with the highest levels of infrastructure coverage and quality (output) concerning their public capital stock (input). Countries positioned at the forefront of infrastructure coverage and quality, relative to their public capital stock and income per capita, serve as benchmarks for efficiency and receive a PIE-X score of 1. Other countries receive PIE-X scores ranging between 0 and 1, contingent upon their vertical distance from the frontier in comparison to peer best performers. The efficiency frontier is defined using three metrics: (i) A physical indicator that uses data on the volume of economic and social infrastructure; (ii) A survey-based indicator drawn from a World Economic Forum survey that measures business leaders' perceptions of infrastructure service quality; (iii) A hybrid indicator that gives equal weight to the physical and survey-based metrics.

The index, which is computed for more than 100 countries and includes both advanced economies and EMDEs, shows that there is a positive relationship between the efficiency of public investment and income per capita. IMF (2015) also finds that that the slope of the efficiency frontier declines as the public capital stock increases, indicating diminishing marginal returns to additional investment.

A limitation of the <mark>of PIE-X is that the physical indicator is based on volume and fails to comprehensively capture quality, while the survey-based indicator is inherently subjective.</mark> The IMF’s Public Investment Management Assessment (PIMA) evaluates the decision-making process of public investment across three key stages: (i) planning; (ii) allocation; and (iii) implementation. Each stage is assessed using five indicators. For planning, the focus is on indicators that recognize the importance of robust institutional frameworks in ensuring the fiscal sustainability of public investment and institutions that facilitate coordination across sectors, governmental levels, and between public and private entities.<sup>35</sup> For allocation, the indicators translate the idea that optimal allocation of capital spending requires a comprehensive, unified, and medium-term perspective on capital budgeting. This involves employing objective criteria and competitive procedures to appraise and select investment projects, ensuring they are directed towards the most productive sectors.<sup>36</sup> For implementation, indicators capture the necessity of executing public investment projects in a timely and cost-effective manner. This calls for institutions that ensure projects are

> 35 Thus, PIMA assesses whether countries have: (i) Fiscal principles or rules which ensure that overall levels of public investment are adequate, predictable, and sustainable; (ii) National and sectoral plans which ensure public investment decisions are based on clear and realistic priorities, cost estimates, and objectives for each sector; (iii) Central-local coordination arrangements that integrate public investment plans across levels of government, provide certainty about funding from the central government, and ensure sustainable levels of subnational borrowing; (iv) Management of public-private partnerships, which ensure effective evaluation, selection, and monitoring of PPP projects and liabilities; and (v) Regulation of infrastructure companies, which promotes open and competitive markets for the provision of infrastructure services, objective pricing of infrastructure outputs, and effective oversight of infrastructure company investment plans (IMF 2015, pp. 20-21).

> 36 Thus, PIMA assesses whether countries have: (i) Multi-year budgeting that provides transparency and predictability regarding levels of investment by ministry, program, and project over the medium term; (ii) Budget comprehensiveness that ensures that all public investment, regardless of the funding channel, is authorized by the legislature and disclosed in the budget documentation; (iii) Budget unity that ensures that decisions about individual projects take account of both their immediate capital and future operating and maintenance costs; (iv) Project appraisal that ensures that project proposals are subject to published appraisal using standard methodology and taking account of potential risks; and (v) Project selection that ensures that projects are systematically vetted, selected based on transparent criteria, and included in a pipeline of approved projects (IMF 2015, p. 21).

43