## 3.1 Cross-sectional evidence

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---

### Main findings
- Strong positive association between investment rates and national savings rates across datasets (each point represents a country-period pair) for 1970-2015 and 1990-2015 samples.
- Positive correlation persists when using WEO data containing only private flows of investment and savings.
- Correlation holds across income groups (AEs, EMs, LICs) and is inversely associated with level of economic development: correlation size is larger in less developed economies.
- Panel-regression coefficients confirm stronger savings-investment correlation in less developed countries.

### Key statistics (scatter and correlation evidence)
- Correlation stands at over 0.5 during the financially turbulent years of the 1980s and 1990s, falls to 0.3 during the “Great Moderation,” and increases again after the Global Financial Crisis (GFC).
- Time-variation pattern is broadly similar across PWT, IMF-WEO, and WB-WDI datasets.
- Correlation persists in WEO private series evidence (Table 5): Savings/GDP coefficients for private series include 0.400*** (0.0502) in pooled full and 0.226** (0.108) in FE full.

### Implications emphasized in text
- Credit market failures and more severe credit constraints in less developed economies are consistent with higher savings-investment correlation in those economies (reference: Coeurdacier, Guibaud, and Jin, 2015).
- Adverse selection and increased risk during turbulent times tighten the domestic savings–investment link; the opposite holds in good times.

---

### 3.3 Benchmark regressions

### Specification and controls
- Parsimonious Pooled and Fixed-Effects OLS regressions of investment rates on national savings.
- Controls: time-effects, property rights indicator (constraints on the power of the executive), initial GDP per capita.

### Core regression results (PWT 9.1 Data, starting in 1970) — selected coefficients
- Savings/GDP coefficients:
  - (1) 0.568*** (0.122)
  - (2) 0.489*** (0.0322)
  - (3) 0.404*** (0.0528)
  - (4) 0.338*** (0.115)
  - (5) 0.403*** (0.0615)
- Constraints on Executive: 0.603*** (0.126) in specification (1).
- Initial GDP coefficients:
  - (1) -1.07e-05 (2.98e-05)
  - (2) -0.000424*** (6.51e-05)
  - (3) -0.000432*** (0.000113)
  - (4) -0.000208** (9.88e-05)
- Observations: 399, 169, 162, 236, 93 (columns 1–5 respectively)
- Number of id: 136, 281, 108

### Robustness across datasets (WEO, WDI, PWT starting in 1990) — selected Savings/GDP coefficients
- WEO:
  - Pooled Full: 0.572*** (0.0489)
  - FE Full: 0.565*** (0.130)
  - FE AE: 0.396*** (0.0911)
  - FE Non-AE: 0.563*** (0.150)
- WDI:
  - Pooled Full: 0.381*** (0.0325)
  - FE Full: 0.491*** (0.0874)
  - FE AE: 0.555*** (0.135)
  - FE Non-AE: 0.464*** (0.0987)
- PWT (1990 start):
  - Pooled Full: 0.379*** (0.0380)
  - FE Full: 0.405*** (0.0663)
  - FE AE: 0.343*** (0.122)
  - FE Non-AE: 0.360*** (0.0751)

### Interpretation
- Preferred specification (Fixed-Effects and Full Sample): initial GDP per capita coefficient is statistically significant and negative, suggesting convergence forces (diminishing returns to capital).
- Protection of property rights enters significantly with expected sign in pooled OLS.
- FH coefficient size relatively stable across specifications; somewhat smaller in AEs and larger in the FH replication specification.
- Findings broadly in line with Cavallo and Pedemonte (2015) result of about 0.39 correlation for LAC (1980-2013).

---

### 3.4 Extensions

### Additional controls introduced
- (i) Relative price of investment (ratio of price of investment to price of consumption).
- (ii) Index of de jure capital account openness.
- (iii) Crises dates (protracted crises defined as lasting more than one year).

### Main results with additional controls — selected coefficients (Table 3)
- Savings/GDP coefficients:
  - Pooled Full: 0.444*** (0.0495)
  - FE Full: 0.515*** (0.0605)
  - FE AE: 0.568*** (0.104)
  - FE Non-AE: 0.468*** (0.0646)
- Inv. Price coefficients:
  - Pooled Full: -0.389*** (0.131)
  - FE Full: -0.246*** (0.0359)
  - FE AE: -8.317* (4.291)
  - FE Non-AE: -0.238*** (0.0337)
- Capital openness coefficients:
  - Pooled Full: 3.039** (1.305)
  - FE Full: 2.867* (1.488)
  - FE AE: 8.147** (3.523)
  - FE Non-AE: 1.633 (1.687)
- Savings#Openness interaction:
  - Pooled Full: -0.0602 (0.0734)
  - FE Full: -0.0765 (0.0876)
  - FE AE: -0.300** (0.140)
  - FE Non-AE: -0.00886 (0.122)
- Crises coefficients:
  - Pooled Full: -4.437** (1.760)
  - FE Full: -1.190 (1.255)
  - FE AE: -0.144 (5.127)
  - FE Non-AE: -1.279 (1.426)
- Savings#Crises interaction:
  - Pooled Full: 0.241*** (0.0796)
  - FE Full: 0.120** (0.0585)
  - FE AE: 0.0162 (0.148)
  - FE Non-AE: 0.124 (0.0831)
- Observations: 586, 586, 153, 433 (columns 1–4)
- Number of id: 119, 279, 2

### Interpretation of extensions
- Savings coefficient remains statistically significant and similar in magnitude across these specifications.
- Relative price of investment is always highly significant with expected negative sign.
- Capital account openness generally enters significantly and positively, suggesting openness boosts investment even after controlling for GDP per capita.
- Interaction Savings#Openness is negative but not statistically significant for the full sample; significant and negative for AEs, indicating in AEs greater capital account openness weakens the savings–investment link.
  - Evidence: for AEs with high capital account openness total impact of domestic savings falls below 0.3; for AEs with lower openness it exceeds 0.5.
- Controlling for crises: crises coefficient negative (significant only in pooled regression); Savings#Crises positive in pooled regressions, indicating stronger link between domestic savings and investment in crisis periods, but not robust across country samples.

