International Monetary Policy Spillovers

International Monetary Policy Spillovers Dennis Nsafoah Department of Economics University of Calgary Canada November 1, 2017 1

Abstract This paper uses monthly data (from January 1997 to April 2017) to explore for spillovers from monetary policy in the United States to a number of other countries, namely Canada, the Eurozone, Denmark, Sweden, and Switzerland. I test for cointegration between the U.S. monetary policy rate and the policy rate in each of the other countries using the ARDL approach to cointegration. I also use a bivariate structural GARCH-in-Mean VAR to investigate whether monetary policy uncertainty in the United States has statistically significant spillover effects in each of the other countries. 2

1 Introduction In a heavily globalized economy the monetary policy stance of one country is often intertwined with that of another country, because of macroeconomic interdependence among countries. As Gai and Kapadia (2010, p. 2401) put it, in modern financial systems, an intricate web of claims and obligations links the balance sheets of a wide variety of intermediaries, such as banks and hedge funds, into a network structure. The advent of sophisticated financial products, such as credit default swaps and collateralized debt obligations, has heightened the complexity of these balance sheet connections still further. Given that financial markets around the world have become more integrated over time and business cycles have become more correlated across countries, it is expected that monetary policy in a large economy like the United States (or the Eurozone) will spill over to other countries. However, there are no studies that empirically investigate monetary policy spillover and interaction effects across different countries. In this paper, I test for common stochastic trends between the Federal Reserve s policy rate and the monetary policy rate in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland see Table 1 for a list of the monetary policy rates used in this study. In testing for common stochastic trends, I use the Pesaran et al. (2001) autoregressive distributed lag (ARDL), bounds test approach to testing for the existence of long-run relationships. This approach has the advantage of testing for long-run relations without requiring that the underlying variables are stationary or integrated of the same order. Moreover, I use the Elder and Serletis (2010) bivariate structural GARCHin-Mean VAR to investigate the effects of U.S. monetary policy uncertainty on the monetary policy in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland. The paper is organized as follows. Section 2 discusses the data and tests for common stochastic trends between the U.S. monetary policy rate and that in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland. Section 3 discusses the Elder and Serletis (2010) methodology and presents the empirical results. The last section summarizes and concludes the paper. 2 Common Stochastic Trends 2.1 Data I use monthly data on central bank monetary policy rates, shown in Table 1, over the period from January 1997 to April 2017. The data were obtained from the various central banks web cites, and are shown in Figures 1-6. The data on the target federal funds rate was obtained from the Federal Reserve Economic Data (FRED) of the Federal Reserve Bank of St. Louis. The United States data uses the specific target rate from January 1997 to November 2008 and continues with the lower bound of the target range from December 2008. The target 3

overnight interest rate, the overnight deposite rate, the certificate of deposite rate, the repo rate and the target 3-month Libor rate data were obtained from Bank of Canada, European Central Bank, Danmarks Nationalbank, Riksbank and the Swiss National Bank respectively. 2.2 Univariate Properties Using the monthly data I conduct unit root and stationarity tests for the various policy rates. I use the Augmented Dickey Fuller (ADF) [see Dickey and Fuller (1981)] and the Dickey-Fuller GLS [see Elliot et al. (1996)] tests to test the null hypothesis of a unit root in the levels of the various policy rates. The optimal lag length is selected using Bayesian information criterion (BIC). I also test the null hypothesis of trend stationary using and the KPSS [see Kwiatkowski et al. (1992)] test. The results are presented in Table 2, and show that at conventional levels of significance the null hypothesis of a unit root cannot be rejected. Moreover, the null hypothesis of trend stationarity is rejected for all the policy rates. In the second half of Table 2, I test for a unit root and stationarity in the first differences of the policy rates. I find that the first differences are integrated of order zero. The conclusion from the two tests is that all the policy rates are integrated of order 1. 2.3 The ARDL Cointegration Testing Approach Let us consider the existence of a single long-run relationship between the federal funds rate, f t, and the monetary policy rate of another country, denoted here by o t. In describing the Pesaran et al. (2001) methodology, I follow Serletis (2007, pp. 170-172) and begin with an unrestricted vector autoregression Z t = µ+δt+ p φ j Z t j + ε t (1) j=1 where Z t = [o t f t ], µ is a vector of constant terms, µ = [µ o µ f ], t is a linear time trend, δ = [δ o δ f ] and φ j is a matrix of VAR parameters for lag j. As noted earlier, the monetary policy rates can be either I(0) or I(1). The vector of error terms ε t = [ε o,t ε f ] IN (0, Ω) where Ω is positive definite and given by [ ωoo ω Ω = of ω fo ω ff Given this, ε o,t can be expressed in terms of ε f,t as where ω = ω of /ω ff and u t IN (0, ω oo ). ]. ε o,t = ωε f,t + u t (2) 4

