metadata: authors: 0: author: Francois,John Nana Darko
1: author: Konte,Maty
2: author: Ruch,Franz Ulrich
count: World,Africa
docna: 0: docna: “Crowding In” Effect of Public Investment on
            Private Investment Revisited
docty: Policy Research Working Paper
abstracts: cdata!: Current investment trends in emerging
            market and developing economies are not enough to meet the
            needs of their growing populations and will fall short of
            achieving the Sustainable Development Goals related to human
            and physical capital development. Public investment can play
            a critical role in addressing this shortfall, especially if
            it can crowd-in private investment.  Using theory and panel
            data for 109 developing countries from 1980&#x2013;2019,
            this paper investigates whether public investment crowds in
            or crowds out private investment. The paper also explores
            how the relationship changes across different groups of
            countries and under different institutional settings.  The
            analysis uses changes in predicted disbursements on loans
            from official creditors to developing country governments as
            an instrument for changes in public investment. The findings
            show that public investment is a complement to private
            investment, raising the marginal productivity of the latter.
            As a result, an extra dollar of public investment raises
            private investment by 1.6 dollars. The findings also reveal
            stronger evidence of crowding-in of private investment in
            low-income countries and Sub-Saharan Africa, where
            investment needs are greatest. Finally, the findings are
            embedded in a model with imperfect capital markets, which
            shows that public investment can be used as an effective
            vehicle to address underinvestment issues induced by capital
            market distortions.
display_title: “Crowding In” Effect of Public
            Investment on Private Investment Revisited
listing_relative_url: /research/2024/08/34381607/“crowding-in”-effect-public-investment-private-investment-revisited
topicv3: Fiscal Policy and Growth m1326899 1072,Capital Markets m1326967 332,Investment Climate(IC) m1327235 401
publishtoextweb_dt: 2024-08-26T00:00:00Z
dois: 10.1596/1813-9450-10881
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 40
author_keys: 0: author_key: 2166801
1: author_key: 1482334
2: author_key: 1684336
model_extractions: Policy Research Working Paper 10881 “Crowding In” Effect of Public Investment on Private Investment Revisited _John Nana Francois Maty Konte Franz U Ruch_ Macroeconomics, Trade and Investment Global Practice August 2024 A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.
Policy Research Working Paper 10881

# **Abstract**

Current investment trends in emerging market and developing economies are not enough to meet the needs of their growing populations and will fall short of achieving the Sustainable Development Goals related to human and physical capital development. Public investment can play a critical role in addressing this shortfall, especially if it can crowd-in private investment. Using theory and panel data for 109 developing countries from 1980–2019, this paper investigates whether public investment crowds in or crowds out private investment. The paper also explores how the relationship changes across different groups of countries and under different institutional settings. The analysis uses changes in predicted disbursements on loans from official creditors to developing country governments as an instrument for changes in public investment. The findings show that public investment is a complement to private investment, raising the marginal productivity of the latter. As a result, an extra dollar of public investment raises private investment by 1.6 dollars. The findings also reveal stronger evidence of crowding-in of private investment in low-income countries and Sub-Saharan Africa, where investment needs are greatest. Finally, the findings are embedded in a model with imperfect capital markets, which shows that public investment can be used as an effective vehicle to address underinvestment issues induced by capital market distortions.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at jfrancois1@worldbank.org, mkonte@ifc.org, or fruch@worldbank.org. A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.

<!-- Start of picture text --> TRANSPARENT<br>ANALYSIS<br>G<br>R E<br>N<br>S<br>I P<br>Y E<br>K A<br>C A<br>R P<br>LI R<br>O E<br>O C<br>W R<br>H<br>S<br>P<br><!-- End of picture text --> _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **“Crowding In” Effect of Public Investment on Private Investment Revisited**<sup>*****</sup>

John Nana Francois<sup>†</sup> Maty Konte<sup>‡</sup> Franz U Ruch<sup>§</sup>

## : E22, E23, H11.

_Keywords_ : Capital markets distortions; Crowding-in; Public investment; Private investment; Instrumental variable.

> * <mark>This paper received funding from the KDI School of Public Policy and Management. We benefted from valuable comments, suggestions, and feedback from Maya Eden, Aart Kraay, Stephen A. O'Connell, James Sampi, Emilia Skrok, Kersten Stamm, and Fulbert Tchana Tchana. We are grateful to Gbenoukpo Robert Djidonou and Suhyun Lee for research assistance. We would like to thank Parul Agarwal for providing the oficial loan level data. We would also like to thank participants at the 2023 1st KDIS-World Bank Fiscal Policy for Growth Workshop in Seoul for their feedback, and the participants at the review meeting for their comments and suggestions. The fndings, interpretations, and conclusions expressed in this paper are entirely those of the authors and should not be attributed to the World Bank, IFC, their Executive Directors, or the countries they represent.</mark>

† Fiscal and Sustainable Growth Unit, Macroeconomic, Trade and Investment Department, World Bank. Email: jfrancois1@worldbank.org.

‡ Economic and Market Research, International Finance Corporation. Email: mkonte@ifc.org § Fiscal and Sustainable Growth Unit, Macroeconomic, Trade and Investment Department, World Bank. Email: fruch@worldbank.org.
# 1 Introduction

Current investment trends in emerging market and developing economies (EMDEs) are not enough to meet the needs of their growing populations. Existing infrastructure requires critical maintenance, and there are massive additional needs for transportation, clean water, and sanitation (Gaspar et al. 2019). The pandemic has only further increased these needs. Infrastructure gaps are estimated at about $3 trillion (approximately 3.4 percent of 2030 world GDP) to achieve the Sustainable Development Goal related to human and physical capital development (Carapella et al. 2023). Moreover, to achieve significant cuts in greenhouse gas emissions, boost the clean energy transition, and limit the rise in global temperatures could require between 1 and 8 percent of GDP in additional investment per year, with higher needs in low-income countries (figure 1A; World Bank 2022).<sup>5</sup>

**Figure 1** : Investment trends in emerging and developing economies

<!-- Start of picture text --> A. Additional investment for a resilient and low- B. Investment growth<br>carbon pathway, 2022-30<br>Percent of GDP Percent<br>10<br>10<br>2011-21 2000-10<br>8<br>8<br>6<br>6<br>4<br>4<br>2<br>2<br>0<br>0<br>Low income Lower middle Upper middle EMDEs EMDEs excluding<br>China<br>income income<br><!-- End of picture text --> _Source:_ World Bank.

_Note:_ EMDEs = emerging market and developing economies.

A. Annual investment needs to build resilience to climate change and put countries on track to reduce emissions by 70 percent by 2050. Depending on availability, estimates include investment needs related to transport, energy, water, urban adaptations, industry, and landscape. In some Country Climate and Development Reports, especially those for low-income and lower-middle-income countries, estimated investments include development needs, especially those linked to closing the infrastructure gaps—such as solar mini grids to provide energy access—and cannot be considered entirely “additional” to pre-existing financing needs. B. Arithmetic annual averages. GDP-weighted averages for the period indicated.

