2.1. Modeling economic policy uncertainty spillovers

To construct the EPU spillover shock $EPUShock$ , we implement the following procedure:

First, we estimate a VAR model for each country $q=1,2,\ldots,N,$ to obtain the innovations for EPU $e_{q}$ :

(1) \begin{equation} \varPsi (0)\left [\begin{array}{c} V_{qt}\\ Y_{t}\\ FU_{qt}\\ EPU_{qt} \end{array}\right ]=\varPsi (L)\left [\begin{array}{c} V_{q,t-1}\\ Y_{t-1}\\ FU_{q,t-1}\\ EPU_{q,t-1} \end{array}\right ]+\left [\begin{array}{c} e_{q,t}^{V}\\ e_{t}^{Y}\\ e_{t}^{F}\\ e_{q,t} \end{array}\right ]. \end{equation}

The VAR includes a set of domestic macroeconomic indicators $V_{q}$ , a global real economic activity indicator $Y$ that are common across all countries, a set of foreign EPU index $FU_{q}$ , and the domestic EPU index $EPU_{q}.$ $V_{q}$ includes the domestic $CPI$ inflation, real $GDP$ , the short-term (policy) interest rate, the real exchange rate, and a stock price index in country $q$ . We use the global real economic activity index by Killian (Reference Kilian2009) for $Y$ . The structural shocks to the $EPU$ equation, $e_{q}$ , capture the innovations to EPU in source country $q$ that are orthogonal to common macroeconomic indicators and foreign influences $.$ We interpret shocks $e_{q}$ as domestic $EPU$ shocks in country $q$ . The VAR model specified in (1) is estimated by imposing a Cholesky structure with $EPU$ ordered last.Footnote ¹

To measure the size of policy uncertainty spillover shocks to a recipient country $i$ , we aggregate $e_{q,t}$ across source countries $q\neq i$ as follows:

(2) \begin{equation} EPUShock_{i,t}=\frac{\sum _{q\neq i}w_{iq,t}e_{q,t}}{\sum _{q\neq i}w_{iq,t}}, \end{equation}

where $EPUShock_{i,t}$ is the EPU spillover shocks to country $i$ , and $w_{iq}$ are the weights that capture the strength of the economic links between countries $i$ and $q$ . In the baseline case, we construct $w_{iq,t}$ using the trade intensity between country $i$ and country $q$ in base year $2005$ . We consider alternative constructions of the weights for robustness. Specifically, we consider constructing $w_{iq,t}$ (1) using country $q$ ’s imports from country $i$ in base year 1998; (2) using time-varying weights given by country $q$ ’s imports from country $i$ from the previous year; (3) using equal weights. Our results are qualitatively robust to alternative weighing schemes.Footnote ²

2.2. Panel ST-VAR

After we construct the EPU spillover shocks to each country $i$ , we include these exogenous regressors in a panel ST-VAR to assess their effects on a set of core macroeconomic variables. Suppose our sample includes $N$ countries indexed by $i=1,2,\ldots,N$ . The specification is as follows:

(3) \begin{eqnarray} X_{i,t} & = & f(z_{i,t-1})\Pi _{R}(L)X_{i,t-1}+[1-f(z_{i,t-1})]\Pi _{E}(L)X_{i,t-1}\\[4pt] & & +f(z_{i,t-1})\Lambda _{R}(L)EPUShock_{i,t}+[1-f(z_{i,t-1})]\Lambda _{E}(L)EPUShock_{i,t}+u_{i,t,}\nonumber \end{eqnarray}

