Business Models as Cash-Flow Structure
Formalization, a Catalogue of Types, and Survey Design
Contents
I Theory
1 Introduction: Choosing the Time Structure of Cash as the Variable
1.1 The problem
1.2 Structure of the text, and how to read it
1.3 What this text does not claim
2 The Business Model: Phi and the Generation of Cash Flow
2.1 Primitive sets
2.2 Schedules and spaces
2.3 The map from delivery to settlement
2.4 Generating the cash flow
2.5 Degrees of freedom of Phi
2.6 Three risk operations
2.7 Divergence between right and exercise
3 The Credit Position: kappa and the Lag tau
3.1 The gap between delivery and settlement
3.2 Decomposing the cash balance
4 Information Structure and the Objective
4.1 Verifiable shared information
4.2 The objective: a cash constraint imposed path by path
4.3 Heterogeneity of discount factors
5 The Growth Constraint: CCC and the Self-Financeable Growth Rate
5.1 The cash conversion cycle
5.2 The fundamental inequality
5.3 Growth and free cash flow
5.4 Level and change are separate constraints
5.5 CCC is a sum of lags
5.6 The path constraint and the peak
5.7 Comparative statics
6 Surplus and Layers: Source, Durability, Mutability
6.1 The three-way decomposition of surplus
6.2 Surplus and cash
6.3 Layers: five levels ordered by mutability
II The Space of Maps
7 A Catalogue of Phi: Seven Families, Twenty-Eight Types
7.1 How the catalogue is built
7.2 Family 1: one-off exchange
7.3 Family 2: continuing access
7.4 Family 3: renting an asset over time
7.5 Family 4: recovery through a complement
7.6 Family 5: outcome- and state-contingent
7.7 Family 6: intermediation
7.8 Family 7: separating beneficiary from payer
7.9 Assigning an observation to a type
7.10 Limits of the catalogue
7.11 A real firm is a bundle of Phi
8 A Subspace Under Constraints: Alone, Without Assets, Without Credit
8.1 The premises imposed in this chapter
8.2 Translating the premises
8.3 What the cloud means structurally
8.4 Sieving the types
8.5 The credit bootstrap problem
8.6 Relaxing a premise: those who hold assets
8.7 The formation of credit
8.8 The trade-off between contract work and publishing
8.9 Employment contracts reread
8.10 Limits of this chapter
9 Unmanned Operation: The Limit With the Operator Removed
9.1 The question
9.2 Formalizing “unmanned”
9.3 Decomposing the bootstrap
9.4 Limits of this chapter
10 The Supplier of the Information Structure: Settlement by Protocol
10.1 The premises imposed in this chapter
10.2 Translating the premises
10.3 Identifiers diverge from parties
10.4 Sieving the types
10.5 The collateral constraint
10.6 Observability
10.7 Limits of this chapter
III Method
11 Design of the Empirical Work: Connecting to Observation
11.1 What is to be tested
11.2 Five stages to pass
11.3 What to check at each stage
11.4 Reconciliation versus verification
11.5 Where each stage is handled in this text
11.6 Priorities for the survey
11.7 Variables to record
11.8 What must be pre-registered
12 Selection Bias: Decomposing the Distortions That Enter Observation
12.1 The problem
12.2 Conditioning on survival: a circularity in the framework
12.3 Selection into disclosure: correlated with the axis of interest
12.4 Age: a problem of domain, not of bias
12.5 Age, period and cohort are not identified
12.6 Retrospective narrative
12.7 Mistaking the unit: what a row denotes versus what its values denote
12.8 Selection of variables: the gaps are not random
12.9 The observation frame in practice
12.10 How to proceed
13 A Taxonomy of Verification Obstacles: Six States
13.1 Why a taxonomy is needed
13.2 Six categories
13.3 The taxonomy also serves as a test before starting
IV Empirics
14 Measuring the Theoretical Quantities: What Could and Could Not Be Measured
14.1 Purpose of this chapter
14.2 The primitive sets made concrete
14.3 The observed range of the map Phi
14.4 Cumulants and the credit position
14.5 Measuring the growth constraint
14.6 Right and exercise, and cognitive surplus
14.7 The information structure G made concrete
14.8 The three-way decomposition of surplus
14.9 The terms of the launch cost
14.10 Quantities relating to selection and identification
14.11 Quantities that could not be measured
15 Empirics of families 2 and 5: prepayment and outcome-contingent forms
15.1 The propositions tested in this chapter
15.2 Family 2: prepaid payment instruments
15.3 Family 5: fee-charging employment placement
15.4 Comparison of the two families and its methodological implications
15.5 The structure of the data source
15.6 What was reached and what was abandoned
15.7 A quantity that is not tabulated: the credit position of sole proprietors
16 Evidence From the Corporate Statistics: kappa and CCC Across Firms
16.1 Position of this chapter
16.2 Hot and cold are not one-dimensional
16.3 Data source
16.4 Size and the direction of credit
16.5 Is a leading indicator of the cycle?
16.6 An observation not anticipated: the long-run rise in CCC
