The Learning Curve and the Yield Factor:
The Case of Korea’s Semiconductor Industry
by
Sangho Chung*
April 2000
*Managing Editor
Korea Economic Weekly
154-11 Samsung-dong, Kangnam-gu 4th Fl.
Seoul 135-090, Korea
Phone: 822-3430-2151
Fax: 822-3430-2170
Email: schung01@koreaeconomy.com
Abstract
This article attempts to find out how the Korean economy has grown so rapidly in a short time span of less than 30 years. For that purpose, it focuses on the development of the Korea's semiconductor industry—more specifically, the memory-chip segment of the industry—as a case in point.
To test the hypothesis that the learning curve effects have been significant in the memory-chip industry, we use “yield factor” (the ratio of sellable chips to total chips in a wafer) in the semiconductor production as a measure of the learning progression. That is, by tracing how the yield factor for each generation of memory chips has increased, we will be able to see how well the Korean chip makers has exploited the learning effects.
This article’s possible contribution would be the following: It improves the learning-by-doing modeling by introducing a richer set of yield data; and the unit of analysis employed throughout the article is at the firm level, which is not common in the literature dealing with the East Asian development as well as the economics of technology, thus enhancing our understanding of the industry dynamics.
I. Introduction
This article focuses on the development of the Korean semiconductor industry which has experienced an impressive growth for little more than 20 years. The country’s semiconductor chip producers at the outset focused on producing products relatively easy to manufacture using mature technology imported from abroad. By producing these products in high volume, mainly memory chips such as dynamic random access memories (or DRAMs) and static RAMs (or SRAMs), the Korean producers were able to capture the benefits of learning effects and economies of scale,1 thus reducing their production costs and diffusing capabilities acquired in the process to other product areas.
From technical perspective, the learning curve effect in the semiconductor industry is represented by yield factor, which is defined as the ratio of non-defective (and sellable) chips to total wafer area fabricated. In an initial production run for a specific generation of chips, the production yield typically remains below 10 percent. The yield, as the production experience accumulates, in many cases asymptotically increases up to 95 percent. The trajectory of this increase is called the learning curve, which since the report on the phenomenon at the U.S. airframe (or airplane fuselage) manufacturing site in the 1930s has been extensively used by many economists and management decision makers.2
Using the concepts introduced above, i.e., the yield factor and the learning curve, we can begin to analyze the Korea’s chip-making industry. That is, by tracing how the yield factor for each subsequent generation of memory chips has increased we can see how well the country's producers exploited the learning effects to increase productivity and reduce costs.
This article relies on the data collected from Dataquest, a U.S. high-tech market research firm, and a Korean semiconductor company, then tests the hypothesis that the learning curve effects were significant in the country’s industry. The first estimation uses the price data, based on the conventional learning curve models. After finding out that this estimation yields poor results in terms of coefficients well out of expected ranges and low t-statistics, the second estimation employs yield data instead of prices as a dependent variable. We find a significant learning curve effect in the estimation, with the learning ratio of 17 percent for 64K DRAMs and 9 percent for 256K DRAMs, confirming our learning hypothesis in the case of the Korean industry.
II. The Economic Literature on Learning3
Wright, an aeronautical engineer, reported in 1936 that the direct labor cost of producing an airframe (fuselage of an airplane) declined with the accumulated number of airframes of the same type produced. That is:
Y = aXb (2.1)
where Y is the direct labor cost, X is the cumulative output of airframes, a is the cost of the first unit of airframe (a > 0), and b is the learning elasticity (0 ³ b ³ -1), which defines the slope of the learning curve.
In so far as World War II airframe data were concerned, every doubling of cumulative airframe output was accompanied by an average reduction in direct labor requirements of about 20 percent. This so-called “eighty percent curve” is the precursor of the present-day learning curve. Following Wright’s article, most of research effort has been directed at finding an appropriate functional form of the learning curve and applying the theory to diverse industries, using different proxy variables for learning, such as time, cumulative output, and so on.
Joskow and Rozanski (1979) apply the learning principle to nuclear plant operations. There are two distinctive features in the model: The first one is that, unlike other models, they utilize capacity factor4 of nuclear plants as a dependent variable in their model. For them, capacity factor reflects power generation cost more accurately than do price data, the usual proxy in other models. So the higher its capacity factor, the lower is the average unit cost of power generated.5
The general form of the learning curve to be estimated is:
y = A g(x) eu (2.2)
where y = annual plant capacity factor; A = asymptotic value of the capacity factor; x = increasing measure of experience (i.e., cumulative output) (x > 0); and g(x) = function describing the nuclear operators’ learning process.
The second feature of their model is that they extend this general model to account for “supplier learning” in addition to “operator learning.” As cumulative output increases, capacity factor increases due to learning on the part of the plant’s operators. This is depicted as the function g1(x)A1 in figure 1 that approaches an asymptote A1. The effect of learning by the suppliers (e.g., plant designers and engineers) responsible for building the plant are modeled as a shift upward in the asymptotic capacity factor. This is shown as a shift in the asymptote from A1 to A2.
The model to be estimated is:
PF = A CAPb ecV g(x) (2.3)
where PF = plant capacity factor (see note 4 for definition); CAP = gross plant capacity (i.e., rated capacity); V = the month during which the plant began commercial operation (a measure of the vintage of the plant); and g(x) = operators’ learning function.6
Except the constant term A, each term in the equation represents a different source of learning: The first term represents supplier learning, the second one the effect of time and the third operator learning. The regression results reported in Joskow et al. show that the learning effect is important in nuclear plant operations, with learning rate approximately 5 percent per annum.
Generally, these empirical studies confirm the importance of learning phenomenon in reducing costs in their respective industries. We will now see how these learning economies has shaped the structure of the semiconductor industry. Gruber (1992) comes up with the following learning equation for memory chips:
Pijt = A Qbijt Vgijt Hdijt exp (uijt) (2.4)
where A = constant, price of the first unit produced; Pijt = average real selling price for memory chips of type i and generation j in year t (proxy for cost); Qijt = annual shipments for memory chips of type i and generation j in year t; b = indicator of static economies of scale (b < 0); Vijt = SQijt, cumulative shipments for memory chips of type i and generation j up to year t; g = learning elasticity (g < 0); Hijt = age of memory device, or time elapsed since production began, i.e., Hijt = 1 for the first year when generation j is introduced; d = indicator of the effect of generation age (alternative indicator for learning by doing); and uijt = random error term.
Taking log for each term:
pijt =ai + bi qijt + gi vijt + di hijt + uijt (2.5)
where lower cases indicate logarithms.
From this he finds the results as shown in table 1.
That is, Gruber finds no significant learning for DRAMs and SRAMs. Only for EPROM did he find a significant learning, which is somewhat counterintuitive. His model measures the learning effects, with cumulative shipments of semiconductor devices and the elapse of time; as well as static economies of scale, with annual shipments of memory chips. The reason he uses average selling prices as a proxy for costs is not different from others; i.e., the unavailability of cost data. So he reiterates the conditions under which reliable estimates of the learning curve can be obtained from price data. That is, (1) price-cost margins are constant over time, (2) price-cost margins change in a way controlled for by other variables, or (3) changes in the margin are small in relation to changes in marginal cost.7 Then he goes on to say that the condition (1) and possibly condition (3) are hard to apply to the semiconductor production, since it is well known that in this industry profit margins fluctuate considerably over the life cycle of a generation of chips.
Nevertheless, he argues that these fluctuations can be controlled for by using variables that are closely correlated with the margins. That is, he says that the time profile of profit margins for a given generation is U-shaped. In other words, the margins are large at the beginning and at the end of the product life cycle, while in-between margins are depressed due to entry of firms and strong competition. Current shipments for a given generation have a time profile which is inversely related to the time profile of profit margins. Thus the fluctuations of the margins can be controlled for by the current shipments variable. But given the dramatic changes in the conditions of competition over the product cycle, price-cost margins might decline steeply as the product matures, which invalidates the Gruber’s procedure to control for fluctuations in price-cost margins.8
III. Regression Analysis of the Learning Curve Model
1. The Learning-by-Doing Model
In many manufacturing operations in which tasks are performed relatively in a repetitive manner, it has been reported that workers tend to learn from their experiences thereby reducing the time and costs it takes to complete given tasks. Many empirical studies have so far attempted to find out significant cost-reduction effects of a cumulative production experience.
Confining the focus on the semiconductor industry, Webbink (1977) reports a coefficient of -0.40 on cumulative production, indicating that, with every doubling of cumulative output, cumulative average price falls by 24 percent. Dick (1991) reports regressions of industry price on lagged cumulative production (an aggregate of U.S. and Japanese firms) of 1K and 4K DRAMs based on annual data for 1974-1980 and 1976-81, respectively. He finds a 19 percent learning curve in 1K DRAMs and a 7 percent learning curve in 4K DRAMs. Gruber (1992) estimates similar models for DRAMs, EPROMs, and SRAMs, but finds no significant learning for DRAMs. Irwin and Klenow (1994) use broader dataset encompassing quarterly, firm-level data on seven generations of DRAMs over 1974-92, for which they find average of 20 percent learning curve on cumulative output.
