Technology Gaps, Do They Explain Growth
Differences Across Countries?
J. R. Perilla Jimenez
June 29, 2013
A model that relates GDP growth differences, across high and low income countries, to differences in adoption and innovation of frontier technologies is proposed and empirically evaluated. The analysis is based on the description of patterns and density functions of these variables using a sample of 60 coun-tries during 1970-2009. The econometric approach relies of IV methods, using an index of economic freedom to instrument technology. The results lead to the conclusion of a pattern of growth divergence explained by differences in technology endowments. Whilst this is in sharp contrast to endogenous growth models that highlight the advantage of backwardness, convergence of DCs is found to be more related to technology upgrading, which is captured by over time technology changes.
1
Introduction.
Are technology differences important to explain GDP growth differences across countries? Clearly, the answer to this question depends on what we understand by technology and the way we measure it. Is it the technology embodied in capital goods such as machines and equipment? or the improved knowledge on the organization of the production activity? or some abstract concept that measures all that is ignored about the mechanism of economic growth?1
Inter-estingly, while the evidence challenges the existence of a convergence pattern in the rates of growth of high and low income countries,it is unclear whether there is a role for technology differences on that result.
In fact, the relative importance of the role of technology vis-`a-vis the ac-cumulation of capital is one of the never end debates in economics both at conceptual and empirical levels.2
1See Nelson and Phelps (1966), and Nelson and Pack (1999), and the questions first raised
by Bernard and Jones (1996), and recently explored by Kumar and Russell (2002) with regard to: How do we economists measure technology?, is it enough to simply consider a labour augmenting technology factor?, Are there other differences in the production function that are important?, and How much convergence that we observe is due to convergence in technology versus convergence in capital labour ratios?
By assuming that technological progress has characteristics of a public good, e.g., that it is freely available, and benefits all countries equally, models in the tradition of the Neo-classical theory hold no role for technology differences. That definition is, nevertheless, at odds with a wide range of models stress-ing on adoption and innovation as the key to explain differences in economic growth.3 In these models, the obvious difficulty arises in disentangling both
effects. The model proposed by Comin and Hobijn (2010) stresses the argu-ment that countries adopt technologies that are embodied in specialized capital goods. Whereas the emphasis in the model developed by Acemoglu, Zilibotti, and Aghion (2006), is in the role of innovations, which are related with disem-bodied technical changes.4
In this paper I joint these views together. I exploit the argument that the lack of distinction between forms of technology, or the focus on only one of the above components, is inappropriate. On applied work it frequently leads to misleading interpretations as that workers are more productive because they produce more output per hour rather than because they are equipped with better machines, or because production benefits from R&D.
Accordingly, I change the focus of analysis. Rather than on labour or multi-factor productivity, the focus in this paper is on forms of technology. I keep a distinction between embodied technologies, which I associate to tangible assets as machines and equipment; and disembodied technologies, which I associate to intangible assets as R&D and other knowledge intensive activities. Furthermore, I relate the former classification to the role of adoption and the concept of capital deepening in other literatures; and relate disembodied technologies to innovation.5
By way of stressing on differences across countries, I measure also each form of technology as a technology-gap; and correspondingly, the differences in eco-nomic growth in terms of GDP-growth gaps. Where gaps are measured relative to corresponding figures in the US Economy. In the paper I use the terms ”gaps and ”differences” indistinctly.6
Based on these definitions, the key contribution of this paper is to assess whether and to what extent technology gaps provide meaningful and robust evidence to explain observed GDP-growth differences between high and low
of growth over long periods (Madsen, Ang, and Banerjee 2010, Mokyr 2005, and Galor 2005), others downplay its role in favour of the capital deepening argument (Allen 2003, Craft 1995). For contrasting findings in shorter and more recent periods see Oxley and Greasly (1998), Jones (1995a, and 1995b)
3For Examples, see Aghion and Howitt 2009 Ch 4 & 5, Acemoglu 2009 Ch 18 & 22 4The distinction between innovations as incorporated in new machines and in new methods
of production is generally ignored in the literature. Zeira (1998), points out that the standard view seems to look at innovations in terms of efficiency. Whereas he looks at them as associated with tangibles assets, i.e., machines.
5Hopefully the distinction that I propose here will prove to be adequate throughout the
pa-per. See Hill(2009), and Corrado, Hulten, and Sichel (2009) to get in context of the difficulties associated with classifying capital assets into tangible and intangible varieties.
6I use the US as a benchmark country. Aside of stressing on differences, the results in this
income countries. To this end, I focus the analysis on three aspects. First, I present a throughout discussion about the tendency of GDP growth differences and technology differences across countries, and provide further evidence of these patterns using the so-called ”twin-peakedness” distributions.7
Second, the distinction between embodied and disembodied forms is pur-ported to provide a formal test on which form of technology is the key driver and how large, if any, are these effects.8
Third, I draw attention to the advantage of backwardness hypothesis, which predicts higher rates of economic growth for countries with comparatively larger technology gaps (Gerschenkron 1962, Abramovitz 1986). Thus, I explore whether the evidence brings supports to the convergence-path implied by this hypothe-sis.9
To implement the assessment, I use a model that combines insights of the product variety approach,10and the Shumpeterian approach to economic growth.11
In the empirical approach I use a sample of 86 developing and hight income countries for which it is possible to raise consistent indicators on a range of embodied and disembodied forms of technology. These information is obtained from diverse sources (CHAT Database, WIPO Database, and WDI). The econo-metric approach rests on the IV-approach for which purpose technology gaps are instrumented using the index of economic freedom - legal system strength and property rights defence - released by the fraser institute.
The rest of the paper proceeds as follows. In section 2, I provide the theo-retical background that underlines the main issues to be discussed throughout. This section serves also to provide a short review of the relevant literature. In Section 3, I present the methodology that underlines the empirical approach and clarify the link between the theory and the equations to be estimated. In section 4, I conduct some motivating descriptive evidence of the cross-country observed patterns of technology adoption, innovation, and economic growth. In section 5, I discuss the econometric results, and in section 6 some concluding remarks are offered.
7Quah (1996, 1997)
8This is an important contrast with previous research that holds embodiment as a weak
form of technology (Keller 2004), or do not make a distinction (Fagerberg 1994). I stress that both forms are important. Whereas less developed countries would only ignite growth after increasing their stocks of embodied technologies. Corrado, Hulten and Sichel (2009) suggest large differences in growth accounting due to the tendency to ignore the role of intangibles (disembodied technologies).
9I frame scenarios in which developing countries only can converge if there is an inverse
relationship between technology gaps and GDP-growth gaps. Conversely, a significant direct relationship between technology and GDP-growth gaps would bring support to a divergence path.
10See Dixit and Stiglitz (1977)
2
Theory.
I lay out a model that combines the main features developed in earlier liter-ature.12 In this model GDP growth is related to embodied and disembodied
technologies. The maintained assumption is that countries adopt technologies embodied in machines and equipment; and invest into the generation of knowl-edge, which is disembodied and accumulates as innovations. The pace of adop-tion and innovaadop-tion depends on the countries’ stage of development. As in the neoclassical framework, factor productivity, and factor prices determine opti-mal choices of both inputs. Nevertheless, growth out of adoption reaches a halt because the condition of diminishing returns. When feasible adoptions are fully exhausted, long-run growth is determined solely by innovations.
