Monetary policy transparency in a forward-looking market: Evidence from the United States

North American Journal of Economics and Finance 42 (2017) 597–617

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North American Journal of Economics and Finance j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e c o fi n

Monetary policy transparency in a forward-looking market: Evidence from the United States Amir Kia Finance and Economics Department, Utah Valley University, Orem, UT 84058-5999, USA

a r t i c l e

i n f o

Article history: Received 22 June 2017 Received in revised form 23 August 2017 Accepted 30 August 2017

JEL Classification: E43 E51 E52 E58

a b s t r a c t Because unsatisfactory measures of the monetary policy transparency were used, the existing literature found mixed empirical results for the relationship between the monetary policy transparency and risk/volatility. This paper extends the literature by using a recently developed monetary transparency index [Kia’s (2011) index] which is dynamic and continuous. Furthermore, the existing literature ignores the fact that market participants can be forward looking and, therefore, not policy invariant. This study also finds that the agents in the market are not policy invariant and the more transparent the monetary policy is the less risky and volatile the money market will be. Ó 2017 Elsevier Inc. All rights reserved.

Keywords: Monetary policy transparency Risk Volatility Money market

1. Introduction The impact of the monetary policy transparency on risk and volatility in the economy in general and in the financial markets in particular depends on the behavior of agents in the economy and specifically in the money market. In fact, when agents are forward looking, say, in the money market, the impact of the monetary policy transparency on risk and volatility may remain constant over time (temporal stability) but is not policy invariant (not stable) since the behavior of forwardlooking agents will change with policy regime changes or other exogenous shocks. In such a case, the monetary policy transparency influences the ex-post risk, but since the behavior of agents in the market is forward looking, it also influences the future or ex-ante risk. This important fact is completely ignored in the existing literature. This paper deals with this issue as well as other shortcomings in this literature. The forward-looking behavior of market participants, if any, in the money market makes the property of monetary policy transparency more efficient as it affects both current and future expected risk and volatility. As Lucas (1976) points out, temporal stability and policy invariance are two distinctly different concepts. The estimated parameters of a given relationship may remain constant over time, but they could still vary in response to a policy regime change or other exogenous shocks in the economy and vice versa. This issue has been completely ignored in this literature. In this study we will also deal with the behavior of market participants with response to monetary policy transparency. E-mail address: [email protected] http://dx.doi.org/10.1016/j.najef.2017.08.013 1062-9408/Ó 2017 Elsevier Inc. All rights reserved.

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Another main problem with the current literature, in general, is that central bank communications are difficult to measure. Furthermore, the use of dummy variables, as it was also mentioned by Lasaosa (2005) and Kia (2011), can result in a misleading conclusion as some announcements may have already been taken into account by the market participants before the announcement. Furthermore, as Blinder, Ehrmann, Fratzscher, De Hann, and Jansen (2008) argue, there are unobserved factors which affect asset prices. A rise in the volatility as a result of central bank communications may be due to the reaction of financial markets to shocks other than central bank communications. Moreover, the communication of the central bank may be due to a sudden change in economic outlook or some other news which also increase the volatility of asset prices. Therefore, the higher volatility is not due to the central bank communications, but to the shocks which caused the communications. Consequently, the dummy variables may not actually reflect the impact of the announcements or the change in the policy. Moreover, as also mentioned by Blinder et al. (2008), among others, the coding approach is subjective and there is always a possibility of misclassifications. To investigate clearly the impact of monetary policy transparency on forecast error, risk or volatility we need to have an objective market-based monetary policy transparency index. Such an index should also be dynamic so that it can be used for a long range of time series data. Kia (2011) has developed such an index for the United States which can be used to measure monetary policy transparency for a country or, simultaneously, a series of countries, using time-series as well as cross-sectional data. Using Kia’s index, this study also investigates the impact of monetary policy transparency on risk (forecast error) and volatility in the money market in the United States. Papadamou and Arvanitis (2015) also use Kia’s (2011) index to investigate the effectiveness of the Federal Reserve’s transparency on the volatility of inflation and output in the United States. The next section is devoted to the survey of the literature which will be followed by a section which briefly explains Kia’s index. Section 4 concentrates on the impact of the index on the risk in the money market. Section 5 is devoted to the analysis of the impact of monetary policy transparency on the volatility in the money market in the United States. The final section provides some concluding remarks. The description of the data and the definitions of dummy variables are given in the Appendix.

2. Survey of the literature The findings in the existing literature on the impact of monetary policy transparency on the volatility of interest rates and/or risk are mixed. Tabellini (1987), for example, shows that when market participants face parameter uncertainty (or multiplicative uncertainty) and learn over time, using Bayes’ rule, the learning process is the source of additional volatility in asset prices. In this case, more transparency tends to reduce market volatility. Furthermore, Thornton (1996), using Fed funds futures and Mean Squared Error, finds the consequences of the Fed’s policy shift toward immediate disclosure on the federal funds rate in 1994 resulted in a lower forecast error for all interest rates. Blinder (1998), theoretically, argues that more open public disclosure of central bank policies may enhance the efficiency of markets. Haldane and Read (2000), using dummy variables for the change in the monetary policy transparency, show that a higher monetary policy transparency leads to a lower conditional variance in the yield curve in the United Kingdom and the United States. Their cross-country (Italy, Germany, UK and US) empirical results also confirm their finding. Blinder, Goodhart, Hildebrand, Lipton, and Wyplosz (2001), using descriptive accounts of transparency (do’s and don’ts of the central bankers’ actions), find a higher market transparency leads to a lower forecast error. Geraats (2002) theoretically shows the transparency reduces the variance of private sector forecast errors. Rafferty and Tomljanovich (2002) study whether the Federal Reserve System’s 1994 policy shift toward more open disclosure improved or worsened the predictability of financial markets. They find that since 1994, the forecasting error has decreased for interest rates on US bonds of most maturity lengths and that the expectations hypothesis has performed better at the low end of the yield curve. Swanson (2004) finds that when the Federal Reserve began to announce its policy action in1994 the financial markets’ uncertainty about the future course of short-term interest rates significantly fell. Reeves and Sawicki (2007), using dummy variables, find evidence that the publication of the Minutes of the Monetary Policy Committee meetings and the Inflation Report in the UK significantly affects near-term interest rate expectations, an effect particularly visible in intraday data. Neuenkirch (2012), using data of nine major central banks, finds that, in general, monetary policy transparency, by lowering the variation of expectations, reduces expectation bias in the money market. Lasaosa (2005) analyzes the impact of the announcements on market activities and concludes that the increase in transparency facilitates the prediction of monetary policy in the UK once the latest macroeconomic data are known. She investigates the impact of the announcement five, fifteen and sixty minutes after an announcement. Then she compares the result with those days with no announcement at the same times. Swanson (2006) argues that increases in the monetary policy transparency in the US have played a significant impact on the private sector’s forecast improvement. He uses Fed futures and Eurodollar options rate to estimate and compare forecast errors as well as implied volatility, respectively, in different periods. Cruijsen and Demertzis (2007), using Eijffinger and Geraats’ (2006) index, and Rosa and Verga (2007), using dummy variables, find that monetary transparency improves the expectation on inflation as well as short-term interest rate, respectively. Ehrmann and Fratzscher (2007) find communication is a tool to prepare markets for upcoming decisions. Blinder et al. (2008) conclude that central bank communications lead to improvement in the ability of the market to predict monetary

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policy. Demiralp, Kara, and Özlü (2012), using dummy variables, find the announcement of monetary statement in Turkey improves the predictability of the next interest rate in Turkey. Ehrmann and Fratzscher (2009), using both dummy variable and coding approach (i.e., the value of
1 for statements indicating an easing inclination, 1 for statements indicating a tightening, and 0 otherwise), find that the timing of statements is important. Specifically, statements in the pre-FOMC (Federal Open Market Committee) purdah resulted in a rise of market volatility, but statements in and outside the post-FOMC purdah period led to significantly lower market volatility. BiefangFrisancho Mariscal and Howells (2010), using dummy variables, show that the various forms of Fed communications are highly significant on the volatility and market’s expectations. Ehrmann, Eijffinger, and Fratzscher (2012), using a set of different measures for the central bank transparency, find monetary transparency reduces, with a decreasing effect, forecast disagreements on inflation, interest rates and other macroeconomic variables among market participants in twelve advanced countries. They found that the announcement of a qualified inflation objective and the release of the central bank’s internal forecasts of inflation and output, in particular, are more effective and also additive.1 Dincer and Eichengreen (2014) using the information available on the websites and the publications of more than 100 central banks for the period 1998–2010 and by employing the coding approach construct political, economic, procedural, policy and operational transparencies as well as develop a measure of independence. The study uses the indices to verify if the trend toward greater central bank transparency has been continued and the impact of financial crisis on central bank transparency. They found that central banks have become more transparent and independent, but the financial crisis resulted in the opposite impact on both transparency and independence of the central banks. Consequently, the study concludes that transparency and independence go together. Furthermore, they checked the impact of strength of political institutions on transparency and independence of the central banks. While the strength of political institutions positively affected transparency of the central banks, they found this strength did not affect the trend of independence. Finally, they found that the central bank transparency negatively affects the level of inflation and its variability. Interestingly, Apergis (2015) using intraday data of 6 US asset prices found the impact of the minutes released by the FOMC has significant effects on the mean of volatility of asset prices only before and not after the 2008 crisis. However, some studies found that monetary policy transparency does not affect the interest rate volatility, but actually contributes to more volatility in the financial markets. In fact, in a 1976 Freedom of Information Act filing, the Fed argued in favor of secrecy motivated by its desire to reduce interest rate variability, see Goodfriend (1986). Dotsey (1987) argues that the cleaner and more frequent the ‘‘signal” (or the more transparent monetary policy) is the larger the responsiveness of interest rates to news will be, and thus the greater their volatility. Biefang-Frisancho Mariscal and Howells (2007), using dummy variables, update Haldane and Read’s (2000) study on the UK by investigating the changes in anticipation on either side of the two major reforms in UK policy making in 1992 and 1997. They conclude that the Bank of England independence and its associated reforms have not added to the understanding of monetary policy by market participants. Chadha and Nolan (2001) use dummy variables accounting for days on and before the announcement day to investigate the impact of the announcement on the volatility of interest rate over selected periods in the UK. They concluded that transparency did not contribute to the volatility of interest rate.2 Again as we can see the existing literature completely ignores the fact that market participants can be forward looking and, therefore, not policy invariant. 3. Brief non-technical description of Kia’s (2011) index Kia’s (2011) index is based on what market participants understand from the central banks’ actions and signals as well as the implementation of the monetary policy. According to this index, it is not important what the central bank intends to convey to the market, but what is important is what market participants understand from the speeches and documents of the central bank. Namely, the index measures the extent to which the public understands what information the central bank has and how it will react to that information. Since the return on excess reserve, even after October 9, 2008 when the Fed pays interest on reserve, is negative, Kia (2011) assumes banks in the United States keep an optimal excess reserve ratio (OER) and then he expresses the daily behavior of FF (Fed funds rate) at time t (t  T, where T is the time of the last change of the target rate or the last FOMC meeting), as: FFt = TFFT + a (OERt
ERt), where ER is the actual excess reserve ratio, TFFT is the target Fed funds rate at time T, the previous event day and a (known by the public) is a coefficient which can change as the behavior of forward-looking market participants changes.3 1 Interestingly, Hayo, Kutan, and Neuenkirch (2010), using dummy variables, find the Fed announcements can influence the European and Pacific stock market returns. 2 There are other arguments in favor or against monetary policy transparency in terms of other factors in the economy. For example, Frenkel, Pierdzioch, and Stastmann (2006) argue that the key reason that European Central Bank’s intervention in the exchange market was ineffective was due to its shortcomings in the information and communication policy. Baghestani (2008) shows that the private forecasts are more informative because they encompass those of the Federal Reserve’s forecast and, consequently, a higher transparency has helped to improve the effectiveness of monetary policy and thus enhanced the economic welfare through a credible commitment to price stability, as it has allowed the public to make better decisions. 3 Note that Kia (2010) provides empirical evidence that agents are forward looking in the money market of the United States in the sense that their behavior is not policy invariant and expectations are formed rationally. Consequently, Kia (2011) assumes a in FF and c in the TB equations (see the last paragraph of this page) are not policy invariant.

