## Appendix A

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---

### I. Introduction — Overview and objectives
- Re-examines relationship between public-capital accumulation and private investment in India by estimating a Structural Vector Error Correction Model (SVECM) in three variables: public investment, private investment, and output, over the period 1950-2012.
- Investigates whether the relationship changed after policy reforms:
  - Using annual observations post-1980.
  - Using quarterly data post liberalization: 1996Q2-2015Q1 (CapEx-CMIE database).
- Main contributions:
  - Novel identification strategy using theory-driven long-run relationships (the "great ratio" of investment to output).
  - Decomposition of structural shocks into permanent and transitory effects for identification.
- Core empirical summary:
  - Full sample 1950-2012: public-capital accumulation "crowds out" private investment in India.
  - Post-1980 annual sample and quarterly data since 1996Q2: public investment is complementary to private investment ("crowds in"), attributed to policy reforms since the early 1990s.

### Structural VECM: model set-up and identification
- Baseline variables: log per capita output, yt; public investment, git; private investment, pit.
- Time series properties:
  - All variables are integrated of order one with evidence of one cointegrating relation among the three variables.
  - Long-run relationship motivated by stationarity of the "great ratio": expression φ1 git + φ2 pit − yt with φ1 and φ2 < 1.
- Reduced form VECM: Δzt = Π zt−1 + Σi=1m Γi Δzt−i + ut, where zt = (yt, git, pit)' and ut = (uyt, ugit, upit)'.
- Structural shocks: ut = B εt where εt = (εyt, εgit, εpit)' with
  - εy: productivity shock (permanent).
  - εgi: structural disturbance to public investment (possibly permanent).
  - εpi: demand shock (assumed transitory).
- Identification strategy:
  - Long-run restrictions: demand shock εpi transitory; productivity and possibly public investment shocks permanent.
  - With K = 3 and r = 1 cointegrating vector → long-run impact matrix Ψ of rank 2 ⇒ one transitory and two permanent shocks.
  - Additional identifying restriction: structural disturbance associated with government investment has no long-run impact on private investment.

### Data: sources, construction, frequency and caveats
- Annual baseline data: GDP, public and private gross fixed capital formation for 1950-2012 (63 observations). Source: National Account Statistics, Indian Central Statistical Office. All variables in real per capita terms (2004-05 prices). National aggregates.
- Quarterly data: CapEx-CMIE database (projects with capital expenditure ≥ 10 million rupees beginning in 1996; about 45,000 projects).
  - Project costs aggregated into quarterly time-series; spending profiles estimated using project total costs and event dates.
  - For completed projects, cash flows apportioned by project duration; for ongoing/abandoned projects expected duration based on averages of comparable completed projects.
  - Two investment series per sector:
    - Type 1: includes estimated spending on abandoned/shelved projects up to abandonment/shelving.
    - Type 2: assigns zero spending to abandoned/shelved projects (preferred).
  - Correlation between new annual series and National Accounts public/private gross fixed capital formation: 0.95 over 1995-2012.
  - Caveat: CapEx data compiled from multiple sources and not comprehensive; cannot account for cost overruns or savings.

### Empirical findings — annual models (Models 1–3)
- Model definitions:
  - Model 1: annual (yt, git, pit) over 1950-2012 (baseline).
  - Model 2: (yt, ginfrt, pit) over 1950-2012 (public infrastructure investment).
  - Model 3: (yt, git, pit) over 1980-2012 (post-break sample).
- Short-run and long-run matrices (B and B∞) indicate:
  - Given ordering (y, gi, pi)′ and (y, gi_infr, pi)′, a structural innovation in public investment crowds out private investment in the short run in Models 1 and 2.
  - Effect of εgi on output is positive and statistically significant on impact and in the long run in both Models 1 and 2.
- Impulse response highlights — Model 1 (1950-2012):
  - Productivity shock: private investment response significantly positive on impact and long run; public investment response not significantly different from zero short- or long-run.
  - Public investment shock: output response positive throughout; private investment experiences temporary crowding out statistically significant for the first 3 years, converging to zero thereafter.
- Impulse response highlights — Model 2 (infrastructure):
  - Similar to Model 1; crowding out of private investment by public infrastructure investment persists.
- Magnitude of crowding out — Model 1 (1950-2012):
  - Interim multipliers (private investment response to one rupee increase in public investment): 0.60, 0.31, and 0.17 rupees after one, two, and three years, respectively.
  - Baseline crowding out results are close to Mitra (2006) and Serven (1999).

