Productivity and Cyclicality in Semiconductors: Trends, Implications, and Questions: Report of a Symposium (2004)

Dale W. Jorgenson

Harvard University

Dr. Jorgenson noted that Dr. Flamm, when he began to experiment with mathematical models of the semiconductor industry a decade ago, was one of the few economists in that specialty. Many others are now applying dynamic modeling techniques to the industry.

Ariel Pakes

Harvard University

Dr. Pakes said that one of the goals of his research was to devise a modeling strategy that can be used to model whole industries. He said that part of this strategy was to construct a framework for dynamic analysis. This approach followed earlier efforts with simple models, which proved to be inadequate to handle the complexity of such large, changing entities as the semiconductor industry.

He began by using data from the industry itself to create inputs called “primitives.” These are rich enough to determine each firm’s profits conditional on the

qualities of the products marketed, the costs of production, and the prices charged by all firms. They also determine the likely impacts of investments, the likelihood of potential entrants’ appearing, and the costs or benefits generated by an exit decision. The framework assembles the primitives in a coherent fashion and uses them to numerically analyze problems that could not be analyzed with simpler theoretical models. The primitives must be realistic, he emphasized, which means that the person working with the model must have direct access to information about the industry. The user can then use the framework to generate quantitative responses to changes in the business environment or in a policy.

Then he discussed the simplest form of the framework, which he said was a publicly available program found on his web site.⁶ The simple form is used mostly for teaching. “The world is a complicated place,” he said, “and we want to show students what can happen if you change a tax, a tariff, or an entry barrier and let the whole industry evolve differently.” When used for research, the framework needs to be extended to incorporate the major institutional features of the industry being studied. The framework has a static portion and a dynamic portion.

Each static model consists of a demand system and a set of cost functions, one for each producer, along with an equilibrium assumption. In the simple applications, this allows one to solve for reasonable pricing or quantity-setting decisions of firms that are faced with the demand and cost primitives. If we were using a Nash equilibrium pricing assumption, for example, the program would solve for a set of prices at which each firm is doing its best, given the prices of other firms. This is a reasonable “textbook” equilibrium assumption.

This static pricing assumption will determine the prices, and through the prices the quantity, of each product sold. This plus the cost functions enables the program to compute the profits of each firm as well as consumer benefits. The profits of each firm are calculated as a function of the characteristics of the firm’s and its competitors’ products and cost functions. The program computes profits for each of the firms for all possible characteristic combinations.

The dynamic model goes a step further and feeds these profit functions into another program, which analyzes the investments in developing the characteris-

tics of the product or in reducing cost. The goal of the larger program is to produce the likely investment decisions that result from those profit estimates and their likely impact on the industry and consumers.

The simplest version of the model, said Dr. Pakes, can be extended in many ways. One is to include multiple states per firm, where firms differ in the quality of the product and cost of production. For the semiconductor industry, one would want multiproduct firms, with each firm producing more than one kind of chip. The model can also allow for mergers and make more complicated pricing decisions. In addition, pricing decisions can be based not simply on how prices affect current profits, but also on an independent effect of prices on future profits through their effect on future demand, on future costs, or on future equilibrium prices. A pricing decision that affects future equilibrium can be used to generate various forms of coordination, which is also relevant to the semiconductor industry. It does so by choosing price to ensure that the coordination is “incentive compatible.” That is, it ensures that coordinated action will be in each firm’s interest; no firm can deviate from the coordination without decreasing its own value.

Dr. Pakes then went through the core version and several extensions of the model in slightly more detail, and he illustrated several challenges in applying it.⁷ The simplest version contains one product per firm and one characteristic per product: product quality. The higher the quality of the product, the more people like it. When all the firms producing a product with a certain quality level are combined into a vector, the result is how many firms are producing this quality level. Given investment decisions, the distribution of future quality is independent of price- or quantity-setting decisions. This assumption makes the model easy to work with; dynamic pricing does not have to be considered.

