Technological diffusion and productivity convergence: a study for manufacturing in the OECD.

1. Introduction

A large empirical literature by now exists on the issue of per capita income or labor productivity convergence between countries. Most of this work makes use of regression analysis and bases itself on the transitional dynamics of the standard neoclassical model of economic growth with exogenous technical progress. As is well-known, this dynamics is characterized by conditional convergence, due to the property of decreasing returns to capital inputs in the production function. Equations are estimated that relate the rate of growth of per capita income or labor productivity to the log of their initial level and to the rates of accumulation of the considered types of capital, as well as to other variables that condition the steady state. When estimated on large cross-sections of countries over an entire period of time, the results would appear to confirm the predictions of the neoclassical model, provided that this includes human capital as a factor input. In the case of the OECD, the results would even seem to suggest the occurrence of unconditional convergence (for a survey, see Sala-i-Martin 1996).

More recent studies that perform estimation on panel data of similar equations allowing for country-specific fixed effects have challenged this view, however. These fixed effects are found to be highly statistically significant, and their inclusion vastly reduces the measured impact of the other conditioning variables. Even in the case of the OECD countries, the fixed effects remain highly significant, suggesting that also here the convergence is conditional in nature. Moreover, and most important, the estimated convergence speed is now found to be much higher than implied by the cross-section results. In fact, it is found to be far higher than explainable by the operation of the mechanism of decreasing returns to capital (see especially Canova and Marcet 1995; Islam 1995: Caselli, Esquivel, and Lefort 1996; De La Fuente 2000).

Although these panel data estimates are, themselves, not without problems, this would appear to suggest that other convergence mechanisms are at work besides the neoclassical one. We think here in the first place at the process of technological diffusion between countries. Open economy versions of new innovation-driven theoretical growth models have emphasized its importance in helping to explain the catching-up by laggards with respect to countries at the technological frontier, because imitation is easier than innovation. They have, thereby, stressed the conditional nature of this process, which is highly dependent on factors that stimulate physical and human capital accumulation and, more generally, allow for an appropriate institutional setting that fosters the operation of market forces (Grossman and Helpman 1991; Segerstorm 1991; Barro and Sala-i-Martin 1995; Aghion and Howitt 1998).

The empirical work on convergence through technological diffusion is still limited, however. Most reliable are probably a set of regression studies on OECD regional and country panel data. allowing for regional- and country-specific fixed effects, by De La Fuente (1996) and De La Fuente and Domenech (2001). They estimate equations that relate the rate of growth of total factor productivity (TFP) to the initial level of technology gap between the technological frontier and the non-frontier country under consideration. Their results provide evidence of significant conditional convergence at a relatively high speed. A drawback of these studies is, however, their aggregate nature. This prevents identification of the sectors responsible for convergence. And, it cannot let us know whether technological convergence occurs, especially, in internationally tradable goods sectors, such as manufacturing, as implied by most open economy innovation-driven growth models.

Earlier cross-section estimates of comparable TFP growth equations by Bernard and Jones (1996a) on large subaggregates, such as manufacturing as a whole, agriculture, mining, services, utilities, and construction across OECD countries, find, surprisingly, no evidence of convergence in the case of manufacturing during the 1970s and 1980s. In another study, Bernard and Jones (1996b) readdress the issue by also analyzing the time series properties of the technology gap variable, by testing for its nonstationary nature by applying a unit root test for panel data on a sample of yearly observations during the same period. The results suggest the presence of a unit root and provide, according to the authors. further evidence of TFP divergence in manufacturing in the OECD. They argue that this may be due to the fact that international trade tends to lead to specialization between countries.

One has to be careful with the interpretation of these results, however. If it is indeed the case that they are caused by differences in product composition of the manufacturing aggregates, this calls for further disaggregation. The regression estimates on cross-sections may, moreover, vastly underestimate the convergence speed. More appropriate estimates on disaggregate panel data may, possibly, find evidence of transitional dynamics characterized by significant convergence. If so, the evidence provided by time series tests on the same period of time may be misleading, as it may mainly reflect the evolution of the difference between transitory movements of the concerned TFP series to their equilibrium growth paths, rather than the evolution of the difference between these paths itself.

A common drawback to the regression estimation approach to convergence analysis is that it only allows capturing of the dynamics of the "average" or "representative" economy in the sample. Most authors have, therefore, complemented it by a study of the evolution of the standard deviation of the considered measure of income or productivity. Although useful, this still does not provide insight into the actual underlying intradistribution dynamics across countries. In order to do so, some attempts have been made to approximate the evolving cross-country distribution by a stochastic process and to identify its law of motion and implied long-ran limit distribution. But this work has, to our knowledge, until now only been performed at an aggregate level and with respect to relative levels of per capita income (see Quah 1993a, b, 1996, 1997).

In this study, we attempt a more systematic investigation of the issue of OECD manufacturing productivity convergence on disaggregate panel data with respect to 22 manufacturing sectors in 14 OECD countries from 1970 to 1995. We start by estimating different TFP growth equations that include the initial level of technology gap as a variable, both on a global panel of sector-country data collected every 5 years and on 22 subsamples, sector by sector. We compare average TFP growth performances of the frontier and non-frontier countries during the period of investigation. We pursue by considering the evolution of the standard deviation of the log of TFP and then study the cross-country distribution dynamics of relative TFP by means of a Markov-chain transition probability matrix approach. Finally, we perform a panel data unit root test on corresponding samples of yearly observations of our measures of technology gap variable.

The article is organized as follows. Section 2 presents the empirical growth equations and section 3 the considered alternate measures of convergence. Section 4 exposes the econometric methods. The estimates are reported in section 5, and section 6 summarizes and concludes. The data sources and measurement issues are mentioned in a separate Appendix.

2. Empirical Growth Equations

The purpose of this section is to present empirical growth equations that allow for total factor productivity convergence through international technological diffusion. In view of the observed relative constancy of the income shares of capital and labor across countries, we follow common practice and assume that the production of output occurs with a technology of the Cobb-Douglas type, with constant returns to scale and augmented by a variable reflecting the level of total factor productivity (TFP). This can be represented as:

(1) [Y.sub.ijt] = [A.sub.ijt][K.sup.[alpha].sub.ijt] [L.sup.1-[alpha].sub.ijt],

where [Y.sub.ijt], is the product or income in country i in sector j at time t, measured by value added at factor costs; [K.sub.ijt], is the corresponding physical capital stock; [L.sub.ijt], is the labor input; and [A.sub.ijt], is the level of Hicks-neutral TFP.

In the standard neoclassical model, the rate of growth of [A.sub.ijt] is determined by the rate of exogenous technical progress. To the extent that it is equally accessible, this is assumed to be the same for all countries in each sector under consideration. Once one does, however, allow for technological diffusion between countries, one has to allow for the fact that countries with a less advanced technology can, moreover, benefit from the possibility of imitation from countries that are technologically more advanced. Other things equal, one should expect that the further a country's technology is behind the technological frontier, the greater are its possibilities of technical advance through imitation, and, therefore, the stronger will be its TFP growth.

Consider a specific sector. Leaving out the sector subscript, the rate of growth of TFP of country i can be presented as follows:

(2) [DELTA][a.sub.it] = [gamma] + [lambda]([a.sub.ft-1] - [a.sub.it-1]),

where small letter variable a stands for the (natural) log of the level of TFP, A; [DELTA] stands for its first difference between t and t - 1; and the subscript f stands for the frontier country. The intercept,

[gamma], captures the long-run rate of growth of TFP. This is supposed to be the same for all countries in the sector under consideration and determined by the sector-specific rate of exogenous technical progress. The term between brackets represents the technology gap at time t - 1. This technology gap reflects both differences between the technologies in use and differences in the efficiency with which they are used. Its coefficient, [lambda], measures the rate of technological convergence. In the case of the frontier country, i = f, and the term between brackets vanishes.

In steady state, [DELTA][a.sup.*.sub.it] = [gamma] and [a.sup.*.sub.ft] = [a.sup.*.sub.it] for all i. All countries grow at the common long-run rate and the levels of TFP become the same, so that the second term in Equation 2 vanishes. The transitional dynamics of TFP is, in this case, said to be characterized by unconditional or absolute convergence. Countries that are technologically backward grow more rapidly than the more advanced ones, so that the respective productivity levels converge.

Although technology may gradually diffuse, there am nevertheless good reasons to believe that some countries may enjoy long-run advantages in productivity that do not get eroded over time. Differences in institutions may persist and imply that the long-run equilibrium paths to which the levels of TFP converge differ between countries. In the absence of technological diffusion, these institutional differences are, in fact, likely to imply divergence of these growth paths. This idea can easily be formalized by adapting Equation 2 as:

(3) [DELTA][a.sub.it] = [[gamma].sub.i] + [lambda]([a.sub.ft-1] - [a.sub.it-1])

where [[gamma].sub.i] are country-specific constants that capture the long-run autonomous country-specific growth rates of TFP that would prevail in the absence of technological diffusion (when [lambda] = 0). In the presence of international technological diffusion (when [lambda] > 0) the equation does, as before, include a catch-up mechanism. When countries with better autonomous growth performances (higher [[gamma].sub.i]) forge ahead, they offer imitation possibilities to the laggards.

In steady slate, the country with the best autonomous growth performance is in the lead or, in other words, at the technological frontier. It acts as the locomotive of growth, pulling the others along through the catch-up effect. Its autonomous growth rate, [[gamma].sub.f], determines the common long-run growth rate, so that [DELTA][a.sup.*.sub.it] = [[gamma].sub.f]. When taking account of Equation 3, this implies that in steady state. [[gamma].sub.f] - [[gamma].sub.i] = [lambda]([a.sup.*.sub.it] - [a.sup.*.sub.ft]). Or, in other words, the advantage of backwardness in being able to act as imitators. [lambda]([a.sup.*.sub.it]-[a.sup.*.sub.ft]), is exactly compensating the autonomous growth drawback, [[gamma].sub.f]- [[gamma].sub.i], due to worse institutions. This also implies that in steady state, the productivity level differentials between countries remain constant: [a.sup.*.sub.it] - [a.sup.*.sub.ft] = 1/[lambda] ([[gamma].sub.f] - [[gamma].sub.i]).sup.1]. (1)

The transitional dynamics is, in this case, characterized by conditional TFP convergence, in the sense that countries converge to their own steady states, depicted by parallel equilibrium paths. It is worth noting that Equation 3 encompasses Equation 2 as a nested equation that relates to the special case in which there is only a common intercept in the sector under consideration. Unconditional or absolute convergence implies, therefore, that [lambda] > 0 and [[gamma].sub.i] = [gamma], whereas conditional convergence implies that [lambda] > 0 and [[gamma].sub.i] [not equal to] [gamma].

