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 Mobil- mobility data with other high-frequency data (air quality)
ity Index,” for nowcasting monthly industrial production over January 1, 2019 to April 30, 2020. Finally, mixed data
growth rates in selected economies in Latin America and sampling regression is implemented for nowcasting indus-
the Caribbean. The index is constructed using the Google trial production growth rates. The Google Mobility Index
COVID-19 Community Mobility Report database via a is a good predictor of industrial production. The results
Kalman filter. The Google database is publicly available suggest a significant decline in output of between 5 and 7
starting from February 15, 2020. The paper uses a back- percent for March and April, respectively, while indicating
casting methodology to increase the historical number of a trough in output in mid-April.
observations and then augments a lag of one week in the
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
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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∗
∗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
1 Introduction
The economic impact of COVID-19 has been severe. The combined impact of government
policies with the health implications is leading to a sharp contraction in economic activity.
The extent of output losses is yet to be determined. Output losses will vary by country, the
rate of infection, and the extent of policy interventions coupled with behavioral responses.
Economic forecasts for 2020 will have to be conditioned on the eﬀects of COVID-19.
This is not an easy task - the latest forecasts of the IMF (World Economic Outlook April
2020) and World Bank (Macro Poverty Outlook April 2020) show signiﬁcant variations
in growth outcomes within and across regions compared to the 2020 outlooks prepared in
October 2019 (see Figure 1). Since we have only surpassed the ﬁrst quarter of 2020 at the
time of writing, the annual forecast estimates remain very uncertain.
Figure 1: WB growth revisions by region. Note: MNA: Middle East and North Africa; EAP:
East Asia and the Paciﬁc; LAC: Latin America and the Caribbean; ECA: Europe and Central
Asia; SA: South Asia and SSA: Sub-Saharan Africa.
To reduce some of the uncertainty, we utilize high-frequency data that proxy the COVID-
19 economic activity responses. The Google mobility data summarize by country various
1
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 success-
fully 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 econo-
metric 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 low-
frequency 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 ith 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 = (y1t , . . . , yN t ) , for t = 1, . . . , T , as
follows
yt = Λft + εt (1)
where Λ = (λ1 , . . . , λN ) is the N × r matrix of factor loading with r as the number of
factors, ft = (f1t , . . . , frt ) 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 esti-
mators 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 distur-
bances.
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 /T needs to be close to the identity
matrix, where ε = (ε1 , . . . , εN ) 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 (εt εt ) = Ω = IN .
Notice that the Google mobility information is composed of six indicators, which conﬁg-
ures 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 Ω and 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 ﬁlter.
5
The ﬁrst stage solves the following PCA optimization problem
N T
−1
V = min(N T ) (yit − λi ft )2 (2)
Λ,f
i=1 t=1
subject to the normalization of either Λ Λ/N = 1 or f f /T = 1. We use the notation λi
as the ith row of Λ for i = 1, . . . , N . The optimization problem is identical to maximizing
tr(f (y y )f ) where y = (y1 , . . . , yN ) 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
1 T
S = T t=1 yt yt . The solution to the above minimization problem is not unique, even
though the sum of squared residuals V is unique, see Bai and Ng (2002). The estimated
parameters of interest can be expressed as
ˆ P CA = P Q1/2
Λ
(3)
ˆ = (yt − P P yt ) (yt − P P yt )
Ω
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,
2
ft = αft−1 + ηt ηt ∼ IID(0, ση ) (4)
where α is the scalar transition parameter and ηt is the 1 × 1 factor error term that has
2
mean zero and variance ση . This speciﬁcation can easily be extended to allow for higher
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 |y1 , . . . , ys ; ψ M LE ) and Pt|s = V ar(at|s −
6
2
ft |y1 , . . . , ys ; ψ M LE ) for t, s = 1, . . . , T , where ψ M LE = {α, ση } contains the parameters
that pertain to the distribution of the factor. Notice that Λ and Ω are estimated in the
ﬁrst stage. Moreover, the initial factor has density N (0, P1 ) where P1 = inv(1 − αα ) and
εt ∼ N ID(0, Ω) is the N × 1 disturbance term.