Despite these large infrastructure needs, sluggish global investment growth continues. Between the decades of 2000-10 and 2011-21, fixed investment growth in EMDEs effectively halved from 9.4 to 4.8 percent (figure 1B). The slowdown in investment growth is geographically widespread, affecting all EMDE regions. Moreover, prevailing economic conditions, including rising global interest rates and high debt levels, have made borrowing

> 5 See also, for example, Gaspar et al. (2019); and IEA (2021).

2
more expensive and suggest sluggish investment growth will continue (Kose and Ohnsorge 2023).

Against this backdrop, this paper investigates the question of whether public investment, as a fiscal policy tool, can crowd-in private investment. We utilize data from a large panel of 109 EMDEs and employ an instrumental variable approach to identify the relationship between these two types of investment. The empirical setting is guided by a tractable model, where we show that the complementarity (substitutability) between public and private investment is sufficient to crowd-in (-out) private investment. Consequently, the parameter of interest we estimate captures, simultaneously, the structural relationship between public and private investment and the crowding-in (-out) of private investment by public investment. We extend the analysis to low-income countries (LICs) and Sub-Saharan Africa (SSA), two subgroups of countries where infrastructure needs are large given low levels of development and growing populations. Furthermore, we examine whether the effect of public investment on private investment varies by the level of corruption and financial development to understand the potential implications of factors that may impede or enhance the effectiveness of public investment in crowding-in private investment.

The relevance of public investment to spur private investment in EMDEs is critical. Yet, systematic evidence of the crowding-in effect of public investment on private investment in EMDEs remains scarce. The existing literature has focused on a limited number of lowincome countries (Eden and Kraay 2014), high-income OECD countries (Boehm 2020) or U.S states, European countries, and Argentine provinces (Izquierdo et al. 2019). Expanding this to a large set of EMDEs will provide systematic and stronger evidence of the crowding-in effect of private investment in these countries, which can help drive policy strategies to address the weak outlook for investment growth.

Importantly, the existing literature studies the implication of the crowding-in effect of public investment under perfect capital markets. Capital market imperfections and distortions are, however, ubiquitous in developing countries. For example, access to financial markets, which is important for the growth of businesses and investment, is still a challenge in LICs and SSA. Moreover, structural conditions such as weak corruption control, asymmetric information, inaccessibility to financial markets, and market distortions induced by poorly designed tax systems can create imperfect capital markets that discourage private sector investment. Governments also tend to face lower interest rates than private agents (Eden and Kraay 2014). If public investment can crowd-in private investment, then governments can take advantage of the low interest rate they face relative to the private sector to help address underinvestment by the private sector.

In this paper, we move away from the assumption of perfect capital markets. In particular, because of the law of diminishing marginal returns on capital, more public investment may not always be desirable even if it crowds-in private investment. However, if capital market distortions exist (for example, distortionary taxes on firms’ output), this can potentially 3
induce private sector underinvestment. A direct implication is that insofar as public investment resolves a market failure by crowding in private investment, it should be allowed a lower marginal rate of return compared to when capital markets are perfect (Ogura and Yohe, 1977).

dollar increase in public investment raises private investment by about 1.6 dollars.<sup>6</sup> This is because public and private investment are complements, which implies that an increase in public investment raises the marginal product of private investment and hence, crowds-in private investment.<sup>7</sup> The evidence of crowding-in of private investment by public investment holds in LICs and SSA. Specifically, a dollar increase in public spending raises private investment by 1.5 and 1.4 dollars in LICs and SSA, respectively. Our estimated crowding-in effect in a smaller sample of 39 LICs is smaller than those estimated by Eden and Kraay (2014), who found that government investment raises private investment by approximately 2 dollars. Our results are, however, starkly different from findings in Boehm (2020), who provided evidence of crowding-out of private investment in OECD countries. We also find evidence that the crowding-in of private investment increases over longer horizons. More precisely, the crowding-in effects are visible for up to three years. Finally, we find that public investment is more effective in crowding-in private investment in countries with strong control of corruption control. Also, the crowding-in effect of public investment is greater than one and statistically significant in countries with lower financial development.

effective vehicle to address underinvestment issues induced by capital market distortions. This is because institutional reforms that aim to resolve market distortions take time to implement. Consequently, while these reforms are the first best solution to solving market distortions, the reform process can be combined with increases in public investment to address private sector underinvestment. Our findings are also a warning to policy makers that cutting public investment may undermine private investment.

The rest of the paper proceeds as follows. Section 2 presents a simple theoretical model linking public investment to private investment. In section 3, we discuss the empirical strategy used to quantify the crowding-in effect and present summary statistics, stylized facts of our investment data and instrumental variable, and. Section 4 presents the main results. Section 5 presents sensitivity, validity, and robustness exercises. In section 6 we

> 6 Boehm (2020) provided evidence of crowding-out of private investment in OECD countries.

> 7 raises the marginal product of private investment and hence, the level of private investment. Real world examples of such complementary public investment include: the construction of a highway linking rural and urban centers, which increases productivity of private capital; safe public water delivery, which can induce higher private investment in sanitation; and reliable irrigation, which can improve private agricultural activities.

4
=F(K ) je{k } (F < 0) (1—t)F(K )=-(r
It is worth mentioning that the presence of distortionary taxes in equation (2.4) highlights an important distinction between our study and that of Eden and Kraay (2014). In particular, Eden and Kraay (2014) assume that capital markets are perfect and hence, the marginal product of private and public capital are the same. They, however, acknowledge that the assumption that there are no capital market distortions inherently implies that: 1) government and private sector face the same interest rates and 2) there are no distortionary taxation. However, as discussed by the authors, these assumptions are strong in that governments do indeed face lower interest rates, are less credit constrained than the private sector, and need to raise revenues to repay debt-financed investment. An introduction of any of these two elements have important implications for the return of public investment, which will not be equal to the returns of private investment. Consequently, we relax this assumption and assume that capital markets are imperfect. This also implies that the marginal product of public and private capital is not equal. For now, we introduce distortionary taxes as the main source of distortions in our framework. We will discuss the implication of this for the returns of public investment in section 7.