Rewriting the production function in Equation 1 in labor-intensive form, expressing the variables in growth terms, adding a time dummy and a stochastic error term, one can, by taking account of Equation 3, obtain a reduced-form empirical growth equation as follows:

(4) [DELTA][y.sub.ijt] = [[delta].sub.t] + [[gamma].sub.ij] + [alpha][DELTA][k.sub.ijt] + [lambda]([a.sub.fjt-1] - [a.sub.ijt-1) + [[epsilon].sub.ijt]

= [[delta].sub.t] + [[gamma].sub.ij] + [alpha][DELTA][k.sub.ijt] + [lambda][([y.sub.fjt-1] - [[alpha][k.sub.fjt-1])-([y.sub.ijt-1]-[alpha][k.sub.ijt-1])] + [[epsilon].sub.ijt],

where small letter variables y and k stand for the (natural) logs of Y and K per unit of labor; [[delta].sub.t] is a time dummy, [[gamma].sub.ij] is a sector-country specific intercept, and [[epsilon].sub.ijt] is a sector-country specific stochastic error term. Because our data are observed every 5 years, t - 1 stands for t 5 years earlier. Because we are interested in obtaining estimates of the average yearly convergence speed, the [DELTA] sign preceding a variable stands now for one-fifth of its first difference between t and t - 1. The time dummy, [[delta].sub.t], is aimed at capturing the effect of common worldwide shocks due, for example, to macroeconomic conditions, whereas the stochastic term, [[epsilon].sub.ijt], captures sector-country specific random shocks.

Equation 4 encompasses the special case where there are only sector-specific (but no sector-country-specific) intercepts, [[gamma].sub.ij] = [[gamma].sub.j], when institutional differences do not matter and the rates of exogenous technical progress are the same across countries. These common sector-specific intercepts capture these sector-specific rates. There are, in other words, no country-specific conditioning influences on TFP. When considering the total panel, unconditional or absolute convergence will, therefore, imply that [lambda] > 0 and [[gamma].sub.ij] = [[gamma].sub.j], whereas conditional convergence implies that [lambda] > 0 and [[gamma].sub.ij] [not equal to] [[gamma].sub.j]. It should be noted, however, that even if the hypothesis of only sector-specific intercepts is rejected, it may still be interesting to find out whether [lambda] > 0 holds in an equation that only includes sector-specific (but no sector-country-specific) intercepts, in order to see whether the conditional convergence at the same time implies actual catching-up during the period under consideration. This may be the case if the levels of TFP of the technical laggards tend to lay further below their steady states than is the case of the technologically more advanced countries. Or it may reflect the fact that the sector-country-specific intercepts are, in fact, capturing the effect of missing variables that move through time and tend themselves to converge. Think, for example, at the occurrence of a process of institutional convergence through economic integration. In the latter case, one may, as suggested by Cohen (1992), refer to quasi steady-states, which are themselves converging.

Following Mankiw, Romer, and Weil (1992), most traditional work on per capita income or labor productivity convergence assumes a human capital extended production function in which human capital per worker is measured by the average rate of educational attainment. This assumption also underlies De La Fuente and Domenech's (2001) reduced-form technology gap growth equation. This is justified provided that human capital affects output as an input in the production process of goods. In order to find out whether this is indeed the case, we first follow De La Fuente and Domenech (2001) and simply extend our production function in Equation 1 in a straightforward manner, such as:

(5) [Y.sub.ijt] = [A.sub.ijt][K.sup.[alpha].sub.ijt] [H.sup.[beta].sub.ijt] [L.sup.1-[alpha]-[beta].sub.ijt] = [A.sub.ijt][K.sup.[alpha].sub.ijt] [L.sup.1-[alpha].sub.ijt][S.sup.[beta].sub.ijt],

where [H.sub.ijt], stands for the level of human capital in county i in sector j at time t, and the level of human capital per worker is measured by the average years of schooling of the workforce, [S.sub.ij]. The corresponding reduced form empirical growth equation then becomes:

(6) [DELTA][y.sub.ijt] = [[delta].sub.t] + [[gamma].sub.ij] + [alpha][DELTA][k.sub.ijt] + [beta][DELTA][s.sub.ijt] + [lambda][([y.sub.fjt-1] - [alpha][k.sub.fjt-1] - [beta][s.sub.fjt-1]) - ([y.sub.ijt-1] - [alpha][k.sub.ijt-1] - [beta] [s.sub.ijt-1])] + [[epsilon].sub.ijt],

where [S.sub.ijt] stands for the log of the average years of schooling in county i in sector j at time t.

In sharp contrast to the standard neoclassical model, the new innovation-driven growth literature has assumed that technical progress is, in essence, endogenous in nature, being the product of commercially oriented innovation efforts by firms. Following Romer (1990a, b), new growth theorists have also suggested that human capital may mainly affect per capita income or labor productivity through its role in the process of technological innovation rather than as a factor input in the production function of goods.

In order to assess whether this is the case, we will again assume that our production function of output is given by Equation 1, but that now the rate of growth of TFP is partly endogenous in nature and influenced by the innovation efforts of firms in the respective countries, as measured by their initial level of R&D intensity. In the case of the technological lead country, these efforts directly help to displace the technological frontier. In the case of the other countries, they may help to introduce new, locally adapted, below-frontier technologies. Or they may also consist of imitation and adaptation or adoption efforts, necessary in order to be able to introduce existing more advanced foreign technologies. (2) It should be noted that, as mentioned in the Appendix, our R&D figures cover expenditures both on researchers (their gross wages) and on research lab equipment. The scope of our R&D variable extends, therefore, beyond a mere measure of research efforts by researchers. Furthermore, the use of a specific measure of research efforts by firms is more appropriate for capturing their innovation efforts than that of a measure of the level of human capital, such as used by Benhabib and Spiegel (1994, 2002). It may, however, be useful to include, in addition, a measure of human capital in order to be able to capture the externalities caused by the dynamic complementarity between innovation efforts by firms and schooling efforts by the population at large, stressed in the new endogenous growth literature (see especially Redding 1996). Considering again the case of a specific sector and leaving out the sector subscript, Equation 3 has then to be replaced by:

(7) [Delta][a.sub.it] = [[gamma].sub.i] + [xi][R.sub.it-1] + [theta][S.sub.it-1] + [lambda] ([a.sub.ft-1] - [a.sub.it-1]),

where [R.sub.it-1] is the initial level of R&D intensity, as given by the proportion of R&D expenditure over value added, and [S.sub.it-1] stands for the initial level of schooling in country i at time t - 1. (3)

In steady state, the country with the best autonomous growth performance will again be in the lead and determine the common growth rate, so that [DELTA][a.sup.*.sub.it] = [[gamma].sub.f] + [xi][R.sup.*.sub.ft] + [theta][S.sup.*.sub.ft]. The advantage of backwardness in being able to act as imitators, [lambda]([a.sup.*.sub.it] - [a.sup.*.sub.ft]), is again exactly compensating the autonomous growth drawback, which is now [[gamma].sub.f] - [[gamma].sub.i] + [xi]([R.sup.*.sub.ft] - [R.sup.*.sub.it]). The transitional dynamics is once more characterized by conditional TFP convergence. When considering the parameters of Equation 7, conditional convergence now implies that [lambda] > 0 with [[gamma].sub.i] [not equal to] [gamma], [xi] > 0 and [theta] > 0.

The corresponding reduced-form empirical growth equation to Equation 7 for estimation on our total sector-country panel now becomes:

(8) [DELTA] [y.sub.ijt] = [[delta].sub.t] + [[gamma].sub.ij] + [alpha][DELTA][k.sub.ijt] + [xi][R.sub.ijt-1] + [theta][S.sub.ijt-1] + [lambda][([y.sub.fjt-1] - [alpha][k.sub.fjt-1]) - ([y.sub.ijt-1] - [alpha][k.sub.ijt-1])] + [[epsilon].sub.ijt].

After estimating Equations 4, 6, and 8 on the total panel, we will then re-perform estimation of the most representative ones and repeat the convergence analysis sector by sector.

3. Alternate Measures of Convergence

Regression estimates of growth equations, such as the ones previously presented, help to capture the dynamics of the "average" or "'representative" economy in the panel. They cannot capture the dynamics of the entire distribution, however. The evidence of [lambda] > 0 in an equation without conditioning variables only indicates that, on average, countries with a lower initial level of TFP grow faster than those with a higher level. In order to find out whether this actually implies a reduction in the inequality of the levels of TFP between countries during the period of investigation, it is useful to consider the evolution of the standard deviation, [sigma], of the log of TFP, sector by sector. It should be noted that unconditional or absolute [lambda]-convergence is a necessary condition for sustained [sigma]-convergence. But it is not a sufficient condition, however, as a positive value of [lambda] is compatible with a temporary increase in productivity dispersion, due to random shocks. Moreover, the mere fact that countries may overtake one another may imply a criss-crossing type of behavior of productivity levels, which may leave their degree of dispersion unchanged through time. The regression estimates will, in this case, still indicate unconditional [lambda]-convergence (as countries with low initial productivity levels grow each time more rapidly than countries with higher levels), but there will be no [sigma]-convergence (since the degree of dispersion remains unchanged). (4) This has become known as Galton's fallacy, and it has been used to warn against drawing unwarranted conclusions from cross-country regression analyses with respect to the evolution of the dispersion of productivity levels across countries (see, especially, Quah 1993b; Durlauf and Quah 1998).

Although studying the evolution of the standard deviation over time is highly useful, it does, however, capture only one characteristic of the cross-country distribution of TFP levels. It cannot indicate whether this distribution is converging toward a unimodal or rather toward a multimodal distribution. In order to gain some insight into this, one may attempt to perform non-parametric estimates of the distribution at subsequent points in time during the period of investigation (see, especially, Bianchi 1997). But this will still not provide insight into the actual underlying intradistribution dynamics. It cannot let us know what the probability is that an economy starting, say, in the bottom 10% of the distribution makes it to the top 10% in the long run.

