Financial Crisis, Taylor Rule and the Fed

Transcription

1 Deparmen of Economics Working Paper Series Financial Crisis, Taylor Rule and he Fed Saen Kumar 2014/02 1

2 Financial Crisis, Taylor Rule and he Fed Saen Kumar * Deparmen of Economics, Auckland Universiy of Technology Absrac We invesigae how he Federal Reserve (Fed) hi he zero lower bound (ZLB) ineres rae while operaing under a Taylor-ype policy rule. We esimae a reacion funcion and he resuls indicae ha during he crisis Fed increased he weigh on oupu wihou also increasing he weigh on inflaion led hem o hi he ZLB. Keywords: Financial crisis; Taylor rule; zero bound JEL: E58 * for correspondence: saen.kumar@au.ac.nz 2

3 1. Inroducion The famous Taylor (1993) rule has received enormous aenion in he moneary policy lieraure. This rule presens he Federal Reserve s (Fed) reacion funcion ha is useful o ascerain how he Fed alers moneary policy in response o economic developmens. Wihin he conex of a macro model, he reacion funcion can be used o analyze he policy Fed adoped o ackle he recen financial crisis. The Fed is using a Taylor-ype policy rule which is based on he dual mandae, i.e. inflaion sabiliy and full employmen. So under such policy rule, how did he Fed hi he zero lower bound (ZLB) ineres rae? Ineresingly, here has been lile research on his issue. This paper aemps o shed some ligh on his issue by esimaing a reacion funcion for he U.S. over he period 1954.Q Q4. 2. The Taylor Rule Taylor (1993) suggess a very specific and simple rule for moneary policy. In wha follows, we derive his rule o be used in our analysis. Following Svensson (1997), we firs specify wo simple models of he economy: Phillips Curve y y (1) 1 1 IS Curve y y y y r r (2) where inflaion rae, y (Fed funds rae), r i y rae ( r ) from naural level ( r ). oupu gap, i nominal shor-erm ineres rae real ineres rae and r r and bank minimizes he following loss funcion: deviaion of real ineres are iid disurbances. Suppose he cenral 2 1 j min L E (3) j i 2 j 0 j 3

4 where ineremporal discoun facor wih 0 1 wrie 2 as a funcion of r :. Based on (1) and (2) we can y y y y y y r r (4) 2 y 1 1 a y y a r r The lag srucure of he model implies ha he ineres rae in period has no effec on inflaion in he period +1 bu only beyond +2 period; a he same ime he ineres rae in +1 will influence he inflaion beyond +3 and his process coninues. The cenral bank problem is simplified because i is possible o fix every period he ineres rae coheren wih he objecive o ake close o. The cenral bank hen will solve for 2 he following problem: min 1 2 L E 2 i 2 where E a y y a r r (5) Deriving wih respec o i r 2 2 2, we obain: a E 0 E (6) To derive he moneary policy rule, we have o subsiue (5) ino (6) and solve for r : 1 a 1 a r r y y i r y y a a a a

5 i y y a a 2 1 r ; ; wih 1; a a a (7) McCallum (1997) argued ha i is unrealisic o assume, as in (7), ha policy can respond o curren-quarer values of inflaion and oupu. In empirical esimaions, he lagged values of hese variables are used and hus (7) becomes: i y y (8) 3. Empirical Resuls Daa We use quarerly daa over he period 1954.Q Q4 for he U.S. The variables used are Fed funds rae ( i ), inflaion rae ( ) and oupu gap ( y y ). is measured by he annual growh rae of he GDP deflaor. The oupu gap ( y y ) is measured as he deviaion of real GDP ( y ) from is poenial ( y ) and i is obained hrough univariae unobserved componen model echnique. This echnique is beer han he radiional Hodrick-Presco filer mehod because i is no affeced by end-sample biases. All daa is exraced from he Federal Reserve Economic Daa (FRED) daabase. Figure 1 illusrae he behavior of i, and ( y y ) over he sample period. The oupu gap is quie volaile and has been negaive during he periods of recession. The Fed funds rae reached a peak during he early 1980s and his depics he coninued conracionary measures adoped by he Fed since mid-1970s. The Fed funds rae reached he ZLB in 2008.Q4. The inflaion rae has been highes during he 1970s possibly due o he oil crisis. Overall, inflaion and he Fed funds rae show a declining rend in he pos-1980 period. 5

6 Figure 1: Fed funds rae, inflaion rae and oupu gap 1954.Q Q4 Uni Roo Tess Carrion-i-Silvesre e al. (2009) developed a uni roo es which allows for muliple srucural breaks in he level and/or slope of he rend funcion under boh he null and alernaive hypoheses. Their es comprises he feasible poin opimal saisic (Ellio e al., 1996) and a class of M-ess (Sock, 1999). The feasible poin opimal saisic is given by: P ( 0 ) S(, 0 ) S(1, 0 ) / s 2 ( 0 ) (9) gls T where is he esimae of he break fracion, = 1 c / T (c is he noncenraliy parameer) and 2 0 s ( ) is an esimae of he specral densiy a frequency zero of. The M-class of ess is defined by: GLS MZ ( ) T y s( ) 2T y T 2 T (10) 6

