What is the growth impact of an increase in the rate of public investment spending? And in particular, how does this depend on the efficiency of public investment spending? These questions have emerged in the debate about the need to bolster public investment to exit a low-growth, high-unemployment conundrum in Europe (e.g. Summers 2014, Teulings and Baldwin 2014, de Grauwe 2015). They have a longer history in the context of the effort to generate sustained growth in developing countries through public investment.^{1} In an influential paper, Pritchett (2000) argues that it is incorrect to consider that one dollar spent on public investment always yields one dollar of public capital. He argues instead that spending one dollar typically yields only a fraction in actual public capital and, plausibly, that the growth impact of additional investment spending will be lower countries that are inefficient in this sense. In the same vein, when discussing the need for a big push to public investment in the October 2014 WEO [4], the IMF (2014) argues that when “the efficiency of the public investment process is relatively low – so that project selection and execution are poor and only a fraction of the amount invested is converted into productive capital stock – increased public investment leads to more limited long-term output gains.”

Efficiency, defined as the ratio between the actual increment of public capital and the amount spent (Pritchett 2000, Caselli 2005), has been incorporated in macroeconomic models (e.g. Berg *et al* 2013). In this context, we came across an initially puzzling theoretical *invariance* result – the growth impact of public investment spending is not higher in countries with a (permanently) higher level of public investment efficiency (Buffie *et al* 2012). This seemed counterintuitive as well as being inconsistent with the conclusions of Pritchett (2000). However, in a recent paper, we have come to the view that this result is generally correct and that it has important policy implications (Berg *et al.* 2015).

## The invariance result

The essential intuition for the *invariance* result comes from the fact that the marginal contribution of an additional dollar of investment spending to output can be broken down into a product of two components:

- the amount of capital actually installed; and
- the marginal productivity of that capital.

Low public investment efficiency implies that less than a dollar of capital is installed. However, a country with (permanently) low efficiency has been installing less capital forever and as a result has a lower public capital stock. With the standard assumption of decreasing returns to any one factor of production, this implies a higher marginal productivity of public capital. These two effects go in opposite directions in terms of the effect of additional investment spending on output. Indeed, for the standard Cobb-Douglas case, the effects exactly offset – high-efficiency and low-efficiency countries have the same growth impact from additional public investment spending.^{2}

Some further intuition may help. Suppose we are assessing a particular country, knowing its history of its GDP and public investment spending, which we have considered to be 100% efficient. We can then judge the potential output gains from further public investment, that is, the rate of return to further investment spending. Suppose now we visit the country and are obliged to revise down our view of efficiency, say to 50%, with an understanding that things have been bad at the ministry of planning for as long as anyone can remember. How should we adjust our forecast of the expected gains from further investment? On the whole, we should not. Why not? Because there are two offsetting effects from our revision to estimated efficiency. On the one hand, if a further $100 is spent, only $50 in public capital will be installed. On the other, somehow this country has been making do with half as much public capital (as a share of GDP), and public capital is twice as scarce, as we had thought prior to our trip. Come to think of it, the roads were a lot worse than we thought they would be, too. So, with the standard Cobb-Douglas assumption, the rate of return to the capital that will actually be installed is twice as high as we thought. The two effects cancel each other out.

The logic of the *invariance* result is powerful and fairly general and it speaks to different ways of thinking about public investment and development. One approach emphasises the need to spend resources where they can be used well. Another emphasises the need to invest where the need is greatest. Our simple model illustrates that both approaches have a point. And it illustrates further that different levels of efficiency have two offsetting effects – one on the marginal product of capital, and one on how much capital is built with a given expenditure.

## Some empirical underpinning

While our argument is essentially theoretical, it is supported by the empirical relationship between measures of the output impact of public capital and measures of efficiency. The coefficient of a regression of (the logarithm of) the level of GDP per capita on the public capital stock country-by-country (controlling for private capital) is a measure of the growth effect of public investment. Figure 1 shows a scatter of the estimated coefficients against the public investment management index (PIMI [5]), a direct measure of investment efficiency calculated for each country (see Dabla Norris *et al.* 2012 for a discussion). As the figure shows, there is no significant correlation between the efficiency measure and the size of the growth impact of public investment, a finding in line with the invariance result.

**Figure 1**. Efficiency and the output impact of public capital stock

*Notes*: In the chart beta is the country-specific estimated coefficient obtained from a regression of the log of real per capita GDP on the log of the measured (i.e. unadjusted for efficiency) real public capital stock per capita, controlling for the log of real private capital stock per capita. The empirical model is estimated by the Common Correlated Effects Mean Group (CCEMG) estimator Pesaran (2006) on a balanced panel of 102 developing countries, with yearly data over the period 1970-2011. This estimator has been used in this context by Calderon *et al* (2015). GDP data are from the Penn World Tables (7.1), capital stock data are measured capital stocks (calculated as the discounted sum of investment spending), from Gupta *et al* (2014). The chart reports the betas and the corresponding values of the PIMI for 54 countries for which data on the PIMI are available (Dabla Norris *et al* 2012).

