## 1. Introduction

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---

### Research motivation and questions
- Since the Global Financial Crisis there has been an explosion of studies on the macroeconomic effects of government spending, with attention to how macro factors affect spending multipliers.
- Known determinants of multiplier size include:
  - the state of the economy (multipliers larger in recessions) — e.g., Auerbach and Gorodnichenko, 2012 and 2013; Riera-Crichton, Vegh, and Vuletin, 2015;
  - the exchange rate regime (larger under fixed regimes) — e.g., Ilzetzki, Mendoza, and Vegh, 2013;
  - the degree of indebtedness (larger when debt is low) — e.g., Ilzetzki, Mendoza, and Vegh, 2013; Huidrom et al., 2019;
  - the degree of accommodation of monetary policy (larger when monetary policy is loose and/or close to the zero lower bound) — Christiano, Eichenbaum, and Rebelo, 2011; Coenen, Straub, and Trabandt, 2013;
  - the degree of openness (multipliers smaller in more open economies) — e.g., Ilzetzki, Mendoza, and Vegh, 2013; Gonzalez-Garcia, Lemus, and Mrkaic, 2013.
- Gap in literature: most studies focus on primary spending or government consumption; less evidence exists on public investment multipliers.
- Central question of this paper: Does the size of the public investment multiplier depend on the initial stock of public capital?
  - Theoretical expectation (neoclassical fiscal policy growth models, e.g., Baxter and King, 1993): lower initial stock of public capital → larger marginal productivity of additional public investment → larger public investment multipliers. Conversely, high initial stock → lower impact.
- Policy relevance: important for decisions on public investment/infrastructure, especially in developing countries where public capital stocks are low and efficiency concerns (cost overruns, implementation delays, institutional weaknesses, waste, corruption) may reduce multiplier effects.

### Contribution and approach
- The paper empirically investigates the dependence of the public investment multiplier on the initial stock of public capital using:
  - multiple samples (European countries, U.S. states, Argentine provinces),
  - multiple levels of government,
  - multiple identification strategies.
- Main empirical finding preview: using different samples and identification strategies, the initial stock of public capital matters for the size of the public investment multiplier in the direction predicted by theory.

### Structure of the paper (overview)
- Section 2: empirical analysis for 31 European countries using Blanchard and Perotti (2002) identification.
- Section 3: analysis for U.S. states using government spending forecast errors (Auerbach and Gorodnichenko, 2012 and 2013).
- Section 4: analysis for Argentine provinces using instrumental variables.
- Section 5: comparison with 17 country-specific external studies and calibrated estimates.
- Section 6: final thoughts.

### Theoretical and empirical context on public investment multipliers
- Prior studies find public investment multipliers can be quite large relative to government consumption multipliers because public investment directly raises productive capacity and spurs private investment and consumption over time.
- Evidence indicates that low spending efficiency (cost overruns, implementation delays, institutional weaknesses, waste, corruption) diminishes the output effect of public investment.

### Empirical strategy (European sample)
- Sample: un-balanced non-interpolated quarterly data for 31 European countries for 1987:Q1-2014:Q4.
- Identification: Blanchard and Perotti (2002) with timing restrictions (government spending can contemporaneously affect economic activity within the quarter; government takes at least one quarter to respond).
- Estimation: single-equation local projections (Jorda, 2005; Stock and Watson, 2007) estimated via least-squares dummy variables (LSDV).
- Specification: linear baseline and augmented specification interacting public investment shock with log initial stock of public capital-to-GDP (initial ratio uses 1980-1985 average for most countries).
- Reporting: multipliers reported with one-standard-error bands; coefficients scaled by average GDP-to-government-spending ratio to obtain $1 change-in-government-spending-on-GDP-level multiplier.

### Key empirical findings (European sample)
- Primary spending multiplier (Panel A, Figure 1):
  - On impact: 0.13 (t = 4.5).
  - After two years of the spending shock: 0.25 (t = 1.3).
  - Low multipliers driven by tepid private consumption response and no private investment response at any horizon.
- Public investment multiplier (Panels D–F, Figure 1):
  - On impact: 0.15 (t = 2.5) — similar to primary spending on impact.
  - After two years: 0.80 (t = 3.3) — more than 3 times the primary spending multiplier at that horizon (0.80 vs. 0.25); at that horizon the null that the multiplier equals one cannot be rejected.
  - Larger medium-term effects reflect stronger responses of private consumption and private investment (crowding-in effect).

---

### 2.3 Does the initial stock of public capital matter?

### Theoretical hypothesis
- Theory predicts the public investment multiplier depends negatively on the ratio of public capital to GDP.
- Empirical test: assess whether multiplier size varies with the initial stock of public capital to GDP.

### Cross-country variation (European sample)
- Large variability in initial stock of public capital to GDP:
  - Coefficient of variation: 0.55.
  - Median ratio: 0.63.
  - Examples: about 0.25 for Hungary, Latvia, Malta, and Greece; above 1 for Romania, Luxembourg, Cyprus, and Denmark.

### Estimated multipliers by initial stock (European sample)
- Regression evaluated at 95th percentile (high ratio = 1.33) and 5th percentile (low ratio = 0.16).
- Impact (short-run) multipliers (GDP):
  - High ratio (Panel A): 0:25 on impact.
  - Low ratio (Panel D): 0:18 on impact.
- Two-year horizon multipliers (GDP):
  - High ratio: 0:15 (t= 0:2) after two years — small and statistically weak.
  - Low ratio: 2:15 (t= 2:1) after two years — much larger; statistically cannot reject that multiplier > 1.
- Mechanisms: stronger private investment and private consumption responses when initial ratio is low.

