metadata: authors: 0: author: Sampi Bravo,James Robert Ezequiel
1: author: Jooste,Charl
count: Latin America,Caribbean
docna: 0: docna: Nowcasting Economic Activity in Times of
            COVID-19 : An Approximation from the Google Community
            Mobility Report
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Health Care Services Industry,Pharmaceuticals Industry,ICT Policy and Strategies,ICT Legal and Regulatory Framework,Economic Conditions and Volatility
teratopic: Macroeconomics and Economic Growth,Industry,Information and Communication Technologies,International Economics and Trade
abstracts: cdata!: This paper proposes a leading indicator,
            the "Google Mobility Index," for nowcasting
            monthly industrial production growth rates in selected
            economies in Latin America and the Caribbean. The index is
            constructed using the Google COVID-19 Community Mobility
            Report database via a Kalman filter. The Google database is
            publicly available starting from February 15, 2020. The
            paper uses a backcasting methodology to increase the
            historical number of observations and then augments a lag of
            one week in the mobility data with other high-frequency data
            (air quality) over January 1, 2019 to April 30, 2020.
            Finally, mixed data sampling regression is implemented for
            nowcasting industrial production growth rates. The Google
            Mobility Index is a good predictor of industrial production.
            The results suggest a significant decline in output of
            between 5 and 7 percent for March and April, respectively,
            while indicating a trough in output in mid-April.
repnme: repnme: Nowcasting Economic Activity in Times of
            COVID-19 : An Approximation from the Google Community
            Mobility Report
display_title: Nowcasting Economic Activity in
            Times of COVID-19 : An Approximation from the Google
            Community Mobility Report
listing_relative_url: /research/2020/05/32036628/nowcasting-economic-activity-times-covid-19-approximation-google-community-mobility-report
topicv3: Macroeconomic Vulnerability and Debt
            m1326057 1104,Open Data Policy m1326174 679,Trade m1326924 698,Health m1504661 3480,Pharmacy m1583121 4501
publishtoextweb_dt: 2020-05-14T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Industry,Information and Communication Technologies,International Economics and Trade
origu: EFI-LCR-MTI-MacroFiscal (ELCMU)
no_of_pages: 24
author_keys: 0: author_key: 1496952
1: author_key: 1368476
model_extractions: Policy Research Working Paper 9247 Nowcasting Economic Activity in Times of COVID-19 An Approximation from the Google Community Mobility Report _James Sampi Charl Jooste_ Macroeconomics, Trade and Investment Global Practice May 2020
Policy Research Working Paper 9247

# **Abstract**

This paper proposes a leading indicator, the “Google Mobility Index,” for nowcasting monthly industrial production growth rates in selected economies in Latin America and the Caribbean. The index is constructed using the Google COVID-19 Community Mobility Report database via a Kalman filter. The Google database is publicly available starting from February 15, 2020. The paper uses a backcasting methodology to increase the historical number of observations and then augments a lag of one week in the mobility data with other high-frequency data (air quality) over January 1, 2019 to April 30, 2020. Finally, mixed data sampling regression is implemented for nowcasting industrial production growth rates. The Google Mobility Index is a good predictor of industrial production. The results suggest a significant decline in output of between 5 and 7 percent for March and April, respectively, while indicating a trough in output in mid-April.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at jsampibravo@worldbank.org and cjooste@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Nowcasting Economic Activity in Times of COVID-19: An Approximation from the Google Community Mobility Report James Sampi and Charl Jooste<sup>_∗_</sup>

> _∗_ We are extremely grateful to Jorge Araujo for his invaluable support in this project. We thank to Pablo Saavedra and Stefano Curto for valuable advice, and Julio Velasco, Barbara Cunha, Marek Hanusch, Gabriel Zaourak and Luigi Butron for helpful discussions. Corresponding authors: jsampibravo@worldbank.org and cjooste@worldbank.org
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mobility trends (e.g. Retail and recreation, Grocery and pharmacy, Parks, among others). From Figure 2, it is quite clear that global mobility indicators have slowed. We use these data to test the correlation with industrial production . Analysts can use the change in industrial production to back out estimates for annual GDP growth.

Unfortunately, some of these data go back only to February 15, 2020. To increase the degrees of freedom in the analysis, we backcast the mobility data using daily weather and pollution data. The assumption is that pleasant weather and low pollution are correlated with an increase in mobility.

The rest of the paper is structured as follows: In Section 2 we describe recent nowcasting literature. The overall methodology is discussed in Section 3, which is followed in Section 4 by a discussion of estimating and approximating the models via a Kalman filter. In Section 4.2 we describe the approximation done using pollution data, while Section 4.3 discusses the links to industrial production. In Section 5 we present the results and Section 6 concludes.