He said that the first module in the program includes only the demand functions, cost functions, and an equilibrium assumption. It is able to calculate the profits of each firm for every possible vector of quality of products in the industry. He then explained the Bellman equation for incumbent behavior. This calculates the value of a firm as the expected discounted value of future net cash flow.

The actual value will depend on the random outcomes of these investments. However, it is this expected value that one assumes the firm is trying to maximize.

The Bellman equation is solved in the following way: The firm can either exit or continue. If it continues, it receives current profits and chooses a quantity of investment. The investment improves the probability of having a higher-quality (or lower-cost) product in the next period. The value of the firm in the next period is not known because it depends on the outcome of the random outcomes of the firm’s investments and of those of the firm’s competitors.

The distribution of tomorrow’s quality, given today’s quality and the amount invested today, is a primitive. The increment in the quality of the product depends on two things. One is a probability distribution which tells that the value of the increment will depend stochastically on the amount invested. The larger the amount invested, the more likely the outcome is to be good. The second is an exogenous shock that concerns the competitiveness to the industry, or demand.

To solve for the firm’s investment we require one more factor: the firm’s perception of where its competitors will be tomorrow (the profits it is likely to make from any given outcome depend on where its competitors will be). These perceptions must, in some sense, be consistent with the actions of those competitors. An equilibrium occurs when each agent chooses the best of the actions available to it, given perceptions of competitors’ behavior that are consistent with what the competitors actually do.

To find an equilibrium in this model assume we know the distribution of where the firm’s competitors will be tomorrow. If a firm knows where its competitors are likely to be in future years, the firm can calculate what it should do. That is, an incumbent can determine whether it should exit or continue and what its investment should be if it continues, and a potential entrant can decide whether it should enter. Once all determine what they will do, there is a real distribution of outcomes from all the primitives. When the realized distribution is the same as the belief distribution, equilibrium is reached. In the equilibrium, given a firm’s perceptions of what all firms will be doing tomorrow, the firm is doing the best it can. Moreover, the firm’s perceptions of where other firms will be tomorrow are stochastically correct. That is, in equilibrium, the distribution a firm perceives is in fact the distribution that derives when all are doing the best they can for themselves. In the second module of the program, the computer in effect solves for investment entry and exit strategies.

The third module of the program allows the analyst to simulate outcomes from an initial position. By entering information about where all firms are today, the program can simulate the most likely path for the industry over time. It also answers questions about the likely trends in market structure, investment, etc., and will do another simulation to calculate producer profits and consumer benefits over time. Users can specify a starting point, then change a policy, or demand, or an environmental parameter and compare the two outcomes. The objective is to have a coherent framework in which to work in a dynamic setting.

He then touched on several extensions of the module that have been developed by others. One was developed for the hospital industry. When the Clinton administration proposed changes in health care, it never analyzed how changing the nature of reimbursement would also change the structure of the hospital industry. When the model was run, the change in reimbursement was predicted to change the equilibrium of the industry, and it was shown that the new equilibrium might not be desirable. This turned out to be the case, with some hospitals merging, others going out of business, and prices actually rising instead of falling in different parts of the country. These things happened, said Dr. Pakes, partly because planners never took into consideration the dynamic impact of changes in the structure of demand.⁸

Another extension was applied to analysis of the effects of coordinated activities on the part of firms. The perception of coordination differs in Europe, Asia, and the United States. Here, price coordination is traditionally regarded as a form of collusion, in which any coordination on pricing is presumed to be per se illegal. The argument behind this presumption is that higher prices are worse for consumers than lower prices. This presumption, he said, ignores the dynamics involved. If firms collude and raise prices, the higher prices may in fact induce more firms to enter, or firms to produce a more favorable range of quality products, and investment can be more productive.⁹

Dr. Pakes and a collaborator wrote a paper in which they showed that consumers could be better off with collusion than without it. They chose an industry with a very small number of products; the simplest case is an industry where there is a monopoly without collusion. In this case, an active antitrust authority would allow only one firm. If collusion were allowed, it would be optimal for a second firm to enter because prices would be higher. Consumers would then receive both a lower-priced product and more variety to choose from. This argues for price collusion to be subject to the rule of reason, as in Europe. In this case price collusion would not be per se illegal, and the court would decide whether collusion is bad or good for consumers.