### Multipliers as a continuous function of initial stock
- After two years, multiplier plotted against initial public capital/GDP:
  - Multiplier is statistically zero at high levels of the ratio (i.e., higher than 1).
  - Multiplier becomes statistically significant and increasingly positive as the ratio decreases.
  - For ratio lower than 0.25, the public investment multiplier exceeds one.

### Policy-relevant cross-time/cross-country illustration (European sample)
- Implied multipliers shown for ratios prevailing in 1990 and 2014:
  - Between 1990 and 2014, the public investment multiplier fell most in Southern economies and new Eastern bloc members.
  - Decline driven by important rises in stock of public capital following ERDF and Cohesion Fund efforts.

### Out-of-sample application (U.S. and Argentina)
- U.S.:
  - Estimated multipliers using U.S. ratio for 1960 and 2015:
    - 1960: 0.4 (statistically zero).
    - 2015: 0.85 (statistically not different from one).
  - Ratio of public capital to GDP: 1960 = 1.04; 2015 = 0.64.
- Argentina:
  - Estimated multipliers for 1960 and 2015:
    - 1960: 1.9 (statistically larger than one).
    - 2015: 1.4 (statistically equal to one).
  - Ratio of public capital to GDP: 1960 = 0.20; 2015 = 0.35.
- Convergence insight:
  - Previously U.S. ratio was more than five times Argentina’s; by 2015 the difference shrank to about two-fold.
  - As ratios converged, estimated multipliers for both countries also tended to converge (both statistically positive and close to one).

### Role of spending efficiency
- Efficiency defined via first principal component of 36 indicators (Global Competitiveness report, 2004-2014); indicators vary between 1 and 7.
  - Efficiency variable effectively varies between 2.5 and 6 globally and between 3.5 and 6 for European sample.
  - First principal component explains about 65 percent of comovement of the 36 indicators.
- Extended specification includes interaction of public investment shock with efficiency.
- Findings:
  - Efficiency matters: for low efficiency, the public investment multiplier tends to be zero; multiplier becomes larger for higher efficiency.
  - Controlling for efficiency does not affect core finding: initial stock of public capital remains a key determinant.

---

### 4.1 Identification strategy (provincial IV approach)

### Empirical specification and IV approach
- Basic linear specification for primary spending multiplier (equation (6)):
  - y_pc_{i;t} = _i +  g_pc_{i;t} +  y_pc_{i;t-1} + % T +  T^2 + _{i;t}
  - Subscripts i and t denote province and year; _i provincial fixed effect; T and T^2 linear and quadratic trends; y_pc and g_pc logarithms of real provincial GDP per capita and real provincial primary spending per capita.
- Coefficients associated with spending shock multiplied by average ratio of GDP to provincial government spending to report $1 change-in-government-spending-on-GDP-level multiplier.
- Robust Driscoll and Kraay (1998) standard errors used; panel unit-root tests reject null that all panels contain a unit root.

### Instrumenting primary spending
- Instrument: provincial over-representation in the Argentine National Chamber of Deputies (difference between actual number of provincial legislators per capita and proportional representation).
- Rationale:
  - About two-thirds of provincial primary spending is financed with federal transfers.
  - Over-represented jurisdictions tend to receive larger federal transfers per capita; over-representation effect dominated by Chamber of Deputies.
  - Constitutional amendments driving over-representation (1949, 1972, 1983) were governance-driven and not responses to macro developments, supporting exogeneity.
- Empirical support:
  - Strong positive association between federal transfers per capita and provincial primary spending per capita (1 percent significance), and between effective distortion and federal transfers per capita (1 percent significance).
  - Effective distortion strongly associated with provincial primary spending per capita (1 percent significance).
- Instrument validity: based on Stock and Yogo (2005), reject null that effective distortion is a weak instrument.

### Instrumenting government consumption and public investment (decomposition)
- Modified specification (equation (7)) includes g^c_pc and g^i_pc (government consumption and public investment per capita).
- Decomposition uses share _{i;t} to express components.
- Instruments for (g^c_pc, g^i_pc):
  - (i) provincial effective distortion in Chamber of Deputies (instrument for g_pc);
  - (ii) provincial population dependency ratio (share under 15 and over 65 over 15–65) to instrument for  and 1- ;
  - (iii) interaction between effective distortion and dependency ratio.
- Rationale for dependency ratio:
  - Higher dependency ratios associated with larger current primary spending (health, social security, education) and lower public investment shares.
  - Evidence: Panels A–B Figure 12 show this relationship for Argentine provinces (1 percent significance), and Panels D–E show it holds in a global sample (43 countries, at least 40 years) (1 percent significance).
  - Panels C–D Figure 12: no statistical relationship between dependency ratio and real GDP growth, supporting exogeneity.
- Instrument strength: Kleibergen-Paap rk Wald f statistic rejects weak-instrument null for government consumption and public investment per capita.