Manipulation of equation (??) allows us to write it as a vector error correction model, as follows p 1 Z t = µ + δt + λz t 1 + γ j Z t j + ε t (3) where = 1 L, and γ fo,j γ ff,j j=1 [ ] γoo,j γ γ j = of,j = p φ k. k=j+1 Here λ is the long-run multiplier matrix and is given by [ ] ( ) λoo λ λ = of p = I φ λ fo λ j, ff where I is an identity matrix. The diagonal elements of this matrix are left unrestricted. This allows for the possibility that each of the series can be either I(0) or I(1). This procedure allows for the testing for the existence of a maximum of one long-run relationship. This implies that only one of λ fo and λ of can be non-zero. As our interest is on the long-run effect of the target federal funds rate on the other policy rate, one can impose the restriction λ fo = 0. Under the assumption λ fo = 0, and using (??), the equation for real money balances from (??) can be written as j=1 o t = α 0 + α 1 t + ϕo t 1 + ψf t 1 (4) p 1 q 1 + β o,j f t j + β f,j f t j + ω f t + u t j=1 j=1 where α 0 = µ o ωµ f, α 1 = δ s + ωδ f, ϕ = λ oo, ψ = λ of ωλ ff, β o,j = γ oo,j ωγ fo,j and β f,j = γ of,j ωγ ff,j. This can also be interpreted as an autoregressive distributed lag [ARDL(p, q)] model. One can estimate equation (??) by ordinary least squares and test the absence of a long-run relationship between o t and f t, by calculating the F statistic for the null hypothesis of φ = ψ = 0. Under the alternative of interest, φ 0 and ψ 0, there is a stable long-run relationship between o t and f t, which is described by o t = θ 0 + θ 1 t + θ 2 f t + v t where θ 0 = α 0 /ϕ, θ 1 = a 1 /ϕ, θ 2 = δ/ϕ and v t is a mean zero stationary process. The distribution of the test statistic under the null depends on the order of integration of o t and f t. In the bivariate case where both variables are I(0), and the regression includes 5