### Financial development and commodity terms of trade
- Financial development (Svirydzenka, 2016 broad-based index): evidence on importance is mixed; savings coefficient remains significant and similar in magnitude (Appendix C, Table 9).
- Commodity exporters (one standard deviation above cross-country average in oil, metals, food export share):
  - Savings/GDP in pooled commodity exporter spec.: 0.267*** (0.0782); in FE commodity exporter: 0.450*** (0.0653).
  - Savings#ToT:
    - Pooled Full: -0.0286* (0.0157)
    - Pooled Commodity Exp.: -0.0325* (0.0187)
    - FE Full: -0.0386** (0.0163)
    - FE Commodity Exp.: -0.0429** (0.0163)
  - Interpretation: coefficient on domestic savings falls somewhat for commodity exporters but differences are economically small; ToT growth does not enter significantly; Savings#ToT negative and small.

---

### 4 Assessing Causality with Instrumental Variables

### Motivation and critique of Granger causality
- Granger-causality tests in panel settings typically find savings Granger-cause investment (null cannot typically be rejected).
- Authors argue Granger-causality is unconvincing for economic identification: temporal precedence does not imply causal economic effect due to potential omitted confounders.

### IV strategy overview and formal model
- Use instrumental variables techniques to assess causality of domestic savings on investment.
- Structural equation:
  - Y_i = X'_i β + W'_i κ + ε_i  (1)
- First-stage:
  - X'_i = Z'_i π + W'_i γ + V'_i  (2)
- Reduced-form:
  - Y_i = Z'_i δ + W'_i τ + U_i  (3)
- Relationship: δ = π β.
- Two-stage-least-squares estimator representation:
  - ˆβ_T SLS = (ˆπ′ Q_ZZ ˆπ)^{-1} ˆπ′ Q_ZZ ˆδ, where Q_ZZ = 1/n ∑ Z_i Z′_i.
- Conditions for consistency: instruments must be strong (E(Z′X) ≠ 0) and excludable (E(Z′ε) = 0).

---

### 4.1 Identification strategy

### Instrument choice and motivation
- Candidate instruments: demographic variables, specifically age structure.
- Instrument used: share of people in the [35:49] age bracket as an instrument for the savings rate (life-cycle hypothesis).
- Empirical patterns:
  - Population structure is positively related to the savings rate and is also related to investment rates.
  - For the US over 1975-2017, no reduced-form association between the [35:49] share and Investment/GDP, supporting exclusion restriction in that context.

### Exclusion restriction and potential violations
- Excludability requirement: E(Z′ε) = 0 must hold.
- Potential challenges:
  - Age structure might affect innovation and thus investment, particularly in AEs (Aksoy et al., 2019).
  - Factor-complementarity: higher working-age share could increase demand for capital; counterarguments cite directed technological change literature (Acemoglu, 2015; Acemoglu and Restrepo, 2017).
  - Narrow focus on the [35:49] bracket strengthens exclusion restriction: unclear why total capital investment would depend specifically on this sub-sample.

### Weak instruments and inference
- Evidence of weak instruments in some specifications:
  - Montiel Olea and Pflueger effective F-statistics are below respective critical values in all specifications.
  - Kleibergen-Paap rk Wald F statistic exceeds critical values in all IV specifications except the one focusing on AEs (critical value: 16.38 following Stock and Yogo, 2005).
  - Montiel Olea and Pflueger weak-instrument test: τ = 10% null corresponds to critical value 23.11.
- Weak-instrument-robust inference:
  - Anderson-Rubin (AR) weak-instrument-robust confidence intervals are reported. In all cases the coefficient on the savings rate passes the AR weak-instrument-robust statistical significance test at the 5 percent level for the full sample and for non-AEs.
  - In cross-sectional two-endogenous-variable IV analysis, the AR test has a p-value of 0.04 for the null that both coefficients of interest equal 0.

---

### 4.2 Panel-IV results with one endogenous variable

### Main IV findings (one endogenous variable: domestic savings rate)
- IV specifications are exactly identified (one instrument for endogenous domestic savings rate).
- IV estimates confirm a positive and statistically significant coefficient for the savings rate for the whole sample and for emerging and developing economies, indicating a causal relationship from domestic savings to investment.
- IV point estimates are larger than OLS counterparts, suggesting measurement error in the savings variable.

### Selected coefficient estimates and diagnostics (Tables 6 and 7)
- Table 6 (dependent variable = Investment/GDP):
  - OLS - Full sample: Savings/GDP = 0.417*** (0.0530); Observations = 916; Number of id = 136; R-squared = 0.270; K-P F-stat = 19.46.
  - IV - Full sample: Savings/GDP = 0.540*** (0.166); Observations = 789; Number of id = 125; R-squared = 0.274; K-P F-stat = 16.82; Effective F-stat = 6.40.
  - OLS - Non-AE: Savings/GDP = 0.430*** (0.0601); Observations = 693; Number of id = 108; R-squared = 0.282; K-P F-stat = 19.46.
  - IV - Non-AE: Savings/GDP = 0.687*** (0.184); Observations = 590; Number of id = 98; R-squared = 0.242; K-P F-stat = 4.80; Effective F-stat = 6.27.
  - OLS - AE: Savings/GDP = 0.287** (0.116); Observations = 223; Number of id = 22; R-squared = 0.361.
  - IV - AE: Savings/GDP = -0.135 (0.445); Observations = 199; Number of id = 27; R-squared = 0.136; K-P F-stat not strong.
- Table 7 (IV with investment price control):
  - IV - Full: Savings/GDP = 0.568*** (0.161); Inv. Price = -0.215*** (0.0666); Observations = 789; Number of id = 125; R-squared = 0.283; K-P F-stat = 20.35; Effective F-stat = 6.69.
  - IV - Non-AE: Savings/GDP = 0.721*** (0.180); Inv. Price = -0.183** (0.0709); Observations = 590; Number of id = 98; R-squared = 0.234; K-P F-stat = 17.68; Effective F-stat = 6.61.
  - IV - AE: Savings/GDP = -0.177 (0.433); Inv. Price = -22.73*** (8.230); Observations = 199; Number of id = 27; R-squared = 0.300; K-P F-stat = 5.62; Effective F-stat = 1.77.

