APPENDIX TO ASSESSING THE EFFECT OF PUBLIC CAPITAL ON GROWTH: AN EXTENSION OF THE WORLD BANK LONG-TERM GROWTH MODEL

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1 APPENDIX TO ASSESSING THE EFFECT OF PUBLIC CAPITAL ON GROWTH: AN EXTENSION OF THE WORLD BANK LONG-TERM GROWTH MODEL Sharmila Devadas and Steven Pennings October 28 Appendix : Comparison between the LTGM-PC and Standard LTGM - effect of investment on growth A. Does the LTGM-PC have a larger effect of public investment on growth than the Standard LTGM? In the public capital extension, it is possible for an increase in the public investment-to-output ratio to have a larger or smaller effect on growth than in the Standard LTGM. A larger effect in the LTGM- PC is more likely to occur when public capital is relatively scarce (starting from a low ratio of public capital to total capital K t Gm ) and when public capital is relatively useful (a large φ relative to ( β)). K t Short run: In the public capital extension, based on equation (6) in the main paper, the shortrun boost to growth (the same with/without congestion) of an increment to I t G assuming unchanged efficiency is: Y t g PC y,t+ I t G Yt = φ K t Gm Yt (a.) In the Standard LTGM (using equation (a.) in Section A.5), the short-run boost to growth of the same increment in total investment is: g PC y,t+ = ( β) I t Y t K t Y t (a.2) Taking the difference between equations (a.) and (a.2): g PC y,t+ I t G Yt LTGM PC g PC y,t+ = φ I t Y t K Gm t Std LTGM Yt ( β) K t Y t = ( β) Y t K t G [ Gm φ K t ] ( β) K t (a.3) What does this mean quantitatively for different countries? Graph A. shows the effect of an ppt increase in I G Y on growth in the short run (28 only) across countries in the LTGM-PC less the same size increase in total I/Y in the Standard LTGM. Here we assume φ =.7 and all other parameters are at their country-specific default values. In Graph A.(a), one can see that countries with low relative public capital stocks tend to have a larger boost to growth in the LTGM-PC, whereas for countries with more public capital, the disaggregation into public and private in the LTGM-PC actually reduces the effect on short-run growth. For most countries in our sample (around 6), the increment to growth is higher in the LTGM-PC. The approximate cut off for the increment to growth to be higher in the LTGM-PC is if K Gm K <.4 (the median K Gm K of countries with a higher increment is.27 and.44 for those with a lower increment). However, the private/total capital share β also determines the relative returns to investment between the LTGM-PC and the Standard LTGM. Graph A.(b) plots β versus the public capital share

2 K. Countries on the upper RHS area with a high β and K Gm K have a greater increment to growth in the Standard LTGM, and other countries on the lower LHS have a higher increment in the LTGM- PC. Different values of the capital share β also drive vertical dispersion in Graph A.(a). K Gm Graph A.: LTGM-PC (φ =. 7) versus Standard LTGM - Differences in Short-Run Incremental Output Growth from Higher Public Investment LTGM-PC - Std. LTGM: SR Incremental Growth, ppt IDN CHL IRL SRBPAN AUS BEL CHE CRI TCD LBN SDN LKA MAR DEU GHA SUR ARM KEN PHL LVA ESP MLI SVK AUT DOM CAN CZE HUN EST UKR ZAF SWE SVN ITA ISL ARGKOR TZA NOR LTU RUS PRT KAZ NPL HKG DNK CYP FINFRA NLD HND MAC USA UGA MDA HRV ALB BGD BEN LBR LUX POL NAM TGO SGP SEN BIH PERIND PRY SWZ KGZ MNE CMR SLV MRT JORJAM MKDSLE ZAR ZMB TUR BFA GAB NER GEO NZL ROM RWA BHR LAO COL JPN PAK THA VNM MDG MWI TUN URY LSO MUS MEX COM LCAKWT BWA MYS ECU CHN SAU MNG KHM COG VCT SYR AZE CAF OMN BLZ Capital Share (-beta) Incremental growth is larger under Standard LTGM -beta=.7/(k(g)/k) IDN CHL LBN SUR PHL PAN ARG DOM KAZ TZA SGP SEN ALB PER MNE SLV MRT TUR MAC PAK GAB THA GEO TUN BHRBWA AZE KHM BLZ ECUCHN CAF VNM LCA MUSMEX LAO KWT NPL URY VCT SAU MN COL MAR UGA CMR IND JOR BGD IRL HKG JPN COG ITA KOR LTU LUX NER MNG ZAF NZL SVKSDN NOR NAM KGZ ROM AUS CZE CYP JAM MKD MDG MWI MYS SYR POL PRY LVA CAN BFA BEL DEU AUT CRI HUN ESTFINHND ARM RUS FRA NLD MLI BEN ZARLBR LSO SRB MDA COM ESP UKRSWESWZ USA HRV SLE ZMB PRTKEN TCD BIHRWA CHELKA SVNISL DNK GHA TGO Incremental growth is larger under LTGM-PC Public Capital/Total Capital, (K(G)/K) Public Capital/Total Capital(K(G)/K) Analytical Difference: ( β) Y t KG [ φ K Gm t t ( β) K t ]. This is the same with or without congestion. See equation (a.3). Long run: However, the effect of investment on growth in the long-run can be different from the short run in the LTGM-PC versus the Standard LTGM, for two reasons. First, any initial increase in growth will crowd in a second-round increase in private investment and public investment as I t G and I P t are fixed Y t Y t ratios. The size of these second-round effects depends on other parameters like the capital share β, the depreciation rate δ and also the initial capital-to-output ratios. Second, in the default congestion specification (ζ = ), this second round increase in private capital makes public capital congested, which reduces the size of its boost to growth. Quantitatively, we measure the increment to long-run growth as the average increase in real GDP growth over due to a ppt increase in I G Y in 27 (scenario minus baseline). In Graph A.2, one can see that the long-run boost to growth from higher public investment in the LTGM-PC relative to the Standard LTGM is much greater in the pure public good specification ( ζ = ) than in the congestion specification ( ζ = ). 2 When φ =., far fewer countries (8) record a higher increment to growth in the LTGM-PC, and the median of K Gm K of countries with a higher increment is slightly lower at.23 (.37 for those with a lower increment) (see Section A.4, Graph A.7). 2 That is, the private capital share is β versus β φ under congestion). When the difference in incremental growth in Graph A.2 is > (LTGM-PC Standard LTGM), we see larger differences between the pure public good setting and the Standard LTGM (than the congestion setting and Standard LTGM) and particularly so when φ =.7. 2

