Statistical Model — OLS and 2SLS Estimation

The regression framework, endogeneity correction, and coefficient interpretation

Learning Objectives

Interpret each coefficient in the CDR OLS regression — including the negative CDR friction term
Explain why latitude serves as a valid instrumental variable for purging endogenous capital stock from C
Distinguish OLS from 2SLS results and understand what the coefficient drop from 1.53 to 1.30 reveals

OLS Model (Stage 1)

ĝ_i = 1.53C_i + 0.14D_i + 0.23R_i − 1.21C_i·D_i·R_i + 0.38N_i

|t| = (6.60) (1.69) (2.60) (4.40) (5.59) · R²_adj = 83% · F ratio = 81 · n = 79 countries

59%

C contribution

D contribution

10%

R contribution

C·D·R friction

N (resources)

83%

Total R²_adj

First-Stage 2SLS (Instrument: Latitude L_i)

Ĉ_i = 0.04 − 0.07L_i − 0.16D_i + 0.22R_i + 1.11C_i·D_i·R_i − 0.02N_i

|t| = (3.7) (4.6) (6.4) (27.1) (0.61) · R²_adj = 95%

Second-Stage 2SLS (Exogenous Capital Ĉ)

ĝ_i = 1.30Ĉ_i + 0.12D_i + 0.28R_i − 0.98Ĉ_i·D_i·R_i + 0.39N_i

|t| = (2.66) (0.88) (1.95) (1.88) (4.45) · R²_adj = 74%
Coefficient drop 1.53→1.30: confirms ~85% of C is exogenous entrepreneurship capital; ~15% is endogenous capital stock from prior ideas.

Extension: Adding Geography (Ridley & Llaugel 2022, §4.3–4.4)

R²_adj = 83% (C, D, R alone) → 90% (C, D, R + geography), n = 79 countries

Adding a geography control alongside C, D, and R raises explained variance from 83% to 90% across the same 79-country sample. This does not reopen the natural-resources paradox from §1 — geography here captures residual variation in trade access, climate, and disease burden left over once institutional quality is accounted for, not an independent wealth endowment.

The C·D·R Friction Term

The negative coefficient on C·D·R (−1.21 OLS, −0.98 2SLS) represents democratic friction — the cost of consensus. In a 51% majority democracy, 49% disagree with every decision. This necessary friction subtracts from the theoretical maximum GDP achievable under perfect agreement. CDR is not rapacious capitalism but capitalism in the presence of democracy and rule of law. The negative sign does not mean that strong Capitalism, Democracy, and Rule of Law working together reduce growth — only that their joint strength carries a decision-making cost when excessive delays in decision-making and over-regulation are present (Ridley & Llaugel 2022, §4.3–4.4).

Residuals & Model Validation

Residual plots (ε vs ĝ_fitted) show no heteroscedasticity patterns. Histogram is bell-shaped. Chi-square goodness-of-fit test: χ² = 2.891 < χ²_crit = 14.067 — residuals are normally distributed. Durbin-Watson = 2.0. Model is apt. The remaining 17% unexplained variation attributed to unpredictable events (natural disasters) and unobserved private market capitalization.

Live 2SLS Pipeline Calculator real OLS & 2SLS formulas

Sources

P1 · §4 Analysis (OLS + 2SLS equations, partial correlations), pp. 6–7 P3 · §5 Statistical Analysis (Table 2 regression, correlation, causation, economic interpretation), pp. 10–13 P2 · Appendix A (OLS model), Appendix B (2SLS), pp. 15–16 P4 · §4 Global Time Invariant CDR model (OLS + 2SLS, Table 2), pp. 6–11