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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.21 No.1 pp.119-127
DOI : https://doi.org/10.7232/iems.2022.21.1.119

# Dynamic Causal Effects of Pandemic-induced Uncertainty on Output, Credit, and Asset Prices: A Symbolic Transfer Entropy Approach

Charles Shaw*
FixedPoint IO, United Kingdom
*Corresponding Author, E-mail: charles@fixedpoint.io
July 30, 2021 January 5, 2022 February 22, 2022

## ABSTRACT

The purpose of this paper is to examine at information transfer between pandemic-induced indices of economic policy uncertainty and economic factors, such as credit growth, economic activity, and asset prices. For this purpose, we implement a Symbolic Transfer Entropy approach proposed by Camacho et al. (2021), which represents an improved specification for detecting Granger-type causality in panel datasets. Specifically, this procedure yields a more robust specification when linearity assumptions break down, when in the presence of structural breaks, or when the data generating process is heterogeneous across the cross-section units. Aggregate economic variables are compared against the world pandemic uncertainty index (WPUI), which is based on the work of Ahir, Bloom, and Furceri (2020) and measures economic uncertainty related to pandemics and other disease outbreaks across the world. Amidst concerns that past economic shocks have left permanent scars on long-term growth, known as hysteresis, we find no robust evidence of a long-run causal effect between pandemic-induced uncertainty and most of key aggregate economic variables. The results have implications for the relevance of economic uncertainty to long-term economic outcomes.

## 1. INTRODUCTION

Assessment of the economic impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 or COVID) has been made difficult by the ferocious speed with which the health crisis unfolded. The health crisis has also prompted a significant spike in uncertainty, with a number of related indices being highest on record. Uncertainties surround almost every aspect of the crisis: the lethality of the virus and control over the infection’s most harmful effects; the availability and deployment of antigen and antibody tests; approval of vaccines, ensuring equitable access to vaccine doses, and detailed understanding of their efficacy; the capacity of healthcare systems; the duration and effectiveness of containment strategies; impact on business survival; the effects and persistence of pandemic-induced shifts on consumer spending; the effectiveness of policy measures on consumption, investment, employment, and other outcomes. This relationship is worth examining, since it has been established that elevated uncertainty tends to make consumers and firms cautious, thereby delaying investment and expenditures.

In terms of measuring effects of uncertainty shocks, various approaches exist to quantify effects of uncertainty shocks on financial and real markets – on a local, regional or global basis. These include:

A survey of the literature is provided by Bloom (2014). In this study, our preferred way we measure economic uncertainty involves quantifying key words in the media, an approach developed by the likes of Bloom and others (Bloom, 2009;Bloom, 2014;Jurado et al., 2015;Segal et al., 2015;Baker et al., 2016;Meinen and Roehe, 2017;Bloom et al., 2018;Altig et al., 2020a;Berger et al., 2020).

Whichever barometer is used, the empirical literature has provided ample evidence indicating the presence of a negative relationship between economic activity and economic uncertainty.

Ilut and Schneider (2014) find that geopolitical threats lead to a protracted rise in uncertainty and induce a persistent decline in real activity as economic agents form expectations using a worst-case probability. Faccini and Palombo (2020) demonstrate the deleterious effects of Brexit-induced news uncertainty on UK growth and firm investment. Wensheng et al. (2017) use crosscountry evidence to argue that there is causal and negative relationship between uncertainty and growth. Gomez- Gonzalez et al. (2020) used a model based on the estimation and aggregation of forecast errors to present evidence that that points to uncertainty as the main driver of global economic cycles, even more than the US interest rate.

Ludvigson et al. (2015) use a structural vector autoregressive (SVAR) model identified with external information and find a bi-directional relationship between the business cycle and uncertainty. Caldara et al. (2016) also deploy a SVAR to document that macroeconomic uncertainty responds endogenously to tightening in financial conditions. Whether this empirical regularity implies that uncertainty is driver of adverse macroeconomic and financial conditions or an endogenous response remains an open question. However, we are able to mitigate issues around potential bidirectional causality of these relationships as we are able to model pandemic-induced uncertainty as a typical exogenous shock, akin to natural disasters.

The literature on measuring effects of economic uncertainty as it relates to post-pandemic recovery is fastdeveloping. Baker et al. (2020) and Toda (2020) discuss effects of uncertainty on stock markets1), while Stock (2020) discusses uncertainty and its implications in the context of antigen and antibody testing.

