Section II as well as how these have also evolved over time and differ during Highly Synchronized Tightening periods (defined in Section IV.1.1)

# V.1. Methodology and Data

In order to estimate the role of our seven global and domestic shocks, we employ the following FAVAR model: R,global π,global where Zt consists of global interest rates (ft ), global inflation (ft ), global output growth (fty,global), oil price growth (∆op), domestic interest rates (Rdomestic), domestic inflation (π<sup>domestic</sup> ), and domestic output growth (y<sup>domestic</sup> ).

The εt is a vector of orthogonal structural innovations, which include the following four global shocks: (i) common changes in monetary policy across countries (“global monetary policy”); (ii) the global demand for goods and services (“global demand shock”); (iii) the global supply of goods and services (“global supply shock”); and (iv) oil prices (“oil price shock”). It also includes the following three domestic shocks: (v) domestic monetary policy (“domestic monetary policy”); (vi) the domestic supply of goods and services (“domestic supply shock”); and (vii) the domestic demand for goods and services (“domestic demand shock”).<sup>52</sup> The model assumes stochastic volatility of the structural shocks—the residuals represented by the time-varying residual covariance matrix ∑t. These shocks are independently (but not identically) distributed across time.<sup>53</sup> This FAVAR model is estimated using monthly data with four lags (based on the AIC and SIC information criteria). The Bayesian routine we employ to estimate the model first searches for 500 successful draws from at least 1,000 iterations with 500 burn-ins; the results are based on the median of these 500 successful draws. The estimation process is standard Gibbs sampling, except that the volatility of residuals is endogenously determined. In the estimation of the model, structural shocks are assumed to have unit variance.

52 Our global and domestic shocks are motivated by theoretical studies on the sources of movements in interest rates, output, and inflation in the United States. For example, Smets and Wouters (2007) develops a model that decomposes the variation in output, inflation, and policy rates into demand shocks (including risk premium, investment, and fiscal shocks), price mark-up shocks (including commodity price shocks), supply shocks, and interest rate shocks. Del Negro et al. (2013, 2022) builds a model analysing an even wider range of shocks behind U.S. macroeconomic and financial variables.

53 Typical VAR models assume that the variance-covariance matrix of residuals is constant over time. However, this assumption could be problematic in our exercise since there are several periods with substantially heightened volatility in our long time series, such as around the COVID-19 pandemic and other major global shocks (Lenza and Primiceri, 2022). The variance-covariance matrix of residuals ∑t is allowed to be period-specific, hence rendering stochastic volatility and introducing heteroskedasticity (Carriero, Corsello, and Marcellino, 2019). εt is serially independent with zero mean and variance ∑t. We assume that ∑t = FΛtF′, where F is a lower triangular matrix with ones on its main diagonal, while Λt is a period-specific diagonal matrix whose diagonal elements Λjj,t (the time-varying variances) follow a stochastic process (Cogley and Sargent, 2005).

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