Customer accumulation, returns to scale, and secular trends

This paper asks how rising returns to scale in production contributed to three concurrent U.S. secular trends since 1980: declining business dynamism, rising markups, and growing firm expenditures on customer acquisition. The author constructs a firm dynamics model in the Hopenhayn (1992) tradition with endogenous entry and exit, heterogeneous markups, and customer accumulation grounded in directed search in the product market. Firms compete for customers through both prices and selling activities; larger firms gain a competitive edge when returns to scale rise because their marginal costs fall more than those of smaller firms—even though the technological shift is uniform across firms. This demand-based channel triggers winners-and-losers dynamics and the rise of superstar firms.

The empirical foundation rests on Compustat data for U.S. publicly traded firms (1977–2014) and Business Dynamics Statistics (BDS) for aggregate and sector-level dynamism measures. Production-function estimation using Ackerberg, Caves, and Frazer (2015) augmented with sales-share controls documents that aggregate returns to scale rose from approximately 1.0 in 1980 to approximately 1.05 by 2014—a within-sector increase, not a reallocation effect. Over the same period, the cost-weighted markup rose by 42%, the firm entry rate fell by 33%, the excess reallocation rate fell by 29%, and selling costs relative to production costs rose by 60%–90% depending on the measure used.

The model is calibrated to 1980 steady-state moments (firm life-cycle patterns, markups, entry and reallocation rates). A 5% increase in returns to scale—matching the empirical estimate—accounts for: a +15 percentage point rise in the average cost-weighted markup (vs. +42% in the data); a 33% decline in the entry rate (exactly matching the data); a 21% decline in the reallocation rate (vs. 29% in the data); and a 23% increase in selling costs relative to production costs (vs. 60%–90% in the data). The model also generates a 53% rise in the share of firms aged 11 years or older (vs. 50% in the data) and a 58% decline in the employment share of firms aged 5 years or younger (vs. 56% in the data), closely tracking the aging of the U.S. firm population. Firm-level responsiveness to productivity shocks declines by 0.08 in the model, versus about 0.01 in Compustat and 0.09 in Decker et al. (2020).

Sector-level panel regressions with sector fixed effects confirm the model’s directional predictions: within-sector increases in returns to scale are associated with lower entry rates (coefficient −2.89, significant at 1%), lower reallocation rates (−1.16, significant at 1%), higher markups (+3.15, significant at 1%), and higher selling costs relative to production costs (+1.85 for the advertising-based measure; +8.52 for adjusted SG&A).

A key scope condition is that the model yields a constrained-efficient allocation: directed search and full internalization of returns to scale imply decentralized equilibrium efficiency, making the paper a laboratory for assessing how far efficient firm responses to technological change can explain the secular trends without invoking market failures. The model fits the post-2000 transition dynamics better than the 1980s–1990s period, and explains a substantial but incomplete share of the trends, suggesting complementary—possibly inefficient—forces also contributed.

Q: What is the core mechanism through which rising returns to scale generate winners-and-losers dynamics?

A: The marginal cost of production under increasing returns to scale (alpha > 1) is MC(z,n) = l(n,z)^(1−alpha) × (1/alpha) × (W/e^z), which depends on firm size l(n,z). A uniform rise in alpha rotates the marginal cost schedule clockwise by firm size: larger firms see a proportionally larger cost reduction than smaller firms, even though the technological change is identical across all firms. Because firms compete for the same pool of customers, this asymmetric cost advantage allows large firms to offer lower prices while sustaining higher margins, attracting customers away from small firms. The result is a demand-based channel that generates winners-and-losers dynamics and increases market concentration.

Q: How does the model capture customer accumulation, and why is it central to the paper’s argument?

