This paper extends and surveys some basic quality-ladder models of education, innovation and trade in order to explain the dynamics of technological change and aggregate growth in developed countries. We analyze how the stochastic processes of innovation and export adaptation are affected by asymmetric factor endowments, transport costs, and barriers to entry in foreign markets. We show that the country-specific innovation rates are permanently increasing in the effectiveness of education and the countries’ relative endowment with labor. Trade liberalization leads to a temporary increase in the innovation rates but to a permanent increase in the rates of export adaptation.
Schumpeterian growth theory is dominated by R&D-based growth models in which stochastic processes of product innovation serve as engine of growth. Grossman and Helpman [
In response to this theoretical shortcoming, a new class of semi-endogenous growth models has emerged (e.g. Jones [
We prefer the scale-invariant, fully endogenous R & D-based growth models of the third generation. As in the semi-endogenous growth theory, the scale effect is removed by an increasing difficulty of R & D, but this deterioration of technological opportunities is compensated by a continuous improvement of researchers’ human capital. Lucas [
Due to the convincing explanatory power with respect to the stochastic innovation dynamics in specific industries as well as with respect to the growth dynamics in the aggregate economy, quality-ladder models of all three generations have been usefully applied to the new trade theory in order to analyze R & D-based growth and trade in the global economy. Two classes of open-economy quality-ladder models can be distinguished. A large part of these models is based on the North-South setting where the world economy consists of the developed countries (or regions) in the North on the one hand, and the developing countries (or regions) in the South on the other hand. This framework is particularly adequate to study international product cycles driven by stochastic sequences of innovations in the North and imitations in the South (e.g. the survey by Stadler [
The other class of models deals in a complementary sense with the North-North setting where the world economy consists of two developed countries (or regions). This framework is extremely appropriate to study patterns of trade between similar countries and the effects of trade restriction or liberalization. While Grossman [
The paper is organized as follows. Section 2 presents an asymmetric quality-ladder model of education, R & D-based growth and North-North trade. Section 3 considers the role of iceberg transport costs. Section 4 studies the role of imitation and barriers to entry in foreign markets. Section 5 summarizes and concludes.
We consider a global economy consisting of two developed countries, the home (H) and the foreign (F) country. The world is populated by a fixed measure of worker-households in the home country,
In both countries
where
is a quality-augmented CES consumption index, where
At each point in time, households allocate their income
taking the product prices
for all product varieties j, where
where
Each household supplies human capital H to production, R & D, and education. When the share
where
where
where the country index is omitted for brevity. In addition, steady-state growth imposes
such that the time path of consumer spending in both countries is given by
Furthermore, in a steady-state equilibrium the growth rates of consumer spending and human capital must coincide. It immediately follows from (2.6) and (2.8) that
Thus, the growth rates of human capital and consumer spending depend positively on the effectiveness of education
All consumer goods are manufactured with human capital as single input. One unit of human capital LH pro- duces one unit of output, regardless of the industry and the quality level. Therefore, each firm has a constant marginal cost which is equal to the wage rate
According to the individual demand functions (2.3), all quality leaders in the home country realize the flow of profits
and all quality leaders in the foreign country realize the flow of profits
These profits are equal only if the wage rates and, hence, the product prices in the two countries coincide.
The quality of consumer products is sequentially upgraded by vertical product innovations. Every industry is characterized by a symmetric quality ladder where each innovation provides a quality level,
They are assumed to depend proportionally on the human capital
ability
that pay nothing if the research fails but pay the flow of profits
where the quality-level index
Absence of arbitrage opportunities implies that the expected return on equities of innovators must equal the return on an equal size investment in a riskless bond, i.e.
and
where the expected rate of return on equities of innovators consists of the dividend rate
By substituting (2.7), (2.10), (2.11), and (2.13), we obtain the no-arbitrage condition
where
Since there is a continuum of industries and the returns from participating in R & D races are independently distributed across firms and industries, each household investor minimizes risk by holding a diversified portfolio of stocks.
At each point in time, a measure
For the measures of
If the aggregate innovation rate of home firms is higher than the aggregate innovation rate of foreign firms, then the home country is characterized by a higher market share and vice versa.
