Still Preliminary;
Not for quotation;
Comments most welcome.
Estimating a Central Bank Reaction Function
During Gradual Disinflation
By
David Elkayam,
Ofer Klein
and
Edward (Akiva) Offenbacher
Revised Draft
December 17, 2002
The authors are Assistant Director, Economist and Acting Director, respectively,
Monetary Department, Bank of Israel. We gratefully acknowledge comments from
participants in seminars at the Bank of Israel’s Monetary Department and its
Research Department, at Tel Aviv University and in the University of Chicago Money
and Banking Workshop. Usual disclaimers apply.
I.
Introduction
The systematic and explicit specification of monetary policy in the form of a
central bank reaction function or some other form of policy rule is, without a doubt,
one of the principal innovations of the New Neoclassical approach to macroeconomic
modeling that has taken the profession by storm in the past decade. The class of small
monetary models that has become the standard workhorse for the analysis of
monetary policy is the outcome of a sequence of theoretical insights including: (1) the
rational expectations revolution of the 1970s, with its initial implications of policy
ineffectiveness and its subsequent influence on modeling policy formulation as a
behavioral function in order to at least generate a basis for expectations formation by
the private sector; (2) the introduction of game-theoretic considerations, starting in the
late 1970s, to analyze the interaction between the public and the monetary authority,
with its “inflationary bias” implication and (3) a process of intellectual and practical
groping for pre-commitment “technologies”, or more accurately, institutions for
governance of the monetary authority, that initially yielded proposals such as the
conservative central banker idea or incentive contracts for central bankers, which
proved to be impractical. From today’s perspective, it appears that inflation targeting,
certainly in its explicit form and, perhaps surprisingly, even in its implicit form,
provides a viable and popular method of generating central bank credibility. Small
macro models incorporating a central bank reaction function with aggressive response
of monetary policy to deviations of actual from target inflation have become the
workhorse for simulating the effects of alternative policies, ie, interest rate paths .
In light of these developments, the recent plethora of work on empirical central
bank reaction functions is completely natural. Initially, these took the form of
postulated policy rules, most notably the Taylor rule, that sought to mimic the path of
the key policy interest rate. More recently, the field has been dominated by
econometric estimation of forward-looking reaction functions, for example the widely
cited paper by Clarida, Gali and Gertler (2000), henceforth denoted CGG.
While the desirability of obtaining empirical estimates of the conceptual central
bank reaction function is impossible to deny, it is perhaps somewhat surprising that
the zeal to accomplish this task has been little dampened by the daunting difficulties
of actually carrying it out, in the face of a uniquely distressing paucity of relevant
2
data. The key conceptual ingredients of such a function are an explicit inflation target,
a measure of inflation expectations, a measure of the Wicksellian natural rate of
interest and a measure of the output gap. For most Western countries it has not been
feasible, until perhaps recently, to directly measure any of these variables! Estimation
of the reaction function in these countries relies, therefore, on a combination of fancy
econometrics and heroic assumptions. While these methods do an admirable job of
squeezing a maximal amount of implications from a minimal amount of data, it is
hard to avoid some skepticism about the results and the conclusions that have been
drawn from them.
In the present paper we take advantage of the unique combination of data that are
readily available in Israel on nearly all of the concepts that have not been directly
measured in the United States and many other countries, namely explicit quantitative
inflation targets, market-based inflation expectations and an ex ante real long term
interest rate. All of these data have been available in Israel for nearly a decade and
they have been extensively employed in monetary policy formulation.
The heart of our paper is the econometric estimation of central bank reaction
functions for Israel that employ the three types of data series that are not available to
CGG or in most other countries., We begin with a specification that nests a variant of
the CGG specification and our data-rich specification. Not surprisingly, we find
support for an axiom that is widely employed in economics, namely “more is better
than less”: In the present case, more data is better than less. We also compare our
fitted policy rate path with the actual path and with paths generated by a Taylor rule
and a CGG specification, finding a superior fit for our estimated path.
Our results bring to the fore an important issue of interpretation: Is a
regression of a short-term interest rate on inflation expectations a Fisher equation or a
central bank reaction function? One feature that can help decide the issue is the
precise interest rate that is used. In a central bank reaction function, it is the current
value of the key central bank rate and in a Fisher equation it is a somewhat longer
term market rate. Nevertheless, given the high degree of serial correlation of the
central bank rate, due possibly to interest rate smoothing by the central bank, this
distinction may not be critical, at least not for econometric purposes. The availability
of an explicit, quantitative inflation target adds precision that can help to “identify”
the nature of the equation. Thus, while the announcement of quantitative inflation
targets does not, in and of itself, constitute full-fledged inflation targeting since the
3
central bank can regard the targets lightly, their existence gives the public a better
benchmark for judging the seriousness of the central bank and provides
econometricians with a means of identifying reaction functions with somewhat greater
precision than otherwise.
Table 1 concludes this section with a summary comparison of a few key
approaches that have been used in empirical central bank reaction functions. We
compare the well-known Taylor rule, the forward-looking CGG reaction function and
the forward-looking rule first estimated in Elkayam (2001), currently installed in the
macroeconometric model of the Bank of Israel’s Monetary Department. The latter
rule embodies the features emphasized in the present paper that are based on the
availability of indexed bond yields.