### Interpretation and robustness
- For the subset of 27 AEs, the IV estimate for savings is not statistically significant, implying the observed FH correlation in AEs may arise from endogeneity bias.
- IV estimates larger than OLS estimates point toward measurement error in savings rates.
- Including the price of capital as an additional control leaves the IV results for savings broadly similar, though instrument weakness concerns persist in some specifications.
- Additional IV specifications instrument the price of capital with the average relative price in all other countries; results similar but show weak instruments and an insignificant control variable coefficient.

---

### 4.3 Cross-sectional IV with two endogenous variables

### Motivation and instruments
- Goal: allow inclusion of slow-moving “constraints on the executive” (expropriation risk), which may be endogenous to investment.
- Instruments for expropriation risk: colonial origins indicators—latitude, aboriginal population density, and settler mortality—following Acemoglu, Johnson, and Robinson (2001).
- Savings instrumented by population-structure [35:49] share.
- Approach: collapse time dimension and estimate IV models on averaged cross-sections.

### Cross-sectional IV results (Table 8, Full sample) — selected estimates
- Savings/GDP:
  - OLS: 0.399*** (0.0665); Observations = 119; R-squared = 0.517.
  - IV1 (latitude for expropriation; population share for savings): 0.623*** (0.173); Observations = 113; R-squared = 0.379; Kleibergen-Paap F-stat = 1.93.
  - IV2 (latitude + aboriginal density): 0.629*** (0.154); Observations = 112; R-squared = 0.377; Kleibergen-Paap F-stat = 2.58.
  - IV3 (latitude + aboriginal density + settler mortality): 0.585*** (0.0804); Observations = 59; R-squared = 0.486; Kleibergen-Paap F-stat = 6.58.
- Constraints on the Executive:
  - OLS: 0.514* (0.278).
  - IV specifications: positive but not statistically significant with larger standard errors.
- Overidentification tests:
  - Hansen-J statistic p-values reported as 0.93 and 0.66 for overidentified models, supporting instrument validity where applicable.
- Weak instrument diagnostics:
  - Kleibergen-Paap F-statistics indicate instruments are weak in some cross-sectional IV specifications; two-dimensional weak-instrument-robust confidence sets and rejection surfaces are presented.
  - AR test p-value = 0.04 for null that both coefficients equal 0; coefficient linking savings to investment remains strictly above 0 across confidence set, while Control of the Executive cannot be confidently different from 0.

---

### 5 Conclusions

- The paper revisits the Feldstein-Horioka (FH) puzzle and finds:
  - The savings–investment correlation holds across time and groups of countries but varies across those dimensions.
  - Two IV approaches support a causal relationship: variations in domestic savings cause variations in investment.
  - IV point estimates exceed OLS estimates, suggesting measurement error in domestic savings.
  - For 27 advanced economies, the estimated coefficient for domestic savings is not statistically significant, implying the FH correlation in AEs is likely driven by endogeneity bias.
- Policy implication:
  - Low national savings are likely to constrain investment even with open capital accounts.
  - Policymakers could consider interventions to promote domestic savings and increase the amount of national savings intermediated through the financial system.
  - One avenue: policies that foster competition and help reduce the costs of provision of financial services.

---

### Appendices (data and robustness highlights)
- Appendix A: Data definitions
  - National savings and investment rates from WEO and WDI; share of gross capital formation in current PPP terms from Feenstra, Inklaar, and Timmer (2015).
  - For PWT 9.1, savings rate = 1 − csh_c − csh_g.
  - GDP per capita in real PPP terms, base year 2011.
  - Constraints on the executive variable (xconst) from Polity IV, seven-category scale 1 to 7.
  - Relative price of capital constructed as pl_i / pl_c in PWT 9.1.
  - Capital account openness index from Chinn and Ito (2006).
  - Demographic structure measures: share [35:49] and share [15:64] from WDI.
  - Terms of trade: commodity net export price index by Gruss (2014).
  - Crises dates from Laeven and Valencia (2018).
- Appendix B: Country classification lists (Advanced economies list provided in source).
- Appendix C: Additional regressions
  - Table 9 (adding Financial Development): Savings/GDP = 0.408*** (0.0335) in pooled full; Financial Development coefficient 9.045*** (2.405) in pooled full.
  - Table 10 (Panel 2SLS instrumenting for Savings and Investment Price): Savings/GDP = 0.526*** (0.165) in IV-Full Controls; K-P F-stat reported as 1.343 in column (1).

*Source: wpiea2020124-print-pdf*

### 3.1    Cross-sectional evidence

### 3.1 Cross-sectional evidence

### Main findings
- Strong positive association between investment rates and national savings rates across datasets (each point represents a country-period pair) for 1970-2015 and 1990-2015 samples.
- Positive correlation persists when using WEO data containing only private flows of investment and savings.
- Correlation holds across income groups (AEs, EMs, LICs) and is inversely associated with level of economic development: correlation size is larger in less developed economies.
- Panel-regression coefficients (Figure 4) confirm stronger savings-investment correlation in less developed countries.