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Kia (2011) shows both actions and signal effect of the Fed influence (OERt
ERt) of the banking system4. Based on the existing literature, e.g., Geraats (2002), Kia assumes at time t, ERt = ERt-1 + st, where sN(0,r2s ) and under opacity it is only known by the Fed and not by the public. He assumes ‘‘s is an economic shock that the central bank decides to offset and it is independent of TFF. When there is full transparency both Fed and the public know s. Since ERt-1 is already known by the public it is a deterministic variable.” (p. 61). Using these two equations FF is determined by: FFt = FFt-1 + a (OERt
ERt-1) + ast. Kia assumes the target rate at the next FOMC meeting or event day (TFFT+1) can be expressed as TFFT+1  N(TFF; r2Tþ1 ), where TFF is the average TFF. Clearly, the more uncertain is the public about TFF at time T + 1, the higher is r2Tþ1 . Kia also develops an equation which expresses the daily behavior of TB (the three-month Treasury bill rate) as TBt = TBt-1 + c1 (FFt
TFFT) + c2 {[E(TFFT+1|FFt)
TFFT+1] + [TFFT+1
TFFT]}, where ci for i = 1 and 2 are coefficients which can change as the behavior of forward-looking market participants changes and are known by the public. He starts at equilibrium when OERt = ERt and shows that an outright sell of Treasury bills by the Fed results in a rise of both FF and TB. This is because such a sell ‘‘results in a reduction of ER. Banks compete for interbank funds and the Federal funds rate will go up. Furthermore, as FF goes up (interbank market becomes tight) banks also sell their other liquid assets, like Treasury bills and, therefore, exert an upward pressure on TB. This means that an increase in FFt–TFFT results in an increase in TB. Furthermore, an increase in [E(TFFT+1|FFt)
TFFT] leads to an expected potential speculative loss in keeping Treasury bills, where E is the expectation operator and E(TFFT+1|FFt) is the expected TFFT+1 conditional on FFt which is known by the public at time t.5 Speculators will sell their bills to reduce their loss and exert an upward pressure on TB” Kia (2011, pp. 61–62). As he noted the expression (FFt–TFFT) is known as unintended Fed funds rate. As Kia (2011, p. 62) mentions ‘‘given TFFT at time t, the expression (FFt–TFFT) reflects the Fed action to influence the interest rates and [E(TFFT+1|TFFt)
TFFT+1] is the unexpected change in the target rate while [TFFT+1
TFFT] is the actual change in the target rate on the next event day. On the next event day, t = T + 1, if the Fed does not change the target rate we will have FFT+1 = TFFT and if the expected target rate for the following event day is the same as the current target rate, everything else being equal, we would expect TBT+1 = TBt-1.”, see Kia (2011) for all relevant literature. Kia mentions that when there is no expected change in the structure of the interbank market and/or the credibility of the United States government to pay its debt at equilibrium we will have Dift = FFt–TBt = risk premium – maturity risk premium = Tdift, where Tdif is the trend value or the equilibrium level of Dif. The risk premium is because there is no default risk with the three-month Treasury bill while Fed funds are issued by banks and so are subject to default risk. Furthermore, since Fed funds are mostly overnight but three-month Treasury bills have a three-month maturity it is subject to maturity risk and so we need to subtract maturity risk premium from default risk premium. ‘‘When both Treasury bills and Fed funds markets are in equilibrium, both TB and FF are equilibrium rates and, therefore, their difference (Tdif) will be an equilibrium value.” Kia (2011) Endnote 11. Kia’s index measures deviations from this equilibrium, which are caused by a lack of monetary policy transparency. Clearly when market participants are not clear on monetary policy they ask a higher premium and Dif deviates from Tdif. As Kia (2011, p. 62) mentions ‘‘there is no reason to believe that Dif deviates from its equilibrium value (its trend) unless Fed actions, and/or other exogenous shocks, change one or both of these rates in a different proportion. In fact, one can consider Dif as a measure of the stance of monetary policy. For example, Simon (1990) provided evidence that the TB-FF spread has a predictive power for the future changes in FF. Furthermore, Bernanke and Blinder (1992) showed the funds rate or the spread between the funds rate and some other interest rates is a good indicator of the Federal Reserve’s monetary policy stance. Specifically, they provide evidence that short-run fluctuations in the Fed funds rate or the spread between the funds rate and some other interest rates are dominated by shifts in the stance of monetary policy. More importantly, they show the Fed funds rate, or its spread from some other interest rates, is not affected by current (within-month in their monthly observations) developments in the economy.” Under full transparency Dif is equal to Tdif and, using FF and TB equations above, Kia finds Dift = Tdift = FFt-1 + a (OERt - ERt-1) + ast
TBt-1
c1 (FFt
TFFT)
c2 [TFFT+1
TFFT], where s and TFFT+1 are known by the public.6 Hence he finds Dif under opacity (Odif) as:

Odif t ¼ FFt
1 þ aðOERt
ERt
1 Þ þ ast
TBt
1
c1 ðFFt
TFFT Þ
c2 f½EðTFFTþ1 jTFFt Þ
TFFTþ1  þ ½TFFTþ1
TFFT g: Note that, under full transparency, market participants know the target rate (TFFT+1) on the next event day, but under opacity, given the existing target rate (TFFt), they should estimate it. Then deviation between Dif under opacity and full transparency (D) will be:

4

See pages 60–61 for more explanation and the relevant literature. Note that {[E(TFFT+1|FFt)
TFFT+1] + [TFFT+1
TFFT]} is in fact {[E(TFFT+1|FFt)
TFFT]}, where {[E(TFFT+1|FFt)
TFFT+1] + [TFFT+1
TFFT]} corresponds to Eq. (8) of Kuttner (2001), which was also tested on three-month Treasury bill rates. 6 Since usually over a few days the actions of the central bank will be fully cleared to market participants Kia (2011) assumes the trend of Dif, i.e., Tdif reflects when market participants fully understand the messages/signals of the central banks. Note that before August 1987 when Paul Volker was the chairman of the Federal Reserve, we had complete secrecy in announcing Fed funds target rate and until February 4, 1994, when the Fed started to announce target changes, it would take a few days until market participants realized the intention of the Fed on the FF target rate. The trend of Dif clearly reflects this fact and, therefore, it can be considered, on average, a full market participants’ understanding of the intention of the Fed. Any deviation from it reflects a partial market understanding of the action of the Fed, i.e., less transparency according to Kia’s index. Kia (2011) measures all of these deviations. A zero deviation reflect 100% transparency and a higher deviation indicates less transparency. 5

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Quartely Monetary Policy Transparency Index

100 90

rate

80 70 60 50 40 1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2010

2012

2014

2016

Quarter Basic Index

Fig. 1. Quarterly monetary policy transparency index.

Daily Monetary Policy Transparency Index

100

80

rate

60

40

20

0 1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Day Daily Extended Index

Fig. 2. Daily monetary policy transparency index.

Dt ¼ Odif t
Tdif t ¼ þc2 f½EðTFFTþ1 jTFFt Þ
TFFTþ1 g: Clearly the higher is the uncertainty about the next event target rate (less transparent the central bank is) the higher premium the market participants want and the higher D will be. He considered the maximum/minimum of |Dt|, at the event (FOMC meetings) dates in the sample period, to be the least/most transparent monetary policy over the period, and calculated the index (defined basic index) Tt = transparency 7 Clearly, the higher |Dt| is, the lower the transparency index will be. In this index = e100 jDt j : If |D| = 0%, we will have T = 100%. formula, Kia calculated Tdif as the average of Dif between two event days. Since event days are at irregular intervals, Kia (2011) takes the quarterly average of the basic index to construct quarterly observations of the index. ^t ¼ 100=ejD^ t j , where D ^ t = |Dift
Adift|, and Dift is defined as He also developed the high frequency data of the index T Pj Dift
i before (=FFt
TBt) and Adift = i¼1n : Here j is the last event day and n is the number of days since the last event day. Using ^t . Kia’s index is dynamic and can be used to calculate an index for each ^ t , we can calculate an index for non-event days T D minute of the day using the intra-day observations on FF and TB. As Fig. 1 (basic index) and 2 (extended index) show, the monetary policy in the United States has been almost fully transparent in the period 2010–2015. 4. Risk/forecast error in the money market and the monetary policy transparency In this section we will investigate, using Kia’s index, whether a higher monetary policy transparency leads to a lower/ higher risk and forecast error in the money market. Consequently, market participants will ask for a lower/higher risk premium as the Fed conveys more its private information to the market. Note that Kia’s index is market based, i.e., it reflects what market participants perceive from hints, actions or reactions (to exogenous shocks) of the monetary authorities and not what these authorities intend to convey to the market. In other words, the public availability of the data does not suffice to achieve transparency, see Kia (2011). As he stressed, market participants may observe a different norm/direction in the policy during the day or within a month or a period than what the central bank actually follows. In this study, risk is measured by using the pure (rational) expectations model of the term structure (RE). According to RE the term premia are set identically to zero, which implies that at any moment in time, the expected TB, for example, prevailing at the beginning of three months from now (1+3TBet ) should be equal to the implied forward three-month Treasury bill rate (FTBt) in the absence of term premium or any other risk. From the first statement of the theory [e.g., Van Horne

7

Note that under full transparency |D| = 0, then the monetary policy is 100% transparent as T indicates.

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(1965)], we know that FTBt = [(1 + TB6t/4)2/(1 + TBt/4)]
1. Here TB6 is the six-month spot rate and we assume both six- and three-month spot Treasury bill rates are at the annual rate. Specifically, we can write:8 e 1þ3 TBt

¼ FTBt :

ð1Þ

If this equality is violated, investors and speculators, trade three- and six-month Treasury bills, to capture potential speculative profits, until Eq. (1) is restored. For example, if 1+3TBet > FTBt, speculators sell their six-month bills and buy threemonth bills, pushing the price of six-month bills down (TB6t will go up) and increasing the price of three-month bills up (TB3t will go down). This speculative activity continues until the potential speculative profit is eliminated, i.e., 1+3TBet is again equal to FTBt. Furthermore, by orthogonal decomposition at any given time t, we have:

TBt ¼ TBet þ Vt

ð2Þ

where Vt is the agents’ forecast error in the absence of transaction costs, risk and other premia (including term premium, liquidity premium and reinvestment premium). Substituting (1) in (2) yields:9

TBtþ1 ¼ FTBt þ Vtþ1 :

ð3Þ

If the market is efficient, TBt+1
FTBt = Vt+1 is stationary [e.g., Campbell and Shiller (1987)] and, in the absence of risk premia and transaction costs, has a zero mean. Using daily data for the sample period 1982 (October 5)–2016 (March 31) it was found that the error term (Vt) is stationary as both the Augmented Dickey-Fuller and Phillips-Perron tests reject the null hypothesis that Vt is not stationary.10 The absolute value of the Augmented Dickey-Fuller t was estimated to be 8.91 and the absolute value of the Phillips-Perron [Phillips and Perron (1988)] non-parametric t was estimated to be 9.06, both t statistic results are higher than 3.43 (1% critical value).11 Furthermore, the estimated Zivot and Andrews’ (1992) t test result also supports the forecast error to be stationary. The absolute value of the test result is 7.99 at a break time of 2007:08:09 which is more than the 1% critical value of 5.34. However, the mean of Vt over our sample period was found to be
0.27%, at the annual rate, with an autocorrelatedheteroscedastic adjusted t statistic of
21.66.12 The mean of the absolute value of V was found to be 0.36%, at the annual rate, with an autocorrelated-heteroscedastic adjusted t statistic of 32.98. Both of these means are far from being zero, indicating term premium or other risk premia exist, assuming a trivial transaction cost. Although a completely different approach was used, this result (i.e., on average, the RE hypothesis is valid in the United States money market, and risk premia exist) is consistent, among many others, with the finding of Van Horne (1965), Mankiw and Miron (1986) and Taylor (1992). We will, consequently, modify Eq. (3) to