The average quality of all available top-of-the-line consumer products is
ity of each product j jumps up from
such that the growth rate
depends proportionally on the aggregate innovation rate of all firms in the world.
The quality index can be decomposed into
and the aggregate quality of the foreign firms’ products is
The time derivatives are
and
and imply the growth rates
and
These growth rates are constant over time only if
Dividing the quality indices by the market shares as determined in (2.17) gives
The average quality of products manufactured by the firms in both countries is equal, regardless of the factor endowment.
The labor markets of both countries are perfectly competitive. Workers can move freely across firms and sectors within each country but not across countries. As was shown above, in both countries the share
and from (2.12) that the aggregate demand in the research sector amounts to
Thus, full employment of workers in the home country implies
and the full employment of workers in the foreign country implies
Substituting for
and
It follows from (2.22) and (2.23) that
The country-specific innovation rates depend on the countries’ relative endowment with labor.
We are now able to solve the model for a steady-state growth path as an equilibrium time path along which all endogenous aggregate variables grow at a constant rate. We conclude from (2.9), (2.18), (2.20) and (2.21) that
The global steady-state innovation rate is therefore determined by
By substituting this expression into (2.24), we obtain the country-specific innovation rates
which depend not only on the effectiveness of education but also on the relative size of a country. This “relative scale effect” diminishes at the global level.
The country-specific consumption index (2.4) reads
and grows in both countries at the scale-invariant rate
which can be decomposed into quantity growth at rate
In contrast to the quality-ladder models of the first and second generations, the steady-state growth rate neither depends on the worker population as in the scale-variant growth models nor on the population growth rate as in the semi-endogenous growth models. Instead, economic growth is endogenously explained in terms of educational and technological conditions. The realization of innovations becomes progressively more difficult as the quality levels climb up the ladders, but researchers compensate for this deterioration of technological opportunities by continuously raising their human capital. Education and innovation are closely related to each other and appear as in-line engines of economic growth.
Trade is not as free as assumed in the previous model. Instead, it is costly for firms to trade consumer goods across countries’ borders. Dinopoulos and Segerstrom [
To keep the model simple, we use the symmetric version of the quality-ladder model as introduced in the previous section to serve a basic scenario for analyzing the influence of trade costs between the two structurally identical countries. While Dinopoulos and Segerstrom [
If we normalize the common wage rate to
This gives a quality leader’s flow of profit
Trade restrictions, measured by the transport-cost parameter
The innovation rate, targeted at any industry j, is again given by
such that free entry into each R & D race implies that the stock-market value of a quality leader is
Taking into account (2.7), we obtain the no-arbitrage conditions
Substituting (3.2) and (3.4) yields
where
In both countries the share
and from (3.3) that the aggregate demand in the research sector is
Full employment of workers in both countries implies
Substituting for IL from (3.5) yields
This condition can now be used to analyze the steady-state growth equilibrium.
In the symmetric balanced-growth equilibrium, (2.9) and (2.18) imply that
The country-specific innovation rates in each industry as well as in the aggregate are therefore determined by
and depend on educational and technological conditions but not on the transport costs. The consumption index
where education and innovation are again the in-line engines of economic growth.
We now consider a certain point in time where a trade-liberalization measure occurs that takes the form of a permanent reduction in the transport costs. A comparative-static analysis of (3.7), given the long-run innovation rate h, shows that
Trade liberalization therefore induces an increase in the quality index. Since neither human capital LH nor the quality index
Transport costs are not the only barrier to trade. There is convincing empirical evidence that some firms do export while others do not. In a seminal paper, Melitz [
The innovation process is modeled as before. Challenger firms participate in R & D races in order to invent higher-quality products. The first firm to succeed in developing the next higher quality product in an industry is granted a patent and takes over the local market from the previous quality leader. At the same time, competitive fringe firms in the foreign country imitate without any cost and take over the production abroad. Production by the foreign imitating firms continues until the new quality leader in the home country has learned how to export and to take over the foreign market, too.
The model is solved for a steady-state equilibrium where half of all products originate from the home and the other half from the foreign country. Home firms do not improve the quality of products originating from the foreign country and vice versa. Furthermore, it is assumed that even exporting leaders have no incentive to improve the quality of their own products.
