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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.

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