### Structural break analysis and Model 3 (post-1980)
- Structural stability tests:
  - Chow break-point and Chow-forecast tests (1975-2000 with 2000 bootstrapped replications) indicate rejection of parameter constancy for a range of years → evidence of an underlying break.
  - 1980 selected as break year (highest break-point and split-sample statistic values).
  - Clemente et al. (1998) unit root tests indicate breaks in 1983-1984 for y, gi, and pi; a second break indicated for y and pi at 1996.
- Model 3 results (1980-2012):
  - Private investment response to public capital accumulation changes sign relative to full-sample Model 1: a policy-induced increase in public investment significantly crowds in private investment in the short run.
  - Interim multipliers (Model 3): 0.37, 0.16, and 0.07 after the first, second, and third years, respectively.
  - Interpretation: public capital accumulation may have become more complementary to private investment since the early 1980s.

### Quarterly analysis using post-liberalization data (Models 4–6)
- Quarterly models use CapEx-CMIE constructed series; two investment measures (type 1 and type 2).
- Model definitions:
  - Model 4: quarterly type 1 (gi1t, pi1t).
  - Model 5: quarterly type 2 (gi2t, pi2t) — preferred specification.
  - Model 6: gi2,infra t replacing gi2t (public infrastructure).
- Estimation notes:
  - Lag order for quarterly VECMs: 7 (in first differences) based on AIC.
  - Loading coefficients and cointegrating vectors for Models 4–6 are smaller in magnitude than annual estimates.
- Impulse response highlights (quarterly):
  - All three specifications: public investment responds positively and significantly to a productivity shock after 4–6 quarters.
  - Private investment response to productivity shock is positive and significant in all models.
  - Output response to public investment shock:
    - Model 4: not significantly different from zero in first 8 quarters.
    - Models 5 and 6: statistically significant positive impact over first 8 quarters and small positive long-run effect.
  - Private investment response to public investment shock:
    - None of the three quarterly specifications predict crowding out.
    - Preferred specification (Model 5) shows positive and significant crowding in of private investment by public sector investment from quarters eight to twelve.
    - Interim multipliers (Model 5): a one rupee increase in public investment crowds in private investment by 0.30, 1.24, and 1.07 rupees after four, eight, and twelve quarters, respectively.
    - Response to public infrastructure investment shocks (Model 6) similar to aggregate public investment case.
- Quarterly conclusion: evidence for "crowding in" of private investment by public investment in post-1980 and post-liberalization samples (1996Q2-2015Q1).

### Interpretation and policy-relevant analysis
- Sample contrast:
  - Full-sample (1950-2012): public investment crowds out private investment in the short run.
  - 1980-2012 and quarterly post-liberalization (1996Q2-2015Q1): public investment crowds in private investment.
- Economic context:
  - Crowding out over full sample likely reflects pre-1980s state-led, inward-oriented growth strategy (capital-intensive industrialization, licensing, sector reservation for state, high trade barriers, mandatory credit allocation).
  - Post-1980s and post-1991 reforms (deregulation, trade liberalization, abolition of many license restrictions, tariff reductions, banking sector easing) plausibly made public investment more complementary to private investment.
  - Large infrastructure deficits imply public investment can raise private sector profitability and stimulate private investment.
- Data and methodology caveats affecting interpretation:
  - CapEx project-announcement-based series are proxies and may not perfectly reflect realized investment; type 2 series preferred to avoid assumptions about failed projects.
  - Cointegration evidence: annual full-sample Models 1 and 2 indicate one cointegrating vector (99% trace test); Model 3 weaker possibly due to sample size; Johansen trace test with structural break at 1980 strongly supports one cointegrating vector.
  - Unit root testing: variables treated as I(1) based on ADF, ADF-GLS, and PP tests; quarterly series treated as I(1) with some mixed test results for pi1 and pi2 but PP test supports I(1) treatment.