Similar exercises can be used to formulate merger policy. With a static horizontal merger model, the reason to merge is to raise prices. When the dynamics of the situation are considered, the merger changes the incentive to enter along with investment incentives.

This discussion seems relevant to the semiconductor industry. It has coordinated interactions in research and development but not in investment. We might want to ask, if we did coordinate our investment strategies, could we get to an equilibrium that would be better for everyone? What would be the implications for consumers, and for the industry itself? This can be done in principle, he said, although further study would have to be done to determine whether it could produce useful answers for the semiconductor industry.

He concluded by saying that his modeling technique still has computational problems, but that solutions to these problems now appeared likely. One that seems to be working well is an artificial-intelligence algorithm that acts in a way similar to the self-teaching function of computers. By keeping information on periods when the industry was in a similar situation in the past, and including an examination of what happened then as a result of various actions, the computer is enabled to choose today what would have given the best response yesterday. If these solutions do emerge as expected, dynamic modeling could be a useful analytic and predictive tool for many industries.

C. Lanier Benkard

Stanford University

Dr. Benkard opened by saying that the aircraft and semiconductor industries have several things in common, including a “learning-by-doing” function. Both

industries also respond better to the kind of dynamic model that Dr. Pakes described than to the older type of static model.

There are differences, however. In referring to the learning curve of the industry, he displayed data for the L-1011 airplane, produced by Lockheed from 1972 through 1984. These data demonstrated the direct labor requirement for every plane manufactured, which totaled about 250 units. The first plane required about 1.5 million man-hours to complete, a figure that was quickly reduced by about 80 percent, to about 200,000 hours. This reduction took about 4 years to accomplish, out of a manufacturing lifetime of 14 to 15 years. That product life-time is near the industry median; the Boeing 747 was brought out in 1969 and is still being manufactured three decades later. By contrast, he said, the semiconductor industry has a much shorter product cycle and learning curve.

Another difference between the two industries can be seen in pricing behavior. Compared to the steadily declining prices of semiconductor products, real aircraft prices tend to remain largely flat; he illustrated this with a series of prices set between 1958 and 1997. Price rises that did occur for aircraft usually reflected the introduction of a new, more expensive model, as did the progression from the Boeing 747-100 to the 747-400, which was 20 percent larger. He said that the traditional, static business model cannot explain the concurrence of two of the trends—one that showed the cost of labor falling 80 percent, another that showed flat prices for aircraft. Static models tend to produce a “cost-plus” pattern: the cost plus a markup of approximately 100 percent. This is why Dr. Benkard began, like Dr. Pakes, to work with the dynamic model.

His overall modeling approach begins with estimates of model primitives, or static profits. The goal is to estimate profits for each period by knowing, for

example, the set of products in the market. He then uses a computer to calculate the model equilibrium—what happens in the dynamic model—from these primitives. The model primitives are a set of variables that summarize the “state of the world”—for example, a list of the products in their market and their qualities. The primitives also include a set of control variables, such as quantity or price.

The second objective is to calculate profits. This entails entering a profit function that calculates how the firm’s profits will respond as the world changes from period to period, based on the actions of the firm. For aircraft the most important feature, or “state variable,” is that planes are differentiated products—that is, they are not all the same. This is probably much more important for aircraft than for semiconductors.¹¹ As shown by the wide variations in the number of seats and range, some planes have close competitors while others do not.