A: The model introduces directed search in the product market, where firms post advertisements and customers—including those already matched with a firm—choose which submarket to enter by trading off offered utility against matching probability. A constant-returns-to-scale matching function governs match creation; in submarket with tightness theta, customers match with probability m(theta) = theta(1+theta)^(−1) and firms attract customers with probability q(theta) = (1+theta)^(−1). The customer accumulation motive creates an investment-harvest trade-off: firms can either post high promised utility (low prices) to grow their customer base or extract surplus through high prices. Rising returns to scale amplify large firms’ ability to resolve this trade-off favorably, linking the technological change directly to markup dynamics, entry incentives, and selling expenditures.

Q: What is the directed search framework’s role in ensuring equilibrium uniqueness and efficiency?

A: The author introduces firm-side commitment contracts—specifying price, separation probability, and continuation utility contingent on productivity realizations—combined with directed search. Because search is directed on both sides and firms fully internalize returns to scale, the decentralized equilibrium is constrained-efficient. This delivers uniquely determined heterogeneous prices in equilibrium (solving the indeterminacy problem common in customer-market models) and establishes the paper’s efficient-mechanism benchmark: it tests how far profit-maximizing firm responses to technological change—without any market failure—can account for the secular trends.

Q: How are prices structured in the model, and what life-cycle pattern do they generate?

A: Each firm charges two distinct prices in each period: one to incumbent customers (the same for all incumbents, since they are identical conditional on being attached to the same firm) and one to newly acquired customers (which varies based on the promised utility in the submarket searched). Firms that are expanding their customer base offer greater promised utility and therefore charge lower prices to attract customers; firms harvesting their existing base charge higher prices. Because firms enter small and grow, this dynamic generates a price life cycle: young firms invest via low prices and mature firms harvest through higher prices, which the model reproduces as a rising markup pattern over the firm life cycle—an untargeted moment the model fits well.

Q: What does the calibration target and what untargeted moments does the model reproduce?

A: The model is calibrated to 1980 using: the number of employees of entrant firms (pinning entry customer base n_e), employees of age-5 firms (pinning convex cost chi_1), share of firms aged 11+ years (pinning chi_2), average firm size (operating cost f), entry rate (entry cost kappa), excess reallocation rate (exit shock delta), and average cost-weighted markup (linear cost c). Untargeted moments reproduced include: a sales-weighted markup of 0.28 (vs. 0.25 in De Loecker et al. 2020), endogenous customer turnover of approximately 9% (vs. 15% in Gourio and Rudanko 2014), and an elasticity of customer base shrinkage to price of 0.08 (within the 0.01–0.16 range from Paciello et al. 2019). The model also matches markup and selling-cost life-cycle patterns that are typically overlooked.

Q: How large is the quantitative contribution of the 5% rise in returns to scale to each secular trend?

A: Comparing the 1980 steady state (alpha = 1) to the 2014 steady state (alpha = 1.05): the average cost-weighted markup rises by 15% in the model versus 42% in the data; the entry rate declines by 33% in the model, exactly matching the data; the reallocation rate declines by 21% in the model versus 29% in the data; and selling costs relative to production costs rise by 23% in the model versus 60%–90% in the data. The model thus explains a substantial share of each trend while leaving a residual requiring additional mechanisms.

Q: How does the model explain the aging of U.S. firms, and how well does it match the data?

A: The winners-and-losers mechanism shifts activity toward larger, older firms, which mechanically ages the firm population. The model generates a 53% increase in the share of firms aged 11 years or older (vs. 50% in the data) and a 58% decline in the employment share of firms aged 5 years or younger (vs. 56% in the data). This aging arises because rising returns to scale increase the cost of customer acquisition, acting as a barrier to entry that disproportionately hurts new, small firms while allowing large incumbents to remain viable at lower productivity thresholds.

Q: What is the channel through which rising returns to scale reduce business dynamism specifically?

A: The unequal reduction in marginal costs intensifies competition for customers and raises customer acquisition costs. This operates through two simultaneous effects on the exit threshold: (i) lower marginal costs allow large firms to remain viable at lower productivity levels despite higher customer acquisition costs; and (ii) heightened competition forces smaller firms to require higher productivity to survive in a market that has become increasingly costly to operate in. Higher customer acquisition costs therefore function as an endogenous barrier to entry, reducing the entry rate and the reallocation of resources across firms.