Log-linearizing equation (2.4) around the steady state and applying some algebra (See annex A), we obtain, = − (2.5) KKpp,KKgg FF pp,tt gg,tt where Δ is the first difference operator so that Δkk FFKKpp,KKpp Δkk for . Now, from substituting equation (2.2) into (2.5), we arrive at ii,tt ii,tt ii,tt−1 Δkk = kk −kk ii∈{gg, pp} = − (2.6) KKpp,KKgg FF pp,tt gg,tt gg,tt Δii KKpp,KKpp Δii = αα⋅Δii where <u>p g</u> is the parameter of crowding-in FF or crowding-out of FFKK p,KK private investment following an increase in public investment. Notice that since αα≡− FFKKpp,KKpp (αα> 0) (αα< 0)< 0, the sign of is strictly governed by ∈R. Here, KK implies pp,KKpp < 0�FF complementarity (substitutability), respectively, which means crowding-in (out) with KKpp,KKgg kkpp,kkgg kkpp,kkgg αα FF FF > 0 �FF . αα> In the empirical section that follows, we estimate the parameter in equation (2.6) to uncover 0(αα< 0) the structural relationship between public and private investment and hence, the crowdingin effect of public investment.

6
3 Empirical strategy Guided by the theoretical relation in equation (2.6), our empirical strategy is implemented using the local projections method á la Jordà (2005), which has been widely applied in the empirical literature that examines the impact of government spending shocks on macroeconomic outcomes. In panel form, the estimable equation is as given as: ll h h h (3.1) = � pp pp gg ii,tt+h ss ii,tt−ss ii,tt ii tt ii,tt+h ΔII ρρ ΔII + αα<sup>h</sup> ΔII + ββ + δδ + εε where ≡ <u>p,i</u> +h <u>p,i</u> −1 and ss=1 ≡ <u>g,i</u> +h <u>g,i</u> −1 ~~.~~ The subscripts represents the i −1 i −1 pp II −II gg II −II country, ΔII the year, and ii,tt+h YY h the horizon, respectively. ΔIIii,tt−ss YY is private investment and ii is public investment and both are measured in constant local currency. We include a one lag term of pp,iitt gg,iitt tt II II private investment in our specification and it is captured by the parameter for horizon h≥0. The parameter of interest is , which captures simultaneously the structural (ll= 1) ρρ<sup>h</sup> relationship between private and public investment and the crowding-in (out) of private investment (that is, the contemporaneous and cumulative change over horizon αα<sup>h</sup> h in private investment because of a change in government investment). Here, notice that the sign of the estimated value of is governed by as highlighted in our simple model in section 2. Hence, a positive (negative) value of kkpp,kk implies that public and private investment are gg αα FF Edgeworth complements (substitutes) and that public investment crowds-in (out) private h ααh investment. The parameters and capture country- and year-effect for different horizons, respectively. The term represents the error term, which capture all other ii ii sources of variation in private investment changes ββ δδ h periods into the future. Finally, notice tt+h that equation (3.1) nests several scenarios. Specifically, when εε h= 0 and , the specification in (3.1) reduces to our baseline model in equation (2.1), and captures the ll= 0 impact multiplier. αα

# 3.1 Data

We use the IMF’s Investment and Capital Stock dataset which provides investment data for the general government and private sector. Investment data is based on gross fixed capital formation. The data is available for 109 economies. In line with equation (3.1), we convert nominal public and private investment in local currency to real using the domestic real GDP deflator. We take the annual changes in public and private investments, and then divide them by lagged real GDP from the IMF’s World Economic Outlook (WEO). One limitation of this dataset is that when public investment data is not available, it is assumed to grow by the same rate as private investment. This affects observations further back in history where data is sparse. The instrumental variable should ameliorate any concerns about the correlation this assumption imposes.

7
Following Kraay (2014), we use predicted disbursements on loans by official creditors from the World Bank’s Debtor Reporting System (DRS) as an instrument for changes in public investment. Official creditors include both multilateral institutions like the World Bank and African Development Bank, and bilateral creditors including sovereign governments like China, Japan, and the United States. This does not include official aid flows. The DRS provides comprehensive coverage of all individual external public and publicly guaranteed loans from all creditors and for all countries that borrow from the World Bank. It tracks the original amount of the loan, loan commitments, terms, disbursements, and repayments of all external loans. The data is confidential. The original amount of the loan as well as disbursements are recorded in the original denomination currency. Loans are generally tied to multi-year spending projects with disbursements linked to the stages of project implementation. See annex B for a discussion of the process of cleaning the data and some of its properties.

The key variable we need from the loan-level data are disbursement rates over the life of a loan defined as the amount dispersed in each year since the loan agreement as a ratio to the original loan amount. Figure 2 shows the average rate of disbursement over 1970-2021 based on the year in which the disbursement occurred. In the year of the loan, about 15 percent of the loan is disbursed to the debtor on average.<sup>9</sup> This rate of disbursement declines over the life of the loan to 11 percent in the year after the loan is agreed. After five years about half the loan amount is disbursed. There is a difference in the rate of disbursement between multilateral and bilateral lenders. Multilateral lenders tend to disburse loans more evenly over several years, with disbursements averaging about 10 percent per year for the first five years of a loan. Bilateral lenders tend to disburse more upfront with less disbursed in later years. These rates of disbursement are below those found in Kraay (2014) despite only updating the data with an additional decade.

Average disbursement rates are then used to estimate predicted disbursements which is the instrumental variable. Predicted disbursements are calculated as in Kraay (2014) as the original loan amount multiplied by the average rate of disbursement over time across all other loans issued by the same creditor during the same decade and in the same region as the debtor. Regions are based on the World Bank’s classification of region (for example, South Asia and Sub-Saharan Africa). For loans from regional multilateral organizations, that only loan to specific regions, the predicted disbursement is applied only to the creditor and decade. These loan-level predicted disbursements are then aggregated to the country-year

> 9 Disbursement rates have changed somewhat over the last half century. In the 1970s, average disbursements in the year of the loan agreement were 17 percent, and within five years was about two-thirds of the total loan. This dropped to less than 10 percent of the loan disburse in the year of the loan in the 1990s and about one-third within five years. By 2010-21, disbursements in the first year had increased back to 17 percent, as in earlier decades, with about half the loan disbursed within five years.

8
respond to contemporaneous shocks.

**Figure 2: Disbursement rates over the life of a loan**

A. Average disbursement rate B. Average disbursement rate, by creditor type <!-- Start of picture text --> Share of loan disbursed Share of loan disbursed<br>0.16 0.18<br>0.14 0.16 Multilateral loans<br>0.12 0.14 Bilateral loans<br>0.12<br>0.10<br>0.10<br>0.08<br>0.08<br>0.06<br>0.06<br>0.04 0.04<br>0.02 0.02<br>0.00 0.00<br>t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10<br><!-- End of picture text --> _Source:_ Authors’ calculations.

_Note:_ Based on average disbursement rates for 73,994 loans (32,965 for multilateral and 41,029 for bilateral) in year of loan and subsequent years.

Since the predicted disbursements are in current US$, to get our instrumental variable relative to GDP, we convert it to local currency using exchange rates from the World Bank’s World Development Indicators, then deflate using the GDP deflator and again divide it by lagged real GDP. Before running regressions, we remove the 1<sup>st</sup> and 99<sup>th</sup> percentiles of each variable. After constructing our variables, we have observations between 1980 and 2019 for our regressions. Table 1 provides summary statistics of the main variables of interest.