Dr. Benkard models this by writing down the variables of different planes being produced today and their qualities. Then he enters the firm’s experience in producing that plane in period “t”—the learning curve—which determines the cost of producing the plane. He uses a “common state,” which is the state of demand in the world. In each period, a firm has to make decisions, such as whether to exit a product it currently produces and how much of that product to produce. Other firms as well will be deciding whether to enter. All these control variables can actually be observed.

In working with the model primitives, the next step is to ask how to calculate profits as a function of those variables. This profit function is very simple and standard: price times quantity minus cost. Quantity is simply the amount of product. The price is what the aircraft will bring in the market, using standard techniques of predicting demand with a nested logic model, and the costs are the expense of producing the aircraft. For the other side of the model—cost—a standard learning-curve formulation is used for production costs. The engineers in semiconductor firms are familiar with finding costs in the same way. Of these inputs to the model the most important is profit function.

The other input needed is how the world changes from today to tomorrow. This value turns out to be straightforward, and it is derived from what has already been done. If a firm with a given experience level produces quantity “q,” its

experience tomorrow is its past experience plus the quantity it produces today. Based on what firms have done, the model suggests what products to exit, what products to enter, and so on.

One key feature of the aircraft industry that differentiates it slightly from the base-case model of Dr. Pakes is dynamic pricing. The learning curve not only determines profits today, but also the cost of production tomorrow. This gives firms an incentive to produce more and price more aggressively. Expanded quantity resembles a form of cost-reducing investment: The amount a firm produces and sells today is also an investment in tomorrow.

One lesson the model can teach is that it is possible to predict prices, markups, and quantities. He showed a graph plotting the predicted price of the L-1011 from 1972 to 1986 vs. the actual price, and they were very similar. Also similar were the predicted and actual price-to-cost ratios for the same period. This shows that Lockheed’s pricing behavior was reasonably close to what it should have been, given the situation. Lockheed’s financial losses, he said, were probably caused by the two major oil shocks during the period. The airplane was never sold at a price below cost.

Next he showed a simulation by the model over a 20-year period. At the starting point, four new planes were coming to market. Because they were new, workers still had to learn their tasks, and the costs of all four were high, though at different levels. As the workers progressed along the learning curve, costs declined steeply. This, he said, looks at first like the semiconductor industry, where everyone starts out with products on the same roadmap and the technology is more or less synchronized. In the aircraft industry, by contrast, a new plane may enter the market populated by competitors that are already efficient. The newcomer, with high initial costs, cannot compete if it sells the planes at that cost and must begin by selling planes at a loss. This is an important difference between the two industries.

He showed two more graphs to give the flavor of the model. One graph showed a simulation over the same 20-year period for unit sales. During some years all planes did well, and in others they did not; there were wide fluctuations indicating boom times and recessions.

The second graph showed the firms’ realized discounted cash flow for 20 years. At first each firm lost money, then started making it—which is generally what happens in reality. He said that he had experimented with an antitrust policy model, also, which showed that firm antitrust regulations usually have a negative impact on the consumer. He concluded by saying that cooperation among firms in

industries like the aircraft and semiconductor industries might be beneficial from an economic point of view.

Minjae Song

Harvard University

Mr. Song said that he is writing his economics thesis on the microprocessor industry, and that he chose that industry because he believed it offered the most dramatic and rapid innovations in the economy. He has developed a dynamic model to help understand this industry and certain of its features that lend themselves to modeling.

A distinctive feature of this industry, he said, is its continuous introduction of new generations of semiconductor chips, and the dramatic difference in performance from one generation to the next. The cost of rapid innovation is very high, and it has been increasing over time. The costs consist of building new fabrication plants, or fabs, upgrading existing fabs, buying new equipment, and performing research and development, which is very expensive in this industry.

Standard models of the industry have used marginal costs, he said, but his objective is to include sunk costs to firms, a factor of predominant importance in this industry. One cause of high sunk costs is the very short life span of products. For example, the longest life span of a single chip, according to his data, has been 8 to 10 quarters. The average life span of the technology is 2 to 3 years. Over the past ten years, the industry has produced five to six different generations of semiconductors.