Since cost data are kept secret by companies and thus difficult, if not impossible, to obtain, most empirical learning curve studies, including those mentioned above, have proxied unit costs with a real price variable and then regressed the log of real price on a constant term and the log of cumulative output. This procedure introduces a major problem and makes separate identification of the learning curve effect very difficult. When one uses price data for the dependent variable, several problems arise. For one thing, the justification for using the proxy is given by the assumption that prices move fairly in sync with costs, with a certain constant markup. In other words, it assumes that price-cost margins are constant over time, price-cost margins change in a way controlled for by other variables, or changes in the margin are small in relation to changes in marginal cost.9
Yet, given the tumultuous state of competition in the semiconductor market in which each generation of product is introduced by a leading firm and later faces a large number of competitors resulting in a substantial drop in prices as the product matures, price-cost margins cannot be stable over time, rather they decline steeply.10 It is even more so in the case of the East Asian semiconductor producers, including the Japanese and the Korean firms, who have frequently been the target of dumping accusations which alleged that their semiconductor components were sold at prices below actual production costs.
Aside from this difficulty, there is another problem in using a proxy variable. As evidenced from the 1996-97 downturn in the semiconductor market, the price movements in the semiconductor market before and during the period have largely been dictated by the forces of supply and demand, rather than by the learning principle by which prices fall continuously over time. Nearly three years from 1993 to 1995, the semiconductor prices, notably those of memory chips, have been propped up by unprecedented high demand from personal computer manufacturers, bringing in profit margins of over 70 percent for some chip makers. As the market conditions reversed in the early 1996, however, the chip prices fell to a level comparable to or lower than its production costs.12 Under these circumstances, it is hard to expect the price-cost margins are within a certain stable range, let alone constant. This possible wide divergence between prices and costs forces us to reconsider the feasibility of the price proxy.
To see this point more clearly, suppose that there are two firms with identical learning curve experiences. Assume that one firm adopted a forward pricing strategy in which the price was initially set very low, thereby increasing demand, market share, and production, while the other firm adopted a “cream-skimming” pricing strategy in which the initial price was set very high and lowered gradually (Intel is a typical firm that has adopted the pricing strategy of cream skimming). If one regressed price on cumulative production for these two firms, one would obtain very different estimates of the learning curve elasticity, even though the potential learning curve effects were identical by assumption. If, instead, unit cost data had been adopted, this difference would not have occurred. It shows that it is preferable to adopt unit cost rather than price data in estimating learning curve parameter, since using price data confounds the effects of pricing strategy with “pure” learning curve effects.
In general, the learning curve model estimates the extent to which the accumulation of production experience contributes to the reduction of costs. The simplest and most commonly used form of the learning curve is as follows:
Ct = A Vta1 eut (3.1)
where Ct is unit cost of production in time period t, Vt is cumulative output produced up to time period t, A is the cost of the first unit of output, a1 is the learning elasticity (0 ³ a1 ³ -1), and ut is a stochastic disturbance term.
Equation (3.1) can be rewritten in logarithmic form as
ln Ct = ln A + a1 ln Vt + ut (3.2)
The learning curve elasticity parameter a1 can be estimated by ordinary least squares, provided that relevant data on unit costs and output are available. The following formula for log transformations implies that every time cumulative experience doubles, cost will decline to s percent of its previous level:
s = 2a1 (3.3)
Therefore, if cost declines to 70 percent of its previous level as cumulative output doubles, then the learning curve is said to have a 70 percent slope. However, when one runs a simple regression for a model such as equation (3.2), regressing unit production cost on cumulative output, it is often difficult to distinguish the cost-reducing effects of learning from that of scale economies. Thus the learning curve elasticity may be over- or under-estimated by omitting the variable representing scale economies. In order to separate the two effects, we add a current output variable to the equation (3.2) as follows:
ln Ct = ln A + b1 ln Vt + b2 ln Xt + wt (3.4)
where Xt is current output, b2 is a coefficient representing the extent to which economies of scale contribute to cost reduction, and b1 is same as a1 in equation (3.1), and wt is random disturbance term.
By running both the simple regression on equation (3.2) and the multiple regression on equation (3.4), we can find the difference in coefficients for cumulative output V. The bias resulting from omitting ln Xt from the learning curve equation is called the “omitted variable bias.”12 To analyze the issues of omitted variable bias, it is convenient to introduce a new equation, called an auxiliary regression equation, in which the omitted variable—in this case ln Xt—is related to the included variable ln Vt and a disturbance term et.
ln Xt = d0 + d1 ln Vt + et (3.5)
Now label the least-squares estimates of the a’s, b’s, and d’s as a’s, b’s, and d’s, respectively. The relationship between a1 (the least squares estimate of a1) and b1 (the least squares estimate of b1) can be shown to be as follows:
a1 = b1 + d1 b2 or a1 - b1 = d1 b2 (3.6)
The bias from omitting ln Xt is simply equal to a1 - b1, which is equal to d1 b2. This omitted variable bias will be zero only if at least one of the following two conditions is satisfied:
1. d1 = 0, i.e., the log of current output and cumulative output are uncorrelated;
2. b2 = 0, i.e., unit cost of production does not depend on current production. Alternatively, returns to scale are constant.
If neither of the two conditions is met, an omitted variable bias will result, meaning that if one estimated the learning curve elasticity using equation (3.2) and omitting ln Xt, one would obtain a biased estimate of the true learning curve parameter. In many cases, one might expect returns to scale to be increasing, so it is plausible to expect that a1 - b1 will be negative. Further, since a1 and b1 are typically negative in value, a1 - b1 < 0 corresponds to b1 being smaller in absolute value than a1. In such a case, estimation of the simple learning curve equation yields a larger estimate of the learning curve elasticity (in absolute value) than if one includes the current output variable as in equation (3.4). Hence in this case the learning curve elasticity is overestimated in absolute value.13
2. The Model with Price Variable
The first equation to be estimated would be the one based on price dependent variable as in most of the conventional models. This way, we can verify the problems of the price proxy explained above. The model is as follows:
Pi = A Vb1i Xb2i eui (3.7)
where P is average selling price in real terms, i is type of memory chips, and the rest are identical to the notations in equations (3.1) and (3.4).
Taking log in each term of equation (3.7),
ln Pi = ln A + b1 ln Vi + b2 ln Xi + ui (3.8)
Following the modified model used in Joskow and Rozanski (1979) which employs the inverse of cumulative output:
ln Pi = ln A + b1 ln (1/Vi) + b2 Xi + ui (3.9)
This functional form has the advantage that it can be linearized easily and simplifies estimation.14 To obtain a real price for the memory chips, the average selling prices have been divided by the U.S. implicit price. There are two reasons for choosing the U.S. price deflator to calculate the real prices: First, the average selling price data provided by Dataquest, the source of the dataset, are quoted in U.S. dollars; and second, the U.S. market has been the largest market for memory chips for most of the observation period.15
There are 350 observations from the first quarter of 1994 to the second quarter of 1996 in the dataset for 19 companies (4M DRAMs) and for 16 companies (16M DRAMs). In addition to estimations of individual company learning parameters, industrywide learning curve has been estimated for both memory products. The regression results based on ordinary least squares are reported in tables 2 and 3 below.
As can be seen in tables 2 and 3, regression results are completely out of expectations based on our hypothesis that as cumulative output increases real prices decrease, thus taking negative coefficients in ln (1/Vi) terms. In the case of 4M DRAMs, all the regressions for 19 individual companies yielded positive coefficients in their cumulative output variable (ranging from 0.044 to 0.490), as opposed to their expected range of -1 to 0. In the case of 16M DRAMs, only five out of 16 regressions yielded negative coefficients in their cumulative output variable (-0.010 to -0.256). For all the five cases, however, coefficients are found to be insignificant based on t-test (t-statistics below 2.0).
It is also noteworthy that four out of 19 cases in 4M DRAMs and only one out of 16 cases in 16M DRAMs produced the Durbin-Watson statistic higher than 2.0, which indicates the positive serial correlation in disturbance terms.16 Some of the estimates have low F-statistics,17 implying that none of the independent variables influences the dependent variable, thus the specification is meaningless. However, we do not go into the subject in detail because the estimates obtained above are well out of the expected range anyway. The results for overall industry estimations (for both 4M and 16M DRAMs) are similar to those of the individual company regressions, yielding positive coefficient for cumulative output variable or negative but insignificant coefficient. Unreported estimations of simple regressions, regressing the log of real price against the log of cumulative output alone, did not improve the results.
