Lockdown Accounting

Charles Gottlieb; Jan Grobovšek; Markus Poschke; Fernando Saltiel

doi:10.1515/bejm-2020-0251

Published by De Gruyter February 9, 2021

Lockdown Accounting

Charles Gottlieb , Jan Grobovšek , Markus Poschke and Fernando Saltiel

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2020-0251

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Abstract

We use an accounting framework to evaluate the aggregate impact of a common lockdown policy for 85 countries. We find that poorer countries devote more labor to essential activities that are unaffected by the lockdown, while richer countries can more easily substitute non-essential employment with work from home. The lockdown generates an employment response that is U-shaped in income: it drops by 32% in the poorest quintile of the distribution, by 36% in the middle quintile, and by 31% in the richest quintile. Annualized GDP declines by 39% in the bottom three quintiles and by 31% in the richest quintile. Agriculture, an essential sector, is key in sustaining employment and economic activity in poorer countries.

Keywords: Covid-19; structural change; work from home; lockdown

JEL Classification: O11; O14; J21

Corresponding author: Charles Gottlieb, University of St. Gallen, Sankt Gallen, Switzerland, E-mail: charles.gottlieb@unisg.ch

Funding source: Leverhulme 10.13039/501100000275

Funding source: University of St. Gallen 10.13039/100009572

Funding source: ESRC-DFID

Award Identifier / Grant number: ES/L012499/1

Acknowledgment

We thank Joel Frischknecht for excellent research assistance.

Research Funding: Research funding from Leverhulme, GFF Fund of the University of St. Gallen and ESRC-DFID (ES/L012499/1) is gratefully acknowledged.

A Appendix

A.1 Model Derivation

Here we derive the model that underpins Equation (2) that is used to calculate GDP relative to trend. Consider a closed economy where gross output in sector i is

g i = z i x i θ i ∏ j = 1 I m i j γ i j ,

with parameters θ i ∈ [ 0 , 1 ] and γ i j ∈ [ 0 , 1 ] such that θ i + ∑ j = 1 I γ i j = 1 . The sector’s TFP is z _i and there are two types of production factors: x i is a bundle of the sector’s human and physical capital and m _ij is intermediate consumption of goods from sector j. Let p _i denote the price of output of sector i. Assuming perfect competition, profit maximization with respect to intermediate inputs implies p j m i j = γ i j g i j , ∀ i , j . In particular, the sector’s value added equals

V i ≡ p i g i − ∑ j = 1 I p j m i j = θ i p i g i .

The representative household chooses final consumption c _i to maximize utility

Y = ∏ s = 1 I c i ϕ i

with parameters ϕ i ∈ [ 0 , 1 ] such that ∑ i = 1 I ϕ i = 1 . The optimality condition is hence p i c i = ϕ i Y , ∀ i . The product market clears according to c i + ∑ j = 1 I m j i = g i , ∀i.

Let Y denote real GDP and P ≡ 1 its normalized price so that P Y = Y = ∑ i = 1 I p i c i . In equilibrium, it can be shown that GDP is

Y ∝ ∏ i = 1 I ( z i x i θ i ) d i

with parameter vector d = ϕ ′ ( I − Γ ) − 1 where I is the identity matrix and Γ is a matrix with elements γ i j . In particular, d _i equals the Domar weight of sector i, d i = p i y i Y . If z _i is constant and the only exogenous shock occurs through the supply of x _i, then Y ∝ ∏ i = 1 I x i ν i where ν i = θ i d i = V i Y equals the (constant) aggregate value added share of sector i in the economy. GDP relative to trend is then y ≡ Y ˜ Y = ∏ i = 1 I ( x ˜ i x i ) v i where x ˜ i / x i denotes the relative utilization of factor x _i following the shock. Our final assumption is that capital and labor (l) enter homothetically into x and that they change in equal proportion following the shock, resulting in

y ≡ Y ˜ Y = ∏ i = 1 I ( l ˜ i l i ) v i .

Economies can differ in their underlying parameters, which implies that v _i is country-specific.

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Received: 2020-11-20

Accepted: 2021-01-11

Published Online: 2021-02-09

Lockdown Accounting

Abstract

Acknowledgment

A Appendix

A.1 Model Derivation

References

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