In order to be able to do so, we will also consider a third method for analyzing convergence. This consists in approximating the evolving cross-country distribution of relative TFP levels by a stochastic process and to identify its law of motion. Following Quah (1993a, b), we will thereby make use of a simple discrete Markov-chain representation. In order to do so, we divide the productivity space into a number of cells. By counting the number of observations in each cell at time t, we can obtain a probability vector, [[omega].sub.t], associated with the cross-country relative TFP distribution in t. Then, by observing which economies transit to different cells from t to t + 1, we can construct a transition probability matrix, M, that encodes how the distribution at time t evolves into one at time t + 1. By construction,

(9) [[omega].sub.t+1] = M'[[omega].sub.t],

where M' is the transpose of M. Assuming M time invariant, iterating Equation 9 gives a predictor of the future cross-country relative TFP distributions, such as:

(10) [[omega].sub.t+s] = [(M').sup.s] [[omega].sub.t] [for all]s [is greater than or equal to] 1.

The law of motion of the stochastic process can be obtained by letting s tend to infinity. It can be shown that all columns of the matrix [lim.sub.s[right arrow][infinity]] [(M').sup.s] will become identical and that they correspond to the normalized eigenvector corresponding to the largest eigenvalue of matrix M'. This is known as the ergodic vector, and it provides the long-run limit of the distribution of relative TFP levels across economies, implied by our law of motion. We will each time estimate this ergodic vector, sector by sector, and assess whether it implies convergence toward a unimodal distribution centered around one of the middle grid-cells, or otherwise.

Finally, we also consider a time series approach to convergence analysis. As is well-known, this approach defines convergence as transitory deviations from identical or parallel long-run stochastic trends. Tests in this framework look for a permanent drifting apart of the productivity trends, by looking for the presence of a unit root in their difference. In our case, we concentrate hereby on the technology gap variable of our growth equations, which measures the difference between the logs of frontier and non-frontier TFP. As emphasized by Bernard and Durlauf (1995, 1996), this time series approach is, in principle, only a valid manner of testing for convergence if the economies under consideration are close to their steady state. If this is not the case and their growth performances are dominated by transitory movements to equilibrium paths, such tests may be highly misleading. A confrontation with our respective other convergence results and a comparison of the measured average sample growth rates of frontier and non-frontier TFP should give an indication in this respect.

4. Econometrics 

Our first purpose will be to estimate Equations 4, 6, and 8 on a global panel of pooled 5-yearly annual time series with respect to all sector-countries under consideration, and then, having done so, to reestimate the most representative one on subsamples, sector by sector. Such estimation poses several problems.

Consider first the form of our equations, say, for example, that of the benchmark Equation 4, presented previously. As noticed, the equation implies that the same parameter, [alpha], appears twice in the expression within brackets, as the coefficient of [k.sub.fjt] and [k.sub.ijt], and once outside this expression, as the coefficient of [DELTA][k.sub.ijt]. This equation can, in principle, be estimated by means of nonlinear least squares, thereby obtaining a parameter estimate of [alpha] simultaneously with the other parameter estimates. This does, however, pose the problem of the identification of the frontier. Because the frontier country in a sector at a moment in time is defined as the country with the highest log of TFP and the log of TFP is itself given by [Y.sub.ijt] - [alpha][k.sub.ijt], we would have to know ?? beforehand in order to identify the frontier. In order to solve this problem, we follow an iterative procedure. In a first step, we choose a plausible value of [alpha], say 0.3, choose the frontier consequently and perform estimation of Equation 4. We thereby obtain a new value of [alpha]. We then use this to re-choose the frontier and reestimate Equation 4 with this frontier, obtaining a new estimate of [alpha], and so on until the frontier remains the same. Alternately, one can start by choosing a country as the frontier, say the United States, perform estimation of Equation 4, thereby obtaining a new value of [alpha], use this to re-choose the frontier, and so forth. We applied both procedures and found each time the same frontier after, at most, two iterations.

It should be noted that, because our data relate to 5 different points in time, the frontier country may differ through time. This allows for what has become known as "leapfrogging," in the sense that countries may overtake one another and act successively as the frontier. It is also worth remarking that in the case of sector-wise estimation, the frontier identification is, in fact, not necessary in order to allow estimation of our parameters of interest. This is so because here the lagged level of the log of frontier TFP, [a.sub.ft-1], is identical for all sample observations at any moment in time. It can, therefore, be absorbed by the included time dummy, which will capture its effect together with that of the common output shocks.

Another problem of estimation of our equations is as follows. It was previously mentioned that the sector-country specific fixed effects included in our equations may capture, in part, the effect of missing variables that actually move through time. As long as these measure long-run influences, they can be conceived as variables that condition "quasi steady-states" that are themselves moving through time. If they do, however, capture short-term adjustments around trend, rather than the long-run growth dynamics, such interpretation becomes invalid. Although our included time dummies, [[delta].sub.t], are aimed at controlling for short-term macroeconomic shocks, they can only do so if these shocks are common to all sector-countries. To the extent that they are not, they will necessarily be captured by the stochastic error term in the regression, [[xi].sub.ijt]. Now, if, as in the case of cyclical adjustment, these short-term shocks are serially correlated, the stochastic error term will be serially correlated. This, together with the presence of the lagged level of the log of labor productivity, [y.sub.ijt-1], as a right-hand-side variable, will make it that the parameter estimates will become inconsistent. Concretely, this implies that the estimated fixed effects, [[gamma].sub.ij], will tend to exaggerate the differences in steady states, whereas the estimated average conditional convergence speed, [lambda], will be biased upward (see, on this, Shioji 1997 and De La Fuente 1998).

This problem is bound to become more important, the shorter the considered time periods or time intervals between the observations in the panel. This is a major reason why we opted for 5-yearly, rather than, say, yearly time observations. Applying an appropriate test for serial correlation on the error term will provide an indication of the seriousness of the problem. As will be seen from the results presented below, the lack of evidence of serial correlation in the error term is comforting in this respect.

Even in the absence of serial correlation, it is well-known that, due to the presence of the lagged level of the log of labor productivity, [y.sub.ijt-1], as a right-hand-side variable, our least square dummy variable (LSDV) parameter estimates may still suffer from a short sample bias (Nickell 1981; Baltagi 1995). This is due to the fact that, in order to perform LSDV estimation, the variables are subjected to a Within transform, which expresses them in deviation from their individual (sector-country) specific average. This implies that the Within form of the lagged level of labor productivity, [y.sub.ijt-1] - [[bar.y].sub.ij.-1], will be correlated with the Within form of the error term, [[xi].sub.ijt-1] - [[bar.xi].sub.ij.-1], because [y.sub.ijt-1] is correlated with [[bar.y].sub.ij.-1] by construction, and therefore, with [[bar.xi].sub.ij.-1]. In order to assess the importance of the bias, we reestimated our equations while using Arellano's (1988) orthogonal deviation procedure. (5) Although not presented here due to space constraints, the results hardly differed from those obtained by means of our least square dummy variable method, suggesting that the bias concerned can at most be very modest.

Another problem of estimation of our respective equations is that the right-hand-side variables may be partly responsive to current random shocks in the economic environment captured by the error term, [[xi].sub.ijt]. This may, again, lead to inconsistent parameter estimates. In view of the lack of evidence of serial correlation in the error term, it is, however, safe to assume that current shocks to the environment do not influence past decisions by economic agents. Variables that enter the equation in a lagged manner, such as the variables that compose the technology gap term, can therefore be viewed as weakly exogenous. And the same holds to a large extent for the contemporaneous rate of growth of human capital per worker. As indicated in the Appendix, human capital is measured by the educational attainment of the working age population, so that its rate of growth is predetermined by previous increases in schooling efforts. This leaves the rate of growth of physical capital per worker. A possible manner of handling this problem may be to instrument the growth rate of capital per worker by its lagged value. Although not presented here due to space constraints, experimentation showed that this was a poor instrument, because, although uncorrelated with future output shocks, it was also poorly correlated with future capital growth. The consequence of this was to bring about a serious downward bias in the unconstrained estimate of [alpha], even though this did not greatly affect the estimated convergence speed, [lambda].

Rather than pursuing along this road, we prefer to check the robustness of our estimates by making use of outside information and repeat estimation while imposing an exogenous given value of [alpha]. A straightforward manner for doing so is to follow a widely used practice in empirical work on TFP and to assume broadly competitive output and factor markets. Our Cobb-Douglas exponent of physical capital, [alpha], can, in this case, be approximated by revenue-based figures on its average income share across countries during the period of investigation. In order to assess whether the data do actually support this constraint on the coefficient of capital, we will subject it to a likelihood ratio test.

In order to obtain explicit measures of TFP for the remaining part of the investigation, we construct these while making use of the estimates of the coefficient of capital, [alpha], obtained from our regression analysis. We consider thereby alternate measures, obtained from the best performing regression estimated on the total panel, and sector by sector, respectively. The value of [alpha] obtained from the total panel estimate has the advantage that it is derived from a much larger sample in which the noise in the data partly cancels-out. The sector-wise estimates of [alpha] have the advantage that they allow to take account of technical variations between sectors.

The computation of standard deviations in the case of the [sigma]-convergence analysis does not pose any problems as such. As far as the Markov-chain transition method is concerned, we take each country's TFP relative to the average TFP of all countries under consideration as our basic data. This normalization is useful in order to alleviate the effect of worldwide TFP growth and fluctuations, which may distort the results. We concentrate on the same six successive points in time over our period of investigation, 1970, 1975, 1980, 1985, 1990, and 1995, as considered in the sample used in our [lambda]-convergence analysis, and we construct five corresponding successive 5-yearly transition probability matrices. We then average these, thus obtaining an average or representative 5-yearly transition matrix for our period of investigation, 1970-1995. Our ergodic vector is obtained by computing the eigenvector corresponding to the largest eigenvalue of the transpose of this matrix and normalizing this to one.

The basic grid-points used to discretize the set of possible values of relative TFP while constructing our transition probability matrices are 0.5, 0.75, 1, 1.25, and 1.5. These points turned out to divide the observed data in roughly equal-sized categories in the starting year of our period of investigation, 1970, in most sectors. In some sectors, a more narrow grid had to be used, however.

Two remarks should be kept in mind while considering the results below. First, our procedure (also used by Quah 1993a, b) of considering an average transition probability matrix has the advantage of reducing the errors of measurement affecting the respective underlying successive individual matrices. But it is strictly only valid for deriving an ergodic vector if the true underlying transition probability matrix is indeed time invariant. Second, although care was taken while choosing the grids, we are aware that there is always something arbitrary to discretizing the relative productivity space. If the grid-points are chosen too far apart, some features of the evolving distribution--intracell movements--could be hidden. In some work on income distribution dynamics, use has therefore also been made of stochastic probability models in which the discrete transition probability matrix is replaced by a continuous conditional probability density function, defined on current and future relative incomes (see Quah 1996, 1997). We do, nevertheless, prefer to keep it to the simpler discrete version, as deriving the implied ergodic distribution is difficult in the more general continuous case.

