when  = 0.3749. In fact, the rates of return to capital are brought closer after incorporation of the transmission channels. In summary, findings from Tables 4 and 5 suggest an important contribution of the transmission channels in influencing the rate of return to capital.

[Table 5: Components of Rate of Return to Capital: Singapore, 1971-2004 (Robustness Check with

 = 0.2449, 0.3749, and 0.53)]

16

5. Conclusion Our quantitative exercise shows that physical and human capital investments can explain only 39 percent of Singapore’s real GDP per worker growth rate over the 1970-2004 period in our baseline case of  = 1/3. By estimating the production of ideas in the G5 countries following the lead of Jones (2002) and being explicit about the channels through which these ideas get implemented in Singapore following the lead of Coe, Helpman and Hoffmaister (1997) and Hejazi and Safarian (1999), we show that the quality of education as well as imports of machinery and foreign direct investment from the G5 countries, by increasing the effectiveness of accessing ideas from abroad, account for 52.1 percent of the growth of Singapore’s real GDP per worker. The finding from our growth accounting exercise for Singapore, a technology follower and the second fastest-growing economy over the 1960-2000 period in the 112-country sample of Barro and Sala-iMartin (2004), that 61 percent of growth in its standard of living is due to multifactor productivity growth is consistent with the finding from international cross-sectional studies that it is mainly the difference in multifactor productivity growth rates that explains the difference in growth rates of real per capita GDP. Our findings raise the question why Tsao (1985) and Young (1992, 1995) found such low multifactor productivity growth for Singapore. An explanation that Hsieh (2002) has offered is that the official statistics have substantially overstated the growth of capital since his use of the dual approach gave an estimate of multifactor productivity growth for Singapore of 2.2 percent per year for the period 1972-90 compared to Young’s 0.2 percent for 1966-1990. We have found, using the more recent and revised data series from the Singapore Department of Statistics currently available to the public and adopting the Mincer approach to accounting for human capital, that there is, in fact, a far larger role played by multifactor productivity growth in explaining Singapore’s real GDP per worker growth. Moreover, we are able to show that the sources of multifactor productivity growth come from factors that growth theories and empirics in the past two decades have shown to be very important in accessing world ideas, namely, educational quality and effective links to the world’s technological leaders through trade and foreign direct investment. Our study also highlights an essential difference between a technology follower and a technology leader. Jones (2002) found that the assumption that ideas produced by the world’s research efforts are immediately disseminated to the U.S. economy is a good one. This assumption, however, does not hold for a technology follower like Singapore where the channels for technological diffusion take center stage. In theory, for a given level of educational quality and strength of international linkage via trade and foreign direct investment, there is a multifactor productivity catch-up if a technology follower is initially far away from its steady-state distance to frontier so multifactor productivity growth gradually declines as the technology follower becomes richer. One finding of our paper is that the strength of the channels of idea transmission in Singapore has been rising steadily thus reducing the steady-state distance to frontier. The result is that there have been new and higher transition paths of multifactor productivity so that the growth rate of multifactor productivity has remained roughly unchanged. So Singapore’s real GDP growth has been stable because its multifactor productivity growth has been stable.