There exists evidence that COVID-related uncertainty shocks lead to greater financial fragility among lowerincome earners. Recent support for this finding comes from Di Maggio et al. (2020) who examine the impact of uncertainty, as measured by idiosyncratic stock market volatility, on individual outcomes and find that increase in firm-level uncertainty is associated with a decline in total compensation, especially in variable pay. Lastly, Barrero et al. (2020), Barro et al. (2020), and Jordà et al. (2020) investigate macroeconomic consequences, both in medium- and long-term.

Other notable studies in this line of research include Atkeson (2020a), Fauci et al. (2020), and Li et al. (2020) who examine uncertainty regarding key parameters in epidemiological models of Covid-19 morbidity and transmission. Anderson et al. (2020), Atkeson (2020b), Berger et al. (2020), and Eichenbaum et al. (2020) discuss uncertainty in standard epidemiological models, as well as models that incorporate behavioural responses, such as social distancing. Guerrieri et al. (2020) discuss potential difficulties arising from elevated supply-side disruptions induced by a major pandemic.

While numerous theoretical models establish this relationship, the direction of the relationship remains a contentious question due to the limitation of statistical methodology. Granger causality tests are the primary methodological strategy for checking for short-run connections between tourism and economic growth. Most causal studies in the literature use linear, parametric models that require the use of an autoregressive representation of the time series. These traditional linear methods, such as Granger causality, have a number of limitations. For example, they overlook the economy’s inherent complexity and non-linearities, as well as potential turning points and structural breaks.

## 2. PROBLEM STATEMENT AND OBJECTIVES OF THE STUDY

Camacho et al. (2021) show that that non-linearity, cross-section heterogeneity, structural breaks, outliers, and higher order moment dependency significantly reduce the size and power of causality tests based on linear representations, such as those popular in the econometrics literature. The objective of this study is to adapt the Symbolic Transfer Entropy (STE) causality test proposed by Camacho et al. (2021) in order to study the information transfer between pandemic-induced indices of economic policy uncertainty and economic factors, such as credit growth, stock prices, economic activity, bond yields, and prices.

### 2.1 Granger Causality

Granger causality, a well-established statistical concept of interdependence in economic time series, is defined in terms of predictability of linear stochastic systems (Granger, 1969), i.e. X Granger causes Y if it improves the prediction of Y when included in the autoregressive model. Whilst this framework may conceptually be traced to Wiener (Wiener, 1956) it was operationalised by Granger in terms of linear autoregressive modelling of stochastic processes.

Let $x t ∈ ℝ p$ be a p -dimension stationary time series, observable at T time points, $( x 1 , … , x T )$. In this specification, the time series at time t, xt, is assumed to be a linear combination of the past R lags of the series

$x t = ∑ r = 1 R A ( r ) x t − r + e t$
(1)

where A(r) is a p×p matrix that specifies how lag r affects the future evolution of the series and et is mean zero noise. In this model, time series j does not Granger cause time series i iff , $∀ r , A i j ( r ) = 0$. A Granger causal analysis in a VAR model thus reduces to determining which values in A(r) are zero over all lags.2)

The standard measure of Granger causality used in the literature is defined for univariate predictor and predictee variables Y and X , and is given by the log of the ratio of the residual variances for the regressions. As shown by Barnett et al. (2009), Granger causality is equivalent to Transfer Entropy under some assumptions, is invariant under a wider range of variable transformations, and is expandable as a sum of standard univariate Granger causalities. For inference in a multivariate setting please see Barrett et al. (2010) and literature cited therein.

### 2.2 Nonlinear Autoregressive Models and Granger Causality

A nonlinear autoregressive model allows xt to evolve according to more general nonlinear dynamics

$x t = ∑ r = 1 R A ( r ) x t − r + e t$
(3)

where $x < t i = ( … , x ( t − 2 ) i , x ( t − 1 ) i )$ denotes the past of series i. The nonlinear autoregressive function g may be written as

$x t i = g i ( x < t 1 , ... , x < t p ) + e t i$
(4)

where gi is a function that specifies how the past R lags influence series i. In this context, Granger noncausality between two series j and i means that the function gi does not depend on x<tj, the past lags of series j. Time series j is said to be Granger noncausal for time series i if for all $( x < t 1 , … , x < t p )$ and all $x < t j ' ≠ x < t j$,

(5)

that is, gi is invariant to x < tj.