Formaly, for a given country the structure of production combines labour and a continuum of intermediate goods as follows.
Yt= L1−αt
Z 1
0
A1−αit Xitαdi (1)
Where 0 < α < 1; labour, L, is assumed to be supplied inelastically; Yt
is final output, here equated to GDP and assumed to be produced competi-tively. Each intermediate good is produced by monopolistic competitors using a production function that transforms one unit of capital into one unit of the intermediate good, Xit = Kit. This can be interpreted as each intermediate
representing technologies embodied in specialized capital goods. An important implication of the Cobb-Douglas specification is that different technologies are perfect substitutes for each other regardless of their differences in productiv-ity.13 Accordingly, A
it is a sector specific parameter interpreted here as to
capture the disembodied technological progress, e.g., knowledge and technical skills associated with the use of specific capital goods.
Equilibrium demand for each intermediate good equals to14
Xit=
α2
Rkt
1−α1
AitLt (2)
Taking into account that Kt=R 1
0 Kitdi =
R1
0 Xitdi, and noting that At =
R1
0 Aitdi, the aggregate capital stock may be written as
12See, among others, Aghion and Howitt (2007, 2009); Acemoglu, Zilibotti, and Aghion
(2006); Benhabib and Spiegel (1994), and Nelson and Phelps (1966)
13for a different specification of the aggregation implied by the Dixit -Stiglitz approach see
for example Caselli and Wilson (2004). Unlike their CES specification, in this paper the issue of substitutability is not captured
14Taking the final product price as numeraire, each intermediate sector faces an inverse
demand curve given by pit= αL1−αt A 1−α it X
α−1
it . The intermediate monopolist cost is given
by an asset specific constant rental rate Rkt, which leads to equilibrium profits given by
πit= α(AitLt)1−αXitα− RktXit. Equation (2) results from deriving the profits equation and
Kt= Z 1 0 α2 Rkt 1−α1 AitLtdi = α2 Rkt 1−α1 AtLt (3)
After some algebra, the assumptions above allow to rewrite the production function in the neoclassical form.15
yt= Atktα (4)
It is, the aggregate production function relates GDP per-worker, yt= Yt/Lt,
to an aggregate of the potentially large number of technologies embodied in per-worker effective units of capital goods, and the aggregate stock of disembodied technologies.
Based on this structure of production, I suggest two, not mutually exclusive, ways through which technology-gaps are related to GDP-growth gaps. The first one defines the effect of technology gaps at the level. Let T be the per-worker technological endowment of a benchmark country located at the technology frontier, and let y denote its GDP. For a given country, at any particular time, the relationship between the GDP-growth gap and the gap in the levels of technology is given by16 ωy˙ y − ˙y y = ˙y = σ(e ez)(T (τ ) − T (τ )) (5) where T = k, A, T = k, A, and T (τ ) = T (τ ) =Rτ 0 R1 0 Titdidt.
The left hand side of this expression represents differences in the GDP growth rate whereas the right hand side represents the difference in total technological resources that are available. Technology differences are an increasing function of ez, which denotes differences in the level of development. It stands for the premise that countries that have more qualified workers, appropriate institu-tions, and are more open to the rest of the world, have a greater ability to absorb technological advances generated in the leading nations (Nelson and Phelps 1966, Abramovitz 1986, Benhabib and Spiegel 1994, Romer 1993, Barro and Sala-I-Martin 1997).
The core insight of the advantage of backwardness hypothesis is that the farther a country falls behind the frontier technology, the larger should be its rate of GDP-growth if it is going to catch-up with the leader. By way of stressing on this aspect, I introduce the factor ω. It scales GDP growth in each country by the ratio in levels of its GDP per-capita relative to the US. The key insight is that the convergence possibilities of a given country relate not just to how faster it grows relative to more advanced countries (convergence in rates of growth). But also to how fast it should grow to catch-up with the level of income of a
15Note that equation (3) may be written in per-worker effective units of capital as k t =
country at the frontier (convergence in levels).17 Note, fo instance, that during 1990-2008 per-capita GDP grew at an average of 1.64% in US, 3.81% in Poland, and 2.15% in Australia. At first sight, these rates bring the idea of a faster convergence pattern of Poland. Nevertheless, in 1990-2008 per-capita income of Poland was around 0.25%, and that of Australia 0.80%, relative to the US. Scaling growth in both countries by these ratios gives to Poland a rate of growth of 0.87% and to Australia 1.61%. Remarkably, whilst at a constant rate of growth of 3.81% Poland would double its GDP per-capita in less that 20 years, at a rate of 0.87% it would take this country around 80 years to catch-up with the GDP per-capita of the US. A similar reasoning for Australia implies that it would take the country around 30 years to double its income, but just around 40 years to catch-up. Note that an strong implication of this weighting mechanism is that countries whose average growth is slower relative to the leader can not converge unless they show a value of ω > 1.
I interpret equation (5) as the impact of the gap in technologies accumulated by a country at time τ on the GDP-growth gap. These differences are hold as an increasing function of differences in the level of development. Why would one expect differences in technology accumulation to be explicative of GDP-growth differences? My suggestion is that, Ceteris Paribus, marginal changes in production depend on the current state of technology because workers en-dowed with better machines are more productive - relative to similar workers in other country - even if the technology is stationary. In addition, aside of quality differences, the advantage of backwardness indeed imply that a country endowed with a smaller amount of ”Trucks” shall show larger increases in their contribution to GDP-growth (Gerschenkron 1962, Abramovitz 1986).
The second way I suggest technology gaps are related to GDP-growth gaps is through differences in the rate of change of technology.18
˙ e
y = φ(z)e Te˙
(6) Where the technology gap is defined by
˙ e T = T˙ T − ˙ T T; T = k, A; T = k, A (7)
I interpret equation (6) as the impact of differences in the rate of growth of technologies on GDP-growth differences. Since factors determining the stage of development change relatively slow over time, technology differences are still hold as an increasing function of differences in the level of development.
Moreover, whilst the previous model stresses on differences in endowment, this stresses on technology upgrading as the key to understand growth differ-ences. It is, I assume that the rate o change of technologies is associated with 17This weighting mechanism implies a gap equal to zero for the benchmark country. It
penalizes relatively more countries that fall farther away from the frontier and leaves relatively unaffected countries with similar levels of GDP per-capita as the benchmark country.
18This equation is obtained from log-linearizing equation (4), taking the time derivative on
the acquisition of new vintages of improved capital goods rather than more items of the existing technologies. Since the adoption of new embodied vintages implies also a new learning, innovation changes are shaped by further knowledge intensive investments purported to master the new acquired technologies. The change of technologies is associated with growth because a country character-ized by an in-depth use of, say, ICT should show a higher positive variation in growth rates compared to countries that rely on its older substitutes.
Aside of the focus in technology and growth ”gaps”, some similarities and differences of this paper with previous research are worth noting. The model in this paper is purported to accommodate the experience of developing and high income countries. It is, even if GDP growth rates of high income coun-tries depend more on the ability to innovate, in backward councoun-tries it depends on the ability to increase the adoption of embodied technologies. Innovation, nevertheless, is not exclusive of countries at the world technology frontier, i.e., one can expect some level of innovation at low levels o development. It copes with arguments by, among others, Acemoglu et. al. (2006) stressing the idea that there is not one but several engines of growth. In less developed and mid-dle income countries growth relies heavily upon factor accumulation, and upon imitating or adapting technologies from more advanced countries. In turn, in more advanced countries growth relies on the creation of new knowledge that pushes the technology frontier forward.
