Sunk costs and the speed of market selection

Abstract

This paper studies the influence of sunk costs on industry evolution using the stylized pure selection model developed by Metcalfe. It is shown that sunk costs influence industry dynamics by reducing the speed of the replicator dynamics of competitive selection. Based on the theoretical model, we argue that sunk costs should lead to a reduction of market share reallocation dynamics and a larger share of stable firms. We validate these predictions empirically, finding that higher-sunk-cost industries have a larger share of stable firms and display lower market share dynamics. The result has practical implications for the interpretation of productivity decompositions.

Appendices

Appendix A: Derivation of the pricing rule of dynamic firms

The overall average price at the population level is defined as

$$\bar{p}_{v}=\theta_{d} \bar{p}_{d} + \theta_{s} \bar{p}_{s} + \left(1-\theta_{d}-\theta_{s}\right) \bar{p}_{m}. $$

This expression accounts for the different pricing behaviors in the three subpopulations. By inserting the expressions of the average prices in the marginal and dynamic groups follows:

$$ \bar{p}_{v}=\frac{\theta_{d}}{1-\theta_{s}}\left(\bar{p}_{d}-\bar{e}_{j}\right) + \bar{e}_{j} $$

(9)

$\bar {p}_{d}$ is obtained by aggregating the price equation for dynamic firms:

$$ \bar{p}_{d}= \frac{1}{\delta\left(1-\frac{\theta_{d}}{1-\theta_{s}}\right)}\left(g_{D}+f\bar{c}_{d}+\delta\left(1-\frac{\theta_{d}}{1-\theta_{s}}\right)\bar{e}_{j}\right) $$

(10)

where $\bar {c}_{d}={\sum }_{i} d_{i} c_{i}$. By eliminating the average price from the pricing equation a dynamic firm and re-arranging we obtain Eq. 5 in the text.

Appendix B: Regressions using NACE three-digit

Table 6 Stable firm share and sunk costs, regressions using the three-digit level

Appendix C: The dynamic Olley-Pakes decompositon

Melitz and Polanec (2009) argue that all productivity decomposition methods used in the literature - the Foster et al. (1998) decomposition and the Griliches and Regev (1995) decomposition - do not allow to identify the different channels of productivity improvement in a correct way. They suggest a different decomposition that avoids fixed weights in the division of the contribution of surviving firms and eliminates the bias towards within-firm productivity improvements. Melitz and Polanec (2009) propose the use of a dynamic decomposition that is based on the static decompositon proposed by Olley and Pakes (1996). The change in aggregate productivity P between time t and time t+Δt is decomposed in the following way:

$${\Delta} P = {\Delta} \bar{p}_{S} + {\Delta} cov_{S} + s_{E,t+{\Delta} t}\left(P_{E,t+{\Delta} t} - P_{S,t+{\Delta} t}\right) + s_{X,t}\left(P_{S,t}-P_{X,t}\right), $$

where ${\Delta } \bar {p}_{S}$ is the difference in the unweighted productivities of surviving firms and captures the within-firm productivity improvement, and Δc o v _S is the difference of the covariances of market share and productivity multiplied by the number of firms between t and t+Δt. This captures the contribution of reallocation. $s_{E,t+{\Delta } t}\left (P_{E,t+{\Delta } t}- P_{S,t+{\Delta } t}\right )$ is the contribution of entry measured as the difference of the productivities between entrants and surviving firms at time t+Δt. $s_{X,t}\left (P_{S,t}-P_{X,t}\right )$ is the contribution of exit measured as the difference between surviving firms and exits at time t. For Slovenian manufacturing, Melitz and Polanec (2009) show that their decomposition leads to a consistently higher contribution of reallocation to productivity growth than other decomposition methods but that the within-firm productivity improvements still dominate the productivity terms. For Austria similar evidence is provided by Hölzl and Lang (2011).