Next, we present the information measures for bivariate time series ${ x t , y t } t = 1 N$. Assuming standard delay embedding with the same embedding dimension m and delay τ, a methodology suited for investigating coupling, the reconstructed points from the two time series are $x t = [ x t , x t - τ , … , x t - ( m - 1 ) τ ]$ and $y t = [ y t , y t - τ , … , y t - ( m - 1 ) τ ]$, respectively. We define the measures for the information flow, or Granger causality, from X to Y, denoted XY, assuming the driving system being represented by X and the response system by Y. The future state of the response is defined in terms of T times ahead denoted $y t T = [ y t + 1 , … , y t + T ]$ t yt yt T , where often the future horizon is limited to $T = 1 ( y t T = y t + 1 )$.

### 2.3 Transfer Entropy

Transfer Entropy (TE) is the conditional mutual information $I ( y t T ; x t | y t )$ that quantifies the information about the future of the response system, $I ( y t T ; x t | y t )$, obtained by the current state of the driving system, $x t$, that is not already contained in the current state of the response system, $y t$. In terms of entropy, TE is defined as

$T E X → Y = I ( y t T ; x t |y t ) = − H ( y t T , x t , y t ) + H ( x t , y t ) + H ( y t T , y t ) − H ( y t )$
(6)

where $H ( x ) = − ∫ X f ( x ) ln f ( x ) d x$ is the differential entropy of a continuous variable x with domain $X$, and f(x) is the probability density function of x.

In estimating $T E X → Y$ one can assume discretization of the observed variables xt and yt and use the Shannon entropy $H ( x ) = − ∑ ​ p ( x ) l n p ( x )$ for the discrete variable x, where the sum is over the possible bins of x and p(x) is the probability mass function (pmf) of x. However, binning methods are found to be more demanding on data size than other methods approximating directly the density function, and subsequently the differential entropy. In particular, for high dimensions, i.e. large m, the k -nearest neighbor estimate turns out to be the most robust to time series length (Kraskov et al., 2004).

The inefficiency of the binning methods for estimating entropies is attributed to the bias due to the estimation of bin probability with the relative frequency of occurrence of entries in the bin, and the variance due to having a number of unpopulated or poorly populated bins. The latter increases with the embedding dimension m , and it is noted that for the discretization of xt and yt in b bins the variable of highest dimension asad$[ y t T , x t , y t ]$ regards $b 2 m + T$ bins.

### 2.4 Symbolic Transfer Entropy

A different discretisation that produces far fewer bins for the high dimensional variables is provided by the rank ordering of the components of vector variables. For each point yt, the ranks of its components, say in ascending order, form a rank vector $y ^ t = [ r t , 1 , r t , 2 , … , r t , m ]$, where $r t , j ∈ { 1 , 2 , … , m }$ for $j = 1 , … , m$, is the rank order of the component $y t − ( j − 1 ) τ$. For two equal components of yt the smallest rank is assigned to the component appearing first in yt. Substituting rank vectors to sample vectors in the expression for Shannon entropy gives the so-called permutation entropy $H ( x ^ ) = − ∑ ​ p ( x ^ ) l n p ( x ^ )$, where the sum is over m! possible permutations of the m components of $x ^$ (Bandt and Pompe, 2002).

Analogous conversion has been suggested for TE. Staniek amd Lenhertz (2008) suggest that arguments in the conditional mutual information (CMI) of $T E X → Y$ are modified as follows: $x t$ and $y t$ are substituted by the respective rank vectors $x ^ t$ and $y ^ t$, and the future response vector $y t T$ is replaced by the response rank vector at time $t + T , y ^ t + T$. This conversion of TE is called symbolic. Symbolic Transfer Entropy (STE) defined as

$S T E X → Y = I ( y ⌢ t + T ; x ^ t | y ^ t ) = − H ( y ⌢ t + T , x ^ t | y ^ t ) + H ( x ⌢ t , y ^ t ) + H ( y ⌢ t + T , y ^ t ) − H ( y ^ t )$
(7)

## 3. DATA

### 3.1 World Pandemic Uncertainty Index of Ahir, Bloom, and Furceri (2020)

To quantify uncertainty related to the coronavirus crisis and compare it with previous pandemics and epidemics, Ahir et al. (2020) developed the World Pandemic Uncertainty Index (WPUI) – a sub-index of the World Uncertainty Index. This index exists for 143 countries starting in 1996Q1. To construct the index, the authors count the number of times ’uncertainty’ is mentioned near a word related to pandemics or epidemics in the Economist Intelligence Unit (EIU) country reports. To make the WPUI index comparable across countries, the count is then scaled by the total occurrence of words in each report. Figure 1 illustrates the World Pandemic Uncertainty Index of Ahir et al. (2020). A higher number indicates higher uncertainty related to pandemics. Data spans from 1996Q1 to 2019Q4.

