Customer Acquisition, Business Dynamism and Aggregate Growth

This paper asks whether firm-level customer acquisition — distinct from productivity differences — is a quantitatively important driver of aggregate economic growth, and whether ignoring it distorts predictions about growth policy efficacy. The authors build a novel endogenous growth model in which innovating firms must first accumulate customers to sell their products, with two channels of customer acquisition operating simultaneously: costly sales-and-marketing expenditure and below-static-markup pricing (sales-driven accumulation). The model is estimated using indirect inference against a combination of aggregate data (U.S. real GDP per worker growth of 1.43% annually, 1979–2019), Business Dynamics Statistics (BDS) life-cycle profiles, and firm-level data from Compustat matched to Capital IQ’s sales-and-marketing expense records covering 1997–2019.

The benchmark model yields four closed-form propositions. First, a “firm-level market size effect”: higher customer retention raises a firm’s future profit base, strengthening incentives to conduct R&D. Second, an endogenous feedback loop: more productive firms invest more in customer acquisition, which expands their customer base and further strengthens R&D incentives. Third, customer base accumulation raises aggregate growth, but only indirectly — by boosting firm-level innovation rates — since aggregate productivity is a customer-weighted average of firm productivity levels. Fourth, the sensitivity of innovation to R&D subsidies increases with customer base growth, because firms with faster-growing customer bases discount future profits less steeply.

In the quantitatively estimated full model — which relaxes the benchmark’s perfect-scaling restrictions and endogenizes firm entry and exit — the authors conduct two decomposition exercises. In a counterfactual scenario where expected customer retention is reduced to make average customer base growth zero among continuing businesses, firm-level innovation rates fall by approximately 40% relative to the full model. Of this 40% decline, only about 6 percentage points are attributable to the direct firm-level market size effect alone; the vast majority is driven by the endogenous feedback loop between innovation and customer acquisition. In a second decomposition focused on aggregate growth, the firm-level market size effect and a reallocation effect — whereby the feedback loop concentrates customers among high-productivity firms — together account for 44% of aggregate growth in the full model.

On policy, the authors compare R&D subsidies and operational subsidies in the full model against an otherwise identical model that ignores customer accumulation. R&D subsidies are approximately twice as effective at boosting aggregate growth in the full model as in the model without customer accumulation. Conversely, operational subsidies produce a stronger decline in aggregate growth in the full model than in the benchmark-without-customer-accumulation, because aggregate growth in the full model is a customer-weighted average of firms’ productivity growth rates, making the joint distribution of productivity and customer bases the relevant object of study.

Firm-level data support three empirical predictions. Marketing expenditure, R&D intensity, and markups co-move in model-consistent directions both contemporaneously and over the life cycle. The estimated relative weight of marketing versus pricing as channels of customer accumulation is γ = 0.745, indicating marketing is the dominant channel. A model-consistent proxy for the severity of customer-base frictions, estimated in the cross-section of industries, shows that stronger frictions correlate with lower R&D investment, as predicted. The customer-base depreciation rate is estimated at ζ = 0.375, R&D cost scaling at σx = 1.264, and marketing cost scaling at σa = 1.405.

Q: What is the firm-level market size effect and why does it arise? A: When a firm retains more customers, successful innovations apply to a larger market, raising the profitability of each unit reduction in production costs. This increases the marginal benefit of R&D investment. In the benchmark model, Proposition 2(a) shows formally that firm-level innovation increases with customer base growth: ∂x/∂(1−ζ) > 0, where ζ is the customer separation rate.

Q: What is the endogenous feedback loop between innovation and customer accumulation? A: More productive firms have lower production costs and can therefore afford greater investment in marketing and can set lower markups, both of which attract more customers. A larger customer base raises firm value and strengthens R&D incentives further (Proposition 2(b)). This bidirectional feedback means that productivity growth and customer accumulation are jointly determined in equilibrium, not independent processes.

Q: How large is the quantitative effect of customer accumulation on firm-level innovation? A: In the counterfactual where expected customer retention is reduced so that average customer base growth among continuing firms is zero, firm-level innovation rates are approximately 40% lower than in the full model. Of this, only about 6% (of the total drop) is attributable to the direct market size effect in isolation; the feedback loop accounts for the remaining roughly 34 percentage points.

Q: How much of aggregate growth do customer-acquisition channels explain? A: The firm-level market size effect and a customer reallocation effect together account for 44% of aggregate growth in the full model. The firm-level market size effect alone reduces aggregate growth by about one-fifth (20%) in the relevant counterfactual. The reallocation effect — by which productive firms accumulate disproportionate market share — contributes the remainder of the 44%.

Q: What is the reallocation channel for aggregate growth? A: Because highly productive firms can invest more in customer acquisition, the feedback loop endogenously concentrates customers (market shares) among high-productivity firms. Since aggregate productivity in the model is a customer-weighted average of firm productivity levels (equation 16), this reallocation raises aggregate productivity growth beyond what the firm-level R&D incentive effect alone would produce.