### Concluding remarks and policy implications
- Main empirical conclusion:
  - Public investment "crowded out" private investment in India over 1950-2012, but "crowded in" private investment over 1980-2012 and in quarterly post-liberalization data (1996Q2-2015Q1).
- Policy interpretation:
  - Structural policy reforms since early 1980s and especially after 1991 likely shifted the relationship, making public investment complementary to private investment.
  - In the presence of large infrastructure deficits, public investment can stimulate private investment rather than displace it.
- Suggestions for future research (policy-relevant extensions):
  - Use the micro quarterly dataset to disentangle region- or sector-wise relationships between public and private investment in India.
  - Examine whether states with policies more conducive to private investment experienced stronger crowding-in effects.
  - Such analyses would have implications for the design of macroeconomic and subnational (state-level) public investment policies.

*Source — _wp15264*

### Appendix A .............................................................................................................

### Appendix A

### I. INTRODUCTION — Overview and objectives
- Re-examines relationship between public-capital accumulation and private investment in India by estimating a Structural Vector Error Correction Model (SVECM) in three variables: public investment, private investment, and output, over the period 1950-2012.
- Investigates whether the relationship changed after policy reforms:
  - Using annual observations post-1980.
  - Using quarterly data post liberalization: 1996Q2-2015Q1 (CapEx-CMIE database).
- Main contributions:
  - Novel identification strategy using theory-driven long-run relationships (the "great ratio" of investment to output).
  - Decomposition of structural shocks into permanent and transitory effects for identification.
- Summary of core empirical findings (from the introduction):
  - Over the full sample 1950-2012, public-capital accumulation "crowds out" private investment in India.
  - Restricting the sample post-1980 or using quarterly data since 1996Q2, the opposite holds: public investment is complementary to (i.e., "crowds in") private investment—largely attributed to policy reforms since the early 1990s.
- Methodological choice:
  - Identification relies on long-run restrictions, motivated by empirical macroeconomics practices and economic theory, rather than short-run restrictions which are described as more restrictive for annual data.
  - Private-sector demand disturbances are assumed to have transitory effects; the two structural innovations with permanent effects are productivity shocks and (possibly) public investment innovations.
- Theoretical motivation and references (as stated):
  - Long-run neutrality of some shocks (e.g., monetary policy) vs. permanence of productivity shocks (Blanchard and Quah (1989) example).
  - Endogenous growth models predict per-capita output follows a stochastic trend and productive public-investment decisions may have long-run consequences (Jones (1995); Kocherlakota and Yi (1996)).
  - Binder and Pesaran (1999) argue long-run per-capita output evolution largely determined by technological process.
  - Rodrik and Subramanian (2005) and Serven (1999) cited on productivity-boosting role and long-run "crowding in" effects of government infrastructure investment in India.

### Literature context and gaps emphasized
- Mixed findings in the literature on public vs. private investment interaction; limited research for developing and emerging market economies and limited analysis of how liberalization/structural reforms change this interaction.
- Prior India-focused findings:
  - Mitra (2006): structural VAR over 1969–2005 finds public investment "crowds out" private investment.
  - Serven (1999): short-run crowding out but long-run crowding in due to infrastructure investment.
  - Aschauer (1989a, 1989b): positive impact of public infrastructure on private investment in the United States; supported by Greene and Villanueva (1991) and Blejer and Khan (1984); critiqued by Evans and Karras (1994).
  - Erden and Holcombe (2005): public investment complementary to private investment in developing countries, opposite in developed countries.
- Methodological departure:
  - The present study emphasizes theory-driven long-run restrictions in SVECMs, a method not previously applied to India’s public-private investment relationship per the authors.
  - Garratt et al. (2012) cited on difficulties interpreting impulse responses from Structural VARs and importance of embedding structural long-run relationships in unrestricted VAR models as steady-state solutions.