As in the hybrid neoclassical/schumpeterian model developed by Aghion and Howitt (2007, 2009), the aggregate production function in equation (4), and the discussion on the process of capital accumulation, are the same as in the neoclassical framework. Moreover, as is the case in Schumpeterian models of economic growth, technology progress is endogeneized rather than assumed exogenous. Nevertheless, in Aghion and Howitt (2007, 2009) the rate of growth of technology is endogenously determined by the increase of the capital stock. Whereas here both capital deepening and innovation are thought to depend on the stage of development.19
The model in this paper relates also to Comin and Hobijn (2010, 2011) in which technologies are associated with differentiated capital goods. The distinguishing feature is that here technology is not only embodied in capital goods but also disembodied in the stock of knowledge.20
Lastly, I draw attention to a number of empirical studies that have tested the ability of technology differences to explain differences in economic growth in cross-country settings. Evidence in this regard, provided among others by Fagerberg (1994, 1995), are generally based on a small sample of countries and 19Whereas technology progress may be an increasing function of the capital stock due to
scale effects and a reduction in the rental rate of capital - as in Aghion and Howitt (2007, 2009)-, the rationality for this causation is not unique. Also the capital stock may be hold an increasing function of technological progress as in Madsen, Ang, and Banerjee (2010). Technological progress may increase expected earnings per unit of capital, and cause Tobin’s Q to exceed its steady state, which initiates a process of capital deepening.
20Comin and Hobijn use their model to explore adoption lags on specific technologies.
a narrow definition and number of technology differences. In addition, in those studies the identification of the effect of the technology gap on economic growth is a major weakness, and the assessment of other covariates is neglected.
More recent attempts using growth accounting, as in Kumar and Russell (2002), are not equipped to address the causality problem, nor to provide an assessment of the role of other covariates. These shortcomings are probably at the outset of the ambiguity in their findings, in the sense that whilst Fager-berg finds evidence of convergence, Kumar and Russell find that technological changes benefit more the rich than the poor countries.
3
Methodology.
In this section I relate embodied technologies to tangible assets and the role of adoption. Accordingly, I relate disembodied technologies with intangible assets and the role of innovation. This is and ad hoc distinction, but one consistent with research that show that most of the world capital assets are produced in a small number of countries (Eaton and Kortum 2001), and with the fact that to some extent all countries are involved in some kind of knowledge creation. In what follows, I will refer to ”technology gaps” in general to mean both forms of technology. Likewise, I will refer to ”Adoption gaps”, and ”Innovations gaps” for comparison purposes.
The data used to capture these different forms of technology may be inter-preted in two ways. One, the output equivalent that is produced with a given technology (e.g., the tons/km carried by transport systems, as an example of embodiment, or the value of ICT exports, as an example of disembodiment). Two, the capital equivalent that accounts for the number of units of specific assets (e.g., the number of trucks used to provide transportation services, or the number of patent applications.).
Both forms of technology (Adoption and innovation) are measured in the intensive margin, which means that every technology is measured in per worker terms. To cope with heterogeneity across countries and technologies, I express all technologies in logarithms. The gaps are measured for each relevant indicator taking a simple difference of the log of the technology for each country relative to that of the US Economy. Formally, for a technology j that is observed in both country i and the us, the gap at time t is defined as
gapi,j,t= xi,j,t− xus,j,t
Consistently, the GDP-growth gap is defined as ∆yi,t = ωi,t∆yi,t− ∆yus,t
where ∆yi,t denotes the year-over-year rate of GDP-growth of country i
Technology Gaps at the Level.
I focus the analysis on overall country aggregates of adoption and innovation gaps. To this end, it is needed to sum up the gaps for each individual technology. One way to aggregate over technologies is by using the GDP share of each technology as a weight.21 Unfortunately the datasets used in this paper do not
account for these GDP shares. Another possibility, is to estimate the relative contribution to economic growth explained by each technology type. But this would need unrealistic assumptions on interpreting the elasticities obtained for different types of technology. To avoid these complications, I restrict the analysis to technologies that are considered to have a significant effect on production, and focus on aggregates of the dispersion of each technology gap across-countries.22 To get in context of how this is achieved, a number of comments are important. First, to ensure sum-ability, the units of measurement should be homoge-neous through the diverse technologies. To this end, each technology gap is normalized using the standard deviation across countries.23. In other words,
the dispersion for each technology gap is interpreted as the number of stan-dard deviations a country falls relative to the US. Formally, this is done in the following way
g
gapi,j,t= ST Dgapi,j,t=
gapi,j,t
DESV EST (gapj,t)
Second, since the number of technologies differ across countries, overall ag-gregates for each country are expressed at the mean of dispersion over different technologies. Note that for each country there are two overall aggregates. One for adoption gap (gap(k)), obtained by summation over tangible assets. Other for innovations gaps(gap(A)), obtained by summation over intangible assets. I calculate averages for each form by summing up individual gaps and dividing the result by the number of technologies that are available.
g gapi(T ) = N1 N P j=0 g gapi,j(T ); T = A, k
Third, it is worth noting that aggregated in this fashion, these dispersion measures reflect only cross country differences in technology. It is, technology gaps measured in this manner do not reflect cross-country differences in capital composition, or differences in the contribution to growth by different capital assets. The obvious shortcoming in this case is that all technologies considered in the analysis are hold as equally important.
21See for example Caselli and Wilson (2004).
22See Comin and Hobijn (2006) for a similar approach. By considering technologies that
play a significant effect I mean that I keep ”Bull-Dozers” and ”Trucks” in the analysis while excluding ”Shovels” and ”Horses”.
23The normalization in this fashion mimics the usual practice to summarize the various
Provided the data used in this paper reflects a consistent set of the most up to date technologies used in production, I suggest that this focus on dispersion is worth to capture the effects of technology differences on growth differences. By construction, the increase in dispersion implies for a given country a larger distance with respect to the frontier, thus a larger technology gap. If the con-vergence path implied by the advantage of backwardness holds, the data should reveal a negative relationship. It is, that large values of dispersion are associ-ated with low values of GDP-growth differences. By contrast, if the association between dispersion and growth differences is positive, it would support the diver-gence view instead. If both measures do not correlate in either form, technology gaps may be hold unable to explain growth differences.
I refer now to the specification of the econometric approach based on these gaps. The analysis at the levels in equation (5) stresses on the accumulation of technology gaps over a period of time. Thus, it relates the gap in levels of technology to the GDP-growth gap. To implement these ideas I note the high volatility that is observed on the rates of economic growth, a problem that is mainly associated with GDP growth of developing countries.24 Furthermore, I note that the coverage of technologies over time in the sources used for this study is highly incomplete. This implies that technology gaps typically only can be calculated for a small number of years, which not necessarily coincide across countries. To address these shortcomings, the implementation of the gap in levels make use of averages over specified periods.
In my approach, I split the sample into two periods from 1970-1980 and from 1981-2009. I hold the first period as the set of initial conditions, and the last as the period of analysis.