(4) \begin{eqnarray} f(z_{i,t}) & = & \frac{\exp\! ({-}\gamma z_{i,t})}{1+\exp\! ({-}\gamma z_{i,t})},\text{ }\gamma \gt 0,\text{ }var(z_{i,t})=1,\text{ }E(z_{i,t})=0. \end{eqnarray}

where $X_{i,t}$ is an $M\times 1$ vector of macroeconomic variables of country $i$ and $z_{i,t}$ is a regime transition indicator.Footnote ³ $u_{i,t}$ is a $M\times 1$ vector of reduced form residuals. $\Pi _{R}$ and $\Pi _{E}$ are $M\times M$ matrices of autocorrelation coefficients capturing the dynamics of $X$ during recessions and expansions. $\Lambda _{R}$ and $\Lambda _{E}$ are $M\times 1$ vector of coefficients capturing the effect of uncertainty spillover shocks during the two regimes. For $\mathbf{u}_{t}=\left[u_{1,t}^{{\prime }},\ldots,u_{N,t}^{{\prime }}\right]^{\prime }$ and $\mathbf{z}_{t}=\left[z_{1,t}^{{\prime }},\ldots,z_{N,t}^{{\prime }}\right]^{\prime }$ ,

(5) \begin{eqnarray} \mathbf{u}_{t} & \sim & N\!\left(\mathbf{0}_{NM\times 1},\boldsymbol{\Omega }_{t}\right), \end{eqnarray}

(6) \begin{eqnarray} \boldsymbol{\Omega }_{t} & = & f(\mathbf{z}_{t-1})\boldsymbol{\Omega }_{R}+[\boldsymbol{{I}}_{NM\times 1}-f(\mathbf{z}_{t-1})]\boldsymbol{\Omega }_{E}, \end{eqnarray}

where $\boldsymbol{\Omega }_{R}$ and $\boldsymbol{\Omega }_{E}$ are $NM\times NM$ positive-definite covariance matrices for recession and expansion regimes, respectively.

In our baseline specification, $X_{i,t}$ includes eight core macroeconomic variables, ordered as CPI inflation, real consumption, real GDP, real exports, short-term interest rate, real effective exchange rate, stock price index, and $EPU$ .

We follow the literature to select the transition indicator $z_{i,t}$ to be the seven-quarter moving average of GDP growth rate in country $i,$ normalized to have zero mean and unit variance. $f(z),$ bounded between 0 and 1, is a logistic transition function that measures the probability or degree of being in a recession given $z$ . Note that $z$ enters the equation (3) with one period lag to avoid contemporaneous feedback from shocks to the state of the economy. The smoothness of the transition function is measured by parameter $\gamma .$ Larger values of $\gamma$ imply more abrupt switches from one regime to another. Intuitively, the above ST-VAR model assumes that the dynamics of $X$ can be described by a linear combination of two linear VARs: one suited to describe the dynamics during recessions and the other suited to describe the dynamics during expansions. Small values of $z$ during economic stress translate into large values of $f(z)$ near 1, resulting in a heavier weight of the recession-regime VAR in the characterization of the data in these periods. The model nests a standard linear VAR in the limiting cases when $f(z)$ $=0$ or $f(z)=1$ .

By adding the international spillover shocks $EPUShock$ as exogenous regressors in the system, we assume that $X_{t}$ and their lags cannot influence $EPUShock_{t}$ . We think the assumption is reasonable given the way that $EPUShock_{t}$ is constructed. We also performed exogeneity tests based on whether $X_{t}$ can Granger-cause $EPUShock_{t}$ using Bayesian information criteria (BIC) selected lags $.$ At the 5% significance level, we cannot reject the hypothesis that $X_{t}$ does not Granger-cause $EPUShock_{t}.$

The model is estimated using two lags as suggested by BIC criteria. Given the nonlinearity of the model,Footnote ⁴ we estimate the model using a Markov Chain Monte Carlo method as in Chernozhukov and Hong (Reference Chernozhukov and Hong2003) to find a global optimum and create confidence intervals. Detailed estimation strategy is discussed in the Section 1 of the online appendix.

2.3. Data

We use quarterly data from 1998Q1 to 2017Q4 to maximize the number of countries in our sample. Our sample includes $N=14$ Organisation for Economic Co-operation and Development (OECD) countries, including Australia, Canada, Chile, France, Germany, Greece, Ireland, Italy, Japan, South Korea, Mexico, Sweden, United Kingdom, and the USA. This selection is based on the availability of EPU index data. The EPU index, proposed by Baker et al. (Reference Baker, Bloom and Davis2016), is available for 23 economies with different lengths of observations going back as early as 1985. The index measures economic policy-related uncertainty based on newspaper frequency counts of relevant key words. Among the 23 economies with EPU data, we dropped non-OECD economies, including Brazil, China, Colombia, India, Hong Kong, Russia, and Singapore. We then exclude the Netherlands and Spain, which only have EPU data going back to 2003 and 2001, respectively. We convert the monthly index into a quarterly index by taking the monthly average within each quarter.

