Business commonality, standardization and product cycles

Abstract

By analyzing production with a continuum of tasks subject to common stochastic effects, the analysis shows that tension between business commonality and standardization is an important source of product cycles. The paper addresses the question of whether business commonality and standardization work in tandem or against each other in a general framework, when fragmentation of production is or is not possible due to contractual incompleteness or technology features. Unlike current literature, the analysis shows that a product cycle can be obtained even with complete contracts. This is so because retaining manufacturing within the firm enhances and exploits commonality in the early stages of production and, hence, reduces the moral hazard cost of providing incentives, which would be a hidden cost of outsourcing instead. Standardization later on can favor offshoring.

Keywords:

• Product cycle
• Globalization
• Offshoring
• Complete and incomplete contracts
• Tournaments

JEL Classifications:

• D21
• D23
• D81
• D86
• F16
• F23
• F66
• J33
• J41
• L24
• M52

Acknowledgements

An earlier version of this paper benefited from very useful discussions with Elias Dinopoulos. I am also grateful to Gregory Wright for useful suggestions, as well as the participants of the South West Economic Theory Conference at the Randy School of Management of UC San Diego on 28 February 2020, at the Economics Seminar of UC Davis on 26 May 2020, and at the Conference on Mechanism and Institution Design on 11 June 2020. The paper also benefited from useful comments and suggestions by anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

The appendix (Setting up a multinational corporation) is available online at tsoulouhas.info.

Notes

1 Hummels, Munch, and Xiang (2018) provide a survey of the literature on the effects of offshoring on labor.

2 Also see Mondal and Gupta (2006).

3 In their seminal work, Grossman and Hart (1986) established that contractual incompleteness disincentivizes relationship-specific investments for fear of a ‘hold-up’ problem inciting opportunistic behavior. Thus, residual rights must be allocated to the investing party contributing the most value to the contractual relationship (also see Hart and Moore 1990). The ‘hold-up’ problem was later studied by Grossman and Helpman (2002) in the context of outsourcing (also see Nunn 2007).

4 Also see Segerstrom, Anant, and Dinopoulos (1990), Feenstra and Hanson (1997), and Baldwin and Venables (2013). Carluccio and Bas (2015) study the negative correlation between the share of intra-firm imports and worker bargaining power; they show that it increases with capital intensity, but only in the case of industries for which relationship-specific investments and, hence, the ‘hold-up’ problem are significant. Similar to Antràs, they consider a model of outsourcing under incomplete contracts.

5 See Carluccio et al. (2019) about the link between firm productivity, skill intensity and offshoring.

6 See La Porta et al. (1998), and Roelfsema and Zhang (2012). A related issue is intellectual property rights. Bilir (2014) shows that, in the face of imitation risk, countries with strong patent laws attract higher levels of multinational activity in sectors with long product life cycles.

7 Even though business commonality is reminiscent of the firm-specific parameter in Bilir (2014) and Melitz (2003), the model specification here in which output is produced by combining tasks is quite different, and so is the specification of commonality.

8 Keep in mind that establishing a multinational corporation involves set up and relocation costs, while arm's length contracting entails transaction costs. Of course, both options involve transportation costs.

9 The latter finding is consistent with empirical evidence in Spearot and McCalman (2013).

10 See Lazear and Rosen (1981), Holmström (1982), Green and Stokey (1983), Nalebuff and Stiglitz (1983), van Dijk, Sonnemans, and van Winden (2001), and more recently Marinakis and Tsoulouhas (2013).

11 Note that even though the founders of tournament theory, Lazear and Rosen (1981), focused on ordinal or rank-order tournaments, such tournaments are informationally wasteful when data on the agents' cardinal performance are available (Holmström 1982). Moreover, Tsoulouhas (2015) has shown that switching from ordinal to cardinal tournaments improves efficiency. Thus, the focus in our analysis is on two-part piece rate (cardinal) tournaments taking the form $b+\text{β}(x_i-\overline{x})$, where $x_i$ is agent output and $\overline{x}$ is average output obtained by the agents.

12 Variability of commonality or common production uncertainty hampers the link between effort and output.

13 See Carluccio and Bas (2015) about the organizational structure of global firms and worker bargaining power.

14 This result is in contrast with Carluccio and Bas (2015). Also see Grossman and Helpman (2004) and Bloom and Van Reenen (2010).

15 Note that commonality can be influenced by managerial (principal) actions. This two-sided moral hazard problem has been analyzed in the literature (see Carmichael 1983 and the references in Tsoulouhas 2015). Overall, commonality includes all common shocks that affect all agents regardless of their actions, even if these shocks are influenced by principal actions.