### Proxy for initial stock of public capital and interaction
- Augmented specification (equation (8)) includes interaction between public investment shock and stock_{i;0} (initial stock of public capital over GDP).
- No direct provincial stock data: constructed proxy from historical kilometers of paved highways by province.
  - Proxy = actual kilometers of paved highways divided by predicted kilometers based on provincial GDP; ratio > 1 indicates endowment larger than predicted by GDP.
  - Use proxy observed in each province in 1964 as stock_{i;0} to avoid endogeneity; stock_{i;0} constant and absorbed by fixed effect.
  - Allowing proxy to change over time (lagged) yields similar results.

### Empirical results (Argentina, province-level IV)
- Primary spending multiplier:
  - Provincial primary spending multiplier = 0:56 (t= 2:5).
  - Government consumption multipliers similar to primary spending multipliers (current primary spending ≈ 90 percent of primary spending).
- Public investment multiplier (aggregate):
  - Public investment multiplier = 1:60 (t= 2:0). Cannot reject that multiplier equals one.
  - Out-of-sample exercise using proxy average stock for Argentina (1964-2014) yields multiplier = 1:71 (t= 2:4), similar to province-level IV result.
- Heterogeneity by initial stock:
  - Proxy variability: coefficient of variation = 0.69; average ratio ≈ 0.50; ratio below 0.20 for some provinces; reaches 1.15 for others.
  - Using equation (8):
    - High initial stock (95th percentile) public investment multiplier = 0:23 (t= 0:85) — small and statistically indistinguishable from zero.
    - Low initial stock (5th percentile) public investment multiplier = 2:03 (t= 2:3) — significantly larger and statistically larger than one.
  - Figure 15: multiplier virtually zero for high initial stock (higher than 1.20), becomes significant and increasingly positive as ratio decreases; for ratios lower than 0.30 multiplier exceeds one.
- Province examples over time (Figure 16):
  - Buenos Aires: GDP increased almost 3-fold since 1964; paved highways increased < 10 percent (4,300 km in 1964 to ~4,700 km in 2014); public investment multiplier rose from 0:80 in 1964 to 1:50 in 2014.
  - La Rioja: paved highways increased about 5-fold (392 km in 1964 to ~1,900 km in 2014); public investment multiplier fell from 1:62 in 1964 to virtually zero in 2014.

---

### Cross-sample synthesis and policy implications

### Robust cross-sample evidence
- Consistent findings across European countries, U.S. states, and Argentine provinces using Blanchard-Perotti, forecast-error, and IV identification:
  - Initial stock of public capital over GDP critically determines public investment multiplier size.
  - Public investment multipliers are higher in jurisdictions with low initial public capital-to-GDP ratios and lower or near zero in jurisdictions with high initial ratios.
- Out-of-sample validation: an out-of-sample exercise based on Section 2 matches well province-level and external country-study estimates (regression R^2 = 0:82 and cannot reject coefficient equals one).

### Key quantitative thresholds and examples
- European sample:
  - For ratio lower than 0.25 the public investment multiplier exceeds one.
  - High-ratio (95th percentile = 1.33) two-year multiplier small (0:15, t= 0:2); low-ratio (5th percentile = 0.16) two-year multiplier large (2:15, t= 2:1).
- U.S. states:
  - Average ratio mid-1980s: 1.02; average ratio 2012: 0.68.
  - High initial ratio (95th percentile) multiplier = 0:51 (t= 2:12); low initial ratio (5th percentile) multiplier = 1:36 (t= 4:2).
  - For ratios lower than 0.5 multiplier becomes larger than one.
- Argentine provinces:
  - Average proxy ratio ≈ 0.50; coefficient of variation = 0.69.
  - High initial stock (95th percentile) multiplier = 0:23 (t= 0:85); low initial stock (5th percentile) multiplier = 2:03 (t= 2:3).
  - For ratios lower than 0.30 multiplier exceeds one.

### Role of spending efficiency
- Higher spending efficiency (first principal component of 36 indicators) increases multipliers; for low efficiency multipliers tend to be zero.
- Controlling for efficiency does not change the central role of initial stock of public capital.

### Policy-relevant conclusions
- Because initial public capital/GDP varies across jurisdictions and over time, public investment multipliers vary across jurisdictions and historical periods.
- Prioritize public investment in jurisdictions with low initial stocks of public capital, where medium-term multipliers can be large (potentially > 1).
- In jurisdictions with high initial public capital/GDP ratios, public investment is likely to have small and statistically insignificant multipliers.
- Improving spending efficiency enhances multiplier outcomes but does not substitute for the effect of the initial stock.

*Source: wpiea2019289-print-pdf — 1. Introduction; 2.3 Does the initial stock of public capital matter?; 4.1 Identification strategy*

### 1. Introduction  .......................................................................................................

### 1. Introduction

### Research motivation and questions
- Since the Global Financial Crisis there has been an explosion of studies on the macroeconomic effects of government spending, with attention to how macro factors affect spending multipliers.
- Known determinants of multiplier size include:
  - the state of the economy (multipliers larger in recessions) — e.g., Auerbach and Gorodnichenko, 2012 and 2013; Riera-Crichton, Vegh, and Vuletin, 2015;
  - the exchange rate regime (larger under fixed regimes) — e.g., Ilzetzki, Mendoza, and Vegh, 2013;
  - the degree of indebtedness (larger when debt is low) — e.g., Ilzetzki, Mendoza, and Vegh, 2013; Huidrom et al., 2019;
  - the degree of accommodation of monetary policy (larger when monetary policy is loose and/or close to the zero lower bound) — Christiano, Eichenbaum, and Rebelo, 2011; Coenen, Straub, and Trabandt, 2013;
  - the degree of openness (multipliers smaller in more open economies) — e.g., Ilzetzki, Mendoza, and Vegh, 2013; Gonzalez-Garcia, Lemus, and Mrkaic, 2013.
- Gap in literature: most studies focus on primary spending or government consumption; less evidence exists on public investment multipliers.
- Central question of this paper: Does the size of the public investment multiplier depend on the initial stock of public capital?
  - Theoretical expectation (neoclassical fiscal policy growth models, e.g., Baxter and King, 1993): lower initial stock of public capital → larger marginal productivity of additional public investment → larger public investment multipliers. Conversely, high initial stock → lower impact.
- Policy relevance: important for decisions on public investment/infrastructure, especially in developing countries where public capital stocks are low and efficiency concerns (cost overruns, implementation delays, institutional weaknesses, waste, corruption) may reduce multiplier effects.

