# International Product Life Cycle Theory Essays About Education

In this section we first develop a measure of product maturity drawing on the insights from product life cycle theory and then compute the average maturity of our countries’ export portfolios. We then present the estimation strategy, as well as the data before turning to our results in Sect. 5.

### 4.1 Measuring product maturity

Our measure of product maturity is based on one of the well established empirical regularities found in the product life cycle literature. Total sales of a product in the market first increase at an increasing rate, then at a decreasing rate and finally decline, tracing out an S-shaped diffusion curve (Klepper 1996). We therefore want to develop our measure of maturity at the product level by looking at the dynamics in market volume at the global level. Following Audretsch (1987) and Bos et al. (2013), we characterise the life cycle stage of a product using the first and second moment in its global export volume.

We calculate product maturity for each of the 427 SITC four-digit products over the period 1988–2005 using global-level export data retrieved from the UN-COMTRADE database. The problem with our real trade data is that we do not have the sales volumes for individual products at more disaggregated levels. Instead we have four-digit product classes in which still any number of different products, potentially all in different stages of their respective life cycles, are being added together. However, it is important to note that our product maturity measure captures the average life cycle stage of these product classes. More importantly, our measure can correctly identify the rejuvenation of the product class that is the result of replacing a mature with a new product. We demonstrate these features of our measure through a simulation exercise below. The findings confirm that our measure indeed captures the product life cycle stage in data we have generated ourselves and four-digit product is the right product category for the purpose of this paper.

To this end we generated artificial global sales volumes for 20 products and 20 periods using a standard logistic curve we took from Pan and Kohler (2007):

\begin{aligned} Y(t)={A_0+{{A_1}\over {\left( 1+A_2 e^{(-A_3(t-A_4))}\right) }^{{1}\over {A_2}}}} \end{aligned}

(13)

where $$A_0$$ is the lower bound and set to 0, $$A_1$$ is the upper bound and set to 100, $$A_2$$ sets the inflection point where maximum growth occurs and is set to 0, 5, $$A_3$$ is the average growth rate, set to 0, 5 and $$A_4$$ is the time at which maximum growth is reached and set to 10. The resulting 20 simulated and S-shaped sales paths are shown in Fig. 2.
It is straightforward to see that fitting a second order polynomial to the simulated data in a window of say 5 periods and obtaining the first and second moment of sales (growth and growth in growth) would be sufficient to characterise the product life cycle stage. Suppose we estimate and compute:

\begin{aligned} ln(Y_{t})=\gamma _0+\gamma _{1}t+\gamma _{2}t^2+\varepsilon _{t} \end{aligned}.

(14)

The exact numerical values are not relevant in this case. If we find a positive coefficient $$\gamma _1$$ and negative coefficient, $$\gamma _2$$ on the quadratic term the product is to the right of the inflection point and might be called mature. If both $$\gamma$$’s are positive the product must be to the left of the inflection point and might be called early stage. Moreover, taking as our measure of maturity the first derivative of the fitted second order polynomial with respect to time ($$\gamma _1+2*\gamma _2*t$$), gives us a continuous measure of maturity, where higher (less negative) values characterise less mature products.
One issue with our real trade data is that we do not have the sales volumes for individual products. Instead we have 4-digit product classes in which still any number of different products at different stages of their respective life cycles are being bundled together. It is clear from Fig. 2 that portfolio’s composed of products in different stages of their life cycle can create quite complex sales dynamics, even if we abstract from all kinds of shocks that can affect sales in addition to the product life cycle. Furthermore, by adding new products and dropping mature ones from existing portfolio’s, the possibility arises that the maturity of a given portfolio actually decreases over time. We can illustrate these cases with our simulated sales data. First we create four portfolio’s of products (artificial product classification codes if you will). One portfolio consists of new products (1–5), one of slightly more mature (6–10), the third of even more mature (11–15) and the fourth of products where there is hardly any growth in sales (16–20). Of course our maturity measure should correctly rank them. Given that we have generated the data we can measure the growth and growth in growth of sales precisely and our maturity index becomes:

\begin{aligned} dln(Y_{t})/dt=\gamma _{1}+2*\gamma _{2}*dt \end{aligned}

(15)