The reasons for this “bad fit” can be found in the following reasons. First, the quarterly average rate of price drop has not been high enough to produce a substantial learning curve effect. The quarterly rate of price fall has been 5.30 percent for 4M DRAMs and 7.84 percent for 16M DRAMs for the two and half year period. Excluding the last two observations (the first and second quarter of 1996) in which the price drop has been steepest, the average rate of drop has been only 0.44 percent and 2.44 percent, respectively. This is because the period from 1993 to 1995 is characterized by a strong demand from PC manufacturers that has propped up the chip prices, reversing the usual pattern of steady and substantial fall in prices. Second, quarterly output has been increasing at a slower rate. Especially in the case of 4M DRAMs, the quarterly rate of increase in industry total output has been only 2.44 percent.18 The observation period of 1994 to 1996 has corresponded to the transition period in which the 4M DRAM generation was being phased out, so the output has not been increased in spite of the high demand. Third, the initial period in which the mass production has begun is not captured in the analysis for both products. In the case of 4M DRAMs, the mass production has started from 1989, while that of 16M DRAMs from 1990. Given the dataset encompasses the years from 1994 to 1996, well after the products were introduced in the market, it is understandable that a substantial part of the learning curve effects is not represented in the observation.
The weak presence of the learning curve effect in the dataset leads us to test if economies of scale have been strong instead. The following model estimates the influence of scale economies on real-price reduction by regressing the log of real price against the log of inverse of shipments:
ln Pi = ln A + b1 (1/Xi) + ui (3.10)
Since the serial correlation has been found in most of the estimations, the term AR(1) is added to the equation. Unreported estimations reveal that in the case of 4M DRAMs seven out of 19 individual company regressions had significant economies of scale.19 For the industry as a whole, the cost-reducing effect coming from economies of scale turned out to be overwhelming 44.02 percent (corresponding coefficient is -0.837). However, in the case of 16M DRAMs, none out of 16 regressions produced significant economies of scale, all of whose coefficients are positive.
3. The Yield Model
Instead of using price data which yielded results that are inconsistent with the learning hypothesis, we use yield data as the dependent variable obtained from a Korean semiconductor company, say Company A, for 64K and 256K DRAMs.20 This richer set of data includes yield and shipment data for Company A from the first quarter of 1985 to the fourth quarter of 1993, consisting of 36 observations.21 All the estimates are obtained by ordinary least squares.
The yield factor model to be estimated here is identical to equation (3.9) except that the price variable Pi is replaced by the yield variable Yi as follows:
ln Yi = ln A + b1 ln (1/Vi) + b2 Xi + ui (3.11)
where Y is yield factor, and the rest are identical to the notations in equations (3.1) through (3.7).
A simple regression model is the one without a current output variable ln Xi.
ln Yi = ln A + a1 ln (1/Vi) + ui (3.12)
This way, we can estimate the learning parameter more directly without employing proxy variable or complicated procedure to estimate production costs. The only model which analyzed the semiconductor industry based on the yield factor data is found in Gruber (1994a). However, its dataset includes only 7 quarters for 4 generations of a single product, EPROM from one European firm, SGS-Thomson, which is too limited to deduce any meaningful conclusion. Therefore, the current yield model that covers quarterly data of a Korean company for nine years for two important memory items can be considered a major improvement of the model.
First, in the case of 64K DRAMs, if one runs a simple regression where the log of yield factor is regressed against the log of cumulative output, the coefficient for ln (1/Vi) turns out to be -0.182 with the corresponding learning ratio of 11.843 percent, which implies that every doubling of cumulative output would result in the yield improvement of 11.8 percent, which in turn reduces the production costs by the same amount. Then we add a current output variable ln Xi and run a multiple regression to separate the learning effect from the cost-reducing effect of economies of scale. The estimation results in the learning coefficient of -0.176, slightly lower in absolute value than that of the simple regression with the learning ratio of 11.493 percent.
To see if omitting the current output variable would result in an estimation bias, we run an auxiliary regression equation similar to equation (3.5).
ln Xi = d0 + d1 ln (1/Vi) + ei (3.5)’
According to equation (4.6), the sign of the difference between a1 (the least squares estimate of a1) and b1 (the least squares estimate of b1) determines whether the omitting variable over- or under-estimates the coefficient. That is,
a1 - b1 = d1 b2 (3.6)
1. a1 - b1 > 0 (the learning curve elasticity is underestimated when the current output variable is omitted)
2. a1 - b1 = 0 (the current output variable has no correlation with yield; that is, constant returns to scale)
3. a1 - b1 < 0 (the learning curve elasticity is overestimated).
Plugging in coefficients obtained from the estimation of the auxiliary regression equation, a1 = -0.182, b1 = -0.176, d1 = 0.111, and b2 = -0.051, it is -0.006 » -0.005661. Since a1 - b1 is negative, equation (3.11) exhibits increasing returns to scale and the simple regression equation (3.12) overestimates the learning curve elasticity.
In the case of 256K DRAMs, the simple regression produces the coefficient of -0.165 for the ln (1/Vi) term and the corresponding learning ratio of 10.807 percent. The estimation for the multiple regression with the current output variable ln Xi results in the learning coefficient of -0.145 with the learning ratio of 9.572 percent.
Running an auxiliary regression equation to check the presence of omitted variable bias yields following numerical results: a1 = -0.165, b1 = -0.145, d1 = -0.277, and b2 = 0.071; therefore, a1 - b1 = -0.020 » d1 b2 = -0.019667. That is, a1 - b1 < 0 and the equation (3.11) exhibits increasing returns to scale and the simple regression overestimates the learning curve elasticity. All the estimates for both memory products are reported in tables 4 and 5 below.
However, it is notable that Durbin-Watson statistics turn out to be 1.476 for 64K and 0.941 for 256K DRAMs which are well below 2, an indication of the presence of positive serial correlation in the residuals. In order to incorporate the serial correlation in the equation, the first-order autocorrelation term AR(1) is added. With the new regression, we get a better fit in terms of the Durbin-Watson statistics close to or higher than 2 as shown in the fourth row of each table below.
As reported in tables 4 and 5, the learning ratios of 16.841 percent (for 64K DRAMs) and 9.382 percent (for 256K DRAMs) are consistent with our hypothesis that with every doubling of cumulative output production yield increases by the same percentage. However, the learning slopes are not as steep as we expected, usually reaching as high as 30 percent. The reason for this rather low ratios can be traced to the following fact: That is, the year when Company A introduced 64K DRAMs to the market was 1984, and the first year for 256K DRAMs was 1985. Meanwhile, the observation period in our analysis starts from 1985 and 1986, respectively, one year later than each product’s market introduction year. Due to this lack of data for the year the learning curve effect could have been most pronounced, the learning curves for the two memory items are estimated at approximately 17 percent and 9 percent as reported in the tables above.
The figures 2 and 3 below have been plotted using the log of the inverse of cumulative output as X-axis and the log of yield as Y-axis. These learning curve diagrams resemble fairly well to the ones drawn by other studies, including Joskow and Rozanski (1979; p. 163).
Aside from the above empirical evidence which shows that the Korean semiconductor industry has grown by rapidly moving down the learning curve,22 there is an ample number of anecdotal evidences demonstrating the Korean industry’s high production yield and resulting high productivity. The yield of 4M DRAMs produced by the Korean chip makers has, for example, run up to 95 percent in 1995, the year at which the product has reached the maturity stage. According to officials of a Korean company, although varied by company and product, the yield of the Korean chip makers is in general 10 percent higher than that of the Japanese, and the yield of Japanese chip makers is again 10 percent higher than that of the American.
In the semiconductor manufacturing process, from raw wafer manufacturing to circuit design, mask generation and wafer processing, almost all processes are automated, so there is little room for quality variations. In these pre-assembly processes, the purity of silicon wafers, the quality of processing chemicals, and the stricter standard of the clean-room operations are important factors affecting the processing yields. But at the stage of assembly and final inspection, human factors largely determine the production yield. This is where “finger tips” of young female workers of Korea have proven important. For example, in a Samsung assembly plant that employs 15,000 female workers, the average age of assembly workers is 21, which is 10 years younger than that of their counterparts in Japan.23 The reason the Korean chip makers have been able to enjoy higher yield is given also by the fact that, similar to the cost advantage of the Japanese makers, most of the Korean firms are large conglomerates with affiliates in consumer electronics, which require components with less stringent performance standards than military or industrial-purpose chips, thus helping to achieve higher yields.
VI. Conclusion
The chip-making industry of Korea deserves a special attention because of its great reliance of the production technology on foreign sources and its intense efforts to internalize the imported technology into its own production, thus making a good study subject for the learning-by-doing theory. Nevertheless, no full-length academic endeavor has been made on the subject except some of the contributions narrowly focusing on the case of one company. Such examples include Kim (1997) and Choi (1996).
When analyzing an industry, there may be two distinct approaches; detailed descriptive approach and quantitative approach. Both are complementary in the sense that what the quantitative part cannot account for can be explained by the rich examples of the country’s chip-making industry, thus providing us with the whole picture of the industry and its dynamics. However, this article has employed quantitative approach alone. Those who wish to understand the Korea’s semiconductor industry more in depth may refer to Chung (1998), which includes descriptive part as well as the quantitative analysis.
Endnotes
[1] Learning effects give rise to dynamic economies of scale which differ from (static) economies of scale. In the case of dynamic economies of scale, increasing current production reduces future costs, not current costs. In econometric modeling, thus, the former concept is usually represented by cumulative output and the latter by current output.
