D List of pre-registered implications

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v0.28.9 — This text is under construction. The structure of the theory, the propositions, and the empirical conclusions may all change. Overview

Appendix D
List of pre-registered implications

This is the list of the advance commitments described in Section 19.2. The main text states only the results; the wording of each registration and its verdict are listed here.

There are 22 registrations: 6 supported (3 of them partially), 11 rejected, and 5 untestable.

D.1 The list

Table D.1: Implications fixed in advance, and their verdicts.

Symbol	Subject	Registered implication and result	Verdict


A	Family 2	Divergence and transaction frequency. The level is supported, but what was measurable was $κ$	Partial
B	Family 5	Refunds and measurability. The sign is not uniquely determined	Untestable
C	Fees	Payment for externalization. A counterexample not explained by function was also found	Partial
D	Unattended operation	Number of dependencies and length of unattended period. The same implication as $Φ$ 1, rejected with it	Rejected
E	Corporate statistics	The leading property of $CCC$ ( $p = 0.72$ )	Rejected
F	Corporate statistics	Size and the direction of credit. The sign is reversed	Rejected
J	Fees	Rate differences correspond to the correlation $ρ$ . $ρ$ is not observable	Untestable
K	$ϕ_{𝑐𝑜𝑔}$	$δ^{*} > δ$ . The sign is negative in all four categories	Rejected
L	Capacity constraint	Contract choice of older cohorts. No consumer-side data	Untestable
M	Corporate statistics	The composition effect in the rise of $CCC$ . Within-industry is 83%	Rejected
N	Corporate statistics	Positive correlation of $Δ \ln W$ and $Δ \ln r$ ( $β = 0.83$ )	Supported
O	Corporate statistics	Lag structure. Not detectable in annual data	Rejected
P	Corporate statistics	Total elasticity including the lag. $0.830 \to 0.821$	Rejected
T	Labour side	Movement of $κ$ under the new statute. No statistics exist	Untestable
U	Sole proprietorships	The operating margin is close to the value with officers’ remuneration added back	Supported
X	Family 5	Negative correlation of fee rate and turnover rate. No correlation across 307 firms	Rejected
Y	Family 5	Ordering by occupation of the correlation between size and turnover. Not reproduced nationally; only the qualitative division holds	Partial
Z	Family 5	Occupations with larger B1 have stronger refunds. Rank correlation $ρ = 0.000$	Rejected
$Φ$ 1	Procedure	Number of dependencies and time to repair. Concentration of replicates was producing the result	Rejected
$Φ$ 2	Procedure	$M (t)$ declines ahead of discontinuation ( $p = 3.2 \times 1 0^{- 9}$ )	Supported
$Φ$ 3	Procedure	Non-negativity of $CCC$ . The corporate sector is non-negative in every industry too, so no contrast can be drawn	Untestable
$Φ$ 4	Procedure	The type in family 7. Rarity was right; the surviving type was wrong	Rejected

G, H and I targeted statutory regulation of fee rates, but were withdrawn at the design stage once the population turned out to contain only three cases. Q, R and S were registered in the examination from the worker’s viewpoint, but testing has not been begun.

D.2 Where registration changed the verdict

Recorded here are the places where, absent an advance commitment, a retrospective interpretation would likely have been adopted.

In family 5, the fact that 99.7% of capped-rate fees have disappeared could have been read as circumstantial support for the measurability hypothesis. In fact the price level of the capped scheme is simply an order of magnitude lower, and the two are unrelated.
In Chapter 16, the contemporaneous negative correlation between $CCC$ and sales could have been read as “ $CCC$ works as a business-cycle indicator”, and the credit position of large firms as “large firms support their counterparties”. Both are retrospective narratives.
In $Φ$ 2, looking only at the fact that the balance of discontinued $Φ$ declines beforehand would read as support. Applying the same window to continuing $Φ$ , the two do not separate at 180 days. Without having decided to place a control, the overall downward trend would have been misread as support.
In $Φ$ 4, the fact that the sole family-7 instance to appear places the selection of beneficiaries outside the procedure could have been offered as circumstantial support for Proposition 10.6. But the registered wording was “what survives is 7-4”, and what appeared was 7-2. A mechanism agreeing with a proposition does not rescue an implication that failed.

D.3 Defects that arose in operating the registry

D and $Φ$ 1 are the same implication registered twice. They were registered separately at stages 13 and 16, and the duplication went unnoticed at the time. The cause was keeping the register of implications by chapter and never reconciling it as a whole.

Appendix 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

Appendix D
List of pre-registered implications