17

The evidence we have presented in this paper illustrates Singapore’s ability to absorb foreign technology and benefit from technological diffusion. We have identified better educational quality, import of capital goods and foreign direct investment inflows from the G5 countries to Singapore as important channels of technological diffusion. However, one could ask whether there are other complementary factors, on top of these channels, that enabled Singapore to absorb foreign technology and thus close the technology gap?7 It appears that Singapore’s choice of an open trading regime---which facilitated the import of capital goods and inflow of foreign direct investment from the G5 countries---was complemented by fiscal incentives as well as the establishment of a set of high-quality institutions. The fiscal incentives consist of the granting to multinational corporations (MNCs) of pioneer industry status carrying exemption from income tax for a certain number of years as well as accelerated capital depreciation allowances. To encourage export-oriented industries, export earnings of MNCs also enjoyed concessionary tax rates after the expiry of their pioneer status (see Goh (1977)). Institutions were set up to make Singapore an attractive host country for foreign firms to offshore their production here. An example of such an institution is the Economic Development Board, set up in 1961, which served as a one-stop center for coordinating the businesses of MNCs in Singapore. Other factors, such as the political stability achieved since the late 1960s, the low level of corruption, secure property rights, and general public sector efficiency, also played a part in attracting foreign direct investment to Singapore (see Hoon (2002)). Yet another complementary factor that enabled Singapore to take advantage of the access to world technology to produce and export to the rest of the world is the harmonious industrial relations climate that was created. The belief that Singapore’s economic survival depended on its being able to attract MNCs here laid the ground for important legislation such as the Employment Act and the Industrial Relations (Amendment) Act, both of 1968, which gave greater discretion to employers in the deployment and development of their workforce and limited the sums payable on bonuses, annual paid leave, retrenchment benefits and overtime. The legislation helped contribute to industrial peace, which was important in attracting MNCs. In turn, the resultant inflow of foreign direct investment along with a commitment to invest in the general training of workers as well as steady improvement in educational quality enabled the Singapore economy to surge towards the world technology frontier, bringing along with it a steady rise in living standards. We conclude with some remarks about future research. One limitation of the present analysis is that technology is treated at an aggregative level. In fact, the experience of Singapore is one in which there has been a constant shift along a technology ladder with new industries replacing old ones, giving rise to a dynamic process of creative destruction. Future research could adopt a more disaggregated view of technology in order to model the shift along the technology ladder. Another possible extension to the work reported here is to explore the compatibility of technologies developed by technology leaders and the domestic capability of technology followers to adopt them, an issue that we have not dealt with explicitly in this paper. 7

This is a question of policy relevance that one of the referees encouraged us to think about.

18

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Table 1: Average Annual Growth Rates of Key Variables: Singapore, 1970 to 2004 Growth Rate of

Variable

Real GDP per worker Capital-output ratio Human capital

g(y) g(K/Y) g(h)

Multifactor productivity

g(A)

 = 0.2449

 = 1/3

 = 0.3749

 = 0.53

0.039552 0.010330 0.010398 0.025918 (65.5%)

0.039552 0.010330 0.010398 0.024334 (61.5%)

0.039552 0.010330 0.010398 0.023453 (59.3%)

0.039552 0.010330 0.010398 0.019006 (48.1%)

Source: Various, as described in Appendix 1. Figures in parentheses refer to the growth rate of MFP as a 

 K 1 percentage of the growth rate of real GDP per worker. MFP is computed as At in Yt / Lt   t  ht At , where  Yt  ht is human capital. As in Jones (2002), ht  e0.07 lht , where lht is the mean years of schooling. Table 2: Accounting for Singapore’s Growth with Transmission Channels: Baseline Case  = 1/3 Description

Variable

70-04 Average 0.039552 (100.00%)

Growth rate of real GDP per worker equals:

g(y)

Capital intensity effect

 K g( ) 1 Y

Educational attainment effect

lh

G5 R&D intensity effect

 g (lA )

Scale effect of G5 labor force

 n

0.005165 (13.06%) 0.010309 (26.07%) 0.001765 (4.46%) 0.001215 (3.07%)

Tertiary enrollment to employment ratio learning effect

 g(E) 1

0.016496 (41.71%)

G5 machinery imports and FDI transmission effect Unexplained

 G 5MT G5 FDI g( . ) 1  Y K

0.004122 (10.42%) 1.21%

Source: Various, as described in Appendix 1. A tilde ~ is used to denote G5 variables. We have assumed γ = 0.099318366, the estimated value in specification (2) in Table A2 of Appendix 4. We have also assumed /(1) = 0.511946, and /(1-) = 0.067384, values estimated when λ is set to 1.