Q: Does the model attribute the secular trends entirely to efficient firm behavior, and what does it conclude about residual explanations?

A: No. The model is explicitly designed as a constrained-efficient benchmark, and the paper finds that while rising returns to scale account for a substantial share of the trends—particularly in magnitude—the transition dynamics show a less accurate fit before the 2000s. The author concludes that complementary mechanisms, likely involving inefficiencies (such as market power from horizontal product differentiation or barriers to entry beyond those captured by the model), played a significant role in the earlier evolution of these trends and in the portion of the trends not explained by the efficient channel.

Q: What evidence supports the rising returns to scale finding, and what are its limitations?

A: Production-function estimation using the Ackerberg-Caves-Frazer method with sales-share controls on Compustat data shows returns to scale rising from approximately 1.0 in 1980 to approximately 1.05 by 2014, driven primarily by within-sector increases rather than reallocation toward high-returns sectors. A translog production function finds limited evidence of heterogeneous increases across firm sizes within Compustat. However, Compustat predominantly covers large publicly traded firms; smaller firms outside the sample may have experienced minimal or no increase in returns to scale. If technology adoption involves fixed costs, the aggregate impact could be larger than estimated, meaning the quantitative exercises likely represent a conservative lower bound.

Q: How does the paper relate to and extend the directed search literature in product markets?

A: The paper builds on Gourio and Rudanko (2014) and Roldan-Blanco and Gilbukh (2020), where customers are locked in once matched, by introducing labor-search tools from Schaal (2017) to allow: (i) incumbent customer switching between firms at rates of 10%–25% annually (Gourio and Rudanko 2014), and (ii) a non-zero price sensitivity of incumbent customers (Paciello et al. 2019). It also allows firms to invest in demand through selling expenditures, which prior directed search models in product markets typically abstracted from, making it possible to study how technological changes affect customer reallocation and firms’ cost structures jointly.

Customer capital: The stock of customers a firm has accumulated through prior selling and pricing decisions; treated as a state variable that firms invest in (by offering low prices and spending on advertisements) or harvest from (by charging high markups), with a customer turnover rate estimated at 10%–25% annually in the literature.

Directed search in the product market: A market structure in which both firms and customers choose which submarket (indexed by the promised utility level) to enter, trading off match probability against terms; delivers constrained-efficient equilibrium and uniquely determined heterogeneous prices.

Investment-harvest trade-off: The firm’s dynamic choice between offering high promised utility (low prices, low current markups) to grow the customer base versus extracting surplus through high prices from an existing customer base; shaped by the firm’s current size, productivity, and the cost structure implied by returns to scale.

Returns to scale (alpha): The curvature of the production function y = e^z × l^alpha; equals 1.0 under constant returns and approximately 1.05 by 2014 in the empirical estimates; the paper’s central technological change parameter, whose rise disproportionately reduces marginal costs for larger firms.

Winners-and-losers dynamics: The reallocation of customers and market share from small to large firms triggered by the asymmetric cost advantage large firms obtain when returns to scale rise; the demand-based channel through which superstar firms emerge.

Cost-weighted markup: The average markup aggregated using each firm’s costs as weights, as opposed to sales-weighted markup; the primary measure of market power used in the paper, rising by 42% in the data between 1980 and 2014.

Constrained-efficient allocation: An equilibrium outcome in which, given the frictions present (search-and-matching in the product market), no social planner operating under the same constraints could improve welfare; the paper uses this as a benchmark to assess how far efficient firm responses explain secular trends without invoking market failures.

Selling costs relative to production costs: The ratio of customer acquisition expenditures (advertising or adjusted SG&A) to cost of goods sold; rose by 60%–90% in the data between 1980 and 2014 and by 23% in the model’s steady-state comparison.