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Quantitative Marketing and Economics

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01.03.2014

Competition and product innovation in dynamic oligopoly

verfasst von: Ronald L. Goettler, Brett R. Gordon

Erschienen in: Quantitative Marketing and Economics | Ausgabe 1/2014

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Abstract

We investigate the relationship between competition and innovation using a dynamic oligopoly model that endogenizes both the long-run innovation rate and market structure. We use the model to examine how various determinants of competition, such as product substitutability, entry costs, and innovation spillovers, affect firms’ equilibrium strategies for entry, exit, and investment in product quality. We find an inverted-U relationship between product substitutability and innovation: the returns to innovation initially rise for all firms but eventually, as the market approaches a winner-take-all environment, laggards have few residual profits to fight over and give up pursuit of the leader, knowing he will defend his lead. The increasing portion of the inverted-U reflects changes in firm’s investment policy functions, whereas the decreasing portion arises from the industry transiting to states with fewer firms and wider quality gaps. Allowing market structure to be endogenous yields different results compared to extant work that fixes or exogenously varies the market structure.

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We define the long-run innovation rate as the average rate at which the industry’s frontier quality improves, averaged across the ergodic set of states. In Pakes and McGuire (1994), the long-run innovation rate equals the exogenous rate at which the outside good’s quality improves, as discussed in Appendix A.

To clarify our terminology, a firm is a leader if its product quality is greater than or equal to all other firms in the industry. Since multiple firms can exist at this industry frontier, there can be multiple lead firms. A laggard is any firm with a quality level strictly below the frontier product quality.

Analyses of dynamic oligopoly with differentiated products include the study of collusive pricing (Fershtman and Pakes 2000), competition among hospitals (Gowrisankaran and Town 1997), advertising dynamics (Dubé et al. 2005), and oblivious equilibrium (Weintraub et al. 2008).

Other work considers different forms of innovation spillovers. Levin and Reiss (1998) incorporate spillovers by allowing a firm’s innovation outcome to depend on the investment levels of all firms in the industry. Similarly, Kamien et al. (1992) capture innovation spillovers in the form of research joint ventures. For our purposes, the key notion behind the innovation spillover is that a laggard firm’s R&D is more efficient.

Work in endogenous growth theory also considers quality-ladder models (e.g., Grossman and Helpman 1991; Aghion and Howitt 1992) to study topics ranging from competition in international trade to optimal policies for national economic growth.

Borkovsky (2012) studies a more realistic innovation process in a dynamic quality-ladder model where firms time the release of new innovations and can stockpile successful innovations.

Although the scale of a ₀, x _jt, and market size M are arbitrary, we consider levels of a ₀ on the order of one which implies a leader’s innovation rate will range from .1 to .9 for x values roughly spanning one to nine. We therefore think of investment (and market size) as being measured in millions to yield investment and profit levels typically observed.

Doraszelski and Satterthwaite (2010) define an investment transition function, such as f(τ | x, ω, s), as being unique investment choice (UIC) admissible if the function leads to a unique investment choice for the firm.

We choose the bound such that the outside good’s share is less than .001, so that firms’ profits would not improve much if the outside good were even further behind.

The distribution of scrap values could be a function of ω.

Iskhakov et al. (2013) examines leapfrogging behavior in the context of a dynamic duopoly model with cost-reducing investments.

We include a complementary slackness condition due to the non-negativity constraint on investment.

The averages we report in the simulations are not necessarily from the recurrent class of states. The innovation rate we report corresponds to the steady-state innovation rate if the initial state falls in the recurrent class, otherwise the measure we report is simply the average over the first 100 years.

To relate these costs to a particular industry, consider that Intel’s 2012 4th-quarter net income was $2.5 billion. Since cost estimates of semiconductor fabrication plants are typically around $3 billion, our range of entry costs seems at least plausible. For estimates of fabrication plants costs, see http://finance.yahoo.com/news/Construction-Of-Chip-twst-2711924876.html, http://topics.nytimes.com/top/news/business/companies/taiwan-semiconductor-manufacturing-company-ltd/index.html, and http://www.optessa.com/industries_semi.htm, all accessed on 2.8.13.

Many of our model’s parameters could be reasonably chosen, via calibration or formal estimation, using industry data. The R&D efficiency and spillover parameters, a ₀ and a ₁, could be estimated using data on R&D expenditures and product innovation outcomes. Quality preferences, γ, could be estimated using standard demand data or calibrated based on data from similar industries. Income can be chosen based on Census information or knowledge of the relevant consumer demographics. Under log utility, the maximum amount any firm can charge is y.

For some parameterizations, we can find equilibria with absorbing states where no firms invest. These equilibria typically either have a single leader at the frontier with multiple laggards below the entry threshold or all firms at the frontier. The laggards serve to deter potential entrants, and the leader prefers not to invest because it could induce the laggards to exit, prompting entry by new firms at a higher quality level. These parameterizations seem unrealistic and so we avoid them, in part by having scrap values that induce distant laggards to exit.