The following section motivates our work in the form of a critical review of
the CGG paper. We emphasize that we single out this paper because we, like many
others, regard this paper as a worthy paradigm that goes a long way towards making
the most of the data available in the US. However, it has a number of important
shortcomings, due primarily to data limitations. Historical and institutional detail on
Israel’s inflation targeting regime and on indexed bonds are in section 3. Estimation
results are in section 4, while section 5 compares a number of simulated interest rate
paths with the actual path and section 6 presents conclusions.
II.
Issues in Estimating Central Bank Reaction Functions
Forward-looking central bank reaction functions are interest rate equations whose
conceptual specification can be described as follows: The dependent variable is the
key policy interest rate of the central bank. The right hand side variables include three
“required” ones, (1) the natural rate of real interest, (2) the inflation target, (3) the
“inflation gap”, i.e., the difference between inflation expectations for the target
horizon and the inflation target, and two “optional” ones, (4) the output or
unemployment gap, i.e., the difference between actual and potential output or the
difference between actual unemployment and its natural rate, in the case of “flexible”
rather than strict inflation targeting and (5) the lagged dependent variable to reflect
possible interest rate smoothing. In the case of a country like the United States, where
there is no explicit inflation target and there are no useful, direct observations on
inflation expectations or the ex ante real interest rate, empirical estimation of such an
4
equation may properly be regarded as entailing a fair degree of intellectual audacity.
The reason is that all three of the “required” rhs variables are not observed directly
and so is one of the optional ones, the output or unemployment gap. In fact, the only
variable that is directly observed is the lagged dependent variable.
Be this as it may, the force of the rational expectations/ game theoretic approach
to monetary policy is so great that estimating forward-looking central bank reaction
functions using a small amount of data and a large number of assumptions has
become a cottage industry, employing a significant group of central bank and
academic economists. The problem is not that the central bank needs such equations
to know itself. Instead, in order to have some chance of properly identifying structural
parameters and expectations it is vital to represent, in some way, the views of the
public about the behavior of the central bank. Some specification of a reaction
function is clearly superior to the alternative where it is assumed that monetary policy
is determined, period-by-period, by ad hoc discretion. While we certainly concur with
this view, we nevertheless believe that it is important to take a critical look at the
assumptions involved in carrying out the empirical exercise of estimating a forwardlooking central bank reaction function. Note that in the absence of data that might
enable testing, such assumptions are untestable maintained hypotheses. In a different
era, one might even have found an econometrician or two who would have regarded
these assumptions as “incredible” but nowadays, following some disappointment with
atheoretical empirics, macro-econometricians apparently have a greater appreciation
for the need for theory-based structure than, say, twenty years ago.
The key assumptions used by CGG and others to estimate a central bank reaction
function where data on the natural rate, the inflation target and inflation expectations
are not available as follows:
(1)
The natural rate of real interest is assumed to be constant over any chosen
estimation period and is proxied by the sample average real interest rate,
for a suitably long sample period.
(2)
Unrestricted estimation of the reaction function does not enable
identification of the natural rate of interest and the inflation target
separately. Therefore, in the absence of an explicit inflation target, CGG
calculate an implicit target from the intercept term in the estimated
equation and the aforementioned assumption on the natural rate of
interest. Clearly, the implicit inflation target is then constant over the
5
chosen sample and any error in the natural rate induces an error in the
inflation target of opposite sign but different magnitude.
(3)
Inflation expectations are proxied by actual future inflation, a process that
involves measurement error, dealt with by instrumental variables
estimation. While this approach incorporates the desirable theoretical
property that the implicit inflation expectations are, by construction,
orthogonal to the forecast errors, there is no straightforward reason to
believe that they were in fact the expected inflation of any typical or
representative economic agent.
In the absence of statistical tests of these assumptions, some judgmental
assessment seems appropriate. The third point can be considered on the basis of the
criterion known as “the proof of the pudding is in the eating.” If the estimated
coefficient on the inflation gap term seems to fit with some prior sensible judgment
about the stance of monetary policy, eg, some general notion of when policy was
relatively weak and when it was tight, then it seems passable. While such an
assessment clearly involves some circularity of reasoning, it appears that it is the best
we can do given the paucity of data.