Finally, as far as our time series approach to convergence analysis is concerned, we will concentrate on panels of pooled annual time observations of our respective measures of technology gap during the period 1970-1995. We note that there is no reason why the data generation process of our TFP, and therefore, technology gap variable should have similar autoregressive coefficients across individual sector-countries. We want, therefore, to make use of a test based on a model that allows not only for individual-specific intercepts (as the Levin-Lin 1992 test used by Bernard and Jones 1996b), but also for individual-specific slopes. Our choice fell thereby on Im, Pesaran, and Shin's (1997) group mean augmented Dickey-Fuller (ADF) test, which has been shown to be highly powerful in accepting the null when it is true. It is an average ADF test derived from the ADF test performed for each individual separately. When expressed in standardized form, its test statistic has been shown to possess an asymptotic standard normal distribution when both the number of time units and the number of individuals in the panel tend to infinity. We apply this test both on the global panel of sector-countries and on 22 subpanels, sector by sector, and this each time for our alternate measures of technology gap.

5. Estimates

Table 1 presents the results of estimation of the respective growth equations on our global sample. Column 1 gives the parameter estimates of Equation 4 presented above, under the assumption that there are only sector-specific (but no country-specific) intercepts, [[gamma].sub.ij] = [[gamma].sub.j]. The equation does, in other words, not allow for country-specific conditioning influences on TFP. The adjusted R2 suggests that the statistical fit is not very high, but is reasonable in view of the fact that data in growth terms are highly noisy at the considered level of disaggregation. The serial correlation test indicates that there is no evidence of serial correlation in the error term. The nonpresented sector-specific intercepts are found highly significant, confirming a priori expectations that the rate of exogenous technical progress varies between sectors. (6) The parameter estimate of the coefficient of capital, [alpha], has a plausible value of about 0.34 and its t-value implies that it is highly statistically significant. This is also the case of the coefficient of the technology gap, [lambda], which has itself an estimated value of 0.036. This would imply that, taking account of sector-specific differences, TFP growth is during the period of investigation, on average, higher in countries with lower initial productivity than in those with higher initial productivity. It gives thereby a clear hint that a degree of actual catching-up has been taken place during this period. This finding is highly interesting when considered in the light of the earlier negative results in this respect presented by Bernard and Jones (1996a) and it shows the importance of disaggregating the data.

The likelihood ratio test on the restriction of constant returns to scale with respect to the factor inputs, presented underneath, easily accepts this hypothesis. This is not the case, however, of the hypothesis of the presence of only common sector-specific intercepts, which is clearly rejected against the alternative of sector-country specific intercepts.

Column 2 presents again estimates of Equation 4, but now with sector-country specific intercepts, [[gamma].sub.ij], included. The joint significance of the individual specific fixed effects translates into a slight improvement in statistical fit. Whereas the estimated coefficient of capital, [alpha], is largely unaffected, the coefficient of the technology gap, [lambda], is now found clearly higher, as expected. Although the measured significance of the sector-country specific fixed effects and of the coefficient of technology gap may be exaggerated somewhat, as they may capture in part short-term cyclical effects, the lack of evidence of serial correlation in the error term suggests that this bias is unlikely to be important. It appears therefore safe to view the sector-country specific effects and the coefficient of technology gap as capturing mainly more long-run influences, implying TFP convergence toward distinct steady states or, in other words, conditional convergence. The estimated conditional convergence speed has a plausible value of about 7% per year. This is, interestingly enough, a similar order of magnitude as that found by De La Fuente and Domenech (2001) in their comparable fixed-effect panel data estimates with respect to a sample of OECD economies as a whole.

Column 3 in the table presents the estimates of Equation 6 above, which assumes a Cobb-Douglas production function that includes human capital. The estimate of the coefficient of the rate of growth and of the lagged levels of the log of schooling, [beta], has a plausible sign, but it is found statistically non-significant. (7) Column 4 gives, for its part, the estimates of Equation 8 above, which includes the lagged level of R&D intensity and the lagged level of schooling as explanatory variables. Their coefficients, [xi] and [theta], are clearly found positive and statistically significant. This would indicate that both the research efforts by firms and the level of schooling of the workers affect labor productivity through the process of technological innovation and diffusion. This would confirm the predictions of new growth theory.

Finally, Columns 5, 6, and 7 in the table present estimates of similar equations as presented in Columns 1, 2, and 4, but now with the coefficient of capital constrained to be equal to the average capital income share, [alpha] = 0.28. The likelihood ratio test, presented underneath, implies each time acceptance of this constraint. (8) As a consequence, the estimated coefficients of the technology gap, [lambda], are left unaffected. This implicitly suggests that the possible endogeneity bias in the estimate of can at most be very modest and that it does not affect our results with respect to convergence.

Table 2 presents the estimates of the coefficient of technology gap, [lambda], obtained from our most representative productivity growth equations estimated sector by sector. The precise coverage of the sectors is given in the Appendix. Column 1 presents the estimates of [lambda] obtained from the sectoral version of our benchmark Equation 4, under the assumption that there is only a common intercept. The nonpresented coefficient of capital, [alpha], is thereby allowed to vary between sectors. The results indicate that the coefficient of technology gap, [lambda], is each time positive and in 19 out of 22 cases also statistically significant. This clearly confirms the evidence of a significant catching-up effect provided by our global panel estimates.

Column 2 presents the estimates of [lambda] obtained from the sectoral version of Equation 4 with country-specific intercepts included. As indicated by a superscript a, the hypothesis of country-specific fixed effects is accepted in 15 out of the 22 cases. As expected, the effect of including these fixed effects is nearly always to raise the estimate of the technology gap, [lambda], which now becomes statistically significant in 21 out of 22 cases. This, again, confirms the finding of strong conditional convergence obtained from our global panel estimates. Column 3 presents, for its part, the estimates of [lambda] obtained from the sectoral version of Equation 8 that includes, in addition, the countries' lagged levels of R&D intensity and of schooling. Their inclusion hardly affects the estimated convergence speeds, and, if anything, even raises them somewhat in certain sectors. The test on the significance of the conditioning variables, that now include the lagged levels of R&D intensity and schooling besides the country-specific intercepts, shows a similar acceptance pattern as in Column 2, where the conditioning variables only include country-specific intercepts.

Columns 4, 5, and 6 in the table present the estimates of [lambda] obtained from the corresponding equations with the coefficients of capital each time constrained to be equal to the corresponding average sector-specific capital income shares. As indicated by a superscript b, these capital income share constraints are, respectively, accepted in 17, 16, and 16 out of 22 cases. Comparison with Columns 1, 2, and 3 shows moreover that, even when they are not, this does not fundamentally alter the picture with respect to the estimates of the coefficient of technology gap, [lambda], thereby confirming previous conclusions. This provides further evidence of the robustness of our estimates in this respect.

The evidence presented in Column 1 of Tables 1 and 2 of a significant positive technology gap effect in an equation that does not allow for country-specific conditioning influences on TFP, implies that, on average, countries with low initial levels of TFP grow more rapidly than those with higher initial levels. In principle, one should also expect this to imply that the average growth of TFP of non-frontier countries substantially exceeds that of the frontier. This does, however, not necessarily have to be the case, as the regression results may be dominated by convergence among the non-frontier countries or among subsamples of these countries. Table 3 presents the average annual rates of growth of alternate measures of TFP of the frontier and of the non-frontier countries for the sample as a whole, as well as sector by sector.

In Columns 1 and 2, TFP is each time derived under the assumption that the coefficient of capital, [alpha]. is equal to 0.33, its total panel-based estimate from Equation 4 presented in Column 2 of Table 1. The figures show that, for the sample as a whole, non-frontier TFP growth is nearly twice as large as frontier TFP growth. The sector-wise figures confirm, for their part, that the growth of non-frontier TFP exceeds that of the frontier in no less than 20 out of 22 cases. When we compare this with the sector-wise estimates of the coefficient of technology gap, [lambda], in Table 2, we see that it is indeed most often the case that sectors where there is evidence of a significant technology gap effect in the unconditional convergence equation (significant [lambda] in Column 1) show a stronger average growth of non-frontier TFP than of frontier TFP. In fact, there is only one case where the reverse is true: Metal Products (MET). Moreover, there are also two sectors, Petrochemicals (PET) and Machinery (MA), where non-frontier TFP growth exceeds frontier TFP growth even though there is only conditional convergence (non-significant [lambda] in Column 1 and significant [lambda] in Column 2). Here the data show that although the majority of non-frontier countries grow more rapidly than the frontier, they do not so according to the respective initial technology gaps because they only converge to their own distinct steady states. This picture is confirmed by Columns 3 and 4 in Table 3, in which the estimates of frontier and non-frontier growth are presented when TFP is derived by making use of the nonreported corresponding sector-specific estimates of [alpha].

In order to find out whether the evidence of a significant positive technology gap effect presented in Column 1 of Tables 1 and 2 does, indeed, imply a decrease in inequality between the levels of TFP during our period of investigation, it is useful to consider the evidence with respect to [sigma]-converge. Columns 1 to 6 of Table 4 present the standard deviation of the log of TFP, sector by sector, measured every 5 years, when TFP is derived under the assumption that [alpha] is equal to 0.33, its total panel-based estimate from Equation 4 presented in Column 2 of Table 1. Columns 7 to 12 present the corresponding standard deviations when TFP is derived on the basis of the nonreported corresponding estimated sector-specific values of [alpha] instead. On the first lines of these columns, we have each time presented the average across sectors of the sector standard deviations presented below.

Consider first the average standard deviation presented on the first line of the first part of the table and compare its value at the beginning and at the end of the period. This shows a substantial decrease, by about one-third, indicating that, on average, the evolution of manufacturing TFP in the OECD was characterized by substantial [sigma]-converge during the period 1970-1995. When looking at the evolution, year per year, it also strikes the eye that this convergence occurred mainly from 1970 to 1985 and tended to peter out afterward. A similar evolution is found back in the second part of the table, where TFP is estimated on the basis of sector-specific values of [alpha].