23

Table 3: Accounting for Singapore’s Growth with Transmission Channels: Robustness Check with α = 0.2449, 0.3749, and 0.53 Value of α Description

Variable

0.2449 70-04 Average 0.039552 (100.00%)

0.3749 70-04 Average 0.039552 (100.00%)

0.53 70-04 Average 0.039552 (100.00%)

0.006195 (15.66%) 0.010309 (26.07%) 0.001804 (4.56%) 0.001242 (3.14%)

0.011649 (29.45%) 0.010309 (26.07%) 0.001798 (4.55%) 0.001238 (3.13%)

Growth rate of real GDP per worker equals:

g(y)

Capital intensity effect

 K g( ) 1 Y

Educational attainment effect

lh

G5 R&D intensity effect

 g (lA )

Scale effect of G5 labor force

 n

0.003350 (8.47%) 0.010309 (26.07%) 0.001553 (3.93%) 0.001069 (2.70%)

Tertiary enrollment to employment ratio learning effect

 g(E) 1

0.014617 (36.96%)

0.016955 (42.87%)

0.019960 (50.46%)

0.012558 (31.75%) -9.87%

0.003047 (7.70%) 0.00%

-0.001960 (-4.95%) -8.71%

G5 machinery imports and FDI transmission effect Unexplained

 G 5MT G5 FDI g( . ) 1  Y K

Source: Various, as described in Appendix 1. A tilde ~ is used to denote G5 variables. The detailed estimated values of γ, /(1-), and /(1-), when λ is set to 1, are available from the personal website of the first author at http://www3.ntu.edu.sg/home/kwho.

24

Table 4: Components of Rate of Return to Capital: Singapore, 1971-2004 (Baseline Case  = 1/3) 71-79 Average 0.1358 (100%)

80-89 Average 0.1064 (100%)

90-99 Average 0.1093 (100%)

71-04 Average 0.1254 (100%)

Direct MPK, given by first part of the right-hand side of (22)

0.1218 (89.67%)

0.0999 (93.88%)

0.1029 (94.09%)

0.1067 (85.10%)

G5 Machinery Imports and FDI Transmission Effect, given by second part of the right-hand side of (22)

0.0140 (10.34%)

0.0065 (6.12%)

0.0065 (5.91%)

0.0187 (14.90%)

Total

Source: Computed based on data from Singapore Department of Statistics. We have assumed /(1-) = 0.067384, which is estimated when λ is set to 1, as given in specification (2) in Table A2 of Appendix 4.

Table 5: Components of Rate of Return to Capital: Singapore, 1971-2004 (Robustness Check with  = 0.2449, 0.3749, and 0.53) Value of  Total

0.2449 0.3749 0.53 1971-2004 Average 0.1429 0.1329 0.1634 (100%) (100%) (100%)

Direct MPK, given by first part of the right-hand side of (22)

0.0784 (54.87%)

0.1200 (90.26%)

0.1696 (103.83%)

G5 Machinery Imports and FDI Transmission Effect, given by second part of the right-hand side of (22)

0.0645 (45.13%)

0.0130 (9.74%)

-0.0063 (-3.83%)

Source: Computed based on data from Singapore Department of Statistics. The detailed estimated values of /(1-), when λ is set to 1, are available from the personal website of the first author at http://www3.ntu.edu.sg/home/kwho.

25

Figure 1: Hodrick-Prescott Filtered Real Growth Rates of Singapore and U.S. Average Long-Run Growth Rate 10.0%

9.0%

8.0%

7.0%

6.0%

5.0%

4.0%

3.0%

2.0%

1.0%

0.0% 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 Year Singapore GDP Per Capita

Singapore GDP Per Worker

US Long-Run Growth Rate

Source: Computed based on data from Singapore Department of Statistics. HP- = 100 for annual data. Jones (2002) pointed out that the average annual growth rate of per capita GDP for U.S. over the last 125 years has been a steady 1.8 percent per year. Barro and Sala-i-Martin (2004, chapter 12) reported a mean growth rate of 1.8 percent per year for a sample of 112 countries from 1960 to 2000. Figure 2: Hodrick-Prescott Filtered Investment Rate and Change in Educational Attainment in Singapore 0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 Year Investment Rate

Change in Educational Attainment

Source: Computed based on data from Singapore Department of Statistics. HP- = 100 for annual data. The vertical scales for the two variables in Figure 2 are different. For the change in educational attainment, it is the increase in number of years of schooling. For instance, the average years of schooling increase by 0.2 year or 2.4 months per annum in the 1990s. For the investment rate, the vertical scale represents a fraction. For instance, 0.3 means 30%.