The first equation to be estimated is as follows
∆y1i= α0+ α1k1i+ α2A1i+ α3y0i+ α4DX1i+ α5Z0i+ i (8)
where ∆y1iis the average gap of the per-capita GDP-growth in country i in the
period of analysis; k1i (respectively A1i) denotes the average gap of per-capita
levels of adoption (innovations) in the same period relative to the US. Higher values for these indicators imply higher technology gaps. y0i is the average
gap in levels of GDP per-capita relative to the US in the conditioning period. Higher values for this variable indicates higher resource constraints and lower levels of initial development. It captures the fact that countries with lower income per-capita find more difficult to adopt new technologies, and to invest in knowledge.
As has being stressed already, the core objective of the analysis is to as-sess if technology gaps contribute to explain observed GDP-growth gaps across high and low income countries. To cope with this, I use a dummy variable for Developing Countries (DCs=1). Thus, I define DX1ias a set of interaction
gaps. These interaction terms capture whether and to what extent technology gaps have different effects for both groups of countries.
The other terms in the specification are Z0i, a set of variables conditioning for
the development stage, and ita disturbance term with mean zero and constant
variance.
The set of variables in Z0i includes growth determinants already suggested
in the literature: educational achievements (Schooling),25trade openness,26and
institutions related to the defence of property rights, and intellectual property (which will be termed economic freedom here onwards).27 In the regression, all
these determinants are measured also as gaps relative to the US and taking the average over the conditioning period. Together with the GDP gap in levels, these variables feature as the initial development conditions of each country. Higher values for these indicators represent a lower level of schooling, institutional development, and economic integration relative to the US. This capture the idea that less developed countries face greater difficulties to absorb technological advances generated in the leading nations
Besides of being measured in gap terms, all conditioning variables in the equation above are also normalized by its standard deviation across-countries. This is aimed to ease the comparison of their relative explanatory power. It is, since they are measured on equal basis, the regression coefficients may be compared directly. A larger coefficient for a given variable, relative to other variables in the regression, implies that its contribution to the explanation is also larger.
I estimate equation (8) using a Robust OLS approach and stress on the robustness of the results to the set of conditions related to the level of devel-opment. To stress on the workings of the weighting mechanism -through the factor ω- I present results for both cases. One in which the dependent variable is the weighted GDP-growth gaps. The other, where the dependent variable is the un-weighted GDP-growth gaps.
Instrumental Variables Approach (IV).
Technology gaps in the OLS regression above may be endogenous as adoption and innovation are most probably caused by, or correlated with, the same de-terminants thought to influence economic growth; and even affected by reverse causation as economic growth may provide the incentives for subsequent tech-25The level of education of the population aged 15 years or more. Figures are taken from
Barro and Lee(2001)
26Calculated as imports plus exports as % of GDP. Relevant figures are taken from the
World Development Indicators at $2000 Constant prices adjusted by PPP
27I use the component of legal system and property rights from the economic freedom index
nology improvements.28
The IV approach is a common approach to deal with this problem, and it is addressed next.29 With a slight change of notation in benefit of the explanation, I start by setting up the estimating equation as follows
∆y1i= α0+ α1G1i+ α3y0i+ α4DX1i+ α5Z0i+ i (9)
where G1i denotes, alternatively, adoption gaps (k1i), and innovation gaps
(A1i). It means, I run equation (9) once for G1i= k1i, and then for G1i= A1i.
I use as instruments a subsetzf0iof the initial conditions included in Z0i. The
standard IV approach is to find a set of instruments that are correlated with the endogenous regressors, G1i, and uncorrelated with the error term. Formally,
Cov(zf0i, G1i) 6= 0
Cov(zf0i, i) = 0
Then the IV approach identifies α1 in equation (9) by30
plim αIV 1 = Cov( f z0i,∆y1i) Cov(fz0i,G1i) = α1
Clearly, the major problem in using the IV approach is that of obtaining a suitable set of instruments that are both sufficiently uncorrelated with the error term, and sufficiently correlated with the relevant explanatory variables. An alternative requirement for a good instrument is that it is predetermined, rather than strictly exogenous. It implies that there must be no simultaneous feedback between the main equation to be estimated, and the equation that uses the instruments. In addition, the instruments should be relevant in that they significantly help the prediction of endogenous regressors.
In the implementation of the IV estimation, I made use of the index of economic freedom, and its interaction term with the dummy for DCs, as prede-termined instruments. I suggest these as consistent instruments to the extent that economic freedom - the strength of the legal system and the defence of property rights - is an important determinant of adoption and innovation de-cisions. Moreover, since they are measured in the conditioning period, these measures of economic freedom are unaffected by economic growth in the period of analysis. In fact, while I find no correlation between these indicators and the error term, they are highly correlated with measures of technology gaps.
28In fact, the endogeneity problem violates the assumption that the residuals in the
regres-sion are uncorrelated with the dependent variables. If this is the case, regresregres-sion estimates are biased and inconsistent, and inference is seriously misleading.
29See, for instance, Hayashi (2000). The assumptions made under the IV approach are
amenable to empirical testing and shows similar statistical properties as OLS estimation (con-sistency, unbiasedness and efficiency).
30Though this is a large sample result, see for example White(1984). In more general
conditions it may be seen that plim αIV1 = α1+ Cov(fz0i,i) Cov(zf0i,G1i)
The important limitation to note to this point is that the coefficient esti-mates are credible just in the case of separate regressions. A couple of reasons justify this approach. First, because measures of technology used in the analysis are strongly correlated with each other. It means that adoption and innovation forms of technology are most probably highly collinear. Second, because there are only two predetermined instruments and 4 endogenous variables (the tech-nology gap, the innovation gap, and their interactions terms with the dummy for DCs). Whilst these instruments may be argued to be equally important in explaining either adoption or innovation, their use in a single regression may lead to misleading conclusions.
Technology Gaps Changes.
Consistently with the calculation of the GDP-growth gap defined above, I rede-fine the technology gap for a technology j that is observed in both the country i and the us in year t
∆gapi,j,t= ∆xi,j,t− ∆xus,j,t
Where ∆gapi,j,tdenotes the year-over-year rate of technology change. Since
each gap is now measured in changes I get rid of the normalization adopted above.
The equation to be estimated using IV approach is a cross section of countries as follows
∆y1i= α0+ α1∆G1i+ α3y0i+ α4DX1i+ α5Z0i+ i (10)
where should be noted that the only difference with equation (9) is in the specification of the set G1i. It now denotes, alternatively, average changes in
adoption (∆k), and innovation (∆A) gaps over the period of analysis.
4
Data and Descriptive Statistics.
The data on different forms of technology are obtained from the Cross-Country Historical Adoption of Technology dataset (CHAT) released by Comin, Ho-bijn, and Rovito (2006, 2008).31 This is supplemented with data from the In-frastructure, and Science and Technology, datasets that are available from the World Development Indicators, and with data released by the World Intellectual Property Organization (WIPO).32The Groningen Growth Development Centre
(GGDC), provides access to the estimates of Maddison (2007) on PPP adjusted 31Available at http://www.hbs.edu/faculty/Pages/profile.aspx?facId=438581
32See http://data.worldbank.org/topic/infrastructure, and
real GDP figures (Base=1990) and population.33 The period of analysis is re-stricted to 1970-2009 to ensure consistency between different data sources.34
The sample of technologies related to Adoption includes a set of 19 tech-nologies. These are chosen on grounds that they cover a range of the main productive technologies in use by a substantial number of countries. In turn, the sample of Innovation technologies includes a set of 10 indicators. (Table 6 and 7 in the Appendix presents a detailed description of these technologies, their source, the period of time in which they are available, and the number of countries with information.).