2 See Wright (1936). This article is considered the seminal paper on the subject.
3 For those interested in history, structure, and dynamics of the semiconductor industry, refer to Kraus (1973), Sciberras (1977), Braun and MacDonald (1978), Hazewindus and Tooker (1982), Dosi (1984), Malerba (1985), United Nations Centre on Transnational Corporations (1986), Steinmueller (1987), Howell et al. (1988), Langlois et al. (1988), Green (1996) and Flamm (1996). However, most of these studies focus on the U.S. and European semiconductor industry. Some of these deal with the Japanese industry, but only in relation to trade conflict with the United States. In these publications, the semiconductor industry of Korea and Taiwan is only treated as passing notes.
4 The annual capacity factor of a plant is defined as the energy generated (Y) divided by the rated power output of the plant (CAP) times the number of hours in the year (H = 8,760 except in leap years). That is, capacity factor PF(%) = Y(WH) /[CAP(W)*H(Hours)]. It is equivalent to saying: capacity factor = [actual energy generated]/[potential capacity*time].
5 The capacity factor in nuclear power generation is notionally identical to the yield factor in the semiconductor industry.
6 In Joskow et al., g(x) is specified as ek/x. They say this form has the advantage that it can be linearized easily and so simplifies estimation.
7 Lieberman (1984).
8 For example, each generation of memory chip is introduced by a pioneering firm, and later on faces considerable competition, thus being forced to cut price-cost margins.
9 This assumption is found in Lieberman (1984) and Gruber (1994a).
10 Irwin and Klenow (1994) p. 1209.
11 For 4M DRAM, the price fell as low as $2.50, a level that industry experts say is below production costs. A break-even point for memory chips is approximately a dollar per megabit; for example, it is $4 for 4M DRAMs and $16 for 16M DRAMs.
12 Berndt (1991) pp. 76-78.
13 For further discussion of omitted variable bias, see section III.3. The Yield Model.
14 Joskow and Rozanski (1979) p. 164.
15 Gruber (1994a) p. 47, note 5.
16 In the next estimation using yield factor data, we will correct the problem of positive serial correlation indicated by a low Durbin-Watson statistic by adding to the equation the first-order autocorrelation term AR(1).
17 For example, Fujitsu and Nippon Steel Semiconductor in the case of 4M DRAMs, Micron Technology and Nippon Steel for 16M DRAMs have low F-statistics, assuming the critical value of F-statistic is 4.
18 For 16M DRAMs, the average rate increase in quarterly output has been 35.05 percent, partially weakening the second claim that the not-high-enough quarterly output increase was responsible for the bad fit.
19 By “significant,” I mean here estimates that satisfy following conditions: -1 < b1 < 0, t-statistic > 2, and Durbin-Watson statistic > 2.
20 The source for the data, a high-ranking official at the company’s corporate research institute, asked for anonymity, which will be maintained throughout.
21 Actually the number of observation is 26 for 64K DRAMs and 32 for 256K DRAMs.
22 Although our analysis based on yield and shipment data of a Korean company produced a substantial learning effects for both memory products, 17 percent for 64K DRAMs and 9 percent for 256K DRAMs, one cannot claim from the results that the Korean companies have moved down the learning curve faster than any other firms in the advanced countries because there is no comparable dataset available for the analysis.
23 Chosun Ilbo, Nov. 7, 1995, p. 12 (in Korean).
References
Abernathy, W. J. and Wayne, K. (1974) Limits of the Learning Curve, Harvard Business Review, 52, 109-120.
Abramovitz, M. (1956) Resource and Output Trends in the United States Since 1870, American Economic Review, Papers and Proceedings, 46, 5-23.
Alchian, A. A. (1963) Reliability of Progress Curves in Airframe Production, Econometrica, 31, 679-693.
Amsden, A. H. (1989) Asia’s Next Giant: South Korea and Late Industrialization, Oxford University Press, Oxford.
__________ and Hikino, T. (1991) Borrowing Technology or Innovating: An Exploration of Two Paths to Industrial Development, Department of Economics, New School for Social Research Working Paper Series 31.
Arrow, K. J. (1962) The Economic Implications of Learning by Doing, Review of Economic Studies, 29, 155-173.
Berndt, E. R. (1990) The Practice of Econometrics: Classic and Contemporary, Addison-Wesley, New York.
Bertram, W. J. (1988) Yield and Reliability, in VLSI Technology, ed., S. M. Sze, McGraw Hill, New York, 612-655.
Boston Consulting Group (1972) Perspectives on Experience, Boston Consulting Group, Boston.
Braun, E. and MacDonald, S. (1978) Revolution in Miniature: The History and Impact of Semiconductor Electronics, Cambridge University Press, Cambridge.
Choi, Y. (1995) Dynamic Techno-Management Capability in the Semiconductor Sector: the Case of Samsung Semiconductor, Science Technology Policy, 7, 27-50 (in Korean).
__________ (1996) Dynamic Techno-Management Capability: the Case of Samsung Semiconductor Sector in Korea, Avebury, Hants.
Chung, S. (1998) The Learning Curve in the Korean Semiconductor Industry, Diss., New School for Social Research, New York.
Dick, A. R. (1991) Learning by Doing and Dumping in the Semiconductor Industry, Journal of Law and Economics, 34, 133-159.
Dosi, G. (1984) Technical Change and Industrial Transformation, St. Martin’s Press, New York.
Flamm, K. S. (1996) Mismanaged Trade?: Strategic Policy and the Semiconductor Industry, Brookings Institution Press,Washington, DC.
Green, E. M. (1996) Economic Security and High Technology Competition in an Age of Transition: The Case of the Semiconductor Industry, Praeger, Westport.
Gruber, H. (1992) The Learning Curve in the Production of Semiconductor Memory Chips, Applied Economics, 24, 885-894.
__________ (1994a) Learning and Strategic Product Innovation, North Holland, Amsterdam.
__________ (1994b) The Yield Factor and the Learning Curve in Semiconductor Production, Applied Economics, 26, 837-843.
Hazewindus, N. and Tooker, J. (1982) The U.S. Microelectronics Industry: Technical Change, Industry Growth and Social Impact, Pergamon Press, New York.
Helper, S. and Lazonick, W. (1984) Learning Curve and Productivity Growth in Institutional Context, Harvard Institute for Economic Research Discussion Papers 1066, Harvard University, Cambridge.
Howell, T. R., Noellert, W. A., MacLaughlin, J. H. and Wolff, A. W. (1988) The Microelectronics Race: The Impact of Government Policy in International Competition, Westview Press, Boulder.
Irwin, D. A. and Klenow, P. J. (1994) Learning-by-Doing Spillovers in the Semiconductor Industry, Journal of Political Economy, 102, 1200-1227.
Joskow, P. L. and Rozanski, G. A. (1979) The Effects of Learning by Doing on Nuclear Plant Operation Reliability, Review of Economics and Statistics, 61, 161-168.
Kim, L. (1997) Imitation to Innovation: The Dynamics of Korea’s Technological Learning, Harvard Business School Press, Boston.
Kraus, J. (1973) An Economic Study of the U.S. Semiconductor Industry, Diss., New School for Social Research, New York.
Langlois, R. N., Pugel, T. A., Haklisch, C. S., Nelson, R. R. and Egelhoff, W. G. (1988) Microelectronics: An Industry in Transition, Unwin Hyman, London.
Lieberman, M. B. (1984) The Learning Curve Pricing in the Chemical Industries, RAND Journal of Economics, 15, 213-228.
Malerba, F. (1985) The Semiconductor Business: The Economics of Rapid Growth and Decline, University of Wisconsin Press, Madison.
Nye, W. W. (1989) Some Evidence on Firm-Specific Learning-by-Doing in Semiconductor Production, Discussion Paper no. 89-11, Department of Justice, Economic Analysis Group, Washington DC.
Oi, W. Y. (1967) The Neoclassical Foundations of Progress Functions, Economic Journal, 77, 579-594.
Sciberras, E. (1977) Multinational Electronics Companies and National Economic Policies, JAI Press, Greenwich.
Solow, R. M. (1957) Technical Change and the Aggregate Production Function, Review of Economics and Statistics, 39, 312-320.
Steinmueller, W. E. (1987) Microeconomics and Microelectronics: Economic Studies of Integrated Circuit Technology, Diss., Stanford University, Stanford.
Tanimitsu, T. (1994) The Trajectory of Semiconductor Industry: The Half Century of U.S.-Japan Competition, Nikkan Gogyo Shimbunsha, Tokyo(in Japanese).
Webbink, D. W. (1977) The Semiconductor Industry: A Survey of Structure, Conduct, and Performance, Staff Report to the FTC, U.S. Government Printing Office, Washington DC.
Wright, T. P. (1936) Factors Affecting the Cost of Airplanes, Journal of The Aeronautical Sciences, 3, 122-128.
The Case of Korea’s Semiconductor Industry
by
Sangho Chung*
April 2000
*Managing Editor
Korea Economic Weekly
154-11 Samsung-dong, Kangnam-gu 4th Fl.