# **2 Literature review**

The seminal papers of Geweke (1989), Stock and Watson (1989), and Bai and Ng (2002) have placed the dynamic factor model (DFM) as the predominant framework for research on macroeconomic forecasting using high-frequency indicators. Overall, this framework allows us to study large panels of time series through a few common factors, especially, when the data series are strongly collinear.

The available methodologies for estimating DFMs can be divided into two groups. The first group of estimators entails nonparametric estimation with large N using cross-sectional averaging methods, primarily principal components. Principal components analysis (PCA) is the most popular factor extraction method in the treatment of dynamic factors models. PCA is appealing because of its computational advantages and asymptotic properties in large data sets, see Bai (2003). Unfortunately, for many empirical applications the PCA 2
assumptions are arguably not realistic, see Onatski (2012).

The second group consists of parametric models estimated in the time domain using maximum likelihood estimation (MLE) and the Kalman filter. MLE has been used successfully to estimate the parameters of low-dimensional DFMs. However, there are significant computational requirements to maximize the likelihood function with many parameters. In order to deal with the dimensionality problem associated with the likelihood function, further estimators have been implemented. The main idea behind these methods is to use the consistent parameters estimated by the first group methods for computing the factors required by the second one, see Doz and Reichlin (2011) and Doz, Giannone and Reichlin (2012).

Regardless of the method for extracting a common factor, increasingly the literature is suggesting mixing sampling frequencies aimed at improving the accuracy of nowcasting techniques. The challenges of mixed data frequency are reviewed in the context of econometric analysis by Ghysels and Marcellino (2016) and discussed in the context of forecasting by Armesto, Engemann and Owyang (2010) and Andreou, Ghysels and Kourtellos (2010). A widely used method for incorporating high-frequency data to produce forecasts of lowfrequency variables is the Mixed Data Sampling (MIDAS) method of Ghysels, Santa-Clara and Valkanov (2004).

MIDAS is a regression-based method that transforms the high-frequency variables into low-frequency indicators via a weighting scheme. The weights reflect the relative importance of recent observations as opposed to older ones as information to predict future values of the low-frequency variable.

In this paper we compress the six Google mobility indicators: Retail & recreation, Grocery & pharmacy, Parks, Transit stations, Workplaces, and Residential into one common factor to capture the economic effects of COVID-19 in Latin America and the Caribbean (LAC) economies. In this exercise the dimensionality of variables is not a big concern, therefore, the parametric methods embedded in the second group are adequate. Meanwhile, 3
we select the MIDAS approach for nowcasting the industrial production growth rate, which performs significantly better when using DFM compared to the PCA methods, see Gorgi, Koopman and Mengheng (2018).

# **3 Approximate factor model**

Let _yit_ be the observed data for the _i_ th variable at time _t_ . In total we have _N_ variables indexed by _i_ = 1 _, . . . , N_ . Also, we have _T_ time periods and _t_ = 1 _, . . . , T_ . The approximate factor model decomposes _N_ dimensional vectors _yt_ = ( _y_ 1 _t, . . . , yNt_ )<sup>_′_</sup> , for _t_ = 1 _, . . . , T_ , as follows where Λ = ( _λ_ 1 _, . . . , λN_ )<sup>_′_</sup> is the _N × r_ matrix of factor loading with _r_ as the number of factors, _ft_ = ( _f_ 1 _t, . . . , frt_ )<sup>_′_</sup> is the _r ×_ 1 vector of factors and _εt_ is the _N ×_ 1 idiosyncratic disturbance term.

In approximate factor settings, the consistency and asymptotic normality of the estimators when both _N_ and _T_ go to infinity have been recently shown by Bai (2003), Bai and Ng (2002) and Doz et al. (2012). In order to prove these properties, Bai (2003) makes a strong assumption related to the eigenvalues of the population covariance matrix of the data. Specifically, it requires that the ratio between the _r − th_ largest and the _r_ + 1 _− th_ largest eigenvalues, _dr_ , increase proportionately to _N_ . Asymptotically, this implies that the cumulative effects of the normalized factors strongly dominate the idiosyncratic disturbances.