The number of countries in the analysis is determined by the following three criteria: 1) The matching between the information on GDP growth and each technology type, 2) The matching between countries with information in the different datasets, and 3) The condition for each country to have information on more than N/2 technology types and more than τ /2 years in the period of analysis, where N and τ refer to the total number of technologies and years of information respectively. It leads to select a sample of 60 countries (See Table 9 in the appendix for the list of these countries.).
Clearly, the classification of the technology variables into ”Adoption” and ”Innovation” in this paper is highly ad-hoc. Not surprisingly, the correlation between the 29 technology variables is large (See the pairwise correlations that are reported in table 8 in the Appendix.). It pin points the fact that countries seldom acquire single varieties of particular technologies, and that innovation is highly correlated with the acquisition and mastery of embodied technologies.35
Note that the hight patterns of correlation between technologies do not allow for a clear distinction between Adoption and Innovation forms using statistical methods. For example, an Exploratory Factor Analysis Technique (EFA) allows a clear distinction between two groups, one that is associated with adoption (Passenger Cars, Cellphones, Road Networks, etc.), and the other with inno-vation (Patents application, royalty payments, high technology exports, etc.). But of these, only the first factor is meaningfully related to all technologies with loadings larger than 0.5. Also, this only factor explains much of the com-monalities between 14 technologies that are retained after the factor, as may be deduced from the low values of ”uniqueness” (See the figure 5 in the Appendix). In addition, the EFA Analysis would discard 15 out the 29 technologies selected for the analysis. Nevertheless, the Kaiser-Mayer-Olkin (KMO) measure of sampling adequacy suggest that a factor analysis is only weakly appropriate for the data at hand. On base of this limitations I consider more convenient to rely on average indicators over the ad-hoc classification of technologies.
33see at http://www.rug.nl/research/ggdc/
34Unfortunately, data coverage is highly incomplete through the different sources, and this
is mainly true for information on technologies and innovation. For example, data on R&D is only available from the World Bank from 1996 onwards. Likewise, patents application in this source presents many blanks and is only available from 1960 onwards. My choice of countries and technologies, and the methodological approach is attempted to deal with this limitations while preserving a large number of countries in the sample
Some Stylized Facts.
In the sample of 60 countries, PPP adjusted real per-capita GDP grew at an average of 1.6% per year between 1970 and 2009. This average, nevertheless, differs greatly between groups of countries. Whilst the list of Developing Coun-tries (DCs) grew at a yearly rate of 1.3%, High Income CounCoun-tries (HICs) grew at an average of 2.3%, and the US at a rate of 1.8%. Thus, at first sight the pattern of growth across countries during this period seems to conform better with a pattern of divergence, rather than convergence, as has been discussed in other literatures.36 I show later in this paper that similar patterns hold in a
framework that conditions on the development stage.
I present both un-weighted and weighted GDP-growth figures to stress on the relevance of the factor ω introduced above. For the un-weighted case, the overall GDP-growth gap in this period is -0.20 percentage points (pp). But, it differs between the two groups of countries that were established above. Whilst the gap of DCs is -0.48 pp that of the HICs is 0.51 pp. This pattern is at odds with the advantage of backwardness hypothesis. Clearly, the negative gap of DCs imply that they were diverging in their GDP-growth through the period 1970-2009 both with respect to the US, and with respect to the HICs. As shall be shown shortly, there are changes in the gap over time. But, they hardly conform to a pattern of convergence.
A similar feature is suggested by the adoption gap. In the period 1970-2009 is was largely more negative for the DCs (-2.35 Standard Deviations - SDs) than for the HICs (-0.89 SDs). The negative figure for both groups of countries is consistent with the leader having a larger per-capita endowment of selected technologies. The lower value of the gap for HICs is also consistent with the fact that after 1970s the US started to lose its technological leadership (Nelson and Wright 1992). The overall adoption gap, nevertheless, is the result of large variations in individual gaps for each country and technology-type. Within the groups of DCs, for instance, it goes from a negative gap in Units of Passenger Cars (excluding tractors and similar vehicles) in Bangladesh (-6.02 SDs), to a positive gap for Railway-transportation (passengers carried by Railway) in Romania (1.74 SDs).
In addition, the data suggest similar patterns of divergence in the innovation activity. The average of the innovation gap for the group of DCs is -2.03 SDs, whilst the HICs show a positive number of 0.15 SDs. In the group of DCs the variation in individual gaps by type of activity and country goes from -5.94 SDs in the gap of Expenditures in R&D in Zambia, to -0.66 SDs in patents applica-tion by non-residents in South-Africa (Figure 4 presented in the Appendix show the evolution of these extreme cases of adoption and innovation in the countries of reference for the period 1970-2009.).
A further feature of these gaps is over time. The DCs GDP-growth gap was wider and negative for the period starting in 1980 (the average un-weighted gap was -0.62 pp). But, this pattern started to change after the 1990s when the gap of DCs became positive. Remarkably, in the period 2000-2009 the gap
of DCs (1.57 pp) is positive and larger than for HICs (0.96 pp).37 Though the un-weighted averages is is more alike with a pattern of convergence, the weighting procedure suggested in this paper is counter-factual. These weighted figures show that the GDP-growth gap of DCs decreased from -1.60 pp in the 1970-2009 period to -0.83 pp in the 2000-2009 period. But the gap of the HICs decreased even faster, and became positive during 2000-2009 (0.16).
In the case of adoption, there is a considerable reduction from the gap for 1970-2009 (-2.35 SD) to that in 2000-2009 (-2.03 SD). But again the reduction is even faster for HICs (from -0.89 to -0.43 SD in the respective periods). In the case of innovation, the gap of DCs first increases in the 1980s and 1990s, and later decreases in the 2000s. But the change is even more interesting for the HICs. For this group of countries the gap goes from positive to negative values after 1990. This is feature of the data in the table that provides support to the view of a divergence pattern in Europe relative to the US, which is more evident in recent decades. Van Ark, O’Mahony and Timmer (2008) provide a discussion in which the reduction is in line with the lower contributions from investment in modern technologies (ICT) to the productivity growth in Europe Vs US.
Table 1: Average GDP-Growth, Technology and Innovation Gaps over Time.
GAP 1970-2009 1980-2009 1990-2009 2000-2009 Unweighted GDP-Growth gaps
GDP-Growth -0.20 -0.34 0.34 1.40
DCs -0.48 -0.62 0.26 1.57
HICs 0.51 0.35 0.53 0.96
Weighted GDP-Growth gaps
GDP-Growth -1.25 -1.21 -0.96 -0.54 DCs -1.60 -1.54 -1.26 -0.83 HICs -0.39 -0.41 -0.23 0.16
Unweighted Adoption gaps
Technology -1.93 -1.86 -1.85 -1.56 DCs -2.35 -2.26 -2.25 -2.03 HICs -0.89 -0.86 -0.85 -0.47
Unweighted Innovation gaps
Innovation -1.23 -1.35 -1.39 -1.31 DCs -2.03 -2.15 -2.19 -2.07 HICs 0.15 0.04 -0.08 -0.11
Source: Author’s elaboration based on the group of 19 adoption and 10 innovation technologies reported in tables 6 and 7 in the Appendix.