an unrestricted intercept and trend, the appropriate 95% asymptotic critical value is 4.947. When both variables are I(1) this critical value is 5.73. For cases in which one series is I(0) and the other is I(1), the 95% asymptotic critical value falls in-between these two bounds see Pesaran et al. (2001, Table C1.v). As can be seen in Table 3, the target federal funds rate has a common stochastic trend with each of the other policy rates. I also find that the Bank of Canada s target overnight interest rate cointegrates with the other policy rates. There is no strong evidence for cointegration between the European Central Bank s policy rate and the policy rates of Sweden and Switzerland, although Denmark s policy rate cointegrates with the Eurozone s policy rate, consistent with the monetary policy of the Danmark Nationalbank that is aimed at keeping the krone stable against the euro. My results are consistent with those in Caporale et al. (2017) who use fractional integration to provide evidence that supports the existence of bilateral cointegration between central bank monetary policy rates. 3 Monetary Policy Uncertainty in the United States My empirical model for investigating the international effects of monetary policy unceratinty in the United States is based on Elder and Serletis (2010). It is a bivariate structural GARCH-in-Mean VAR in the federal funds rate and the monetary policy rate in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland, as follows Bz t = C + k Γ i z t i + Ψ H t + ɛ t (5) i=1 [ ] hf,t 0 ɛ t Ω t 1 (0, H t ), H t = 0 h o,t where z t is a column vector in the federal funds rate, f t, and the monetary policy rates in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland, denoted by o t. Ω t 1 denotes the information set at time t 1, and [ b11 b B = 12 b 12 b 22 ] ; Γ i = [ γi,11 γ i,12 γ i,21 γ i,22 ] ; Ψ = [ 0 0 ψ 0 ] [ hf,t ; h t = h o,t ] [ ɛf,t ; ɛ t = ɛ o,t The system is identified, as in Elder and Serletis (2010), by assuming that the diagonal elements of B are unity (b 11 = b 22 = 1), that B is lower triangular (b 12 = 0), and that the structural shocks, ɛ t, are uncorrelated. The conditional variance is modeled as m diag (H t ) = C v + F j diag ( ) n ɛ t j ɛ t j + G i diag (H t i ) (6) j=1 6 i=1 ].

where diag is the operator that extracts the diagonal from a square matrix. We assume that the parameter matrices F j and G i are also diagonal. I select the optimal value of k in equation (??) using the Schwartz Information Criterion (SIC), which suggests that k = 3 is sufficient to capture the dynamics of the system. I also assume that m = n = 1 in equation (??) and that each of the F and G matrices are diagonal. The model is estimated using the full information maximum likelihood (FIML) method, as in Elder and Serletis (2010). The point estimates of the mean and variance equation parameters of the bivariate GARCH-in-Mean VAR are reported in Tables 4-8 for each of Canada, the Eurozone, Denmark, Sweden, and Switzerland, respectively. The primary coefficient of interest is the GARCH-in-mean coefficient, ψ. This coefficient indicates the effect of uncertainty in monetary policy in the United States on the monetary policy rate of each of the other countries. It is the coefficient on the conditional standard deviation of the target federal funds rate in the second mean equation. As can be seen in Tables 4-8, ˆψ = 0.011 with a p-value of 0.011 for Canada, ˆψ = 0.050 with a p-value of 0.000 for the Eurozone, ˆψ = 0.008 with a p-value of 0.683 for Denmark, ˆψ = 0.6031 with a p-value of 0.000 for Switzerland, and ˆψ = 0.0127 with a p-value of 0.5416 for Sweden. Thus, monetary policy uncertainty in the United States has negative and statistically significant effects on monetary policy rates in Canada, the Eurozone, and Switzerland, but statistically insignificant effects in Denmark and Sweden. 4 Conclusion Motivated by the idea that the monetary policies of financial centre countries has large spillover effects on smaller economies, I test for the existence of long-run relationships between the monetray policy of the United States and the monetary policy in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland. I use monthly data, over the period from January 1997 to April 2017, and the ARDL bounds test approach, introduced by Pesaran et al. (2001), and find that the Fed s policy rate has a common stochastic trend with each of the other monetary policy rates. This implies that monetary policy in the United States, which is the main world centre of global finance, sets the tone for the rest of the world. I also examine the effects of monetary policy uncertainty in the United States on monetary policy in each of Canada, the Eurozone, Denmark, Sweden, and Switzerland. In doing so, I use a dynamic bivariate framework in which a structural vector autoregression is modified to accommodate bivariate GARCH-in-mean errors, as in Elder and Serletis (2010). In this model, U.S. monetary policy uncertainty is the conditional standard deviation of the one-period-ahead forecast error of the change in the U.S. monetary policy rate. My main empirical result is that uncertainty about monetary policy in the United States has had a negative and statistically significant effect on monetary policy rates in Canada, the Euro- 7

zone, and Sweden, but insignificant effects in Denmark and Switzerland, suggesting that only these two countries enjoy monetary policy independence. 8