where $$dt=1$$.13 We then obtain the Fig. 3.
One can see that the composed portfolios still retain the imposed S-shaped sales pattern (left panel) and our maturity measure accurately captures the average lifecycle stage of the four portfolios.14 In Fig. 4 we show the maturity index for a baseline portfolio (1–10) where in period 4 we took out product 10 (the most mature product) in the “drop 10” simulation and added product 1 (the newest product) in the “add 1” simulation. It is clearly visible in this figure that our maturity index picks up the rejuvenation of the portfolio that is the result of replacing a mature with a new product. But it does so only with a lag. We see that adding a very early stage product (in the near horizontal left part of the S-shape) to replace a product around the inflection point where sales growth is maximised (recall this is around year 10 or for product 10 in year 1 by construction) will “fool” our maturity index and cause it to initially drop below the baseline portfolio score. Still, after only a few periods and faster when products exit closer to the horizontal part on the right, our index will quickly show an increase relative to the baseline. In the real trade data it is most unlikely that products will exit the portfolio at the peak of their global market growth, so we do not expect this “fooling”—effect to be a big problem. Moreover, as many more than 10 product varieties are typically in a single 4-digit product class, it is unlikely for any single product to have a noticeable impact. Still this figure illustrates that over time, if many new products and product varieties enter an existing product class, our proposed maturity index may actually go up, signifying the portfolio of products in that class becomes less mature over time.
Before we can take our index to the data, however, we need to deal with the fact that some changes in global export sales growth (and growth in growth) do not originate from technology and the individual product life cycle, but rather come from the demand side, affecting all product sales (growth rates) at the same time. To control for the global business cycle we therefore estimate the following equation:

\begin{aligned} ln(exp_{it})=\gamma _0+\gamma _{1i}t+\gamma _{2i}t^2+\gamma _{3} ln(exp_{t})+\varepsilon _{it} \end{aligned}

(16)

where $$ln(exp_{it})$$ is the log of global exports of product i at time t in constant dollars; t and $$t^2$$ are time (set to 1 at the start of the relevant time window) and time squared, respectively; $$ln(exp_t)$$ is the log of global total exports of all products; $$\varepsilon$$ is the disturbance term. We can then set our measure of maturity, $$M_{it}$$, equal to the effect of an increase in time t on the log of global exports $$ln(exp_{it})$$, controlling for global demand shocks. $$M_{it}$$ is thus defined as:

\begin{aligned} M_{it}=\frac{\partial ln(exp_{it})}{\partial t}=\gamma _{1i}+2\times \gamma _{2i}\times t, t=1,2\ldots 9 \end{aligned}

(17)

where we have taken a 9 year window to estimate the moments of total global exports. Assuming the typical S-shaped pattern of sales over the life cycle we can show that the lower (more negative) $$M_{it}$$ is, the more mature a product is. For early stage products both coefficients are typically positive, whereas for more mature products first $$\gamma _{2i}$$ and then $$\gamma _{1i}$$ will first show up insignificant and than negative in the regression.

We calculated $$M_{it}$$ for each of the 427 SITC four-digit products over the period 1988–2005 using global-level export data retrieved from the UN-COMTRADE database.15 More specifically, we estimate Eq. (16) taking a rolling window of 9 years, namely 1988–1996, 1989–1997, 1990–1998, 1991–1999, 1992–2000, 1993–2001, 1994–2002, 1995–2003, 1996–2004, 1997–2005 setting the first year to 1 to calculate $$M_{it}$$ as in Eq. (17) and taking the average of all $$M_{it}$$ over the different sub-samples. This implies that only if we estimate different coefficients per window, the corresponding average maturity for that window will change over time. In this way, we allow for maturity to change over time in a non-linear fashion and movements up and down are allowed.16

Four important aspects of our measure $$M_{it}$$ are worth pointing out at this stage. First, in contrast to a binary measure to classify industries into either “growing” or “declining” as in Audretsch (1987), our measure is continuous.17 This property permits a sensible ranking of products based on maturity level in the global export market.

Second, our measure is time-varying. In other words, we allow products to move from one stage of the life cycle to the next and back. This latter property may seem undesirable, but in fact there are good reasons not to exclude such dynamics by construction. As we have illustrated above, mature product categories can rejuvenate through the upgrading of existing products and/or the introduction of new product varieties in the same product category. Such rejuvenation could set off a new S-shaped pattern in global sales that we want our measure to pick up. In this respect, our measure also differs from Bos et al. (2013) who evaluates Eq. (17) at the mean of t for all industries and does not allow for the changes of product maturity over time.