The GDP-Growth Gap is in percentage points. Adoption and Innovation Gaps are in Standard Deviations. The calculation of the normalized variables in thousands of peoples is to address data distortions due to small numbers recorded for some technologies.
To further illustrate what is going on in the data, scatter plots of the (weighted) GDP-growth gap on each adoption gap are presented in figure 1 37This gap is the resultant of the higher GDP growth in DCs (2.7% on average) as compared
for the period 1970-2009. The positive sloped lines running towards the zero GDP-growth gap reveals, in most cases, that for individual countries a higher (smaller) gap in economic growth is correlated with a higher (smaller) adoption gap. Note that the dashed and solid lines represent HICs and DCs respectively. Consistent with the evidence presented in Table 1, these linear projections show different patterns: Adoption gaps for each technology-type are largely more negative for DCs relative to HICs.
Figure 1: GDP-Growth Gap Vs. Adoption Gaps.
Source: Author’s elaboration. GDP-growth weighted by the ratio of each country’s GDP percapita relative to the US. Each line is simple linear fit of GDP-Growth Gap (∆gdpi−
∆gdpus) on each technology-type Gap (ki− kus). In each case the dashed line stands for
HICs, and the solid line for DCs. A 95% confidence interval is included. The graph and linear projections are obtained using the command ”lfitci” and scatterplot options in Stata.
I summarize the evidence in Figure 1 in three points: i) The data reveal a pattern of divergence, rather than the process of catching-up that is suggested by the advantage of backwardness hypothesis. To see that this is the case, note that a catching-up process of DCs should be characterized by a negatively sloped line running on the positive side of the vertical axis. That would imply that on average countries falling farther away from the frontier -i.e., those with larger Adoption gaps- would experience a reduction in the GDP-growth gap.38 ii) The pattern of divergence, nevertheless, is less marked in the most advanced 38In fact, the Un-weighted GDP-growth gaps would reveal that for most technologies the
economies. This can be seen because the group of HICs exhibits a shorter distance towards the zero line in both vertical and horizontal axis. This is consistent with the figures in table 1 showing smaller gaps for this group of countries. iii) The difference in the slopes for both groups of countries is clearly statistically significant at the conventional level of confidence, as can be seen from the 95% interval that is included together with each slope.
Figure 2 replicates the above scatter plot for the case of innovations gaps. The positively sloped line running towards the zero GDP-growth gap reveals again a general pattern in which countries with lower GDP-growth gaps tend to have lower innovations gaps. The kind of divergence between HICs and DCs that was discussed in the case of Adoption gaps is again observed. Moreover, differences between both groups of countries are again statistically significant.
Figure 2: GDP-Growth Gap Vs. Innovation-Type Gaps.
Source: Author’s elaboration. GDP-growth weighted by the ratio of each country’s GDP per-capita relative to the US. Each line is simple linear fit of GDP-Growth Gap (∆gdpi− ∆gdpus)
on each technology-type Gap (Ai− Aus). In each case the dashed line stands for HICs,
and the solid line for DCs. A 95% confidence interval is included. The graph and linear projections are obtained using the command ”lfitci” and scatterplot options in Stata.
Twin Peakedness.
Innovation gaps. Figure 3 shows the kernel distributions of the three across-countries average gap indicators over the period 1970-2009.
Looking at the un-weighted density of GDP-growth gaps a bipolar distribu-tion is not evident at first sight, except for a small mass of the left tail. The split of the density when GDP-growth gaps are scaled by the factor ω, nevertheless, makes clear that a large mass of countries faces huge negative growth differences relative to the US. Accordingly with the weighted GDP-growth gaps in table 1, it is clear that the leftmost peak represents the density of DCs. Since countries whose average growth is slower relative to the leader can not converge (unless ω > 1), the implication of the twin peakedness that arise here is of a divergence pattern for DCs.
Figure 3: Kernel Distributions of Gaps. 1970-2009.
Note: The Epanechnikov kernel function over each of the gap indicators using the optimal bandwidth (the inverse of the number of bins). Other choices, as a Gaussian or Parzen type kernels yields similar results. The two kernel for GDP-Growth correspond to weighted (the thick black line) and unweighted gaps.
the distribution, hence more countries in the sample, present large negative innovation gaps.
All in all, the stylized fact in international growth patterns argued in previous literature also holds in the analysis of Adoption and innovation gaps. To save in space, the detailed analysis of the distribution for each of the 25 Adoption and 10 Innovation technologies is omitted from the presentation. Yet, is worth to mention that they resemble the same patterns found in figure 3.
The bipolar distribution of GDP-growth, Adoption, and Innovation gaps found here shed new evidence and raise questions above the mechanisms behind observed patterns of economic growth. On the first side, the evidence displayed in figure 3 shows that DCs are characterized by larger (weighted) GDP-growth gaps than HICs. They also exhibit larger negative Adoption and Innovation gaps -as in comparison with the less negative Adoption and positive innovation gaps that are observed for HICs. As it has been shown in table 1, GDP-growth differences between HICs and DCs exhibit a slow reduction over time. But still support the view of wide Adoption and Innovation differences.
5
Econometric Results.
Table 2 provide the estimation results of applying an OLS Robust approach to the specification in equation (8). I present these results for both un-weighted and weighted GDP-Growth gaps. The first thing to note is the better fit in cases where the dependent variable is weighted. The results in columns (I) and (II), at the bottom panel of the table, show a high statistical significance for all variables. But, as it has been warned above, it may be a misleading result due to the high collinearity between Adoption and Innovation forms of technology. Columns III, and IV, address this issue by running separate regressions. By doing so, the only significant effects remain for the interaction of the DCs dummy with the adoption (0.44), and the innovation gap (0.38). The result in column (III) for Adoption (interacted with DCs) is consistent with the result from the un-weighted regression. But, in column (IV), un-weighted and weighted results are conflicting with regards to the statistical significance of Innovation and its interaction with the dummy for DCs.
The second interesting fact to note in table 2 is that results at the top and bottom panels in columns (III) and (IV) consistently show positive signs for the effect of adoption and innovation gaps. Based on the weighted results, one can infer that the increase of one Standard Deviation (SDs) in the Adoption gap of DCs explains 0.44 percentage points (pp) of their GDP-growth gap during 1981-2009. In turn, 1 SDs increase in the Innovation gap would explain 0.38 pp of the GDP-growth gap in all countries.
conventional levels of significance, and the results hold even after controlling for initial development conditions.
The third thing to note from the table is the low or none statistical signif-icance of the variables intended to capture cross country differences in devel-opment conditions. Aside of the initial GDP, which most of the time predicts a convergence path, the effect of initial schooling, openness, and institutional environment are not statistically significant.
Table 2: OLS Robust Regressions.