References [1] Baillie, R. T. and Bollerslev, T. Cointegration, fractional cointegration, and exchange rate dynamics. The Journal of Finance 49 (1994), 737-745. [2] Caporale, G. M., Carcel, H. and Gil-Alana, L. Central bank policy rates: Are they cointegrated? CESifo Working Paper No. 6389 (March, 2017). [3] Dickey, D.A. and W.A. Fuller. Likelihood ratio tests for autoregressive time series with a unit root. Econometrica 49 (1981), 1057-1072. [4] Elder, J. Some emperical evidence on the real effects of nominal volatility. Journal of Economics and Finance 28 (2004), 1-13. [5] Elder, J. and Serletis, A. Oil price uncertainty. Journal of Money, Credit and Banking 42 (2010), 1137-1159. [6] Elliot, B. E., T. J. Rothenberg, and J. H. Stock. Efficient tests of the unit root hypothesis. Econometrica (1996), 13-36. [7] Engel, R. F. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica (1982), 987-1007. [8] Engle, R. F and Granger, C. Long-run economic relationships: Readings in cointegration. Oxford University Press (1991). [9] Gai, P. and S. Kapadia. Contagion in financial networks. Proc. R. Soc. A 466 (2010), 2401 2423. [10] Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54 (1992), 159-178. [11] Pesaran, M. H., Shin, Y. and Smith, R. J. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16 (2001). [12] Serletis, A. The demand for money: Theoretical and empirical approaches. Springer (2007). 9

Figure 1: Canada's overnight target interest rate 7 6 5 Interest rate (%) 4 3 2 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Source : Bank of Canada 10

Figure 2: Denmark's certificate of deposit rate 6 5 4 3 Interest rate (%) 2 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017-1 -2 Source: Danmarks Nationalbank

Figure 3: The Eurozone's overnight deposit rate 4 4 3 3 2 Interest rate (%) 2 1 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017-1 -1 Source : European Central Bank

Figure 4: Sweden's repo rate 6 5 4 Interest rate (%) 3 2 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017-1 Source: Riksbank

Figure 5: Switzerland's target 3-month Libor rate 4 4 3 3 2 Interest rate (%) 2 1 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017-1 -1 Source: Swiss National Bank

Figure 6: The Federal Reserve's federal funds target rate 7 6 5 Interest rate (%) 4 3 2 1 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Source : FRED, Federal Reserve of St.Lious

Table 1: Central banks and their monetary policy instruments Country Central bank Policy instrument Canada Bank of Canada Overnight interest rate Denmark Danmarks Nationalbank Certificate of deposit rate Eurozone European Central Bank Overnight deposit rate Sweden Riksbank Repo rate Switzerland Swiss National Bank 3-month Libor rate United States Federal Reserve Federal funds rate

Table 3: ARDL bounds tests of cointegration US Canada Denmark Eurozone Sweden Canada 9.411* Denmark 22.605* 8.829* Eurozone 18.247* 17.508* 7.042* Sweden 7.397* 6.366* 3.470 1.764 Switzerland 11.299* 9.235* 4.381 4.385 3.870 Note: An asterisk indicates significance at the 5% level.

Table 4: Estimates of the GARCH-in-mean VAR for Canada Mean equation Coefficient Fed funds rate Canada C 1.060 (0.000) -0.226 (0.000) B 0.000 (0.000) -0.286 (0.000) Γ 1,1 0.025 (0.000) -0.007 (0.000) Γ 1,2-0.093 (0.000) -0.012 (0.000) Γ 2,1 0.019 (0.000) 1.124 (0.000) Γ 2,2-0.041 (0.000) 0.001 (0.558) Γ 3,1 0.039 (0.000) -0.157 (0.000) Γ 3,2-0.017 (0.000) 0.020 (0.000) Ψ 0.000 (0.000) -0.011 (0.011) Variance Equation Coefficient Fed funds rate Canada Cv 0.000 (0.704) 0.000 (0.000) F 52.211 (0.000) 0.173 (0.000) G 0.000 (0.000) 0.827 (0.000) Note: Numbers in parenthesis are p-values.