### Data and empirical approach (as described)
- Annual sample: 1950-2012.
- Post-1980 annual sub-sample analyzed.
- Quarterly sample: 1996Q2-2015Q1, using public and private investment data from the Indian CapEx-CMIE database.
- SVECM identification:
  - Imposes long-run relationship based on the "great ratio" of aggregate investment to output.
  - Assumes presence of one cointegrating (long-run) relationship among the three variables.
  - Classifies shocks: private-sector demand shocks = transitory; productivity shocks and possibly public investment shocks = permanent.

### Key empirical conclusions reiterated
- Full sample (1950-2012): public-capital accumulation crowds out private investment.
- Post-1980 annual sample and quarterly sample (1996Q2-2015Q1): public investment complements private investment ("crowding in"), associated with policy reforms since the early 1990s.
- Quarterly SVECM results corroborate the post-1996 "crowding in" finding using CapEx-CMIE constructed series.

*Source: _wp15264 - Appendix A*

### section 4 presents the empirical findings. Finally, Section 5 concludes and offers some policy

### _wp15264 - section 4 presents the empirical findings. Finally, Section 5 concludes and offers some policy

### Structural VECM: model set-up and identification
- Baseline variables: log per capita output, yt; public investment, git; private investment, pit.
- Sample properties: all variables are integrated of order one with evidence of one cointegrating relation among the three variables.
- Long-run relationship motivated by stationarity of the "great ratio" of aggregate investment and output; Appendix A expression: φ1 git + φ2 pit − yt where both φ1 and φ2 are less than 1.
- Reduced form VECM (equation (1)): Δzt = Π zt−1 + Σi=1m Γi Δzt−i + ut, where zt = (yt, git, pit)' and ut = (uyt, ugit, upit)'.
- Structural shocks: ut = B εt where εt = (εyt, εgit, εpit)' with εy as productivity shock, εgi as structural disturbance to public investment, εpi as demand shock.
- Identification strategy:
  - Use long-run restrictions: productivity and (potentially) public investment shocks have long-term effects; demand shock εpi is transitory.
  - System with K = 3 variables and r = 1 cointegrating vector → matrix Ψ (long-run impact) of rank 2 ⇒ one transitory and two permanent shocks.
  - Transitory shock εpi is identified (r(r−1)=2 restrictions). One additional restriction required to distinguish the two permanent shocks.
  - Imposed restriction: structural disturbance associated with government investment has no long-run impact on private investment.
  - Contemporaneous and long-run matrices reported as:
    - B = [ ... ] and B∞ = [ ... with specified zero columns ] (see equation (4) in source).

### Data: sources, construction, frequency and caveats
- Annual baseline data: GDP, public and private sector gross fixed capital formation for the period 1950-2012 (63 observations). Source: National Account Statistics, Indian Central Statistical Office. All variables measured in real per capita terms (in 2004-05 prices). All variables are national aggregates.
- Quarterly data: CapEx database (CMIE), monitoring investment projects with capital expenditure ≥ 10 million rupees beginning in 1996; comprises about 45,000 projects.
  - Project-level costs aggregated into quarterly time-series for sector- and industry-level investment activity.
  - Quarterly spending profiles estimated using project total costs and project event dates (announcement, implementation, regulatory clearances, completion, abandonment).
  - For completed projects, cash flows apportioned by project duration; for ongoing/abandoned projects expected duration based on averages of comparable completed projects.
  - Cash flows time-allocated using equal discounted cash flow with gross fixed capital formation deflators. Methodology cannot account for cost overruns or savings.
- Two investment series constructed per sector:
  - Type 1: includes estimated investment spending on abandoned/shelved projects up to abandonment/shelving.
  - Type 2: assigns zero spending to abandoned/shelved projects.
- Robustness: trimmed end-point checks undertaken; correlation between new annual series and National Accounts public/private gross fixed capital formation is 0.95 over 1995-2012.
- Caveat: CapEx data compiled from multiple sources and not comprehensive or perfect in coverage.