3 Graph A.2: Pure Public Good versus Congestion in the LTGM-PC - Differences in Long-Run Incremental Output Growth from Higher Public Investment vis-à-vis the Standard LTGM (a): φ =.7 (b): φ = Congestion - Std LTGM: LR Incremental Growth, ppt DEU BEL HND CHL DOM IDN AUT AUS ALB HRV TCD CRI CAN CYP SLV DNK FIN EST CZE FRA ITA ISL ARM BIH BEN BGD BFA BWA BHR CHN COL COM ZAR GHA GAB GEO INDJOR KAZ JAM JPN KEN NLD PRT ESP CHE UKR KOR RUS SRB USA LTU LVA NAMMEX ZAF MARPHLTZA KGZ LUX HKG MAC MKD HUNLAO LBR COG LSO MDG ARG KHM CMR KWT CAF ECU MWI MYS MLI MRT MDA NPL NOR POL SWE ROM URY ZMBPAN SVNSVK LKA MUS BLZ AZE MNG MNE NZL PRY PER RWA PAK SAU NER SEN SGP TGO TUNTUR VNM VCT LCA THA UGASLE OMN SWZSYR LBN SUR IRL SDN SUR LBN IRL SDN BEL DEU AUT AUS ARM CAN TCD CRI BFA ALB BIH BGD BEN FIN CHL CYP CZE EST DNK HRV FRA ISL ESPHND DOM IDN GHA KEN ITA IND KOR COL CHN SLV BWA COG HKG GAB GEO ZAR HUN JAM KGZ JPN LVA NAM PRT LSO LAO LBR JOR LTU RUS SRB MKD MLI LUX MAC NLD MAR MEX MDGKAZ KWT CMR MWI MYS MDA NPL NOR POL PAN PHL MRT NZL MUS BHR COM CAF BLZ ARG AZE MNG KHM MNE NER PRY PER SVN RWA ROM ZAF SWE CHE LKA ZMB USA UKR TZA SAU SEN SGP SVK TGO THA VCT LCA TUN TUR URY VNM UGA SLE OMN SYR ECU SWZ PAK Pure Public Good - Std. LTGM: LR Incremental Growth, ppt Pure Public Good - Std. LTGM: LR Incremental Growth, ppt Graph A.3(a) reports the difference in the long-run incremental growth (Y-axis) and short-run incremental growth (X- axis) between the LTGM-PC (when φ =.7 and ζ = ) less the equivalent calculation for the Standard LTGM. While short-run and long-run differences in incremental growth are correlated, many countries that had lower short-run incremental growth in the Public Capital Extension vis-à-vis the Standard LTGM, have larger incremental growth in the long run. Graph A.3(b) plots the same change in the long run growth on the Y axis against the K Gm K ratio on the X axis. As before, countries with lower initial K Gm K ratios tended to have a larger increase in long- run growth in the LTGM-PC relative to the Standard LTGM (again the cutoff is approximately K Gm K <.4). The median K Gm K of countries with a higher long-run increment vis-à-vis the Standard LTGM is.3 under the congestion setting (73 of countries). 3 3 See Section A.4, Graph A.8(i) for the pure public good scenario. When φ =., the median K Gm K of countries with a higher long-run increment is.27 under the congestion setting (44 of countries) and.28 under the pure public good setting (59 of countries) (see Graph A.8(ii)). 3

4 Graph A.3: LTGM-PC (φ =. 7, Congestion, ζ = ) versus Standard LTGM - Differences in Long-Run Incremental Output Growth from Higher Public Investment LTGM-PC,Congestion - Std. LTGM: LR Incremental Growth, ppt SUR LBN SDN IRL HND DOM UKR DEU BEL CHLIDN AUT ALB CYPRUS ISL SLV FRA AUS HRV CAN FIN ARM TCD CRI GEO ITA KOR LTU PRT SRB MEX INDNAM DNK CZEST BIH BGD BEN BFA CAF KHM CHN BWA COM ARG AZE BHR GAB KAZ NLD ZAF PHL CHE USA TZA MAR POL SWE URY ZMB LVA GHA JPNJAM ZAR MAC KGZ LUX HKG KEN MUS LAO NZLMKD MYS MDGMRT HUN COG KWTLSO MWI BLZ CMR MDA NPL NOR PAN TUNTUR ROM PER SGP MLI SVN SVK LKA PAK PRY SAU LCA THA NER RWA SEN TGO VCT VNMMNE SLEUGA SYR MNG OMN ECU SWZ LTGM-PC,Congestion - Std. LTGM: SR Incremental Growth, ppt LTGM-PC,Congestion - Std. LTGM: LR Incremental Growth,ppt SUR LBN IRL SDN BEL IDN CHL DEU DOM HND SRB CHE AUS AUT ESP ITA CYP CAN ALBSLV CRI CZE ESTFIN FRA ISL MAR PHL TZA UKR KOR LTU RUS PRT ZAF USA IND DNK ARM TCD HRV JOR MEX PAN LVA NLD SWE KAZ GHA GAB GEO HKGLUX MAC NAM NOR POL SVK NPL SGP LKA SVN PERTUR MDA KEN HUN BGDMLI TUN URY ZMB ROM JAM KGZJPN LAO MKD MRT NZL MUS COL BEN ZARBIH ARG PAK PRY TGO SEN THA MNE MDG BFA BHR BWAKHM LBRMYS UGA NER VNM LCA CHN KWT SLE VCT RWA CMR LSO MWI SAU COG CAF COM SWZ AZE BLZ MNG SYR ECU OMN Public Capital/Total Capital, (K(G)/K) A.2 Does the LTGM-PC have a larger effect of private investment on growth than the Standard LTGM? Short Run: For an increment to the private investment-to-output ratio, I t P, the short-run boost to Y t growth under the Standard LTGM remains the same as in equation (a.2). In the public capital extension, it depends on congestion and from equation (6) in the main paper, is given by: g PC y,t+ I P = β ζφ t Yt K P t Yt (a.4) The differential effect on short-run growth based on equations (a.2) and (a.4): g PC y,t+ I t P Yt LTGM PC g PC y,t+ = β ζφ I t Y t K P ( β) t Yt K t Y t Std LTGM = ( β) Y t ( β) K t P [ ( β ζφ) K t P K t ] (a.5) From equation (a.5), it is apparent that under the pure public good model an increase in private investment-to-output always gives a bigger short run boost to output than the Standard LTGM, since ( β ζφ) = and K t P <. For sizeable φ however this is less often the case with congestion ( ζ = ). ( β) K t 4