26

Figure 3: Logarithm of Multifactor Productivity in Singapore, 1960-2004 12

10

Natural Log Scale

8

6

4

2

0 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Year

Source: Computed based on data from Singapore Department of Statistics. Multifactor productivity is 

 K 1 computed as At in Yt / Lt   t  ht At , with  = 1/3.  Yt 

Figure 4: Hodrick-Prescott Filtered Channels of Idea Transmission for Singapore 0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Year Tertiary Enrollment to Employment

G5 Machinery & Transport Equipment Imports to GDP

G5 FDI Stock to Capital Stock

Source: Computed based on data from Singapore Department of Statistics. HP- = 100 for annual data.

27

Figure 5: Hodrick-Prescott Filtered Rate of Return to Capital (Baseline Case  = 1/3) 0.25

0.2

0.15

0.1

0.05

0 1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year With Transmission Channels

Without Transmission Channels

Source: Computed based on data from Singapore Department of Statistics. HP- = 100 for annual data. We have assumed /(1-) = 0.067384, which is estimated when λ is set to 1, as given in specification (2) in Table A2 of Appendix 4.

28

Appendix 1: Data Sources and Data Construction The data used are obtained from and computed based on various sources. Singapore Population. Data on Singapore’s population is obtained from the Singapore Department of Statistics at http://www.singstat.gov.sg. The data presented in the website are mid-year estimates. Employment. Population Censuses 1970, 1980, 1990, and 2000 provide data for 1957, 1970, 1980, 1995, and 2000. Report on the Labor Force Survey of Singapore provides data from 1973 to 1999 and Report on Labor Force in Singapore provides data from 2001 to 2004, excluding those reported by the various censuses. Missing observations are log-linearly interpolated. GDP. Data on Singapore’s real GDP at 1995 prices and nominal GDP are taken from the Singstat Time Series (STS) available from the Singapore Department of Statistics. Real GDP per capita at 1995 prices is derived by dividing the above series by the population. Real GDP per worker at 1995 prices is derived by dividing real GDP by the number of employed workers. We have also divided the nominal GDP by the real GDP at 1995 prices to obtain the GDP deflator with base year in 1995. Imports of Machinery and Transport Equipment from G5 nations.

Singapore External Trade

Statistics provides data from 1958 to 1974, Singapore Trade Statistics Imports and Exports provides data from 1975 to 1990, and the Singstat Time Series (STS) available from the Singapore Department of Statistics provides data from 1991 to 2004. The data correspond to category 7 of the Standard International Trade Classification (SITC). The price index is constructed from nominal (current prices) and real (in 1995 prices) machinery and transport equipment components of Gross Fixed Capital Formation (GFCF) from the Singstat Time Series available from the Singapore Department of Statistics. Real imports of machinery and transport equipment from G5 are then obtained by dividing the nominal imports by the constructed price index. Foreign Direct Equity Investment. Data for stock of foreign direct equity investment in Singapore by country of origin (G5 countries, Netherlands, and European Union) are obtained from the Singapore Department of Statistics for the years 1970 to 1979, with that of 1980 to 2004 taken from Foreign Equity Investment in Singapore. France’s data for 1970 to 1987, and 1990 to 1993 are not available. We estimate them by adopting the following procedure (with details available upon request in a spreadsheet): Foreign direct equity investment from France is a fraction of the difference between the sum of Japan, U.S., European Union less Netherlands, and foreign direct equity investment from G4 countries (that is, excluding France). France’s share of the difference is computed for 1988, 1989, and 1994 to 2004. For 1970 to 1987, its share is assumed to be the same as that of 1988. For 1990 to 1993, its share is log-linearly interpolated. Based on these shares, we estimate France’s foreign direct equity investment for 1970 to 1987, and 1990 to 1993. Nominal stock values of foreign direct equity investment from G5 are obtained. To obtain real stock values of foreign direct equity investment, the nominal values are divided by the constructed price index of capital based on the nominal and real values of total capital stock estimated and described below. Educational Attainment. The average number of years of schooling for residents aged 25 and above is obtained from Barro and Lee (2000) for years 1960, 1965, 1970, and 1975 and from the Yearbook of