### Contribution and approach
- The paper empirically investigates the dependence of the public investment multiplier on the initial stock of public capital using:
  - multiple samples (European countries, U.S. states, Argentine provinces),
  - multiple levels of government,
  - multiple identification strategies.
- Main empirical finding preview: using different samples and identification strategies, the initial stock of public capital matters for the size of the public investment multiplier in the direction predicted by theory.

### Structure of the paper (overview)
- Section 2: empirical analysis for 31 European countries using Blanchard and Perotti (2002) identification.
- Section 3: analysis for U.S. states using government spending forecast errors (Auerbach and Gorodnichenko, 2012 and 2013).
- Section 4: analysis for Argentine provinces using instrumental variables.
- Section 5: comparison with 17 country-specific external studies and calibrated estimates.
- Section 6: final thoughts.

### Theoretical and empirical context on public investment multipliers
- Prior studies (Aschauer 1989a, 1989b; Baxter and King 1993; Auerbach and Gorodnichenko, 2013; Leduc and Wilson, 2012; Eden and Kraay, 2014; Calderon, Moral-Benito, and Serven, 2015; Furceri and Li, 2017) find public investment multipliers can be quite large relative to government consumption multipliers, because public investment directly raises the productive capacity of the economy and spurs private investment and consumption over time.
- Evidence indicates that low spending efficiency (cost overruns, implementation delays, institutional weaknesses, waste, corruption) diminishes the output effect of public investment (Leeper, Walker, and Yang, 2010; Cavallo and Daude, 2011; Leduc and Wilson, 2012; Furceri and Li, 2017; Izquierdo, Pessino, and Vuletin, 2018).

### Empirical strategy (as applied in Section 2 for European countries)
- Sample: un-balanced non-interpolated quarterly data for 31 European countries for 1987:Q1-2014:Q4.
- Identification of exogenous government spending shocks: Blanchard and Perotti (2002) methodology with timing restrictions:
  - government spending changes can contemporaneously affect economic activity (within the quarter);
  - government takes at least one quarter to respond to developments in the economy.
- Estimation method: single-equation local projections (Jorda, 2005; Stock and Watson, 2007) estimated via least-squares dummy variables (LSDV).
  - Advantages: single-regression estimation, greater robustness to misspecification, ability to accommodate highly non-linear and flexible specifications.
- Linear baseline specification (cumulative output growth response) and an augmented specification for public investment that interacts the public investment shock with the ratio of initial stock of public capital to GDP (logarithms), where the initial ratio uses the period 1980-1985 for most European countries to avoid endogeneity.
- Reporting: multipliers reported with one-standard-error bands; coefficients scaled by average GDP-to-government-spending ratio to obtain the $1 change-in-government-spending-on-GDP-level multiplier.

### Key empirical findings (European sample: primary spending vs. public investment)
- Primary spending multiplier (Panel A, Figure 1):
  - On impact: 0.13 (t = 4.5).
  - After two years of the spending shock: 0.25 (t = 1.3).
  - Low multipliers driven by:
    - tepid response of private consumption (Panel B), and
    - no response of private investment at any time horizon (Panel C).
  - Government consumption multipliers (not shown) are virtually identical to primary spending multipliers.
- Public investment multiplier (Panels D–F, Figure 1):
  - On impact: 0.15 (t = 2.5) — virtually identical to the primary spending on-impact figure.
  - After two years of the public investment shock: 0.80 (t = 3.3).
    - This medium-term multiplier is more than 3 times the primary spending multiplier at that horizon (0.80 vs. 0.25).
    - At that horizon the null that the multiplier equals one cannot be rejected.
  - The larger and more lasting effects reflect stronger responses of both private consumption (Panel E) and private investment (Panel F), evidencing a crowding-in effect of private investment from productive public capital.

*Source: wpiea2019289-print-pdf — 1. Introduction*

### 2.3  Does the initial stock of public capital matter?

### 2.3  Does the initial stock of public capital matter?

### Theoretical hypothesis
- Theory predicts the public investment multiplier depends negatively on the ratio of public capital to GDP.
- Empirical test: assess whether the size of the public investment multiplier varies with the initial stock of public capital to GDP.

### Cross-country variation (European sample)
- Large variability in the ratio of the initial stock of public capital to GDP across the European countries in the sample:
  - Coefficient of variation: 0.55.
  - Median ratio: 0.63.
  - Examples: about 0.25 for Hungary, Latvia, Malta, and Greece; above 1 for Romania, Luxembourg, Cyprus, and Denmark.