The additive production function is pretty standard in the literature. It allows to disentangle the effects of ability, effort, common shocks and idiosyncratic shocks, and provides for closed-form solutions. Nalebuff and Stiglitz (1983), among others, have looked into alternative more complicated production functions. It is conjectured that the main results are qualitatively similar.

16 Note that Assumption (ii) is exactly symmetric to the assumption made in Dinopoulos and Tsoulouhas (2016). Here, $\tau \left(\theta \right)$ is strictly decreasing but ‘lower’ tasks are offshored. In Dinopoulos and Tsoulouhas (2016), instead, it is strictly increasing but ‘higher’ tasks are offshored. A similar assumption is also made by Grossman and Rossi-Hansberg (2008). The assumption serves the same purpose in all three papers: it delivers an interior solution to the fraction of offshored tasks.

17 This is so because $E[\exp (-r{w}_i+\frac{1}{2}\frac{r}{a}{e}_i^2\left)\right]=\exp [m+\frac{{\sigma }^2}{2}],$ when $-r{w}_i+\frac{1}{2}\frac{r}{a}{e}_i^2\sim N(m,{\sigma }^2),$ which allows us to obtain a closed form solution for the expected utility.

18 See Lazear (1986) and Gibbons (1987) on piece rates.

19 In addition, for institutional reasons, managerial practices in the South may be less advanced or there is a lack of know-how in characterizing and implementing more sophisticated incentive contracts.

20 There is a question about whether the firm should use $w_i\left(\theta \right)=b\left(\theta \right)+\text{β}\left(\theta \right)\left[x_i\right(\theta )-\overline{x}(\theta \left)\right]$ with $\overline{x}\left(\theta \right)=\frac{\sum _{i=1}^n{x}_i\left(\theta \right)}{n}$ being the average output obtained per task, or $w_i\left(\theta \right)=b\left(\theta \right)+\text{β}\left(\theta \right)\left[x_i\right(\theta )-\overline{x}]$ with $\overline{x}=\frac{{\int }_0^1\sum _{i=1}^n{x}_i\left(\theta \right)\mathrm{d}\theta }{n}$ being the average output obtained by all workers. Recall that by the strong law of large numbers, $\overline{x}$ provides an informative signal about the value of common shock η. Given that η is defined to capture all common shocks within the firm, and tournaments shield agents from the impact of these socks, one could argue that the second form is the correct one, even though the first one appears more intuitive at first glance. However, in this framework it does not matter; all tasks are subjected to the same shock η. Further, the solution for $b\left(\theta \right),\text{β}\left(\theta \right)$ and $ET\mathrm{\Pi }$ turns out to be identical regardless of the tournament form used, yet the algebraic calculations are easier with the first formulation.

For tournaments with multi-tasking, see Franckx, D'Amato, and Brose (2004).

21 To be technical, if activity ${\theta }^{\ast }$ is undertaken in the South, we need to subtract the corresponding output $\sum _{i=1}^n{x}_i\left({\theta }^{\ast }\right)$ from the output in the North in order to avoid double-counting for this activity. However, with a continuum of tasks, output per task is relatively small. Hence, we ignore this double-counting for simplicity.

22 To see this, note that $\frac{\mathrm{d}{\int }_0^{{\theta }^{\ast }}\tau \left(\theta \right)\mathrm{d}\theta }{\mathrm{d}{\theta }^{\ast }}=\tau \left({\theta }^{\ast }\right)$. Hence, if $\tau \left(\theta \right)$ is strictly decreasing, expected profit in (37(37) $\begin{array}{rl}& n(1-{\theta }^{\ast })(a+\mu )+n(1-{\theta }^{\ast })\frac{1}{2}\frac{a^2}{a+r({\sigma }_{\eta }^2+{\sigma }_{\xi }^2)}\\ & +n\delta [a^S+\frac{1}{2}\frac{(a^S{)}^2}{a^S+r{\varsigma }_{\xi }^2}-\hat{U}]{\int }_0^{{\theta }^{\ast }}\tau \left(\theta \right)\mathrm{d}\theta .\end{array}$(37) ) is strictly concave.

23 Note that the analysis could easily be expanded to $\tau \left(\theta \right)=\frac{1}{\theta +ϵ},$ with $ϵ>0.$

24 An extension to consider is standardization with ${\sigma }_{\xi }^2={\varsigma }_{\xi }^2=ϵ\left(\theta \right)>0,\mathrm{\forall }\theta ,$ with ${ϵ}^{\mathrm{\prime }}\left(\theta \right)>0$, that is, the case when idiosyncratic uncertainty is a function of the task. However, the analysis gets pretty complicated pretty quickly, limiting the availability of analytical solutions in closed form.