An assessment of the first two assumptions must be based on some judgment
about key stylized facts during the period at hand. Here we feel that there is a sound
basis for some strong reservations. CGG claim that the target Federal funds rate,
ignoring interest rate smoothing, tracks the “broad swings in the actual rate
reasonably well”. We certainly agree that this is a fair assessment for the entire period
of nearly forty years analyzed by CGG but we note that there is one fairly long period
of a big miss, 1980 – 85, and especially 1981 and 1982. From Figure II (p. 159) in
CGG we can observe that the actual Federal funds rate from 1980 – 1985 was always
in excess of 7.5 percent and above 10 percent in 1981 and most of 1982 but the
predicted funds rate from the CGG equation began to fall below the actual rate
beginning early in 1981, was below 7.5 percent for nearly all of the 1981 –1985
period and was close to zero in 1982. This is, of course, a very important period, when
the war against the development of a chronic inflationary environment in the US was
fought and won, largely with tight monetary policy, a feature strongly supported by
the CGG results. However, other things were going on at the same time. As discussed
extensively by CGG, the US experienced a significant negative supply shock in 1979,
the second oil crisis. While we agree with CGG’s assessment that the oil shocks by
6
themselves were unlikely to have generated extended periods of continued inflation,
they may well have had a substantial effect to raise real interest rates over a number of
years when the aggregate supply curve shifted to the left. Furthermore, fiscal policy
turned very expansionary in the early 1980s, a fact not dwelt on at all by CGG. The
election of Ronald Regan in November 1980 heralded the combination of
significantly increased defense spending and large “supply-side” tax cuts (this along
with a promise to balance the budget by 1983, with the full package being described
as the Administration’s own OMB Director as “voodoo economics”). Actual deficit
figures ballooned from the $70 billion range in the late 1970s to over $250 billion by
1983. While the magnitude of the increase in the deficit came as a surprise to some
(but one of the present authors recalls that the Federal Reserve Board’s MPS model
predicted this jump with remarkable accuracy already in 1981), the general direction
was well anticipated certainly by the time the 1982 budget was proposed by the new
Administration in mid-1981. So we have three potentially powerful effects for
increasing real interest rates, that occurred roughly at the same time, tight monetary
policy, a negative supply shock and expansionary fiscal policy. By assuming that the
natural rate of interest is constant over the entire long sample of 1979:3 to 1996:4, the
CGG approach effectively ignores any variation in the real side determinants of the
long-term rate. Instead, all of the in-sample variation of the interest rate is attributed
to monetary tightness. We feel that this is too much of a good thing. The large
overshoot of the actual Funds rate relative to predicted in the early 1980s may well be
attributable to the failure to take proper account of fiscal policy and, possibly, the oil
shock. Failure to control for the effects of the fiscal expansion may also induce
upward bias in the estimated parameter on the inflation gap for this period since an
expansionary fiscal shock may well be positively correlated with a forward-looking
inflation gap. This possibility even calls into question CGG’s main conclusion that
monetary policy was much tighter during the Volcker-Greenspan period than the preVolcker times. Casual empiricism would certainly support this conclusion but we feel
that CGG’s empirical work should be expected to have done a better job of
controlling for other key factors and, therefore, has not closed the book on alternative
conclusionsa.
One way to address these specific reservations would be to redo the CGG
estimation, including some parsimonious representation of the variation of the natural
rate of interest that accounts explicitly for fiscal policy and the oil price shock.
7
However, that episode occurred two decades ago and is of limited relevance now. Our
purpose in discussing it is to emphasize that in order to identify correctly the
magnitude of a given effect, e.g., the central bank’s reaction to an inflation gap, it is
vital to control for all other major influences on the level of interest rates. This
motivates our suggested alternative methodology of using interest rates on indexed
bonds and break-even inflation expectations in estimating empirical central bank
reaction function for today’s world. This approach is gaining greater feasibility due to
the increased availability of such instruments in a growing number of jurisdictions,
including the UK, the EMU, Canada, and even the US.
III.
Data Description
This section provides some detail on the data series used in this paper that are
not available in the United States, namely the inflation target, yields on indexed bonds
and market-based inflation expectations (MBIEs). One purpose of the discussion in
this section is to note that using actual data series as proxies for conceptual variables
is not without problems either.
The other time series are completely conventional. Specifically, the dependent
variable in the equations is monthly averages of daily data on the Bank of Israel’s
(BoI) key policy rate, the interbank lending rate. This is analogous to the Federal
funds rate. The BoI uses the interbank rate as a proxy for its policy rate since the
micro nature of the interbank market has been more stable than the micro-structure of
the Bank’s policy instruments. The other variable we use is the unemployment rate,
produced by Israel’s Central Bureau of Statistics by a large survey of households of
high standard.
a. Israel’s Inflation Targeting Regime
Israel has had an explicit inflation targeting regime since 1992. Details are
presented in table 2. A number of features of this policy are of significance for the
empirical results we present so we briefly describe the history of this policy. By and
large, the policy had a very significant role in reducing Israel’s inflation rate from low
double digit levels in the six years prior to its introduction to low single digit levels
8
since 1999. However, attitudes towards the inflation targeting policy of politicians,
and to a lesser degree the general public, has always been highly ambivalent.
The introduction of explicit inflation targets in 1992 was done “through the
back door”, as a subordinate part of a policy package, whose main component was the
adoption of an upwardly crawling target zone for the exchange rate. The main
objective of the policy package, announced on December 16, 1991, was to put an end
to recurrent speculative attacks on the Israeli shekel. These attacks had occurred with
increasing frequency and severity throughout the six year period 1986 – 1991, when
Israeli inflation ranged from 15 to 20 percent per year but exchange rate policy was
not accommodative of the non-negligible inflation differential with Israel’s major
trading partners, the United States, Western Europe and Japan. Specifically, the
exchange rate was always highly managed, either as an adjustable peg or as a
horizontal target zone with varying bandwidth of up to 10 percent. Following a
particularly severe attack in the autumn of 1991 that was fought off with high interest
rates, the BoI (under newly appointed Governor, Prof. Jacob Frenkel) and the
Ministry of Finance adopted the new policy of an upwardly crawling target zone.