Seoul 135-090, Korea
Phone: 822-3430-2151
Fax: 822-3430-2170
Email: schung01@koreaeconomy.com
Abstract
This article attempts to find out how the Korean economy has grown so rapidly in a short time span of less than 30 years. For that purpose, it focuses on the development of the Korea's semiconductor industry—more specifically, the memory-chip segment of the industry—as a case in point.
To test the hypothesis that the learning curve effects have been significant in the memory-chip industry, we use “yield factor” (the ratio of sellable chips to total chips in a wafer) in the semiconductor production as a measure of the learning progression. That is, by tracing how the yield factor for each generation of memory chips has increased, we will be able to see how well the Korean chip makers has exploited the learning effects.
This article’s possible contribution would be the following: It improves the learning-by-doing modeling by introducing a richer set of yield data; and the unit of analysis employed throughout the article is at the firm level, which is not common in the literature dealing with the East Asian development as well as the economics of technology, thus enhancing our understanding of the industry dynamics.
I. Introduction
This article focuses on the development of the Korean semiconductor industry which has experienced an impressive growth for little more than 20 years. The country’s semiconductor chip producers at the outset focused on producing products relatively easy to manufacture using mature technology imported from abroad. By producing these products in high volume, mainly memory chips such as dynamic random access memories (or DRAMs) and static RAMs (or SRAMs), the Korean producers were able to capture the benefits of learning effects and economies of scale,1 thus reducing their production costs and diffusing capabilities acquired in the process to other product areas.
From technical perspective, the learning curve effect in the semiconductor industry is represented by yield factor, which is defined as the ratio of non-defective (and sellable) chips to total wafer area fabricated. In an initial production run for a specific generation of chips, the production yield typically remains below 10 percent. The yield, as the production experience accumulates, in many cases asymptotically increases up to 95 percent. The trajectory of this increase is called the learning curve, which since the report on the phenomenon at the U.S. airframe (or airplane fuselage) manufacturing site in the 1930s has been extensively used by many economists and management decision makers.2
Using the concepts introduced above, i.e., the yield factor and the learning curve, we can begin to analyze the Korea’s chip-making industry. That is, by tracing how the yield factor for each subsequent generation of memory chips has increased we can see how well the country's producers exploited the learning effects to increase productivity and reduce costs.
This article relies on the data collected from Dataquest, a U.S. high-tech market research firm, and a Korean semiconductor company, then tests the hypothesis that the learning curve effects were significant in the country’s industry. The first estimation uses the price data, based on the conventional learning curve models. After finding out that this estimation yields poor results in terms of coefficients well out of expected ranges and low t-statistics, the second estimation employs yield data instead of prices as a dependent variable. We find a significant learning curve effect in the estimation, with the learning ratio of 17 percent for 64K DRAMs and 9 percent for 256K DRAMs, confirming our learning hypothesis in the case of the Korean industry.
II. The Economic Literature on Learning3
Wright, an aeronautical engineer, reported in 1936 that the direct labor cost of producing an airframe (fuselage of an airplane) declined with the accumulated number of airframes of the same type produced. That is:
Y = aXb (2.1)
where Y is the direct labor cost, X is the cumulative output of airframes, a is the cost of the first unit of airframe (a > 0), and b is the learning elasticity (0 ³ b ³ -1), which defines the slope of the learning curve.
In so far as World War II airframe data were concerned, every doubling of cumulative airframe output was accompanied by an average reduction in direct labor requirements of about 20 percent. This so-called “eighty percent curve” is the precursor of the present-day learning curve. Following Wright’s article, most of research effort has been directed at finding an appropriate functional form of the learning curve and applying the theory to diverse industries, using different proxy variables for learning, such as time, cumulative output, and so on.
Joskow and Rozanski (1979) apply the learning principle to nuclear plant operations. There are two distinctive features in the model: The first one is that, unlike other models, they utilize capacity factor4 of nuclear plants as a dependent variable in their model. For them, capacity factor reflects power generation cost more accurately than do price data, the usual proxy in other models. So the higher its capacity factor, the lower is the average unit cost of power generated.5
The general form of the learning curve to be estimated is:
y = A g(x) eu (2.2)
where y = annual plant capacity factor; A = asymptotic value of the capacity factor; x = increasing measure of experience (i.e., cumulative output) (x > 0); and g(x) = function describing the nuclear operators’ learning process.
The second feature of their model is that they extend this general model to account for “supplier learning” in addition to “operator learning.” As cumulative output increases, capacity factor increases due to learning on the part of the plant’s operators. This is depicted as the function g1(x)A1 in figure 1 that approaches an asymptote A1. The effect of learning by the suppliers (e.g., plant designers and engineers) responsible for building the plant are modeled as a shift upward in the asymptotic capacity factor. This is shown as a shift in the asymptote from A1 to A2.
The model to be estimated is:
PF = A CAPb ecV g(x) (2.3)
where PF = plant capacity factor (see note 4 for definition); CAP = gross plant capacity (i.e., rated capacity); V = the month during which the plant began commercial operation (a measure of the vintage of the plant); and g(x) = operators’ learning function.6
Except the constant term A, each term in the equation represents a different source of learning: The first term represents supplier learning, the second one the effect of time and the third operator learning. The regression results reported in Joskow et al. show that the learning effect is important in nuclear plant operations, with learning rate approximately 5 percent per annum.
Generally, these empirical studies confirm the importance of learning phenomenon in reducing costs in their respective industries. We will now see how these learning economies has shaped the structure of the semiconductor industry. Gruber (1992) comes up with the following learning equation for memory chips:
Pijt = A Qbijt Vgijt Hdijt exp (uijt) (2.4)
where A = constant, price of the first unit produced; Pijt = average real selling price for memory chips of type i and generation j in year t (proxy for cost); Qijt = annual shipments for memory chips of type i and generation j in year t; b = indicator of static economies of scale (b < 0); Vijt = SQijt, cumulative shipments for memory chips of type i and generation j up to year t; g = learning elasticity (g < 0); Hijt = age of memory device, or time elapsed since production began, i.e., Hijt = 1 for the first year when generation j is introduced; d = indicator of the effect of generation age (alternative indicator for learning by doing); and uijt = random error term.
Taking log for each term:
pijt =ai + bi qijt + gi vijt + di hijt + uijt (2.5)
where lower cases indicate logarithms.
From this he finds the results as shown in table 1.
That is, Gruber finds no significant learning for DRAMs and SRAMs. Only for EPROM did he find a significant learning, which is somewhat counterintuitive. His model measures the learning effects, with cumulative shipments of semiconductor devices and the elapse of time; as well as static economies of scale, with annual shipments of memory chips. The reason he uses average selling prices as a proxy for costs is not different from others; i.e., the unavailability of cost data. So he reiterates the conditions under which reliable estimates of the learning curve can be obtained from price data. That is, (1) price-cost margins are constant over time, (2) price-cost margins change in a way controlled for by other variables, or (3) changes in the margin are small in relation to changes in marginal cost.7 Then he goes on to say that the condition (1) and possibly condition (3) are hard to apply to the semiconductor production, since it is well known that in this industry profit margins fluctuate considerably over the life cycle of a generation of chips.
Nevertheless, he argues that these fluctuations can be controlled for by using variables that are closely correlated with the margins. That is, he says that the time profile of profit margins for a given generation is U-shaped. In other words, the margins are large at the beginning and at the end of the product life cycle, while in-between margins are depressed due to entry of firms and strong competition. Current shipments for a given generation have a time profile which is inversely related to the time profile of profit margins. Thus the fluctuations of the margins can be controlled for by the current shipments variable. But given the dramatic changes in the conditions of competition over the product cycle, price-cost margins might decline steeply as the product matures, which invalidates the Gruber’s procedure to control for fluctuations in price-cost margins.8
III. Regression Analysis of the Learning Curve Model
1. The Learning-by-Doing Model
In many manufacturing operations in which tasks are performed relatively in a repetitive manner, it has been reported that workers tend to learn from their experiences thereby reducing the time and costs it takes to complete given tasks. Many empirical studies have so far attempted to find out significant cost-reduction effects of a cumulative production experience.
Confining the focus on the semiconductor industry, Webbink (1977) reports a coefficient of -0.40 on cumulative production, indicating that, with every doubling of cumulative output, cumulative average price falls by 24 percent. Dick (1991) reports regressions of industry price on lagged cumulative production (an aggregate of U.S. and Japanese firms) of 1K and 4K DRAMs based on annual data for 1974-1980 and 1976-81, respectively. He finds a 19 percent learning curve in 1K DRAMs and a 7 percent learning curve in 4K DRAMs. Gruber (1992) estimates similar models for DRAMs, EPROMs, and SRAMs, but finds no significant learning for DRAMs. Irwin and Klenow (1994) use broader dataset encompassing quarterly, firm-level data on seven generations of DRAMs over 1974-92, for which they find average of 20 percent learning curve on cumulative output.