29

Statistics for years 1980, and 1985 to 2004. Log-linear interpolation is carried out for years where such data are unavailable. Tertiary Enrollment. Data are obtained from the Yearbook of Statistics. Data on enrollment in institutes of higher learning (IHL) combined are available for 1960 to 1992. From 1993 onwards, figures for polytechnics, the National Institute of Education, and the universities are available. Gross Fixed Capital Formation and Increase in Stocks. These are obtained from the SingStat Time Series (STS), available from the Singapore Department of Statistics. The base year is 1995. Data on various asset classes of Gross Fixed Capital Formation (GFCF) are also obtained from Economic Survey of Singapore for data since 1993 and Singapore System of National Accounts 1995 for earlier years. Data Pertaining to Depreciation. Let Gross Fixed Capital Formation (GFCF) as a whole be xt, and the GFCF of asset class i be xit, where t denotes year. Straight-line depreciation is assumed for the various asset classes, as in OECD (2001). Hence, depreciation rate of asset class i, di, is the reciprocal of the average service life of asset class i. The average service lives of Residential Buildings (80 years), Non-Residential Buildings (40 years), Other Construction and Works (40 years), Transport Equipment (15 years) (assumed to be the simple average of Ships and Boats (20 years), Aircraft (15 years), and Road Vehicles (10 years)), and Machinery and Equipment (15 years) are supplied by the Singapore Department of Statistics in OECD (2001, page 98). We first compute the average proportion of GFCF on asset class i by the following:

xi 

1 T xit  , T t 1 xt

where T is the total number of years in the period considered. The weighted depreciation rate is computed as follows:

d   xi di . i

Construction of capital stock series. The steps taken are: 1.

Real figures for Gross fixed capital formation (GFCF) and increase in stocks (IIS) are

obtained from the Singstat Time Series (STS) available from the Singapore Department of Statistics. The base year is 1995. Real gross investment is obtained by adding up real GFCF and IIS. 2.

An initial net real capital stock figure is computed by the following: K (0) 

I (0)(1  g ) , g d

where g is the growth rate of gross investment and d is the depreciation rate of capital stock as computed above. Note that g is computed by running a regression of the natural logarithm of gross investment on an intercept and trend term. The coefficient of the trend term indicates the growth rate of gross investment. 3.

Subsequent

net

real

capital

stock

figures

are

computed

by

the

following:

K (t )  (1  d ) K (t  1)  I (t ) , where all figures used are in real terms. 4.

The above method of computing the net real capital stock is based on Park (1995, page 590)

and Gong, Greiner and Semmler (2004, pages 158-159). G5 nations

30

Research Scientists and Engineers. Data prior to 1993 are taken from Jones (2002). To extend Jones’ series beyond 1993, we use data from OECD (2005). Missing observations for Germany (1994) and the U.S. (1986, 1988, 1990, 1992, 1994, 1996, 1998) are log-linearly interpolated. Data for U.K. from 1999 to 2002 are estimated from Higher Education Statistical Agency (1998/99 to 2002/03) and OECD (2006, Table 6). Based on these (estimated) data, we sum up the RSE’s of G5 countries and compute the annual growth rates of combined G5 RSE’s from 1994 to 2004. We then use these growth rates to extend Jones’ G5 RSE’s to cover 1994 to 2004. Details are given in a spreadsheet available upon request. Labor Force.