When the common wage rate is normalized to
and the flow of profits from exporting
Due to Bertrand competition, imitating firms realize no profits, that is
Following Segerstrom and Stepanok [
Second, quality leaders which only produce for the local market invest in R & D to learn how to export, i.e. to adapt the higher-quality products to the less familiar markets in the foreign country. Non-exporting quality leaders invest
where the inverse of
According to (3.3), the stock-market value of a non-exporting local quality leader is
Using (4.1) and (4.4), the Bellman equation for non-exporting leaders can be written as
where
Substituting (4.7) back into (4.6) to eliminate
where
where its stock-market value can be derived from (4.5) and (4.7) as
Substituting (4.1), (4.2), and (4.10) into (4.9) and taking into account (2.7) gives
This expression can be substituted into (4.8) to obtain the no-arbitrage condition
which determines the export adaptation rates of quality leaders, given the long-run innovation rates.
There are four types of firms that sell the products available in a country: home leaders with a measure
Due to the assumed symmetry across countries, the share of product varieties produced by home exporters equals the share of product varieties produced by foreign exporters, that is,
For the world market shares
An increase in the innovation rates leads to a greater market share of exporting leaders and to lower market shares of non-exporting quality leaders and imitators.
In both countries, the quality index of all available products can be decomposed into
the aggregate quality of the non-exporting domestic firms’ products is
and the aggregate quality of the domestic Bertrand firms’ products is
The time derivatives are
and
It can be shown that the growth rates of these quality indices are equal only if
and
Taking into account the market shares (4.13), this implies
indicating that the average quality of the products manufactured by non-exporting quality leaders is higher than the average quality of products manufactured by the exporting quality leaders which in turn is higher than the average quality of products manufactured by the imitating Bertrand firms.
In both countries the share of workers’ human capital
Substituting (4.11) and taking into account that, due to the modified assumptions in this section,
Therefore, the innovation rates in specific industries as well as in the aggregate are determined by
and thus depend again on the educational and technological conditions. As in the previous models the consumer index grows at the scale-invariant rate
with education and innovation as the two in-line engines of economic growth.
Let us again consider a certain point in time where a trade-liberalization measure occurs that takes the form of a permanent reduction in the transport costs. Having solved for the steady-state innovation rate, we can use (4.12) to determine the export adaptation rate. A comparative-static analysis shows that
When barriers to entry in foreign markets are reduced, export becomes more profitable. Local quality leaders invest more in export adaptation such that the share of exporting firms increases.
The higher rate of export adaptation reduces the average length of an international product cycle, since the expression
We present a class of quality-ladder models of education, innovation and export adaptation to explain the evolutionary dynamics of industries, economic growth, and international trade. Semi-endogenous quality-ladder models have accomplished a valuable task by removing the scale effect present in quality-ladder models of the first generation. A shortcoming of these non-scale models is, however, that the innovation and per-capita growth rates depend proportionally on population growth. Without population growth these models predict a stationary equilibrium without innovation and growth.
We offer an alternative mechanism of non-scale growth by relying on the education and human-capital accumulation of workers. Education has not only a direct effect on economic growth but also an indirect effect via an acceleration of the innovation and export adaptation processes. The effectiveness of the educational system is therefore most important for industry evolution, growth dynamics, and trade patterns. The scale effect is eliminated by the assumption that the realization of innovation and export adaptation becomes more difficult as the quality levels of products increase, but this deterioration of innovation and export opportunities is compensated by an improvement of the workers’ human capital.
The industry dynamics is generated by innovation and export adaptation. Trade liberalization leads to a temporary increase in the innovation rates and to a permanent increase in the export adaptation rates. In addition, the country-specific innovation rates are permanently increasing in a country’s relative endowment with labor.
As is well-known, Northern firms not only engage in innovation and export adaptation, but also in transferring technology into the less developed South, while Southern firms engage in imitative activities to copy the advanced technologies (e.g. Dinopoulos and Segerstrom [
ManfredStadler, (2015) Education, Innovation and Growth in Quality-Ladder Models of North-North Trade. Modern Economy,06,1115-1128. doi: 10.4236/me.2015.610107