5 Graph A.4: LTGM-PC (φ =. 7, Congestion, ζ = ) versus Standard LTGM - Differences in Short-Run Incremental Output Growth from Higher Private Investment LTGM-PC,Congestion - Std. LTGM: SR Incremental Growth, ppt OMN CAF SYRCOG BLZ COM MNG SAU VCTAZE CHN KHM ECU LSO MYS BWA MWI MDG KWT BFAJPN MEX COL BHR BIHZAR BEN LAO MUS LCA RWA GEO GAB LBR ROM URY MKD KGZ NZL VNM TUN NER THA PAK ZMBSLE JAM NAM PRY JOR BGD IND SLV CMR ALB HRV MAC TUR SWZ MRT POL MNE LUX PER SEN DNK MDA SGP TGO USA HND FRA FIN UGA CYPCZE ARG ISL LTU ARM HKG CAN KOR EST HUN ITA NPL AUT KAZ DOM MLI NLD PRT RUS NOR SVN ZAFESP TZA SVK DEU LVA PHL MAR SUR BEL AUS LBN CHL GHA CRIRL IDN KEN SWE UKR PAN SRB TCD LKA SDN CHE Private Capital/Total Capital, (K(P)/K) Capital Share (-beta) Incremental growth is larger under LTGM-PC -beta=.7/(-k(p)/k) OMN CAF CHN SAUECU BLZ VCT KHM AZE BWA KWT MEX BHR ALB ARG CHL COL URY LAO MUS LCA VNM TUN GEO THA GAB PAK MAC TUR MRT SLV MNE PER SEN SGP TZA KAZ DOM PAN PHLBN MNG JOR IND NPL SUR NER IDN BGD CMR COG JPN NZL KGZ LUX UGA MAR SYR MYS MWI MDG ROM NAM LTU NOR ZAF SDN HKGIRL JAM KOR AUS BFA MKD CYPCZE ITA PRY POL SVK HNDCANLVA COM LSO LBR ZMB ZAR BEN MLI FINEST ARM CRI AUT DEUBEL HRV MDA NLD FRA RUS HUN SLE SWZSWE USA SRB RWA BIH GHA TCD KENPRT UKR ESP TGO DNK ISLSVN LKACHE Incremental growth is larger under Standard LTGM Private Capital/Total Capital (K(P)/K) For the same set of countries as above, we look at the difference in the short-run boost to growth (28 only) and the long-run increment to growth (average over ) of a ppt increase in I P Y between the LTGM-PC (with φ =.7 and ζ = ) and the Standard LTGM. We focus exclusively on the congestion setting (ζ = ) since incremental growth from an increase in private investment is always larger in the pure public good setting than the Standard LTGM, as noted previously. In the short run, (Graph A.4), the increment to growth is higher in the LTGM-PC for 4 of countries, and the median K P K of countries with a higher increment is Graph A.5: LTGM-PC (φ =. 7, Congestion, ζ = ) versus Standard LTGM - Differences in Long-Run Incremental Output Growth from Higher Private Investment LTGM-PC,Congestion - Std. LTGM: LR Incremental Growth, ppt ARM AUS ARGBHR AZE BLZ BEL AUT BIH BEN LB BGD CMR TCDCAN BFA BWA ECU CHL ZAR COL CHN COG GHA LKA KENKOR CRIHRV MLI DNK CZE DOM KHM DEU EST HUN FRAGAB FIN CAF IRL ITA IDN ISLIND LVA HND HKG CYP SLV GEO KAZ LBR LBN KGZ JAM JOR JPN LAO MWI KWT LSOMNG PANPRY SRB LTULUX MDA MAC MKDMDG MNE PRTROM MAR RUS NLDNZL PHL NOR NPL POL NAM SEN PER MRTMUS RWA NER PAK MEX MYS SAU COM ESP SVN ZAF SVK SWZ CHE SWE TZATHA UGA SGP SLE LCA VCT SYR SDNSUR UKR TGO USAURY ZMB TUR VNM TUN OMN LTGM-PC,Congestion - Std. LTGM: SR Incremental Growth, ppt LTGM-PC,Congestion - Std. LTGM: LR Incremental Growth, ppt OMN ECU COG BLZ AZE BWA BHR CMR CAF LSO MNG CHN LBR MWI BFA BGD ARG BIH KHMBEN KWT MYS ZAR MDGMKD COLGEO GAB GHA TCD ALB ARM CAN CRI AUT BEL AUS COM HRV DNK EST CZE JPN KGZ JAM MLI JOR KEN IND MAC MRT SLV HND ISL FRA FIN KOR HUN MEX NZL MUS NAM SWZ SYR SAURWA VCT SLE MDA MNE ROM LCA PRY PAK POLNLD LUX SEN UGA ZMB VNM THASWE CYP LTU NORNPL ITA KAZ DOM DEU PAN PRT RUS SVN ZAFESP SGPSVK TZACHE PHL MAR CHL IDN TGO URY TUN USA TUR IRL SRB SDN UKR SUR Private Capital/Total Capital, (K(P)/K) In the long run (Graph A.5), the difference in incremental growth between the LTGM-PC (when φ =.7 and ζ = ) and the Standard LTGM is smaller than in the short run. 5 The median K P K of 4 When φ =., more countries record a higher increment to growth in the LTGM-PC (84 of countries), with the median K P K of countries with a higher increment slightly higher at.63 (see Section A.4, Graph A.9). 5 This is also true for the pure public good setting (not shown here). 5

6 countries with a higher long-run increment (9 of countries) is.48. When φ =., the median K P K of countries with a higher long-run increment (44 of countries) is.57 (see Section A.4, Graph A.). This contrasts somewhat with the result in the previous sub-section on public investment, where more countries had larger increments in the long-run than short-run in the LTGM-PC (with ζ = ). A.3 The baseline and choosing between congestion and pure public good setting in the LTGM-PC In additional to generating TFP growth consistent with growth accounting exercises (Section in the main text) another reason to prefer the congestion specification (ζ = ) to the pure public good speciis that it generates very similar baseline growth rates (on average) as the Standard LTGM - requiring little adjustment to growth fundamentals for consistency. One can see this in Graph A.6 where the gap between growth in the LTGM-PC (with congestion) and the Standard LTGM is close to zero for almost all countries (Y axis). This is equally true with φ =.7 (Graph A.6(a)) and with φ =. (Graph A.6(b)). In contrast, the pure public good setting of the LTGM-PC generates baseline growth rates often substantially different (usually higher) than the Standard LTGM The implication of this is that assumed TFP growth (excluding public capital effects) needs to be adjusted (mostly downwards) to generate consistency with the Standard LTGM. 6 In short, the congestion setting allows for similar growth rates between overall TFP growth and TFP growth driven by components other than public capital, more so than the pure public good setting. Graph A.6: LTGM-PC (Congestion and Pure Public Good) versus Standard LTGM - Difference in Initial Baseline Growth (a) φ =.7 (b) φ =. OMN Congestion - Std. LTGM: Initial Baseline Growth, ppt CHN CAF VCT ARG BHR AUT BEL BIH HUN COM CHL KHM CAN ZAR CMR ALB ARM COL SWZ CYP SLV DNK HRV CZE EST GEO ITA FIN JPN GAB HND BGD BEN BFA FRA KOR JAM HKG AUS DOM CRI ECU ISL DEU KAZ JOR KWT MEX LVA LAO LUX IND KEN LSO KGZ MAC MDG MDA MUS MYS MRT LTU MKD MWI MNG MNEMAR NLD NZL SAU SLESGP PAK SVN PRYPER SRB SVK PRT PHL NOR POL NPL NER ROM THA TGO RUS SEN ZAF RWA NAM ESP LKA LCA UGA SUR UKR USA CHE TUNTUR URY VNM TZA ZMB BWA LBN AZE COG BLZ IRL SDN IDN SWE PAN TCD GHA SYR MLI OMN CAF MEX NAM VCT GEO KGZ MAC BFA ALB ARG AUT BHR ARM COL BGD BEN CYPCZE BIH DNK BEL FINFRA SLV AUS KHM CHL HRV EST CAN ZARCRI TCD COM DOM GAB ZMB HND IND ITA HUN HKG ISL DEU JPN KOR KAZ JAM IRL KWT JOR LAO MLI MKD LVA LBNLTU IDN KEN LSO LUXMDA MRT NLD GHA MYS MDG MNEMAR NOR MUS NPL NZL PAN PAK PRY PER MNGNER PHL POL URY ROM SAU PRT SRB RUS SEN SLE SGP SUR SVN SVK ESPZAF SDN LKALCA SWE TZA CHE SWZTHA TGO UKR USA TUN VNM TUR ECU COG CMR BWA BLZ AZE RWA UGA MWI SYR CHN Pure Public Good - Std. LTGM: Initial Baseline Growth, ppt Pure Public Good - Std. LTGM: Initial Baseline Growth, ppt Note: Excludes outlier, Liberia, which displays a relatively very large difference in the incremental growth between the pure public good setting and the Standard LTGM. 6 If the downward adjustment of measured TFP growth is too large, it could become negative. Pritchett (2) argues against negative TFP growth rates, and instead suggests they might reflect deteriorating capital efficiency, which is not captured in growth accounting exercises. 6