Q: How does customer accumulation change the efficacy of R&D subsidies? A: R&D subsidies are approximately twice as effective at raising aggregate growth in the full model (with customer accumulation) as in an otherwise identical model that ignores customer accumulation. The mechanism is Proposition 4(b): faster customer base growth makes firms weight future profits more heavily, increasing their sensitivity to any change in R&D costs, including that brought about by a government subsidy.

Q: What happens to aggregate growth under operational subsidies in the two models? A: Operational subsidies lead to a stronger decline in aggregate growth in the full model than in the model without customer accumulation. The reason is that aggregate growth in the full model depends on the joint distribution of firm productivity and customer bases; operational subsidies alter this distribution in ways that reduce the customer-weighted average of productivity growth rates, an effect absent when customer accumulation is ignored.

Q: How are the two customer-acquisition channels (marketing and pricing) measured empirically? A: Marketing is measured using sales-and-marketing expenses from Capital IQ, available for 48% of the Compustat sample (34% report directly; an additional 14% report advertising or marketing sub-components). Markups are measured following De Loecker et al. (2020) as the inverse share of variable costs in sales multiplied by the cost-output elasticity, with variation across firms identified from balance sheet data under the assumption that cost-output elasticities are constant within industry-year cells.

Q: What is the estimated relative strength of marketing versus pricing in customer accumulation? A: The relative weight on marketing is γ = 0.745, estimated by targeting the coefficient βµ = 0.04 (standard error 0.01) from a reduced-form regression of firm-level sales growth on changes in markups (equation 29). This implies that marketing is the dominant channel, consistent with evidence in Afrouzi et al. (2021) and Fitzgerald et al. (forthcoming).

Q: What is the estimated customer-base depreciation rate and how is it disciplined? A: The depreciation rate ζ is estimated at 0.375, targeted to match average firm-level employment growth from the BDS. This falls toward the lower end of existing estimates, which range from about 0.3 to 0.7 across studies.

Q: How do R&D costs scale with firm size in the estimated model? A: The R&D cost scaling parameter is σx = 1.264, estimated by targeting the reduced-form coefficient of −0.01 from a regression of log R&D intensity on log sales with industry-time fixed effects (equation 28). This is close to the estimate in Akcigit and Kerr (2018).

Q: How do marketing costs scale with firm size? A: The marketing cost scaling parameter is σa = 1.405, estimated by targeting a reduced-form coefficient of −0.01 from a regression of log sales-and-marketing intensity on log sales with industry-time fixed effects (equation 30).

Q: What empirical co-movement evidence supports the model’s predictions? A: In the cross-section of firms, marketing expenditure, R&D intensity, and markups all co-move in model-predicted directions, for both static (contemporaneous) relationships and dynamic (life-cycle) patterns. Additionally, a model-consistent industry-level proxy for the severity of customer-base frictions shows that stronger frictions are associated with lower R&D investment, as the model predicts.

Q: How does endogenous firm exit work in the full model and why does it differ from standard models? A: Firms pay a stochastic per-period operational cost and exit when that cost exceeds a threshold κ*_j = v(q_j, b_j)/W. Unlike standard growth models where exit depends only on productivity, here the exit threshold depends on both productivity and accumulated customers, so customer loss can trigger exit even for relatively productive firms.

Q: What data sources are used and what are their key limitations? A: The three primary firm-level sources are the Census Bureau’s BDS (broad coverage, employment-focused), Compustat (rich financial data but limited to publicly traded firms and lacking direct customer-acquisition measures), and Capital IQ (sales-and-marketing expenses available from 1997, matched to 91% of the Compustat sample). To address Compustat’s non-representativeness, employment-based weights aligning Compustat and BDS firm-size distributions are applied when computing model moments against Compustat targets.

Firm-level market size effect: The mechanism by which higher customer retention raises a firm’s future profit base — because lower production costs from successful innovation apply to a larger market — thereby strengthening incentives to conduct R&D. This is the primary channel linking customer accumulation to innovation.

Customer base (b_j): The mass of household members consuming a firm’s product variety, which varies endogenously across firms. It enters demand directly (equation 4) and serves as a state variable in the firm’s value function alongside productivity.

Endogenous feedback loop: The bidirectional reinforcement between productivity growth and customer accumulation. More productive firms invest more in customers; a larger customer base raises the value of innovation; higher innovation raises productivity further.

Reallocation effect: The concentration of customers (market shares) toward high-productivity firms that arises endogenously from the feedback loop, contributing to aggregate growth because aggregate productivity is a customer-weighted average of firm-level productivity.

Customer-base depreciation rate (ζ): The exogenous rate at which a firm loses its existing customers each period, estimated at 0.375 in the paper’s calibration. It governs the baseline speed of customer attrition and is the key parameter for the firm-level market size effect.

Sales-and-marketing expenses: Expenditures on sales force, brand development, customer service, advertising, and customer data acquisition — measured from Capital IQ — that directly drive marketing-based customer accumulation (the dominant channel with estimated weight γ = 0.745).

Perfect scaling (Assumption 1): The benchmark restriction that R&D and marketing costs, and the sales-driven customer accumulation benefit, all scale one-for-one with a composite of firm productivity and customer base. This assumption enables closed-form solutions and is relaxed in the full model using estimated scaling parameters.