### Estimated multipliers by initial stock (European sample)
- Estimation approach: regression (2) evaluated at 95th percentile (high ratio = 1.33) and 5th percentile (low ratio = 0.16) of initial public capital/GDP.
- Impact (short-run) multipliers (GDP):
  - High ratio (Panel A): 0:25 on impact.
  - Low ratio (Panel D): 0:18 on impact.
- Two-year horizon multipliers (GDP):
  - High ratio: 0:15 (t= 0:2) after two years — small and statistically weak.
  - Low ratio: 2:15 (t= 2:1) after two years — much larger; statistically cannot reject that multiplier > 1.
- Mechanisms: stronger responses of private investment and private consumption when initial ratio is low (Panels E and F).

### Multipliers as a continuous function of initial stock
- After two years, multiplier plotted against initial public capital/GDP:
  - Multiplier is statistically zero at high levels of the ratio (i.e., higher than 1).
  - Multiplier becomes statistically significant and increasingly positive as the ratio decreases.
  - For ratio lower than 0.25, the public investment multiplier exceeds one.
- Interpretation: an increase (decrease) of GDP associated with increasing (reducing) public investment by $1 tends to be zero for high initial ratios and becomes larger as the initial ratio decreases.

### Policy-relevant cross-time/cross-country illustration (European sample)
- Implied multipliers shown for ratios prevailing in 1990 and 2014:
  - Between 1990 and 2014, the public investment multiplier fell most in Southern economies and new Eastern bloc members.
  - Decline driven by important rises in the stock of public capital following ERDF and Cohesion Fund efforts.

### Out-of-sample application (U.S. and Argentina)
- U.S.:
  - Estimated multipliers using U.S. ratio of initial stock for 1960 and 2015:
    - 1960: 0.4 (statistically zero).
    - 2015: 0.85 (statistically not different from one).
  - Ratio of public capital to GDP: 1960 = 1.04; 2015 = 0.64.
- Argentina:
  - Estimated multipliers for 1960 and 2015:
    - 1960: 1.9 (statistically larger than one).
    - 2015: 1.4 (statistically equal to one).
  - Ratio of public capital to GDP: 1960 = 0.20; 2015 = 0.35.
- Convergence insight:
  - Previously the U.S. ratio was more than five times Argentina’s; by 2015 the difference shrank to about two-fold.
  - As the ratios converged, estimated multipliers for both countries also tended to converge (both statistically positive and close to one).

### Role of spending efficiency
- Spending efficiency defined via first principal component of 36 indicators of institutional quality and indicators of infrastructure, education, and health (Global Competitiveness report, 2004-2014).
  - Each indicator varies between 1 (worst) and 7 (best).
  - Efficiency variable effectively varies, for the global sample, between 2.5 and 6 and, for the European sample, between 3.5 and 6.
  - First principal component explains about 65 percent of comovement of the 36 indicators.
- Extended specification (3) includes interaction of public investment shock with efficiency to control for spending quality.
- Findings:
  - Efficiency matters: for low levels of efficiency, the public investment multiplier tends to be zero; multiplier becomes larger for higher efficiency.
  - Crucially, controlling for efficiency does not affect the core finding: the initial stock of public capital remains a key determinant of the multiplier (the novel insight remains virtually unaffected).
- Additional notes:
  - Using a global sample of 128 countries, cannot reject that correlation between stock_i,0 and efficiency_i is statistically zero.
  - stock_i,0 is not statistically correlated with a range of macroeconomic factors (exchange rate regimes, trade openness, capital account openness, real PPP GDP per capita, public debt/GDP, external debt/GDP, cyclicality of government spending) in the global sample; results unchanged when focusing on European sample.

### Empirical evidence for U.S. states (summary)
- Data: balanced annual data for 1987-2016 for U.S. states (Hawaii and Alaska excluded).
- Identification: government spending forecast error approach (GFE = actual minus anticipated spending), using NASBO reports; one lag (L = 1); robust Driscoll and Kraay (1998) standard errors.
- Linear specification (4) and nonlinear interaction specification (5) include interaction of GFE with stock_i,0 (average ratio 1980-1985 in logs).
- State-level findings:
  - Multiplier for state primary spending: 0:08 (t= 1:3) — quite low and statistically indistinguishable from zero.
  - Public investment multiplier (state level): 0:98 (t= 3:0) — large; cannot reject multiplier = 1.
  - Out-of-sample estimate using national U.S. average stock for 1987-2016: 0:85 (t= 2:4) — similar to state-level estimate.
- Cross-state variation in initial stock:
  - Coefficient of variation across U.S. states: 0.43.
- Effect of initial stock on state public investment multipliers:
  - High initial ratio (95th percentile): multiplier = 0:51 (t= 2:12).
  - Low initial ratio (5th percentile): multiplier = 1:36 (t= 4:2).
  - High-ratio multiplier less than half the low-ratio multiplier.
  - Cannot reject that high-ratio multiplier < 1; cannot reject that low-ratio multiplier > 1.
- Continuous function result (Figure 9 analogue):
  - Multiplier virtually zero at high initial ratios (i.e., higher than 1.9).
  - Multiplier statistically significant and increasingly positive as ratio decreases.
  - For ratios lower than 0.5, the public investment multiplier becomes larger than one.
- Cross-time change example:
  - Stock of public capital/GDP ratio fell in almost all U.S. states (except Wyoming) from mid-1980s to 2012:
    - Average ratio mid-1980s: 1.02.
    - Average ratio 2012: 0.68.
    - Fall greater than 30 percent in all but one state.
  - Result: public investment multipliers increased across the board.