7 A.4 LTGM-PC versus Standard LTGM-Robustness to alternative parameterizations (a lower importance of public capital (φ=.) or pure public goods (ζ=)) Graph A.7: Differences in Short-Run Incremental Output Growth from Higher Public Investment (φ =. ) SRB IDN BEL CHE AUS CHL LBN DEU CRI ESP LKA IRL LVAUT EST ARM UKR SVN PRTDNK TCD GHA CZE HUN ISL SUR MAR ITACAN RUS SVKOR FINFRA CYPNLD SWE KEN HRV PHL MDA USA PANPL HND ARG DOM KAZHKG NOR LTU MLI SWZ ZAR TGO SGP ZAF SDN ALB LUX POL MKD BGD NAM BEN BIH LBR TZASEN PER SLV JORJAM MNE PRY ROM ZMB JPN MRT NER COM GEO BHR NZL KGZ COL LSO BFA IND LAO MWI THA VNM GAB URYSLE RWA MYS BWA MDG CMR TUNMEX CHN ECU MNG UGA MAC MUS KWT SAU PAK TUR SYR COG OMN KHM CAF LCA AZEVCT Capital Share (-beta) BLZ Incremental growth is larger under Standard LTGM -beta =./(K(G)/K) IDN CHL LBN SUR PHL PAN ARG DOM KAZ TZA SGP SEN ALB PER MNE SLV MRT TUR MAC PAK GAB THA GEO TUN BHRBWA AZE KHM BLZ ECUCHNCAF VNM LCA MUSMEX LAO KWT NPL URY VCT SAU MN COL CMR IND JOR BGD IRL HKG JPN COG ITA KOR LTU LUX MNG MAR UGA NER ZAF NZL SVKSDN NOR NAM KGZ ROM AUS CZE CYP JAM MKD MDG MWI MYS SYR POL PRY LVACAN BFA BELDEU AUT CRI HUN ESTFIN HND ARM RUS FRA NLD MLI BEN ZARLBR LSO SRB MDA COM ESP UKRSWESWZ USA HRV SLE ZMB PRTKEN TCD BIHRWA CHELKA SVNISL DNK GHA TGO Incremental growth is larger under Public Capital Extension Public Capital/Total Capital, (K(G)/K) Public Capital/Total Capital(K(G)/K) Graph A.8(i): Differences in Long-Run Incremental Output Growth from Higher Public Investment (φ =. 7, Pure public good, ζ = ) Pure Public Good - Std. LTGM: LR Incremental Growth, ppt SDN SUR LBN DOM IDN TZA CHL ALB KAZ HND UKR PHL DEUBEL MEX JOR MAC RUS LTU ZAF MAR SRB AUT PAN SLV AUS CYP GAB GEO IND ITA ISL ESP CHE FRA KOR PAK TUN TUR PER USA URY POL NAM PRT CANARM HRV CZE TCD CRI KHM BGD FIN HKG CAF ARG CHN COM COL ZAR DNK EST LVA MUS ROM ZMB LAO JPNJAM KGZ LUX KEN GHA MDGMRT MDA NPL NLD NOR NZLSLE MKD SEN PRY SGP SVK SWE LCATHA TGO BIH BEN BLZ AZE KWT MYS MNE SVN LKA VCT SAU BWA BHR HUNMLI SYR VNM MNG NER UGA CMR BFA COG MWI LSORWA ECU SWZ LBR OMN IRL Pure Public Good - Std. LTGM: SR Incremental Growth, ppt LBN SUR SDN IRL IDN DOM CHL TZA PHLKAZ ALBHND BEL DEUUKR SRB MAR LTU PAN JOR CHEZAF RUS MAC MEX AUS AUT ESP ITA CAN ARM CYP ISLIND SLV TUR KORPRT PER USA LVA CRI FRA GAB GEO NAM CZE ESTFIN TCD HRV HKG NORNLD SWEPOL PAKTUN URY ZMB SVKSGP NPL DNK MUS ROM ARG LKA SEN LUX MRT MDA KHM BGD KEN GHA PRY THAJAM NZL KGZ LAOSLE SVN LCA MKDMDG COL JPN ZAR TGO BEN CAF HUN UGA MNE MLI KWT BIH MYSCHN NER VNM VCT COM CMR BHR BWA AZE BFA MWI BLZ MNG LBR RWA SAU SYR LSO SWZ COG ECU OMN Public Capital/Total Capital, (K(G)/K) 7