### Empirical findings — annual models (Models 1–3)
- Model definitions:
  - Model 1: annual yt, git, pit over 1950-2012 (baseline).
  - Model 2: yt, ginfrt (public infrastructure investment), pit over 1950-2012.
  - Model 3: yt, git, pit over 1980-2012 (post-break sample).
- Cointegration and loading:
  - Columns 1 and 2 of Table 3 report estimated loading coefficients and cointegrating vectors for Models 1 and 2; coefficients on public and private investment have theoretically-correct positive signs.
- Short-run (B) and long-run (B∞) matrices:
  - Estimated B and B∞ for Models 1 and 2 reported in Table 4; zeros in B∞ impose long-run identification restrictions.
  - Given ordering (y, gi, pi)′ and (y, gi_infr, pi)′, a structural innovation in public investment crowds out private investment in the short run in both Models 1 and 2.
  - Effect of εgi on output is positive and statistically significant on impact and in the long run in both models.
- Impulse response summaries:
  - Model 1:
    - Productivity shock: impact on public investment not significantly different from zero short- or long-run; private investment response is significantly positive on impact and long run.
    - Public investment shock: output response positive throughout; private investment temporary crowding out statistically significant for first 3 years, converging to zero thereafter.
  - Model 2 (infrastructure public investment):
    - Similar to Model 1: ginfr does not respond significantly to productivity shock; private investment positive and significant (after 1 year) and grows over time; output response comparable.
    - Crowding out of private investment by public infrastructure investment remains.
- Magnitude of crowding out — Model 1 (1950-2012):
  - Interim multipliers (private investment response to one rupee increase in public investment): 0.60, 0.31, and 0.17 rupees after one, two, and three years, respectively.
  - Baseline crowding out results are close to Mitra (2006) and Serven (1999).

### Structural break analysis and Model 3 (post-1980)
- Structural stability tests:
  - Chow break-point and Chow-forecast tests over 1975-2000 with 2000 bootstrapped replications indicate rejection of parameter constancy for a range of years → evidence of an underlying break.
  - 1980 selected as break year (highest break-point and split-sample statistic values).
  - Clemente et al. (1998) unit root tests indicate breaks in 1983-1984 for y, gi, and pi; a second break indicated for y and pi at 1996.
- Model 3 results (1980-2012):
  - Loading and cointegrating vectors in Table 3 row 3; short- and long-run matrices in Table 4 row 3; impulse responses in Figure 1 column 3.
  - Public and private investment responses to productivity shocks, and output response to public investment, similar to Model 1.
  - Key difference: private investment response to public capital accumulation changes sign — a policy-induced increase in public investment significantly crowds in private investment in the short run in Model 3.
  - Interim multipliers (Model 3): 0.37, 0.16, and 0.07 after the first, second, and third years, respectively.
  - Interpretation: public capital accumulation may have become more complementary to private investment since the early 1980s.

### Quarterly analysis using post-liberalization data (Models 4–6)
- Quarterly series construction from CapEx-CMIE; two investment measures (type 1 and type 2) as above.
- Model definitions:
  - Model 4: quarterly series type 1 (gi1t, pi1t).
  - Model 5: quarterly series type 2 (gi2t, pi2t) — preferred specification.
  - Model 6: gi2,infra t replacing gi2t (public infrastructure investment).
- Estimation notes:
  - For quarterly VECMs, a lag order of 7 (in first differences) selected based on AIC.
  - Rows 4–6 of Table 3 report loading coefficients and cointegrating vectors for Models 4–6; coefficients are smaller in magnitude than annual estimates.
- Impulse response summaries (Figure 2):
  - All three specifications: public investment responds positively and significantly to a productivity shock after 4–6 quarters.
  - Private investment response to productivity shock is positive and significant in all models.
  - Output response to public investment shock:
    - Model 4: not significantly different from zero in first 8 quarters.
    - Models 5 and 6: statistically significant positive impact over first 8 quarters and small positive long-run effect.
  - Private investment response to public investment shock:
    - None of the three quarterly specifications predict crowding out.
    - Preferred specification (Model 5) shows positive and significant crowding in of private investment by public sector investment from quarters eight to twelve.
    - Interim multipliers (Model 5): a one rupee increase in public investment crowds in private investment by 0.30, 1.24, and 1.07 rupees after four, eight, and twelve quarters, respectively.
    - Response to public infrastructure investment shocks (Model 6) similar to aggregate public investment case.
- Overall quarterly conclusion: evidence for "crowding in" of private investment by public investment in post-1980 and post-liberalization samples (1996Q2-2015Q1).