TBtþ1 ¼ FTBt þ RPtþ1 þ Vtþ1 ¼ FTBt þ Wtþ1 ;

ð4Þ

where RP is risk premia and Wt = RPt + Vt. Note that RP includes term, liquidity, interest exposure and reinvestment risk premia where reinvestment risk premium has a negative effect on RP. To test the impact of monetary policy transparency on the forecast errors and risk in the money market we need to test the relationship between Wt in Eq. (4) and the transparency index. For arguments and econometric tests on the relationship between transparency and forecast errors of market participants, see, e.g., Thornton (1996), Haldane and Read (2000) and Blinder et al. (2001). As it would be expected, the higher the volatility of the interest rate is, the higher the investors’ demand for term, liquidity and interest exposure as well as reinvestment risk premia will be. For example, a higher volatility would make the forecasting more difficult, see, e.g., Ehrmann et al. (2012) and the references in it. Consequently, we would expect the volatility of three-month Treasury bill rates (VTB) to have a positive impact on Wt, while a higher monetary policy transparency reduces this risk and forecast error variable. Using daily data we estimate the following equation:

jWt j ¼ n0 þ n1 Tt
60 þ n2 VTBt
60 þ DUM0t
60 1 þ 2t ;

ð5Þ

where jWt j is the absolute value of the risk premia plus forecast error from Eq. (4), Tt is the monetary transparency index developed by Kia (2011), n’s are constant parameters, 1 is a vector of constant parameters and Єt is a heteroscedastic and autocorrelated (due to overlapping observations), normally, identically and independently distributed disturbance term. To construct the conditional volatility of the Treasury bill rate (VTB), following Schwert (1989) and Kia (2003), the methodology developed by Davidian and Carroll (1978) was used. In the next section we will fully explain the construction of this conditional volatility.13 Note that today’s calculated 3-month forward rate is equal to the expected three-month Treasury bill rate three months from now, i.e., 1+3TBte = FTBt. In Eq. (3), FTBt is calculated forward three-month rate at time t while TBt+1 is the actual three-month Treasury bill rate three months from now. 10 See the Appendix for the sources of the data. 11 The lag length in Augmented Dickey-Fuller or Phillips-Perron non-parametric tests was obtained according to Akaike Information Criterion (AIC) and Schwarz Information Criterion (SIC) for a global lag of 20 days. 12 Autocorrelation is due to the overlapping observations. I used Newey and West’s (1987) robusterror for 5-order moving average to correct the standard error. 13 It should also be mentioned that, as we will demonstrate in the next section, the index also influences the volatility of the three-month TB rate and so there is a possibility of multicollinearity. However, as we can see in Table 1, both variables are highly statistically significant when we estimate Eq. (5), and when one of these variables was dropped the other variable remains statistically significant while R-bar squared fell drastically to 0.20. Therefore, we conclude the existence of multicollinearity does not create a serious problem. 8 9

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603

Vector DUM is defined as: DUM = (Mt, Tt, WEDt, THt, D851231t, D861231t, Greent, Bernanket, Yellent, OCT87t, ASIAt, TAt, TAFt, SWEDt, REMAt, minutest, transcriptst, statet, D940418t, D970819t, lrrt, D981015t, D99518t, D000202t, D010103t, D010418t, D010917t, D020319t, EDAYt, TARATEt, USCrisist). For the definition of these dummy variables see the Appendix. DUM is included in the equation in order to capture the impact of monetary policy regime changes as well as other shocks on the risk premia as well as the forecast error. These policy regime changes or the exogenous shocks should affect the intercept only, if any. Note that variables T, VTB and DUM enter in Eq. (5) with one lag length (three months earlier) since the implied forward rate was used three months before (at the time of forecast) the actual rate was realized. However, one may argue that T may be influenced by W. Although there is no theoretical reason to believe that the index can be influenced by the calculated forward rate, we can investigate the causality between these two variables. Since our sample is daily observations, T is Kia’s (2011) extended index, which, based on the formula suggested by Kia (2011), was constructed for our sample period. The lag length is one quarter (60 business days). According to the Augmented Dickey-Fuller and Phillips-Perron test results |W|, VTB and T are stationary. The absolute value of the Augmented Dickey-Fuller t was estimated for |W| to be 9.63, for VTB to be 9.50 and for T to be 14.15. The absolute value of the Phillips-Perron non-parametric t was estimated to be 9.61 for |W|, 14.59 for VTB and 46.93 for T. All t statistic results are higher than 3.43 (1% critical value).14 Furthermore, the estimated Zivot and Andrews’ (1992) t test result also supports the conclusion that |W|, VTB and T are stationary. The absolute value of the test result for |W| is 8.34 at the break time of 2007:08:07, for VTB is 12.18 at the break time of 2007:05:16 and for T is 17.63 at the break time of 2008:12:03, all are more than the 1% critical value of 5.34. To test causality relationship between T and |W|, two stationary variables, we estimated each variable by its 20 lagged values as well as the lagged values of the other variable. We found the Wald test on the coefficients of twenty lagged values of Tt in a regression of Tt on its twenty lagged values as well as twenty lagged values of jWt j is 53.05 (p-value = 0.00), while the Wald test on twenty lagged values of jWt j is 0.99 (p-value = 0.49). At the same time, the Wald test on the coefficients of twenty lagged values of jWt j in a regression of jWt j on its twenty lagged values as well as twenty lagged values of Tt is 66701.83 (p-value = 0.00), while the Wald test on twenty lagged values of Tt is 88.78 (p-value=0.00). This result implies that Tt Granger causes jWt j while jWt j does not Grange cause Tt. Specifically; we conclude Tt is strongly exogenous in Eq. (5).15 Table 1 reports the parsimonious estimation result of Eq. (5), where the standard errors are adjusted for autocorrelation and heteroscedasticity. According to Godfrey’s test result, the error is autocorrelated and both White and ARCH tests results confirm the existence of heteroscedasticity16. The estimated coefficient of T is negative and statistically significant implying that as the monetary policy is more transparent the forecast errors and risk premia will fall. This result confirms the finding of Thornton (1996), Haldane and Read (2000), Blinder et al. (2001) and Swanson (2006). The estimated coefficient of the volatility in money market (VTB) as it would be expected is positive and statistically significant. The positive and statistically significant estimated coefficient of REMA implies that modifying the reserve maintenance period from one week (for most large institutions) to two weeks (for all institutions) in February 1984 resulted in a higher forecast error, while the negative and statistically significant coefficient of the dummy variable Yellen means the forecast error and risk in the money market fell since Janet Yellen became the chair of the Federal Reserve. Furthermore, as the positive and statistically significant estimated coefficient of D010103 indicates, the unexpected change in the target rate on January 3, 2001 resulted in a higher risk and forecast error. But the negative and statistically significant estimated coefficient of D010418 indicates that the unexpected change in the target rate on April 18, 2001 resulted in a reduction in risk/forecast error. The surprising result is the estimated coefficient of dummy variable D861231 which is negative and statistically significant implying a high volatility of FF on December 30 and 31, 1986 resulted in a lower risk and forecast error on those days. The positive estimated coefficient of D940418 indicates that when the Fed changed the FF target rate outside its regular meetings, the risk and forecast error went up. The negative estimated coefficient of the dummy variable minutes indicates that since March 23, 1993, when the Fed began releasing the minutes of the FOMC meetings (with 6–8 week lags), it resulted in a reduction of risk and forecast error. Finally, according to the estimated coefficient of USCrisis during the US Credit Crisis, both risk and forecast error increased. However, according to Hansen’s (1992) stability test result, most coefficients and the variance are not stable. Because of the existence of heteroscedasticity, we would expect the variance not to be stable. Furthermore, in a more than 33-year sample of daily data (more than 8737 observations) one would expect some instability in the estimated coefficients. The main question is if the estimated coefficients of the relevant variables have the same impact (negative or positive), even though with a different magnitude in the different sub-samples of the sample period. To test this question, I estimated the model for two 10-year sub-samples, 1982:10:06-1992:10:06 and 1992:10:07-2002:10:06 and one 13-year sub-sample 2002:10: 07-2016:03:31 periods. In all three cases the estimated sign of coefficients of our two main variables, i.e., the index and the volatility, and relevant dummy variables remain the same, though in different magnitudes. For example, the estimated coefficient of the index was
0.002,
0.001 and
0.004 in the first, second and last subsamples, respectively, indicating the monetary transparency had a stronger impact on risk and forecast error in the recent period. The estimated coefficient of the volatility variable was 3.10, 1.35 and 5.29 in the first, second and last sub-samples,

14 15 16

The lag length in Augmented Dickey-Fuller or Phillips-Perron non-parametric tests was obtained according to AIC and SIC for a global lag of 20 days. All Wald test results are adjusted for autocorrelation and heteroscedasticity. Because of overlapping observations these results would be expected.

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

Table 1 Parsimonious estimation result of Eq. (5). Dependent Variable = |W| = Risk and Forecast Error. Explanatory Variables*

Coefficients

Standard Error**

Hansen’s Stability Li Test (p-value)

Constant Tt-60 VTBt-60 REMAt-60 D010418t-60 D010103t-60 D010418t-60 D861231t-60 D940418t-60 minutest-60 USCrisist-60 Yellent-60 Specification Tests

0.38
0.002 4.26 0.15
0.10 0.13
0.12
0.64 0.24
0.19 0.63
0.04

0.09 0.0007 0.46 0.06 0.02 0.03 0.02 0.07 0.01 0.03 0.12 0.01

0.00 0.00 0.00 0.00 0.06 0.05 NA NA 0.02 0.00 0.46 0.00 Variance = 33 (p-value = 0.00) Joint (coeffs + var.) = 60 (p-value = 0.00)

R2 = 0.30, r=0.35 DW = 0.08, Godfrey (5) = 17813 (p-value = 0.00), White = 1089 (p-value = 0.00), ARCH (5) = 7914 (p-value = 0.00) REST = 2.29 p-value = 0.51)***

* The sample period is 1982:10:06-2016:03:31. Tt is the monetary transparency index, and VTB is the volatility of the three-month Treasury bill rate. For the definition of the dummy variables, see Table A in the Appendix. ** The estimation method is OLS where Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity. *** R2 , r and DW, respectively, denote the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. Godfrey is the five-order Godfrey’s (1978) test, White is White’s (1980) general test for heteroscedasticity, ARCH is the five-order Engle’s (1982) test and REST is Ramsey’s (1969) misspecification test.