“These are the basic features that I want in my model,” Mr. Song said.

The model allows for two firms in the market producing two types of products. The “frontier” product and the “non-frontier” product coexist in the industry at the same time, with the former having better technology than the latter. When a firm introduces the frontier product, the previous frontier product becomes a non-frontier product. Thus frontier and non-frontier are relative terms. For example, when both Pentium 2 and Pentium 3 processors were in the market,

Pentium 3 was used as the frontier product for the model. Then Pentium 3 became the non-frontier product with the introduction of Pentium 4.

The firm produces each product in a separate plant, so that a plant represents a particular type of product. The entry of a firm into the production of a new product can be expressed as the “entry” of a new plant. But the plant does not have to represent a single fab; it can represent a group of fabs that use the same technology. There are at most four plants in this industry shared by two firms, with one plant producing one type of product or two plants producing both types of the product at the same time. In the model, the sunk cost to the firm is introduced by the entry cost of each plant.

In his model are two state variables. First, efficiency variables for each firm are present in the standard dynamic model. To this a second state variable called the “technology variable” is added to represent whether the product is a frontier or non-frontier product. Quality here is defined as a certain value plus other attributes the firm tries to improve.

The firm can then choose among several strategies. Along with entry into and exit from the market and average period of investment, another strategy choice for firms is the entry and exit of the plant. A firm with one plant can keep producing its one product, or introduce a frontier product by setting up a new plant, or exit the market. A firm with two plants can keep producing two products, or choose one and exit the other, or introduce another frontier product and take the non-frontier product out of the market. Thus a single firm uses this kind of decision tree, depending on where the firm is. It computes the value of each strategy at given points and chooses the one that gives the firm the highest value. That value is not just current profit, but the sum of all net cash flow and the option value of having or not having plants in the market.The model can also include other features of industry. One is increasing firm cost over time. For example, it is reasonable to allow the entry cost of a plant to increase over time. The entry cost of introducing a new type of product yesterday was lower than it is today. Another feature of the model is that it allows firms to be asymmetric in terms of the entry costs, so that one firm is more efficient than others at introducing a new product. The model can also introduce spillover effects in the market. When one firm is first to introduce a frontier product in the market, it is easier for the other firms to follow suit. So the entry costs of a new plant depend on whether it is producing a frontier product or not.

From this model, one can expect to measure the value of a firm’s innovations and investments. It is also possible to measure the benefit of the innovations to society. This measurement of welfare is based on demand, which is estimated outside the model. This estimate involves collecting product-level data for the microprocessors, making an estimate of demand, and incorporating that demand into the model to make it as realistic as possible.

The entry and exit of the plant may represent the product cycle for this model. The entry of the plant may represent the beginning point for one generation of product, and the exit of that plant may represent the ending point. The model allows a study of whether the plant is more likely to enter or to exit.

The model can also simulate the market outcomes of various market structures. If this industry were a monopoly, for example, how would market outcomes change? What if social planners made a certain decision that affected this industry—what would happen? One can also ask policy questions, such as: If we want more spillovers in this market, does the government have to do something? One can also evaluate the role of SEMATECH or other mechanisms that affect the industry.

Dr. Wessner asked several questions:

• Did the Boeing 747 in effect have a monopoly on the large-airplane market?

• Could the model, in the case of the European Airbus, take into account government subsidies?

• Do aircraft manufacturers make money on aircraft-body maintenance contracts, as engine manufacturers are said to?

• Is the initial low pricing of aircraft a form of forward pricing or dumping which is designed to drive a competitor out of business?

Dr. Benkard responded that the Boeing 747 has a monopoly in certain markets because it has a very long range. But its size does not create a monopoly, because a competitor can compete by flying two smaller planes. This is a condition the model can create.