**Table 1: Summary statistics**

||Mean|Median|Standard<br>deviation|Minimum|Maximum|Interquartile<br>range|Skewness|Kurtosis|Number of<br>observations|
|---|---|---|---|---|---|---|---|---|---|
|Change in private||||||||||
|investment to|0.74|0.63|4.11|-34.72|62.77|2.78|1.44|38.02|3737|
|GDP||||||||||
|Change in public||||||||||
|investment to|0.27|0.19|2.43|-42.52|29.81|1.41|-0.85|50.31|3737|
|GDP||||||||||
|Predicted loan||||||||||
|disbursements to|0.07|0.00|2.30|-33.18|46.20|0.39|6.40|213.70|3774|
|GDP||||||||||
|Predicted multi.||||||||||
|loan<br>disbursements to|0.05|0.00|0.45|-7.68|6.54|0.22|1.41|58.36|3756|
|GDP||||||||||

_Source:_ Authors’ calculations.

_Note:_ Multi. = multilateral. All variables are as a ratio to GDP. “Change” refers to the annual change as described in equation (3.1).

9
#

A primary challenge with estimating the effect of public investment on private is the issue of endogeneity of government investment. This issue occurs because public investment is a fiscal policy tool often used to help stimulate the economy during economic downturns. There is a strong possibility that during economic downturns where private investment is low, governments may increase public investment to stimulate the economy. Consequently, an estimated negative relationship between public and private investment is likely to be driven by the negative shock to the economy. This means that there will be a negative correlation between the error term and public investment, thereby, inducing a downward biased OLS estimate of _α_ . On the other hand, if government investment is procyclical (that is, increases during economic booms), which is historically the case for several developing countries, then during good times such as booms in commodity prices, government investment will rise (Galeano et al., 2021). Procyclicality would create an upward bias on the OLS estimate of _α._ Additionally, and perhaps a more critical issue of endogeneity is measurement errors in investment data. The presence of measurement errors in the independent variable can lead to attenuation bias. This may imply a positive relationship between the error term and public investment, inducing an upward bias in the OLS estimate of the crowding-in parameter. Generally, this endogeneity issue that causes government investment to be contemporaneously correlated to the error term, _εit_ , will render the OLS estimation inconsistent.

Evidently, failure to address the issue of endogeneity can lead to inaccurately estimating the size, and potentially the sign of _α_ . The natural strategy to employ to address the endogeneity is an instrumental variable estimation. We, therefore, utilize the identification strategy of Kraay (2012) and Kraay (2014). While focusing on the output multiplier and government spending, these studies exploit two conditions: (1) The studies argue that a significant fraction of government spending in developing economies is financed by loans from official creditors, and (2) these loans typically disburse over a period of many years following the initial approval of the loan. Kraay (2014), therefore, constructs a measure of predicted disbursements on loans from official creditors that reflects only fluctuations in loan approval decisions made in previous years, but not the current year. We update the instrumental variable using the same unique loan-level dataset from 1980 to 2021 (extended it from 2010) on about 79,000 individual loans from official creditors to governments in developing countries.

The key identifying assumption is that loan approval decisions in a given year do not anticipate shocks to private investment or output in subsequent years. Given this identifying assumption, subsequent predicted disbursements are uncorrelated with contemporaneous macroeconomic shocks, and are a valid instrument for changes in government investment.<sup>10</sup>

> 10 As discussed in Kraay (2012, 2014), conditional on the identifying assumption that loan approvals do not respond to future shocks to growth, our choice of instrument will be uncorrelated the error term for all h ≥ 0.

10
Moreover, in countries where official creditor financing of government investment is large, predicted disbursements will also be a strong instrument for changes in government investment.<sup>11</sup> We, therefore, employ the predicted disbursements on loans from official creditors to identify the exogenous component of government investment.

There are several challenges associated with using predicted disbursements as an instrument for public investment. First, as described in Kraay (2014), for the first-stage regression, predicted disbursements are correlated with overall government spending, which comprise investment and non-investment spending. Hence, if one is regressing private investment on public investment and using predicted disbursements as an instrument, it may be the case that non-investment government spending affects private investment, and if the latter is not controlled for, could lead to a violation of the exclusion restriction. However, controlling for non-investment government spending in the first-stage regression can be problematic as non-investment government spending might be correlated with the error-term in the first-stage regression. Second, it may be that predicted loan disbursements acts as a signal to private investors that the involvement of multilateral creditors may lower policy uncertainty. We attempt to address these challenges by employing an instrument-free estimator in section 6.3.

investment. This empirical strategy is guided by two arguments in Kraay (2012). First, although loan commitments are made before subsequent shocks are realized, the shocks may be persistent and possibly predictable. Second, if loan commitments are correlated with contemporaneous macroeconomic shocks, they will also be correlate with future shocks, which will violate the exclusion restriction. Consequently, including the lagged dependent variable in the regression helps address this possibility and improves the credibility of our identifying assumption.

# 4 Main results

Based on the two-stage least squares (2SLS) regression, using predicted disbursement as the instrumental variable, the coefficient on public investment is 1.6 (in the case of _h_ =0) and The cumulative is statistically significant at the 5% level of significance (table 2; panel B).<sup>12</sup> impact of public investment on private investment rises to a peak of 2.4 after two years. The estimates have two economic meanings, as highlighted in section 2. Specifically, recall that a positive coefficient on public investment in the private investment equation means that government investment is an Edgeworth-Pareto complement to private investment, suggesting that an increase in public investment raises the marginal product of private investment. Additionally, the estimated positive coefficient implies the crowding-in of private investment following an increase in public investment. In particular, the results

> 11 Total disbursements average 77 percent of public investment and 2.8 percent of GDP for country-year pairs. 12 In annex C we look at the impact of alternative censoring rules applied to the loan-level data.

11
suggest that an extra dollar increase in government investment crowds-in private investment by approximately 1.8 dollars after one-year and by 2.1 after four-years.