We obtain real GDP, consumption, investment, consumer price index (CPI), imports and exports, short-term interest rate, exchange rate, and share price indices data for the OECD countries from the Federal Reserve Economic Data (FRED) dataset by the Federal Reserve Bank of St. Louis. The bilateral import flow data is from the United Nations. The world economic activity index is from Killian’s website. The EPU data is from www.policyuncertainty.com.

4.1. Strategy

To examine the importance of the possible transmission channels, we perform the following counterfactual experiments that allow us to isolate the role of one particular channel at a time. The basic idea is to assume an economy with the same underlying economic environment as described by Equations (3) and (4), except that the international EPU spillover shocks are restricted not to affect one particular macroeconomic variable that directly links to the transmission channel of interest, so any propagation effect caused by the response of the variable is removed. For example, to study the importance of the trade channel, we restrict that the EPU spillover shocks do not affect exports (imports) at all horizons, so the shock’s influence on other macroeconomic variables through trade is shut down. We then compare the baseline responses (unrestricted) and restricted responses to examine the importance of the channel.

Specifically, conditional on a particular regime $s=E,R,$ the VAR system (3) and (4) is linear with regime-specific parameters. We rewrite the VAR system in the structural form:

(7) \begin{equation} A_{0}^{(s)}\mathbf{X}_{t}=\sum _{k=1}^{K}A_{k}^{(s)}\mathbf{X}_{t-k}+\sum _{k=1}^{K}B_{k}^{(s)}\mathbf{EPUShock}_{t-k+1}+\boldsymbol{\varepsilon }_{t}, \end{equation}

where $s=E,R.$ Parameters with superscript $(s)$ indicate the parameter estimates conditional on the regime. $\boldsymbol{\varepsilon }_{t}$ is a vector of orthogonal structural shocks given by $\boldsymbol{\varepsilon }_{t}=A_{0}^{(s)}\mathbf{u}_{t}$ where $A_{0}^{(s)}$ is a lower-triangular regime-dependent impact matrix.

Let $e_{i}$ be a $1\times M$ selection row vector with a one in the $i^{\text{th}}$ place and zeros elsewhere, $A_{0}^{(s)\text{ -1}}(i)$ be the $i$ th column of the matrix $A_{0}^{(s)\text{ -1}},$ and $A_{0}^{(s)\text{ -1}}B_{k}^{(s)}(i)$ be the $i^{\text{th}}$ element of the vector $A_{0}^{(s)\text{ -1}}B_{k}^{(s)}.$ The impulse response of variable $i$ to a unit $EPU$ spillover shock at horizon $h$ in regime $s$ is

\begin{equation*} \delta _{i,h}^{(s)}=\sum _{q=1}^{\min\! (h,K)}e_{i}\Phi ^{(s)\text { }h-q\text { }}A_{0}^{(s)\text { -1}}B_{q}^{(s)}(i). \end{equation*}

where $\Phi$ is the companion matrix defined as:

\begin{equation*} \Phi ^{(s)}=\left [\begin {array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} A_{0}^{(s)\text { -1}}A_{1}^{(s)} & A_{0}^{(s)\text { -1}}A_{2}^{(s)} & \ldots & \ldots & A_{0}^{(s)\text { -1}}A_{K}^{(s)}\\[4pt] I & 0 & 0 & \ldots & 0\\[4pt] 0 & I & 0 & \ldots & 0\\[4pt] \vdots & \vdots & \ddots & \vdots & \vdots \\[4pt] 0 & \ldots & \ldots & I & 0 \end {array}\right ]. \end{equation*}

Meanwhile, the impulse response of variable $i$ to a unit size structural shock to endogenous variable $j$ at horizon $h$ is $e_{i}\Phi ^{(s)\text{ }h-1\text{ }}A_{0}^{(s)\text{ -1}}(j).$