8 Graph A.8(ii): Differences in Long-Run Incremental Output Growth from Higher Public Investment (φ =. ) (a) Congestion, ζ = (b) Pure public good, ζ = Pure Public Good - Std. LTGM: LR Incremental Growth, ppt SDN SUR IRL LBN BEL HND DOM AUTAUS BFABGD BEN ALB CYP HRV FIN CZE CAN TCD CHL BIH ARM ISL DEUIDN IND ITA GHA EST CRI COG CHNCOL SLV GAB GEOJPN NAM JAM BWA ZAR HKG KOR MAC MEXKGZ LVA LAO LSO LBRLTU MKD PAN MLINLD MAR KAZ HUN MDG MYS NZL LUX NPL MDA MUS MRT NER PER NOR PRT ESPCHE RUS SRB TZA ZMB ZAF USA SWE UKR RWAROM SAU CMR BLZ AZEKHM KWT MWI CAF OMN MNG BHR PRY SEN LKA URY VCT LCA TUR UGA TUN SYR SLE THA VNM TGO ECU COMARG PAK SWZ Congestion - Std. LTGM: SR Incremental Growth, ppt SDN SURLBN IRL DOM HND DEUBEL IDN TZA ALB AUTAUS CHL CYP HRV CZE CAN DNK TCD CRI ARM BFASLV BGD BEN FIN FRA ISL IND LTU MAC MEX GAB GEOJOR NAM PAN PHL KOR ITA MAR EST GHA KGZ KAZ KEN LVA BIH HKG COG CHNCOL LAO JPN JAM ZAR HUN BWALSO LBR MKD MLI NPL MDG MYS MRTLUX MDA NLD RUS PRT UKR ESP SRB ZAF SWE CHE ZMB USA ROM POL NOR MUS NZLPER RWA BLZ AZEKHM KWT CMR MWI NER CAF MNG BHR MNE PRY SEN SGP SVKSVN LKA TUR URY VCT LCA COMARG OMN PAK SAU UGA TUN SLE THA VNM TGO SYR ECU SWZ Pure Public Good - Std. LTGM: SR Incremental Growth, ppt Pure Public Good - Std. LTGM: LR Incremental Growth, ppt LBN SUR IRL SDN BEL DEU IDN CHE ESP HND ISL CHL SRB AUS DOM AUT UKR RUS PRT ITA CRI KOR CAN TCD CZE EST DNK CYP HRV ARM ALB FIN FRA SWE LTU GHA NAM MAR PAN TZA NLD USA ZMB PHL LVA ZAF LKA IND KEN POL MLI MAC JORGEO KGZ MKD MEX BEN HKG SLV BGD GAB BFA BIH LBR NPL NOR ROM SVK SVN HUNPERMDA JAM LAOJPN KAZ LUX NZL URY RWA SGP MRT COLZAR CHN LSOCOG UGATUR NER PRY BWA MDG MYS SEN MUS MNE THA TUN VNM LCA MWI TGOVCT CMR SAU KWT SLE BHR AZE KHM ARG BLZ MNG SYR CAF COM OMN PAK SWZ ECU Public Capital/Total Capital, (K(G)/K) LBN SUR SDN IRL BEL IDN DEU HND CHL CHE DOM SRB AUS AUT ESP TZA UKRISL ITA CRI KOR LTU RUS MAR PHL PAN CAN ZAF ALB PRT FRA SWE USA IND TCDNAM LVACZE EST NLD ARM CYP FIN MAC DNK HRV JOR GHA MEX ZMB KAZLKA KEN POL SLVGAB GEO NPL HKG NOR PER MLI BGD KGZBEN JAM MKD ROM SVK SVN HUN SGP TUR MDA URY LAO COL JPNBFA BIH LUX MRT NZL LBR MUS MDG ZAR RWA UGA SEN PRY MYSCHN NER TUN THA VNM LCA BWA LSOCOG MNE CMR KWT SLE TGOVCT MWI SAU KHM ARG PAKBHR AZE BLZ MNG SYR CAF COM SWZ ECU OMN Public Capital/Total Capital, (K(G)/K) Graph A.9: Differences in Short-Run Incremental Output Growth from Higher Private Investment (φ =., Congestion, ζ = ) Incremental growth is larger under Public Capital Extension Capital Share (-beta) OMN CAF BLZ SYRCOG VCTAZE COM KHM MNG SAU CHNECU LSO MYS RWA BFA BWA LCA KWT MWI MDG SLE MEXMUS LBR BIH BEN COL BHR CMR ZAR JPNLAO KGZ NZL TUNPAK ZMB ROM URY GEO GAB IND MAC TGO JAMJOR VNM MKD NAM NER THATUR MLI PRY BGD MRT SLV MNE UGA SWZ POL ALB GHA HRV TCD KEN DNK USA MDA HND NLD FRA LUX PER SEN SWE FIN CYPCZE LTU NOR ZAF ARM HKG ISL PRT RUS SDN SGP TZA CAN KOR EST HUN CRI ITAIRL NPL AUT KAZ SVN DOM SVK ARG ESP DEU LVA PAN PHL LKA UKR CHE MAR SUR BEL AUS LBN SRB CHL IDN beta =./(-K(P)/K) OMN CAF CHN SAUECU BLZ VCT KHM AZE BWA KWT MEX BHR ALB ARG CHL COL URY LAO MUS LCA VNM TUN GEO THA GAB PAK MAC TUR MRT SLV MNE PER SEN SGP TZA KAZ DOM PAN PHL SUR LBN MNG NER JOR IDN IND NPL BGD CMR COG JPN NZL KGZ LUX UGA MAR SYR MYS MWI MDG ROM NAM LTU NOR SDN ZAF HKGIRL JAM KOR AUS BFA MKD CYPCZE ITA PRY POL SVK HNDCANLVA COM LSO LBR ZMB ZAR BEN MLI FINEST AUT ARM CRI BEL HRVFRA HUN DEU MDA NLD SLE SWZSWE USARUS SRB RWA BIH GHA TCD KENPRT UKR ESP TGO DNK ISLSVN LKACHE Incremental growth is larger under Standard LTGM Private Capital/Total Capital, (K(P)/K) Private Capital/Total Capital (K(P)/K) 8