Essentially, this was a decision to accommodate the inflation differentials, at least
initially, with a general intention and hope of dealing with the inflation problem
gradually and later. Of course, the upwardly crawling exchange rate target zone
required the announcement of its slope, ie the rate of crawl. It was clear that the slope
should reflect the inflation differential and that the foreign component should be
based on some forecast. However, when it came to determining the domestic
component of the differential, it was realized that merely accommodating forecasts
would involve loss of the system’s nominal anchor. The domestic inflation component
had to be presented as a “target”, rather than a forecast. Thus was born the inflation
targeting regime in Israel, sort of a step-child at birth but a child, nevertheless.
By way of contrast, in Western countries that adopted inflation targeting at
that time, the inflation target was the key component of policy and the exchange rate
regime was immediately and strictly subordinated to the inflation target. In the one
other emerging market economy that adopted inflation targeting at that time, Chile,
there was also a notable exchange rate constraint.
The distinction between “target” and “forecast”, that was not at all clear to the
Israeli public in the first two and a half years of the regime, was brought up in full
force in mid-1994, when it became clear that the actual inflation rate would exceed
9
the target by a large margin. Specifically, the target for 1994 had been set in the
summer of 1993 when there was a large degree of slack in the economy, at 8 percent
and the outturn for 1994 was 14.5 percent. By September 1994, the writing was on the
wall and Governor Frenkel requested that the Government convene to determine
whether Israel would accommodate actual inflation and, most likely, return to the pre1991 inflation environment, or whether a mandate would be given to the BoI to
attempt to return to the inflation target. The result, again reflecting some ambivalence,
was a decision to try to hit the target by announcing a target range for 1995 of 8 to 10
percent. The BoI then proceeded to raise interest rates significantly and the serious
period of Israel’s inflation targeting began.
This history is important for our work, as we chose two alternative sample
periods, one starting in 1993, after formal inflation targeting had begun but before it
became serious, and the second starting in 1994Q4, when serious inflation targeting
began.
Between the end of 1994 and mid-1996, disinflationary policy was of a “stop
and go” variety, as the BoI tightened policy but loosened it too soon after “good
news” on the inflation front began to come in. In mid-1996, the BoI began a more
sustained policy of monetary tightening, with positive results on the inflation front
beginning to be realized in the summer of 1997. The world-wide currency crisis of
August – October 1998 hit Israel quite hard, as foreign investors bailed out of Israel in
search of liquidity and the shekel fell against the dollar by 17 percent in less than two
months. Inflation picked up for three months and the BoI increased interest rates from
9 to 13 percent in early November but it did not intervene in the foreign exchange
market. This episode appears to have been of great importance in building the BoI’s
reputation for commitment to the inflation target and gradual subordination of the
exchange rate as a policy objective.
Since 1999, inflation in Israel has been well below 3 percent. In August 2000
the government adopted the current parameters of the inflation targeting regime that
called for a gradual reduction of the target from 3 to 4 percent in 2000 to 1 to 3
percent from 2003 and onwards, a target with an indefinite time horizon defined as
price stability. Actual inflation during that period has been below target until the past
three months, when the BoI agreed to lower interest rates at once by 2 percent as part
of a package that included some fiscal correction and some capital market reform. The
sharp interest rate drop caused significant confusion in the financial markets,
10
especially a sharp depreciation of the shekel following remarkable stability during the
previous two years, as well as what appears now to be a one-time price level shock.
The inflation target variable used in the regressions is either the point target or
the mid-point of the target range, as appropriate.
b. Indexed Bonds and Market-Based Inflation Expectations
With the exception of the past five years, inflation in Israel has always been
higher than in Western countries, with differentials ranging from small magnitudes
during most of the 1950s and 1960s to triple digit ranges in the first half of the 1980s.
It is therefore not surprising that indexation, mainly to the consumer price index
(CPI), and linkage to foreign currency exchange rates has been prevalent throughout
Israel’s history. The Israeli government began to issue indexed bonds in 1955 with the
share of indexation rising in the 1970s and 1980s along with the increase in inflation
from single digit levels in the 1960s to a range of 10 to 40 percent throughout most of
the 1970s and a range of 100 to 450 percent from 1979 to mid-1985. Indexation in
Israel is so widespread and common that the word “interest” in the vernacular refers
to real interest, with compensation for inflation being referred to by other
terminology.
The share of indexed and linked assets in the public’s portfolio never reached
100 percent, however. At the end of 1984, when inflation was peaking at over 400%,
the share of CPI indexed assets was 57%, assets in foreign currency or linked to it
were an additional 39% and nominal, domestic currency assets (then called Israeli
pounds) amounted to 4% of the portfolio. The latter were mostly M1, indicating that
even at high triple digit inflation, currency substitution was not complete. Conversely,
at the end of 2001, following nearly five years of inflation near 1% (per year)
excepting autumn 1998, the share of nominal, domestic currency assets (now called
shekels) reached nearly 40%, while indexed assets amounted to 45% of the portfolio
and foreign currency assets came in at 15%. The significance of the current figures for
the present work is that they indicate that there is no limitation from the supply side
on the degree to which nominal and indexed assets can be substituted by individual
traders.