7 T GLS MSB ( ) s( ) T y 1 1 1/2 (11) MZ T y s s T y T GLS ( ) T ( ) 4 ( ) 1 1 1/2 (12) wih 0 y y ˆ ' z ( ), where ˆ minimizes he objecive funcion (see eq 4 in Carrion- 0 2 i-silvesre e al., 2009, p.1759). For definiion of s( ), see eq 6 in Carrion-i-Silvesre e al., 2009, p Table 1 presen he uni roo es resuls for i, and ( y y ). We es for a maximum of five srucural breaks when deerminisic ime rend is included in he es regressions. All he es saisics poin o rend saionary processes in he hree series. The es saisics are less negaive han he criical values implying ha he uni roo null can be rejeced a he 5% level. The endogenous break daes yield by each es is plausible. Mos break daes correspond o recessions ha affeced he U.S. economy. Table 1: Carrion-i-Silvesre e al. (2009) uni roo es, 1954.Q Q4 Tes and Variables gls T 0 P ( ) GLS 0 MZ ( ) GLS 0 MSB ( ) GLS 0 MZ ( ) i y y i y y i y y i y y Tes Saisic (Criical Value) (-5.100) (-1.154) ( ) (-9.439) (-3.492) (-4.507) (-5.641) (-7.750) (-2.321) ( ) ( ) ( ) Break Daes 1974.Q2;1981.Q2;1995.Q1;2007.Q2;2007.Q Q1;1984.Q3;1991.Q4;1992.Q1;2008.Q Q4;1980.Q3;1992.Q2;2002.Q3;2007.Q Q4;1981.Q3;1994.Q4;2000.Q1;2008.Q Q4;1992.Q1;2001.Q3;2007.Q2;2007.Q Q1;1981.Q4;2007.Q1;2007.Q3;2008.Q Q2;1991.Q3;1999.Q1;2003.Q3;2008.Q Q1;1980.Q2;1992.Q1;1992.Q4;2004.Q Q2;1992.Q1;2000.Q2;2007.Q3;2007.Q Q3;1992.Q4;2000.Q4;2005.Q1;2007.Q Q4;1974.Q4;1982.Q1;1996.Q2;2008.Q Q4;2000.Q3;2007.Q1;2007.Q1;2008.Q1 Noes: All ess consider breaks in consan and ime rend. The 5% criical values are given in parenheses. 7

8 Taylor Rule Esimaes We esimae he Taylor rule (equaion 8) using he seemingly unrelaed regression (SUR) mehod. This mehod accouns for he disurbance correlaion across equaions and yields more efficien esimaes compared o he ordinary leas squares (OLS). In addiion, i does no require any insrumens as he case in insrumenal variable mehods. The Taylor rule esimaion is performed as follows: i. excluding he financial crisis period (1954.Q Q4) and ii. adding a quarer sequenially from 2007.Q1 o 2011.Q4. For he laer, we consruc 20 samples such as 1954.Q Q1, 1954.Q Q2,...,1954.Q Q3 and 1954.Q Q4. In all esimaions, we inegrae hree dummy variables viz., DUM73, DUM80 and DUM91. 1 The former correspond o he oil crisis, while he laer wo highligh he occurrence of recessions in he U.S. The sequenial esimaion samples also include a dummy (DUMFC) o capure he impacs of he recen financial crisis. 2 Figure 2 illusrae he coefficiens of inflaion ( 1 ) and oupu gap ( 2 ). 3 In all equaions, and are saisically significan a he 5% level. 4 The esimae of is fairly consisen overime (around 1.1 in pre-crisis and crisis-inclusive periods). Since he real ineres rae drives privae decisions, he size of needs o be larger han one. This is 1 he so-called Taylor principle (Clarida e al., 1998). Furher, moneary policy o effecively sabilize oupu, a less resricive condiion has o be fulfilled, i.e Prior o he crisis, he esimae of was However, when he sample is exended 2 o include he crisis period, increased o around Dummies are seleced according o he es resuls of Carrion-i-Silvesre e al. (2009). Oher dummies are ignored because hey are saisically insignifican a he convenional levels. These dummies are consruced as follows: DUM73 = 1 from 1973.Q Q4 and 0 oherwise, DUM80 = 1 from 1980.Q Q4 and 0 oherwise, and DUM91 = 1 from 1991.Q Q4 and 0 oherwise. 2 For example, DUMFC in 1954.Q Q1 sample is consruced as 1 in 2007.Q1 and 0 oherwise. DUMFC in 1954.Q3-2007Q2 sample is consruced as 1 in 2007.Q1 and 2007.Q2 and 0 oherwise. Similar process is used o consruc DUMFC for samples beyond 2007.Q2. 3 Esimaes of he inercep and dummies are no repored for breviy. 4 The -saisics or p-values are no repored for breviy. 8