### Interpretation and policy-relevant analysis
- Full-sample (1950-2012) vs recent-sample (post-1980) contrast:
  - 1950-2012: public investment crowds out private investment in the short run.
  - 1980-2012 and quarterly post-liberalization periods: public investment crowds in private investment.
- Economic context and interpretation:
  - Crowding out over full sample likely reflects India’s state-led, inward-oriented growth strategy pre-1980s (capital-intensive industrialization, licensing, sector reservation for state, high trade barriers, mandatory credit allocation).
  - Post-1980s and post-1991 reforms (deregulation, trade liberalization, abolition of many license restrictions, tariff reductions, banking sector easing) plausibly made public investment more complementary to private investment.
  - Large infrastructure deficits imply that public investment can raise private sector profitability and stimulate private investment (crowding in).
- Data and methodology notes affecting interpretation:
  - Quarterly project-announcement-based investment series are proxies and may not perfectly reflect realized investment; type 2 series (excluding failed projects) is preferred to avoid assumptions about failed projects.
  - Cointegration tests: annual full-sample Models 1 and 2 indicate one cointegrating vector (99% trace test), Model 3 has weaker evidence possibly due to sample size; Johansen trace test with structural break at 1980 strongly supports one cointegrating vector.
  - Unit root testing: variables treated as I(1) based on ADF, ADF-GLS, and PP tests; quarterly series treated as I(1) with some mixed test results for pi1 and pi2 but PP test supports I(1) treatment.

### Concluding remarks and policy implications
- Main empirical conclusion:
  - Public investment "crowded out" private investment in India over 1950-2012, but "crowded in" private investment over 1980-2012 and in quarterly post-liberalization data (1996Q2-2015Q1).
- Policy interpretation:
  - Structural policy reforms since early 1980s and especially after 1991 likely shifted the relationship, making public investment complementary to private investment.
  - For large infrastructure deficits, public investment can stimulate private investment rather than displace it.
- Suggestions for future research (policy-relevant extensions):
  - Exploit the micro quarterly dataset to disentangle region- or sector-wise relationships between public and private investment in India.
  - Examine whether states with policies more conducive to private investment experienced stronger crowding-in effects.
  - Such analyses would have implications for the design of macroeconomic and subnational (state-level) public investment policies.

*Italic: Source — _wp15264 (sections 2–5 and appendices summarized from the supplied content).*

### REFERENCES

### _wp15264 - REFERENCES

### Bibliographic references
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- Aschauer, D. A. (1989b). Is Public Expenditure Productive? Journal of Monetary Economics 23(2), 177 – 200.
- Binder, M. and M. Pesaran (1999). Stochastic Growth Models and Their Econometric Implications. Journal of Economic Growth 4(2), 139–183.
- Blanchard, O. and R. Perotti (2002). An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output. The Quarterly Journal of Economics 117(4), 1329–1368.
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- Greene, J. and D. Villanueva (1991). Private Investment in Developing Countries: An Empirical Analysis. Staff Papers (International Monetary Fund) 38(1), pp. 33–58.
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- Serven, L. (1999). Does Public Capital Crowd Out Private Capital? Evidence from India.