The empirical work in this paper uses returns on nominal and indexed bonds,
as explained shortly. The nominal bonds are one year Treasury bills, auctioned
11
weekly on a discount basis. They are about as “plain vanilla” as you can get. All of
the Israeli banks and a number of NBFIs are active in the auctions; the secondary
market in T-bills is more active than the markets for most other bonds in Israel but is
still limited by international standards, even for other, successful emerging markets.
Turning to the indexed bonds (henceforth referred to simply as “bonds”), the
following institutional features are worth noting:
(1)
Both principal and interest are fully linked to the CPI, on a “last
known” basis. That is, the base for indexation is the CPI figure that
was published just prior to the introduction of each series and the
indexation is to the last figure known at maturity. So there is no
indexation lag that is typical of indexed bonds in Western
countries.
(2)
Tradable bonds are issued with original maturities of medium and
long terms, eg, 7 years or 20 years. Exact maturities have varied
over the years but this is of limited consequence for the present
work. There have always been bonds with maturities well in excess
of ten years.
(3)
The decline of budget deficits as a share of GDP in the 1990s has
limited the supplies of tradable bonds, both nominal and indexed.
Besides tradable bonds, the government also issues non-tradable,
indexed bonds for earmarked purposes such as coverage for
pension funds and some types of life insurance. The real yields on
these bonds is set by administrative decree and, presumably, has
some effect on the yields of traded bonds, though substitution
possibilities between non-traded and traded bonds are highly
limited. In any event, the smaller scope for issuing tradable bonds
has led to a greater spacing out of the series issued in order to
insure a minimal degree of liquidity in the secondary markets,
which is not too great to begin with.
The availability of both nominal and real yields on tradable bonds of similar
maturity enables the calculation of market based inflation expectations. This is a
straightforward application of the simple arbitrage condition that if two bonds are
perfect substitutes except for being nominal or indexed, then the difference in yields
must be a measure of inflation expectations. The intuitive appeal of this proposition is
12
so great that Milton Friedman and others have proposed a rule for monetary policy
that essentially amounts to pegging these market based inflation expectations.
“An extension of Hetzel’s proposal (to require the Treasury to issue
equal amounts of nominal and indexed bonds - present authors) would be the
enactment of legislation to require the Federal Reserve to keep the difference
between the two interest rates less than a specified amount, say, 3 percentage
points. That would provide a congressional guide for monetary policy far more
specific than anything in the current law. There have been recent proposals for
legislation requiring the Fed to aim at zero inflation. The objective is
desirable, but such a requirement cannot be effectively monitored or enforced
– again because of the “long lag”, which would visit the sins (or the reverse)
of the current monetary authorities on their successors. That problem does not
arise with a requirement based on the difference between the two interest
rates.” (Friedman, 1992, p. 229; a similar passage is contained in private
correspondence between Friedman and the late Prof. Michael Bruno, then BoI
Governor, dated March 22, 1991 but priority for this idea, to the best of the
present authors’ knowledge should go to John Boschen and the late Jared
Enzler, then of the Board of Governors of the Federal Reserve System, who
proposed the idea as early as 1984.)
While the terms of Israel’s nominal and indexed bonds seem to come about as
close to the ideal as any place on the planet, there are still a number of significant
problems including the following: (1) There are differences in the tax treatment
between nominal yields (basically not taxed) and real yields (some investors pay tax,
others do not) whose exact effect is difficult to quantify, although a number of
imaginative efforts have been made to get at an upper bound on this effect. (2) The
interest differential is likely to include a variable inflation risk premium; a recent
attempt (Stein 2001) to measure this premium using the CAPM on a fairly
comprehensive portfolio of financial assets estimates the average risk premium during
1996 through 2000 at 40 basis points, with inflation expectations having ranged from
roughly 10 percent at the end of 1998 to less than 2 percent in the past two years. (3)
The secondary market for indexed bonds is less liquid than for nominal ones so one
can assume that the real yields include an illiquidity premium, whose magnitude is not
known; this offsets the inflation risk premium; (4) The maturity dates of the nominal
and real yields are not exactly matched, with nominal yields of one year generally
13
being available and the problem being with the real yields; until recently the mismatch was small so the BoI simply averaged real yields on maturities near one year to
get a proxy for the one-year horizon but as the gap has been widening, the BoI will
switch to reading a point off a zero-coupon yield curve; (5) Finally, mention should
be made of the Bernanke-Woodford (1997) problem, known to some as the “monkey
in the mirror” problem which argues that in a credible inflation targeting regime, both
market-based and professional inflation forecasts will not be informative and simply
reflect the target; we take issue with this point on the grounds that Israel’s inflation
targets have probably not been sufficiently credible as evidenced by the frequent
deviations of MBIEs from the target and, more basically, there should be sufficient
profits to be made by producing only slightly better forecasts than the next guy, but to
do so requires an informed forecasting effort.
In light of the above problems, the BoI has never gone so far as to target
MBIEs but they are one of the most important indicators used in the formulation of
monetary policy in Israel.