respectively. The interesting result was that the R-bar squared was the highest (0.56) in the last sub-sample, indicating the model is stronger in the last sub-sample. The full estimated results are available upon request. Having established that monetary policy transparency can reduce the current risk we would need to investigate if it also changes the behavior of market participants toward future or ex-ante risk à la Kia (2003). If the index T is superexogenous in the sense of Engle, Hendry, and Richard (1983) and Engle and Hendry (1993), then the monetary policy transparency affects only the ex-post risk and the behavior of market participants is invariant to the change of the transparency. Alternatively, if the market participants are forward looking the monetary policy transparency can influence the ex-ante risk. To formulate the superexogeneity and invariance hypothesis associated with conditional Eq. (5) let the set of variables Zt include Tt-1, VTBt-1. Note that the joint density function of jWt j and Tt-1 as well as VTBt-1 conditional on information set It, is equal to the product of the conditional model (5) and information set It, i.e., E (jWt j|Zt, It), and the marginal model of T and VTB, given information set It, where E is the expectation operator. The marginal models of T and VTB are E(Tt|It) and E(VTBt|It). Information set I includes lagged values of T, VTB and jWt j; as well as current and lagged values of other valid conditioning variables. Disturbances terms of conditional and marginal models are independent by construction. Define, respectively, the conditional moments of jWt j and Zt as g jWt jt = E(jWt j|Zt, It), gTt = E(Tt|It), gVTB = E(VTBt|It), t Zt rtjWt j = E[(jWt j
gtjWt j)2|It], rTt = E[(Tt
gT)2|It], and rVTB = E[(VTBt
gVTB)2|It]. Let rt jWt jZt = E[(jWt j
gZt )) t t ) ((Zt
g |It]. Consider the joint distribution of jWt j, Zt conditional on information set It to be normally distributed with mean  PP PZ  P r r ; where P= |W |. Then, following Engle et al. gt = [gt jWt j;gZt ¼ t ] and a non-constant error covariance matrix t ZP ZZ

r r

(1983) and Engle and Hendry (1993), we can write the relationship between |Wt| and Z, i.e., conditional model (5) as: Zt Zt jWt j ¼ a0 þ f0 Zt þ ðd0
f0 ÞðZt
gZt Þ þ d1 rZt t ðZt
g Þ þ f1 ðg Þ 3

2

2

2

Zt Zt Zt Zt Zt 0 þf2 ðgZt Þ þ f3 rZt t g þ f4 rt ðg Þ þ f5 ðrt Þ g þ f6 Devzt þ qt a þ 2t ;

ð6Þ

where a0, f0, f1, f2, f3, f4, f5, f6, d0 and d1 are regression coefficients of jWt j on Zt conditional on q’t a where q includes past values jWt j, Zt and other valid conditioning variables included in Eq. (5). The error term Єt is assumed, as before, to be heteroscedastic and autocorrelated (due to the overlapping observations), normally, identically and independently distributed. Because the error is heteroscedastic, the term Devz (=the deviation of the variance of the error term from a fiveperiod ARCH error of Z) is added, see Engle and Hendry (1993). The control/target variable Zt is subject to policy interventions. Although the parameters of Zt are assumed to be constant over the sample period, it is possible that this parameter changes (Lucas, 1976) under interventions affecting the DGP (data generating process) of Zt, i.e., marginal models of T and VTB. In this case, agents have a forward-looking behavior and the conditional model (5) is not policy invariant. Hence, the parameters of interest in the analysis will be d and f in the behavioral relationship (6). Under the null of weak exogeneity, d0– f 0=0. Under the null of invariance, f1 = f2 = f3 = f4 = f5 = f6 = 0 in order to have f0 = f. Finally, if we assume that rZt has distinct values over different, but clearly defined regimes, then under the null of constancy of d, we need d1 = 0. If these entire hypotheses are accepted, the equation will be reduced to Eq. (5), and

A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

605

the agents in the market are not forward looking. In other words, expectations are not formed rationally. It should also be mentioned that ‘‘superexogeneity is sufficient but not a necessary condition for valid inference under intervention” (Engle et al., 1983, p. 284). This is due to the fact that estimable models with invariant parameters, but with no weakly exogenous variables are easily formulated. The stochastic mechanism, which generates variables T and VTB in the conditional model (5), i.e., the marginal models, needs to be specified. To estimate the marginal models, both intercept and slopes of the marginal equations were allowed to be influenced by the dummy variables included in DUM. For the behavioral Eq. (5) we can, therefore, have the following marginal models:

Tt ¼ Constant þ

k X

xi Tt
i þ

i¼1

VTBt ¼ Constant þ

k X

Hi VTBt
i þ Dum0t
i a þ v0t ;

ð50 Þ

i¼1 k X i¼1

Ci Tt
i þ

k X

hi VTBt
i þ Dum0t
i b þ v0t :

ð500 Þ

i¼1

Dum in the above equations is a column vector of all dummy variables in DUM and the product of these dummy variables and T as well as VTB. The parameters a and b are column vectors of the parameters associated with these variables. The superexogeneity condition (i.e., weak exogeneity, constancy and invariance conditions) is an important criteria in policy interventions. Under superexogeneity, the coefficients of the marginal model, i.e., x’s, H’s, C’s, h’s, a’s and b’s in the above equations can change without affecting the coefficients of the conditional model, i.e., Eq. (5). Since governments usually base their policies on past outcomes of the variables, strong exogeneity is an unlikely condition for policy variables. But superexogeneity can be a valid condition for government interventions to be successful, Kia (2010). Tables 2 and 3 report the parsimonious estimation of the marginal models (50 ) and (500 ). Diagnostic tests reported in the last row of tables 2 and 3 suggest that, due to overlapping observations, the error term is both autocorrelated and ARCH heteroscedastic. Hansen’s (1992) stability Li tests reported in the last column of these tables show that all coefficients are stable. However, the variance is not stable. Consequently, the joint stability Lc test result, 82.07 (p-value = 0.00) in Table 2 and 37.46 (p-value = 0.00) in Table 3, rejects the null of joint stability of the coefficients together with the estimated associated variance. The estimated model seems a reasonable marginal model for the analogue of gZ for Zt equals to Tt-1 and VTBt-1.17 According to the estimation result reported in tables 2 and 3, there is a structural break in the marginal model of the monetary policy index and the volatility of Treasury bill rate when the Fed started to announce the target rate on February 4, 1994 and when the Fed started to adopt the practice of changing the FF targets by 25 or 50 basis points on October 19, 1989. Furthermore, based on the significance of the dummy coefficients, the policy regime changes of February 2, 1984, when the modification in the reserve maintenance period from one week (for most large institutions) to two weeks (for all institutions) took place, August 19, 1997, when FOMC started to include a quantitative Fed funds target rate in its Directive to the New York Fed Trading Desk, May 18, 1999, when the Fed extended its explanations regarding policy decisions and started to include in press statements an indication of the FOMC’s view regarding prospective developments (or the policy bias), February 2, 2000, when the FOMC started to include a balance-of-risks sentence in its statements replacing the previous bias statement, March 19, 2002, when the Fed included in FOMC statements the vote on the directive and the name of dissenter members (if any) there is a structural break in the coefficients of these marginal models. There is also evidence of a structural break during the tenure of the Chairman Greenspan (August 11, 1987-January 31, 2006), Chairman Bernanke (February 1, 2006 to January 31, 2014) and since February 3, 2014 when Janet Yellen started to chair the Fed. Moreover, there is strong evidence for a structural break due to the October 1987, Asian 1997 and US (September 30, 2007-September 30, 2008) crises. When the Fed changed the FF target rate outside its regular meetings on January 3, 2001, April 18, 2001 and September 17, 2001, it created a structural break in the coefficients. The instability of the marginal models implies that the parameters of the associated conditional model will not be policy invariant when economic agents are forward-looking. ZZ From the estimated marginal models, the estimates of gZ, and rZZ t , for Z = T and VTB were calculated. As for rt , since the error in both marginal models, at the conventional level, is heteroscedastic according to the ARCH test, a five-period ARCH error, therefore, was estimated. The variable Devz (for Z = T and VTB), as differences between the variance of the error term in the marginal model for T and VTB and the variance constructed by the ARCH estimation, was also constructed. All of these constructed variables were then included in Eq. (5) reported in Table 1. The estimation results on these constructed variables are given in Table 4. The individual v2-test result is on the null hypothesis that the coefficient of each constructed variable is zero. The v2-test results, given in the third to last row in Table 4, are on the hypothesis that only the constructed variables related to each contemporaneous variable while all other constructed variables are included, are jointly zero. The v2-test results, given in the second to last row of the table, are on the null hypothesis the constructed variables related to each contemporaneous

17 Note that when there are few observations in the sample, e.g., OCT8 or ASIA, Hansen’s (1992) stability Li test cannot be calculated. Consequently, NA appears for the test result.

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

Table 2 Marginal model of index (T) – Eq. (50 ). Explanatory Variables*

Dependent Variable = T Coeff. (Std.Error**)

Hansen’s Stability Li Test (p-value)

Constant Tt-1 Tt-11 Tt-20 (T*TA)t-5 (T*TA)t-9 (T*TA)t-15 (T*TA)t-19 (T*TAF)t-2 (T*TAF)t-19 (T*REMA)t-10 (T*REMA)t-17 (T*GREEN)t-1 (T*D970819)t-10 (T*D970819)t-11 (T*D99518)t-1 (T*D000202)t-13 (T*D000202)t-15 (T*D000202)t-17 (T*D000202)t-20 (T*D020319)t-3 (T*OCT87)t-14 (T*USCrisis)t-2 (T*USCrisis)t-6 VTBt-12 VTBt-13 (VTB*TA)t-5 (VTB*TA)t-15 (VTB*TAF)t-2 (VTB*TAF)t-15 (VTB*TAF)t-17 (VTB*REMA)t-5 (VTB*GREEN)t-4 (VTB*GREEN)t-14 (VTB*GREEN)t-15 (VTB*GREEN)t-17 (VTB*GREEN)t-19 (VTB*D970819)t-5 (VTB*D970819)t-13 (VTB*D970819)t-17 (VTB*D970819)t-19 (VTB*D99518)t-12 (VTB*ASIA)t-19 (VTB*OCT87)t-3 (VTB*OCT87)t-12 (VTB*OCT87)t-13 (VTB*Bernanke)t-2 (VTB*Bernanke)t-19 (VTB*USCrisis)t-1 (VTB*USCrisis)t-6 (VTB*USCrisis)t-9 (VTB*USCrisis)t-11 VFFt-1 (VFF*TA)t-4 (VFF*TA)t-9 (VFF*TA)t-12 (VFF*TAF)t-2 (VFF*TAF)t-6 (VFF*TAF)t-11 (VFF*TAF)t-13 (VFF*TAF)t-19 (VFF*REMA)t-13 (VFF*REMA)t-15 (VFF*GREEN)t-1 (VFF*GREEN)t-9 (VFF*GREEN)t-15 (VFF*D970819)t-12 (VFF*D020319)t-11


0.44.09 (3.66) 0.44 (0.03)
0.05 (0.02) 0.06 (0.02) 0.08 (0.02)
0.05 (0.02)
0.08 (0.02) 0.04 (0.02) 0.10 (0.01)
0.05 (0.02) 0.10 (0.01)
0.05 (0.01)
0.05 (0.03)
0.07 (0.03) 0.07 (0.03) 0.16 (0.03)
0.06 (0.02) 0.08 (0.02) 0.06 (0.02)
0.08 (0.02) 0.03 (0.01) 0.31 (0.04)
0.12 (0.06)
0.12 (0.05)
52.13 (18.49) 63.27 (27.10)
85.66 (31.82) 75.47 (30.42)
58.19 (18.77)
67.15 (32.32) 108.47 (29.58)
59.53 (15.53) 67.75 (17.17)
39.44 (19.65) 55.83 (23.71)
56.24 (22.62)
51.80 (20.52) 99.39 (31.42)
95.93 (24.39)
96.09 (29.92) 73.71 (23.47) 65.47 (18.99) 164.92 (30.31)
485.35 (23.45)
200.44 (25.14) 201.42 (21.84) 110.45 (24.68)
89.87 (21.82)
104.83 (28.92) 70.76 (29.03)
115.75 (35.99) 92.87 (28.72)
3.49 (0.82) 7.17 (2.90) 15.36 (3.41)
9.09 (4.06)
8.87 (3.04)
7.64 (2.23) 9.46 (2.54)
7.57 (2.76)
7.49 (2.22) 4.15 (1.71)
4.30 (1.85) 9.37 (2.92)
15.50 (10.50) 10.82 (2.47) 10.44 (4.25)
18.34 (5.40)