The data are taken from Bureau of Labor Statistics (2006), also available at

http://www.bls.gov/fls. Appendix 2: Statistical Tests on g(g(A)) and g(A) This appendix provides statistical evidence to justify the assumption that g(A) is a constant for the growth accounting exercise in section 4. To check for constancy of g(A), we first conduct a simple student-t test on g(g(A). To check whether g(A) is stationary, we conduct unit root tests. Using Stata’s command ttest, based on the assumption that the underlying distribution is asymptotically normal, a simple student-t test on g(g(A)) for the period from 1962 to 2004 gives: Observations: Mean: Standard Error:

43 16.45 12.42

H0: Mean of g(g(A)) = 0 H1: Mean of g(g(A))  0 t = 1.3247 P > |t| = 0.1924 Hence we do not reject the null hypothesis that the mean of g(g(A)) = 0 even at the 10% level of significance. In other words, we infer that g(A) can be considered a constant. Next, using Stata’s command dfuller, we perform the (Augmented) Dickey-Fuller tests for unit root on g(A) for the period 1961 to 2004. The results are presented in Table A1. Based on the t-ratios on the last lag of difference for the separate regressions, we conclude that the problem of serial correlation is absent. Hence, the Dickey Fuller test is appropriate. Given a test statistic of -5.088, we can reject the null hypothesis that there is unit root at the 1% level of significance. Although not necessary, but for the sake of completeness, Table A1 also shows the results of the Augmented Dickey-Fuller tests for lags of up to 3 periods. The results confirm that g(A) is stationary. We have also conducted statistical tests for the period 1970 to 2004 and the conclusion remains the same. Detailed results are available upon request. Table A1: (Augmented) Dickey-Fuller Tests on g(A)

Lags(0) Lags(1) Lags(2) Lags(3)

Test Statistic

1% Critical Value

5% Critical Value

10% Critical Value

-5.088*** -3.749*** -3.068** -3.590**

-3.628 -3.634 -3.641 -3.648

-2.950 -2.952 -2.955 -2.958

-2.608 -2.610 -2.611 -2.612

MacKinnon approximate pvalue 0.0000 0.0035 0.0290 0.0059

t-Ratio on Last Lag of Difference -0.21 -0.22 1.67

Note: ** and *** denote 5% and 1% level of significance, respectively.

31

Appendix 3: Mathematical Derivation of (16) From (2), we have

Kt sKt sKt   , Yt K t nt  g (kt )  d d Kt where kt = Kt/Lt. Noting (9), we have  At G 5FDIt    1   G 5MTt  g ( At )    H At At Et    . At Kt   Yt

Putting At as the subject, we have 1







  1  1 1  G 5MTt G5 FDI t 1 At     H At Et   , or Kt   g ( At )   Yt 



        G5MTt G5FDI t   At     H At Et   , Kt   g ( At )   Yt K   . and   1   . Substituting the above expressions for t and At into Yt 1 1 (15), we get (16). Hence, the derivation does not require constant growth rates in K and A. where we have used  

Appendix 4: Regression Results This appendix gives details on the estimation of (9) under different assumptions. The coefficients estimated are used in the growth accounting exercises. Following Jones (2002), let the unobserved actual stock of ideas be A and the observed or measured multifactor productivity be B. Suppose

ln Bt  ln At   t , where t is a stationary disturbance term. The discrete version of (9) is

 At 1  H    At1 At  A  t



     G 5MTt G 5FDI t  E .  .  t  Y Kt   t  

Next, we log-linearize the above around a path where Bt and H At are growing at constant rates, and express in terms of the measured multifactor productivity:

  G5MTt G5 FDI t 1  ln Bt 1   0   g ( B )[ln H At  ln Et  ln( . )  ln Bt ]   t 1 ,   Yt Kt 

32

g ( B)  g ( B) )) is a constant, and  t 1   t 1   t is an error term. An estimation of   the above seems to make one worry about reverse causality. We proceed by performing the Dickey-Fuller and Augmented Dickey-Fuller tests on the variables. We find that  ln Bt 1 is stationary (up to a lag order of 5 at where  0  g ( B)(1  ln(