Recently, Onatski (2012) and Onatski (2015) show that the strong factor assumption requires one of the following two scenarios. Either, an overwhelming domination of the factors represented by higher values of _dr_ for all _r_ , or _εε_<sup>_′_</sup> _/T_ needs to be close to the identity matrix, where _ε_ = ( _ε_ 1 _, . . . , εN_ )<sup>_′_</sup> is the _N × T_ disturbances matrix. It implies that all the commonalities across variables occur through the factors and that the individual elements of 4
_εt_ are purely shocks which are idiosyncratic to each variable. However, the former scenario is unwanted as long as we do not assume an overwhelming domination of factors over the idiosyncratic disturbances. The latter scenario does not hold as typically the expected covariance matrix of the disturbances is not the identity, _E_ ( _εtε_<sup>_′_</sup> _t_<sup>) = Ω =</sup><sup>_IN_.</sup> Notice that the Google mobility information is composed of six indicators, which configures _N_ = 6, and those became available from February 15, 2020, making the time dimension roughly _T_ = 60. Notably, with short _N_ and _T_ it becomes difficult to assume that the strong factor assumption holds, and we would need to consider a more consistent approach besides the standard Principal Component Analysis (PCA).

# **4 Estimation procedure**

This section provides a detailed explanation of the empirical procedure for estimating the leading factor, the “Google Mobility Index”, and extending back the resultant index by using air quality-related information with the overall objective of nowcasting the effects of COVID-19 on the industrial production growth rates. Because _T_ and _N_ dimensions are small for consistency of Principal Component Analysis (PCA) or the standard Kalman Filter methods, the econometric procedure relies on the two-step approach introduced by Doz et al. (2012) or typically known as the “quasi-maximum likelihood approach ”, where asymptotic properties perform significantly better for small _T, N_ when compared to standard methods. In addition, the construction of one single Google leading indicator requires that _r_ = 1.

## **4.1 The two-step approach for estimating the leading factor**

The first stage proceeds to obtain consistent estimates of the parameters Ωand Λ for estimating the unobservable factor, _ft_ , using Maximum Likelihood approaches. Specifically, the first stage uses Principal Component Analysis (PCA), while the second stage involves the Kalman 5
The first stage solves the following PCA optimization problem subject to the normalization of either Λ<sup>_′_</sup> Λ _/N_ = 1 or _ff_<sup>_′_</sup> _/T_ = 1. We use the notation _λi_ as the _i_<sup>_th_</sup> row of Λ for _i_ = 1 _, . . . , N_ . The optimization problem is identical to maximizing tr( _f_ ( _y_<sup>_′_</sup> _y_ ) _f_<sup>_′_</sup> ) where _y_ = ( _y_ 1 _, . . . , yN_ )<sup>_′_</sup> is the _N × T_ matrix of the observed data. Here tr() denotes the trace operator. Let _Q_ be the largest eigenvalue of the sample covariance matrix <u>1</u> _T S_ = _T_ � _t_ =1<sup>_yty_</sup> _t_<sup>_′_.Thesolutiontotheaboveminimizationproblemisnotunique,even</sup> though the sum of squared residuals _V_ is unique, see Bai and Ng (2002). The estimated parameters of interest can be expressed as where _P_ , the eigenvector associated with _Q_ .

For the second stage we need to make an assumption about the stochastic process of the factor, such that the model can be written in state space form. In particular, the factor is assumed to follow a vector auto-regressive model of order one. We have, where _α_ is the scalar transition parameter and _ηt_ is the 1 _×_ 1 factor error term that has mean zero and variance _σ_<sup>2Thisspecificationcaneasilybeextendedtoallowforhigher</sup> _η_<sup>.</sup> order vector auto-regressions. Together with the observation of equation (1), the model can be viewed as a state space model.

The parametric MLE method is well documented in Durbin and Koopman (2012) and Ghahramani and Hinton (1996). The method relies on the Kalman filter. They start by defining the conditional moments as _at|s_ = _E_ ( _ft|y_ 1 _, . . . , ys_ ; _ψ_<sup>_MLE_</sup> ) and _Pt|s_ = _V ar_ ( _at|s −_

6
_ft|y_ 1 _, . . . , ys_ ; _ψ_<sup>_MLE_</sup> ) for _t, s_ = 1 _, . . . , T_ , where _ψ_<sup>_MLE_</sup> = _{α, ση_<sup>2</sup><sup>_}_containstheparameters</sup> that pertain to the distribution of the factor. Notice that Λ and Ωare estimated in the first stage. Moreover, the initial factor has density _N_ (0 _, P_ 1) where _P_ 1 = inv(1 _− αα_<sup>_′_</sup> ) and _εt ∼ NID_ (0 _,_ Ω) is the _N ×_ 1 disturbance term.