### Key statistics (scatter and correlation evidence)
- Correlation stands at over 0.5 during the financially turbulent years of the 1980s and 1990s, falls to 0.3 during the “Great Moderation,” and increases again after the Global Financial Crisis (GFC) (Figure 5).
- Time-variation pattern is broadly similar across PWT, IMF-WEO, and WB-WDI datasets (Figure 6).

---

### Implications emphasized in text
- Credit market failures and more severe credit constraints in less developed economies (referenced model: Coeurdacier, Guibaud, and Jin, 2015) are consistent with higher savings-investment correlation in those economies.
- Adverse selection and increased risk during turbulent times tighten the domestic savings–investment link; the opposite holds in good times.

---

### 3.3 Benchmark regressions

### Specification and controls
- Parsimonious Pooled and Fixed-Effects OLS regressions of investment rates on national savings.
- Controls: time-effects, property rights indicator (constraints on the power of the executive), initial GDP per capita.

### Core regression results (PWT 9.1 Data, starting in 1970) — Table 1
- Specification labels: (1) Pooled FH (1980) Controls; (2) Pooled Full; (3) FE Full; (4) FE AE; (5) FE Non-AE.
- Savings/GDP coefficients:
  - (1) 0.568*** (0.122)
  - (2) 0.489*** (0.0322)
  - (3) 0.404*** (0.0528)
  - (4) 0.338*** (0.115)
  - (5) 0.403*** (0.0615)
- Constraints on Executive: 0.603*** (0.126) in (1).
- Initial GDP coefficients:
  - (1) -1.07e-05 (2.98e-05)
  - (2) -0.000424*** (6.51e-05)
  - (3) -0.000432*** (0.000113)
  - (4) -0.000208** (9.88e-05)
- Observations and identifiers:
  - Observations: 399, 169, 162, 236, 93 (for columns 1–5 respectively)
  - Number of id: 136, 281, 108

### Robustness across datasets (WEO, WDI, PWT starting in 1990) — Table 2
- WEO Savings/GDP coefficients:
  - Pooled Full: 0.572*** (0.0489)
  - FE Full: 0.565*** (0.130)
  - FE AE: 0.396*** (0.0911)
  - FE Non-AE: 0.563*** (0.150)
- WDI Savings/GDP coefficients:
  - Pooled Full: 0.381*** (0.0325)
  - FE Full: 0.491*** (0.0874)
  - FE AE: 0.555*** (0.135)
  - FE Non-AE: 0.464*** (0.0987)
- PWT (1990 start) Savings/GDP coefficients:
  - Pooled Full: 0.379*** (0.0380)
  - FE Full: 0.405*** (0.0663)
  - FE AE: 0.343*** (0.122)
  - FE Non-AE: 0.360*** (0.0751)

### Interpretation
- Preferred specification (Fixed-Effects and Full Sample): initial GDP per capita coefficient is statistically significant and negative, suggesting convergence forces (diminishing returns to capital).
- Protection of property rights enters significantly with expected sign in pooled OLS.
- FH (Feldstein-Horioka) coefficient size relatively stable across specifications; somewhat smaller in AEs and larger in the FH replication specification.
- Findings broadly in line with Cavallo and Pedemonte (2015) result of about 0.39 correlation for LAC (1980-2013).

---

### 3.4 Extensions

### Additional controls introduced
- (i) Relative price of investment (ratio of price of investment to price of consumption).
- (ii) Index of de jure capital account openness.
- (iii) Crises dates (protracted crises defined as lasting more than one year).

### Main results with additional controls — Table 3
- Savings/GDP coefficients:
  - Pooled Full: 0.444*** (0.0495)
  - FE Full: 0.515*** (0.0605)
  - FE AE: 0.568*** (0.104)
  - FE Non-AE: 0.468*** (0.0646)
- Inv. Price coefficients:
  - Pooled Full: -0.389*** (0.131)
  - FE Full: -0.246*** (0.0359)
  - FE AE: -8.317* (4.291)
  - FE Non-AE: -0.238*** (0.0337)
- Capital openness coefficients:
  - Pooled Full: 3.039** (1.305)
  - FE Full: 2.867* (1.488)
  - FE AE: 8.147** (3.523)
  - FE Non-AE: 1.633 (1.687)
- Savings#Openness interaction:
  - Pooled Full: -0.0602 (0.0734)
  - FE Full: -0.0765 (0.0876)
  - FE AE: -0.300** (0.140)
  - FE Non-AE: -0.00886 (0.122)
- Crises coefficients:
  - Pooled Full: -4.437** (1.760)
  - FE Full: -1.190 (1.255)
  - FE AE: -0.144 (5.127)
  - FE Non-AE: -1.279 (1.426)
- Savings#Crises interaction:
  - Pooled Full: 0.241*** (0.0796)
  - FE Full: 0.120** (0.0585)
  - FE AE: 0.0162 (0.148)
  - FE Non-AE: 0.124 (0.0831)
- Observations: 586, 586, 153, 433 (columns 1–4)
- Number of id: 119, 279, 2

### Interpretation of extensions
- Savings coefficient remains statistically significant and similar in magnitude across these specifications.
- Relative price of investment is always highly significant with expected negative sign.
- Capital account openness generally enters significantly and positively (except in last specification focusing on non-advanced economies), suggesting openness boosts investment even after controlling for GDP per capita.
- Interaction term Savings#Openness is negative but not statistically significant for the full sample; significant and negative for AEs, indicating in AEs greater capital account openness weakens the savings–investment link.
  - Figure 7 evidence: for AEs with high capital account openness total impact of domestic savings falls below 0.3; for AEs with lower openness it exceeds 0.5.
- Controlling for crises: crises coefficient negative (significant only in pooled regression); Savings#Crises positive in pooled regressions, indicating stronger link between domestic savings and investment in crisis periods, but not robust across country samples.