## Investing in investing

The conclusion that public investment increases growth the same amount in efficient and inefficient countries does not mean that efficiency is unimportant. Quite the contrary. *Changes* in efficiency can matter greatly for growth. For example, an increase in efficiency relative to the past increases the output effect of public investment. Increases might be associated with structural reforms or ‘investing in investing’ (Collier 2007), in this context investing in investment efficiency. The rate of return to increased spending on raising efficiency may be higher – possibly much higher – than on raising the *level* of investment spending itself. Along the same lines, decreases in efficiency that might result from investment surges that overwhelm administrative and implementation capacity could be critical (see Presbitero 2016 for a discussion of absorptive capacity and its relationship with investment efficiency). However, much discussion and most measures of public investment inefficiency are static, and in these cases the lessons from the invariance result need to be kept in mind. Moreover, changes in public investment efficiency are likely to be slow (Pritchett *et al.* 2013), so waiting for them to occur may not be a viable strategy in some cases.

## Implications

Our main result is that in a simple benchmark model, cross-country differences in the level of public investment efficiency do not matter for the growth impact of increases in public investment spending.

This is no mathematical curiosity or technical detail. Countries are poor for many reasons, and our work discusses two important ones: the scarcity of public capital, and the weak institutions that make it difficult to convert public investment spending into usable public capital. As we show, public capital scarcity and inefficiency are likely to be inversely related, and this has important implications for policy. Most importantly, blanket recommendations that inefficient countries will likely see lower growth impact public investment spending (as in Pritchett 2000 and IMF 2014) need to be reconsidered.

We are not saying that low-efficiency countries should necessarily increase public investment. Neither would we say that high-efficiency countries can expect higher output effects of increased investment. Ultimately, there is no short-cut – the merits of additional public investment spending in a particular case will depend on the marginal product of the resulting capital, efficiency, the cost of financing, the ‘fiscal space’, and more generally the discretionary effects of taxation required to finance the investment, the prospects for and costs of required operations and maintenance, and the risks of debt distress, among other factors.

## References

Berg A, R Portillo, S C S Yang and L F Zanna (2013) “Public investment in resource-abundant developing countries”, *IMF Economic Review*, 61(1):92–129.

Berg A, E F Buffie, C Pattillo, R Portillo, A F Presbitero and L F Zanna (2015) “Some misconceptions about public investment efficiency and growth [6]”, IMF Working Paper, No. 15/272.

Buffie E F, R Portillo, L F Zanna, C A Pattillo and A Berg (2012) “Public investment, growth, and debt sustainability: Putting together the pieces”, IMF Working Papers 12/144.

Calderon, C, E Moral-Benito and L Serven (2015) “Is infrastructure capital productive? A dynamic heterogeneous approach”, *Journal of Applied Econometrics*, 30(2):177–198.

Caselli, F (2005) “Accounting for cross-country income differences”, In *Handbook of Economic Growth*, P Aghion and S N Durlauf (eds), 1(4): 679–741.

Collier, P (2007) *The bottom billion*, New York: Oxford University Press.

Dabla-Norris, E, J Brumby, A Kyobe, Z Mills and C Papageorgiou (2012) “Investing in public investment: An index of public investment efficiency”, *Journal of Economic Growth,* 17(3): 235–266.

De Grauwe, P. (2015), “Secular stagnation in the Eurozone”, VoxEU.org, 30 January. http://www.voxeu.org/article/secular-stagnation-eurozone [7]

Gupta, S, A Kangur, C Papageorgiou and A Wane (2014) “Efficiency-adjusted public capital and growth”, *World Development*, 57:164–178.

IMF (2014) *World Economic Outlook – Legacies, Clouds, Uncertainties*. Washington D.C.: International Monetary Fund.

Pesaran, M H (2006) “Estimation and inference in large heterogeneous panels with a multifactor error structure”, *Econometrica*, 74(4): 967–1012.

Presbitero, A. (2016), "Too much and too fast? Public investment scaling-up and absorptive capacity", *Journal of Development Economics,* forthcoming.

Pritchett, L (2000) “The tyranny of concepts: CUDIE (Cumulated, Depreciated, Investment Effort) is not capital”, *Journal of Economic Growth*, 5: 361-384.

Pritchett L, M Woolcock and M Andrews (2013) “Looking like a state: Techniques of persistent failure in state capability for implementation”, *The Journal of Development Studies,* 49(1):1–18.

Summers, L. (2014), “Reflections on the new 'Secular Stagnation hypothesis'”, VoxEU.org, 30 October. http://www.voxeu.org/article/larry-summers-secular-stagnation [8]

Teulings, C. and R. Baldwin (2014), “Introduction” in *Secular Stagnation: Facts, Causes and Cures*, a VoxEU.org eBook. http://www.voxeu.org/content/secular-stagnation-facts-causes-and-cures [9]

## Footnotes

1 We abstract from aggregate demand effects, focusing on public investment per se rather than government spending in general.

2 See Berg *et al* 2015, for a full technical discussion. The exact invariance result depends on the Cobb-Douglas specification for the production function. However, it is not a knife-edge result; rather, it is approximately true if the production function is Cobb-Douglas, as some empirical evidence suggests (Calderon *et al.* 2015). Moreover, careful treatments of private capital, adjustment costs, and different definitions of inefficiency do not change this broad conclusion. Finally, if, as is sometimes argued (e.g. in IMF 2014) public and private capital are complements—as captured by a CES production function with an elasticity of substitution for inputs smaller than one – then the scarcity effect outweighs the direct efficiency effect and low-efficiency countries can expect a *higher* output impact.