9 Congestion - Std. LTGM: LR Incremental Growth, ppt Graph A.: Differences in Long-Run Incremental Output Growth from Higher Private Investment (φ =., Congestion, ζ = ) OMN SWZ ARGBHR AZE BLZ BGD BEL AUS AUT ARM ALB CMR CAN BEN BIHBFA BWA ECU MWI KHM CAF CRIZAR CHL TCD COL CHN COM COG EST DNK CZE FIN CYP HRV DOM SLV DEU GHA HUN IDN ISL LBN LVA IRL ITAJAM FRAGAB KOR KEN KAZ LTU HND HKG LUXMAC MLI MKDMDG JOR LBR IND KGZ JPN GEO LAO KWT MYS MDA MNE MRTMUS MEX LSO MNG MAR PHL NLDNZL NPL PANPRY NOR PER POL NAM NER PAK CHE SRB LKA ESP SVN PRTROM RUS SVK SGP ZAF SEN SLE RWA LCA SAU VCT SUR SWE SDN TZATHA TGO UGA SYR UKR USAURY VNM ZMB TUR TUN Congestion - Std. LTGM: SR Incremental Growth, ppt OMN ECU SWZ BLZ MNG AZE BHR ARG BIH BWA CMR COM CAF COG MWI SYR SLE LSO KHM CHN SAU KWT BFA ZAR BEN COL BGD MYS RWA VCT LBR TGO MDG GAB JPN MKD LAO KGZ MUS JAM GEO MLI GHA JOR HRV TCD KEN IND DNK MAC MRT MNE MEXNZL LCA VNM NER PAK ROM PRY NAM MDA SLV HND NLD ISL FRA LUX PER SEN ZMB URY TUN THA POL TUR SWE FIN ALB CYPCZE LTU NOR ARM CAN EST CRI AUT DOM DEUBEL AUS CHL HKG KOR HUN ITA NPL KAZ PRT RUS UGA USA SVN LKA ZAFESP SGPSVK TZALVA PAN PHL IRL MAR LBN SRB IDN SDN UKR CHE SUR Private Capital/Total Capital, (K(P)/K) A.5 The LTGM-PC and Standard LTGM as special cases of a CES production function Consider first a nested constant elasticity of substitution production function: Y t = A[(a(K t G ) ρ + a(k t P ) ρ )] γ( β) ρ (h t L t ) β (a.6) G P where A is TFP; K t is public capital stock; K t is private capital stock; h t L t is effective labor (h t is human capital per worker and L t is number of workers); ρ is a parameter related to the elasticity of substitution, which is given by σ = ( ρ); a, b, are share parameters reflecting the relative importance of the two capital inputs; γ is a scale parameter and β is labor income share. To get the Standard LTGM, ρ =, a = b =, γ =. Public and private capital are perfect substitutes. The Standard LTGM is thus the standard production function: Y t = A(K t ) β (h t L t ) β (a.7) where K t is aggregate capital stock. (a.7) can be expressed in per capita terms, using L t = ρ t ω t N t, where N t is total population, ω t is the working age-population ratio and ρ t is the participation rate (labor force-to-working age population ratio. y t PC Y t N t = Y t L t ρ t ω t = Aρ t ω t (k t ) β (h t ) β (a.8) Rewriting (a.8) in terms of various growth rates from t to t + : PC + g y,t+ = ( + g ρ,t+ )( + g ω,t+ )( + g A,t+ )( + g k,t+ ) β ( + g h,t+ ) β (a.9) Aggregate capital accumulation follows the same process as described in Section 2 of the main paper for private capital. Consequently, the growth rate of aggregate capital per worker can be expressed as follows: + g k,t+ = ( δ)+ I t Y t K t Y t (+g ρ,t+ )(+g ω,t+ )(+g N,t+ ) (a.) 9

10 Substituting (a.) into (a.9) and taking a log-linear approximation, as was done in sub-section 3.3, we get a drivers of growth equation. This can be compared to equation (6) in the main text. PC g y,t+ g A,t+ + β( + g ρ,t+ + + g ω,t+ + + g h,t+ ) ( β) + g N,t+ + ( β) [ I t Y t δ] K t Y t (a.) Note that from (a.6), to get the general specification version of the production function with public capital in Section 2 of the main paper, ρ, which results in (a) collapsing into a Cobb-Douglas type specification: Y t = A[(K t G ) aγ (K t P ) bγ )] β (h t L t ) β (a.2) In equation (3) in the main text, aγ( β) = φ; and bγ( β) = β ζφ. With this Cobb-Douglas type specification, public and private capital are complements/imperfect substitutes. We do not consider different patterns of substitutability and shares between the two types of capital (there is little consensus and empirical evidence on this is scarce). This specification is common in the theoretical literature and studies that evaluate the elasticity of output to public capital. Gupta et al. (24) find ρ to be negative but statistically insignificant when considering CES production technology as an alternative to their Cobb-Douglas baseline specification when investigating the impact of public capital on growth. Eden and Kraay (24) estimate the extent to which public investment crowds in private investment (one dollar of public investment results in two additional dollars of private investment). They use the results to calibrate a CES production function which in turn, demonstrates a strong degree of complementarity between public and private capital (stronger than the Cobb-Douglas case). They further note that while evidence of crowding-in may point to the desirability of public investment, their calibrated production function indicates that the return to public investment is low (vis-à-vis the world interest rate) when public capital and investment is already high.

11 Appendix 2: Construction of the Infrastructure Efficiency Index (IEI) A. Data Source and Availability The IEI is constructed using the following three indicators: (i) Electric power transmission and distribution losses ( of output). Electric power transmission and distribution losses include losses in transmission between sources of supply and points of distribution and in the distribution to consumers, including pilferage. Source: International Energy Agency (IEA) Statistics via World Development Indicators (WDI). (ii) Non-revenue water (). Non-revenue water represents water that has been produced and is "lost" before it reaches the consumer (through leaks, theft, or legal usage for which no payment is made). It is measured as the difference between water supplied and water sold expressed as a percentage of net water supplied; as volume of water "lost" per kilometer of water distribution network per day; and volume of water "lost" per water connection per day. Source: The International Benchmarking Network for Water and Sanitation Utilities (IBNET); downloaded and compiled from individual country reports available on website. (iii) Paved roads as a percentage of total roads (). Paved roads are those surfaced with crushed stone (macadam) and hydrocarbon binder or bituminized agents, with concrete, or with cobblestones, as a percentage of all the country's roads, measured in length. Source: International Road Federation (IRF), World Road Statistics. The statistics are available as follows, albeit with missing data points. We focus on 2 onwards, and as such, we could only come up with a composite index for 83 countries. Table A2.: Infrastructure Efficiency Indicators Individual Indicator Time Series (Annual) Number of Countries a/ Electricity losses Water losses Paved roads ( of total) a/ With at least one observation recorded during the period. A key concern is the comparability of data across countries given missing time series points. We find that the main variation in the indicators comes from between countries rather than within countries (using xtsum in Stata). Given this, and by taking a simple average of each country s time series mean (from 2 onwards) and last observation, we hope that issues of comparability are reduced in cross-country plots.

12 B. Summary Statistics for the IEI Table A2.2: Summary Statistics for the IEI Income group Obs. Mean Std. Dev. Min. Max. All HI UMI LMI LI Note: In this table, countries are classified into different income groups based on the World Bank classification of countries by income, as at June 28 (for the calendar year 27). The construction of individual country IEI using the Fay and Yepes (23) weights is based on the income classification that has been most commonly assigned to each country in the past five years (23-27). C. Robustness Checks We consider the following checks: (i) Using a shorter time series average for the indicators (26 onwards) and use the last value available (not earlier than 2) where such averages are not available. (ii) Use alternative weights to Fay and Yepes (23), namely weights derived through principal components analysis (PCA). On (i) using a shorter time series average; we find that the full-sample correlations with the WEF Global Competitiveness Report s infrastructure quality score and per capita income do not improve. The composite index based on the shorter time series is highly correlated with the initial index (almost ) so it adds to the argument that within country differences do not matter too much. On (ii) using PCA-based weights; we find the resulting composite index to be highly correlated with an equal weights scheme (almost ). This is similar to the result in Calderon and Serven (24, 2), which use two of the same indicators (power losses and share of paved roads; the third indicator being the waiting time for main telephone line installation). Comparing the initial index based on Fay and Yepes weights versus the index constructed from PCA-based weights, we find that the full-sample correlations with other variables do not vary too much, but the former weighting scheme still performs slightly better. The Fay and Yepes weights are also simple and transparent, as well as intuitively appealing in our paper since they are meant to reflect the monetary value of the relevant infrastructure stocks. The weights from PCA are harder to interpret for our purposes as we are not simply trying to summarize several correlated variables. PCA was applied to three quantity variables (as proxies for stock/coverage) to obtain weights for the corresponding infrastructure effectiveness indicators: (i) electric power consumption (kwh per capita), (ii) roads (km)/land area (sq. km), and (iii) improved water source ( of population with water access). The variables were normalized first - for each country time series (2 to latest available), by their respective mean and standard deviation. We take the first principal component of the three variables, which accounts for between 6-7 of the variation in the data, depending on whether we look at the full sample of countries or income groups. 2