### Financial development and commodity terms of trade
- Financial development: Svirydzenka (2016) broad-based index used; evidence on financial development importance is mixed (results in Appendix C). Savings coefficient remains significant and similar in magnitude.
- Commodity exporters (defined as countries where export share of oil, metals, and food on total exports is one standard deviation above cross-country average):
  - Coefficient on domestic savings falls somewhat for commodity exporters but differences are economically small.
  - ToT (terms of trade) growth does not enter significantly; Savings#ToT interaction is negative and significantly different from zero (economically small), indicating increases in terms of trade modestly weaken the savings–investment link.
- Table 4 key coefficients (Commodity exporters focus):
  - Savings/GDP:
    - Pooled Full: 0.474*** (0.0439)
    - Pooled Commodity Exp.: 0.267*** (0.0782)
    - FE Full: 0.536*** (0.0576)
    - FE Commodity Exp.: 0.450*** (0.0653)
  - Savings#ToT:
    - Pooled Full: -0.0286* (0.0157)
    - Pooled Commodity Exp.: -0.0325* (0.0187)
    - FE Full: -0.0386** (0.0163)
    - FE Commodity Exp.: -0.0429** (0.0163)
  - Inv. Price and Capital openness coefficients are also reported (see Table 4).

### Robustness: private savings and investment (WEO, smaller samples) — Table 5
- Savings/GDP coefficients for private series:
  - Pooled Full: 0.400*** (0.0502)
  - FE Full: 0.226** (0.108)
  - FE AE: 0.0718 (0.0709)
  - FE Non-AE: 0.230 (0.138)
- Constraints on Executive: 0.785*** (0.184)
- Initial GDP coefficients reported (see Table 5).
- Interpretation: coefficients somewhat lower than benchmark but still statistically significant in most cases; coefficient for AEs not statistically significant at conventional levels.

---

### 4 Assessing Causality with Instrumental Variables

### Motivation and critique of Granger causality
- Granger-causality tests in panel settings typically find savings Granger-cause investment (null cannot typically be rejected).
- Authors argue Granger-causality is unconvincing for economic identification: temporal precedence does not imply causal economic effect due to potential omitted confounders.

### IV strategy overview
- Use instrumental variables techniques to assess causality of domestic savings on investment.
- Reference to Dooley, Frankel and Mathieson (1987) as only similar IV approach noted.

### Formal model (equations preserved)
- Structural equation:
  - Y_i = X'_i β + W'_i κ + ε_i  (1)
- First-stage:
  - X'_i = Z'_i π + W'_i γ + V'_i  (2)
- Reduced-form:
  - Y_i = Z'_i δ + W'_i τ + U_i  (3)
- Relationship: δ = π β.
- Two-stage-least-squares estimator ˆβ_T SLS is a function of ˆδ and ˆπ (OLS estimates of δ and π).
- Conditions for consistency: instruments must be strong (E(Z′X) ≠ 0) and excludable (E(Z′ε) = 0).

---

*Source: wpiea2020124-print-pdf - 3.1    Cross-sectional evidence*

### 4.1    Identification strategy

### 4.1 Identification strategy

### Instrument choice and motivation
- Candidate instruments: demographic variables, specifically age structure, chosen because they are strongly correlated with savings rates but, if chosen carefully, unlikely to affect investment via other channels.
- Instrument used: share of people in the [35:49] age bracket as an instrument for the savings rate (life-cycle hypothesis: working-age adults save more; the eldest dissave and the young mostly consume).
- Advantage: the [35:49] share varies across countries and across time, allowing panel IV estimation.
- Empirical patterns:
  - Figure 9 (described) indicates population structure is positively related to the savings rate in a statistically significant way; it is also related to investment rates.
  - For the US over 1975-2017, Figure 10 shows no reduced-form association between the share of population in the [35:49] bracket and Investment/GDP, supporting the exclusion restriction in a context where domestic savings do not constrain investment.

### Exclusion restriction and potential violations
- Excludability requirement: E(Z′ε) = 0 must hold for valid instruments.
- Potential challenges discussed:
  - Population age structure might affect innovation (Aksoy et al., 2019) and thus investment, particularly in advanced economies; however, this does not necessarily invalidate the exclusion restriction for developing economies that are catching up rather than pushing the technological frontier.
  - Factor-complementarity argument: a higher working-age share could increase demand for capital if capital and labor are complementary. Counterargument: directed technological change literature (Acemoglu, 2015; Acemoglu and Restrepo, 2017) suggests firms adjust technology and investment composition (e.g., toward labor-saving technologies) rather than simply reducing total capital investment.
  - Narrow focus on the [35:49] bracket strengthens the exclusion restriction: it is unclear why total capital investment would depend specifically on this sub-sample.

### Formal estimator representation
- Two-stage least squares point estimator (as given in source):
  - ˆβ_T SLS = (ˆπ′ Q_ZZ ˆπ)^{-1} ˆπ′ Q_ZZ ˆδ, where Q_ZZ = 1/n ∑ Z_i Z′_i.

### Weak instruments and inference
- Evidence of weak instruments in some specifications:
  - Montiel Olea and Pflueger effective F-statistics are below respective critical values in all specifications.
  - Kleinbergen-Paap rk Wald F statistic exceeds critical values in all IV specifications except for the one focusing on advanced economies (critical value considered: 16.38 following Stock and Yogo, 2005).
  - Montiel Olea and Pflueger weak-instrument threshold discussion: τ = 10% is considered for the test; the null is that IV asymptotic bias exceeds 10 percent of the OLS bias; the critical value in this case is 23.11.
- Weak-instrument-robust inference:
  - Anderson-Rubin (AR) weak-instrument-robust confidence intervals are reported (Figure 11). In all cases the coefficient on the savings rate passes the weak-instrument-robust statistical significance test at the 5 percent level for the full sample and for non-AEs (i.e., coefficients on national savings rate are different from zero).
  - In cross-sectional two-endogenous-variable IV analysis, the AR test has a p-value of 0.04 for the null that both coefficients of interest equal 0.