A comparison with the existing evidence with respect to the behavior of the dispersion of GDP per capita in the OECD indicates that the average degree of [sigma]-converge implied by our estimates with respect to manufacturing TFP is substantially higher. The end of period average degree of dispersion is also found lower than in the case of GDP per capita. (9) Even so, this is still seen to remain substantial, and it would suggest that by the end of the period, the economies are found to be approaching distinct equilibrium paths, conforming with the conditional convergence result implied by our regression estimates on the total panel.

Consider now the results sector by sector presented in Table 4. A comparison of the degree of dispersion at the beginning and at the end of the period provides evidence of [sigma]-converge in 19 out of 22 cases, and this is again seen to be mainly due to a reduction in dispersion between 1970 and 1985. The three sectors where there is no evidence of [sigma]-converge are Textiles (TX) and Petrochemicals (PET) (in both parts of the table) and Machinery (MA) (in the second part of the table). These are, interestingly enough, precisely the sectors where the coefficient of technology gap, [lambda], was found non-significant in the estimates of Equation 4 presented in Column 1 of Table 2, which does not include country-specific conditioning influences. Our [sigma]-convergence analysis is, therefore, consistent with the evidence of our regression analysis with respect to catching-up. Although there is a certain degree of criss-crossing of TFP levels due to countries overtaking one another, this cannot prevent the catching-up effect from dominating, and thereby, helping to reduce the degree of TFP dispersion in the sectors where the regression estimates show a positive significant estimate of [lambda], the coefficient of technology gap. There is, therefore, in other words, no evidence of Galton's fallacy.

In view of the above-mentioned inherent shortcomings of the [lambda]- and [sigma]-convergence analyses, it is interesting to find out whether their results can be confirmed by studying the observed intradistribution dynamics. Table 5 presents the sector-wise estimates of the ergodic vector describing the long-ran limit distribution of relative TFP levels, implied by the law of motion characteristic for the dynamics observed during our period of investigation. Due to space constraints, we only present results with respect to TFP derived under the assumption that [alpha] is equal to 0.33. its total panel-based estimate from Equation 4 presented in Column 2 of Table 1. The picture obtained when making use of TFP measures based on nonreported corresponding estimated sector-specific values of at instead is, however, highly similar and confirms all our conclusions.

The first thing to notice is that, in all but two cases, the long-run limit distribution appears to be unimodal in nature, in the sense that it is centered around one peak, located in one of the middle cells of the considered grid. The degree centration and its symmetry do, however, vary between sectors and there is no evidence of concentration of the probability mass into a single grid-cell. We view these results as being consistent with the occurrence of conditional convergence, whereby the original degree of dispersion in TFP levels is reduced but does not tend to disappear. In the two remaining sectors, Textiles (TX) and Petrochemicals (PET), the results indicate, on the contrary, a tendency toward a bimodal distribution, with the peaks lying in the outside grid-cells. This would clearly suggest a tendency of productivity divergence in these sectors. When comparing these results with our earlier findings with respect to [lambda]-convergence and [sigma]-convergence in Tables 2 and 4, it is again comforting to note that these two sectors are precisely those where there was the clearest evidence of divergence earlier on.

We conclude that the respective approaches considered thus far appear to provide results that are broadly consistent with one another. But are the observed differences in sectoral behavior plausible? These differences can be caused by actual behavioral differences or by problems of measurement. Behavioral differences may reflect differences in the channels and in the intensity of technological spillovers. Although our considered technology gap equations are well-suited for their purpose--that is, to estimate the catch-up effect implied by international technological diffusion--they cannot teach us much about the precise channels through which this diffusion occurs. The existing literature on international technology spillovers has considered different such channels.

Most of these studies concentrate on the OECD. They are aggregate in nature and estimate equations that relate TFP to domestic and to foreign R&D capital, where the latter is obtained as a weighted sum of the R&D capital stocks of the other countries, and the weights measure the technological proximity between the sender and the receiver of spillovers. Most often, they follow, thereby, Coe and Helpman (1995) by considering foreign trade as the main channel of spillovers and base their weights on bilateral import shares. Some have also considered foreign activities of multinational enterprises (MNEs) as a channel of technology spillovers and used weights based on inward or on outward foreign direct investment or employment (see, e.g., Lichtenberg and van Pottelsberghe 1996).

More disaggregate studies have concentrated on OECD manufacturing industries. They have estimated, in a similar manner, the impact of intersectoral as well as international technology spillovers, while basing the weights capturing the technological distance between sectors on bilateral intermediate input flows or on patent information (Verspagen 1997; Frantzen 2002; Keller 2002). Some studies have examined the contribution of the used weighting schemes by confronting the performance of the corresponding spillover variables with comparable spillover variables based on random or on equal weights (Keller 1998, 1999). Making use of firm-based micro-data, some authors have also attempted to examine the impact of technology spillovers on TFP in an implicit manner. They concentrate on specific countries, such as the United States or the United Kingdom, and estimate equations relating TFP of domestic firms to the import share in the industry concerned, the investment or employment share of foreign MNEs, and variables controlling for the effect of differences in market structure (Haskel, Pereira, and Slaughter 2001; Keller and Yeaple 2003).

The general picture to emerge from this literature is the following: International technology spillovers have a significant impact on productivity in the OECD; they occur through different channels; they are both intrasectoral and intersectoral in nature; and they are especially strong in research intensive industries. The precise relative importance of the respective channels of transmission remains, however, unclear, and this, mainly, due to measurement problems. The most promising progress in this respect is currently being made by studies with respect to specific countries based on micro-data. Thus, for instance, Keller and Yeaple (2003) find a much more significant impact of technology spillovers from foreign MNEs on U.S. manufacturing productivity than estimated until now by constructing a more appropriate measure of foreign MNE employment per industry. This type of work will have to be further sharpened by analyzing intersectoral differences, and a great deal of database construction efforts will have to be performed in order to allow comparable studies with respect to most other OECD countries.

Measurement problems in the data used in our study can probably, by themselves, explain pan of the differences in observed convergence behavior between sectors. Consider especially the sectors where we cannot find evidence of productivity convergence. One of these sectors is Petrochemicals (PET, ISIC 353+354). As its name suggests, this sector produces petroleum derivatives and has, therefore, oil products as major material inputs. Now, as is well-known, oil prices have shown a highly erratic behavior during the period under consideration, with large fluctuations caused by successive oil price shocks. We can, therefore, presume that this may have caused significant errors of measurement in the figures of real gross value added that underlay our measure of productivity. Only modest differences in sectoral product composition between countries can thereby have caused significant measured TFP divergence.

The other sector with the most clearcut evidence of productivity divergence is Textiles (TX, ISIC 32). This is a sector that has been subject to significant restructuring during the period under consideration, due to increasing competition from developing countries. Now, as this restructuring has occurred to different extents and partly in different directions, with some countries redirecting their activities toward luxury products such as high-fashion clothing, others toward industrial synthetic carpeting, and so on, this has increased the differences in product composition between OECD countries. This may again help to explain, in part, the noticed evidence of TFP divergence in this sector.

It may, at first view, appear somewhat surprising that the Machinery sector (MA, ISIC 382-3825) fails to show significant evidence of productivity convergence, while, say, the Aerospace industry (AE, ISIC 3845) does, despite its much higher barriers to entry and government involvement. But, again, the considered Machinery product grouping, which is in essence at the three-digit ISIC level, is far larger in scope, and therefore likely to be more heterogeneous in nature between countries. Moreover, Aerospace is highly research intensive, also in its non-defense-related civil production, which allows its firms to capture more easily outside knowledge. Although its market is dominated by a few large MNEs, these work with a much larger number of medium-sized and small subcontractors. In fact, in a majority of the smaller considered OECD economies, the AE sector mainly consists of such subcontractors working for foreign MNEs or for their local subsidiaries. There are. therefore, ample possibilities of international technological diffusion in this industry.

These and other peculiarities in the observed differences in behavior between sectors clearly need to be further investigated by means of a case study approach. This falls well beyond the scope of the current study. Suffice to note here that the results presented thus far are broadly consistent with one another and do, apparently, not show unexplainable anomalies. If measurement could be improved, by, among others, performing the analysis at an even lower level of aggregation whenever necessary, this is likely to tilt the results even further in the direction of convergence.

To recap, our respective approaches considered thus far provide a picture of manufacturing productivity growth performances dominated, during the period under consideration, by transitional dynamics characterized not only by conditional convergence, but also by a degree of actual catching-up, through technological diffusion. Our explicit evidence of an average rate of productivity growth of the non-frontier countries exceeding that of the frontier fits perfectly with this picture of technological catching-up during the transitional dynamics. But it also implies that, if we were to follow a time series approach to convergence analysis and perform unit root tests on the technology gap variable during the same period, we should expect these to suggest the presence of a unit root.

Table 6 presents the results of a group mean ADF test for the null of the presence of a unit root in the distance between the logs of frontier and non-frontier TFP on pooled annual time series during the period under consideration. The test is performed both on the global panel and sector by sector.

In Columns 1 and 2, TFP is derived under the assumption that the coefficient of capital, [alpha], is equal to 0.33, its total panel-based estimate from Equation 4 presented in Column 2 of Table 1. The results each time clearly suggest the presence of a unit root, both for the panel as a whole and in a great majority of sectors. And even in these where it does not--Wood (WO), Automobiles (AUT), and Instruments (IN)--a closer look at the unreported underlying individual country-wise ADF tests shows that the rejection of the null is only caused by one or two outliners, most likely explainable by errors of measurement. This picture is confirmed by that given by Columns 3 and 4, where TFP is based on the nonreported corresponding estimated sector-specific values of [alpha] instead.

Our results in this respect are, therefore, in line with those of Bernard and Jones (1996b). But, when considered in the light of what precedes, they cannot, however, be viewed as evidence for asymptotic productivity divergence. Given that our evidence above clearly suggests that, during a major part of the period of investigation, the economies are behaving well out of their steady state, the results of unit root tests are, in fact, misleading. They capture mainly transitory growth performances dominated by catching-up, which necessarily implies differences in growth rates.

6. Summary and Conclusions

A study was presented of the issue of total factor productivity convergence through international technological diffusion in OECD manufacturing on disaggregate panel data with respect to 22 sectors in 14 countries from 1970 to 1995. Regression estimates were performed of equations relating TFP growth to initial technology gap and conditioning variables, such as country-specific fixed effects, the level of R&D intensity, and the level of schooling of the working-age population. The estimates on the global panel showed that both the coefficients of the conditioning variables and of the technology gap are found to be statistically significant. Leaving out the conditioning variables reduces the parameter estimate of the technology gap, but still shows this to be significant. These results are confirmed by the estimates sector by sector in a great majority of sectors. They imply the occurrence of conditional convergence with institutional factors, the research efforts by firms, and the schooling efforts by the population acting as major conditioning influences. And they also suggest that a degree of actual catching-up has been taking place during the period under consideration.