### Table 1 — Unit Root Tests (annual and quarterly samples)
- Annual Data 1950-2012: variables listed as ygipigi infra with test statistics:
  - ADF: 1:15 2:98 0:31 1:23
  - ADF-GLS: 0:16 1:61 0:76 1:30
  - PP: 1:02 2:55 1:28 0:86
- First differences 
y
gi
pi
gi infra:
  - ADF: 6:88  5:66  4:40  6:35 
  - ADF-GLS: 6:54  5:70  2:39  6:00 
  - PP: 6:88  5:71  7:81  6:35 
- Annual Data 1980-2012: ygipi
  - ADF: 0:58 0:53 2:07
  - ADF-GLS: 0:68 0:85 1:49
  - PP: 0:37 0:47 3:02
- First differences 
y
gi
pi:
  - ADF: 4:32  4:48  3:66 
  - ADF-GLS: 4:40  4:45  3:63 
  - PP: 4:32  4:48  6:98 
- Quarterly Data 1996Q2-2015Q1: ygi1 pi1 gi2 pi2 gi infra2 with test statistics
  - ADF: 1:99 2:32 2:70 1:71 2:46 1:38
  - ADF-GLS: 1:27 1:86 2:10 1:09 1:89 1:37
  - PP: 2:47 1:42 1:66 1:45 1:83 1:96
- First differences 
y
gi1
pi1
gi2
pi2:
  - ADF: 9:14  2:81  2:01 6:20  2:06 0:80
  - ADF-GLS: 4:54  2:82  1:97  6:11  1:73 3:77 
  - PP: 9:14  5:82  4:72  6:20  5:72  6:37 
- Significance notation:
  - p <0:1;
  - p <0:05;
  - p <0:01.
- Notes:
  - ADF denotes the Augmented Dickey-Fuller Test, ADF-GLS the generalized least squares version of the ADF test, and PP the Phillips-Perron test.
  - Trend and intercept are included as deterministic terms in tests with level variables while only intercept is included in tests with differenced variables.
  - For each variable, the number of lags are selected on Ng–Perron modified Akaike information criterion (MAIC) as reported in ADF-GLS.

### Table 2 — Lag Orders and Cointegrating Rank of the VECMs
- Annual Data (lag order* and cointegrating relations):
  - Model 1: (y; gi; pi) — 0 01
  - Model 2: (y; gi_i; pi) — 0 01
  - Model 3: (y; gi; pi) — 0 1980 00
- Quarterly Data:
  - Model 4: (y; gi_1; pi_1) — 0 71
  - Model 5: (y; gi_2; pi_2) — 0 72
  - Model 6: (y; gi_infra2; pi_2) — 0 71
- Notes:
  - * denotes lag order in first differences selected by the Akaike Information Criterion, with the maximum lag orders set to 2 in models with annual data and 8 in models with quarterly data (see Appendix B for details).
  - Selection of the number of cointegrating relations is based on the trace test statistics calculated at 99% critical values.

### Table 3 — Loading Coefficients and Cointegrating Vectors
- Annual Data
  - Model 1: (y; gi; pi)
    - 0  0:0010:76  0:71 
    - Cointegrating vector: 
   10:12  0:44  

  - Model 2: (y; gi_i; pi)
    - 0  0:16  0:70  0:90 
    - Cointegrating vector: 
   10:20  0:35  

  - Model 3: (y; gi; pi) 0 1980
    - 0:110:52  0:76 
    - Cointegrating vector: 
    10:13  0:65  

- Quarterly Data
  - Model 4: (y; gi_1; pi_1)
    - 0  0:74  0:101:73 
    - Cointegrating vector: 
    10:07  0:12  

  - Model 5: (y; gi_2; pi_2)
    - 0  0:25  0:150:97 
    - Cointegrating vector: 
    10:030:13  

  - Model 6: (y; gi_infra2; pi_2)
    - 0  0:24  0:37  0:99 
    - Cointegrating vector: 
   10:030:13  

- Significance markers:
  - p <0:1;
  - p <0:05;
  - p <0:01.