Table 5: Estimates of the GARCH-in-mean VAR for the Eurozone Mean equation Coefficient Fed funds rate Eurozone C 1.029 (0.000) 0.011 (0.279) B 0.000 (0.000) -0.031 (0.003) Γ 1,1-0.071 (0.000) 0.001 (0.001) Γ 1,2 0.957 (0.000) -0.028 (0.000) Ψ 0.000 (0.000) -0.050 (0.000) Variance Equation Coefficient Fed funds rate Eurozone Cv 0.000 (0.547) 0.000 (0.281) F 4.180 (0.000) 3.439 (0.000) G 0.177 (0.001) 0.000 (0.000) Note: Numbers in parenthesis are p-values.

Table 6: Estimates of the GARCH-in-mean VAR for Denmark Mean equation Coefficient Fed funds rate Denmark C 1.034 (0.000) 0.094 (0.000) B 0.000 (0.000) 0.022 (0.001) Γ 1,1-0.061 (0.000) 0.027 (0.003) Γ 1,2 0.095 (0.000) -0.051 (0.000) Ψ 0.000 (0.000) -0.008 (0.683) Variance Equation Coefficient Fed funds rate Denmark Cv 0.011 (0.000) 0.000 (0.100) F 1.973 (0.000) 2.484 (0.000) G 0.000 (0.001) 0.125 (0.001) Note: Numbers in parenthesis are p-values.

Table 7: Estimates of the GARCH-in-mean VAR for Sweden Mean equation Coefficient Fed funds rate Sweden C 1.057 (0.000) -0.144 (0.015) B 0.000 (0.000) -0.130 (0.003) Γ 1,1 0.388 (0.000) -0.116 (0.000) Γ 1,2-0.047 (0.324) 0.069 (0.137) Γ 2,1-0.329 (0.000) -0.037 (0.000) Γ 2,2 0.015 (0.714) 1.021 (0.000) Γ 3,1-0.040 (0.000) -0.089 (0.000) Γ 3,2 0.119 (0.184) 0.068 (0.319) Γ 4,1 0.150 (0.000) 0.016 (0.000) Γ 4,2-0.238 (0.000) 0.003 (0.808) Ψ 0.000 (0.000) 0.013 (0.542) Variance Equation Coefficient Fed funds rate Sweden Cv 0.000 (0.077) 0.012 (0.000) F 9.115 (0.000) 0.359 (0.000) G 0.000 (0.000) 0.175 (0.184) Note: Numbers in parenthesis are p-values.

Table 8: Estimates of the GARCH-in-mean VAR for Switzerland Mean equation Coefficient Fed funds rate Switzerland C 1.327 (0.000) -0.104 (0.201) B 0.000 (0.000) -0.272 (0.000) Γ 1,1-0.302 (0.000) 0.071 (0.009) Γ 1,2-0.128 (0.042) 0.964 (0.000) Γ 2,1-0.155 (0.000) 0.111 (0.075) Γ 2,2-0.011 (0.936) 0.036 (0.001) Ψ 0.000 (0.000) -0.603 (0.000) Variance Equation Coefficient Fed funds rate Switzerland Cv 0.007 (0.000) 0.001 (0.000) F 0.979 (0.000) 1.352 (0.022) G 0.000 (0.000) 0.363 (0.000) Note: Numbers in parenthesis are p-values.

Table 9: Summary of country response to U.S monetary policy uncertainty Policy rate ˆψ Canada -0.011 (0.011) Denmark -0.008 (0.683) Eurozone -0.050 (0.000) Sweden 0.013 (0.542) Switzerland -0.603 (0.000) Note: Numbers in parenthesis are p-values.