14.1 On Linear Addition
CBT uses the following linear additive notation:
This notation is adopted for explanatory clarity. In reality, the components interact and exhibit nonlinearity:
- r_policy and r_institution can affect each other;
- changes in r_geo can both raise r_u and alter r_s;
- the effects of some variables are better represented through multiplicative or threshold functions.
CBT therefore adopts the following approach:
- At the framework level, it uses a “linear decomposition + nonlinear criteria” approach;
- In concrete analysis, nonlinearity is represented through scenarios, comparative cases, and “high / medium / low” ranges rather than through complex equations everywhere.
14.2 On the R-I-S-C Hierarchical State Map
The R-I-S-C Hierarchical State Map describes the long-run structural states of nations and cities.
It must be emphasized:
- It is a multi-state map, not a one-way linear stage theory;
- real-world paths may jump, reverse, or remain stuck at one layer for long periods;
- CBT asks whether each generation’s FCF is capitalized into higher-quality Buses, not whether the system has “completed” some predetermined stage.
14.3 On Formalizing the Capability Bus
The Capability Bus uses the relation:
a_i(t + 1) = a_i(t) + g_i( Invest_i(t), Context(t) )
This relation serves as a structural illustration rather than a universal differential equation.
The specific form of g_i must be modeled separately for different people and contexts:
- sometimes it resembles diminishing marginal returns;
- sometimes it contains pronounced thresholds (admission to a particular school, obtaining a certification);
- sometimes it becomes suddenly invalid or is amplified because of institutional or technological change.
CBT encourages readers to construct a context-specific g_i within this framework rather than trying to produce one “formula for everyone.”
14.4 On the Scissors Gap Δr
The Scissors Gap Δr = r_social − r_decision is an alignment-gap indicator:
- It does not subdivide r into additional components; it compares differences in discount rates across actors;
- It reminds us that under the same institutional structure, “upper levels” and “lower levels” may live on entirely different time scales;
- In application, it is better described qualitatively in terms of “direction + magnitude” than estimated as a precise number.
14.5 On Prediction and Control
CBT aims to:
- provide a unified language and structured perspective;
- help identify structural strengths and structural risks;
- support scenario analysis and stress testing.
It is neither a “crystal ball” for precisely forecasting prices and turning points nor a universal controller in which “adjusting one parameter solves everything.”
When using CBT, the more important task is:
First clarify who, under what Boundaries, through which Buses, and at what r and Δr is extracting or building FCF; only then discuss strategy and choice.
14.6 Common Systematic Errors in Identifying Components of r
Because decomposing r depends on qualitative judgment by the analyst, the following five systematic errors should be checked whenever a component is assigned:
1) Reverse inference from the conclusion: starting with an overall impression that “the system is good or bad,” then assembling components to fit that impression. Self-check: is the evidence for each component independent of the overall impression?
2) Recency amplification: treating a recent event shock as a structural change and mistaking short-run fluctuation in r for its long-run level. Self-check: if the time window is extended to five or ten years, does the judgment still hold?
3) Viewpoint contamination: mixing the analyst’s own political or emotional position into the estimate of r_s, the Social Subjective Discount Rate. Self-check: would a qualified analyst holding the opposite position accept this judgment about r_s?
4) Double counting: entering the same risk source into multiple components—for example, an institutional crisis raising r_institution, r_u, and r_s simultaneously—thereby systematically overstating total r. Self-check: each risk source should be assigned only one primary landing point.
5) Precision illusion: using a specific number (for example, “r_institution equals 4.2%”) to disguise the imprecision of a qualitative judgment. Discipline: unless supported by real market data, components should be expressed as “high / medium / low + direction.”