Appendix 2 Long-term growth model

shIftIng geArs

The Long-term Growth Model (Loayza and Pennings 2018) is based on Solow (1956), Swan (1956), and Hevia and Loayza (2012). The economy consists of a single sector that produces output using physical capital K t and effective labor h t L t. A t denotes total factor productivity (TFP), which determines the aggregate efficiency of the economy. The relationship between inputs and output is governed by the CobbDouglas production function given by:

Yt = A t K t

1−β (h t L t)β

where β is the aggregate labor share of income, while effective labor is decomposed into human capital per worker h t and the number of workers L t. The total number of workers can be written as:

Lt = ρt ωt N t

where ρt is the participation rate, ωt is the working age to total population ratio, and N t is the total population.

Physical capital in the next period K t+1 is formed by undepreciated capital (1 − δ)K t and new investment I t:

Kt+1 = (1 − δ) K t + I t

Headline GDP growth gy, t+1 could be decomposed using a log-linear approximation into different growth fundamentals, where gx, t+1 is the growth rate of factor x from t to t+1:

gy, t+1 = gA,t+1 + β(gh, t+1 + g

ω, t+1 + g

ρ, t+1) + [1 − β _ K t _ Y t ] I t _ Y t − (1 − β)δ + gN,t+1

AppendIx 2 long-term growth model

(1 − β)/(K t/Y t) is the marginal product of capital (MPK), or the inverse of the marginal ICOR (mICOR), which determines the effectiveness of investment in boosting growth. An increase in K t/Y t, for example, from excessive investment, would decrease the MPK and increase the ICOR.

In order to solve the model, we need to input several exogenous variables:

• Parameters for β (the labor share), δ (the capital depreciation), and K0/Y0 (initial capital-to-output ratio)

• Assumption of paths for {gA,t ,gh, t,gω, t,gρ, t, gN,t,I t/Y t }

T

t=1

The model is calibrated for South Asia, as a weighted average of parameter values for three countries (Bangladesh, India, and Pakistan) that comprise more than 95 percent of the regional GDP. Specific values come from a range of data sources (as single values or historical averages), including PWT10, GTAP, ILO, WDI, World Bank Health Nutrition and Population Statistics, or country authorities. When missing, parameters or initial values are interpolated based on income group averages (the labor share for Bangladesh).

Assumptions necessary for the scenario analyses are also data driven.

Calculation of human capital decrease as a result of years of schooling loss relies on a beta version of an in-house developed tool LTGM-HC. For each of Bangladesh, India, and Pakistan, we assume that kids lose one year of schooling in 2020. This only affects kids in school in 2020: the 5-9 year old cohort, the 10-14 year old cohort, and the 15-19 year old cohort (earlier and later cohorts are by assumption unaffected).

This causes human capital (HC) growth to fall in 2025 when the 15-19 year old cohort joins the workforce (they will be ages 20-24 then). The level of HC will continue to be lower than the no-COVID-19 baseline until the age 5-9 cohort leaves the workforce—but that will be after 2050. However, the growth rate of human capital depends mostly on the HC of those people entering relative to those leaving. The 5-9 year old cohort in 2020 will join the labor force in the model by 2035, which will be the last year of slower human capital growth. From 2040 onward the new cohorts entering the labor force (who were ages 0-4 in 2020), were mostly unaffected by school closures and so will have the same HC as in the baseline. However, as the level of human capital is lower, the education of the unaffected cohorts will be marginally higher in relative terms, leading to a slightly higher growth rate of human capital in the scenario with COVID-19.

shIftIng geArs

The return to quality-adjusted education in the LTGM-HC is 12 percent. We assume a one-year fall in education of selected cohorts. However, in India, quality is 0.638, so the HC of the affected cohort falls by e 0.12×0.638 − 1=-7.4 percent. In 2025, the oldest cohort affected is about 14.5 percent of the working-age population, and so a rough estimate of the fall in HC is -7.4 × −14.5 =- 1.07 percent. However, this happens over five years as that cohort joins the workforce, and so the annual change in human capital is closer to (1 − 0.0107)1 _ 5 − 1 = −0.2 percent (very similar to the rates in the sheet). For the COVID-19 shock, this occurs for about 15 years, as the three affected cohorts join the working-age population. In Bangladesh, the education quality (scaled test scores) is 0.589, and the workforce share of the 20-24 year-old cohort in 2025 is also about 14.5 percent. Hence the effect on HC growth is e0.12×0.589 − 1 = -6.8 percent and scaling by the population share is 14.5 × −6.8 = −0.99 percent. And annual HC growth will be (1 − 0.0099)1/5 − 1 = −0.2 percent—very similar to India. In Pakistan, the quality of education is marginally lower (0.542), yielding a slightly smaller five-year fall in HC of the affected cohort (-6.3 percent). But that cohort in 2025 is a slightly larger fraction of the working age population (17 percent), and so the five-year average fall in HC growth is a very similar -0.22 percent.

In the short run, the effect of a fall in human capital growth on GDP growth is βΔgh, where β is the labor share of GDP. As above: Δgh = −0.22 and in South Asia β ≈ 0.5. This suggests that growth should fall by around 0.1-0.15 percentage points for 15 years.