### Policy implications (cross-cutting)
- The size of the public investment multiplier depends importantly on the initial stock of public capital to GDP.
- Because the ratio varies across countries and over time, the multiplier will vary across jurisdictions and historical periods.
- For jurisdictions with low initial public capital/GDP ratios, public investment can have large multipliers (potentially > 1) over medium horizons (two years).
- For jurisdictions with high initial public capital/GDP ratios, public investment multipliers are small and statistically indistinguishable from zero.
- Spending efficiency improves multiplier outcomes but does not alter the central role of the initial stock of public capital.

*Source: wpiea2019289-print-pdf - 2.3  Does the initial stock of public capital matter?*

### 4.1  IdentiÖcation strategy

### 4.1  IdentiÖcation strategy

### Empirical specification and overall IV approach
- Basic linear specification for the primary spending multiplier:
  - y_pc_{i;t} = _i +  g_pc_{i;t} +  y_pc_{i;t-1} + % T +  T^2 + _{i;t} (equation (6))
  - Subscripts i and t denote province and year; _i is the provincial fixed effect; T and T^2 are linear and quadratic trends; y_pc and g_pc are logarithms of real provincial GDP per capita and real provincial primary spending per capita;  is the error term.
- To report the usual government spending multiplier (effect of a $1 change in government spending on level of GDP), regression coefficients associated with the spending shock are multiplied by the average ratio of GDP to provincial government spending.
- Robust Driscoll and Kraay (1998) standard errors used for heteroskedasticity, autocorrelation, and cross-panel correlation. Im, Pesaran, and Shin (2003) panel unit-root tests reject the null that all panels contain a unit root.

### Instrumenting primary spending
- Instrument proposed: provincial over-representation in the Argentine National Chamber of Deputies (difference between actual number of provincial legislators per capita and that based on proportional representation).
- Rationale (three key factors):
  - About two-thirds of provincial primary spending is financed with federal fiscal transfers.
  - Over-represented jurisdictions tend to receive larger federal fiscal transfers per capita due to bargaining power; in Argentina over-representation effect is dominated by the Chamber of Deputies (not the Senate).
  - Constitutional amendments driving over-representation (1949, 1972, 1983) were driven by governance/political considerations and not enacted in response to macroeconomic developments, making over-representation exogenous.
- Empirical support:
  - Panel A Figure 11: strong positive association between federal fiscal transfers per capita and provincial primary spending per capita (1 percent significance), after controlling for provincial fixed effects and trends.
  - Panel B Figure 11: tight positive association between provincial effective distortion in the Chamber of Deputies and federal fiscal transfers per capita (1 percent significance).
  - Panel C Figure 11: strong positive association between provincial effective distortion in the Chamber of Deputies (instrument) and provincial primary spending per capita (instrumented variable) (1 percent significance).
- Instrument validity tests:
  - Based on Stock and Yogo (2005), reject null that the effective distortion in the Chamber of Deputies is a weak instrument for provincial primary spending per capita.

### Instrumenting government consumption and public investment (decomposition)
- Modified linear specification to include both components (equation (7)):
  - y_pc_{i;t} = _i + _c g^c_pc_{i;t} + _i g^i_pc_{i;t} +  y_pc_{i;t-1} + % T +  T^2 + _{i;t}
  - g^c_pc and g^i_pc are logarithms of real provincial government consumption per capita and real provincial public investment per capita.
- Relationship: g_pc_{i;t} ≡ g^c_pc_{i;t} + g^i_pc_{i;t}; express g^c_pc_{i;t} = _{i;t} * g_pc_{i;t} and g^i_pc_{i;t} = (1- _{i;t}) * g_pc_{i;t}, where _{i;t} measures share of primary spending allocated to consumption.
- Instruments used for (g^c_pc, g^i_pc):
  - (i) provincial effective distortion in the Chamber of Deputies (instrument for g_pc);
  - (ii) provincial population dependency ratio (population share under 15 and older than 65 over population between 15 and 65) to instrument for  (and 1- );
  - (iii) interaction term between provincial effective distortion and provincial population dependency ratio.
- Rationale for population dependency ratio as instrument for composition:
  - Higher dependency ratios are associated with larger current primary spending (health, social security, education) and lower public investment shares (cited literature).
  - Panels A and B Figure 12: Argentine provinces show this relationship (1 percent significance) controlling for fixed effects and trends.
  - Panels D and E Figure 12: same regularity holds in a global sample of countries (43 countries, at least 40 years of data) controlling for country fixed effects and trends (1 percent significance).
  - Panels C and D Figure 12: no statistical relationship between population dependency ratio and real GDP growth in Argentine provinces or globally, supporting exogeneity.
- Instrument strength: Kleibergen-Paap rk Wald f statistic rejects null that proposed instruments are weak for provincial government consumption per capita and provincial public investment per capita.