Suppose, we would like to shut down the effect of EPU spillover shocks channeled by variable $j$ . We need to restrict the response of variable $j$ at all horizons $h=1,2,\ldots,H$ to be zero. This is achieved by creating a sequence of hypothetical structural shocks to variable $j$ , $\{\tilde{\varepsilon }_{j,h}^{(s)}\}_{h=1,\ldots,H},$ so that the created shocks offset the effect of the spillover shock on variable $j$ at $\mathit{all}$ horizons $.$

In the first period, to shut down the effect of a one unit shock in $EPUShock$ on variable $j$ on impact, $\tilde{\varepsilon }_{j,1}^{(s)}$ must satisfy

\begin{equation*} \delta _{j,1}^{(s)}+A_{0}^{(s)\text { -1}}(j,j)\tilde {\varepsilon }_{j,1}^{(s)}=0,\text { or }\tilde {\varepsilon }_{j,1}^{(s)}=-\frac {A_{0}^{(s)\text { -1}}B_{1}^{(s)}(j)}{A_{0}^{(s)\text { -1}}(j,j)}. \end{equation*}

The subsequent shocks $\{\tilde{\varepsilon }_{j,h}^{(s)}\}_{h=2,\ldots,H}$ starting from the second period can be computed recursively by solving

\begin{equation*} \delta _{j,h}^{(s)}+\sum _{q=1}^{h-1}e_{j}\Phi ^{(s)\text { }h-q\text { }}A_{0}^{(s)\text { -1}}(j)\tilde {\varepsilon }_{j,q}^{(s)}+A_{0}^{(s)\text { -1}}(j,j)\tilde {\varepsilon }_{j,h}^{(s)}=0. \end{equation*}

The solution yields the shock sequence:

\begin{equation*} \tilde {\varepsilon }_{j,h}^{(s)}=-\frac {\delta _{j,h}^{(s)}+\sum _{q=1}^{h-1}e_{j}\Phi ^{(s)\text { }h-q\text { }}A_{0}^{(s)\text { -1}}(j)\tilde {\varepsilon }_{j,q}^{(s)}}{A_{0}^{(s)\text { -1}}(j,j)}, \,\,\, h=2,\ldots,H. \end{equation*}

Given $\{\tilde{\varepsilon }_{j,h}^{s}\}_{h=1,\ldots,H}$ and unrestricted impulse responses $,$ we can construct the hypothetical impulse responses (restricted) of any variable $i$ in the VAR system to a unit shock to $EPUShock$ as:

\begin{equation*} \tilde {\delta }_{i,h}^{(s)}=\delta _{i,h}^{(s)}+\sum _{q=1}^{h}e_{i}\Phi ^{(s)\text { }h-q\text { }}A_{0}^{(s)\text { -1}}(j)\tilde {\varepsilon }_{j,q}^{(s)},\,\,\,\, i=1,2,\ldots,M. \end{equation*}

Comparing the restricted responses $\tilde{\delta }_{i,h}^{(s)}$ to the baseline unrestricted responses $\delta _{i,h}^{(s)}$ allows us to examine the importance of variable $j$ in transmitting the effects of the $EPUShock$ to variable $i$ .

4.2. Possible channels

We apply the above method to our model and examine a few possible transmission channels.

4.2.1. Interconnected economic policy uncertainty

Given the increasing interconnectedness of the global economy, policymakers may need to respond not only to changes in domestic economic conditions but also to shocks emanating from abroad, including policy changes. When uncertainty rises about the economic policies that foreign policymakers may adopt, it makes deciding the country’s own economic policy more challenging and increases domestic policy uncertainty. As shown in Figure 2, the EPU spillover shocks significantly increase the domestic EPU level. An increase in domestic policy uncertainty, in turn, has contractionary effects on its economy. A large literature that focuses on the local effects of policy uncertainty, including Bloom (Reference Bloom2014), Caldara et al. (Reference Caldara, Fuentes-Albero, Gilchrist and Zakrajëk2016), Baker et al. (Reference Baker, Bloom and Davis2016), and Bloom et al. (Reference Bloom, Floetotto, Jaimovich, Saporta-Eksten and Terry2018), finds that higher uncertainty can reduce both investment and hiring, make households too cautious in spending, increase risk premium in financial markets, and undercut productivity growth by resource misallocation.