A sector-wise analysis of the evolution of the standard deviation of the log of TFP provided, for its part, evidence of [sigma] convergence in a large majority of sectors. This was essentially the case in these sectors where the regression estimates of the equations without country conditioning influences suggested that a degree of actual catching-up has been taking place. This process of [sigma]-convergence did, however, tend to peter out by the end of the period of investigation, suggesting that, by then, the economies are approaching distinct equilibrium paths, conforming with the conditional convergence result implied by the regression analysis.

Studying the intradistribution dynamics of relative TFP levels by means of a Markov-chain transition probability matrix approach indicated, moreover, a tendency towards a unimodal distribution, centered around the middle of the relative productivity space, in a great majority of sectors. This was, again, especially the case in the sectors where there was evidence of a degree of actual catching-up and [sigma]-convergence. The level of dispersion in the implied limit distribution was, however, still found to be significant, suggesting, once more, that the convergence is conditional in nature.

These various results appear consistent with one another. They suggest that, during a major part of the period of investigation, the manufacturing sectors of the considered OECD economies were behaving well out of their steady state, and their productivity growth performances were dominated by transitional dynamics. This dominance of transitional dynamics implies that a time series approach to convergence analysis is, in fact, inappropriate for the period under consideration. The evidence in favor of the presence of a unit root in our alternate measures of the technology gap between frontier and non-frontier is misleading, as it captures mainly transitory movements, characterized by a stronger TFP growth of the non-frontier than of the frontier due do catching-up.

Appendix

The 14 countries considered in this study were chosen for reasons of data availability with respect to the variables under consideration. They are Australia, Canada, Denmark, Finland, France, West Germany, Italy, Japan, The Netherlands, Norway, Spain, Sweden, the United Kingdom and the United States. (10) They account for more than 90% of manufacturing value added and for more than 95% of R&D expenditure in the OECD. Manufacturing is disaggregated into the following 22 sectors (abbreviation, ISIC codes): Food, Beverage, and Tobacco (FO, 31), Textiles, Leather, and Footwear (TX, 32), Wood and Wooden Products (WO, 33), Paper, Printing, and Publishing (PA, 34), Chemicals exclusive Drugs (CH, 351+352-3522), Drugs (DR, 3522), Petrochemicals (PET, 353+354), Rubber and Plastic Products (RP, 355+356), Non Metallic Minerals (NM, 36), Steel (ST, 371), Non Ferrous Metals (NF, 372), Simple Metal Products (MET. 381). Machinery (MA, 382-3825), Computers (CO, 3825). Electrical Goods (EG, 383-3832). Radio, TV, and Telecommunication Equipment (CE, 3832), Ships and Boats (SH, 3841), Automobiles (AUT, 3843), Aerospace (AE, 3845), Other Transport Equipment (OTR, 384-3841-3843-3845), Instruments (IN, 385), Other Manufacturing (OTM, 39).

The main data with respect to income (value added at factor costs), [Y.sub.ijt], physical capital, [K.sub.ijt], and labor (employment), [L.sub.ijt], were obtained from the OECD STAN Database. In the case of physical capital, we only dispose of figures on nominal capital investment. We had, therefore, first to deflate these in order to obtain figures in real terms. We did so by using the business sector value added price deflator, obtained from the OECD Business Sector Database. We then constructed the corresponding capital stock figures by applying the perpetual inventory method while using a depreciation rate of 5%. All income and capital stock figures are expressed in dollars at 1990 purchasing power parity (PPP).

The chosen rate of capital depreciation of 5% has unavoidably something arbitrary to it. It does, however, lie in-between the rate of 3% generally assumed in the aggregate work on convergence (where the capital stock includes a large pan of long-lived buildings and infrastructure) and the average value of the estimated rates with respect to manufacturing of about 7% presented by Jorgenson and Landau (1993) (where capital mainly contains equipment goods). Experimentation with alternate rates of 3% and 7% hardly affected our regression results. As far as labor is concerned, the lack of data on hours worked in the case of a majority of countries meant that use had to be made of unadjusted employment data. This may have caused an underestimation of the actual long-run growth of productivity to the extent that the working time was reduced somewhat during the period of investigation.

The average level of education of the workforce is measured by the educational attainment of the working age population in terms of years of schooling. Use was thereby made of the data computed by De La Fuente and Domenech (2000) that mainly consist of an improved version of earlier data in this respect constructed by Barro and Lee (1996). Its main drawback is that it is only available at the aggregate level rather than sector by sector.

The level of R&D intensity was measured by dividing nominal R&D expenditure by nominal value added at factor costs. The figures with respect to nominal R&D expenditure were obtained from the OECD Science and Technology Database (for 1970) and from the OECD ANBERD Database (from 1975 onward). They cover total sectoral business enterprise R&D expenditures, both on researchers and on capital equipment goods used in the research process.

For reasons of data availability, the starting date of the respective series is 1970 and the period of investigation is 1970-1995. In some countries, entire series of certain variables were missing in certain sectors. These sectors were therefore dropped.

Table 1. Productivity Growth Equations Estimated on Panel of
Sector-Country 5-Yearly Annual Data (1970-1995, 14 OECD Countries, 22
Sectors)

Coefficient            (1)        (2)        (3)        (4)

[alpha]               0.344      0.337      0.338      0.344
                    (12.34) *  (12.50) *  (12.59) *  (12.75) *
[beta]                                      0.207
                                           (1.16)
[xi]                                                   0.070
                                                     (2.85) *
[theta]                                                0.015
                                                     (2.62) *
[lambda]              0.036      0.073      0.073      0.073
                    (14.73) *  (16.16) *  (16.21) *  (16.04) *
Time dummies           Yes        Yes        Yes        Yes
Sector intercepts      Yes        No         No         No
Sector-count. int.     No         Yes        Yes        Yes
No. observations      1490       1490       1490       1490
Adjusted [R.sup.2]    0.250      0.284      0.284      0.293
Stand. err. regr.     0.037      0.036      0.036      0.036
Serial correlation    1.761      1.986      1.988      1.994
Constraints
  Constant returns to scale
                      3.34       0.00       0.16       0.06
                       (1)        (1)        (1)        (1)
  Coefficient capital terms = average capital income share
  Only sector specific intercepts
                    379.84 *
                      (276)

Coefficient            (5)        (6)        (7)

[alpha]               0.280      0.280      0.280
[beta]
[xi]                                        0.064
                                          (2.62) *
[theta]                                     0.015
                                          (2.66) *
[lambda]              0.036      0.073      0.073
                    (14.31) *  (16.08) *  (15.91) *
Time dummies           Yes        Yes        Yes
Sector intercepts      Yes        No         No
Sector-count. int.     No         Yes        Yes
No. observations      1490       1490       1490
Adjusted [R.sup.2]    0.249      0.282      0.290
Stand. err. regr.     0.037      0.036      0.036
Serial correlation    1.760      1.983      1.993
Constraints
  Constant returns to scale
  Coefficient capital terms = average capital income share
                      6.00       7.62       7.26
                       (3)        (3)        (3)
  Only sector specific intercepts
                    386.96 *
                      (276)

Columns 5, 6, and 7 present estimates of equations similar to those
presented in Columns 1, 2, and 4, except that here the coefficient of
the capital terms is constrained to be equal to the average capital
income share, 0.28.

The time dummies and the various intercepts are not presented. The
method of estimation is nonlinear least squares. The t-tests on the
parameter estimates are one-tailed tests, and their statistics are
presented between parentheses underneath.

The serial correlation test is Bhargava, Franzini, and Narendranathan's
(1982) Durbin-Watson test for panel data based on a fixed effects
model. The manner of computing the upper and lower bounds for our panel
dimension is indicated in that paper.

The likelihood ratio tests on the respective constraints have
chi-square distributions with degrees of freedom indicated in
brackets underneath.

* Denotes statistical significance at the 5% level.

Table 2. Coefficient of Technology Gap [lambda] from Productivity
Growth Equations Estimated Sector by Sector (1970-1995, 14 OECD
Countries)

Sector            (1)               (2)                 (3)

FO           0.019 (3.76) *  0.062 (2.28) *      0.060 (2.08) *
TX           0.005 (0.37)    0.134 (a) (4.20) *  0.145 (a) (4.46) *
WO           0.058 (5.16) *  0.102 (4.32) *      0.112 (4.55) *
PA           0.042 (3.49) *  0.132 (a) (5.03) *  0.166 (a) (6.07) *
CH           0.036 (4.19) *  0.084 (a) (4.64) *  0.083 (a) (4.72) *
DR           0.033 (4.52) *  0.089 (3.44) *      0.077 (3.05) *
PET          0.006 (0.98)    0.141 (a) (6.21) *  0.142 (a) (6.19) *
RP           0.040 (3.07) *  0.095 (a) (4.07) *  0.095 (a) (3.92) *
NM           0.024 (2.04) *  0.106 (a) (5.00) *  0.132 (a) (5.66) *
ST           0.090 (6.81) *  0.160 (a) (7.22) *  0.175 (a) (7.81) *
NF           0.053 (4.38) *  0.198 (a) (8.11) *  0.198 (a) (7.96) *
MET          0.047 (4.73) *  0.053 (a) (2.77) *  0.061 (a) (3.06) *
MA           0.023 (1.38)    0.063 (a) (2.59) *  0.067 (a) (2.66) *
CO           0.101 (4.59) *  0.168 (a) (6.09) *  0.164 (a) (5.76) *
EG           0.070 (6.29) *  0.086 (4.92) *      0.096 (5.40) *
CE           0.044 (3.70) *  0.040 (a) (2.13) *  0.038 (a) (1.96) *
SH           0.065 (3.75) *  0.108 (a) (4.27) *  0.107 (a) (3.94) *
AUT          0.068 (4.43) *  0.118 (4.57) *      0.118 (4.39) *
AE           0.040 (4.99) *  0.070 (321) *       0.075 (2.64) *
OTR          0.037 (5.78) *  0.013 (0.64)        0.014 (0.70)
IN           0.055 (4.54) *  0.100 (a) (4.95) *  0.109 (a) (5.23) *
OTM          0.030 (3.29) *  0.145 (a) (4.88) *  0.170 (a) (5.21) *
Time dum.         Yes               Yes                 Yes
Count. int.        No               Yes                 Yes