The estimation of the parameter vector _ψ_<sup>_MLE_</sup> is based upon maximizing the log-likelihood function associated with (1) and (4). Meanwhile the estimated factor, _ft_<sup>_MLE_</sup> , is obtained through a recursive procedure. Specifically, the log-likelihood function associated to the Gaussian density is given by where the quantities _υt_ and _Ft_ represent the prediction residuals ( _yt −_ Λ _at|s_ ) and the predicted variance (Λ _Pt|s_ Λ<sup>_′_</sup> + Ω), which are evaluated by the Kalman filter.

# **4.2 Expanding the series using air quality information**

In this section we propose a simple methodology for expanding the “Google Mobility Index”obtained in the previous section by using air quality-related information. Specifically, we use the Air Quality Open Data Platform for extracting temperature and fine particulate matter (PM2.5) information per city in each country worldwide. Then, the information is averaged per country such as it can be easily associated with the Google Mobility Index over time.

Let’s consider _pj_ and _qj_ for _j_ = _t−J, . . . , t, . . . , T_ the normalized temperature and PM2.5 information at time _j_ , while _fj_<sup>_MLE_</sup> for _j_ = _t, . . . , T_ is the Google Mobility Index. Notice that _pj_ and _qj_ contain _J_ more data points than _fj_<sup>_MLE_</sup> . Therefore, we recover backwards the information as follows 7
for all _j_ = _t − J, . . . , t_ and _ρ_ 1 _,_ 2 the weighted correlation coefficient between the Google Mobility Index and the normalized series.

## **4.3 Nowcasting industrial production**

In this section we consider the Mixed Data Sampling (MIDAS) regression of Ghysels et al. (2004) for nowcasting industrial production growth rates (sourced from OECD Main Economic Indicators database), _xt_ . Industrial production is published on a monthly basis. _ft_<sup>(</sup><sup>_d_)</sup><sup>_,MLE_</sup> represents the daily ”Google Mobility Index”, which is observed _d_ days in a particular _M_ month. Specifically, we want to predict the variable _xt_ onto a history of lagged observations of _ft_<sup>(</sup> _−_<sup>_d_)</sup> _j_<sup>_,MLE_</sup> . The superscript ( _d_ ) denotes the higher frequency sampling and its exact timing lag is expressed as a fraction of the unit interval between months _M_ and _M −_ 1. The MIDAS regression is expressed as follows: for _t_ = 1 _, . . . , T_ , and where _B_ ( _L_<sup>1</sup><sup>_/d_</sup> ; Θ) =<sup>�</sup><sup>_K_</sup> _k_ =0<sup>_B_(</sup><sup>_k_; Θ)</sup><sup>_Lk/d_and</sup><sup>_L_1</sup><sup>_/d_isalagoperator</sup> such that _L_<sup>1</sup><sup>_/d_</sup> _ft_<sup>_d,MLE_</sup> = _ft_<sup>_d,MLE_</sup> _−_ 1 , and the lag coefficient in _B_ ( _k_ ; Θ) of the corresponding lag operator _L_<sup>_k/d_</sup> are parameterized as a function of a small-dimensional vector of parameters Θ. In order of addressing the parameter proliferation, in a MIDAS regression the coefficients of the polynomial in _L_<sup>1</sup><sup>_/d_</sup> are captured by a known function _B_ ( _L_<sup>1</sup><sup>_/d_</sup> ; Θ) of a few parameters summarized in a vector Θ, typically, polynomial specifications.

# **5 Results**

Figure 2 presents the results of the two-step estimator for extracting one common factor of the six Google Mobility indicators, the “Google Mobility Index”, for each Latin America and the Caribbean (LAC) country available in the Google database. The gray lines represent the non-smoothed indicators while the bold red line represents the smoothed Kalman filter 8
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this anecdotal explanation - since the baseline matters - e.g. if pollution is persistent.

Figure 4 presents the results of extending the Google Mobility Index (which always lags by one week) with air quality-related information: temperature and fine particulate matter (PM2.5), for countries for which data are available. The information is gathered from the Air Quality Open Data Platform from January 1, 2019 to April 30, 2020 for Argentina, Brazil, Chile, Colombia, Mexico, Peru and El Salvador. The shaded areas represent the information estimated backward and forward using Equation 6. The extended information suggests that the period prior to the COVID-19 crisis was signaling a recovery in Argentina, and a significant decline in Chile and Mexico, although stronger in the former. Meanwhile, the index points to stability in Brazil, Peru and El Salvador. Appending air quality data to the mobility index is warranted on both statistical and economic grounds, with the latter being the main motivation for this analysis. The predicted value of the Google Mobility Index using more up-to-date information confirms that economies may have bottomed-out in April, with Mexico being the exception.