Third, we based our measure on the global exports of a product. Under the assumption that total global exports correlate with total global production and sales, this will reflect the true product life cycle. Our proxy, however, will also carry some exogenous elements that reflect the growth potential of products in the global market place. As we are interested in the composition of countries’ export bundles, however, it seems only fitting we consider the global market for classifying products as mature or early stage.

Finally, we prefer a product specific measure based on global export volumes over the alternative of country level maturity measures as this measure is less prone to endogeneity problems in the country level growth regressions that follow.18 Table 1 provides descriptive statistics on these products, aggregated to the one-digit level.19 According to Table 1, we find that manufacturing products account for more than 70% of world total exports. The product maturity exhibits significant variations both across and within one digit categories.
Table 1

Descriptive statistics

A first check on our maturity measure is to simply look at which products actually get classified as mature and young. Ranking products based on their maturity in the global market yields Tables 8 and 9 in the “Appendix”, which show the maturity and ranking of the 50 products with the lowest and highest maturity values at the end of our sample period (i.e., 2005), respectively. The corresponding rank number at the start of the period (i.e., 1988) is also given. The pairwise correlation between maturity 2005 and maturity 1988 is −0.021, which is not significant at any conventional level. The negative correlation may imply that products classified as mature in 1988 are classified as newer in 2005 and the other way around. The reason is that most products apparently have a (very) negative $$\gamma _2$$, such that they start with a very high $$M_{it}$$ (low maturity) and end with a very low value (high maturity), whereas the products with a positive $$\gamma _2$$ tend to start from a very low $$\gamma _1$$. This is consistent with a more or less random distribution over the life cycle stages as early stage products would be expected to have low average growth (captured by a low $$\gamma _1$$) but high growth in growth (captured in a positive $$\gamma _2$$), whereas mature products have low average growth and negative growth in growth. The Spearman rank correlation (0.053), however, shows that the ranking at 1988 and 2005 is independent (p value is 0.254).

The products at the extremes of the ranking, are perhaps not making a very convincing case at first glance. In particular, the list of least mature products includes several raw materials, ores, basic metals and food products that cannot be considered early stage products. Our measure is clearly sensitive to the 90s resource boom. Rising demand for many internationally traded raw materials, ores and energy resources have caused the trade volumes for those commodities to increase faster than the global trade volume for which we correct. Consequently, the boom in commodities trade is interpreted by our measure as a rejuvenation of these commodities, when of course nothing has happened to the product itself. We will leave these products in for now, exactly because this will bias the estimations against finding the results we are most interested in.20 Of course we have also excluded these products in robustness tests. The reader should keep in mind, however, that what we measure as maturity is a rough proxy and measurement error is an issue.

The second check is to explore the trend of major products in the global market. Figure 5 shows the maturity of the most important five products (in terms of their size in the global trade) over time. As can be seen from the figure, most manufacturing products are relatively stable and mature. Only petrol oil is moving up and down significantly. Obviously this reflects the peculiarities of global oil markets.
The third check is to explore the volatility of product maturity over time. We want to eliminate those products that exhibit too much volatility over time, e.g. oil. We therefore computed the standard deviation of maturity for each product over the entire sample period. Figure 6 shows the maturity of four products, for which the standard deviation of maturity was above the 99 percentile of the sample. It too suggests that oil products should be treated with caution in our analysis. We keep these “products” in our sample for now, however, to avoid selection bias in our empirical analysis below.

### 4.2 Measuring the export maturity of countries

The overall maturity associated with a country’s export basket, $$M^{All}_{jt}$$, in turn can now be defined as

\begin{aligned} M^{All}_{jt}= \sum _is_{ijt}M_{it}=\sum _i\frac{exp_{ijt}}{exp_{jt}}M_{it} \end{aligned}

(18)

where $$M^{All}_{jt}$$ is a weighted average of product maturity $$M_{it}$$ (at the global level) across all products for country j over time t. The weights are the export shares of these products in country j’s total exports.
To get a first impression of our export maturity measure $$M^{All}$$, Fig. 7a shows that on average, a weak positive relationship exists between export maturity and the level of GDP per capita. High income countries appear to have younger export baskets. Figure 7b plots the export maturity measure against the growth rate of GDP per capita. We do not find a strong association, suggesting that the relationship between export maturity and growth might be heterogeneous across countries.

To check the robustness of our results, we also use four other country-level maturity indices by considering sub-samples of products. To account for the peculiarities of commodities, in particular oil, we compute two measures M1 and M2. M1 excludes the oil-related products, i.e. those for which the first digit product code is 3, whereas M2 includes only the manufacturing products, i.e. those for which the first digit is between 6 and 9.