Beyond using the one-year real returns as an ingredient in calculating MBIEs,
we use the ten-year real returns as a proxy for the “natural” rate of interest, ie, the real
rate of interest that would be determined if price stability prevailed and is expected to
continue to prevail. Inflation would then be at a suitably defined, low target and be
expected to remain there. This would be an environment consistent with the
Greenspan definition of price stability, ie, that inflation is not a consideration in the
business dealings of households and firms (our loose paraphrase). While it may be
reasonably argued that low inflation has not prevailed in Israel for a sufficiently long
period to completely eliminate the possibility that the prospect of future inflation
affects the long-term indexed bond yields, we believe that this implicit assumption is
far more benign than the practical alternative that the natural rate is constant. The
empirical work we present below uses the 10-year real yield to maturity. Our key
results are robust to using the 10th year-ahead implied forward rate instead. While the
latter is preferable on theoretical grounds, we are concerned that it may be affected by
idiosyncratic noise substantially more so than the former.
We conclude this section by examining the time series behavior of the
inflation target, of inflation expectations and of the real long rate and consider the
implications for the inflation gap reaction parameter of assuming that the first and last
of these are constant. Table 2 shows that the inflation target trended down throughout
14
the period that this policy has been implemented. Inflation expectations also trended
down and there is no discernable trend in the inflation gap, though it has been quite
variable. Assuming that the inflation target is constant would have induced a
downward trend in the inflation gap that is not, in fact, present. Since the BoI policy
rate also trended down during the sample period we use, failure to take account of the
actual path of the inflation target would most likely have generated a much larger
reaction parameter than the one actually observed. Figure 1 shows a time series plot
of the 10-year real rate, which exhibits a notable upward trend. It is likely that the
reduction in the level and variability of inflation during the sample period has had
some role in reducing the value to investors of the inflation protection provided by
indexed bonds so they require a steadily higher real return. However, we feel that
there were a number of major real developments that were of greater importance in
accounting for the upward trend of real rates, including the massive immigration to
Israel in the early 1990s, various structural reforms in the real side of the economy
and the spectacular development of Israel’s high technology sector. All of these
contributed to higher marginal productivity of capital and of investment, ie, to an
upwardly trending natural rate. Since this trend is due primarily to positive supply
shocks that are negatively related to the inflation gap, omitting the real rate would
probably also have generated a higher inflation gap reaction parameter.
IV.
Estimation Results
The key equation we estimate nests the two alternative treatments of the
natural rate of interest. It is specified as follows:
it = α [δ0 +δ1rt + πtT + β (πte - πtT)] + (1-α) it-1
where,
it = Bank of Israel policy rate,
rt = real rate of interest,
πtT = inflation target,
15
πte = expected inflation one-year ahead.
The key parameters are the central bank’s reaction parameter to an inflation gap,
β, and the interest rate smoothing parameter, (1 – α). The δ parameters are included to
test the hypothesis that they are zero and one, respectively.
Table 3 presents estimates of the basic equations that we estimate. All equations
in this table are estimated by non-linear two-stage least squares to take account of
possible simultaneity between the central bank rate and inflation expectations. As
mentioned, the measurement error problems inherent in using actual future inflation as a
proxy for inflation expectations are not present here. The 10-year rate is treated as
exogenous, as is the inflation target, of course. Instruments are lagged values of all the
variables as well as current values of the real volume of world imports and dollar price
indexes of Israel’s imports, including energy of course, and exports. Choice of
instruments is based on Elkayam (2001); intuitively, the instruments are the exogenous
variables in the full model.
Our treatment of the 10-year rate as exogenous is, in our opinion, the most
problematic assumption in this list. It reflects what we regard as some of the most
important and challenging questions for empirical macroeconomics in Israel these days:
(1) What determines this real rate, including factors that affect the conceptual natural rate
such as immigration, productivity of labor and capital, fiscal policy, and more, and
possible long-lived monetary effects related to the nature of the monetary regime,
credibility, etc. and (2) How should the effects, if any, of the real economy on changes in
the inflation rate (or vice versa) be specified and estimated – by output gaps or by
Wicksellian interest gaps? In the absence of consensus on the full macro model that might
provide some sense of direction to get at these issues, we believe that our assumption is
no less reasonable than available alternatives.
Turning to the estimation results, in the most general equation, that includes both
a constant and the 10-year real rate, we see that the constant has the wrong sign and is not
significantly different from zero while the coefficient on the real rate is positive and not
significantly different from one. The other two coefficients are reasonable, ie, the reaction
to an inflation gap exceeds unity and the interest-smoothing coefficient is of typical order
of magnitude. In the second equation, we drop the constant; this yields a coefficient on
16
the real rate quite close to unity, slightly improved error diagnostics and a stronger
reaction coefficient. Imposing unity on the real rate coefficient, in the final equation of
table3, improves matters a bit more, both in terms of the theoretical appeal of the
magnitudes of the remaining coefficients and the error diagnostics. This is the most
parsimonious of the equations. It is our preferred specification and is the one used in
Elkayam’s (2001) Monetary Department model.
Our conclusion from these three main equations is that reaction functions using
data on the 10-year real rate are superior to functions that assume the real rate is constant
on the basis of two types of criteria, conformance to theoretically expected coefficients
and error diagnostics.
We now report briefly on results of sensitivity to two alternative specifications.