Since cost data are kept secret by companies and thus difficult, if not impossible, to obtain, most empirical learning curve studies, including those mentioned above, have proxied unit costs with a real price variable and then regressed the log of real price on a constant term and the log of cumulative output. This procedure introduces a major problem and makes separate identification of the learning curve effect very difficult. When one uses price data for the dependent variable, several problems arise. For one thing, the justification for using the proxy is given by the assumption that prices move fairly in sync with costs, with a certain constant markup. In other words, it assumes that price-cost margins are constant over time, price-cost margins change in a way controlled for by other variables, or changes in the margin are small in relation to changes in marginal cost.9
Yet, given the tumultuous state of competition in the semiconductor market in which each generation of product is introduced by a leading firm and later faces a large number of competitors resulting in a substantial drop in prices as the product matures, price-cost margins cannot be stable over time, rather they decline steeply.10 It is even more so in the case of the East Asian semiconductor producers, including the Japanese and the Korean firms, who have frequently been the target of dumping accusations which alleged that their semiconductor components were sold at prices below actual production costs.
Aside from this difficulty, there is another problem in using a proxy variable. As evidenced from the 1996-97 downturn in the semiconductor market, the price movements in the semiconductor market before and during the period have largely been dictated by the forces of supply and demand, rather than by the learning principle by which prices fall continuously over time. Nearly three years from 1993 to 1995, the semiconductor prices, notably those of memory chips, have been propped up by unprecedented high demand from personal computer manufacturers, bringing in profit margins of over 70 percent for some chip makers. As the market conditions reversed in the early 1996, however, the chip prices fell to a level comparable to or lower than its production costs.12 Under these circumstances, it is hard to expect the price-cost margins are within a certain stable range, let alone constant. This possible wide divergence between prices and costs forces us to reconsider the feasibility of the price proxy.
To see this point more clearly, suppose that there are two firms with identical learning curve experiences. Assume that one firm adopted a forward pricing strategy in which the price was initially set very low, thereby increasing demand, market share, and production, while the other firm adopted a “cream-skimming” pricing strategy in which the initial price was set very high and lowered gradually (Intel is a typical firm that has adopted the pricing strategy of cream skimming). If one regressed price on cumulative production for these two firms, one would obtain very different estimates of the learning curve elasticity, even though the potential learning curve effects were identical by assumption. If, instead, unit cost data had been adopted, this difference would not have occurred. It shows that it is preferable to adopt unit cost rather than price data in estimating learning curve parameter, since using price data confounds the effects of pricing strategy with “pure” learning curve effects.
In general, the learning curve model estimates the extent to which the accumulation of production experience contributes to the reduction of costs. The simplest and most commonly used form of the learning curve is as follows:
Ct = A Vta1 eut (3.1)
where Ct is unit cost of production in time period t, Vt is cumulative output produced up to time period t, A is the cost of the first unit of output, a1 is the learning elasticity (0 ³ a1 ³ -1), and ut is a stochastic disturbance term.
Equation (3.1) can be rewritten in logarithmic form as
ln Ct = ln A + a1 ln Vt + ut (3.2)
The learning curve elasticity parameter a1 can be estimated by ordinary least squares, provided that relevant data on unit costs and output are available. The following formula for log transformations implies that every time cumulative experience doubles, cost will decline to s percent of its previous level:
s = 2a1 (3.3)
Therefore, if cost declines to 70 percent of its previous level as cumulative output doubles, then the learning curve is said to have a 70 percent slope. However, when one runs a simple regression for a model such as equation (3.2), regressing unit production cost on cumulative output, it is often difficult to distinguish the cost-reducing effects of learning from that of scale economies. Thus the learning curve elasticity may be over- or under-estimated by omitting the variable representing scale economies. In order to separate the two effects, we add a current output variable to the equation (3.2) as follows:
ln Ct = ln A + b1 ln Vt + b2 ln Xt + wt (3.4)
where Xt is current output, b2 is a coefficient representing the extent to which economies of scale contribute to cost reduction, and b1 is same as a1 in equation (3.1), and wt is random disturbance term.
By running both the simple regression on equation (3.2) and the multiple regression on equation (3.4), we can find the difference in coefficients for cumulative output V. The bias resulting from omitting ln Xt from the learning curve equation is called the “omitted variable bias.”12 To analyze the issues of omitted variable bias, it is convenient to introduce a new equation, called an auxiliary regression equation, in which the omitted variable—in this case ln Xt—is related to the included variable ln Vt and a disturbance term et.
ln Xt = d0 + d1 ln Vt + et (3.5)
Now label the least-squares estimates of the a’s, b’s, and d’s as a’s, b’s, and d’s, respectively. The relationship between a1 (the least squares estimate of a1) and b1 (the least squares estimate of b1) can be shown to be as follows:
a1 = b1 + d1 b2 or a1 - b1 = d1 b2 (3.6)
The bias from omitting ln Xt is simply equal to a1 - b1, which is equal to d1 b2. This omitted variable bias will be zero only if at least one of the following two conditions is satisfied:
1. d1 = 0, i.e., the log of current output and cumulative output are uncorrelated;
2. b2 = 0, i.e., unit cost of production does not depend on current production. Alternatively, returns to scale are constant.
If neither of the two conditions is met, an omitted variable bias will result, meaning that if one estimated the learning curve elasticity using equation (3.2) and omitting ln Xt, one would obtain a biased estimate of the true learning curve parameter. In many cases, one might expect returns to scale to be increasing, so it is plausible to expect that a1 - b1 will be negative. Further, since a1 and b1 are typically negative in value, a1 - b1 < 0 corresponds to b1 being smaller in absolute value than a1. In such a case, estimation of the simple learning curve equation yields a larger estimate of the learning curve elasticity (in absolute value) than if one includes the current output variable as in equation (3.4). Hence in this case the learning curve elasticity is overestimated in absolute value.13
2. The Model with Price Variable
The first equation to be estimated would be the one based on price dependent variable as in most of the conventional models. This way, we can verify the problems of the price proxy explained above. The model is as follows:
Pi = A Vb1i Xb2i eui (3.7)
where P is average selling price in real terms, i is type of memory chips, and the rest are identical to the notations in equations (3.1) and (3.4).
Taking log in each term of equation (3.7),
ln Pi = ln A + b1 ln Vi + b2 ln Xi + ui (3.8)
Following the modified model used in Joskow and Rozanski (1979) which employs the inverse of cumulative output:
ln Pi = ln A + b1 ln (1/Vi) + b2 Xi + ui (3.9)
This functional form has the advantage that it can be linearized easily and simplifies estimation.14 To obtain a real price for the memory chips, the average selling prices have been divided by the U.S. implicit price. There are two reasons for choosing the U.S. price deflator to calculate the real prices: First, the average selling price data provided by Dataquest, the source of the dataset, are quoted in U.S. dollars; and second, the U.S. market has been the largest market for memory chips for most of the observation period.15
There are 350 observations from the first quarter of 1994 to the second quarter of 1996 in the dataset for 19 companies (4M DRAMs) and for 16 companies (16M DRAMs). In addition to estimations of individual company learning parameters, industrywide learning curve has been estimated for both memory products. The regression results based on ordinary least squares are reported in tables 2 and 3 below.
As can be seen in tables 2 and 3, regression results are completely out of expectations based on our hypothesis that as cumulative output increases real prices decrease, thus taking negative coefficients in ln (1/Vi) terms. In the case of 4M DRAMs, all the regressions for 19 individual companies yielded positive coefficients in their cumulative output variable (ranging from 0.044 to 0.490), as opposed to their expected range of -1 to 0. In the case of 16M DRAMs, only five out of 16 regressions yielded negative coefficients in their cumulative output variable (-0.010 to -0.256). For all the five cases, however, coefficients are found to be insignificant based on t-test (t-statistics below 2.0).
It is also noteworthy that four out of 19 cases in 4M DRAMs and only one out of 16 cases in 16M DRAMs produced the Durbin-Watson statistic higher than 2.0, which indicates the positive serial correlation in disturbance terms.16 Some of the estimates have low F-statistics,17 implying that none of the independent variables influences the dependent variable, thus the specification is meaningless. However, we do not go into the subject in detail because the estimates obtained above are well out of the expected range anyway. The results for overall industry estimations (for both 4M and 16M DRAMs) are similar to those of the individual company regressions, yielding positive coefficient for cumulative output variable or negative but insignificant coefficient. Unreported estimations of simple regressions, regressing the log of real price against the log of cumulative output alone, did not improve the results.
The reasons for this “bad fit” can be found in the following reasons. First, the quarterly average rate of price drop has not been high enough to produce a substantial learning curve effect. The quarterly rate of price fall has been 5.30 percent for 4M DRAMs and 7.84 percent for 16M DRAMs for the two and half year period. Excluding the last two observations (the first and second quarter of 1996) in which the price drop has been steepest, the average rate of drop has been only 0.44 percent and 2.44 percent, respectively. This is because the period from 1993 to 1995 is characterized by a strong demand from PC manufacturers that has propped up the chip prices, reversing the usual pattern of steady and substantial fall in prices. Second, quarterly output has been increasing at a slower rate. Especially in the case of 4M DRAMs, the quarterly rate of increase in industry total output has been only 2.44 percent.18 The observation period of 1994 to 1996 has corresponded to the transition period in which the 4M DRAM generation was being phased out, so the output has not been increased in spite of the high demand. Third, the initial period in which the mass production has begun is not captured in the analysis for both products. In the case of 4M DRAMs, the mass production has started from 1989, while that of 16M DRAMs from 1990. Given the dataset encompasses the years from 1994 to 1996, well after the products were introduced in the market, it is understandable that a substantial part of the learning curve effects is not represented in the observation.