A handful of studies observe that product quality varies hugely within finely disaggregated products (Schott 2004; Hallak 2006; Khandelwal 2010; Hallak and Schott 2011). To examine whether our results are sensitive to product quality variations across countries, we adopt two other measures M3 and M4 by selecting a sub-sample of products that are more homogenous in quality. Following Sutton and Trefler (2011), we compute M3 using informative products, i.e. products with small quality range across countries. We calculate M4 excluding a category of differentiated products, i.e., products without organised exchange markets or reference prices based on a classification developed by Rauch (1999). Table 2 reports pairwise and ranking correlations of all of our five differently constructed measures. We find that these measures are positively and significantly but certainly not perfectly correlated using both pairwise correlations and ranking correlations.
Table 2

Correlation matrices for the export maturity indices (pooled data)

We conclude from these results that our time varying, continuous measure of export maturity reflects something that is correlated with the alternative measures suggested in the literature, is easy to compute based on conventional trade data and is founded in well established empirical regularities over the product life cycle. The proof of the pudding, however, is in the eating. Our measure picks up something of substance if we can show it has explanatory power in a panel growth regression, to which we turn below. For our purpose, we will use $$M^{All}$$ in the main analysis and use the other four maturity measures in our robustness analysis.

### 4.3 Other variables and data

Economic growth (g), measured as the change of the real GDP per capita is taken from the Penn World Table, version 6.3 (PWT 6.3). To estimate a growth regression we obviously require, in addition to our country level export maturity measure, the standard set of control variables. Levine and Renelt (1992) find that most of the independent variables in standard growth regressions are fragile. Since the effect of export maturity on growth is our primary interest, we minimise the data mining bias for the other variables by closely mimicking the regression in Hausmann et al. (2007). The initial level of GDP per capita $$gdp_0$$ (2005 international purchasing power parity (PPP) dollars chain index) is set equal to the start of the different periods.21 The capital to labor ratio (KL) is computed as the physical capital stock divided by the total number of workers. We construct the capital stock (K) applying the perpetual inventory method as in Hall and Jones (1999).22 Human capital (HC) is measured as the average years of schooling of the population that is at least 25 years old and is obtained from the Barro and Lee (2010) database on educational attainment.23 The rule of law index (Law), ranging from 0.5 (low institutional quality) to 6 (high institutional quality) is retrieved from the International Country Risk Guide (ICRG) and our de jure trade openness measure (Jure) is taken from Wacziarg and Welch (2008). It takes a value of one when a country’s trade regime is liberalised, and zero otherwise. In line with Lederman and Maloney (2012), we further add the Hirschman-Herfindahl index as a measure of export concentration, which captures the overall structure of a country’s export using the COMTRADE data. They find that export concentration has important implications for understanding the characteristics of a country’s export basket in relation to growth. The conditioning variable that we rely on to estimate the latent class model is the stage of economic development for which we proxy by using the level of GDP per capita (GDPPC), retrieved from PWT 6.3. Table 3 summarises the definitions, sources and descriptive statistics of country-level variables used in our analysis.
Table 3

Descriptive statistics—growth regression

### 4.4 Empirical methodology

A general investigation of the relationship of export maturity and economic growth starts with the following standard growth regression:

\begin{aligned} g_{jt} =\beta _0 + \beta _1 M^{All}_{jt} + \beta ^\prime Z_{jt} + \varepsilon _{jt} \end{aligned}

(19)

where j denotes country and t denotes time; g is per capita GDP growth; $$M^{All}$$ measures the maturity of a country’s export basket; To prevent simultaneity or reverse causality, we take the initial level of the export maturity measure at the beginning of four different time periods (i.e., at 1988, 1993, 1998 and 2003); $$\beta ^\prime$$ is a $$1\times n$$ parameter vector; Z is a $$n \times 1$$ vector of control variables that contains the usual determinants of economic growth described above, including a country’s initial level of GDP per capita ($$gdp_0$$) to capture beta-convergence, the capital to labour ratio (KL), the level of human capital(HC) and rule of law index (Law), a de jure trade openness index (Trade) and a trade concentration index (HHI); finally, $$\varepsilon$$ is an i.i.d. error term.

