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:

r = r_0 + r_policy + r_institution + r_geo + r_u + r_s

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:

Δr = r_social − r_decision

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.