I II III IV
Dep. Var.: Unweighted GDP-Growth Gaps
Constant -0,44 -0,05 0,41 -0,26 Initial GDP Gap -1,85** -1,79** -1,53** -1,74*** Adoption Gap 0.15 0,28 0.37 DCs ×AdoptionGap -0,02 -0,20 0,83* Innovation Gap 0,45 0,33 0.51 DCs ×InnovationGap 1,18 1,29 1,07*** E. Freedom Index Gap 0,27 0,44 0,25 Schooling Gap -0,17 0,002 -0,16 Openness Gap -0,10 -0,09 -0,09
Adj-R2 0.27 0.29 0.22 0.28
No. Countries 60 60 60 60
Dep. Var.: Weighted GDP-Growth Gaps
Constant -1,02*** -0,96*** -0,43*** -0,57*** Initial GDP Gap -0,30** -0,32** -0,23 -0,28 Adoption Gap -0.46** -0.43** 0.014 DCs ×AdoptionGap 0,71*** 0,71*** 0,44** Innovation Gap 0,72*** 0,75*** 0,38** DCs ×InnovationGap -0,48** -0,48** 0,20 E. Freedom Index Gap -0,006 0,14* 0,087 Schooling Gap -0,02 -0,04 -0,02 Openness Gap -0,04 -0,03 -0,05
Adj-R2 0.78 0.78 0.70 0.72
No. Countries 60 60 60 60
Results obtained using the robust Huber/White/sandwich estimator using Stata12. The dependent variable is the 1981-2009 average of per capita GDP-growth Gap. The independent variables are normalized across different technologies representing Adoption and Innovation gaps, and averaged over the period 1981-2009. I) controls only for the initial level of GDP (relative to the US) averaged over 1970-1980. II) controls for other initial conditions averaged over 1970-1980. III) includes only the effect of Adoption gaps (plus the interaction of Adoption × the dummy for DCs), and controls for initial conditions. IV) includes only the effect of Innovation gaps (plus the interaction of Innovation gaps × the dummy for DCs), and initial conditions. Because these are normalized figures the interpretation is that the increase in one standard deviation in the gap for a given regressor leads to the increase (decrease) of x percentage points in the GDP-growth gap. *, **, *** are set to denote statistical significance at 10%, 5% and 1% respectively
This may seem odd in light of the theoretical predictions discussed above. I assert, without proof, one possible explanation for this result. Since these de-velopment conditions are measured in terms of gaps at the initial period -rather than contemporaneously, the result may differ widely from other studies.39 But 39For example Dollar and Kraay 2003 who find strong linkages between openness, good
still this is consistent with the low contributions found in other studies for ed-ucation -relative to physical capital and multifactor productivity- to explain variations in economic growth.40
Instrumental Variables Results.
The results of running equation (9) using the IV approach based on the general moments method (GMM) are shown in Table 3. Columns (I) and (II) focus on Adoption, and Columns (III) and (IV) on Innovation. Once more the key remark is the better fit obtained by using weighted GDP-growth gaps as the dependent variable.
The results in this table confirm the divergence pattern that is predicted by Adoption gaps on GDP growth differences. Though they are only statistically different from zero for the interaction with DCs. In fact, the coefficient estimate of the interaction term is large and consistent with the pattern of divergence that has been discussed for this group of countries. Remarkably, the effect does not depend on the weighting mechanism introduced in this paper. Also it holds even after controlling for the initial level of development.
The results for the innovation case suggest a similar divergence effect. The key fact to note in this case is the larger size of the coefficient estimates. Looking at the bottom panel in table 3, the increase of 1 SD leads Innovation to explain between 0.78-0.80 pp in GDP-growth gaps, whereas Adoption explains around 0.67-0.68 pp. Because I normalize all figures using their respective Standard Deviations across countries, the size of these coefficients give an idea of their relative explanatory power. Hence, according to the results in the table, Inno-vation gaps arise as the most important factor in explaining growth differences between HICs and DCs. The comparison between un-weighted and weighted results in Table 3, show that this result indeed hinges on the weighting mecha-nism, i.e., the results at the top panel of the table does not allow to discern the relative importance of each technology form.
As noted before, the IV approach is an appropriate technique to address the endogeneity of Adoption and Innovation forms of technology. But for that to be the case, the validity and relevance of the instruments should be guaranteed. In fact, the standard tests on the first stage (FS) regressions validate the use of economic freedom and the interaction of economic freedom with DCs as instru-ments. These results are reported at the bottom part of the un-weighted and weighted regressions in Table 3.41
All in all, the results in Table 3 provide additional evidence to answer the questions posed at the outset. Increasing patterns in the (levels of) Adoption and innovation gaps explain a pattern of GDP-Growth differences across HICs
40See Bosworth and Collins 2003.
41The FS partial R2, at the bottom of each column in Table 3, measure the correlation
and DCs. In other words, the results show no support for the convergence path that is predicted by the advantage of backwardness hypothesis.
Table 3: Instrumental Variables Estimates for period 1981-2009.
GMM GMM GMM GMM
Adoption-Gap Adoption-Gap Inn.-Gap Inn.-Gap
I II III IV
Dep. Var.: Unweighted GDP-Growth Gaps
Constant 0,34 0,68 -0,67 -0,73 Initial GDP Gap -2,79* -3,05* -2,18** -2,21** Adoption Gap 1.59 2.14 DCs ×AdoptionGap 1.17*** 1.18*** Innovation Gap 0,82 1,09 DCs ×InnovationGap 1,18*** 1,15*** Schooling Gap -0.36 -0,34 Openness Gap -0.17 -0.11 Adj-R2 0.06 -0.04 0.22 0.19 No. Countries 60 60 60 60 Instruments’ tests: GMM C statistic chi2(2) 0,88 (p = 0.64) 0,89 (p = 0.64) 0.42 (p = 0.81) 0.42 (p = 0.80) 1st Stage Partial R2 G-Gap 0,18 0,11 0,37 0,30 DCs×G − Gap 0,67 0,65 0,54 0,50 1st Stage Prob > F G-Gap 0.01 0.03 0.00 0.00 DCs×G − Gap 0.00 0.00 0.00 0.01
Dep. Var.: Weighted GDP-Growth Gaps
Constant -0,59*** -0,49** -0,75*** -0,75*** Initial GDP Gap -0,58** -0,63* -0,49** -0,49** Adoption Gap 0.22 0.33 DCs ×AdoptionGap 0.68*** 0.67*** Innovation Gap 0,02 0,09 DCs ×InnovationGap 0,80*** 0,78*** Schooling Gap -0.05 -0,07 Openness Gap -0.05 -0.03 Adj-R2 0.64 0.61 0.60 0.59 No. Countries 60 60 60 60 Instruments’ tests: GMM C statistic chi2(2) 6,71 (p = 0.04) 6,08 (p = 0.05) 12.3 (p = 0.00) 13.4 (p = 0.00) 1st Stage Partial R2 G-Gap 0,18 0,11 0,37 0,30 DCs×G − Gap 0,67 0,65 0,54 0,50 1st Stage Prob > F G-Gap 0.01 0.03 0.00 0.00 DCs×G − Gap 0.00 0.00 0.00 0.01
The dependent variable is the 1981-2009 per-capita GDP-growth Gap. Results are obtained using the comman ivregress in Stata12. Columns (I) and (III) control only for the GDP relative to US in 1970-1980. Columns (II) and (IV) include other development conditions. The GMM C statistic is a Sargan test for endogenous regressors. The F-test is for the overall list of regressors in the first-stage. In columns (I) and (II) Adoption-Gaps and DCs × adoption-Gaps are instrumented on economic freedom and the interaction of economic freedom with DCs. In columns (III) and (IV) a similar instrumentation is performed for Innovation Gaps and the interaction of Innovation-Gaps with DCs. The G-Gap in the result of the 1ststage partial R2
refers to the Adoption and Innovation gaps in the respective column. The interpretation of coefficients is that the increase in one SD in a given regressor leads to the increase (decrease) of x pp in the average GDP-growth gap. *, **, *** denote statistical significance at 10%, 5% and 1% respectively
technologies selected, and the average over specific periods, I present in table 4 a set of robustness checks. In all cases, the conditioning period is kept the same. The first and second segments show results where the period of analysis changes to 1991-2009 and 2001-2009 respectively.