**Table 2:** The response of private investment to government investment

||||Cumulative<br>|Multipliers(horizo<br>|n h inyears)<br>||
|---|---|---|---|---|---|---|
||Baseline<br>(1)|h=0<br>(2)|h=1<br>(3)|h=2<br>(4)|h=3<br>(5)|h=4<br>(6)|
|Panel A: OLS|||||||
|Change in government<br>investment|-0.041|-0.069|0.169**|0.165*|0.211**|0.297***|
||(0.057)|(0.051)|(0.081)|(0.097)|(0.099)|(0.097)|
|Panel B: 2SLS|||||||
|Change in government|||||||
|investment|1.843**|1.623**|2.394**|2.239***|2.067**|1.351|
||(0.821)|(0.698)|(0.944)|(0.829)|(0.881)|(1.149)|
||[0.706, 5.06]|[0.60, 4.36]|[0.71, 5.57]|[0.43, 4.44]|[ 0.22, 4.20]|[-1.24, 4.03]|
|Panel C: First-stage estimates|||||||
|Change in predicted disb.|0.212***|0.231***|0.212***|0.230***|0.255***|0.252***|
||(0.070)|(0.072)|(0.072)|(0.073)|(0.071)|(0.074)|
|Observations|3,437|3,349|3,242|3,136|3,029|2,922|
|F-statistic|9.340|10.32|9.268|10.03|12.83|11.63|
|KP Underid stat|0.00454|0.00295|0.00457|0.00326|0.00115|0.00175|
|No. of countries|109|109|109|109|109|109|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence a ́ la Boehm (2020). All estimations include country-fixed effects and year effects. “Baseline” specification does not include the lagged dependent while all the estimations in columns (2)-(6) include one year lag of the dependent variable.“KP” is Kleibergen and Paap underidentification test.

_F_ -statistic follows Olea The 2SLS effective F-statistic lies between 9.3 and 12.8. The effective and Pflueger (2013) and has recently been advocated by Andrews et al. (2019) as the more Similar reliable metric of first stage strength in the presence of heteroskedastic residuals.<sup>13</sup> to the standard rule-of-thumb value for the standard _F_ -statistic, in a just-identified model, the yardstick value for the effective _F_ -statistic is 10 (Andrews et al. 2019). A welldocumented issue of using instrumental variables is that when they turn out weak, the estimated coefficient of interest can be biased and unreliable; a possibility here with some F-statistics below the benchmark. Hence, the Andersen-Rubin instrument consistent 95 percent confidence intervals for the baseline 2SLS are 0.73 to 5.19 and for h=0 is 0.6 to 4.36 (and slightly smaller for Driscroll-Kraay standard errors). Indeed, Eden and Kraay (2014), who focus on 39 LICs countries, acknowledge that although their reported weak-instrument

> 13 This statistic coincides with the conventional F-statistic when residuals are homoskedastic.

12
extremely large. Specifically, the estimated response of private investment to an increase in public investment can range from as low as 0.18 to as high as 9.85 with a point estimate of about 2 in Eden and Kraay (2014). Furthermore, our point estimates are smaller than the ones estimated in Eden and Kraay (2014).

Evidently, the 2SLS estimates are larger over all horizons than that of the ordinary least squares (OLS) estimates. As we can observe for the full sample, the OLS estimate is -0.04 (in the baseline regression, which excluded a lagged dependent), and it is statistically insignificant (table 2; panel A). The cumulative response rises over the horizon ( _h_ ), with the _h_ multiplier becoming significant at two-years ahead ( = 1) at 0.17 and also at five-years ahead ( _h_ = 4) at 0.3. Recall, however, that the OLS estimates are likely to be biased (downward) because of the negative correlation between changes in public investment and the error term.

#

Investment needs in low-income countries, several of which are in Sub-Saharan Africa (SSA) as well as IDA countries, remain large and are fundamental to ensuring poverty reduction and sustainable development. For example, according to Rozenberg and Fay (2019), the SSA region has the highest infrastructure gap of any EMDE region, estimated at about 9 percent of GDP per year. This is almost four times the size of current infrastructure investment spending (Kasyanenko et al., 2023). Several examples of this underinvestment across many sectors are available. In the power sector, one-half of the population in SSA had access to electricity in 2021 compared with closer to nine-in-ten worldwide. In telecommunications, about one-third of the population is using the internet compared to about two thirds globally. In agriculture, which is a source of employment for about two-thirds of the population, productivity is low (Kasyanenko et al., 2023; Fuglie et al., 2019). Hence, we re-estimate the relationship between public and private investment separately for subgroups, including lowincome countries, International Development Association (IDA) members, and Sub-Saharan African countries.

crowding-in in all three subgroups. The impact multipliers (h=0) in LICs and SSA are smaller than in all EMDEs but cumulative multipliers at longer horizons are higher. In LICs, there is evidence that public investment also crowds-in private investment with an additional dollar of public investment associated with up to 1.5 dollars in private investment after one year ( _h_ = 0), rising to peak at 2.5 after three years ( _h_ = 2). The impact multiplier, which can be directly compared, is lower than that estimated by Eden and Kraay (2014) which is equal to 2. The effective F-statistic is consistently above the 10 benchmark threshold. Crowding-in may be even larger in IDA countries at 2.1 dollars for each additional dollar of public investment after 13
between 5 and 6.7. In SSA, the impact multiplier is 1.5, slightly lower than in the overall sample but not statistically significantly different. The cumulative multiplier rises to 3.1 after three years suggesting a strong complementarity between public and private investment in this region. The effective F-statistics remain above 10 across all horizons suggesting a relevant instrument.

**Table 3:** The response of private investment to government investment

||Cu|mulative Mu|ltipliers (hori|zon h in yea|rs)|
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
|||Low-i|ncome coun|tries||
||_h=0_|_h=1_|_h=2_|_h=3_|_h=4_|
|Change in government investment|1.511***|1.664**|2.540**|2.341**|1.283|
||(0.532)|(0.776)|(1.019)|(1.062)|(1.106)|
|Observations|722|699|677|654|631|
|F-statistic|12.38|11.04|11.26|12.75|12.23|
|KP Underid stat|0.00324|0.00511|0.00481|0.00343|0.00384|
|||I|DA countries|||
|Change in government investment|2.120*|3.441*|3.067**|3.478**|2.583|
||(1.113)|(1.762)|(1.516)|(1.650)|(1.894)|
|Observations|1,479|1,432|1,387|1,341|1,296|
|F-statistic|5.912|4.999|5.932|6.679|6.041|
|KP Underid stat|0.0165|0.0263|0.0157|0.0108|0.0148|
|||Sub|-Saharan Afr|ica||
|Change in government investment|1.446**|2.191**|2.997**|3.054**|1.543|
||(0.625)|(0.937)|(1.222)|(1.191)|(1.291)|
|Observations|1,363|1,321|1,280|1,239|1,197|
|F-statistic|12.26|10.84|10.83|12.46|10.76|
|KP Underid stat|0.00147|0.00251|0.00242|0.00131|0.00238|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence a ́ la Boehm (2020). All estimations include country and year effects and one year lagged dependent variable. “KP” is Kleibergen and Paap underidentification test.

# 4.2 Crowding-in and the role of corruption control

It may be the case that the effectiveness of public investment and the ability to crowd-in private investment is affected by the level of corruption. There exists a well-established literature that provides evidence of the negative impact of corruption on the business environment, investment efficiency, infrastructure, and public service delivery (for example, Mauro 1995; Davis 2004; Barr et al. 1995, Beekman et al. 2014; and Kaufmann et al. 2002).

14
Poor governance spurs rent-seeking behaviors and diverts public funds to unintended activities, lowering the effectiveness of public investment.

