A Checkpoint: From Adoption to Scope

The subject here is the connection between the Census study's two empirical margins and the mechanism that can join them. Firms with more establishments are more likely to adopt custom software, yet adopters with greater scope devote a smaller share of capital spending to it. The useful judgment is that these findings are compatible once software is treated as a reusable input: adoption changes the economics of scope, while scope and the rest of the production system determine how important software remains in the firm's total mix.

One chain explains the two margins

The empirical pattern begins with a distinction between entering a technology regime and allocating resources within that regime. On the extensive margin, a firm either reports positive investment in custom software or it does not. On the intensive margin, the analysis looks only at adopters and asks how much of their capital expenditure is devoted to custom software. These are not two measurements of the same behavior. The first concerns access to a capability; the second concerns the composition of a firm's activity after access.

The model connects them through scope. A firm that operates more establishments has more places over which it can share a custom-software investment. That makes adoption more valuable, provided the capability can actually be reused. Once adopted, the software component does not have to be repeated in the same way as labor and physical capital. The firm can therefore add establishments while allowing the software share of the complete capital budget to fall. More scope raises the return to adopting; it does not require software to occupy a larger fraction of every subsequent investment decision.

This is the central reconciliation:

flowchart LR A["Observed: adoption rises with scope"] --> B["Model mechanism: software is shared within the firm"] B --> C["Effective software cost falls as scope rises"] C --> D["Firm chooses establishments and input mix"] D --> E["Observed: adopter software share can fall with scope"] D --> F["Modeled possibility: scope and activity reallocate across firms"] A -. "descriptive pattern" .-> G["Evidence boundary"] F -. "conditional on model" .-> G

The arrows do not all have the same evidentiary status. The relationship between adoption and scope, and the relationship between software intensity and scope among adopters, are measured patterns in the Census data. The cost-sharing link is supplied by the structural model. The possibility that firms reallocate establishments and activity in ways that change aggregate concentration is a counterfactual implication that requires still more assumptions about demand, productivity, wages, entry, exit, and competition.

That distinction prevents a common misreading. One might see that large firms are more likely to adopt and conclude that software simply rewards size. But the model says something more specific. Scope increases the number of uses available to a non-rival input, which changes the payoff to adoption. The same firm may then choose a different scope because the input is available. Size is not only a precondition or a label; it is part of the feedback between technology and organization.

Nor does the pattern mean that adoption is a reward reserved for already large firms. A small firm can adopt if its productivity, expected demand, and software fit make the investment worthwhile. The data show a positive relationship, not an absolute rule. The model treats adoption and scope as choices made by heterogeneous firms, so the relevant comparison is between the payoff from adopting and the payoff from remaining a non-adopter under the firm's own conditions.