0.99 0.92 0.98 0.98 0.97 0.94 0.96 0.97 0.97 0.99 0.89 0.90 0.97 0.84 0.81 0.68 0.65 0.65 0.65 0.63 0.52 NA 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.88 0.97 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 NA NA NA NA 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.97 0.98 1.00 1.00 0.99 1.00 1.00 0.99 0.91 0.84 1.00 1.00 0.99 1.00 1.00

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617 Table 2 (continued) Explanatory Variables*

Dependent Variable = T Coeff. (Std.Error**)

Hansen’s Stability Li Test (p-value)

(VFF*D010917)t-1 (VFF*D010917)t-2 (VFF*D010917)t-3 (VFF*D010917)t-4 (VFF*D010917)t-5 (VFF*D010917)t-9 (VFF*D010917)t-10 (VFF*D010917)t-11 (VFF*D010917)t-13 (VFF*D010418)t-3 (VFF*D010418)t-10 (VFF*D010418)t-11 (VFF*ASIA)t-4 (VFF*OCT8)t-2 (VFF*OCT8)t-4 (VFF*OCT8)t-12 (VFF*Bernanke)t-2 (VFF*Bernanke)t-3 (VFF*Bernanke)t-16 (VFF*USCrisis)t-3 D99518 D010917 GREEN D010103 OCT87 USCrisis Variance


88.21 (12.39) 134.92 (13.47)
227.86 (13.96)
233.63 (15.32)
121.99 (16.58) 116.04 (13.13)
85.77 (12.23) 104.15 (15.00)
58.01 (16.41) 99.47 (9.72)
94.50 (6.62) 114.13 (6.62) 35.59 (9.44) 178.22 (17.77) 141.45 (10.59)
66.44 (10.01) 27.33 (7.81)
57.75 (13.37) 20.99 (6.87) 53.66 (12.39)
14.99 (3.21)
26.09 (0.77) 15.67 (3.45) 18.87 (3.06)
10.52 (1.33) 16.14 (5.65)

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.05 0.05 NA NA NA NA 1.00 1.00 1.00 1.00 0.79 0.06 1.00 0.05 NA 1.00 0.00 Joint (coeffs + var.) = 82.07 (p-value = 0.00)

R2 = 0.47, r=9.51 DW = 2.01, Godfrey (5) = 4.60 (p-value = 0.00), White = 3248 (p-value = 0.00), ARCH (5) = 512 (p-value = 0.00) REST = 11.88 (p-value = 0.01)***

* T is the transparency index, VTB is the volatility of the three-month Treasury bill rate and VFF is the volatility of the Fed funds rate. For the definitions of the dummy variables see Table A in the Appendix. ** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity. *** R2 , r and DW, respectively, denote the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. Furthermore, White is White’s (1980) general test for heteroscedasticity, ARCH is the five-order Engle’s (1982) test, Godfrey is the five-order Godfrey’s (1978) test and REST is Ramsey’s (1969) misspecification test.

variable, while excluding constructed variables related to other contemporaneous variables, are jointly zero. Finally the v2-test result in the last row is on the null hypothesis that all coefficients of the constructed variables are jointly zero. As the estimation results in Table 4 show, the joint v2-test on the null hypothesis that coefficients of these constructed variables are jointly zero is significant, indicating that these variables together should be included. This result immediately implies that the contemporaneous variables in the conditional model, reported in Table 1, are not jointly superexogenous, i.e., agents are forward looking and, consequently, the estimated risk/forecast error can be a measure of current/ex-post and future/ex-ante risk. This result confirms the finding of Kia (2010) that agents in the money market are forward looking and their expectations are formed rationally in the US money market. Since the monetary policy index T, which is an objective market-based monetary policy transparency index, is not superexogenous we can conclude that a higher monetary policy transparency results not just in a lower ex-post risk, but also a lower ex-ante risk à la Kia (2003). It must, of course, be emphasized that in this case Eq. (5) can be used for future prediction of the risk in the money market. As for the monetary policy transparency index T since the coefficient of (Z-gZ) for Z = T is statistically insignificant this variable is weakly exogenous. Furthermore, based on the test result on the coefficient of rZZ(Z-gZ) for Z equal to T, which is statistically insignificant we cannot reject the null of constancy. The variable T is also policy invariant since the coefficient of all other constructed variables is statistically insignificant. Note that constancy and invariance are different concepts. Parameters could vary over time, but be invariant with respect to policy changes and vice versa. So T is weakly exogenous and policy invariant as well as constant, but not superexogenous. Consequently, T influences both ex-post and ex-ante risks. As for the contemporaneous variable VTB, since the coefficient of (Z-gZ) and rZZ(Z-gZ) for Z = VTB is statistically insignificant, this variable is weakly exogenous and constant. But, since the coefficient of (rZZ)2 gZ, for Z = VTB is statistically significant, even though the coefficients of all other constructed variables are statistically insignificant, we reject the null of policy invariance. Note that since both constructed variables are weakly exogenous the inferences on the parameters of the agents’ model are efficient. The estimation result of both T and VTB justify the result of the last three rows in the table since, as it was mentioned by Engle and Hendry (1993), we need all three conditions to be satisfied in order to ensure superexogeneity. The failure of the invariance condition, for these variables, therefore, justifies the result of the joint v2-test on the null hypothesis that all coefficients of the constructed variables are jointly zero. Namely, in general, we reject the null hypothesis that these variables are superexogenous. The overall conclusion is that the monetary policy transparency reduces not just the ex-post risk, but also the ex-ante risk. This issue is completely ignored in the existing literature.

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

Table 3 Marginal model of volatility of treasury bill rate (VTB) – Eq. (500 ). Explanatory Variables*

Dependent Variable = VTB Coeff. (Std.Error**)

Hansen’s Stability Li Test (p-value)

Constant Tt-12 (T*TA)t-2 (T*TA)t-13 (T*TAF)t-13 (T*TAF)t-19 (T*REMA)t-11 (T*REMA)t-12 (T*GREEN)t-16 (T*D970819)t-9 (T*D970819)t-20 (T*D99518)t-11 (T*D000202)t-6 (T*OCT87)t-1 (T*OCT87)t-2 (T*OCT87)t-4 (T*OCT87)t-13 (T*OCT87)t-19 (T*OCT87)t-20 (T*Bernanke)t-1 (T*Bernanke)t-4 (T*Bernanke)t-7 (T*Bernanke)t-11 (T*USCrisis)t-2 (T*USCrisis)t-3 (T*USCrisis)t-7 (T*USCrisis)t-18 VTBt-1 VTBt-2 VTBt-4 VTBt-5 VTBt-15 VTBt-17 (VTB*TA)t-20 (VTB*REMA)t-14 (VTB*REMA)t-17 (VTB*REMA)t-19 (VTB*REMA)t-20 (VTB*GREEN)t-20 (VTB*D970819)t-6 (VTB*D99518)t-5 (VTB*D000202)t-2 (VTB*D000202)t-10 (VTB*D000202)t-11 (VTB*D020319)t-1 (VTB*ASIA)t-2 (VTB*ASIA)t-18 (VTB*ASIA)t-19 (VTB*OCT87)t-2 (VTB*OCT87)t-16 (VTB*OCT87)t-20 (VTB*Yellen)t-18 (VTB*Bernanke)t-2 (VTB*Bernanke)t-19 (VTB*USCrisis)t-14 VFFt-1 VFFt-5 VFFt-7 VFFt-11 VFFt-14 VFFt-18 (VFF*TA)t-20 (VFF*TAF)t-11 (VFF*REMA)t-6 (VFF*REMA)t-17 (VFF*GREEN)t-10 (VFF*D010917)t-3 (VFF*D010917)t-5

0.01 (0.0001)
5.e
005.(2.e
005)
4.e
005.(1.e
005) 6.e
005.(1.e
005) 4.e
005.(1.e
005) 4.e
005.(1.e
005)
3.e
005.(1.e
005) 5.e
005.(9.e
006)
2.e
005.(2.e
005)
6.e
005.(1.e
005) 4.e
005.(1.e
005) 7.e
005.(1.e
005) 5.e
005.(1.e
005) 9.e
004.(5.e
005) 1.e
003.(4.e
005) 8.e
004.(9.e
005) 3.e
004.(4.e
005) 4.e
004.(4.e
005)
5.e
004.(4.e
005)
2.e
004.(6.e
005) 1.e
004.(5.e
005)
1.e
004.(5.e
005) 1.e
004.(3.e
005) 2.e
004.(1.e
005)
3.e
004.(1.e
004) 3.e
004.(8.e
005)
1.e
004.(4.e
005) 0.80 (0.018) 0.14 (0.019)
0.35 (0.02) 0.27 (0.02)
0.09 (0.02) 0.11 (0.03)
0.07 (0.02) 0.10 (0.02)
0.10 (0.03) 0.17 (0.02)
0.20 (0.02) 0.07 (0.03) 0.06 (0.02)
0.16 (0.04) 0.12 (0.03) 0.09 (0.03)
0.09 (0.03)
0.06 (0.02)
0.44 (0.04)
0.25 (0.02) 0.22 (0.02)
0.74 (0.02) 0.05.(9.e
003) 0.13 (0.02) 0.23 (0.05) 0.06 (0.02) 0.10 (0.03)
0.12 (0.03) 1.e
003.(6.e
004)
5.e
003.(3.e
004) 2.e
003.(3.e
004)
2.e
003.(5.e
004) 9.e
004.(3.e
004)
2.e
003.(5.e
004) 3.e
003.(1.e
003)
0.01 (1.e
003)
3.8 e
003 (1.e
003) 4. e
003 (1.e
003) 9. e
003 (2.e
003) 0.08 (0.02)
0.11 (0.01)

0.87 0.79 0.81 0.69 0.73 0.72 0.81 0.77 0.70 0.69 0.70 0.63 0.64 NA NA NA NA NA NA 1.00 0.99 1.00 0.97 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.97 1.00 1.00 0.99 1.00 1.00 1.00 0.95 1.00 1.00 1.00 1.00 1.00 1.00 NA NA NA NA NA NA 1.00 1.00 1.00 1.00 0.24 0.81 0.95 0.32 0.19 0.92 1.00 0.90 0.84 0.87 0.67 0.06 0.06

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617 Table 3 (continued) Explanatory Variables*

Dependent Variable = VTB Coeff. (Std.Error**)

Hansen’s Stability Li Test (p-value)

(VFF*D010917)t-9 (VFF*D010917)t-10 (VFF*D010917)t-12 (VFF*D010917)t-13 (VFF*D010917)t-14 (VFF*D010917)t-17 (VFF*D010917)t-18 (VFF*D010418)t-1 (VFF*D010418)t-7 (VFF*D010418)t-9 (VFF*D010418)t-11 (VFF*D010418)t-12 (VFF*D010418)t-14 (VFF*D010418)t-15 (VFF*D010418)t-20 (VFF*D010103)t-2 (VFF*D010103)t-3 (VFF*D010103)t-6 (VFF*D010103)t-7 (VFF*D010103)t-11 (VFF*D010103)t-12 (VFF*D010103)t-13 (VFF*D010103)t-18 (VFF*D010103)t-20 (VFF*ASIA)t-2 (VFF*ASIA)t-3 (VFF*OCT8)t-1 (VFF*OCT8)t-3 (VFF*OCT8)t-4 (VFF*OCT8)t-11 (VFF*OCT8)t-18 (VFF*Bernanke)t-1 (VFF*Bernanke)t-7 (VFF*Bernanke)t-20 (VFF*USCrisis)t-7 (VFF*USCrisis)t-14 D010418 GREEN OCT87 Yellen Variance