**Table 4:** The response of private investment to government investment, corruption of control

||(1)<br>C<br>|(2)<br>umulative M<br>|(3)<br>ultipliers (ho<br>|(4)<br>rizon h in year<br>|(5)<br>s)<br>|
|---|---|---|---|---|---|
||h=0|h=1|h=2|h=3|h=4|
|||Higher<br>|control of co<br>|rruption<br>||
|Change in government investment|0.870*|2.519**|2.514**|2.272**|1.450|
||(0.484)|(1.094)|(1.074)|(1.122)|(1.307)|
|Observations|1,955|1,902|1,849|1,795|1,742|
|F-statistic|11.67|10.80|11.06|13.53|13.05|
|KP Underid stat|0.00171|0.00263|0.00232|0.000934|0.00112|
|No. of countries|93|93|93|93|93|
|||Lower<br>|control of co<br>|rruption<br>||
|Change in government investment|4.764|1.661|1.686|1.965|2.005|
||(4.312)|(3.069)|(3.010)|(2.449)|(3.164)|
|Observations|1,394|1,340|1,287|1,234|1,180|
|F-statistic|1.580|1.378|1.658|2.049|1.617|
|KP Underid stat|0.196|0.225|0.183|0.140|0.186|
|No. of countries|70|70|70|70|70|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence a ́ la Boehm (2020). All estimations include country-fixed effects and year effects and one year lagged dependent variable. “KP” is Kleibergen and Paap underidentification test.

To examine for the impact of corruption on the ability to crowd-in private investment, we divide the sample (that is, country-year pairs) into those above (high corruption control) and below (low corruption control) the median outcome for corruption control from the Worldwide Governance Indicators (Kaufmann et al. 2011). The control of corruption indicator measures perceptions of the extent to which public power is exercised for private gain.

We find that the crowding-in effect of public investment on private investment is only statistically significant in the high control of corruption group, with the cumulative impact increasing up to four years ahead (table 4). When control of corruption is weak, the estimated coefficient across the different horizons, while generally smaller in magnitude, is 15
fostering private investment.

#

development. A well-developed financial sector promotes investment because it reduces liquidity constraints, facilitating access to financial resources to businesses, reduces information asymmetry that increases the cost of sending and borrowing and ensures an efficient allocation of financial resources (Allen and Ndikumana, 2000). Moreover, financial development plays a critical role in pooling savings and allocating capital to productive investment (Svirydzenka, 2016). Consequently, the accumulation of capital depends on financial development. Yet, financial development may be undermined and be less relevant if there are large inefficiencies in the financial system because of the misallocation of capital or if there is little to no access to financial markets and institutions. Furthermore, the marginal returns to growth from further financial development diminish at high levels of financial development—that is, there is a significant, bell-shaped, relationship between financial development and growth (Sahay et al., 2015). These non-linear relationships may be present for the impact of public investment on private investment.

financial development tend to have high crowding-in. We again divide the sample into those above and below the median level of financial development across time. The results are reported in table 5. The estimated effect of public investment on private investment is positive and statistically significant for the low levels of financial development (below median). When financial development is low, the cumulative effect of public investment on private investment increases and reaches a value of 3.2 after two years. The crowding-in effect turns insignificant after five years. For the high levels of financial development, the crowding-in effect is not statistically significant, and the estimated coefficients are generally lower than those obtained with the low level of financial development sample.

openness (See annex D). We divide the sample between those above and below the median level of capital account openness. Economies with more restrictive capital account openness have positive and significant crowding-in of private investment. The effect is large, with a peak multiplier of about 4.1 in year three ( _h=2_ ).

development often face higher borrowing costs and, thus, a lower return on investment, which makes private investment less profitable. Therefore, more public investment could increase the incentive to invest as it may increase the expected return on investment and alleviate the risk of investing in countries with a low level of financial development. It is worth noting that these results do not provide evidence that there is a statistical difference 16
only find that there is clear evidence of crowding-in when financial development is low.

**Table 5:**

||(1)|(2)|(3)|(4)|(5)|
|---|---|---|---|---|---|
||C<br>|umulative M<br>|ultipliers (ho<br>|rizon h in ye<br>|ars)<br>|
||h=0|h=1|h=2|h=3|h=4|
|||<br>|Below Media<br>|n<br>||
|Change in government investment|2.799*|3.189*|3.007**|2.768*|1.217|
||(1.498)|(1.730)|(1.370)|(1.516)|(2.084)|
|Observations|1,640|1,601|1,570|1,533|1,496|
|F-statistic|4.719|4.213|4.686|5.629|4.829|
|KP Underid stat|0.0248|0.0335|0.0244|0.0134|0.0215|
|No. of countries|82|82|82|82|82|
|||<br>|Above Media<br>|n<br>||
|Change in government investment|0.269|0.878|1.130|0.702|0.318|
||(0.635)|(1.167)|(1.487)|(1.413)|(1.687)|
|Observations|1,658|1,593|1,522|1,456|1,390|
|F-statistic|6.267|5.523|5.308|5.567|5.167|
|KP Underid stat|0.0183|0.0264|0.0292|0.0258|0.0316|
|No. of countries|80|80|78|77|75|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence a ́ la Boehm (2020). All estimations include country and year effects and one year lagged dependent variable. “KP” is Kleibergen and Paap underidentification test.

# 5 Robustness and validity of the instrument

In this section we conduct a battery of robustness exercises by re-estimating our empirical model with alternative instruments in bilateral and multilateral loans. We also use alternative model specifications to check for the robustness of our main findings. Finally, we use an alternative estimator in _kinky_ least squares to test the robustness and validity of our results.<sup>14</sup>

> 14 In annex D we look at the impact of alternative censoring rules on our main instrumental variable.

17
# 5.1 Alternative instruments

Table 6 presents the results for the case of alternative instrumental variable, where we employ multilateral and bilateral loans. The results show that a dollar increase in public investment increases private investment by about 2 dollars on impact in the case where predicted disbursements from multilateral creditors is used as instrument for public investment (Panel A, Table 6).

**Table 6: The response of private investment to government investment, alternative instruments**

||(1)|(2)|(3)|(4)|(5)|
|---|---|---|---|---|---|
||Cu<br>|mulative Mult<br>|ipliers (horiz<br>|on h in year<br>|s)<br>|
||h=0|h=1|h=2|h=3|h=4|
|||Panel A: M|ultilateral N|= 109||
|Change in government investment|2.146**|2.045**|2.476**|1.708|1.622|
||(0.860)|(0.802)|(1.216)|(1.365)|(1.493)|
|Observations|3,429|3,344|3,237|3,131|3,024|
|F-statistic|7.405|7.501|6.976|7.118|8.106|
|KP Underid stat|0.0110|0.00998|0.0128|0.0119|0.00733|

|||Panel B:|Bilateral N =|109||
|---|---|---|---|---|---|
|Change in government investment|1.593|1.280|2.356|2.983*|2.490|
||(1.076)|(0.883)|(1.698)|(1.786)|(1.640)|
|Observations|3,404|3,317|3,211|3,106|3,000|
|F-statistic|5.185|6.048|5.094|5.928|7.929|
|KP Underid stat|0.0267|0.0163|0.0264|0.0165|0.00637|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence a ́ la Boehm (2020). All estimations include country and year fixed effects and one year lagged dependent variable. “KP” is Kleibergen and Paap underidentification test.