The weak presence of the learning curve effect in the dataset leads us to test if economies of scale have been strong instead. The following model estimates the influence of scale economies on real-price reduction by regressing the log of real price against the log of inverse of shipments:
ln Pi = ln A + b1 (1/Xi) + ui (3.10)
Since the serial correlation has been found in most of the estimations, the term AR(1) is added to the equation. Unreported estimations reveal that in the case of 4M DRAMs seven out of 19 individual company regressions had significant economies of scale.19 For the industry as a whole, the cost-reducing effect coming from economies of scale turned out to be overwhelming 44.02 percent (corresponding coefficient is -0.837). However, in the case of 16M DRAMs, none out of 16 regressions produced significant economies of scale, all of whose coefficients are positive.
3. The Yield Model
Instead of using price data which yielded results that are inconsistent with the learning hypothesis, we use yield data as the dependent variable obtained from a Korean semiconductor company, say Company A, for 64K and 256K DRAMs.20 This richer set of data includes yield and shipment data for Company A from the first quarter of 1985 to the fourth quarter of 1993, consisting of 36 observations.21 All the estimates are obtained by ordinary least squares.
The yield factor model to be estimated here is identical to equation (3.9) except that the price variable Pi is replaced by the yield variable Yi as follows:
ln Yi = ln A + b1 ln (1/Vi) + b2 Xi + ui (3.11)
where Y is yield factor, and the rest are identical to the notations in equations (3.1) through (3.7).
A simple regression model is the one without a current output variable ln Xi.
ln Yi = ln A + a1 ln (1/Vi) + ui (3.12)
This way, we can estimate the learning parameter more directly without employing proxy variable or complicated procedure to estimate production costs. The only model which analyzed the semiconductor industry based on the yield factor data is found in Gruber (1994a). However, its dataset includes only 7 quarters for 4 generations of a single product, EPROM from one European firm, SGS-Thomson, which is too limited to deduce any meaningful conclusion. Therefore, the current yield model that covers quarterly data of a Korean company for nine years for two important memory items can be considered a major improvement of the model.
First, in the case of 64K DRAMs, if one runs a simple regression where the log of yield factor is regressed against the log of cumulative output, the coefficient for ln (1/Vi) turns out to be -0.182 with the corresponding learning ratio of 11.843 percent, which implies that every doubling of cumulative output would result in the yield improvement of 11.8 percent, which in turn reduces the production costs by the same amount. Then we add a current output variable ln Xi and run a multiple regression to separate the learning effect from the cost-reducing effect of economies of scale. The estimation results in the learning coefficient of -0.176, slightly lower in absolute value than that of the simple regression with the learning ratio of 11.493 percent.
To see if omitting the current output variable would result in an estimation bias, we run an auxiliary regression equation similar to equation (3.5).
ln Xi = d0 + d1 ln (1/Vi) + ei (3.5)’
According to equation (4.6), the sign of the difference between a1 (the least squares estimate of a1) and b1 (the least squares estimate of b1) determines whether the omitting variable over- or under-estimates the coefficient. That is,
a1 - b1 = d1 b2 (3.6)
1. a1 - b1 > 0 (the learning curve elasticity is underestimated when the current output variable is omitted)
2. a1 - b1 = 0 (the current output variable has no correlation with yield; that is, constant returns to scale)
3. a1 - b1 < 0 (the learning curve elasticity is overestimated).
Plugging in coefficients obtained from the estimation of the auxiliary regression equation, a1 = -0.182, b1 = -0.176, d1 = 0.111, and b2 = -0.051, it is -0.006 » -0.005661. Since a1 - b1 is negative, equation (3.11) exhibits increasing returns to scale and the simple regression equation (3.12) overestimates the learning curve elasticity.
In the case of 256K DRAMs, the simple regression produces the coefficient of -0.165 for the ln (1/Vi) term and the corresponding learning ratio of 10.807 percent. The estimation for the multiple regression with the current output variable ln Xi results in the learning coefficient of -0.145 with the learning ratio of 9.572 percent.
Running an auxiliary regression equation to check the presence of omitted variable bias yields following numerical results: a1 = -0.165, b1 = -0.145, d1 = -0.277, and b2 = 0.071; therefore, a1 - b1 = -0.020 » d1 b2 = -0.019667. That is, a1 - b1 < 0 and the equation (3.11) exhibits increasing returns to scale and the simple regression overestimates the learning curve elasticity. All the estimates for both memory products are reported in tables 4 and 5 below.
However, it is notable that Durbin-Watson statistics turn out to be 1.476 for 64K and 0.941 for 256K DRAMs which are well below 2, an indication of the presence of positive serial correlation in the residuals. In order to incorporate the serial correlation in the equation, the first-order autocorrelation term AR(1) is added. With the new regression, we get a better fit in terms of the Durbin-Watson statistics close to or higher than 2 as shown in the fourth row of each table below.
As reported in tables 4 and 5, the learning ratios of 16.841 percent (for 64K DRAMs) and 9.382 percent (for 256K DRAMs) are consistent with our hypothesis that with every doubling of cumulative output production yield increases by the same percentage. However, the learning slopes are not as steep as we expected, usually reaching as high as 30 percent. The reason for this rather low ratios can be traced to the following fact: That is, the year when Company A introduced 64K DRAMs to the market was 1984, and the first year for 256K DRAMs was 1985. Meanwhile, the observation period in our analysis starts from 1985 and 1986, respectively, one year later than each product’s market introduction year. Due to this lack of data for the year the learning curve effect could have been most pronounced, the learning curves for the two memory items are estimated at approximately 17 percent and 9 percent as reported in the tables above.
The figures 2 and 3 below have been plotted using the log of the inverse of cumulative output as X-axis and the log of yield as Y-axis. These learning curve diagrams resemble fairly well to the ones drawn by other studies, including Joskow and Rozanski (1979; p. 163).
Aside from the above empirical evidence which shows that the Korean semiconductor industry has grown by rapidly moving down the learning curve,22 there is an ample number of anecdotal evidences demonstrating the Korean industry’s high production yield and resulting high productivity. The yield of 4M DRAMs produced by the Korean chip makers has, for example, run up to 95 percent in 1995, the year at which the product has reached the maturity stage. According to officials of a Korean company, although varied by company and product, the yield of the Korean chip makers is in general 10 percent higher than that of the Japanese, and the yield of Japanese chip makers is again 10 percent higher than that of the American.
In the semiconductor manufacturing process, from raw wafer manufacturing to circuit design, mask generation and wafer processing, almost all processes are automated, so there is little room for quality variations. In these pre-assembly processes, the purity of silicon wafers, the quality of processing chemicals, and the stricter standard of the clean-room operations are important factors affecting the processing yields. But at the stage of assembly and final inspection, human factors largely determine the production yield. This is where “finger tips” of young female workers of Korea have proven important. For example, in a Samsung assembly plant that employs 15,000 female workers, the average age of assembly workers is 21, which is 10 years younger than that of their counterparts in Japan.23 The reason the Korean chip makers have been able to enjoy higher yield is given also by the fact that, similar to the cost advantage of the Japanese makers, most of the Korean firms are large conglomerates with affiliates in consumer electronics, which require components with less stringent performance standards than military or industrial-purpose chips, thus helping to achieve higher yields.
VI. Conclusion
The chip-making industry of Korea deserves a special attention because of its great reliance of the production technology on foreign sources and its intense efforts to internalize the imported technology into its own production, thus making a good study subject for the learning-by-doing theory. Nevertheless, no full-length academic endeavor has been made on the subject except some of the contributions narrowly focusing on the case of one company. Such examples include Kim (1997) and Choi (1996).
When analyzing an industry, there may be two distinct approaches; detailed descriptive approach and quantitative approach. Both are complementary in the sense that what the quantitative part cannot account for can be explained by the rich examples of the country’s chip-making industry, thus providing us with the whole picture of the industry and its dynamics. However, this article has employed quantitative approach alone. Those who wish to understand the Korea’s semiconductor industry more in depth may refer to Chung (1998), which includes descriptive part as well as the quantitative analysis.
Endnotes
[1] Learning effects give rise to dynamic economies of scale which differ from (static) economies of scale. In the case of dynamic economies of scale, increasing current production reduces future costs, not current costs. In econometric modeling, thus, the former concept is usually represented by cumulative output and the latter by current output.