Second, he said that a desire to evaluate the question of subsidies was one of the reasons for developing the model. He said that it is difficult to quantify the value of Airbus subsidies, however, because they take the form of low-cost loans for new-product investment, along with what seems to be a small output subsidy when state-run airlines purchase the plane.

Third, he said he knew of no case where a company had been able to use forward pricing to drive competitors out of business. The primary reason for low initial pricing is that it is the only way a company can sell its planes into a market already occupied by competitors’ products. The market simply adapts in a way that allows this pricing behavior: It must be profitable for a producer to bring in a plane at a low initial price and eventually to make the money back. Otherwise, all the companies would go out of business, whether state-owned or privately owned. He pointed out that this held true even during the postwar years, when the industry was truly competitive, with 22 aircraft producers. Since then, pricing behavior does not seem to have changed, even at a time when the global industry has only two firms manufacturing a relatively small number of products.

Dr. Pakes pursued the idea of when it makes sense to price forward: i.e., for manufacturers to market goods at prices lower than marginal costs. One reason for a company to do that, he said, is to get down its learning curve faster, decrease its cost tomorrow, and perhaps force its competitors out of business. That is in fact what happened in the competition for wide-bodied aircraft, where Lockheed was eventually forced out of the business. A dynamic model is needed to rationalize this order of behavior, which does not appear in the standard static models that economists generally use. If costs tomorrow did not depend on pricing conditions today, a company would never price something at less than marginal variable costs. It would lose money, and there would be no gain tomorrow. Dr. Benkard’s model, he said, showed that it makes sense in the aircraft industry to price below cost in the early stages of marketing the good. A company may not recover those costs, as in the case of Lockheed, or it may recover them and much more, as in the case of the Boeing 747.

David Morgenthaler offered several points about the semiconductor industry and cyclicality. He emphasized Dr. Doering’s point about the long-term dynamics of the demand side in the semiconductor industry, which is the declining cost per function. This has the effect of expanding markets, and presumably also of expanding the diversity of markets—the number of different end-use applications. One anomaly is why this increased diversity of end-users does not seem to translate into smoother cycles, especially if all the different markets are moving synchronously.

Second, it is important that in the industry as a whole much of the expansion of foundry capacity is really inframarginal capacity. Foundry products are slightly behind the technological frontier. In this behavior, the semiconductor industry differs both from the aircraft industry and the microprocessor subsegment. He suggested that what is really happening is that the expanding diversity of the market for semiconductors is creating opportunities for short product runs that are one or sometimes two generations behind the frontier. This is where foundries have historically done very well, at least partly because semiconductors constitute input for many diverse products.

Third, he discussed the practice of leasing for both industries. For aircraft, leasing of the product has been an important and growing source of demand. Lease companies in some cases take advantage of cyclicality by buying aircraft in down cycles. In the semiconductor industry, leasing in the equipment segment is also growing fairly rapidly. This may be driven partly by increased cost of capacity and partly by increased diversity of demand for equipment. It has interesting implications for entry into the industry, for capacity extension, for demand cycles, and for the cyclical behavior of markets for semiconductor equipment.

Dr. Flamm complimented the modelers for the realism of their results and asked a question about calibrating the models to actual data: Did the modelers assume that the observed histories reflected equilibrium positions, or did they begin out of equilibrium and move toward it?

Dr. Benkard said that he could take either approach. His own approach, which was to estimate demand and cost and to use them as inputs, did not rely on the real world being in equilibrium. It took the inputs and then asked what the equilibrium would be. However, he said, he could also use the model in such a way that it required the real world to be in equilibrium.

Dr. Pakes agreed. He said that the preferred way of modeling is to have estimates for cost and estimates for demand. However, this is difficult for some parameters, such as the cost of entry. As a technical matter, it is virtually impossible to estimate all the parameters by using the equilibrium behavior. For parameters that were difficult to get at, he suggested gathering data from people in the industry and using a range of reasonable values.