### Table 4 — Short and Long Run Matrices (B and B∞)
- Annual Data — selected matrix entries (exact formatting preserved):
  - Model 1: (y; gi; pi)
    - Short-run matrix B:
      - 0:03  0:01  0:00 0:02 0:06  0:04  0:07  0:05  0:04  1
    - Long-run matrix B∞:
      - 0:03  0:01  0 0:02 0:11  0 0:07  00 1
  - Model 2: (y; gi_i; pi)
    - Short-run matrix B:
      - 0:03  0:01  0:01  0:03  0:05  0:05  0:030:06  0:06  1
    - Long-run matrix B∞:
      - 0:04  0:02  0 0:02 0:09  0 0:09  00 1
  - Model 3: (y; gi; pi) 0 1980
    - Short-run matrix B:
      - 0:02  0:01  0:01  0:01 0:05  0:03  0:07  0:02  0:04  1
    - Long-run matrix B∞:
      - 0:02  0:01  0 0:01 0:07  0 0:04  00 1
- Quarterly Data — selected matrix entries:
  - Model 4: (y; gi_1; pi_1)
    - Short-run matrix B:
      - 0:01  0:000:01 0:010:020:00 0:04  0:010:02 1
    - Long-run matrix B∞:
      - 0:010:002  0 0:070:02  0 0:1600 1
  - Model 5: (y; gi_2; pi_2)
    - Short-run matrix B:
      - 0:01  0:000:01  0:010:02  0:00 0:03  0:000:02  1
    - Long-run matrix B∞:
      - 0:020:001  0 0:030:03  0 0:1100 1
  - Model 6: (y; gi_infra2; pi_2)
    - Short-run matrix B:
      - 0:001  0:01  0:01  0:01  0:02  0:01  0:03  0:010:02  1
    - Long-run matrix B∞:
      - 0:020:002  0 0:030:02  0 0:1300 1
- Significance markers:
  - p <0:1;
  - p <0:05;
  - p <0:01.

### Figures — Structural impulse responses (captions and notes)
- Figure 1. Structural Impulse Responses to Productivity and Public Investment Shocks (Annual)
  - Models:
    - Model 1 : (y; gi; pi) 0
    - Model 2 : (y; gi_i; pi) 0
    - Model 3 : (y; gi; pi) 0 1980
  - Panels:
    - (a) Productivity Shock (" y ): responses of Public Investment, Infrastructure Investment, Private Investment.
    - (b) Public Investment Shock (" g ): responses of Output, Private Investment.
  - Notes:
    - Figures are impulse responses to a one standard deviation shock to productivity or government investment, together with the 5th and 95th percentile bootstrapped error bands with 2000 replications.
    - Columns 1 and 3 correspond to baseline specification which includes output, public investment, and private investment over 1950-2012 and 1980-2012 periods, respectively.
    - Model in column 2 considers public infrastructure investment instead of total public investment.
- Figure 2. Structural Impulse Responses to Productivity and Public Investment Shocks (Quarterly)
  - Models:
    - Model4 : (y; gi_1; pi_1) 0
    - Model5 : (y; gi_2; pi_2) 0
    - Model6 : (y; gi_infra2; pi_2) 0
  - Panels:
    - (a) Productivity Shock (" y ): responses of Public Investment and Private Investment.
    - (b) Public Investment Shock (" g ): responses of Output and Private Investment.
  - Notes:
    - Figures are impulse responses to a one standard deviation shock to productivity or public investment, together with the 5th and 95th percentile bootstrapped error bands with 2000 replications.
    - The impulse responses correspond to models with quarterly data on public and private investment projects constructed from CAPEX-CMIE database.
    - Columns 1, 2, and 3 show impulse responses of models 4, 5, and 6, respectively.
    - Model 4: shelved or abandoned projects (for both public and private sectors) are not included in the construction of the investment series once they are shelved or abandoned.
    - Model 5: shelved or abandoned projects are not excluded from the investment series altogether from the date of announcement.
    - Model 6: takes public investment as constructed in Model 4 and private investment as in Model 5.

*Source: _wp15264 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15264.pdf_