0.09 (0.02)
0.19 (0.01) 0.12 (0.01)
0.11 (0.01)
0.10 (0.01)
0.04 (0.01) 0.19 (0.01) 0.20 (8.e
003)
0.09 (9.e
003) 0.13 (9.e
003)
0.05 (9.e
003) 0.07 (9.e
003)
0.07 (7.e
003) 0.08 (7.e
003) 0.08 (7.e
003) 0.05 (5.e
003) 0.03 (3.e
003)
0.06 (5.e
003)
0.03 (4.e
003) 0.05 (3.e
003)
0.04 (3.e
003)
0.05 (3.e
003) 0.04 (3.e
003) 0.03 (2.e
003) 0.10 (0.03) 0.12 (0.01)
0.17 (0.02) 0.21 (0.02)
0.16 (8.e
003)
0.11 (0.01)
0.15 (0.01) 0.05 (0.01) 0.04 (0.01)
0.03 (0.01)
0.08 (0.02) 0.07 (0.02)
5.e
003 (1.e
003)
3.e
003 (1.e
003) 0.03 (2.e
003)
9.e
003 (1.e
003) –

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 NA NA NA NA NA NA NA 1.00 1.00 1.00 1.00 1.00 0.05 0.71 NA 0.91 0.00 Joint (coeffs + var.) = 37.46 (p-value = 0.00)

R2 = 0.93, r = 0.008 DW = 1.97, Godfrey (5) = 6.41 (p-value = 0.00), White = 15957 (p-value = 0.00), ARCH (5) = 557 (p-value = 0.00), REST = 0.21 (p–value = 0.98)***

* T is the transparency index, VTB is the volatility of the three-month Treasury bill rate and VFF is the volatility of the Fed funds rate. For the definitions of the dummy variables see Table A in the Appendix. ** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity. *** R2 , r and DW, respectively, denote the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. Furthermore, White is White’s (1980) general test for heteroscedasticity, ARCH is the five-order Engle’s (1982) test, Godfrey is the five-order Godfrey’s (1978) test and REST is Ramsey’s (1969) misspecification test.

To further ensure the robustness of the results, additional tests are pursued. Specifically, the conditional model (6) is adjusted by sequentially deleting constructed variables with insignificant coefficients. The only variable (Z-gZ) for Z = VTB was found to be only statistically significant. This result further confirms that the contemporaneous variable VTB in the conditional model (5) is not superexogenous. As a second check, the significance of the dummy variables, affecting the intercept or slopes in the marginal models for T and VTB, when added to the conditional model (5) was examined. The variables with statistically significant coefficients were found to be T*TA, T*TAF, T*SWED, T*REMA, T*Green, T*Yellen, T*Bernanke, T* D970819, T* D020319, T*OCT87, VTB*TA, VTB*TAF, VTB*REMA, VTB⁄UScrisis, VTB*Yellen, VTB*Bernanke, VTB*D970819, VTB*D000202, and VTB*OCT87. This result further rejects the null of supererogeneity for both T and VTB. 5. Volatility in the money market and the monetary policy transparency In this section I will examine the relationship between monetary policy transparency, using Kia’s (2011) index, and risk, measured by the volatility, in the money market. We know that FF and TB are cointegrated and the adjustment toward the

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

Table 4 Estimation results of superexogeneity tests for contemporaneous variables in Eq. (5).

v2 (1) (p-value) Variable (Z)* Z
g

Z

ZZ

Z

r (Z
g ) (gZ)2 (gZ)3

rZZ gZ rZZ (gZ)2 (rZZ)2 gZ Devz

v2-statistics on null hypothesis that coefficients of all constructed variables in this column are jointly zero. The equation includes the constructed variables related to other contemporaneous variables

v2-statistics on null hypothesis that coefficients of all constructed variables in this column are jointly zero. The equation excludes the constructed variables related to other contemporaneous variables v -statistics on coefficients of all variables in rows and columns 2

T

VTB

0.13 (0.72) 1.65 (0.20) 0.16 (0.70) 0.31 (0.58) 0.32 (0.57) 0.29 (0.59) 0.36 (0.55) 1.97 (0.16) 21.85 (0.01)

1.36 (0.24) 0.01 (0.92) 0.00 (0.99) 0.09 (0.28) 1.14 (0.58) 1.48 (0.22) 4.65 (0.03) 2.23 (0.13) 22.98 (0.00)

27.98 (0.00)

30.80 (0.00) 56.58 (0.00)

Zt Zt 2 Zt 3 Zt Zt 2 Zt Zt Zt Zt 2 0 jWt j = a0 + f0 Zt + (d0
f0) (Zt
gZt) + d1 rZt t (Zt
g ) + f1 (g ) + f2 (g ) + f3 rt g + f4 rt (g ) + f5 (rt ) g + f6 Devzt + q t a + Єt, where jWt j is the forecast error and risk, gZ is the conditional mean of Z, rZZ is the conditional variance of Z, and DevZ is the deviation of variance of the error term from a five-period ARCH error of Z. Since the error is ARCH heteroscedastic the estimation method is robust error OLS. * Z = T or VTB. T is the monetary policy transparency index and VTB is the volatility of the three-month Treasury bill rate.

long-run equilibrium largely occurs through the movements in the FF rate rather than the TB rate [Sarno and Thornton (2003) and Kia (2010)]. Hence, we would expect the volatility of the daily movements in FF, say VFF, to affect the volatility of the daily movements in TB (i.e., VTB the risk in the money market). Let us assume the volatility of TB is a function of the volatility of FF and policy regime changes as well as other exogenous shocks specified in EDUM defined below. Furthermore, assume such a relationship has a linear approximation as specified by Eq. (7):

VTBt ¼ C0 þ cTt þ

k X

Ci VFFt
i þ

k X

i¼0

Ui VTBt
i þ EDUM0t C þ et ;

ð7Þ

i¼1

where C0,. . ., Ck, U0, . . ., Uk, c and C are constant parameters. Dummy vector EDUM = (DUMt, STUt, TUE1t, HB1t, HA1t, HB3t, HA3t, LDYt, LDBYAt LQBAt, LQt). Dummy variables included in EDUM are defined in Table A in the Data Appendix. To capture the possible volatility in the money market created by other factors, like window dressing, holidays and other seasonality, following Hamilton (1996), beside dummy variables in vector DUM, I included dummy variables STUt, TUE1t, HB1t, HA1t, HB3t, HA3t, LDYt, LDBYAt, LQBAt and LQt, see Table A in the Appendix. Note that in Eq. (7) C0 is expected to be positive, indicating a higher volatility in FF rate results in a volatility of TB rate, and if c is negative/positive then the higher the monetary policy transparency (T) is, the lower/higher the volatility of the three-month Treasury bill rate will be. However, if agents in the money market are forward-looking, as we saw in the previous section, both T and VFF will fail to be superexogenous and the impact of these two variables on VTB will reflect on their impact on the ex-post risk, but also on the ex-ante risk. Following, among many, Schwert (1989) and Kia (2003), the methodology developed by Davidian and Carroll (1978) was used. Let x be any variable in column vector xt = (DTBt, DFFt,)’ and estimate Eq. (8) for DTBt and DFFt.

xt ¼

20 X



axi xt
i þ uxt ; uxt  niid 0;

X :

ð8Þ

i¼1

The parameters ax, for i = 1–20, are assumed to be constant. I assume a lag length of 20 days (reflecting a month) is sufficient for the market participants to learn from the past movements in the TB and Fed funds rates. Furthermore, we estimate a 20th-order autoregression for the absolute values of the errors from Eq. (8), which reflects different daily standard deviations:

^ xt j ¼ rxt ¼ ju

20 X dxi rxt
i þ vt ; i¼1

ð9Þ

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

where the parameters dix , for i = 1–20, are constant parameters. The absolute value of the fitted value of uxt (i.e., |ûxt|) is the standard deviation (adjusted for heteroscedasticity and autocorrelation due to overlapping observations) of xt, for xt = DTBt and DFFt. However, since the expected error is lower than the standard deviation from a normal distribution, following Schwert (1989), all absolute errors are multiplied by the constant 1.2533. As it was also mentioned by Kia (2003), the conditional volatility in Eq. (9) represents a generalization of the 20-day rolling standard estimator used by Officer (1973), Fama (1976) and Merton (1980). This is due to the fact that the conditional volatility estimated by Eq. (9) allows the conditional mean to vary over time in Eq. (8), while it also allows different weights to be applied to the lagged absolute unpredicted changes in Treasury bills and Fed funds rates. Furthermore, Engle (1993) reviews the merit of this measure of volatility, among others. This measure of volatility is similar to the autoregressive conditional heteroscedasticity (ARCH) model of Engle (1982), which, in its various forms, has been widely used in the finance literature. Davidian and Carroll (1978) argue that the specification in Eq. (9) based on the absolute value of the prediction errors is more robust than those based on the squared residuals in Eq. (8). However, it should be noted that the variables in Eqs. (7) and (9), excluding dummy variables, are generated regressors. Consequently, when these equations are estimated, their t statistics should be interpreted with caution. To cope with this problem, following, among many, Kia (2003), the equation for the conditional volatility [i.e., Eq. (7)] is estimated jointly with the equations determining the conditional volatilities of DTB and DFF using the Generalized Least Squares (GLS) estimation procedure (SUR).18 In the GLS system, two equations are generated by Eq. (8), two equations are generated by Eq. (9) and including Eq. (7) a system of five equations with 8737 observations is estimated. In the GLS estimation, for each equation and the system of equations, I used Newey and West’s (1987) robusterror for 5-order moving average to correct for heteroscedasticity and autocorrelation. The GLS estimator incorporates the possibility of cross-equation correlation among the error terms as well as endogeneity if it exists. The final parsimonious GLS estimation result of Eq. (7) is given in Table 5.19 The specification test results indicate the existence of both autocorrelation and heteroscedasticiy. Furthermore, as it would be expected for 33-year data, with 8737 daily observations, not all of the coefficients, based on Hansen’s (1992) stability test result, individually are stable. Furthermore, because of heteroscedasticity the variance and joint coefficients are not stable. The estimated coefficient of our monetary policy index (T) is negative, indicating that a more transparent monetary policy leads to a lower volatile money market.20 This result confirms, among many, the finding of Tabellini (1987), Haldane and Read (2000), Swanson (2006), Ehrmann and Fratzscher (2009) and Biefang-Frisancho Mariscal and Howells (2010) that a higher degree of transparency tends to lower market volatility. The volatility of FF, as it would be expected has an immediate positive impact on the volatility of the TB rate, but after two and eight days, influences negatively the VTB. However, the overall estimated result (sum of all coefficients) is negative. Among all dummy variables included in EDUM, the coefficients of dummy variables TH, LDBYA, LQBA and UScrisis were found to be statistically significant. As it would be expected, days before and after New Year, markets are more quiet and so the coefficients of dummy variables LDBYA and LQBA are negative. Finally, as the estimated coefficient of UScrisis indicates during the US crisis of 2007 the money market was more volatile in the United States. The next task is to investigate if market participants are forward looking or not. This is also a robust test for the result in the previous section. Namely, we would expect both T and VFF not to be superexogenous. Following the same approach, as in the previous section, we can use a similar equation for the conditional model of (7), as the following: 2

3

2

Zt Zt Zt Zt Zt Zt Zt VTBt ¼ a0 þ f0 Zt þ ðd0
f0 ÞðZt
gZt Þ þ d1 rZt t ðZt
g Þ þ f1 ðg Þ þ f2 ðg Þ þ f3 rt g þ f4 rt ðg Þ 2

Zt 0 þ f5 ðrZt t Þ g þ f6 Devzt þ qt a þ 2t ;