### Proxy for initial stock of public capital and interaction
- To allow public investment multiplier to depend on initial stock of public capital to GDP, augmented specification (equation (8)):
  - y_pc_{i;t} = _i + _c g^c_pc_{i;t} + _i g^i_pc_{i;t} +  [_i g^i_pc_{i;t} * stock_{i;0}] +  y_pc_{i;t-1} + % T +  T^2 + _{i;t}
  - Interaction term between public investment shock and stock_{i;0} (initial stock of public capital over GDP).
- No direct data for provincial stock of public capital: constructed proxy using newly collected historical data on kilometers of paved highways by province.
  - Proxy: ratio of actual kilometers of paved highways to predicted kilometers based on provincial GDP (for balanced panel for entire period); ratio > 1 indicates endowment larger than predicted by GDP.
  - Use proxy observed in each province in 1964 as stock_{i;0} to avoid endogeneity; stock_{i;0} is constant and absorbed by provincial fixed effect.
  - If proxy is allowed to change over time (e.g., lagged), similar results obtain.

### Empirical results (province-level, Argentina)
- Primary spending multiplier:
  - Provincial primary spending multiplier = 0:56 (t= 2:5).
  - Government consumption multipliers are similar to primary spending multipliers (current primary spending typically represents about 90 percent of primary spending for Argentine provinces).
- Public investment multiplier (aggregate):
  - Public investment multiplier = 1:60 (t= 2:0). Cannot reject null that multiplier equals one.
  - Out-of-sample exercise using proxy average stock for Argentina (1964-2014) based on Section 2.3 yields multiplier = 1:71 (t= 2:4), similar to province-level IV result.
- Heterogeneity by initial stock of public capital:
  - Proxy variability across provinces: coefficient of variation = 0.69; average ratio ≈ 0.50; ratio below 0.20 for some provinces (e.g., Tierra del Fuego, Formosa, Misiones); reaches 1.15 for others (e.g., Mendoza, Santa Fe, Cordoba, Buenos Aires).
  - Using equation (8):
    - Public investment multiplier for high initial stock (95th percentile) = 0:23 (t= 0:85) — much smaller and statistically indistinguishable from zero.
    - Public investment multiplier for low initial stock (5th percentile) = 2:03 (t= 2:3) — significantly larger and statistically larger than one.
  - Figure 15 evidence: multiplier virtually zero for high levels of initial stock (higher than 1.20), becomes statistically significant and increasingly positive with lower initial ratios; for ratios lower than 0.30 multiplier exceeds one.
- Province examples over time (Figure 16):
  - Buenos Aires: GDP increased almost 3-fold since 1964; paved highways increased < 10 percent (from 4,300 km in 1964 to ~4,700 km in 2014); public investment multiplier rose from 0:80 in 1964 to 1:50 in 2014.
  - La Rioja: paved highways increased about 5-fold (from 392 km in 1964 to ~1,900 km in 2014); public investment multiplier fell from 1:62 in 1964 to virtually zero in 2014.

### Synthesis and implications
- Consistent evidence across samples and identification strategies:
  - European countries, U.S. states, and Argentine provinces; identification via Blanchard-Perotti, forecast errors, and instrumental variables all indicate that the initial stock of public capital over GDP critically determines the size of public investment multipliers.
- Key empirical conclusion:
  - Public investment multipliers are higher in jurisdictions with low initial public capital-to-GDP ratios and lower (or near zero) in jurisdictions with high initial ratios.
- Out-of-sample validation:
  - An out-of-sample exercise based on Section 2 matches well province-level and external country-study estimates (see Section 5 discussion of 17 country studies; regression R^2 = 0:82 and cannot reject coefficient equals one).
- Policy relevance:
  - Results provide strong empirical support for prioritizing public investment in jurisdictions or countries with low initial stocks of public capital, especially in developing countries with large infrastructure gaps, since returns (multipliers) are substantially larger where initial stocks are low.

*Source: wpiea2019289-print-pdf - 4.1  IdentiÖcation strategy*

### References

### wpiea2019289-print-pdf - References

### Major sources and literature cited
- Extensive list of empirical and theoretical references on fiscal multipliers, public investment, and related topics, including (but not limited to) works by Alesina, Auerbach, Blanchard, Baxter and King, Ilzetzki, Mendoza, Vegh and Vuletin, Ramey, Christiano et al., Coenen et al., and many IMF, World Bank, NBER, OECD, and country‑level studies.
- Specific references address: the output effect of fiscal consolidation, determinants of capital flows, estimation of fiscal multipliers in Argentina and other countries, public capital productivity and crowding out, political economy of grants, aging and public finance, and methods for impulse response estimation (e.g., Jorda 2005).