9 Figure 2: SUR esimaes of inflaion and oupu gap Implicaions Our resuls indicae ha unil 2007.Q2 he Fed gave higher weigh o inflaion han o oupu gap. The Fed s reacion o inflaion is fairly consisen overime (pre-crisis and crisis-inclusive periods). However, Fed s reacion o he oupu gap increased rapidly during he crisis. Increasing he weigh on oupu wihou also increasing he weigh on inflaion signifies he possibiliy of hiing he ZLB. Acually he Fed funds rae did reach he ZLB in 2008.Q4 and remained low hereafer. If he cenral bank decides o reduce he volailiy of oupu, his resuls in unrealisically large volailiy in inflaion (Gavin and Keen, 2012). Consequenly, here was some concern over he rising inflaion uncerainy during he crisis, see Wrigh (2011). Gavin and Keen (2012) argued ha a cenral bank mus be commied o a long-run average-inflaion objecive if i wishes o achieve a dual mandae while avoiding he ZLB. The problem wih Taylor rule is ha i arges he shor-run inflaion rae and herefore i becomes difficul o achieve he dual mandae and a he same ime avoid he ZLB. Reflecing on Figure 2, he Fed would have no encounered ZLB if i had lowered he weigh on oupu. Gavin and Keen (2012) show ha placing more weigh 9

10 on oupu increases he likelihood of a ZLB even and increases he volailiy of inflaion bu decreases he volailiy of oupu. Robusness To assess robusness in our resuls, we esimae he reacion funcion using he wo sage leas squares insrumenal variable (TSLS-IV) mehod. The insrumens used are long-erm ineres raes, unemploymen rae and price volailiy. 5 In mos equaions, insrumens lagged up o 3 periods were used; we do no repor he exac insrumens for each esimaed equaion for breviy. In all cases, Hansen s (1982) J-es indicaes ha our seleced insrumens are valid. DUM73, DUM80, DUM91 and DUMFC were used as dummy variables. Figure 3 illusrae he esimaes of inflaion and oupu gap and hey are very consisen wih our SUR esimaes. These resuls also indicae ha Fed s reacion o inflaion is fairly consan, while reacion o he oupu gap is much sronger hroughou he crisis period. Figure 3: TSLS-IV esimaes of inflaion and oupu gap 5 We derive price volailiy using he GDP deflaor. GARCH model was used o aain he series. 10

11 4. Conclusion We invesigae how he Fed hi he ZLB ineres rae while operaing under a Taylorype policy rule. In doing so, we esimae a reacion funcion o aain insighs on how much weigh he Fed placed on inflaion and oupu during he recen crisis. Our resuls indicae ha Fed s reacion o inflaion has been fairly consisen overime (i.e. precrisis and crisis-inclusive periods). However, Fed s reacion o he oupu gap increased rapidly during he crisis period. Since he Fed increased he weigh on oupu wihou also increasing he weigh on inflaion led hem o hi he ZLB. Our inferences are consisen wih Gavin and Keen (2012). 11

12 References Carrion-i-Silvesre, J.L., Kim, D. and Perron, P. (2009) GLS-based uni roo ess wih muliple srucural breaks under boh he null and he alernaive hypoheses, Economeric Theory, 25, Clarida, R., Galì, J. and Gerler, M. (1998) Moneary policy rules in pracice: Some inernaional evidence, European Economic Review, 42, Ellio, G., Rohenberg, T.J. and Sock, J.H. (1996) Efficien ess for an auoregressive uni roo, Economerica, 64, Gavin, W.T. and Keen, B.D. (2012) The zero lower bound and he dual mandae, Federal Reserve Bank of S. Louis Working Paper No. 026A. Hansen, L. (1982) Large sample properies of generalized mehod of momens esimaors, Economerica, 50, McCallum, B. T. (1997) Issues in he design of moneary policy rules, NBER Working Paper No Sock, J.H. (1999) A class of ess for inegraion and coinegraion, in Coinegraion, Causaliy, and Forecasing: A Fesschrif for Clive W.J. Granger, pp Oxford Universiy Press. Svensson, L. E. O. (1997) Inflaion forecas argeing: Implemening and monioring inflaion arges, European Economic Review, 41, Taylor, J. B. (1993) Discreion versus policy rules in pracice, Carnegie-Rocheser Series on Public Policy, 39, Wrigh, J.H. (2011) "Term premiums and inflaion uncerainy: empirical evidence from an inernaional panel daase," American Economic Review, 101,