ð10Þ

However, now the set of variables Zt in Eq. (8) includes Tt and VFFt. As before, the marginal model of T is reported in Table 2. The estimated parsimonious marginal model of VFF is reported in Table 6. Diagnostic tests reported in the last row of the table suggest that, due to overlapping observations, the error term is both autocorrelated and ARCH heteroscedastic. Hansen’s (1992) stability Li tests reported in the last column of the table show that all coefficients are stable. However, the variance due to the existence of heteroscedasticity is not stable. Consequently, the joint stability test result, 21.15 (p-value=0.00) rejects the null of joint stability of the coefficients together with the estimated associated variance. The estimated model seems a reasonable marginal model for the analogue of gZ for Z equals to VFF.21

18

See Kia (2003), Footnote 4, for a full explanation on why in our case the GLS estimation technique should be used. The stationarity test results for VFF are as follows: The absolute value of the Augmented Dickey-Fuller t, for a lag length of 19 is 11.93 and the absolute value of the Phillips-Perron non-parametric t test for the lag length of 4 is 58.48, both t statistics are higher than 3.43 (1% critical value) indicating the conditional volatility VFF is stationary. Note that the lag length for these tests was determined in such a way that, for a global lag of 20 days, the AIC and SC criteria are at their minimum. Furthermore, the absolute value of Zivot-Andrews’ (1992) t-test, at 1990:08:13 break point, is 18.86, which confirms the Augmented Dickey-Fuller and the Phillips-Perron test results. 20 Note that the estimated coefficients of Tt-20 and Tt-15 are positive, which may indicate that the monetary policy after two or four weeks may result in a higher volatility in the money market. But the sum of all the estimated coefficients of the index is negative, indicating further that the overall impact of the monetary policy transparency on the volatility in the money market is negative. 21 Note that, like the marginal models of T and VTB, when there are few observations in the sample for OCT8 Hansen’s (1992) stability Li test cannot be calculated. Consequently, NA appears for the test result. 19

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A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

Table 5 Parsimonious estimation result of Eq. (7). dependent variable = VTB = conditional volatility of three-month TB rate. Explanatory Variables*

Coefficients

Standard Error**

Hansen’s Stability Li Test (p-value)

Constant Tt Tt-1 Tt-3 Tt-15 Tt-16 Tt-20 VFFt VFFt-2 VFFt-8 VFFt-10 VTBt-1 VTBt-2 VTBt-4 VTBt-5 VTBt-6 VTBt-11 VTBt-13 VTBt-15 VTBt-19 VTBt-20 THt LDBYAt LQBAt UScrisist Variance Specification Tests

0.02
0.00006
0.00004
0.00005 0.00003
0.00003 0.00002 0.002
0.005
0.002 0.003 0.83 0.20
0.37 0.19
0.07
0.08 0.16
0.09 0.20
0.19
0.0007
0.002
0.002 0.0003

0.002 0.000009 0.00001 0.000009 0.000008 0.000008 0.000008 0.001 0.001 0.0009 0.0009 0.01 0.01 0.01 0.01 0.01 0.008 0.01 0.01 0.01 0.01 0.0002 0.0007 0.0007 0.0005

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.18 0.09 0.03 0.02 0.51 0.53 0.24 0.12 0.14 0.06 0.03 0.05 0.09 0.03 0.85 0.00. 0.32 1.00 0.00 Joint (coeffs + var.)= 14 (p-value = 0.00)

r = 0.008 DW = 1.99, Godfrey (5) = 5.72 (p-value = 0.00), White = 3637 (p-value = 0.00), ARCH (5) = 964 (p-value = 0.00)***

* The sample period is 1982:10:06-2016:3:31. Tt is the monetary transparency index, and VFF is the volatility of the Fed funds rate. For the definition of the dummy variables, see Table A in the Appendix. ** The estimation method is the Generalized Least Squared (SURE) while Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity. *** r and DW, respectively, denote the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. Godfrey is the five-order Godfrey’s (1978) test, White is White’s (1980) general test for heteroscedasticity and ARCH is the five-order Engle’s (1982) test.

As we can see, similar to other marginal models, reported in tables 2 and 3, there is a structural break in the marginal model of VFF. The breaks occur similar to the marginal models of T and VTB. Similarly, the instability of the marginal model of VFF implies that the parameters of the associated conditional model (7) will not be policy invariant when economic agents are forward-looking. As before from the estimated marginal model of VFF, the estimate of gVFF and rVFF was calculated. As t for rFF t , since the error is ARCH test heteroscedastic, a five-period ARCH error, therefore, was estimated. I also constructed DevVFF, as differences between the variance of the error term of the marginal model of VFF and the variance constructed by ARCH estimation. All of these constructed variables plus constructed variables associated with the variable T were used to estimate Eq. (10). The GLS estimation result of these constructed variables is given in Table 7. Here in the GLS system, two equations are generated by Eq. (8), two equations are generated by Eq. (9) and including Eq. (10) a system of five equations with 8737 observations is estimated. As before in the GLS estimation, for each equation and the system of equations, I used Newey and West’s (1987) robusterror for 5-order moving average to correct for heteroscedasticity and autocorrelation. The reported test results in Table 7 are similar to what was explained in Table 4. As for the monetary policy transparency index T since the coefficient of (Z-gZ) for Zt = Tt is statistically significant, this variable is not weakly exogenous. Furthermore, based on the test result on the coefficient of rZZ(Z-gZ) for Zt equal to Tt, which is statistically significant, we reject the null of constancy. Variable T is not policy invariant since, except the coefficients of rZZ (gZ)2 and Devz, the coefficient of all other constructed variables is statistically significant. We can also reject the null hypothesis all of the coefficients of constructed variables are jointly zero, see the last two rows of the table. So T is not superexogenous. Consequently, T influences both ex-post and ex-ante risks. As for the contemporaneous variable VFF, since the coefficient of rZZ(Z-gZ) for Zt = VFFt is statistically insignificant, we cannot reject the null of constancy. But, since the coefficient of (gZ)2 and Devz is statistically significant, even though the coefficients of all other constructed variables are statistically insignificant, we reject the null of policy invariance. As the result in the last three rows indicates, the coefficients of all constructed variables are not jointly zero and, consequently, VFF is not superexogenous. Therefore, as before we conclude that market participants are forward looking and expectations are formed rationally. This result also confirms the finding of Kia (2010). As before as a second check, the significance of the dummy variables, affecting the intercept or slopes in the marginal models for T and VFF, when added to the conditional model (7), was examined. The variables with statistically significant

A. Kia / North American Journal of Economics and Finance 42 (2017) 597–617

613

Table 6 Marginal Model of Volatility of Fed funds Rate (VFF). Explanatory Variables*

Dependent Variable = VTB Coeff. (Std.Error**)

Hansen’s Stability Li Test (p-value)

Constant Tt-1 Tt-2 Tt-10 Tt-16 Tt-20 (T*TA)t-4 (T*TA)t-10 (T*TA)t-11 (T*TA)t-20 (T*TAF)t-2 (T*TAF)t-3 (T*REMA)t-6 (T*GREEN)t-14 (T*GREEN)t-16 (T*D970819)t-1 (T*D970819)t-3 (T*OCT87)t-1 (T*OCT87)t-4 (T*USCrisis)t-6 VTBt-20 (VTB*GREEN)t-2 (VTB*GREEN)t-13 (VTB*GREEN)t-19 (VTB*D970819)t-19 (VTB*D000202)t-3 (VTB*D000202)t-4 (VTB*OCT87)t-4 (VTB*USCrisis)t-1 (VTB*USCrisis)t-14 VFFt-1 VFFt-2 VFFt-3 VFFt-13 (VFF*TA)t-4 (VFF*TAF)t-2 (VFF*REMA)t-7 (VFF*GREEN)t-2 (VFF*GREEN)t-4 (VFF*GREEN)t-5 (VFF*GREEN)t-20 (VFF*D010917)t-1 (VFF*D010917)t-2 (VFF*D010917)t-17 (VFF*D010103)t-2 (VFF*OCT8)t-1 (VFF*OCT8)t-4 (VFF*Bernanke)t-2 (VFF*Bernanke)t-3 (VFF*USCrisis)t-3 (VFF*USCrisis)t-4 (VFF*USCrisis)t-7 (VFF*USCrisis)t-15 (VFF*USCrisis)t-17 D000202 D010917 USCrisis Variance

0.58 (0.08)
0.004.(0.001) 0.004 (0.001)
0.003 (0.0005) 0.001 (0.0002)
0.002 (0.0005)
0.001.(0.0003) 0.002 (0.0005)
0.001 (0.0003) 0.00009 (0.0004)
0.003 (0.0009) 0.002 (0.0009)
0.0004 (0.0002) 0.0009 (0.0003)
0.0009 (0.0003) 0.002 (0.0009)
0.003 (0.0009) 0.01 (0.001) 0.01 (0.001) 0.002 (0.0008)
0.81 (0.33) 0.60 (0.26)
0.66 (0.19) 0.54 (0.26) 0.58 (0.27)
0.84 (0.29) 0.88 (0.33)
2.31 (0.70) 0.67 (0.32)
0.79 (0.23) 0.21 (0.05) 0.09 (0.04) 0.21 (0.10)
0.07 (0.02)
0.23 (0.07) 0.30 (0.09) 0.15 (0.03)
0.64 (0.16) 0.38 (0.10)
0.27 (0.06) 0.16 (0.06) 6.18 (0.26) 1.76 (0.34) 1.24 (0.15)
0.56 (0.09)
2.41 (0.39) 1.40 (0.42)
0.65 (0.22) 0.46 (0.20)
0.44 (0.23) 0.51 (0.20)
0.27 (0.12) 0.85 (0.16)
0.44 (0.12)
0.03 (0.01) 1.23 (0.01)
0.18 (0.08)

1.00 0.97 1.00 1.00 0.99 1.00 0.99 0.96 0.94 0.96 0.99 0.99 0.98 1.00 0.99 0.78 0.78 NA NA 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.97 NA 1.00 1.00 1.00 0.98 1.00 0.77 1.00 0.99 1.00 1.00 0.99 0.99 1.00 0.06 0.06 0.06 0.05 NA NA 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.43 0.06 1.00 0.00 Joint (coeffs + var.) = 21.15 (p-value = 0.00)

R2 = 0.33, r = 0.22 DW = 1.99, Godfrey (5) = 3.35 (p-value = 0.00), White = 3057 (p-value = 0.00), ARCH (5) = 151 (p-value = 0.00), REST = 27.87 (p–value = 0.00)***

* T is the transparency index, VTB is the volatility of the three-month Treasury bill rate and VFF is the volatility of the Fed funds rate. For the definitions of the dummy variables see Table A in the Appendix. ** Newey and West’s (1987) robusterror for 5-order moving average was used to correct for autocorrelation and heteroscedasticity. *** R2 , r and DW, respectively, denote the adjusted squared multiple correlation coefficient, the residual standard deviation and the Durbin-Watson statistic. Furthermore, White is White’s (1980) general test for heteroscedasticity, ARCH is the five-order Engle’s (1982) test, Godfrey is the five-order Godfrey’s (1978) test and REST is Ramsey’s (1969) misspecification test.