The final set of results, which nowcasts industrial production using the appended Google Mobility Index, is summarized in Table 1 for Brazil, Chile, Colombia and Mexico.<sup>1</sup> The monthly growth rates are gathered from the Economic Indicators database of the OECD. The _R − sq._ achieves a maximum of 25 percent in Brazil and a minimum of 18 percent in Colombia. In most cases, the results point to a deterioration of March growth rates compared to February, and an even stronger decline in April. Specifically, Mexico is expected to decline by 5 and 6 percent for March and April, respectively, from a 0.7 percent decline in February. Similarly, Brazil is expected to decline by nearly 7 and 3 percent, while Chile is expected to decline by 1 and 2 percent; and Colombia 0.4 and 2 percent, respectively. In all regressions the optimal number of lags is 3, while the polynomial degree varies from 3

> 1In Table 3 in the Appendix section, various consistency checks with different combinations of the Google Index and the air quality data are compared. The differences between the various explanatory variables are insignificant.

11
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|Country|_R −sq._|Lag|Polynomial|Feb. Actual|Mar. proj.|Apr. proj.|
|---|---|---|---|---|---|---|
|Brazil|0.25|3|3|-0.009|-0.069|-0.034|
|Chile|0.21|3|3|-0.018|-0.010|-0.020|
|Colombia|0.18|5|3|-0.004|-0.004|-0.018|
|Mexico|0.20|5|3|-0.007|-0.047|-0.059|

Table 1. MIDAS results for nowcasting industrial production growth rate (m/m). The _R − sq._ reflects the one-step ahead projection residuals for the period 2019-Feb until 2020-Feb, while Lag and Polynomial represent the optimal number of lags and polynomial degree in Equation 7.

to 5 in Colombia and Mexico. In addition, the one-step-ahead predicted values are plotted for each economy in Figures 5 to 8

# **5.1 Comparison with other methods**

The predictive test contrasts the MIDAS approach to an autoregressive method of first and second orders in Table 2. The results reveal a significant forecast improvement when incorporating high-frequency information from Google indicators in all cases except Colombia. We use the root-mean-square error ( _RMSE_ ) for model comparison. The _RMSE_ represents the quadratic mean of the differences between the one-step ahead predicted values and the observed data. Therefore, the lower the _RMSE_ the better model performance. Table 2 shows that _RMSE_ is almost three times higher when compared to _AR_ specifications in Brazil, 26 percent higher in the case of Chile, while 14 percent higher in case of Mexico. Overall, the results provide strong evidence in favor of using a MIDAS regression combining high-frequency indicators gathered from Google mobility in comparison to standard methods.

13
|Country|_AR_(1)|_AR_(2)|_MIDAS_|_MIDAS_ with|_MIDAS_ with|
|---|---|---|---|---|---|
|||||_AR_(1)|_AR_(2)|
|Brazil|0.041|0.038|0.009|0.009|0.011|
|Chile|0.024|0.024|0.022|0.019|0.019|
|Colombia|0.010|0.011|0.011|0.011|0.011|
|Mexico|0.009|0.008|0.007|0.007|0.007|

Table 2. Comparison for predicting the industrial production growth rates (m/m) by using the Root-mean-square error ( _RMSE_ ). Note: The data sample ranges from February 2018 until February 2020 for _AR_ regressions while January 2019 until February 2020 for MIDAS regression.

# **6 Conclusion**

A novel database is used to generate high frequency forecasts of economic activity in the wake of COVID-19. The World Bank and IMF have revised growth estimates significantly downward during COVID-19. The health and economic policy responses and subsequent economic outcomes are very uncertain. To reduce some of this uncertainty this paper details the use of daily mobility and air quality data to predict movements in industrial production, which is typically used to assess within-year movement of GDP growth. The database includes Google’s Community Mobility Report data, air quality data and OECD industrial production data.

Estimation proceeds in three steps: (i) lagged mobility data are patched with air quality data; (ii) the mobility data are then combined to extract a common Mobility Index via Kalman filtering; and finally (iii) a MIDAS approach nowcasts industrial production from the smoothed Mobility Index. The results can be updated daily. This paper illustrates its use for a set of Latin American countries.

The Mobility Index is compared to a standard auto-regressive forecast model. The 14
results of the exercise suggest that our approach beats the AR models for pseudo out of sample forecasts. The index predicts a strong decline in industrial production monthly growth rates of 7 (5) and 4 (6) percent for March and April, respectively, for Brazil (Mexico). Chile and Colombia follow a similar decline. Finally, the index, while still negative, suggests that the trough in output occurred in April 2020.

15