On the impact of the Covid-19 health crisis on GDP forecasting: An empirical approach

Gabriel Illanes; Ernesto Mordecki; Andrés Sosa

doi:10.3934/jdg.2022008

Article Contents

2022, Volume 9, Issue 3: 229-239. Doi: 10.3934/jdg.2022008

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On the impact of the Covid-19 health crisis on GDP forecasting: An empirical approach

1.
Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400, Montevideo, Uruguay
2.
Instituto de Estadística, Facultad de Ciencias Económicas y de Administración, Universidad de la República, Gonzalo Ramírez 1926, CP 11200, Montevideo, Uruguay

^* Corresponding author: Andrés Sosa
^* Corresponding author: Andrés Sosa

Received: November 30, 2021

Revised: January 31, 2022

Early access: April 2022

Published: July 2022

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Abstract

Statistical dependence between the GDP growth projection adjustments for the end of 2020 and the health impact of the Covid-19 pandemic is detected and quantified for a broad set of countries. A $\texttt{rate }$ that captures this health impact for each country is contrasted to the difference in GDP growth projections for the end of 2020 released in two subsequent times: 2019 (pre-pandemic) and early 2020 (post-pandemic). The difference of this two variables exhibited a significant rank correlation with the $\texttt{rate }$, and a linear model was successfully fitted, concluding that at the beginning of the pandemic health conditions played a significant role in the GDP projections.

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Mathematics Subject Classification: Primary: 62P20: ; Secondary: 91B55.

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Figure 1. Smoothed deaths per one million population (03/01/2020 - 12/31/2020)

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Figure 2. Boxplots of the variables. Left: $ \texttt{rate}$. Right: GDP growth projections for 2020

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Figure 3. Relation of the duration (in years) of the pandemic, deaths per million people due to Covid-19, and the levels of the variable rate for 30 reference countries. Data for April 2020 is shown in red, whereas data for June 2020 is shown in blue

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Figure 4. Scatter plot of the IMF GDP growth projections for 2020 generated in April 2020, and the $\texttt{rate} $. Left: countries without deaths due to the pandemic. Right: countries with positive $\texttt{rate} $. Countries are represented by their alpha-3 ISO 3166 code

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Figure 5. Scatter plot of the IMF GDP growth projections for 2020 generated in April and June 2020, and the $\texttt{rate} $. Only the 30 reference countries selected by the IMF are considered. Left: Data set for April 2020. Right: Data set for June 2020

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Figure 6. Scatter plot of the WB GDP growth projections for 2020 generated in June 2020, and the $\texttt{rate} $

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Table 1. Spearman rank correlation $ r_s $

Growth projection difference	Variable	$ r_s $	$ p $-value
$\texttt{Apr2020_IMF} - \texttt{Apr2019_IMF}$	$\texttt{Rate April} $	-0.423	2.4e-09
$\texttt{Jun2020_IMF} - \texttt{Apr2019_IMF}$	$\texttt{Rate June} $	-0.554	8.8e-04
$\texttt{Jun2020_WB} - \texttt{Dic2019_WB} $	$ \texttt{Rate June}$	-0.37	2.0e-05

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Table 2. IMF data set for April 2020, countries without deaths due to Covid-19. Residual standard error: $ 4.102 $; Adjusted R-squared: $ 0.1954 $. Significance codes: 0 $‘ \ast\ast\ast ’$; 0.001 $ ‘\ast\ast’ $; 0.01 $ ‘\ast’ $; 0.05 $‘ \ \cdot\ ’$; 0.1 $‘ \quad ’$

	Par.	Estimate	Std. Error	$ t $-value	$ {\bf{Pr}}(>\|t\|) $	Signif. codes
$ \texttt{Intercept}$	$ \hat{b} $	-5.77	1.62	-3.60	0.00140	$ \ast\ast $
$ \texttt{Apr2019_IMF}$	$ \hat{a}_1 $	0.83	0.30	2.79	0.00948	$ \ast\ast $

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Table 3. IMF data set for April 2020, countries with deaths due to Covid-19. Residual standard error: 2.079; Adjusted R-squared: 0.6417

	Par.	Estimate	Std. Error	$ t $-value	$ {\bf{Pr}}(>\|t\|) $	Signif. codes
$\texttt{Intercept} $	$ \hat{b} $	-5.43	0.63	-8.65	1.34e-14	$ \ast\ast\ast $
$\texttt{Apr2019_IMF} $	$ \hat{a}_1 $	1.12	0.20	10.22	2.0e-16	$ \ast\ast\ast $
$ \texttt{Rate April}$	$ \hat{a}_2 $	-0.65	0.10	-6.21	6.16e-09	$ \ast\ast\ast $

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Table 4. IMF data set for April 2020, only 30 reference countries. Residual standard error: 1.568; Adjusted R-squared: 0.7522

	Par.	Estimate	Std. Error	$ t $-value	$ {\bf{Pr}}(>\|t\|) $	Signif. codes
$ \texttt{Intercept}$	$ \hat{b} $	-6.39	0.99	-6.47	6.16e-07	$ \ast\ast\ast $
$\texttt{Apr2019_IMF} $	$ \hat{a}_1 $	1.25	0.18	6.86	2.28e-07	$ \ast\ast\ast $
$ \texttt{Rate April}$	$ \hat{a}_2 $	-0.37	0.16	-2.35	0.0262	$ \ast $

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Table 5. IMF data set for June 2020, only 30 reference countries. Residual standard error: 2.625; Adjusted R-squared: 0.5478

	Par.	Estimate	Std. Error	$ t $-value	$ {\bf{Pr}}(>\|t\|) $	Signif. codes
$\texttt{Intercept} $	$ \hat{b} $	-3.91	2.15	-1.82	0.08016
$\texttt{Apr2019_IMF} $	$ \hat{a}_1 $	0.82	0.32	2.52	0.01813	$ \ast $
$\texttt{Rate June} $	$ \hat{a}_2 $	-0.99	0.31	-3.15	0.00402	$ \ast\ast $

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Table 6. WB data set for June 2020, all countries. Residual standard error: 2.674; Adjusted R-squared: 0.4546

	Par.	Estimate	Std. Error	$ t $-value	$ {\bf{Pr}}(>\|t\|) $	Signif. codes
$ \texttt{Intercept}$	$ \hat{b} $	-4.92	0.98	-5.01	2.84e-06	$ \ast\ast\ast $
$ \texttt{Dic2019_WB}$	$ \hat{a}_1 $	1.02	0.15	6.79	1.39e-09	$ \ast\ast\ast $
$\texttt{Rate June} $	$ \hat{a}_2 $	-0.56	0.18	-3.03	0.00322	$ \ast\ast $

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