One major drawback of Eq. (19) is that the relationship between the maturity of exports and economic growth is now assumed to be identical across countries. Therefore, the estimated parameters, e.g., $$\beta _1$$ and $$\beta ^\prime$$ are common to all countries by construction. In practice, it may well be the case that this relationship is not homogeneous and Eq. (19) masks potentially important parameter heterogeneity across countries.

We therefore adopt a flexible modelling framework in which the export maturity-growth relationship is allowed to be heterogeneous across different groups of countries (or growth regimes), depending on the stage of economic development. Two strands of literature motivate our choice of relying on GDP per capita as a proxy of economic development. The first strand has examined the heterogeneity of growth experience of countries in general and has well established the substantial differences in the determinants of growth between developing and developed countries. These studies (e.g., Durlauf and Johnson 1995; Canova 2004; Papageorgiou 2002) typically use the initial level of GDP per capita as a regime splitting variable to examine multiple growth regimes. However, such an ex ante classification is somewhat arbitrary and subject to debate since the appropriate cut-off point is not always clear. In contrast, our approach endogenizes the cut-off points and is thus much more flexible. The second strand has established a non-linear relationship between export structure (specialised vs. diversified) and economic growth (Imbs and Wacziarg 2003; Aditya and Roy 2007; Cadot et al. 2007; Hesse 2008). These papers typically find that the relationship differs by the development stage of countries as proxied by GDP per capita.

We thus treat the stage of development as a latent variable, and use a latent class model to endogenise the sorting of countries into different growth regimes. To model the latent variable, we use a multinomial logit sorting equation, and include the stage of development, proxied by real GDP per capita, to estimate the likelihood of being in a particular growth regime. Our conditional latent class model consists of a system of two equations: an equation to estimate the maturity-growth nexus for each regime, and a multinomial sorting equation where the regime membership is a function of the development stage, i.e. GDP per capita.

To allow for endogenous sorting into regimes $$k(=1,\ldots K)$$, we can rewrite Eq. (19) as follows:

\begin{aligned} g_{jt|k} =\beta _k + \beta _{1|k} M^{All}_{jt} + \beta ^\prime _k Z_{jt} + \varepsilon _{jt|k} \end{aligned}

(20)

where $$k=1,\ldots ,K$$ indicates the regime and K refers to the (endogenous) total number of regimes. Each regime has its own parameter vector $$\beta$$. In other words, $$\beta _0$$, $$\beta _1$$, $$\beta ^\prime$$ are allowed to differ across regimes.

To estimate Eq. (20), we must first find the suitable number of K. As this is not a parameter to be estimated directly from Eq. (20) Greene (2007

## International Product Life Cycle Essay

INTRODUCTION

In this essay will explain and evaluate the stages of the international product life cycle and identify locus of operations and target market at each stage. We also will identify the different dimensions of the international product mix with company illustrations and examine the new product development process and the activities involved at each stage in international markets. Finally we will also will examine the degrees of product newness and address international diffusion processes and providing some examples regarding international product life cycle.

IPLC was create by Raymond Vernon in late 60s.It was a model that explain about the international pattern of organisation.Product life cycle theory divides the marketing of a product into four stages: introduction, growth, maturity and decline. When product life cycle is based on sales volume, introduction and growth often become one stage. For internationally available products, these three remaining stages include the effects of outsourcing and foreign production. When a product grows rapidly in a home market, it experiences saturation when low-wage countries imitate it and flood the international markets. Afterward, a product declines as new, better products or products with new features repeat the cycle.Vernon focused on the dynamics of comparative advantage and draw inspiration from the product life cycle to explain how trade patterns change over time.
His product life cycle described an internationalization process where in a local manufacturer in an advanced country begins selling a new, technologically advanced product to consumers in its home market. Production capabilities build locally to stay in close contact with its client and to minimize the risk that will get.
As demand from consumers in other markets rises, production increasingly shifts abroad enabling the firm to maximize economies of scale and to bypass trade barriers. As the product matures and becomes more of a commodity, the number of competitors increases.

Finally, the creator from the advanced nation becomes challenged in its own home market making the advanced nation a net importer of the product. This product is produced either by competitors in lesser developed countries or, if the producer has developed into a multinational manufacturer, by its foreign based production facilities.

The IPLC international trade cycle consists of three stages which are new product,maturing product,and standardizing product.Below are the explanation of the stages:

Introduction
When a product is first introduced in a particular country, it sees rapid growth in sales volume because market demand is unsatisfied. As more people who want the product buy it, demand and sales level off. When demand has been satisfied, product sales decline to the level required for product replacement. In...

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