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Table 7 Estimation results of superexogeneity tests for contemporaneous variables in Eq. (7).

v2 (1) (p-value) Variable (Z)* Z
g

Z

ZZ

Z

r (Z
g ) (gZ)2 (gZ)3

rZZ gZ rZZ (gZ)2 (rZZ)2 gZ Devz

v2-statistics on null hypothesis that coefficients of all constructed variables in this column are jointly zero. The equation includes the constructed variables related to other contemporaneous variables

v2-statistics on null hypothesis that coefficients of all constructed variables in this column are jointly zero. The equation excludes the constructed variables related to other contemporaneous variables v -statistics on coefficients of all variables in rows and columns 2

T

VFF

23.06 (0.00) 5.99 (0.01) 15.79 (0.00) 11.69 (0.00) 5.06 (0.02) 2.93 (0.09) 9.25 (0.00) 0.74 (0.39) 70.81 (0.01)

16.21 (0.00) 3.64 (0.06) 4.38 (0.03) 0.78 (0.38) 0.02 (0.90) 0.15 (0.70) 0.59 (0.44) 5.47 (0.02) 51.78 (0.00)

62.32 (0.00)

39.55 (0.00) 110.72 (0.00)

Zt Zt 2 Zt 3 Zt Zt 2 Zt Zt Zt Zt 2 0 jWt j = a0 + f0 Zt + (d0
f0) (Zt
gZt) + d1 rZt t (Zt
g ) + f1 (g ) + f2 (g ) + f3 rt g + f4 rt (g ) + f5 (rt ) g + f6 Devzt + q t a + Єt, where jWt j is the forecast error and risk, gZ is the conditional mean of Z, rZZ is the conditional variance of Z, and DevZ is the deviation of variance of the error term from a five-period ARCH error of Z. Since the error is ARCH heteroscedastic the estimation method is robust error OLS. * Z = T or VTB. T is the monetary policy transparency index and VTB is the volatility of the three-month Treasury bill rate.

coefficients were found to be REMA, T*EDAY, T*SWED, T*REMA, VTB*EDAY, VTB*SWED and VTB*REMA. This result further rejects the null of supererogeneity for both T and VFF. 6. Concluding remarks The empirical findings on the impact of monetary policy transparency on risk and volatility are mixed. One possible explanation for these findings is the lack of a proper index to measure monetary policy transparency. The literature so far has been using dummy variables constructed according to the central banks’ announcements and actions or coding approach. However, these measures for the monetary policy transparency have some limitations, such as a lack of an objectively designed index or indexes without time-series properties. Furthermore, dummy variables may not really reflect the impact of an announcement or changes in the policy. That is because market participants may have already incorporated the impact of a policy change before the central bank communication. This is also possible when shocks which resulted in the central bank communications already affected the economy, say, the volatility. Clearly, using different measures for monetary policy transparency results in mixed empirical findings. This is especially true when these different measures have different shortcomings. Kia (2011) developed an objective market-based monetary policy transparency index. The index is dynamic and continuous and can be used to measure monetary policy transparency for a country or, simultaneously, a series of countries, using time-series as well as cross-sectional data. In this paper I used Kia’s (2011) index to investigate the impact of monetary policy transparency on risk and volatility in the United States. One very important issue which was completely missed in the existing literature is how the expectation is formed in the market. In other words, are market participants forward looking, i.e., are their expectations formed rationally when it comes to monetary policy transparency or not? If agents are forward looking their behaviors are not policy invariant. Then the more transparent the monetary authorities are, the more market participants change their behaviors toward the future. This study overcomes this shortcoming of the literature and finds that a higher monetary policy transparency leads to a lower ex-post risk, but also to a lower ex-ante risk because the agents in the money market in the United States are forward looking. Moreover, the rational expectations model of the term structure is valid in the United States money market, but risk premia in this market exist. It was also found that modifying the reserve maintenance period from one week (for most large institutions) to two weeks (for all institutions) in February 1984 resulted in a higher risk in the money market, while the risk fell since the tenure of Chair Yellen. Furthermore, the unexpected change in the target rate on January 3, 2001 resulted in a higher risk in the United States. However, such an action on April 18, 2001 resulted in an opposite effect on the risk. Furthermore, a higher volatility of FF on

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December 31, 1986 resulted in a lower risk as well as volatility on those days. It was also found that the policy regime change of releasing the minutes of the FOMC meetings (with 6–8 week lag) since March 23, 1993, resulted in a reduction of risk and forecast error in the United States. It was also found that the 2008 US financial crisis led to a higher risk and forecast error. We conclude that the practice of a more transparent monetary policy leads to more stability (lower volatility) and lower risk in the financial markets. Based on the findings of this paper we recommend a 100% monetary policy transparency in the United States. Clearly, if a higher monetary policy transparency results in lower forecast errors, risk premia and volatility, a 100% monetary policy transparency should lead to the elimination of risks associated with forecasting errors and volatility in a large country like the United States. Namely, the Fed should be as clear in its monetary policy so that market participants fully understand the central bank actions. In such a case, they would not ask for extra premium so that Kia’s transparency index will be 100%. Furthermore, such transparency can be shown to be optimum in all countries. Since Kia’s monetary policy index can be easily constructed for any country, future research should be devoted to a similar study on other countries to further justify the policy recommendation of this paper. Appendix The daily data on the effective Fed funds rate and the three-month Treasury bill rate (secondary market) for the period 1982 (October 5)–2016 (March 31) are used. The choice of the sample period is based on the availability of data for the construction of the transparency index which was developed by Kia (2011). The period covers more than 33 years with 8737 effective daily observations. The source of these data is the Board of Governors of the Federal Reserve System website, http://www.federalreserve.gov/releases/h15/data.htm. The effective Fed funds rate is a weighted average of the rates on Fed funds reported daily by a group of brokers to the Federal Reserve Bank of New York. The definitions of the dummy variables in DUM and EDUM are given in the following table.

Table A Definition of DUM and EDUM.* Dummy variables

Definitions

Mt, Tt, WEDt and THt

Mt, Tt, WEDt and THt = 1 for Mondays, Tuesdays, Wednesdays and Thursdays, respectively, and are equal to zero, otherwise D851231t and D861231t = 1 on December 31, 1985 and December 30 and 31, 1986, respectively, and are equal to zero, otherwise. These dummy variables are included to capture the high volatility of Fed funds rate on those days Greent = 1 from August 11, 1987 to January 31, 2006 when Alan Greenspan was the chair of the Fed and is equal to zero, otherwise Bernanket = 1 from February 1, 2006 to January 31, 2014 when Ben Bernanke was the chair of the Fed and is zero, otherwise Yellent = 1 from February 3, 2014 when Janet Yellen became chair of the Fed and is zero, otherwise OCT87t = 1 for October 19–30, 1987 and is equal to zero, otherwise, and ASIAt = 1 for October 17–30, 1997 and is equal to zero, otherwise. These dummy variables account for the October 87 and Asian crises, respectively. In both events, central banks in industrial countries flooded the money markets with liquidity to ease the downfall in the stock markets. The easing of the markets took at least until the end of October of the year the crisis took place TAt = 1 since February 4, 1994 (when the Fed started to announce target changes) and is equal to zero, otherwise TAFt = 1 since October 19, 1989 (when the Fed adopted the practice of changing the FF targets by 25 or 50 basis points) and is equal to zero, otherwise SWEDt accounts for settlement days on Wednesdays, i.e., it is equal to one on Wednesdays when it is a settlement day and is equal to zero, otherwise REMAt = 1 since February 2, 1984 when the reserve maintenance period was modified from one week (for most large institutions) to two weeks (for all institutions) and is equal to zero, otherwise minutest = 1 since March 23, 1993 when the Fed began releasing the minutes of the FOMC meetings (with 6–8 week lags) and is equal to zero, otherwise transcriptst = 1 since November 16, 1993 when the Fed began releasing the transcripts of the FOMC meetings (with 5-year lags) and is equal to zero, otherwise. statet = 1 since August 16, 1994 when the Fed began describing the state of the economy and further rationale for the policy action after FOMC decisions, and is equal to zero, otherwise lrrt = 1, since July 30, 1998 and is equal to zero, otherwise. On March 26, 1998, the Fed moved from contemporaneous reserve requirements back to lagged reserve requirements. This policy went into effect with the reserve maintenance period beginning July 30, 1998 D970819t = 1 since August 19, 1997 when the FOMC started to include a quantitative Fed funds target rate in its Directive to the New York Fed Trading Desk, and is equal to zero, otherwise. D99518t = 1 since May 18, 1999 when the Fed extended its explanations regarding policy decisions and started to include in press statements an indication of the FOMC’s view regarding prospective developments (or the policy bias), and is equal to zero, otherwise

D851231t and D861231t

Greent Bernanket Yellent OCT87t and ASIAt

TAt TAFt SWEDt REMAt minutest transcriptst statet lrrt

D970819t D99518t

(continued on next page)

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Table A (continued) Dummy variables

Definitions

D000202t

D000202t = 1 since February 2, 2000 when the FOMC started to include a balance-of-risks sentence in its statements replacing the previous bias statement, and is equal to zero, otherwise. D020319t = 1 since March 19, 2002 when the Fed included in FOMC statements the vote on the directive and the name of dissenter members (if any), and is equal to zero, otherwise D940418t, D981015t, D010103t, D010418t and D010917t are equal to one for April 18, 1994; October 15, 1998; January 3, 2001; April 18, 2001 and September 17, 2001 (when the Fed changed the FF target rate outside its regular meetings), respectively, and is equal to zero, otherwise EDAYt = 1 for the days (‘‘event”) when the Fed funds target rate was changed whether at a regularly scheduled FOMC meeting, or otherwise, and also for the days on which the FOMC met, but did not change the target rate. It is equal to zero, otherwise TARATEt = 1 for the days when the Fed funds target rate actually was changed and is equal to zero, otherwise. These days can be among the regularly scheduled FOMC meeting dates or other days. Note that TARATE is a subset of EDAY, as it excludes the days when the FOMC met, but did not change the target USCrisist = 1 for the period September 30, 2007–September 30, 2008 and is equal to zero, otherwise. The housing bubble started to burst in 2006, and the decline accelerated in 2007 and 2008. Housing prices stopped increasing in 2006 and started to decrease in 2007. The decline in prices meant that homeowners could no longer refinance when their mortgage rates were reset, which caused delinquencies and defaults of mortgages to increase sharply, especially among subprime borrowers. ‘‘It was in August 2007 when BNP Paribas, a large French bank, froze withdrawals in three investment funds that people began to panic. If a bank with zero obvious exposure to the U.S. mortgage sector could have this measure of difficulty, anyone could be hiding untold losses. This marked the official beginning of the credit crisis.” Harrison (2008) STUt = 1 on Tuesdays before settlement Wednesdays and is equal to zero, otherwise TUE1t = 1 on Tuesdays before settlement Wednesdays if Wednesday was a holiday, and is equal to zero, otherwise HB1t = 1 for the day before a one-day holiday, and is equal to zero, otherwise. HA1t = 1 for the day after a one-day holiday, and is equal to zero, otherwise. HB3t = 1 for the day before a three-day holiday, and is equal to zero, otherwise. HA3t = 1 for the day after a three-day holiday, and is equal to zero, otherwise LDYt = 1 for the last day of the year, and is equal to zero, otherwise. LDBYAt = 1 for 2 days before, 1 day before, 1 day after, or 2 days after the end of the year, and is equal to zero, otherwise LQBAt = 1 for the day before, on, or after the last day of the first, second and third quarters, and is equal to zero, otherwise. LQt = 1 for the last day of the first, second, third and fourth quarters, and is equal to zero, otherwise

D020319t D940418t, D981015t, D010103t, D010418t and D010917t EDAYt

TARATEt

USCrisist

STUt TUE1t HB1t, HA1t, HB3t and HA3t

LDYt and LDBYAt LQBAt and LQt

DUM = (Mt, Tt, WEDt, THt, D851231t, D861231t, Greent, Bernanket, Yellent, OCT87t, ASIAt, TAt, TAFt, SWEDt, REMAt, minutest, transcriptst, statet, D940418t, D970819t, lrrt, D981015t, D99518t, D000202t, D010103t, D010418t, D010917t, D020319t, EDAYt, TARATEt, USCrisist). EDUM = (DUMt, STUt, TUE1t, HB1t, HA1t, HB3t, HA3t, LDYt, LDBYAt, LQBAt, LQt). * Part of this table is taken from Kia (2010). See also Kia (2011).

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