13 Table A2.3: PCA-Derived Weights versus Fay and Yepes (23) Weights PCA-Derived Weights Power Water Roads All HI (incl. OECD) UMI LMI LI Fay and Yepes Weights Power Water Roads HI (incl. OECD) UMI/LMI LI Table A2.4: Comparison of IEI based on Fay and Yepes (23) Weights versus PCA Weights Infrastructure Efficiency Index (IEI) Fay and Yepes PCA Weights Correlation with: Weights Per capita income^.72.5 WEF GCI Infrastructure Quality 24-5 WEF GCI Institutional.54.5 Quality 24-5 IMF PIMI.36.7 Average IEI by Income Fay and Yepes PCA Weights Groups: Weights HI (incl. OECD) UMI LMI LI All ^ln (per capita income, PPP (constant 2 international dollar $)). 3

14 Appendix 3: LTGM-PC results on the effect of an increase in investment on growth robustness to alternative parameterizations A3. The effect of an increase in public/private investment on growth pure public good scenario Graph A3.: ppt. Increase in Public Investment (Pure Public Good).25 HI.25 UMI Standard LTGM Pure public good, φ =.7 Pure public good, φ = Standard LTGM Pure public good, φ =.7 Pure public good, φ = LMI.25 LI Standard LTGM Pure public good, φ =.7 Pure public good, φ = Standard LTGM Pure public good, φ =.7 Pure public good, φ =. 4

15 Graph A3.2: ppt. Increase in Private Investment (Pure Public Good) HI UMI Standard LTGM Pure public good, φ =.7 Pure public good, φ =. Standard LTGM Pure public good, φ =.7 Pure public good, φ = LMI LI Standard LTGM Pure public good, φ =.7 Pure public good, φ =. Standard LTGM Pure public good, φ =.7 Pure public good, φ =. Table A3.: Additional Income Group Medians (Supplementary to Table 5 in Section 6 of the Main Paper) Parameter/Variable Note HI UMI LMI LI TFP growth g A () Human capital growth rate g h Working age-to-population growth rate g ω (average, 26-25) (2) Population growth rate g N (2) () Negative TFP growth rates were changed to. (2) Linear interpolation is carried out to fill in data between the median start and end values of ω and g N. Labor participation rate ρ is assumed constant. 5

16 A3.2 Incremental output growth from public investment versus private investment cross-country comparison under alternatives (φ =. or pure public good, ζ = ) Graph A3.3(i): Differences in Short-Run Incremental Output Growth (φ =. 7, Pure public good, ζ = ).5 Incremental growth is larger for private investment.5 OMN CAF BLZ SYR COG VCT AZE KHM COM MNG CHN SAU RWA LCA ECU LSO MYS BFA MDG BWA KWT MWI SLE MEX MUS BIHBEN COL BHR CMR ZAR JPN LAO TUN PAK LBRROM KGZ NZL GEO GAB JAM NER THA IND MAC TUR ZMBURY VNM MKD JOR BGD MRT UGA TGO NAM SWZ PRY POLSLV MNE ALB MLI HRV GHA KEN CYP ARG TCD DNK MDA HND LUX PER SEN USA NLD FRA FINLTU NOR ZAF SGP HKG TZA SWE ISL ARM CAN KOR EST HUN CZE NPL KAZ PRT RUS SVN SDN UKRITA DOM AUT SVK CRIDEU LVA PAN PHL LKA ESP MAR SUR CHE IRL BEL AUS LBN SRCHL IDN OMN CAF CHN SAU ECU BLZ VCT KHM AZEBHR BWA KWT MEX ALB ARG CHL COL URY LAO MUS LCA VNM TUN GEO THA GAB PAK MAC TUR MRT SLV MNE PER SEN SGP TZAKAZ DOMPAN PHL LBN MNG JOR IND NPL SUR NER IDN BGD CMR COG JPN NZL LUX UGA MAR SYRMYSMWI MDG ROM KGZ NAM LTU NOR ZAF SDN HKG IRL JAM KOR AUS BFAMKD PRY POL CYPCZE ITA SVK HND CAN LVA COM LSO LBR ZMB ZAR BENMLI FIN EST AUT ARMCRI BEL HRVFRA HUNDEU MDA NLD SLESWZSWE USA RUS SRB RWA BIH GHA TCD KEN PRT UKR ESP TGO DNK ISL SVN LKA CHE Incremental growth is larger for public investment Private - Public Investment: LR Incremental Growth, ppt Private - Public Investment: SR Incremental Growth, ppt Capital Share (-beta) Private Capital/Public Capital, (K(P)/K(G)) Private Capital/Public Capital (K(P)/K(G)) Graph A3.3(ii): Differences in Short-Run Incremental Output Growth (φ =. ) (a) Congestion, ζ = (b) Pure public good, ζ = OMN BLZ CAF SYR COGVCT AZE KHM LCA COMNG SAU CHN ECU BWA KWT LSO MYS RWA BFA MDG MEX MUS PAK MAC MWI SLETUN BHR CMR COL URY GAB TUR UGA GEO BIH ZAR BEN JPN LAO KGZ IND BGD ALB LBR ZMB NZL ROM MKD JAM VNM NER THA NAM PRY JOR MRT SLV MNE TGO MLI POL HRV HND LUX PER SEN CYP HKGKAZ DOM ARG GHA KEN MDA LTU NOR ZAF SDN SGP TZA SWZ USA NLD TCD DNK FRA FINARM CAN KOR NPL PAN SWE EST HUN CZE ITA PHL ISLPRT RUS SVK SVN UKR CRI AUTDEU LVA IRL MAR LBN LKA ESP SUR BEL AUS CHL CHE SRB IDN Private Capital/Public Capital, (K(P)/K(G)) OMN BLZ CAF COG VCT SYR AZE KHM LCA COM MNG SAU RWA CHN LSO MYS ECU BFA MDG BWA SLE KWT MUSMAC MEXPAK TUR CMRUGA BIHBEN COL KGZ TUN BHR GEO GAB LBR ZMB MWI URY IND JPN LAO NZL TGO ZAR ROM JAM VNM BGD MKD NAM NER MLI THA PRY POL JOR MRT SLV MNE TCD KEN HND LUX PER ALB SEN SDN ZAF TZA SWZ LTU NOR SGP HKGKAZ GHA DOM PAN HRV USA MDA SWE NLDCYP ARG DNK FRA FINARM CAN KOR ISL EST HUN CZE NPL CRI ITA AUT IRLPHL PRT RUS SVK DEU LVA MAR SVN SUR LKAESP UKR BEL AUS LBN CHL CHE SR IDN Private Capital/Public Capital, (K(P)/K(G)) Graph A3.4(i): Differences in Long-Run Incremental Output Growth (φ =. 7, Pure public good, ζ = ) OMN SWZ ECU AZE BLZ ARG BHR CMR MWI SLE ARM BGD BEN BIH BWA MNG KWT COM KHMCOG CAF HUN ZAR COL BFA CHN AUSAUT CRI TCD EST CAN CZE DNK FRA FIN CYP HRV ALB SLV GEO GAB CHL BEL DEU GHA KAZ HKG ISL ITA KOR KENJOR JAM IND JPN LSO LBR KGZ LAO LVA LTU LUX MKD MDG SYR MNE MRTMUS NER MYS NPL MDA MLI MAR NLDNAM NZL PAK SEN TGO PRY NOR PER PAN PHL PRT MAC MEX IDN DOM POL ROM VNM UGA THA RWA SAU LCA VCT LKA SVN SVKSGP TUR TUN SRB CHE ESP USA UKR SWE ZAF HND TZAZMB URY IRL LBN SUR SDN OMN BLZ CAF MNG ECU AZE SWZ COM SYR COG KHM MWI BHR ARG BIH BFA BWA SLE CMR LSO CHN SAU KWT MYS ZAR MDG BGD BEN COL LBR JPN MKD LAO KGZ MUS NER PAK RWA VCT TGOLCA JAM GEO GAB MRT GHA HRV TCD DNK SLV FRA FINARM HKG IND ALB CYPCZE CAN EST HUN JOR KENLUX MEX MLI MDA MNE NZL VNM PRY ROM TUN THA MAC CRI KAZ NAM POL TUR SEN UGA NLD PER NOR SVN SGPNPL SVK ZMB URY USA SWE AUT BEL AUS HND ISL PRT LKA LTUKOR ITA LVA RUS ZAF UKR TZA ESP PAN PHL MAR DOM CHE DEU SRB CHL IDN SDN IRL SUR LBN Private - Public Investment: SR Incremental Growth, ppt Private Capital/Public Capital, (K(P)/K(G)) 6