Sector              (4)                  (5)

FO           0.024 (3.08) *      0.073 (2.88) *
TX           0.006 (b) (0.47)    0.128 (ab) (3.98) *
WO           0.052 (b) (4.28) *  0.104 (b) (4.25) *
PA           0.047 (b) (3.79) *  0.110 (a) (3.94) *
CH           0.036 (b) (4.13) *  0.083 (ab) (4.93) *
DR           0.032 (b) (3.69) *  0.088 (b) (3.58) *
PET          0.006 (b) (0.95) *  0.158 (ab) (6.39) *
RP           0.040 (b) (3.04) *  0.100 (ab) (4.42) *
NM           0.024 (b) (2.24) *  0.106 (ab) (5.17) *
ST           0.069 (5.08) *      0.168 (a) (7.51) *
NF           0.041 (b) (3.56) *  0.203 (ab) (8.86) *
MET          0.041 (b) (3.84) *  0.053 (ab) (2.79) *
MA           0.039 (b) (2.52) *  0.071 (ab) (3.01) *
CO           0.102 (b) (4.71) *  0.160 (ab) (5.91) *
EG           0.070 (b) (6.41) *  0.086 (b) (4.98) *
CE           0.041 (3.17) *      0.058 (a) (2.81) *
SH           0.069 (b) (3.94) *  0.101 (ab) (4.49) *
AUT          0.067 (b) (4.46) *  0.118 (b) (4.88) *
AE           0.049 (4.03) *      0.101 (3.86) *
OTR          0.045 (3.44) *      0.112 (3.83) *
IN           0.055 (b) (5.59) *  0.094 (ab) (4.99) *
OTM          0.027 (b) (2.99) *  0.136 (ab) (4.71) *
Time dum.           Yes                  Yes
Count. int.          No                  Yes

Sector              (6)

FO           0.071 (2.75) *
TX           0.135 (ab) (4.07) *
WO           0.114 (b) (4.50) *
PA           0.132 (a) (4.44) *
CH           0.083 (ab) (5.04) *
DR           0.079 (b) (3.20) *
PET          0.159 (ab) (6.24) *
RP           0.100 (ab) (4.27) *
NM           0.132 (ab) (5.76) *
ST           0.172 (a) (7.51) *
NF           0.204 (ab) (8.70) *
MET          0.061 (ab) (3.13) *
MA           0.074 (ab) (3.09) *
CO           0.159 (ab) (5.72) *
EG           0.096 (b) (5.47) *
CE           0.052 (a) (2.19) *
SH           0.098 (ab) (4.08) *
AUT          0.120 (b) (4.64) *
AE           0.127 (3.99) *
OTR          0.107 (3.47) *
IN           0.102 (ab) (5.32) *
OTM          0.166 (ab) (5.16) *
Time dum.           Yes
Count. int.         Yes

Abbreviations: Food, Beverage, and Tobacco (FO). Textiles, Leather, and
Footwear (TX), Wood and Wooden Products (WO), Paper, Printing, and
Publishing (PA), Chemicals exclusive Drugs (CH), Drugs (DR),
Petrochemicals (PET), Rubber and Plastic Products (RP), Non Metallic
Minerals (NM), Steel (ST), Non Ferrous Metals (NF), Simple Metal
Products (MET), Machinery (MA), Computers (CO), Electrical Goods (EG),
Radio, TV, and Telecommunication Equipment (CE), Ships and Boats (SH),
Automobiles (AUT), Aerospace (AE), Other Transport Equipment (OTR),
Instruments (IN), Other Manufacturing (OTM).

The coefficients of the other variables in the equations are not
presented. Columns 1 to 3 present the sector-specific estimates of
[lambda] obtained from equations similar to those presented in Columns
1, 2, and 4 of Table 1. Columns 4 to 6 present the corresponding
estimates of [lambda] obtained from similar equations where the
coefficient of the capital terms is constrained to be equal to the
average sector-specific capital income share. The method of estimation
is nonlinear least squares. The t-test on [lambda] is one-tailed, and
its statistic is presented between parentheses beside.

(a) Indicates acceptance at the 5% level by the likelihood ratio test
on the presence of country-specific intercepts in Columns 2 and 5 and
of such intercepts and of a R&D intensity and schooling effect in
Columns 3 and 6.

(b) Denotes acceptance at the 5% level by the likelihood ratio test on
the equality of the capital terms with the average sector-specific
income share of capital.

* Denotes statistical significance of the t-statistic at the 5% level.

Table 3. Average Annual Growth Rate of Total Factor Productivity of the
Technological Frontier and Non-Frontier Countries (%, 1970-1995)

Sector  Frontier (1)  Non-Frontier (2)  Frontier (3)  Non-Frontier (4)

All         1.29            2.44            1.19            2.31
FO          0.77            1.66           -0.37            0.71
TX          2.44            1.85            2.40            1.71
WO         -0.69            1.27           -0.99            1.16
PA         -0.18            1.29           -0.45            1.04
CH          3.57            3.58            3.51            3.52
DR          3.62            3.72            3.51            3.65
PET         0.19            1.52            0.06            0.98
RP          1.29            2.72            1.04            2.65
NM          1.38            1.67            1.72            2.08
ST          1.66            3.22            1.05            2.67
NF          1.88            2.81            1.31            2.67
MET         2.13            2.07            2.27            2.17
MA          0.47            2.49            2.37            2.93
CO          1.72            3.34            1.33            3.80
EG          3.16            5.51            3.14            5.13
CE          4.05            5.19            5.81            6.06
SH         -2.06            1.49           -2.06            1.49
AUT        -0.34            1.52            0.05            1.72
AE         -1.81           -0.48           -3.87           -1.35
OTR         1.86            2.80            0.14            1.72
IN          1.76            2.33            1.85            2.07
OTM         1.40            2.01            2.24            2.26

Abbreviations: Food, Beverage, and Tobacco (FO), Textiles, Leather, and
Footwear (TX), Wood and Wooden Products (WO), Paper, Printing, and
Publishing (PA), Chemicals exclusive Drugs (CH), Drugs (DR),
Petrochemicals (PET), Rubber and Plastic Products (RP), Non Metallic
Minerals (NM), Steel (ST), Non Ferrous Metals (NF), Simple Metal
Products (MET), Machinery (MA), Computers (CO), Electrical Goods (EG),
Radio, TV, and Telecommunication Equipment (CE), Ships and Boats (SH),
Automobiles (AUT), Aerospace (AE). Other Transport Equipment (OTR).
Instruments (IN), Other Manufacturing (OTM).

In Columns 1 and 2, total factor productivity is derived under the
assumption that [alpha] is equal to 0.33, its total panel-based
estimate from Equation 4 presented in Column 2 of Table 1. In Columns 3
and 4, the nonreported corresponding estimated sector-specific values
of [alpha] are used instead.

Table 4. Standard Deviation of the Log of Total Factor Productivity
Sector by Sector (14 OECD Countries)

         1970   1975   1980   1985   1990   1995
Sector    (1)    (2)    (3)    (4)    (5)    (6)

All (a)  0.441  0.406  0.349  0.303  0.288  0.293
FO       0.288  0.288  0.277  0.259  0.215  0.191
TX       0.192  0.168  0.164  0.185  0.209  0.267
WO       0.327  0.258  0.184  0.197  0.187  0.167
PA       0.254  0.268  0.232  0.192  0.168  0.147
CH       0.409  0.358  0.282  0.255  0.268  0.265
DR       0.566  0.581  0.419  0.364  0.386  0.376
PET      0.714  0.698  0.838  0.719  0.676  0.719
RP       0.282  0.280  0.242  0.237  0.221  0.224
NM       0.216  0.245  0.204  0.187  0.197  0.193
ST       0.412  0.331  0.364  0.207  0.188  0.154
NF       0.428  0.390  0.390  0.310  0.272  0.284
MET      0.352  0.284  0.234  0.181  0.187  0.224
MA       0.319  0.300  0.242  0.170  0.212  0.300
CO       0.363  0.272  0.296  0.333  0.311  0.349
EG       0.730  0.615  0.350  0.284  0.271  0.290
CE       0.542  0.565  0.393  0.337  0.417  0.436
SH       0.527  0.475  0.435  0.539  0.355  0.375
AUT      0.363  0.364  0.252  0.230  0.165  0.191
AE       0.675  0.635  0.456  0.365  0.352  0.345
OTR      0.593  0.598  0.524  0.445  0.338  0.216
IN       0.535  0.428  0.295  0.239  0.281  0.322
OTM      0.612  0.544  0.602  0.441  0.463  0.400

         1970   1975   1980   1985   1990   1995
Sector    (7)    (8)    (9)   (10)   (11)   (12)

All (a)  0.487  0.441  0.379  0.338  0.320  0.323
FO       0.371  0.385  0.356  0.328  0.282  0.242
TX       0.198  0.173  0.165  0.187  0.213  0.268
WO       0.336  0.269  0.188  0.199  0.186  0.158
PA       0.262  0.276  0.244  0.202  0.179  0.156
CH       0.414  0.362  0.284  0.255  0.267  0.264
DR       0.831  0.783  0.683  0.712  0.743  0.723
PET      0.759  0.699  0.829  0.712  0.699  0.765
RP       0.294  0.289  0.251  0.240  0.226  0.226
NM       0.180  0.212  0.190  0.181  0.179  0.178
ST       0.452  0.311  0.296  0.168  0.179  0.132
NF       0.430  0.377  0.376  0.300  0.258  0.271
MET      0.339  0.277  0.232  0.179  0.192  0.231
MA       0.230  0.229  0.201  0.164  0.222  0.303
CO       0.451  0.311  0.296  0.381  0.330  0.404
EG       0.748  0.642  0.369  0.306  0.295  0.315
CE       0.549  0.563  0.380  0.361  0.380  0.406
SH       0.527  0.476  0.435  0.539  0.355  0.375
AUT      0.361  0.361  0.254  0.230  0.173  0.201
AE       0.829  0.775  0.572  0.443  0.406  0.386
OTR      1.004  0.952  0.818  0.643  0.484  0.309
IN       0.556  0.436  0.306  0.253  0.294  0.338
OTM      0.596  0.547  0.623  0.453  0.498  0.449

Abbreviations: Food, Beverage, and Tobacco (FO), Textiles, Leather, and
Footwear (TX), Wood and Wooden Products (WO), Paper, Printing, and
Publishing (PA), Chemicals exclusive Drugs (CH), Drugs (DR),
Petrochemicals (PET), Rubber and Plastic Products (RP). Non Metallic
Minerals (NM), Steel (ST), Non Ferrous Metals (NF), Simple Metal
Products (MET), Machinery (MA), Computers (CO), Electrical Goods (EG),
Radio, TV, and Telecommunication Equipment (CE), Ships and Boats (SH),
Automobiles (AUT), Aerospace (AE), Other Transport Equipment (OTR),
Instruments (IN), Other Manufacturing (OTM).