Table 4: Robustness Checks Adoption and Innovation at the Level.
Note In all cases the conditioning period is kept to be the same (1970-1980). Also in all cases the regressions are by the IV approach and includes the full set of initial conditions. 1/Includes technologies selected by the EFA analysis, namely Adoption (Cars, Cellphones, Rail Transportation services, air transportation services, roads network, and road trasnpor-tation services), and Innovation (Royalty and license fees, patents applications, researchers in R&D, and exports of high tech.
2/ includes a group of 30 countries between 1996-2008 that show consistent information on 5 innovation technologies: R&D expenditures (rde), patents application, trademark applications, and Scientific publications.).
, **, *** are set to denote statistical significance at 10%, 5% and 1% respectively
to the 14 indicators selected by the EFA analysis (see figure 5 in the Appendix). The fourth segment keeps the technologies from EFA analysis but constraints the selection of countries to those that show information on the availability of technologies at least in 3\4 of the years between 1981-2009.42. The last segment at the bottom of the table shows more stringent criteria. It keeps in the analysis only countries with full information on a given range of technologies and on a year over year basis. This leads to the selection of a set of 30 countries with information on 5 innovation indicators between 1996-2008.
The robustness check results are consistent with the discussion of divergence. Looking at the results of the weighted regression at the right hand side of table 4, in almost all cases the effect of Adoption and Innovation gaps interacted with DCs remains positive and statistically significant. Remarkably, the sign of these effects do not depend on the weighting mechanism; though in some cases the statistical significance do. A further thing to note from these results is a slightly larger effect from Innovation relative to Adoption, which is evident from the size of the coefficients in regressions for 1991-2009, 2001-2009, and the results of the EFA analysis for countries with information in 3\4 of the years between 1981-2009.
To this point, the evidence provided by the regression analysis consistently favours the view of a divergence pattern in GDP growth across countries that is explained by technology differences. Though the results suggest that both forms of technology matter to explain growth differentials between HICs and DCs, Innovations arises as more relevant in explaining the divergence path that is clearly identified by the weighting mechanism adopted throughout. These results are found in framework intended to capture the key insight from the advantage of backwardness, according to which differences in levels of technology explain differences in rates of growth of GDP.
Technology Gaps in Changes.
Whilst the previous results stressed on differences in technology endowment, the view on the specification in equation (10) is on differences in the year-over-year change of technologies. I have referred to these changes in terms of technology upgrading. This view assumes that for a given country the yearly rate o change in technologies is associated with the acquisition of new vintages of capital goods and new investments in knowledge.
The econometric results in table 5 are consistent with this view. The fit of the regressions is rather small. But the coefficient estimates suggest that for DCs technology upgrading, through adoption of new capital vintages, explains a reduction of growth differences for DCs. The two columns on the right of the uppermost panel in the table suggest that in 1981-2009 the increase of 1 pp in Adoption leads to increase growth differences of HICs by 0.32 pp. But it leads to reduce growth differential of DCs by 0.27 pp. Results based on the un-weighted GDP-growth, in the two columns to the left, show a larger effect.
42Recall that the criteria adopted before was for each country to have information on more
Table 5: Technology Change Gaps (IV Estimates.).
Innovation changes are neither statistically significant nor large in size. But they also suggest that a 1 pp increase in innovation reduces growth differentials by 0.10 pp.
The robustness checks, conducted here in a fashion alike to table 4, show results that are similar in kind for the period 1991-2009. Namely, technology upgrading leads to a statistically significant reduction of growth differential for DCs. Innovation changes again are associated with a reduction of growth differential that are not statistically significant, though larger in size.
The remainder robustness results at the bottom of the table fail to provide a clear clue on the upgrading view. The low fit of the regressions clearly suggest a lack of explanatory power of both technology forms in regressions based on the period 2001-2009, the technologies selected by the EFA analysis, the selection of countries based on availability of technologies at least in 3\4 of the period of analysis, and the analysis based only on countries with full information.
6
Concluding Remarks.
Throughout this paper I suggest a view to analyse the empirical relationship between technology differences, and GDP-growth differences across high income (HICs), and low income countries (DCs). A distinction is made between embod-ied technologies, which are associated to Adoption, and disembodembod-ied technolo-gies, which are associated to innovation. I suggest two, not mutually exclusive, ways through which the relationship may arise. The first stresses on differences at the level - or the endowment - of technology. The second, on technology changes - or technology upgrading. Whilst the first is intended to capture the insights from the advantage of backwardness hypothesis, the second is to make sense that typically over time countries acquire new capital vintages to replace old ones. The adoption of new embodied vintages are accompanied by further investments in knowledge purported to master the new acquired technologies.
According to these views I provide an empirical analysis in which GDP growth differences are scaled by the ratio, in levels, of its GDP per-capita relative to the US. This weighting procedure of each country GDP-growth is purported to set a linkage between convergence in rates of growth, and convergence in levels of GDP. From this view-point convergence possibilities depend not just on how faster a country grows, but also on how fast it should grow to catch-up with the level of income of more advanced countries.
At first sight, simple descriptive analysis does not reveal the pattern of catching-up that is suggested by the advantage of backwardness hypothesis. By contrast a pattern of divergence arises that is more marked for the case of DCs. These divergence is confirmed by the analysis of density functions, which show that DCs are characterized by larger (weighted) GDP-growth gaps, and larger negative Adoption and Innovation gaps than HICs.
effects do not depend on it, the weighting mechanism introduced in the paper leads to two differences in the results. First, it generally improves the goodness of fit of the regressions. Second, it allows to disentangle a relatively larger ex-planatory power that is associated to differences in (the levels of) Innovation. Remarkably, the divergence pattern found for the endowment view is statisti-cally significant and robust, and it is in strong contrast with the suggestions of the advantage of backwardness.
On the other side, the econometric results show evidence in support of the upgrading view. In this context, technology changes, through adoption of new capital vintages, explains a reduction of growth differences for DCs. By contrast with this upgrading, and with the results at the level, Innovation changes are neither statistically significant nor large in size. But still they also suggest a view in which changes in innovation reduces growth differentials.
Though the number of countries in this study is relative large, and the data representative of the most up to date productive technologies, the results found here are hard to generalize. The current availability of a great deal of informa-tion related to specific forms of technology across a large number of countries has been a substantial contribution from which this study has benefited. but still the biggest spot in the analysis relates to data quality and coverage. Large improvements in both these aspects may be an important avenue for further research.
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