17 Graph A3.4(ii): Differences in Long-Run Incremental Output Growth (φ =. ) (a) Congestion, ζ = (b) Pure public good, ζ = Private - Public Investment: LR Incremental Growth, ppt SWZ ARG BHR AZE BLZ CMR ARM AUS AUT ALB BGD BIH BEN BWA KHM CAF COL COM ECU OMN ZAR TCD CAN BFA CHN COG BEL CHL CRIHRV EST DNKDOM CZE FIN CYPSLVGAB FRA GEO DEU GHA HUN HKG IDNISL ITA JAM JPN KWT KAZ KOR KEN IND HND JOR MNE MWI LVA LUX LBR KGZ LAO LSO LTU MKD MDG PAK MNG MDAMRT MLI MAC MYS MUS MAR NPL NER NLD PHLPOL PAN NOR PER NAM SEN PRY NZL SLE PRT ROM MEX RWA SAU SRB LKA SVN SVK TGO SGP LCAVCT SYR ESP ZAF CHE SWE VNM TZA THA UGA TUN TUR UKR USA ZMB URY LBN IRL SDN SUR Private - Public Investment: SR Incremental Growth, ppt OMN SWZ ECU ARGBHR AZE BLZ ARM ALB BGD BIH AUS AUT BEN BWA CMR COMKHM CAF HUN KAZ ZAR COL CAN BFA CHN COG BEL CHL DNKDOM CRI CZE HRV CYPSLV EST FRA FIN GAB TCD DEU GHA HKG IDN ISL ITA HND JOR JAM JPN KWT LVA LUX KOR KEN LAO GEO LSO LTU MKD LBR KGZ IND MDG PAK MNG MNE MWI MRTMYS MUS MAR MDA NLD NPL NOR PAN NAM MLI PRY SLE PER SEN TGO NER SYR PRT PHLPOL ROM NZL SAU SVK SGP RUS MEX MAC RWA LCAVCT SRB SVN ZAF CHE ESP LKASWE VNM THA TUN UGA TUR UKR USATZA ZMB URY LBN IRL SUR SDN Private - Public Investment: SR Incremental Growth, ppt Private - Public Investment: LR Incremental Growth, ppt OMN ECU SWZ BLZ COM CAF MZE SYR KHM BHR ARG MWI SLE PAK BWA KWT CMR COG LSO SAU CHN MYS VCT TGO BIH BFA ZAR MDG COL BGD ALBARM BEN JPN LAO MUS LCA NER MNE RWA JAM GEO GABSLV HKG HUN KAZ LBR LUX MKD KGZ NZL VNM TUN THA PRYMRT MEXMLI GHA JOR HRV TCD KEN IND MAC DNK MDA SEN ROM URY TUR UGA PER FRA FIN CYPCZE NOR SGPNPL NAM POLNLD LTU SVN SVK ZMB USA SWE CAN EST KOR CRI ITA LVA PAN PHL AUT DOM MAR AUS CHL HND ISL PRT RUS LKA ZAF TZA UKR ESP CHE SRB DEU BEL IDN SDN IRL SUR LBN Private Capital/Public Capital, (K(P)/K(G)).5 OMN ECU SWZ BLZ AZE COM CAF SYR MNG KHM SLE PAK BHR CMR ARG COG SAU TGO MWI KWT LSOVCT BWA CHNZAR MDGMUS LCA MYS NER PRY MNE BIH COL KAZ RWA BFA BGD SLVALBARM BEN JPN LAO GEO GAB MRT JAMJOR LUX HKG HUN LBRMEX NZL VNM TUN THA MKD KGZ MLI GHA HRV TCD KEN IND MAC DNK MDA TURPER SEN UGA ROM URY FRA FIN CYPCZE LTU NOR SGPNPL SVK POL CAN EST KOR CRI ITA AUT DOM LVA NAM NLD SVN PAN PHL ZMB USA SWE MAR BEL AUS CHL HND ISL PRT RUS LKA ZAF UKR TZA ESP CHE DEU SRB IDN SDN IRL SUR LBN Private Capital/Public Capital, (K(P)/K(G)) 7

18 A3.3 Increase in the efficiency of public investment pure public good scenario Graph A3.5: Incremental Output Growth from a 5-ppt. Increase in the Efficiency of Public Investment (Pure Public Good).5. HI Initial. 7 Scenario, N in 27 and onwards:.92 in 235:.9.5. UMI Initial.7 Scenario, N in 27 and onwards:.8 in 235: Pure public good, φ =.7 Pure public good, φ =. Pure public good, φ =.7 Pure public good, φ =..5. LMI Initial.7 Scenario, N in 27 and onwards:.78 in 235: LI Initial. Scenario, N in 27 and onwards:.64 in 235: Pure public good, φ =.7 Pure public good, φ =. Pure public good, φ =.7 Pure public good, φ =. 8