Moreover, the crowding-in effect after one year of the public investment shock (h=1) is about 2.5 and is statistically significant at the 5 percent level. Albeit slightly larger than the crowding-in effect from our main results, the evidence of crowding-in of private investment by public investment is consistent with the main results in the previous section. For longer horizons, however, the multiplier is statistically not different from zero. In the case of using predicted disbursements from bilateral loans only one horizon estimate (h = 2) is found to be statistically significant, and the effective F-statistics are lower still. Our results are somewhat in line with Kraay (2014) who finds a greater strength of identification from 18
multilateral loans than bilateral based on the logic that multilateral loans are a greater part of the loan-level dataset sample and are disbursed more slowly.

# 5.2 Accounting for global shocks

financial cycle suggest that investment across countries may be subject to common global shocks (Miranda-Agrippino and Rey, 2022; Kose et al., 2009). While time fixed effects control for common shocks in the main results, as an alternative we include cross-sectional averages of public and private investment in our regressions. Based on guidance from Chudik et al. (2017) we include three lags of the cross-sectional averages. The multipliers presented in table 7 are consistent with the multiplier estimated in our main results, where time effect was used to account for common shocks. Specifically, we find a baseline estimate of 1.6, which rises to 2.3 after three years.

**Table 7:** The response of private investment to government investment, cross sectional dependence

||(1)<br>|(2)<br> <br>|(3)<br>Cumulative M<br>|(4)<br>ultipliers (hor<br>|(5)<br>izon h in years<br>|(6)<br>)<br>|
|---|---|---|---|---|---|---|
||Baseline|h=0|h=1|h=2|h=3|h=4|
|Change in government investment|1.558**|1.581**|2.237***|2.373***|2.300***|1.420|
||(0.623)|(0.658)|(0.863)|(0.782)|(0.815)|(1.092)|
|Observations|3,245|3,223|3,116|3,010|2,903|2,796|
|F-statistic|13.61|10.78|10.05|10.67|13.98|12.90|
|KP Underid stat|0.00115|0.00259|0.00359|0.00267|0.000847|0.00122|
|No. of countries|109|109|109|109|109|109|

_Notes_ : *** p <0.01, ** p <0.05, * p <0.1. Dependent variable is change in private investment to lagged GDP. Robust standard errors in parentheses are Driscroll-Kraay standard errors to control for the presence of error cross-sectional dependence á la Boehm (2020). All estimations include country and year fixed-effects and one year lag of the dependent variable. “KP” is Kleibergen and Paap underidentification test.

# 5.3 Exogeneity of the instrument

So far, we have estimated the effect of public investment on private investment using instrumental variable approach. Nonetheless, our results above rely on the assumption that our selected instrument satisfies the exclusion restriction for all endogeneity correlation between the error term and public investment. Importantly, the associated F-statistics for the IV are often marginally greater than the rule of thumb of 10 and in several cases smaller than 10. This suggests a weak instruments problem and challenges the assumption that our IV strictly satisfies the exclusion restrictions. At a more intuitive level, we are recycling an instrumental variable from Kraay (2014), where the instrument was used to identify the exogenous shocks in government spending. In our case, we are regressing private investment on public investment (a subcomponent of public spending) and are using 19
predicted disbursements as an instrument. It may, however, be the case that noninvestment government spending affects private investment, and if it is not controlled for, could lead to a violation of the exclusion restriction. The challenge, however, is that noninvestment government spending is in itself endogenous, which raises other empirical roadblocks including searching for another instrument. In this section, with appropriate assumptions, we apply a novel instrument-free estimator in kinky least squares (KLS) developed by Kiviet (2013, 2020, 2022) as both an alternative estimator for robustness checks of our results and to formally test the exclusion restriction.

Our IV estimates produce a crowding-in effect of private investment that are larger than the OLS estimates. This suggests the presence of a combination of measurement errors and potential countercyclicality of public investment might be the dominate endogeneity issues in our case.<sup>15</sup> In fact, the issue of measurement errors is likely the dominant endogeneity issue given that historically there has been evidence of the procyclicality of public investment in developing countries, although there are cases where countercyclicality of public investment is observed (see, for example, Galeano et al., 2021), which will instead bias the OLS estimates upward. Furthermore, economic theory often predicts the crowdingin of private investment by productive government investment (Berg et al., 2019). In this sense, an empirical estimate of a negative or near-zero effect from the OLS estimator will be at odds with predictions from standard economic theory. This suggests that the true impact of public investment on private investment is positive, and that the OLS estimate may be biased downwards. Consequently, it is not unreasonable to assume a prior negative correlation between the error term and public investment governed by the presence of measurement errors. To what degree measurement errors can explain the large difference between the OLS and IV estimates, however, remains an open question.

The KLS allows us to check the validity of our instrument as well as the crowding-in effect for different degrees (or sizes) of the negative correlation between the error term and the endogenous variable. More precisely, for identification of the regression coefficients, the KLS can restrict the admissible correlation of the regressor with the error term within plausible bounds. Here, no instruments are needed. Rather, the bias of the OLS estimator is analytically corrected for all values on a grid of endogeneity correlations (Kripfganz and Kiviet, 2021). Consequently, for a narrow and plausible range of a postulated endogeneity correlations, the KLS confidence intervals are—as a general rule—narrower than those from 2SLS (Kripfganz and Kiviet, 2021). The latter point is especially true if there is the possibility of weak instruments, which might be the case for our IV given the F-statistics reported. Finally, and perhaps more importantly, the KLS approach enables testing of any potential exclusion restrictions, which is not possible under a just-identified model when the 2SLS estimator is applied.

> 15 Eden and Kraay (2014) allude to similar sources of endogeneity.

20
# The KLS estimator is given by:

# _βKLS_ = _βOLS_ − Bias Correction( _ρ_ ) _,_

where _βOLS_ is the standard OLS estimator, which is inconsistent when _ρ_ correlation coefficient between public investment and the error term is not equal to zero. The bias correction is analytically described in Kiviet (2020, 2022); Kripfganz and Kiviet (2021).<sup>16</sup> The KLS estimator requires specifying admissible correlation values of the regressor (public investment) with the error term within plausible bounds. Hence, to estimate _βKLS_ , we postulate values for _ρ_ . Under our reasonable assumption of the presence of measurement error, we specify _ρ_ to lie between [-0.7, 0.1]. We include a low positive correlation coefficient (that is, 0.1) to allow for the case that government investment is procyclical. Notice that the interval allows us to conduct sensitivity analysis on the degree or severity of measurement errors.