1) Flexible inflation targeting: Table 4 reports results of equations analogous to
the ones in table 3, but including an unemployment gap term. The unemployment gap is
measured as the deviation of actual unemployment from a Hodrick-Prescott trend. Since
simultaneity may also be present with unemployment, we add two instruments, the
deviation of population from a linear trend and real, per capita, non-interest government
expenditures. In all cases, the coefficient on the inflation gap exceeds unity, error
diagnostics are reasonable and equations using the 10-year real rate outperform the ones
that exclude it in the same senses as reported earlier. However, the coefficient on the
unemployment gap is not statistically significant. A possible interpretation for this result
is that the Bank of Israel placed very low weight on the real economy during the period of
disinflation, which was an overriding consideration due to the need to build reputation as
a strong inflation fighting central bank. Flexible inflation targeting in the usual sense is
possible only when the central bank’s credibility in the eyes of the public has already
been built up. This type of credibility has only existed recently in Israel, if at all. But
other explanations are also possible; for example, the insignificant coefficient on
unemployment may be due to the presence of both demand and supply shocks of large
magnitude during the sample period. Further analysis of this point is beyond the scope of
the present paper.
1)
Monthly equation: Table 5 presents results from estimation of the three
basic equations estimated using monthly data on interest rates, inflation expectations and
the real rate of interest. The equations are estimated by OLS since there are no monthly
17
data on some of the instruments used in the quarterly equations. The results at the
monthly frequency are qualitatively similar to the quarterly ones.
In addition to these tests for robustness of the results, we also estimated the quarterly
equations with the implied forward tenth year real rate and for a sample period that begins
not in 1993Q1 but in 1994Q4, when inflation targeting got more serious. In each of the
cases, the results are highly similar to respective results in tables 3 and 4 so we do not
report them.
Our reluctance to report results with the implied forward rates stems
primarily from our reservations about the validity of this calculation from raw data (ie,
not from a smoothed yield curve) generated by thin markets.
V. Comparing the Actual Interest Rate Path and Alternative Simulations
We now turn to a comparison of the actual interest rate path with alternative
simulations from estimated reaction functions, including a few variants of the CGG
approach and our preferred equation. Estimation results are in table 6 while actual and
simulated interest rate paths are in figure 2. Equation A is an exact application of CGG’s
methodology and assumptions. Specifically, [a] the natural rate of interest is proxied as
the average ex post real central bank rate over the sample period (5.6 percent), [b] an
implicit average inflation target (denoted τ) is “backed out” from the estimated constant
term in the expression in brackets (5.6 + τ), [c] actual one-year ahead inflation is used as a
proxy for expected inflation with the usual treatement for the errors in variables problem,
[d] the inflation targeting regime is assumed to be flexible as expressed by the u_gap term
(the deviation of unemployment from its Hodrick-Prescott trend), and [e] there is interest
rate smoothing. The calculated real rate turns out to be 5.6 percent and the “backed out”
inflation target is 11 percent. Equation B is a variant of equation A, identical
econometrically and differing only in its assumptions regarding the constant, namely we
use the actual average inflation target value over the sample, 7 percent, to back out the
natural rate (denoted δ in equation B) from the estimated constant. The estimate of the
natural rate in this case is 4. 5 percent, about one percentage point lower than the ex post
Bank of Israel real rate. In each of these equations, the reaction coefficient to an inflation
gap exceeds unity but is lower than in our preferred equation, (table3, equation C), the
interest smoothing parameter (1 – α) is much higher and the unemployment gap
18
parameter is negative (correct sign) but is highly insignificant. In equation C we
incorporate data on the actual path of the announced inflation target but we do not use
time series data on the real rate and we drop the u_gap term. In this equation, the value of
the reaction parameter is similar to the one obtained in the preferred equation but the
smoothing parameter remains very high. (We drop the first observation, 93.1, from the
sample period in CGG-type estimation because this improves the performance of the first
two equations.)
On comparing the equations in table 6 with our preferred equation, table 3, equation
C, it appears that just including the actual path of inflation targets rather than the sample
period average, but not including the time path of the real interest rate, gets the point
estimate of the Bank of Israel’s reaction function in line with the value in the preferred
equation. The smoothing parameter remains relatively high, however, as omitting the
upwardly trending real interest rate causes the lagged dependent variable to pick up some
of the residual autocorrelation. Once the real rate is included, the smoothing parameter
falls and error diagnostics improve a bit.
Examination of the actual and simulated interest rate paths in figure 2 reveals clearly
that equation C provides the closest simulated path to the actual. (Statistical comparison
to follow in next revision.)
VI.
Conclusions
Our analysis indicates that incorporating market-based proxies for the natural rate
of interest and inflation expectations as well as for the downward trending path of
announced inflation targets improves the empirical performance of an estimated,
forward-looking reaction function for the Bank of Israel during Israel’s gradual
disinflation in the 1990s. This is in comparison to CGG specifications, where the
natural rate and the inflation target are based on some type of sample average and the
actual inflation rate proxies for inflation expectations using IV methods to address
the errors in variables issue. Improvement is evident with regard to the magnitude
and significance of the parameter estimates and with regard to the ability of the
equation to track the actual interest rate.