2 See Wright (1936). This article is considered the seminal paper on the subject.
3 For those interested in history, structure, and dynamics of the semiconductor industry, refer to Kraus (1973), Sciberras (1977), Braun and MacDonald (1978), Hazewindus and Tooker (1982), Dosi (1984), Malerba (1985), United Nations Centre on Transnational Corporations (1986), Steinmueller (1987), Howell et al. (1988), Langlois et al. (1988), Green (1996) and Flamm (1996). However, most of these studies focus on the U.S. and European semiconductor industry. Some of these deal with the Japanese industry, but only in relation to trade conflict with the United States. In these publications, the semiconductor industry of Korea and Taiwan is only treated as passing notes.
4 The annual capacity factor of a plant is defined as the energy generated (Y) divided by the rated power output of the plant (CAP) times the number of hours in the year (H = 8,760 except in leap years). That is, capacity factor PF(%) = Y(WH) /[CAP(W)*H(Hours)]. It is equivalent to saying: capacity factor = [actual energy generated]/[potential capacity*time].
5 The capacity factor in nuclear power generation is notionally identical to the yield factor in the semiconductor industry.
6 In Joskow et al., g(x) is specified as ek/x. They say this form has the advantage that it can be linearized easily and so simplifies estimation.
7 Lieberman (1984).
8 For example, each generation of memory chip is introduced by a pioneering firm, and later on faces considerable competition, thus being forced to cut price-cost margins.
9 This assumption is found in Lieberman (1984) and Gruber (1994a).
10 Irwin and Klenow (1994) p. 1209.
11 For 4M DRAM, the price fell as low as $2.50, a level that industry experts say is below production costs. A break-even point for memory chips is approximately a dollar per megabit; for example, it is $4 for 4M DRAMs and $16 for 16M DRAMs.
12 Berndt (1991) pp. 76-78.
13 For further discussion of omitted variable bias, see section III.3. The Yield Model.
14 Joskow and Rozanski (1979) p. 164.
15 Gruber (1994a) p. 47, note 5.
16 In the next estimation using yield factor data, we will correct the problem of positive serial correlation indicated by a low Durbin-Watson statistic by adding to the equation the first-order autocorrelation term AR(1).
17 For example, Fujitsu and Nippon Steel Semiconductor in the case of 4M DRAMs, Micron Technology and Nippon Steel for 16M DRAMs have low F-statistics, assuming the critical value of F-statistic is 4.
18 For 16M DRAMs, the average rate increase in quarterly output has been 35.05 percent, partially weakening the second claim that the not-high-enough quarterly output increase was responsible for the bad fit.
19 By “significant,” I mean here estimates that satisfy following conditions: -1 < b1 < 0, t-statistic > 2, and Durbin-Watson statistic > 2.
20 The source for the data, a high-ranking official at the company’s corporate research institute, asked for anonymity, which will be maintained throughout.
21 Actually the number of observation is 26 for 64K DRAMs and 32 for 256K DRAMs.
22 Although our analysis based on yield and shipment data of a Korean company produced a substantial learning effects for both memory products, 17 percent for 64K DRAMs and 9 percent for 256K DRAMs, one cannot claim from the results that the Korean companies have moved down the learning curve faster than any other firms in the advanced countries because there is no comparable dataset available for the analysis.
23 Chosun Ilbo, Nov. 7, 1995, p. 12 (in Korean).
References
Abernathy, W. J. and Wayne, K. (1974) Limits of the Learning Curve, Harvard Business Review, 52, 109-120.
Abramovitz, M. (1956) Resource and Output Trends in the United States Since 1870, American Economic Review, Papers and Proceedings, 46, 5-23.
Alchian, A. A. (1963) Reliability of Progress Curves in Airframe Production, Econometrica, 31, 679-693.
Amsden, A. H. (1989) Asia’s Next Giant: South Korea and Late Industrialization, Oxford University Press, Oxford.
__________ and Hikino, T. (1991) Borrowing Technology or Innovating: An Exploration of Two Paths to Industrial Development, Department of Economics, New School for Social Research Working Paper Series 31.
Arrow, K. J. (1962) The Economic Implications of Learning by Doing, Review of Economic Studies, 29, 155-173.
Berndt, E. R. (1990) The Practice of Econometrics: Classic and Contemporary, Addison-Wesley, New York.
Bertram, W. J. (1988) Yield and Reliability, in VLSI Technology, ed., S. M. Sze, McGraw Hill, New York, 612-655.
Boston Consulting Group (1972) Perspectives on Experience, Boston Consulting Group, Boston.
Braun, E. and MacDonald, S. (1978) Revolution in Miniature: The History and Impact of Semiconductor Electronics, Cambridge University Press, Cambridge.
Choi, Y. (1995) Dynamic Techno-Management Capability in the Semiconductor Sector: the Case of Samsung Semiconductor, Science Technology Policy, 7, 27-50 (in Korean).
__________ (1996) Dynamic Techno-Management Capability: the Case of Samsung Semiconductor Sector in Korea, Avebury, Hants.
Chung, S. (1998) The Learning Curve in the Korean Semiconductor Industry, Diss., New School for Social Research, New York.
Dick, A. R. (1991) Learning by Doing and Dumping in the Semiconductor Industry, Journal of Law and Economics, 34, 133-159.
Dosi, G. (1984) Technical Change and Industrial Transformation, St. Martin’s Press, New York.
Flamm, K. S. (1996) Mismanaged Trade?: Strategic Policy and the Semiconductor Industry, Brookings Institution Press,Washington, DC.
Green, E. M. (1996) Economic Security and High Technology Competition in an Age of Transition: The Case of the Semiconductor Industry, Praeger, Westport.
Gruber, H. (1992) The Learning Curve in the Production of Semiconductor Memory Chips, Applied Economics, 24, 885-894.
__________ (1994a) Learning and Strategic Product Innovation, North Holland, Amsterdam.
__________ (1994b) The Yield Factor and the Learning Curve in Semiconductor Production, Applied Economics, 26, 837-843.
Hazewindus, N. and Tooker, J. (1982) The U.S. Microelectronics Industry: Technical Change, Industry Growth and Social Impact, Pergamon Press, New York.
Helper, S. and Lazonick, W. (1984) Learning Curve and Productivity Growth in Institutional Context, Harvard Institute for Economic Research Discussion Papers 1066, Harvard University, Cambridge.
Howell, T. R., Noellert, W. A., MacLaughlin, J. H. and Wolff, A. W. (1988) The Microelectronics Race: The Impact of Government Policy in International Competition, Westview Press, Boulder.
Irwin, D. A. and Klenow, P. J. (1994) Learning-by-Doing Spillovers in the Semiconductor Industry, Journal of Political Economy, 102, 1200-1227.
Joskow, P. L. and Rozanski, G. A. (1979) The Effects of Learning by Doing on Nuclear Plant Operation Reliability, Review of Economics and Statistics, 61, 161-168.
Kim, L. (1997) Imitation to Innovation: The Dynamics of Korea’s Technological Learning, Harvard Business School Press, Boston.
Kraus, J. (1973) An Economic Study of the U.S. Semiconductor Industry, Diss., New School for Social Research, New York.
Langlois, R. N., Pugel, T. A., Haklisch, C. S., Nelson, R. R. and Egelhoff, W. G. (1988) Microelectronics: An Industry in Transition, Unwin Hyman, London.
Lieberman, M. B. (1984) The Learning Curve Pricing in the Chemical Industries, RAND Journal of Economics, 15, 213-228.
Malerba, F. (1985) The Semiconductor Business: The Economics of Rapid Growth and Decline, University of Wisconsin Press, Madison.
Nye, W. W. (1989) Some Evidence on Firm-Specific Learning-by-Doing in Semiconductor Production, Discussion Paper no. 89-11, Department of Justice, Economic Analysis Group, Washington DC.
Oi, W. Y. (1967) The Neoclassical Foundations of Progress Functions, Economic Journal, 77, 579-594.
Sciberras, E. (1977) Multinational Electronics Companies and National Economic Policies, JAI Press, Greenwich.
Solow, R. M. (1957) Technical Change and the Aggregate Production Function, Review of Economics and Statistics, 39, 312-320.
Steinmueller, W. E. (1987) Microeconomics and Microelectronics: Economic Studies of Integrated Circuit Technology, Diss., Stanford University, Stanford.
Tanimitsu, T. (1994) The Trajectory of Semiconductor Industry: The Half Century of U.S.-Japan Competition, Nikkan Gogyo Shimbunsha, Tokyo(in Japanese).
Webbink, D. W. (1977) The Semiconductor Industry: A Survey of Structure, Conduct, and Performance, Staff Report to the FTC, U.S. Government Printing Office, Washington DC.
Wright, T. P. (1936) Factors Affecting the Cost of Airplanes, Journal of The Aeronautical Sciences, 3, 122-128.
'형설지공 > 경제경영' 카테고리의 다른 글
| 국제 유가 하향 추세와 기술 변화 (0) | 2001.03.08 |
|---|---|
| 통합 방송법이 산업에 미치는 영향과 전망 (0) | 2001.03.08 |
| 제 2 절 더불어 사는 사회 (0) | 2001.03.08 |
| 제 1 절 경제정의의 실현 (0) | 2001.03.08 |
| 제 2 절 세금의 종류 (0) | 2001.03.08 |