make the budget constraint variable. These technical features are further described in the following sections, which describe IPF step‐by‐step.

# _Constructing the IPF Indices_

The first step of IPF is to identify the set of indicators that will be combined to construct the social‐environmental and financial‐economic indices. The selection of variables – or project comparison indicators – may differ amongst application contexts based on government policy goals (e.g., particular sectoral, economic, social, and environmental aims) and stakeholder consultation. For explanatory purposes, however, we will discuss the IPF index construction as performed in the first conceptualization of IPF in Vietnam and initial pilot test in Panama.<sup>10</sup> The selection of variables seeks to preserve the principle of parsimony. Accordingly, this methodology relies on and requires a minimum level of relevant information to compare expected outcomes of alternative infrastructure investments. Multiple variables are selected to reflect different aspects of expected performance in two composite indicators, the Social and Environmental Index (SEI) and the Financial and Economic Index (FEI), each built on quantitative and transformed qualitative variables combined via an additive model.<sup>11</sup> To condense dissimilar data types and scales of measurement into indices, three data transformations are required. One must (a) transform qualitative data and ordinal quantitative data into usable scalar data, wherein the intervals between values reflect degrees of difference; (b) standardize criteria measurements to a common scale; and (c) establish weights for each criterion in the additive model.

The transformation of categorical and ordinal qualitative and quantitative data into usable numerical data may be done using the Alternating Least Squares Optimal Scaling (ALSOS) algorithm, a widely accepted transformation approach. Within a quantified categorical variable, the numbers assigned by the ALSOS algorithm to each category reflect the distance _between_ categories, revealing the implicit metric of the variable (Perreault & Young, 1976).<sup>12</sup> Numerical values are thereafter standardized via a typical standardization formula to transform the measurements to have a mean value of zero and unit variance. The standard score � of a raw score � is where � is the sample mean and � is the standard deviation of the variable _j_ for project _i_ .

> 10. The work in Vietnam is described in detail in Mandri‐Perrott, Marcelo, and Haddon, 2014. At the request of Vietnam's Ministry of Planning and Investment (MPI), the World Bank piloted the IPF to prioritize and select public infrastructure investments. One of the objectives of the IPF in this case was to provide the Government of Vietnam (GoV) with the means to operationalize the guidelines and requirements of the Public Investment Law (PIML) in an open and transparent manner. The Pilot Test covered over projects in three sectors: transport, irrigation and urban.

> 11. To generate a valid numerical expression for the composite indices, it is required that qualitative information is transformed into quantitative variables.

> 12. Statistical software such as SPSS and SAS include routines to easily perform transformations of qualitative variables into numerical variables.

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