Human Capital Index (HCI) – from uncertainty to robustness of comparisons

ABSTRACT

In order to monitor progress in human development within and between countries and over time, several simple and composite indices have been developed and are regularly used, particularly in public policy decision-making. In 2019, the World Bank adopted an index developed by Kraay (2018), the Human Capital Index (HCI).It combines demographic, education, and health dimensions on a complementary statistical and econometric basis. It is used by the World Bank in the area of human development for monitoring and comparison purposes, in time and space. Beyond the debate about the construction of the index itself in terms of weighting and aggregation, the $HCI$ is subject to statistical and econometric uncertainties that are not adequately captured by comparisons and are therefore, not robust.In this article, we propose a systematic approach taking into account these simultaneous uncertainties using a projection method. We present its practical implementation to construct confidence intervals to the $HCI$ that reflect these uncertainties. It appears that if confidence intervals overlap for two countries or for the same country over time, then comparisons would be inconclusive regardless of the point estimates.

KEYWORDS:

• Human Capital Index (HCI)
• Uncertainty
• Robustness
• Comparisons
• Projection method

JEL CLASSIFICATION:

• C18
• I15
• I25

Disclosure statement

No potential conflict of interest was reportedby the authors.

Notes

¹ We are aware that in the construction of the index itself, the components may have interactions between them as pointed out by OECD (2006), Paruolo, Saisana, and Saltelli (2013), Greco et al. (2019) and Otoiu et al. (2021). Indeed, the problem of uncertainty that we consider in this article remains even if the problem of interaction between the variables considered in the construction of the composite index did not occur and even if it were taken into account.

² See Table A1 in Appendix.

³ See Kraay (2018) Section A2.2 for details on the methodology to determine the adjustment of education quality through harmonization of multinational tests.

⁴ Cf. https://data.unicef.org/topic/child-survival/under-five-mortality/.

⁵ Or at least the non-availability of a variance-covariance matrix for the estimators of these components.

⁶ These authors only consider one dimension in the health component.

⁷ See in Section 2.1 the origin of the values of $\varphi$ and ${\gamma }_{ASR}$ used by Kraay (2018).

⁸ See Figure 14 p. 25 of Pasquini and Rosati (2020).

⁹ The confidence region is rectangular since it is impossible to have an estimate of the variance-covariance matrix relative to the estimators of the eight parameters/variables considered. If such a matrix is available, ellipsoidal confidence regions can be constructed and retained at this level. For more details see the comment of Kraay (2018) (P. 51) and the solution proposed in Abdelkhalek and Dufour (1998).

¹⁰ The mathematical formulation of this system is detailed below.

¹¹ The system we propose here is general and remains unchanged even in the case where one or more uncertainties disappear (the lower and upper bounds would then be equal for the uncertainty concerned). In the case of correlations between the statistical measures of $TME$, $ESY$, $TS$, $ASR$ and $NSR$ and$/$ or the estimators of the parameters $\varphi$, ${\gamma }_{ASR}$ and ${\gamma }_{Stunting}$ these conditions would be summarized in one or more quadratic forms, functions of the estimates of variance-covariance matrices (See Davidson and MacKinnon 2004, 189). These quadratic forms would then represent ellipsoidal confidence regions instead of the ones we have considered as rectangular. The numerical resolution would not be altered and could even be simplified.

¹² For a detailed definition of the indicators used in the calculation of the $HCI$ and to access the raw database see https://databank.banquemondiale.org/source/human-capital-index.

¹³ See https://donnees.banquemondiale.org/.

¹⁴ This variable could also be used for intra-regional comparisons.

¹⁵ We focused our work on the year 2020. However, it can be replicated for any year and for any number of countries or groups of countries.

¹⁶ The five variables that have been treated with this approach are: $NSR$, $ASR$, $ESY$, $TS$ and $p$.

¹⁷ This data processing was carried out with STATA software, version 16.

¹⁸ In the annexed Table A1 to A4, we reproduce the point estimates and bounds for the five sources of uncertainty varying according to the region of the 91 countries under consideration.

19 In our case, we used the GAMS software.

20 At this step, $\varphi$, ${\gamma }_{ASR}$ and ${\gamma }_{Stunting}$ are considered as variables and not as parameters.

21 Note that our method can be used several successive years for the same country. The resulting confidence intervals can be examined to conclude about the significance of the progress made on the $HCI$ over time.