We re-estimate equation (3.1) in Jorda (2005) projection form using the KLS approach. Figures 3 and 4 present the KLS estimates of the crowding-in effect of public investment and the test for the exclusion restriction for correlation coefficients under our assumption of _ρ_ ∈ [−0 _._ 7 _,_ 0 _._ 1], respectively. We report estimates for each horizon. To elucidate the results, we present our finding diagrammatically.

of public investment on private investment for a wide range of our specified coefficient of correlation for all horizons. For example, in panel A, the KLS reports a positive and statistically significant impact of public investment at the 5% level of significance for _ρ_ ∈ [−0 _._ 7 _,_ −0 _._ 1], although the effect declines with larger _ρ_ values. In panel E, the positive impact of public investment on private investment holds in the KLS estimates for _ρ_ up to about 0.03. In all cases, we notice that the KLS estimate overlaps with the IV and for longer horizons ( _h >_ 0), the KLS point estimates coincide with the IV point estimates. Turning to test of exclusion restriction in figure 4, we observe that only for large negative endogeneity correlations (that is, around _ρ <_ −0 _._ 5 in the case of panel A) do we not reject the null hypothesis that the instruments are validly excluded from the model at the 5% level. Nonetheless, the validity of instruments tends to hold for smaller negative endogeneity correlation in the case of longer horizons and even for smaller positive endogeneity correlation (panel F). In summary, while challenges of weak instrument are present in our model, there is conditional evidence that our instrument is valid for reasonable assumptions of the direction and degree of endogeneity, particularly over longer horizons.

> 16 See Kripfganz and Kiviet (2021) and Kiviet (2020, 2022) for detailed discussion on the analytics of the bias correction term.

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F(K )=C (kK ) ~~=—~~ a CD ec )-(K ) )+ (kK)
FOC for foreign debt: There are several observations from the equation describing the optimal marginal return to public capital. First, it is evident that an assumption that the marginal return to public capital is equal to the marginal return to private capital is stringent and is a special case of equation (6.8). Specifically, this scenario only arises when public and private investment are perfect substitutes so that is equal to . Second, in the presence capital market distortions like distortionary taxes captured by KKgg,KKpp KKpp,KKpp , we observe that the term in the square FF FF bracket is greater than zero.<sup>18</sup> Here, the question of misallocation of resource and the power ττ> 0 of the government to effectively intervene with its own investment decision arise. More precisely, in this case, the economy provides too much current consumption at the expense of too little investment for the future. That is, it is cheaper to borrow to finance consumption than borrow to invest due to the wedge created by . Thus, depending on the sign of in equation (6.8), we can answer the question of how much power the government can marshal KKpp,KKgg ττ FF to optimally counterbalance the underinvestment with increases in government investment (Ogura and Yohe, 1977). Given the benefit of hindsight and uncovering that public and private investment are Edgeworth complements in our empirical estimation in the previous Section, we focus on the complementarity case to answer this question. Notice that for any degree of Edgeworth complementarity (i.e., > 0 ), an increase in public investment will induce a rise in private investment by increasing its marginal product; KKpp,KKgg FF see equation (2.6). Consequently, public investment becomes an effective tool to help counterbalance the private sector underinvestment induced by the imperfect risk spreading in the capital market. This, however, has an implication for the optimal marginal return to <u>p g</u> − public capital. That is, the last term in equation (6.8) is negative (i.e., � FFKK p,KK rr<sup>∗</sup> +δδ ) suggesting that in the case where capital market distortions exists and private FFKKpp,KKpp 1−ττ investment is discouraged, public investments that crowd-in private investment should be (rr<sup>∗</sup> + δδ)�< 0

> 17 For exposition purposes, we provide the details of the derivation of equation (7.8) in Annex B. 18 Notice that in our case distortionary taxes were used to demonstrate the implications of capital market distortions in our framework. However, even in the absence of distortionary taxes, other imperfect capital market conditions, such as access to debt with lower interest rates by governments, can drive a similar wedge between the rates faced by private agents versus the government.

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at lower rates of return compared to the scenario where capital markets are perfect and there are no distortions ( , where . KKgg The contrasting conclusion is straightforward in that in the case where market “distortions” ττ= 0) FF = rr<sup>∗</sup> + δδ encourage extra incentives for private investment. For example, consider the scenario where the government provides subsidies to firms (i.e., and public and private investment are Edgeworth complements. In this case, the last term in equation (6.8) is positive (i.e., <u>p g</u> ). In this case, the marginal return of public investment should be ττ< 0) � FFKK p,KK rr<sup>∗</sup> +δδ expected to be higher than when markets have no distortions.FFKKpp,KKpp 1−ττ −(rr<sup>∗</sup> + δδ)�> 0 Finally, it is worth mentioning that these conclusions are not intended to discount the role of how the correction of capital market distortions can be the first best solution in addressing underinvestment. Instead, it highlights that the latter, which takes effective regulations and reforms to correct, can be carried out in conjunction with increased public investment. Indeed, our results in section 4.2 show that policy reforms along the line of better corruption control can also enhance the crowding-in effect of public investment on private investment.

# 7 Conclusion

Developing countries face a widening investment gap estimated at $3 trillion per year to achieve the Sustainable Development Goals. Yet, private investment growth remains weak in the post-pandemic high interest rate environment. This paper estimates the effect of public investment on private investment in a large panel of 109 developing countries over the period 1980-2019. In our setup, the parameter of interest simultaneously captures the crowding-in (-out) of private investment by public investment and complementarity (substitutability) between public and private investment. To identify the impact, we update and extend predicted loan disbursements from official loans as an instrumental variable à la Kraay (2014).

_Edgeworth complement_ to private investment in that an increase in the former raises the marginal productivity of private investment. Second, the complementarity implies crowding-in of private investment by public investment such that an extra dollar of public investment raises private investment by 1.6 dollars. Over time, the cumulative multiplier rises to a peak of 2.4 dollars. This crowding-in effect holds true for low-income countries and Sub-Saharan Africa—economies where investment needs are largest. We find that the cumulative effect of crowding-in is larger in these subgroups over time than for all EMDEs. Moreover, we find evidence that public investment is more effective in crowding-in private investment in countries with strong corruption control Third, when we embed our empirical results into a model with capital market distortions, we demonstrate that public investment should be allowed a lower rate of return than under perfect capital markets. From a policy perspective, our results suggest that public investment, in conjunction with policy efforts and regulations 25
to correct capital market distortions, can be used to address underinvestment induced by imperfect capital markets. Nonetheless, any scale-up in investment would be more effective in an environment where corruption is well-controlled.

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