Using the method described in Section 4.1 and comparing the impulse responses with and without the endogenous responses in domestic EPU, we find that the domestic EPU channel is an important transmission channel for international EPU spillover shocks, especially during expansions. As shown in Figure 3, the spillover shocks during expansions have significantly smaller and less persistent contractionary effects on important real economic indicators once the channel is shut down. Removing the EPU channel reduces the maximum responses in real GDP, consumption, and exports by 54.2%, 46.8%, and 31.2% during expansions, and the declines in real GDP, consumption, and exports only last four quarters in expansions, compared to 7–8 quarters in the unrestricted baseline. During recessions, removing the EPU channel reduces the maximum responses in real GDP, consumption, and exports by 7.0%, 22.4%, and 11.3%, but it does not shorten the duration of real contractions caused by the EPU spillover shocks.

Figure 3. Impulse responses after removing the endogenous responses in EPU.

4.2.2. Financial channel

A literature, including Gilchrist et al. (Reference Gilchrist, Sim and Zakrajëk2014) and Popp and Zhang (Reference Popp and Zhang2016), finds that the financial channel is important for transmitting domestic uncertainty shocks. We also explore the role of the financial channel in transmitting international spillovers of EPU shocks. Our ST-VAR includes stock market returns, measured by the first log differences in share price indices, to proxy the financial market conditions in our sample countries. An unexpected elevation of uncertainty in another country can increase the degree of financial stress domestically, and through the international connectedness of the financial markets and financial institutions, such shocks can have spillover effects on financial conditions. The changes in financial conditions then affect the availability of credit, and the liquidity and risk premium required by investors in the affected country, propagating the effects of the spillover EPU shocks on its macroeconomic variables.

Figure 2 shows that a positive EPU spillover shock lowers stock market returns, consistent with this intuition. Figure 4 reports the IRFs when the share price indices are restricted not to move after the shock occurs. We have two main comments. First, the financial channel is an important transmission channel in both regimes. Though the initial responses to the shock remain similar, removing the financial channel significantly reduces the subsequent responses to the shock and lowers the persistence of the shock’s effect on many real macroeconomic indicators. There is a 68.1%, 68.2%, and 80.3% reduction in the maximum responses of consumption, output, and export during expansions, and a 23.6%, 31.6%, and 22.6% reduction during recessions. Second, the restricted impact of the shocks is more front-loaded during recessions. Over 50% of the maximum impact on real GDP is recovered by the second quarter during recessions and by the third quarter during expansions, while it takes 4–5 quarters in the unrestricted baseline. This result suggests that the endogenous responses of the financial conditions make the shock effects more persistent and longer-lasting.

Figure 4. Impulse responses after removing the financial channel.

4.2.3. Confidence

Confidence is likely another channel for EPU spillover shocks, since elevated global uncertainty creates anxiety for households and firms. Their caution in spending, investment, and hiring decreases domestic aggregate demand. To examine this channel, we estimated our model with the business confidence index (BCI) from OECD following the same method described in Section 4.1. To see the importance of the confidence channel, we restrict the BCI index to remain fixed when there is a spillover shock $EPUShock$ . The BCI index is not available for Ireland prior to 2008Q4 and for Canada prior to 1998Q3, so we remove Ireland from our sample and adjust the sample period to 1998Q4−2017Q4. We re-estimate equations (1)−(4) to include the BCI index using the reduced sample, and the result is reported in Figure 5. First, we observe that business confidence falls significantly following a positive EPU spillover shock during recessions, while the effect is much smaller during expansions. Second, the confidence channel appears to be important during recessions but not in expansions. During recessions, removing the BCI responses lowers the maximum response of real GDP and exports by 23.2% and 24.1%. We do not observe that the channel is as important during expansions, since the impulse responses are similar with and without the endogenous response in the BCI index during this state.

Figure 5. Impulse responses after removing the BCI index.

Figure 6. Impulse responses after removing exports.