# American Institute of Mathematical Sciences

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

Received  December 2021 Revised  February 2022 Early access April 2022

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.

Citation: Gabriel Illanes, Ernesto Mordecki, Andrés Sosa. On the impact of the Covid-19 health crisis on GDP forecasting: An empirical approach. Journal of Dynamics and Games, doi: 10.3934/jdg.2022008
##### References:
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##### References:
 [1] F. Aldenhoff, Are economic forecasts of the International Monetary Fund politically biased? A public choice analysis, The Review of International Organizations, 2 (2007), 239-260.  doi: 10.1007/s11558-006-9010-x. [2] H. Arora and D. Smyth, Forecasting the developing world. An accuracy analysis of the IMF's forecasts, International Journal of Forecasting, 6 (1990), 393-400.  doi: 10.1016/0169-2070(90)90065-J. [3] F. M. Fisher, Tests of equality between sets of coefficients in two linear regressions: An expository note, Econometrica: Journal of the Econometric Society, (1970), 361–366. [4] G. J. Glasser and R. F. Winter, Critical values of the coefficient of rank correlation for testing the hypothesis of independance, Biometrika, 48 (1961), 444-448. [5] Global Economic Prospects, World Bank Group, January 2020. [6] Global Economic Prospects., World Bank Group, June 2020. [7] T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning, Second edition. Springer Series in Statistics. Springer, New York, 2009. doi: 10.1007/978-0-387-84858-7. [8] P. Hong and Z. Tan, A Comparative Study of the Forecasting Performance of Three International Organizations, Department of Economic & Social Affairs. Working Paper No. 133. June 2014. [9] E. Kreinin, Accuracy of OECD and IMF Projection, Journal of Policy Modelling, Vol 22, 2000. [10] C. Spearman, The proof and measurement of association between two things, American Journal of Psychology, 15 (1904), 72-101. [11] World Economic Outlook, International Monetary Fund. April 2020. [12] World Economic Outlook Update, International Monetary Fund. June 2020. [13] [14] Considerations for implementing and adjusting public health and social measures in the context of COVID-19: Interim guidance, 4 November 2020, https://apps.who.int/iris/handle/10665/336374. Accessed 07/12/2021. [15] Our world in data. Coronavirus Pandemic (COVID-19), https://ourworldindata.org/coronavirus. Accessed 07/12/2021. [16] Timeline of the Coronavirus, https://www.thinkglobalhealth.org/article/updated-timeline-coronavirus. Accessed 07/12/2021. [17] COVID-19 pandemic, https://en.wikipedia.org/wiki/COVID-19_pandemic, Accessed 07/12/2021.
Smoothed deaths per one million population (03/01/2020 - 12/31/2020)
Boxplots of the variables. Left: $\texttt{rate}$. Right: GDP growth projections for 2020
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
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
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
Scatter plot of the WB GDP growth projections for 2020 generated in June 2020, and the $\texttt{rate}$
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
 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
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 $\ast\ast$
 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 $\ast\ast$
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 $\ast\ast\ast$
 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 $\ast\ast\ast$
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 $\ast$
 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 $\ast$
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 $\ast\ast$
 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 $\ast\ast$
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 $\ast\ast$
 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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