---

### 4.2 Panel-IV results with one endogenous variable

### Main IV findings (panel, one endogenous variable: domestic savings rate)
- IV specifications are exactly identified (one instrument for the endogenous domestic savings rate).
- Savings rate effect on investment:
  - IV estimates confirm a positive and statistically significant coefficient for the savings rate in investment rate regressions for the whole sample and for emerging and developing economies, indicating a causal relationship from domestic savings to investment.
  - IV point estimates are larger than OLS counterparts, suggesting measurement error in the savings variable.

### Selected coefficient estimates and diagnostics (from Table 6 and Table 7)
- Table 6 (Panel 2SLS and OLS; dependent variable = Investment/GDP):
  - OLS - Full sample: Savings/GDP = 0.417*** (0.0530); Observations = 916; Number of id = 136; R-squared = 0.270; K-P F-stat = 19.46.
  - IV - Full sample: Savings/GDP = 0.540*** (0.166); Observations = 789; Number of id = 125; R-squared = 0.274; K-P F-stat = 16.82; Effective F-stat = 6.40.
  - OLS - Non-AE: Savings/GDP = 0.430*** (0.0601); Observations = 693; Number of id = 108; R-squared = 0.282; K-P F-stat = 19.46.
  - IV - Non-AE: Savings/GDP = 0.687*** (0.184); Observations = 590; Number of id = 98; R-squared = 0.242; K-P F-stat = 4.80; Effective F-stat = 6.27.
  - OLS - AE: Savings/GDP = 0.287** (0.116); Observations = 223; Number of id = 22; R-squared = 0.361; K-P F-stat = 19.46.
  - IV - AE: Savings/GDP = -0.135 (0.445); Observations = 199; Number of id = 27; R-squared = 0.136; K-P F-stat not strong.
- Table 7 (Panel IV with investment price control; dependent variable = Investment/GDP):
  - IV - Full: Savings/GDP = 0.568*** (0.161); Inv. Price = -0.215*** (0.0666); Observations = 789; Number of id = 125; R-squared = 0.283; K-P F-stat = 20.35; Effective F-stat = 6.69.
  - IV - Non-AE: Savings/GDP = 0.721*** (0.180); Inv. Price = -0.183** (0.0709); Observations = 590; Number of id = 98; R-squared = 0.234; K-P F-stat = 17.68; Effective F-stat = 6.61.
  - IV - AE: Savings/GDP = -0.177 (0.433); Inv. Price = -22.73*** (8.230); Observations = 199; Number of id = 27; R-squared = 0.300; K-P F-stat = 5.62; Effective F-stat = 1.77.

### Interpretation and robustness
- For the subset of 27 advanced economies (AEs), the IV estimate for savings is not statistically significant, implying the observed FH correlation in AEs may arise from endogeneity bias.
- IV estimates larger than OLS estimates point toward measurement error in savings rates.
- Including the price of capital as an additional control (Table 7) leaves the IV results for savings broadly similar, though instrument weakness concerns persist in some specifications.
- Additional IV specifications (Appendix C) instrument the price of capital with the average relative price in all other countries (following Lian et al., 2019); results on the savings rate coefficient are similar but show weak instruments and an insignificant control variable coefficient.

---

### 4.3 Cross-sectional IV with two endogenous variables

### Motivation and instruments
- Goal: allow inclusion of slow-moving “controls of the executive” variable (expropriation risk), which may be endogenous to investment.
- Instruments for expropriation risk: colonial origins indicators—latitude, aboriginal population density, and settler mortality—following Acemoglu, Johnson, and Robinson (2001).
- Approach: collapse the time dimension and estimate IV models on averaged cross-sections; instrument savings with the population-structure [35:49] share.

### Cross-sectional IV results (Table 8, Full sample)
- Savings/GDP coefficient across specifications:
  - OLS: S/GDP = 0.399*** (0.0665); Observations = 119; R-squared = 0.517.
  - IV1 (latitude instrument for expropriation, savings instrumented by population share): S/GDP = 0.623*** (0.173); Observations = 113; R-squared = 0.379; Kleibergen-Paap F-stat = 1.93.
  - IV2 (latitude + aboriginal population density): S/GDP = 0.629*** (0.154); Observations = 112; R-squared = 0.377; Kleibergen-Paap F-stat = 2.58.
  - IV3 (latitude + aboriginal population density + settler mortality): S/GDP = 0.585*** (0.0804); Observations = 59; R-squared = 0.486; Kleibergen-Paap F-stat = 6.58.
- Constraints on the Executive (expropriation risk) estimates:
  - OLS: 0.514* (0.278).
  - IV specifications: coefficients are positive but not statistically significant in IV models, with much larger standard errors.
- Overidentification tests:
  - Hansen-J statistic p-values (for overidentified models) reported as 0.93 and 0.66, supporting validity of instruments set where applicable.
- Weak instrument diagnostics:
  - Kleibergen-Paap F-statistics indicate instruments are weak in some cross-sectional IV specifications; hence two-dimensional weak-instrument-robust confidence sets and rejection surfaces are presented (Figure 12).
  - The AR test p-value = 0.04 for null that both coefficients equal 0; the coefficient linking savings to investment remains strictly above 0 across the confidence set, while the Control of the Executive variable cannot be confidently different from 0.

