Specification of the GVAR model

In specifying the underlying VARX models for the individual countries, we treat the U.S. equations differently than the EMEs equations. On the one hand, we include a different set of weakly exogenous variables, similar to what is commonly done in GVAR applications due to the dominant role of the U.S. in global financial markets (see, for instance, Eickmeier and Ng, 2015, Georgiadis, 2015a, or Chen et al., 2015). More importantly, as we are interested in an unconventional monetary policy shock, we set up a model that allows identifying such a shock.

Hence, the VARX model for the U.S. resembles VAR specifications from the litera- ture on identifying conventional monetary policy shocks, usually containing output, inflation, and the Fed funds rate (see, among many others, Christiano et al., 1999). However, we replace the Fed funds rate as the monetary policy instrument by the size of the Fed balance sheet as in Gambacorta et al. (2014). Following the beginning of the financial crisis in 2008, the Federal funds rate soon reached its effective lower bound and stayed there for most of our sample period. Instead, the Fed introduced a number of (new) policy tools, most of which have altered both the size and the composition of its balance sheet, commonly referred to as unconventional monetary policy. The purpose of these tools has been to stabilize the functioning of financial

markets, especially during the crisis, and to provide support to the economy during the recession and the subsequent sluggish recovery.

The balance sheet of the Fed more than quadrupled between 2007 and 2014 (see Figure 1.B.2 in Appendix 1.B). By using the size of the Federal Reserve balance sheet as the monetary policy instrument, the identified unconventional monetary policy shocks will be linked to all measures that increased the balance sheet. Notable policies that affected the balance sheet size start after the failure of Lehman Brothers in September 2008, as the Fed immediately provided credit to intermediaries and key markets. Other notable expansions are associated with the three programs of Quantitative Easing (QE) that were conducted. First, QE1, announced in November 2008 and expanded in March 2009, included purchases of mortgage backed securities and Treasury securities. In November 2010, it was succeeded by QE2 that focused on buying long-term Treasury securities. Lastly, QE3 was initiated in September 2012 and again included both mortgage backed securities and Treasury securities. Although these programs also affected the composition of the Fed balance sheet, the main change in the monetary policy stance was initiated through its expansion.11

Hence, the size of the balance sheet should be a suitable instrument to measure the Fed’s unconventional policy stance over our sample period.

Changes in the balance sheet size, however, do not only capture exogenous in- novations to UMP, but also the endogenous reaction of the Fed to the state of the economy and, importantly, to financial market turmoil as e.g. in the immediate af- termath of the Lehman collapse. To identify an exogenous innovation to the balance sheet, we add the volatility index VIX to the model to capture financial market un- certainty. Lastly, we add total U.S. portfolio outflows as the variable of interest for our research questions. In sum, the following definition of endogenous and foreign

11_{In contrast, two unconventional monetary policy measures that did only alter the composition}

of the balance sheet are on the one hand the Fed’s response to the run on Bear Stearns in March 2008, when it increased its lending to investment banks and other stressed financial intermediaries, but at the same time lowered its holding of short-term Treasury securities. On the other hand, between 2011 and 2012, the Fed ran a maturity extension program in which short- and medium-term Treasury securities were sold and proceeds used to purchase long-term Treasury securities to flatten the yield curve.

variables is used for the U.S. model:12

y_{U S,t}= (output,inflation,VIX,Fed balance sheet,portfolio outflows)0,

y∗_{U S,t}= (foreign output,foreign inflation)0,

where the balance sheet is included in its logarithm for the ease of interpretation. To distinguish between an exogenous innovation to the Fed balance sheet and an endogenous reaction of the central bank to the state of the economy or financial market turmoil, we follow Gambacorta et al. (2014) and impose a mixture of zero and sign restrictions on the structural impulse response functions. First, in accordance with standard assumptions in the literature, we assume that a shock to the policy instrument, in our case the Fed balance sheet, only has a lagged impact on output and inflation. The Fed itself reacts instantaneously to innovations to output and inflation as commonly assumed in VAR analysis of monetary policy transmission. Second, to account for the endogenous reaction to financial market turmoil, we use the sign restrictions displayed in Table 1.3.1. On the one hand, we assume that an expansionary UMP shock does not increase the VIX. This reflects the notion that UMP had the effect of mitigating concerns about financial instability. It is also in line with results by Bekaert et al. (2013) who show that an expansionary conventional monetary policy shock has a lowering effect on the VIX.13 On the other hand, we define a shock that affects both the VIX and the Fed balance sheet in the same direction as a financial market risk shock to which the Fed responds, most notably seen in the immediate Lehman aftermath. The sign restrictions are imposed on impact and in the first month after the shock. Note that, as outlined in Section 1.2, the shock will primarily capture the actual implementation of UMP, namely measures that enlarge the balance sheet.14

12_{All models for the U.S. and for the EMEs include a constant and a linear time trend.}

13_{In theory, it is also possible that unconventional monetary policy expansions increase the volatil-}

ity by increasing the uncertainty about the future path of monetary policy or if the expansion is perceived as a harbinger of less encouraging prospects (compare Section 1.2). Fratzscher et al. (2016), however, show that, on average, press announcements by the Fed regarding unconven- tional monetary policy lowered the VIX on impact. Unfortunately, there is no comprehensive assessment of the impact of QE purchases on the VIX available, which is a subject potentially worth examining in future studies.

14_{Identifying the UMP shock using a Cholesky ordering and sign restrictions might pose a problem}

given the inclusion of financial variables, in this application most importantly U.S. portfolio outflows. Therefore, we have assessed the sensitivity of the results towards a different ordering of

Table 1.3.1: Sign restrictions to identify UMP shock

Output Inflation VIX Fed Balance Sheet

Unconv. Monetary Policy Shock 0 0 ≤0 > 0

Financial Market Risk Shock 0 0 > 0 > 0

The table shows the sign and zero restrictions on the endogenous variables (columns) applied to identify the unconventional monetary policy shock and distinguish it from a financial market risk shock (rows).

The VARX specification for the EMEs is restricted by the rather short period of U.S. UMP. Given the limited number of observations, we cannot include all variables of interest into one large model. Instead, we consider two different models for different economic concepts of interest. First, we estimate a model which is focused on the response of real economic conditions to a U.S. UMP shock (“business cycle” (BC) model):

y_it = (output,real exchange rate change,portfolio inflows,real interest rate)0,

y∗_it = (U.S. portfolio outflows,foreign output)0.

Second, we estimate a model to analyze the effect of a U.S. UMP shock on financial conditions in EMEs (FC model):

y_it = (portfolio inflows,real interest rate,real exchange rate change,equity returns)0,

y∗_it = (U.S. portfolio outflows,foreign output)0.

The two models share the same VARX model for the U.S. to ensure that the UMP shock is the same across models. In the baseline specification, we include U.S. total portfolio outflows, the transmission channel of interest, and foreign output, as stan- dard in the literature, as foreign variablesy∗ in the EMEs VARX models. Following Georgiadis (2015b), we include the potentially non-stationary level variables real GDP and real exchange rate in first difference form in all models.15

portfolio flows and using an identification strategy based on a shadow interest rate (see Section 1.4.3). Another approach would be to identify the VAR using external instruments as pioneered by Gertler and Karadi (2015) for conventional monetary policy. For a pure UMP shock and our sample, however, we did not find a valid instrument, most notably due to the zero lower bound.

15_{This has mainly two reasons. First, using differences ensures stability of the model across all}