16.7 Levels by industry (for reference)
16.8 Decomposing the rise in CCC
16.9 Separating the contemporaneous negative correlation
16.10 The effect of the scope of inventories on the conclusions
16.11 An observation the simplified capacity constraint does not fit
16.12 Limitations of this chapter
16.13 On both implications being rejected
17 The Price of Externalization: Platform Fees
17.1 The implication tested
17.2 Result: a ladder of rates
17.3 A natural experiment within one platform
17.4 A counterexample: price discrimination by size
17.5 Verdict
17.6 Practical implications
17.7 Limits of the measurement
17.8 How the institutional layer acts
17.9 Assessing feasibility of further investigation
17.10 Limits of this chapter
18 Evidence From Protocol Records: M(t) and the Rate of Modification
18.1 The implications tested
18.2 Results
18.3 Quantities measurable from the same records
V Conclusion
19 Where This Stands: What Was Established and What Remains Open
19.1 What was established and what was not
19.2 Fixing the implications in advance
19.3 Open problems
19.4 Known weaknesses of the framework
VI Appendices
A Supplement: proofs concerning method
A.1 Correlation induced by conditioning on a collider
A.2 Non-identification of age, period and cohort
A.3 Preference for variance under a deadline
A.4 Substitutability of capital and credit
B Notation
C Correspondences with existing theory
D List of pre-registered implications
D.1 The list
D.2 Where registration changed the verdict
D.3 Defects that arose in operating the registry
E Revision history
E.1 History of versions
E.2 Claims withdrawn
E.3 Corrections deriving from measurement
E.4 Corrections deriving from reasoning
E.5 A record of pre-registration at work
E.6 Making assumptions explicit
E.7 Introducing the lag
E.8 Re-evaluating the relation to existing theory
E.9 Filling in definitions
E.10 Examining reversibility, and a correction
E.11 Examination from the worker’s viewpoint
E.12 Extending the taxonomy of obstacles
E.13 Extending the taxonomy of biases
E.14 Reorganizing the list of open problems
E.15 The means of reproduction were not included
E.16 Removing a description resting on a single observation
E.17 Setting theorem-type body text in roman
E.18 Testing implication Y, and a defect in the registration
E.19 A route for testing the deductions of Part II
E.20 Registering implications Y and Z
E.21 Checking the scope of inventories
E.22 Filling in operationalization and reorganizing the list of open problems
E.23 Placing the empirical design first
E.24 Implication Z tested
E.25 Giving deductive grounds for choosing families 2 and 5
E.26 Removing references to places that do not exist
E.27 Resolving a contradiction in the description of phi-cog
E.28 Extending the scope of inventories to 62 industries
E.29 Stating the handling of per-firm data
E.30 Multiple definitions of a symbol
E.31 Correcting a count
E.32 Considered but not adopted in the body
E.33 Changes of structure
F Data sources
Bibliography
Abstract
This text is under construction. The structure of the theory, the propositions, and the empirical conclusions may all change. Claims that have been withdrawn, and the reasoning that led to each withdrawal, are recorded in Appendix D.3. Version numbers correspond to the stages listed there.
This text formalizes a business model as a map from a schedule of deliveries to a schedule of settlements, and derives from it the credit position , the self-financeable growth rate , and a three-way decomposition of surplus. Part I builds the theory. Part II generates seven families and twenty-eight types from the degrees of freedom of , then deduces the subspaces that remain once constraints on capital and labour are imposed, the limit in which the operator is removed, and the subspace obtained by replacing the supplier of the information structure. Part III sets out the five stages that connect the theory to observation, together with the treatment of selection bias, the pre-registration procedure, and a taxonomy of verification obstacles. Part IV reports the empirical work: families 2 and 5, the Financial Statements Statistics of Corporations by Industry, platform fees, and the records of a public distributed ledger; its opening chapter (Chapter 14) tabulates which theoretical quantities could be measured and which could not. Twenty-two implications derived from the theory were fixed in writing before the observations were made; six were supported, eleven rejected, and five could not be tested, and the record here includes the parts that were wrong. Because the empirical work is not complete, the deductions about under constraints (Chapters 8, 9 and 10) are not presented as a separate part on applications but placed in Part II, which treats the space of . Proofs appear in the body and in Appendix VI, notation in Appendix A.4.1, and correspondences with existing theory in Appendix A.4.1.