---

### 5 Conclusions (implications drawn in source)
- The paper revisits the Feldstein-Horioka (FH) puzzle and finds:
  - The savings–investment correlation holds across time and groups of countries but varies across those dimensions.
  - Two IV approaches support a causal relationship: variations in domestic savings cause variations in investment.
  - IV point estimates exceed OLS estimates, suggesting measurement error in domestic savings.
  - For 27 advanced economies, the estimated coefficient for domestic savings is not statistically significant, implying the FH correlation in AEs is likely driven by endogeneity bias.
- Policy implication highlighted:
  - Low national savings are likely to constrain investment even with open capital accounts.
  - Policymakers could consider interventions to promote domestic savings and increase the amount of national savings intermediated through the financial system.
  - One avenue: policies that foster competition and help reduce the costs of provision of financial services.

*Source: wpiea2020124-print-pdf — section 4.1 and surrounding text*

### References

### References

### Bibliographic entries
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- Acemoglu, D., 2015. “Localized and Biased Technologies: Atkinson and Stiglitz’s New View, Induced Innovations, and Directed Technological Change.” Economic Journal 125: 443-463.
- Acemoglu, D., and Restrepo, P., 2017. “Secular Stagnation? The Effect of Aging on Economic Growth in the Age of Automation.” American Economic Review 107: 174-179.
- Aksoy, Y., Basso, H., Smith, R. P., and Grasil, T., 2019 “Demographic Structure and Macroeconomic Trends” American Economic Journal: Macroeconomics 11: 193-222.
- Andrews, I., Stock, J., and Sun, L., 2019. “Weak Instruments in IV Regression: Theory and Practice” Annual Review of Economics, Forthcoming.
- Aspergis, N. and Tsoumas, C., 2009. “A Survey of the Feldstein-Horioka Puzzle: What has been Done and Where We Stand.” Research in Economics 63: 64-76.
- Attanasio, O., Picci, L., and Scorcu, A. E., 2000. “Saving, Growth, and Investment: A Macroeconomic Analysis Using a Panel of Countries” Review of Economics and Statistics 82: 182-211.
- Bai, Y. and Zhang, J., 2010. “Solving the Feldstein-Horioka Puzzle with Financial Frictions.” Econometrica 78: 603-632.
- Barro, R., Mankiw, N. G., Sala-i-Martin, X., 1995. “Capital Mobility in Neoclassical Models of Growth” American Economic Review 85: 103-115.
- Baxter, M. and Crucini, M. J., 1993. “Explaining Saving-Investment Correlations” American Economic Review 83: 416-436.
- Bazzi, S. and Clemens, M., 2013. “Blunt Instruments: Avoiding Common Pitfalls in Identifying the Causes of Economic Growth.” American Economic Journal: Macroeconomics 5: 152-186.
- Benhabib, J., and Spiegel, M., 2000. “The Role of Financial Development in Growth and Investment.” Journal of Economic Growth 5: 341-306.
- Cavallo, E. and Pedemonte, M., 2015. “What is the Relationship between National Saving and Investment in Latin America and the Caribbean?” IDB Working Paper IDB-WP-617 (Washington: Interamerican Development Bank).
- Cavallo, E., Sanchez, G., and Valenzuela, P., 2016. “Gone with the Wind: Demographic Transitions and Domestic Saving.” IDB Working Paper IDB-WP-688 (Washington: Interamerican Development Bank).
- Chinn, M. D., and Ito, H., 2006. “What Matters for Financial Development? Capital Controls, Institutions, and Interactions”. Journal of Development Economics, 81: 163-192.
- Coeurdacier, N., Guibaud, S. and Jin, K., 2015. “Credit Constraints and Growth in a Global Economy”. American Economic Review, 105: 2838-2881.
- Dooley, M., Frankel, J. and Mathieson, D. J., 1987. “What Do Saving-Investment Correlations Tell Us?” IMF Staff Papers, 34: 503-530.
- Feenstra, R. C., Inklaar, R. and Timmer, M. P., 2015. “The Next Generation of the Penn World Table.” American Economic Review 105: 3150-3182.
- Feldstein, M. S. and Horioka, C. Y., 1980. “Domestic Saving and International Capital Flows” Economic Journal 90: 314-329.
- Glick, R. and Rogoff, K., 1995. “Global versus Country-Specific Productivity Shocks and the Current Account.” Journal of Monetary Economics 35: 159-132.
- Grigoli, F., Herman, A., and Schmidt-Hebbel, K. 2018. “Saving in the World” World Development 104: 257-270.
- Gruss, B., 2014. “After the Boom: Commodity Prices and Economic Growth in Latin America and the Caribbean”. IMF Working Paper 14/154. (Washington: International Monetary Fund).
- Horioka, C. Y. and Terada-Hagiwara, A., 2011. “The Determinants and Long-term Projections of Saving Rates in Developing Asia” NBER Working Paper 17581 (Cambridge: National Bureau of Economic Research).
- Irandoust, M., 2019 “Saving and Investment Causality: Implications for Financial Integration in Transition Countries of Eastern Europe.” International Econ Policy 16: 397-416.
- Laeven, L. and Valencia, F., 2018. “Systemic Banking Crises Revisited” IMF Working Paper No. 18/206 (Washington: International Monetary Fund).
- Lian, W., Novta, N., Pugacheva, E., Timmer, Y., and Topalova, P., 2019. “The Price of Capital Goods: A Driver of Investment Under Threat?” IMF Working Paper No. 19/134 (Washington: International Monetary Fund).
- Marshall, M., G., Gurr, R., and Jaggers, K., 2019. “Polity IV Project Political Regime Characteristics and Transitions, 1800-2018” Center for Systemic Peace.
- Montiel Olea, J. L., and Pflueger, C. E., 2013. “A Robust Test for Weak Instruments” Journal of Business and Economic Statistics 31: 358-369.
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### Appendix A: Data Sources and Definitions

### Investment and National Savings Rates
- National savings and investment rates (capital formation) are available directly from the WEO and WDI datasets.
- Both variables are expressed as a share of GDP.
- The WEO database also contains information on private savings and investment rates.
- Share of gross capital formation in current PPP terms from Feenstra, Inklaar, and Timmer (2015).
- For PWT 9.1 data, the savings rate is calcualted as 1−csh_c − csh_g, where csh_c is the share of share of household consumption in current PPP terms and csh_g is the share of government consumption in current PPP terms.

