5.1 Decomposition of the Discount Rate
The discount rate r determines how much the future is worth today.
CBT decomposes r into multiple components:
Where:
- r_0: base rate (time-preference baseline);
- r_policy: policy and macro-environment component;
- r_institution: institutional and rule-of-law component;
- r_geo: geopolitical-risk component;
- r_u: uncertainty premium (tail-risk component);
- r_s: social subjective discount rate (collective-psychology component).
At the individual level, one may additionally define:
- r_psy: individual psychological discount rate.
At the decision-center level—governments, central banks, senior management of large firms, and similar bodies—one may define:
- r_decision: decision-center discount rate.
At the national level, r_g is often used to denote the implicit discount rate of the government or policy-making authority.
5.2 Meaning of Each Component
- r_0
- Derived from the Time Axiom, it is the baseline preference between benefits now and benefits later under idealized conditions.
- r_policy
- The effect of monetary, fiscal, industrial, and regulatory policies—and of their stability—on expectations about the future;
- The more frequently policy swings or is made ad hoc, the higher r_policy.
- r_institution
- Property-rights protection, contract enforcement, judicial credibility, and the degree to which public power is constrained;
- The more selectively institutions are enforced or arbitrarily changed, the higher r_institution.
- r_geo
- Risks from external shocks such as war, sanctions, blockades, and supply-chain security disruptions.
- r_u
- The possibility of irreversible jumps in future outcomes: coups, institutional collapse, monetary reset, large-scale disorder, and similar events;
- It is the price of tail risk.
- r_s
- Society-wide confidence in and patience toward the future:
- Whether people believe the future will be better;
- Whether they are willing to make long-term commitments;
- Whether cynicism or a “live for today” mentality is widespread.
- r_psy
- The degree to which an individual subjectively discounts the future;
- Affected by perceived security, formative experience, family structure, status anxiety, faith, and related factors.
- r_decision / r_g
- The degree to which a decision center discounts the future when setting policy, planning projects, and allocating resources;
- At the national level, it can be read as the “time preference” of the government or policy-making authority.
5.3 Rules for Distinguishing r_psy, r_s, and r_u
The three can be distinguished using the following logic:
- If a factor mainly affects whether an actor is willing to wait and how patient it is, it belongs more naturally to r_psy at the individual level or r_s at the social level.
- If a factor mainly affects whether the future might suddenly collapse or the rules might rupture, it belongs more naturally to r_u, the tail-risk premium.
- If a factor is an external conflict or sanction but has not yet reached the level of rupture, it is reflected mainly in r_geo; if it escalates into a risk of irreversible rupture, the relevant portion shifts into r_u.
5.4 The Dynamic View of r: r(t)
In practice, r varies over time; it is better represented as a sequence r(t) than as a constant:
- Policy changes, institutional reform, war, and crisis may each alter the structure of r at particular moments;
- When analyzing the long-run trajectory of a nation, industry, or firm, time often needs to be divided into several phases, with a different r-structure applied to each.
For simplicity, CBT often uses a piecewise-constant approximation—for example, one r-structure for a country from 2000–2010 and another from 2010–2020.
5.5 Decision-Center Discount Rate and the Scissors Gap Δr
In any system with a “decision center”—a nation, city, large firm, or major organization—we can define a decision-center discount rate r_decision and compare it with the discount rate r_s of society or ordinary actors.
Let:
- r_decision: decision-center discount rate;
- r_social: subjective discount rate of social actors (usually approximated by r_s);
Define the Scissors Gap Δr:
At the national level, the common notation is:
- r_g: discount rate of the government or policy-makers;
- r_s: social subjective discount rate;
- Δr = r_s − r_g.
Intuitively:
- When Δr > 0:
- The decision center is more “patient,” while society discounts the future more heavily;
- Decision-makers at the top discuss twenty-year plans, while those below focus on next month’s cash flow;
- Long-term projects require additional persuasion and compensation, and long-range planning risks remaining rhetorical rather than being implemented.
- When Δr < 0:
- Society is willing to commit to the long term, while the decision center is short-horizon or repeatedly changes course;
- Long-term investment and innovation are easily interrupted by policy swings or short-horizon performance metrics;
- Society experiences a sense that “the path is visible, but cannot be taken.”
The Scissors Gap Δr is not a new component of r. It is an indicator of inter-actor misalignment:
It measures the alignment between the time preferences of the decision center and ordinary actors, as well as the tension between long-term narratives and real incentives.
Δr will recur throughout the later analysis of nations, cities, institutions, and power.