Pandemics and uncertainty, 1996Q1-2020Q3, from Ahir et al. (2020).

### 3.2 Macro-Finance Data on Output, Credit, and Asset Prices of Monnet and Puy (2020)

Our analysis also makes use of data compiled by Monnet and Puy (2020), who have compiled a macrofinancial series using the paper archives of the IMF International Financial Statistics (IFS). This dataset contains details of credit, output, and prices (assets and goods) for a wide range of advanced and emerging countries over the post-war period at quarterly frequency. The database contains (a) real GDP, (b) Credit, (c) Consumer Prices, (d) Stock Prices, and (e) Sovereign Bond Yields. As with WPUI, data spans from 1996Q1 to 2019Q4.

## 4. METHODOLOGY

Let ${ x i , t }$ represent the world pandemic uncertainty index (WPUI). Let ${ y i , t }$ represent variables of interest taken from Monnet and Puy (2020), such as either (a) real GDP, (b) Credit, (c) Consumer Prices, (d) Stock Prices, or (e) Sovereign Bond Yields. Variables are observed at time t =1,…,T, whilst i =1,…,N represents countries.

These real-valued variables are mapped into the space of symbols of embedding dimension m ≥2 , creating m - dimensional histories

(8)

(9)

We wish to examine whether the r-lagged stacked series {xt−r} reduces the entropy of series {yt} , conditional on {yt−r} . The symbolic transfer entropy of Camacho et al. (2021) allows us to consider the informational content of {xt−r} on pooled conditional entropy

(10)

(11)

where m represents the embedding dimension of the time series. The Camacho et al. (2021) symbolic transfer entropy (STE) test measures the information transfer from {xt−r} to {yt} given {yt−r} :

(12)

All variables are log-differenced to deal with potential unit root problems. We perform a unit-root test on each panel’s series separately, then combine the p-values to obtain an overall test of whether the panel series contains a unit root. Table 1 displays the results of panel unit root tests for the variables in question. We select the number of lags for the ADF regressions by minimising the AIC criterion.

## 5. RESULTS

We proceed with testing the presence of information transfer from the World Panedmic Uncertainty Index to economic variables in question. Tables [Tbl:Prices], [Tbl:Credit], [Tbl:Shares], [Tbl:GDP], and [Tbl:Bonds] in Section 5 present the results of various specifications of our tests. Column (1) presents the results of Granger Causality GLS-test, Column (2) presents the results of a Holtz-Eakin et al. (1988) test. Column (3) shows the results of the Symbolic Transfer Entropy (STE) causality test and the one-tailed and two-tailed net transfer entropy test. We set the embedding dimension at m = 3. We specify lag length specification from 1 to 3 years (Camacho et al., 2021). The p values reported in Table 3 show an acceptance of the null hypothesis specified as noncausality relationship between energy consumption and globalization, and between economic growth and FDI.

## 7. CONCLUSION

In this paper we sought to contribute to the literature by revisiting the long-run causal (in a strict statistical sense) effects of pandemic-induced uncertainty on credit growth, stock prices, economic activity, bond yields, and prices (assets and goods). For this purpose, we deployed a symbolic Symbolic Transfer Entropy causality test a la Camacho et al. (2021) that is robust to the data problems that characterize empirical analyses with large panels, such as outliers, when the linearity assumption does not hold, when the data generating process is heterogeneous across the cross-section units or presents structural breaks, when there are extreme observations in some of the crosssection units, or when the process exhibits causal dependence on the conditional variance.

We find evidence of a long-run information transfer between pandemic-induced uncertainty and Stock Prices in our sample of 26 countries. On the other hand, we find no robust evidence of a long-run information transfer between pandemic-induced uncertainty and real GDP, Credit, Consumer Prices, or Sovereign Bond Yields.

## Figure

Pandemics and uncertainty, 1996Q1-2020Q3, from Ahir et al, (2020)

## Table

Panel unit root test results: 1st difference

Symbolic transfer entropy causality test. direction of causality: WPUI ->Prices

symbolic transfer entropy causality test. direction of causality: WPUI ->Credit

Symbolic transfer entropy causality test. direction of causality: WPUI ->Shares

Symbolic transfer entropy causality test. direction of causality: WPUI ->GDP

Symbolic transfer entropy causality test. direction of causality: WPUI ->Bonds

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