G5MTt G5 FDI t 5% critical value) while ln H At , ln Et , ln( . ) , and ln Bt have unit roots. Working on the rightYt Kt hand-side variables, we obtain the pre-estimation lag-order selection statistics given by Final Prediction Error (FPE), Akaike’s Information Criterion (AIC), Schwarz’ Bayesian Information Criterion (SBIC), and the Hannan Quinn Information Criterion (HQIC). FPE, SBIC, and HQIC suggest an appropriate lag order of 1 while AIC suggests a lag order of 2. Next, the Johansen’s tests of cointegration show that ln H At , ln Et , G5MTt G5 FDI t . ) , and ln Bt are cointegrated: trace statistics finds 2 cointegrating equations at lag 2, more Yt Kt than 3 cointegrating equations at lag 3, and 3 cointegrating equations at lag 4; SBIC finds 1 cointegrating equation at lag 2 and 3 cointegrating equations at lag 2 and lag 4; HQIC finds 3 cointegrating equations at lag 2, lag 3, and lag 4. Hence our statistical tests conclude that the right-hand-side variables are cointegrated. Furthermore, following the argument of Jones (2002), the above equation looks like a standard errorcorrection model in time series analysis, and as there are linear time trends in the right-hand-side variables, the coefficients can be estimated by OLS, and they are consistent and have normal distributions. ln(

We have a total of 4 specifications in our regressions for each value of : setting  free, fixing  = 1, 0.5, and 0.25. When  is fixed, the left-hand-side variable will be transformed to  ln Bt 1   g ( B ) ln H At , which is stationary according to the Dickey-Fuller at 1% critical value for all fixed values of . The right-hand-side G5MTt G5 FDI t variables are given by ln Et , ln( . ) , and ln Bt . As before, we proceed to obtain the preYt Kt estimation lag-order selection statistics. FPE suggests a lag order of 2; AIC, a lag order of 3; HQIC and SBIC, G5MTt G5 FDI t a lag order of 1. The Johansen’s tests of cointegration show that ln Et , ln( . ) , and ln Bt are Yt Kt cointegrated: trace statistics and SBIC find 2 cointegrating equations at lag 3; HQIC finds 2 cointegrating equations at lag 2, lag 3, and lag 4. Hence, the right-hand-side variables are cointegrated. Table A2 presents the results for these 4 specifications when  = 1/3. To check for robustness, we re-do the exercise for  = 0.2449, 0.3749, and 0.53, and the results are available at the personal website of the first author at http://www3.ntu.edu.sg/home/kwho. The results from Table A2 show that  is statistically significant when  is set to 1, 0.5, or 0.25, and for different assumptions on . When  is set free, the significance of  cannot be established because the delta-method of computing the standard error involves a square root of a negative number. Furthermore, when  is set free, the estimated  is greater than unity, inconsistent with the theory. Hence, we prefer the case of  = 1 and the associated estimated coefficients are used in the growth accounting exercises which are presented in the main text. Note also that  is at least moderately significant for most cases when  is set equal to 1, 0.5, or 0.25.

33

Table A2: Log-Linearized Estimation of (9), 1970-2004,  = 1/3

 g(B) 

   R2

Specification where  = 1/3 (1) (2) (3) (4) 3.0737 1 0.5 0.25 (5.971) 0.0243 0.0243 0.0243 0.0243 0.3300 0.0993 0.0488 0.0242 (0.043) (0.021) (0.010) -8.3129 -9.0686 -9.2508 -9.3419 (4.946) (4.376) (4.381) (4.384) 3.6900 5.1546 5.5077 5.6843 (4.849) (2.358) (2.360) (2.362) -0.0218 0.6785 0.8473 0.9317 (2.355) (1.198) (1.199) (1.200) 0.1847 0.1627 0.1619 0.1676

Note: Numbers within parentheses are standard errors, computed using the delta-method. When  is set free, the standard error for  cannot be computed because it involves a square root of a negative number. The corresponding tables for other values of  are available from the personal website of the first author at http://www3.ntu.edu.sg/home/kwho. Furthermore, the website contains the data set used in our quantitative analysis.

34