# RDP 2019-03: Explaining Monetary Spillovers: The Matrix Reloaded 3. Research Design: Detecting and Explaining Spillovers

This section provides a brief summary of the main features of the research design. Our empirical analysis of spillovers proceeds in two stages.

Detecting spillovers. First, we test which central banks' policy actions trigger spillovers to others, and which economies' interest rates are most receptive. Specifically, we start with separate regressions for each originator-recipient combination of economies to compare spillovers from shock-originating central banks to recipient economies for interest rates. The equation we estimate is given as

1 $Δ r i,t = α ij + β ij ′ MP S j,t + ε i,j,t$

where Δri,t is the change in interest rates in economy i and MPSj,t is our measure of monetary policy shocks from central bank j. We provide exact details on measurement in Section 4 below.

Explaining spillovers. Second, we aim to distinguish between the different spillover channels outlined above drawing on the richness of our data in the cross-section of economies. The three channels differ in the types of macro and financial conditions affecting the strengths of spillovers across economies. For the channel of domestic economic conditions, we expect that spillovers should positively relate to bilateral trade flows as well as macroeconomic interlinkages (e.g. as proxied by correlations of the business cycle and inflation across economies). The FX regime channel posits that, when an exchange rate is tied to that of a major currency, volatility in the corresponding exchange rate cross will be significantly muted. Hence, one would expect FX volatility and spillover strengths to be negatively correlated. As for the channel of bond risk premia and financial conditions, a key prediction is that economies that are more financially open should receive larger spillovers.

To shed light on the empirical relevance of the three channels as spillover determinants, we run the following regression with interaction terms

2 $Δ r i,t = α j + θ j ′ Z t +( β j ′ + γ j ′ X i,t−1 )MP S j,t + ε j,t$

where Zt is a global control; Xi,t is a recipient-specific conditioning variable; θj measures the sensitivity to global controls; βj is a vector that measures the unconditional spillover from our three monetary policy shocks.[13] Our main object of interest here is γj, which measures the spillover conditional on (recipient) economy-specific controls.

Our conditioning variable Xi,t either measures economic linkages, conditions governing the FX regime of the economy, or financial linkages between the originator and recipient economies. Another important dimension to differentiate our channels is the maturity of the interest rates that will be more affected by spillovers. The domestic economic channel will be more prevalent for short rates (or expectations of future short rates embedded in long-term rates). The FX regime channel, by contrast, will operate predominantly via short-term interest rates, but longer-term rates might also be affected to some extent. As for the risk premium channel, we expect mostly long-term rates to be subject to spillover effects. This is because yields at the longer end of the yield curve are more susceptible to risk premium fluctuations than yields at the shorter end. The latter will be driven to a larger extent by expectations about the path of future short rates. Table 1 summarises the different predictions of the three spillover channels and our empirical approach to differentiate among them.

Table 1: Distinguishing Spillover Channels
Channel Maturity of affected interest rates Macrofinancial conditioning variables
(a) Domestic macroeconomic conditions Mainly short Trade (+); commonality in growth and inflation (+)
(b) FX regime Both short and long FX volatility (−)
(c) Bond risk premia and financial conditions Long Financial openness (+)
Notes: The table summarises testable implications of the three spillover channels along two key dimensions: (i) maturity of the affected interest rates, and (ii) macroeconomic or financial conditioning variables determining whether spillovers might be stronger or weaker; the (+)/(−) sign in parentheses indicates whether the expected relationship between the conditioning variables and spillover strength is positive/negative

## Footnote

For conditional variables, some of them measure bilateral relations. In that case, they are not only recipient-specific but also originator-specific. [13]