(a) "All" (all sectors) refers each time to the average of the
sector-wise standard deviations presented below. In Columns 1 to 6,
total factor productivity is derived under the assumption that [alpha]
is equal to 0.33, its total panel-based estimate from Equation 4
presented in Column 2 of Table 1. In Columns 7 to 12, the nonreported
corresponding estimated sector-specific values of [alpha] are used

instead.

Table 5. Ergodic Vector of Relative Total Factor Productivity Derived
from 5-Yearly Transition Matrices During the Period 1970 to 1995

Sector       Grid (Upper End-Points) and Ergodic Vector

FO
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.000  0.773  0.153  0.074    0.000
TX
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.206  0.069  0.114  0.153  0.178    0.280
WO
  Grid:     0.8    0.9    1      1.1    1.2    [infinity]
  Ergodic:  0.080  0.118  0.163  0.294  0.269    0.076
PA
  Grid:     0.8    0.9    1      1.1    1.2    [infinity]
  Ergodic:  0.125  0.153  0.241  0.309  0.172    0.000
CH
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.180  0.586  0.234  0.000    0.000
DR
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.138  0.288  0.328  0.117  0.091    0.038
PET
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.263  0.237  0.000  0.106  0.131    0.263
RP
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.090  0.428  0.371  0.111    0.000
NM
  Grid:     0.8    0.9    1      1.1    1.2    [infinity]
  Ergodic:  0.158  0.176  0.174  0.283  0.118    0.091
ST
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.066  0.412  0.424  0.057    0.041
NF
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.014  0.035  0.238  0.432  0.281    0.000
MET
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.037  0.428  0.365  0.142    0.028
MA
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.160  0.510  0.264  0.049    0.017
CO
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.012  0.174  0.340  0.292  0.118    0.064
EG
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.005  0.057  0.380  0.414  0.081    0.063
CE
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.096  0.320  0.236  0.142  0.138    0.068
SH
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.032  0.219  0.244  0.127  0.158    0.220
AUT
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.005  0.079  0.493  0.281  0.081    0.061
AE
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.183  0.083  0.734  0.000    0.000
OTR
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.183  0.195  0.307  0.193    0.122
IN
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.277  0.308  0.305  0.082    0.028
OTM
  Grid:     0.5    0.75   1      1.25   1.5    [infinity]
  Ergodic:  0.000  0.132  0.413  0.232  0.134    0.089

Abbreviations: Food, Beverage, and Tobacco (FO), Textiles, Leather, and
Footwear (TX), Wood and Wooden Products (WO), Paper, Printing, and
Publishing (PA), Chemicals exclusive Drugs (CH), Drugs (DR),
Petrochemicals (PET), Rubber and Plastic Products (RP), Non Metallic
Minerals (NM), Steel (ST), Non Ferrous Metals (NF), Simple Metal
Products (MET), Machinery (MA), Computers (CO), Electrical Goods (EG),
Radio, TV, and Telecommunication Equipment (CE), Ships and Boats (SH),
Automobiles (AUT), Aerospace (AE), Other Transport Equipment (OTR),
Instruments (IN), Other Manufacturing (OTM).

Total factor productivity is derived under the assumption that [alpha]
is equal to 0.33. its total panel-based estimate from Equation 4
presented in Column 2 of Table 1. Its relative value is obtained by
dividing this by the corresponding average value over the countries
under consideration. The ergodic vector is given by the normalized
eigenvector corresponding to the largest eigenvalue of the transposed
average 5-yearly transition matrix obtained by averaging the 5
subsequent 5-yearly transition matrices during the period 1970-1995.

Table 6. Group Mean ADF Test for the Presence of a Unit Root in the
Technological Distance Between Frontier and Non-Frontier on Annual
Panel Data (1970-1995)

Sector       dist (1)  [DELTA]dist (2)  dist (3)  [DELTA]dist (4)

All sectors  -0.24        -37.54 *      -0.25        -37.83 *
FO            3.86         -6.89 *       4.11         -7.10 *
TX           -0.211        -6.65 *       0.81         -5.53 *
WO           -2.76 *       -9.52 *      -2.91 *       -9.94 *
PA            2.13         -8.73 *       2.03         -8.57 *
CH           -1.47         -8.00 *      -1.49         -7.97 *
DR            0.70         -8.25 *       0.71         -8.25 *
PET           0.87         -9.18 *      -0.63         -9.55 *
RP           -0.37         -7.54 *       -.01         -7.69 *
NM           -1.35         -7.30 *      -1.35         -7.54 *
ST           -0.28         -9.56 *      -0.23         -9.39 *
NF            0.28         -8.36 *       1.10         -8.26 *
MET          -0.50         -8.40 *      -0.30         -8.26 *
MA            3.73         -6.77 *      -0.28         -6.54 *
CO           -0.47        -11.57 *      -1.80 *      -10.47 *
EG           -0.57         -6.26 *       0.04         -6.72 *
CE            1.41         -6.83 *       2.94         -7.21
SH           -1.31         -8.42 *      -1.31         -8.41 *
AUT          -1.93 *       -7.86 *      -1.86 *       -7.83 *
AE           -0.74         -8.68 *       0.21         -8.73 *
OTR           0.41         -6.72 *       2.47         -8.18 *
IN           -2.62 *       -8.33 *      -2.72 *       -8.45 *
OTM          -0.68         -6.41 *      -1.19         -6.70

* Abbreviations: Food, Beverage, and Tobacco (FO), Textiles, Leather,
and Footwear (TX), Wood and Wooden Products (WO), Paper, Printing, and
Publishing (PA), Chemicals exclusive Drugs (CH), Drugs (DR),
Petrochemicals (PET), Rubber and Plastic Products (RP), Non Metallic
Minerals (NM), Steel (ST), Non Ferrous Metals (NF), Simple Metal
Products (MET), Machinery (MA), Computers (CO), Electrical Goods (EG),
Radio, TV, and Telecommunication Equipment (CE), Ships and Boats (SH),
Automobiles (AUT), Aerospace (AE), Other Transport Equipment (OTR),
Instruments (IN), Other Manufacturing (OTM).

The technological distance, dish is obtained as the difference between
the log of total factor productivity of the frontier and of the
non-frontier. [DELTA]dist stands for its first difference. In Columns 1
and 2, total factor productivity is derived under the assumption that
[alpha] is equal to 0.33, its total panel based estimate from Equation
4 presented in Column 2 of Table 1. In Columns 3 and 4 the non-reported
corresponding estimated sector-specific values of [alpha] are used
instead. The used test is Inn, Pesaran, and Shin's (1997) standardized
average Augmented Dickey-Fuller (ADF) test obtained from the
corresponding sector-country specific ADF tests. The mean and variance
adjustment terms used to perform the standardization are presented in
table 2 of Im, Pesaran, and Shin (1997). The test-statistic has an
asymptotic standard normal distribution.

* Denotes rejection of the null at a 5% level of significance.

(1) This can also be shown more formally by rewriting Equation 3 as a first-order differential equation that describes the behavior of the level of TFP. [A.sub.it], through time. By considering its solution both for the frontier country and for an imitator country and by evaluating the limit value of their proportion, one obtains exactly the same result.

(2) The importance of adoption efforts has long been known (see, especially, Cohen and Levinthal 1989). Using a linear programming approach, Jerzmanowski (2003) has decomposed cross-country differences in TFP into differences in availability of technologies and differences in efficiency in their implementation. His estimates show that differences in efficiency due to varying adoption efforts account for a significant part of the differences in TFP across countries.

(3) Note that since our R&D variable concerns the proportion of R&D expenditure over value added and our schooling variable the average level of schooling per worker, our specification does not include a counterfactual growth scale effect, such as implied by the original endogenous growth models. It is, in this respect, in line with the more recent generation of endogenous growth models without growth scale effect of Aghion and Howitt (1998) and others.

(4) Examples may even be constructed where the intradistribution criss-crossing is such that there is [sigma]-divergence, despite the fact that regression estimates would imply [lambda]-convergence.

(5) More precisely, we applied Arellano's orthogonal deviation procedure on equations using TFP constructs, [a.sub.ijt], based on the corresponding nonlinear least squares estimates of the parameters [alpha] and [beta] presented in Table 1. Arellano's procedure implies that the variables are first subjected to a Within transform whereby they are expressed in deviation from the individual specific average value of their corresponding future observations. A system of cross-section equations (one for each time observation) is then estimated by two-stages least squares, using each time all the lagged values of initial TFP as instruments.

(6) The test-statistic of the likelihood ratio test on the presence of sector-specific intercepts against that of only a single common intercept has a value of 217.02 and possesses a chi-square distribution with 21 degrees of freedom.

(7) We also experimented with an alternate growth equation in which the rate of growth and the log of the level of schooling are replaced, respectively, by the first difference and by the level of schooling as such, under the assumption that schooling enters the production function of goods as an exponential function, as assumed by Bloom, Canning, and Sevilla (2002). This did not show any significant effect of schooling either.

(8) Note that its chi-square test-statistic has 3 degrees of freedom because [alpha] enters three times in the equation.

(9) Sala-i-Martin (1996) presents estimates of the standard deviation of the log of GDP per capita in the OECD from 1950 to 1990. This shows a reduction from about 0.600 in 1950 to 0.350 in 1990, or by about 40% in 40 years. There is evidence of a petering out of this process from 1975 onward. The reduction in dispersion between 1970 and 1990 is only around 15%, or, in other words, about half of the degree of reduction that we find for manufacturing TFP during the same period.

(10) After reunification, the German data relate to the western part of Germany, corresponding to the former West Germany.

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Dick Frantzen, Faculty of Economics, Free University of Brussels (VUB), Lok. 2C 149. Pleinlaan 2. 1050 Brussels. Belgium; E-mail [e-mail].

The author would like to thank two anonymous referees for valuable comments that led to the improvement of the article.

Received January 2003; accepted February 2004.