See Song (2011) for a dynamic oligopoly model of research joint ventures.

PMC = 0.78 corresponds to $\frac {1}{\pi /\sqrt {6}}$, the inverse of the standard deviation of a logit error term. A PMC of 1.56 is therefore equivalent to doubling the coefficients on all terms in the utility function while maintaining the standard variance of the logit error.

In some markets, PMC evolves over time. When idiosyncratic shocks are perception errors about unknown product quality, PMC intensifies as consumers learn firms’ qualities. Consider the search engine market, born in the 1990’s with the sequential entry of Excite, Yahoo!, WebCrawler, Lycos, Infoseek, Altavista, Inktomi, AskJeeves, Google, MSN, Overture, and Alltheweb. Consumer uncertainty was initially high regarding search engine quality because most people lacked experience in the domain and evaluating the quality of a given query was difficult. Over time, the search engines refined their algorithms and consumers gained general experience with web-based search technologies. Four years after entering, Google led the U.S. search query market with a 29.2 % market share and now maintains its market dominance with a 65.6 % share, according to comScore. Google’s profits have soared as its competitors struggle (PCWorld 2010, Forbes 2011).

For values of 1 / σ _ε < 0.3, the industry continues to fill up with an increasing number of firms (as illustrated on the left-hand side of Fig. 3d) and industry innovation continues to drop for reasons explained in this section. For values of 1 / σ _ε > 1. 9, entry continues to fall (as illustrated on the right-hand side of Fig. 3d) and the industry moves closer to a persistent monopoly with industry innovation continuing to decline.

The bottom row of Fig. 5 plots the policy functions to show the absorbing states when the laggard is sufficiently far behind the leader (who is always at 30 for these plots). Figure 5d and e depicts policy functions for duopolies with high and low PMC, respectively. Figure 5f considers a triopoly to show that the presence of the third firm (at ω = 14) only has a small effect on the other two firms’ innovation policies, by comparing panel (e) to (f). Note that the leader’s higher innovation for ω ₂ < 14 results from the third firm being at ω ₃ = 14. When both laggards in Fig. 5f are tied at ω ₂ = ω ₃ = 14 or lower, neither invests. Even with low PMC, the residual profits are insufficient motivation to invest when they are far behind the leader.

To draw a comparison with the results in Aghion et al. (2005) and Goettler and Gordon (2011) conduct a comparative static in PMC in a nondurable version of their model where the laggard is at most one step behind the leader. Figure 11 of Goettler and Gordon (2011) shows that industry innovation increases in PMC and they claim the same result would hold even if the maximum quality gap between the firms is widened. That claim is correct, but only for moderate increases in the maximum quality gap. If the maximum gap is sufficiently wide that a laggard eventually gives up (as in the current paper), then innovation is decreasing in PMC because the point of giving up is reached more quickly the higher is PMC.

The industry innovation rate at an arbitrary state s equals one minus the probability that all frontier firms fail to innovate: $1 - (1 - f\left (\tau = 1 \right |\bar {x}(s)))^{\sum _{j=1}^{J(s)} I(\omega _{j} = \bar {\omega })}$ where $\bar {x}(s)$ is the investment by each firm at the frontier and the exponent gives the number of firms at the frontier.

(2010) does, however, find that process R&D (to lower costs) increases as import tariffs fall.

PM set λ = − 4, γ = 3, and report ω∗ = 12. However, the GAUSS code for their model (http://www.economics.harvard.edu/faculty/pakes/program), uses a value of 12 for the point of concavity after scaling by 3 and shifting by − 4. The corresponding value for ω∗ on the ω grid (0, 1, 2, … ) is 16 / 3.

The positive relationship between δ and profits in PM would extend to values lower than 0.4 if we were to increase the maximum number of firms, which becomes binding at δ = 0.4 in these simulations.

For our model, we can calculate an alternative measure of consumer surplus without imposing $\bar {\omega }_{max}$. To compute this alternative measure, we simulate the model using policy functions obtained from the model that imposes $\bar {\omega }_{max}$ but track and use the absolute quality grid when computing consumer surplus in each period. When equilibrium in our model never yields a monopoly, the equilibrium policies are good approximations to the policies when $\bar {\omega }_{max}$ is relaxed. When the constraint is relaxed, the difference is much greater, particularly when δ is low.

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Titel: Competition and product innovation in dynamic oligopoly
verfasst von: Ronald L. Goettler
Brett R. Gordon
Publikationsdatum: 01.03.2014
Verlag: Springer US
Erschienen in: Quantitative Marketing and Economics / Ausgabe 1/2014
Print ISSN: 1570-7156
Elektronische ISSN: 1573-711X
DOI: https://doi.org/10.1007/s11129-013-9142-2