### GDP per Capita
- GDP per capita in real PPP terms compiled by Feenstra, Inklaar, and Timmer (2015). 2011 is the base year.

### Property Rights
- Constraints on the power of the executive variable (xconst) from the Polity IV project (Marshall, Gurr, and Jaggers, 2019).
- Seven-category scale ranging from 1 (Unlimited authority) to 7 (Executive parity or subordination).

### Relative Price of Capital
- Constructed as the ratio of pl_i / pl_c in PWT 9.1 (Feenstra, Inklaar, and Timmer, 2015) i..e the ratio of the price level of capital formation to the price level of household consumption both expressed relative to the price level of US GDP in 2011.

### Capital account restrictions
- Index of de jure capital account openness constructed by Chinn and Ito (2006) based on information from the IMF’s Annual Report on Exchange Arrangements and Exchange Restrictions (AREAER).
- Higher levels of the index indicate a more open capital account.

### Demographic Structure
- Two alternative measures: the share of the population in the [35:49] age bracket and the share of the population in the [15:64] age bracket.
- Both variables come from the World Bank’s WDI database.

### Terms of trade
- Commodity net export price index constructed by Gruss (2014).

### Crises Dates
- Dummy variable taking the value of one is a banking crisis and/or currency crisis and/or sovereign debt crisis occurred in a given year based on Laeven and Valencia (2018).

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### Appendix B: Country Classification

### Advanced
- AUSAGOGNQPANBDISWZ
- AUTALBGTMPERBENTCD
- BELAREHNDPHLBFATGO
- CANARGHRVPOLBGDTZA
- CHEARMHUNPRYBTNUGA
- CZEAZEIDNQATCAFYEM
- DEUBGRINDROUCIVZMB
- DNKBHRIRNRUSCMRZWE
- ESPBLRIRQSAUETH
- FINBOLJAMSLVGIN
- FRABRAJORSRBGMB
- GBRBWAKAZSYRHTI
- GRCCHLKWTTHAKEN
- IRLCHNLAOTKMKGZ
- ISRCODLBNTTOKHM
- ITACOGLTUTUNLBR
- JPNCOLLVATURLKA
- KORCPVMARTWNLSO
- LUXCRIMDGUKRMDA
- NLDCYPMEXURYMLI
- NORDJIMKDUZBMOZ
- NZLDOMMMRVENMRT
- PRTDZAMNEVNMMWI
- SGPECUMNGZAFNER
- SVKEGYMUSNGA
- SVNESTMYSNPL
- SWEFJINAMRWA
- USAGABNICSDN
- GEOOMNSEN
- GHAPAKSUR

### Emerging Markets
- (no separate list items beyond those embedded above in the source)

### Low Income
- 32

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### Appendix C: Additional Regressions

### Table 9: Regressions Adding Financial Development as a Control
- Specification columns: (1) Pooled Full Controls, (2) FE Full I/GDP, (3) FE AE I/GDP, (4) FE Non-AE I/GDP.
- Coefficients and statistics (robust standard errors in parentheses):
  - Savings/GDP: 0.408*** (0.0335); 0.494*** (0.0484); 0.338*** (0.0787); 0.475*** (0.0596)
  - Constraints on Executive: 0.465*** (0.133)
  - Initial GDP-: -0.000121** (4.69e-05); -0.000481*** (5.51e-05); -0.000251** (0.000117); -0.000214 (0.000162)
  - Inv. Price: -0.404*** (0.154); -0.249*** (0.0353); -13.71** (5.039); -0.236*** (0.0314)
  - Crises: -2.095*** (0.548)
  - Financial Development: 9.045*** (2.405); 2.607 (3.818); 13.14** (5.645); 4.169 (6.418)
  - Capital Openness: 1.365 (0.943); 0.286 (1.191); 1.557 (1.274)
- Fixed-Effects: N Y Y Y
- Time-Effects: Y Y Y Y
- Observations: 7225; 8153; 428;  (as listed) 7225 8153 428 (source shows "Observations722581153428")
- R-squared: 0.501; 0.486; 0.436; 0.533
- Number of id: 1182791 (as presented)
- Significance: *** p<0.01, ** p<0.05, * p<0.1
- 33

### Table 10: Panel 2SLS Regressions Instrumenting for Savings and Investment Price
- Specification columns: (1) IV-Full Controls I/GDP, (2) IV-Non-AE I/GDP, (3) IV-AE I/GDP.
- Coefficients and statistics (robust standard errors in parentheses):
  - Savings/GDP: 0.526*** (0.165); 0.610*** (0.190); -0.159 (0.437)
  - Inv. Price: 0.107 (0.385); 0.415 (0.493); -13.44 (9.467)
  - Initial GDP-: -0.000347*** (5.16e-05); 9.97e-05 (0.000178); -1.66e-05 (0.000249)
- Fixed-Effects: Y Y Y
- Time-Effects: Y Y Y
- Observations: 7895; 909; 199 (as listed)
- R-squared: 0.256; 0.137; 0.280
- Number of id: 1259827 (as presented)
- K-P F-stat: 1.343; 1.712; 2.665
- Significance: *** p<0.01, ** p<0.05, * p<0.1
- 34

*Source: References, Appendices A–C from the PDF content unit*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020124-print-pdf.pdf_