### Data: European sample (coverage and construction)
- Coverage: 31 European countries with quarterly data starting in the following year-quarter for each country:
  - Austria (1999:Q1), Belgium (1995:Q1), Bulgaria (1999:Q1), Croatia (2012:Q1), Cyprus (1995:Q1), Czech Republic (1999:Q1), Denmark (1999:Q1), Estonia (1999:Q1), Finland (1998:Q1), France (1991:Q1), Germany (1995:Q1), Greece (1999:Q1), Hungary (1999:Q1), Iceland (2004:Q1), Ireland (1999:Q1), Italy (1999:Q1), Latvia (1999:Q1), Lithuania (1999:Q1), Luxembourg (2000:Q1), Malta (2000:Q1), Netherlands (1999:Q1), Norway (1996:Q1), Poland (2002:Q1), Portugal (1999:Q1), Romania (199:Q1), Slovakia (1999:Q1), Slovenia (1999:Q1), Spain (1995:Q1), Sweden Kingdom (1993:Q1), Switzerland (1990:Q1), United Kingdom (1987:Q1).
- Sources and variable construction:
  - Government finance and national accounts statistics: Eurostat.
  - Ratio of public stock of capital to GDP: IMF‑FAD (general government capital stock) at annual frequency.
  - Initial stock of public capital to GDP: computed as the average for the years 1980-1985 for most countries; for Croatia, Czech Republic, Estonia, Latvia, Lithuania, Slovakia, and Slovenia the average is computed over the period 1990-1995.
  - Efficiency variable: first principal component of a wide set of indicators (36 to be specific) covering institutional quality and quality of infrastructure, education, and health; indicators sourced from the Global Competitiveness report (World Economic Forum) covering 142 countries for 2004-2014.
- Indicators composing the efficiency principal component:
  - Institutional quality indicators (selected examples preserved verbatim): property rights; intellectual property protection; diversion of public funds; public trust in politicians; irregular payments and bribes; judicial independence; favoritism in decisions of government officials; wastefulness of government spending; burden of government regulation; efficiency of legal framework in settling disputes; efficiency of legal framework in challenging regulations; transparency of government policymaking; business costs of terrorism; business costs of crime and violence; organized crime; reliability of police services; ethical behavior of firms; strength of auditing and reporting standards; efficacy of corporate boards; protection of minority shareholders' interests; strength of investor protection; government procurement of advanced tech products.
  - Infrastructure quality indicators: quality of overall infrastructure; quality of roads; quality of railroad infrastructure; quality of port infrastructure; quality of air transport infrastructure; quality of electricity supply.
  - Education and health quality indicators: quality of primary education; quality of the education system; quality of math and science education; quality of management schools; quality of scientific research institutions; business impact of malaria; business impact of tuberculosis; business impact of HIV/AIDS.

### Data: U.S. states (variables and sources)
- Total State Expenditures (estimated and actual) — Capital Inclusive: National Association of Budget Officers, State Expenditure Report.
- Total capital expenditures (estimated and actual) — Capital inclusive: National Association of Budget Officers, State Expenditure Report.
- Real gross domestic product: Bureau of Economic Activity. Regional Accounts.
- Total, private and public stock of capital: Zegeye (2000).
- Shares of stock of public capital over GDP per state for 2012: obtained using shares of consumption expenditure from the U.S. Bureau of Economic Analysis and U.S. fiscal data from the U.S. Census Bureau in the 2012 Census of Government; applied to total stock of public capital in the U.S. obtained from the Investment and Capital Stock Dataset from the Fiscal Affairs Department at the IMF. Same method applied for the estimate for the period 1980-1985.

### Data: Argentine provinces (variables and sources)
- Total subnational public expenditure and components (consumption and investment), and total transfers from federal government to provinces:
  - Period 1964-2000: Porto (2004).
  - Period 2001-2014: Ministry of Economy and Public Finance of the Republic.
- Subnational Geographical Gross Product:
  - Period 1964-2000: Porto (2004).
  - Period 2001-2014: Center for Production Studies (CEP) (Argentina Ministry of Industry); missing years supplemented with Provincial Statistics Offices and Secretariat of Economic Policy and Development Planning (Ministry of Economy and Public Finance of the Argentine Republic).
- Provincial population:
  - Period 1964-2000: Porto (2004).
  - Period 2001-2014: National Institute of Statistics and Census (INDEC).
- Effective distortion in Chamber of Deputies: Vegh and Vuletin (2015).
- Kilometers of paved highways in each province:
  - 1964 to 2001: historical archives from (i) Anuarios Estadísticos del Instituto Nacional de Estadística y Censos (INDEC), (ii) Censos Nacionales Económicos del INDEC, and (iii) Dirección de Vialidad Nacional y de Oficinas de Estadísticas Provinciales.
  - 2001 to 2014: Observatorio Nacional de Datos de Transporte - Centro Tecnológico de Transporte, Tránsito y Seguridad Vial de la Universidad Tecnológica Nacional.

### Appendix 2: External studies and own calibrations (overview)
- Table 1 compares the public investment multiplier from 17 country‑specific external studies with the multiplier estimated using the report's non-linear arguments (Section 2).
- For these 17 countries, IMF‑FAD (general government capital stock) at annual frequency is used to compute the public stock of capital over GDP ratio.
- References for the 17 external studies are indicated in the note to Table 1 (examples preserved verbatim in the source material).

### Figures and estimation notes (methodological commonalities)
- Panels and figures present empirical evidence for:
  - Primary spending and public investment multipliers in European countries, U.S. states, and Argentinean provinces.
  - Ratio of initial stock of public capital to GDP across samples.
  - Public investment multipliers evaluated at high (95th percentile) and low (5th percentile) initial stock ratios, and evaluated at different years (e.g., 1990, 2014) or different levels of efficiency.
  - Multiplier dynamics (e.g., after two years of the spending shock).
  - Partial correlations underpinning instrumental variable choices in provincial-level analyses (e.g., over‑representation in Chamber of Deputies; provincial population dependency ratio).
  - Comparison of the study's non-linear public investment multiplier with external source estimates for 17 countries.
- Common estimation details across panels and figures:
  - Country/state/provincial fixed effect panel regression with linear and quadratic trends.
  - Standard errors are Driscoll‑Kraay standard errors and bootstrapped.
  - Identification of low and high ratio of initial stock of public capital to GDP often uses the 5th percentile and 95th percentile, respectively.
  - Partial correlation graphs control for fixed effects and linear and quadratic trends; graphs use residuals and report T‑statistics in brackets.

*Source: wpiea2019289-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019289-print-pdf.pdf_