The estimation of the parameter vector ψ M LE is based upon maximizing the log-likelihood
function associated with (1) and (4). Meanwhile the estimated factor, ftM LE , is obtained
through a recursive procedure. Speciﬁcally, the log-likelihood function associated to the
Gaussian density is given by
T
NT 1
log L y ; ψ M LE
=− log 2π − log|Ft | + υt Ft−1 υt (5)
2 2 t=1
where the quantities υt and Ft represent the prediction residuals (yt − Λat|s ) and the pre-
dicted variance (ΛPt|s Λ + 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 In-
dex”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 fjM LE for j = t, . . . , T is the Google Mobility Index. Notice
that pj and qj contain J more data points than fjM LE . Therefore, we recover backwards
the information as follows
fjM LE
fjM LE
−1 = (6)
1 + ρ 1 × pj + ρ 2 × qj
7
for all j = t − J, . . . , t and ρ1,2 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 Eco-
nomic Indicators database), xt . Industrial production is published on a monthly basis.
(d),M LE
ft represents the daily ”Google Mobility Index”, which is observed d days in a par-
ticular M month. Speciﬁcally, we want to predict the variable xt onto a history of lagged
(d),M LE
observations of ft−j . 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:
xt = β0 + β1 B (L1/d ; Θ)ftd,M LE + ud
t (7)
K
for t = 1, . . . , T , and where B (L1/d ; Θ) = k=0 B (k ; Θ)Lk/d and L1/d is a lag operator
such that L1/d ftd,M LE = ftd,M
−1
LE
, and the lag coeﬃcient in B (k ; Θ) of the corresponding lag
operator Lk/d 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 L1/d are captured by a known function B (L1/d ; 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
Figure 2: Google leading indicator for Latin American and the Caribbean(LAC) economies
estimate. As expected, in all countries the index declined signiﬁcantly from mid-February.
Interestingly, the bottom of the indicator is in early April with the index starting to recover
to its baseline (which is a value reﬂected in February 2020). Notably, there are economies
in which the decline is steeper than in others. As an example, the index suggests a stronger
decline in Mexico compared to Brazil or Chile.
Figure 3 presents the correlation coeﬃcients between pollution, measured as the ﬁne
particulate matter(PM2.5), and the average temperature per country with the estimated
Google Mobility Index. In most cases, the correlation coeﬃcient is greater than 0.2 in
absolute terms. We found a negative correlation between pollution and Google Mobility
Index in three countries, Brazil, Chile and Mexico. Temperature is positively correlated
with the Google Mobility Index in all cases but Mexico. The rationale is as follows: with
few people in the street, the average temperature should decline, while high pollution will
prevent people from spending longer hours in the street. Obviously, there are caveats to
9
Figure 3: Google index correlations with air quality related information. Note: AR =
Argentina, BR = Brazil, CL = Chile, CO = Colombia, MX = Mexico and PE = Peru
10
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.1 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 com-
pared 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
1
In 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
Figure 4: Google index expanded by the air quality related information. Note: The shaded
area represents the information estimated backward and forward by using Equation 6
12
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 incor-
porating high-frequency information from Google indicators in all cases except Colombia.
We use the root-mean-square error (RM SE ) for model comparison. The RM SE represents
the quadratic mean of the diﬀerences between the one-step ahead predicted values and the
observed data. Therefore, the lower the RM SE the better model performance. Table 2
shows that RM SE 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 com-
bining high-frequency indicators gathered from Google mobility in comparison to standard
methods.
13
Country AR(1) AR(2) M IDAS M IDAS with M IDAS 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 (RM SE ). 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
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17
Appendices
Explanatory variables BRA CHL COL MEX
Google Index -5.96 -4.40 -5.69 -6.47
PM2.5 -6.18 -4.58 -5.64 -6.57
Temperature -5.95 -4.31 -5.60 -6.30
PM2.5 and Temperature -6.22 -4.99 -5.48 -6.48
PM2.5 and Temperature and Google Index -6.93 -5.59 -6.50 -8.88
Table 3. AIC values for diﬀerent model speciﬁcations for nowcasting industrial production
growth rate (m/m).
Figure 5: Actual versus one-step ahead predicted industrial production growth rate in Brazil
18
Figure 6: Actual versus one-step ahead predicted industrial production growth rate in Chile
19
Figure 7: Actual versus one-step ahead predicted industrial production growth rate in
Colombia
20
Figure 8: Actual versus one-step ahead predicted industrial production growth rate in
Mexico
21