The present work raises an important conceptual issue over and beyond the
empirical refinements. In any successful disinflation, the co-movement of nominal
interest rates and the growth rates of other nominal variables, including inflation
19
itself, expected inflation, depreciation, money growth, etc., are quite likely to be
dominated by the common downward trend that constitutes the disinflation itself. It
therefore makes little empirical difference for an interest rate equation if the rhs
variable that captures the trend of the nominal rate is an explicit inflation target, the
(possibly instrumented) actual future inflation rate or measured inflation
expectations. Estimation of any of these types is quite likely to yield results that look
like a central bank reaction function but the results may just as well be capturing a
Fisher effect or some combination of the twob. When the only available measured
rhs variable is actual inflation, the only basis for distinguishing these possibilities is
the precise choice of interest rate variable on the lhs. If the central bank smoothes its
interest rate policy, using the central bank rate on the lhs rather than, say, a threemonth T-bill rate, is not a good basis for distinguishing between these two
possibilities. The availability of more data, especially an explicit inflation target and
some measure of inflation expectations that enables the calculation of an inflation
gap, goes a long way to identifying (in the semantic sense) the resulting equation as a
central bank reaction function, rather than a Fisher equation.
20
References
1. Bernanke, Ben S. and Michael Woodford, “Inflation Forecasts and Monetary
Policy”, Journal of Money, Credit and Banking, 1997.
2. Boschen, John, “Monetary Policy and the Information Content of Indexed
Bonds”, Journal of Macroeconomics, v. 10, Spring 1988, pp. 163-82.
3. Clarida, Richard, Jordi Gali and Mark Gertler, “Monetary Policy Rules and
Macroeconomic Stability: Evidence and Some Theory”, Quarterly Journal of
Economics, v. 115, February 2000, pp. 147-180.
4. Cochrane, John and Monika Piazessi, “The Fed and Interest Rates – a High
Frequency Interpretation”, AEA Papers and Proceedings, (May 2002), pp.
90 – 95.
5. Elkayam, David, “A Model for Monetary Policy Under Inflation Targeting:
The Case of Israel”, Bank of Israel, Monetary Department, Monetary Studies,
Discussion Paper Series, no. 2001.03, July 2001.
6. Friedman, Milton, Monetary Mischief, New York: Harcourt, Brace,
Jovanovich, 1992.
7. Gali, Jordi, “New Perspectives on Monetary Policy, Inflation and the Business
Cycle”, NBER Working Paper No. 8767, February 2002.
8. Goodfriend, Marvin and Robert G. King, “The New Neoclassical Synthesis
and the Role of Monetary Policy”, NBER Macroeconomics Annual, 199x, pp.
231-295.
9. Orphanides, Athanasios, “Monetary Policy Rules, Macroeconomic Stability
and Inflation: A View from the Trenches”, European Central Bank Working
Paper No. 115, December 2001.
10. Stein, Roy, The Risk Premium Included in Expectations of Inflation and of
Exchange Rate Changes in Israel, Tel Aviv University Faculty of
Management, unpublished MA thesis, August 2001.
21
Table 1:
A Comparison of Three Types of Central Bank Reaction Functions
Taylor rule
CGG, (QJE, 2000)
Elkayam
(BoI, 2001)
Monetary Framework
Flexible inflation
Flexible inflation
“Strict” inflation target;
target; implicit
target; implicit
explicit target values
constant target value
constant target value
with downward trend.
assumed.
“backed out” from
assumptions.
Natural Rate of
Assumed constant
Assumed equal to
Varies; proxied by 10-
Interest
value
average expost real
year real rate on
monetary rate
indexed bonds
Interest smoothing
No
Yes
Yes
Time frame for
Backward looking;
Forward looking;
Forward looking, uses
reaction;
expected inflation not
inflation expectations
market-based inflation
required
“inferred” from actual
expectations
treatment of
future inflation using
expected inflation
IV methods
in estimation
22
Table 2:
Inflation Targets and Actual Inflation, 1992–2003
(rates of change during the year, percent)
Inflation target
1992
14–15
1993
10
1994
8
1995
8–11
1996
8–10
1997
7–10
1998
7–10
1999
4
2000
3–4
2001
2.5–3.5
2002
2–3
2003 and subsequently
1–3
23
Actual inflation
9.4
11.2
14.5
8.1
10.6
7.0
8.6
1.3
0.0
1.4
Table 3. Basic Results Using Real Rate
A. it = α [δ0 +δ1rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
Α
Β
δ0
δ1
Coefficient
Std. Error
0.55
1.31
2.331.67
Sample: 93:1-01:4
t- Statistic
0.11
0.24
1.50
0.35
Adjusted R2 = 0.923
5.0
5.3
-1.5
4.8
DW = 1.86
B. it = α [δ1rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
Α
Β
δ1
Coefficient
Std. Error
0.47
1.36
1.12
Sample: 93:1-01:4
t- Statistic
0.09
0.29
0.09
Adjusted R2 = 0.924
5.1
4.6
11.8
DW = 1.88
C. it = α [rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
α
β
Coefficient
Std. Error
0.40
1.63
Sample: 93:1-01:4
t- Statistic
0.07
0.25
Adjusted R2 = 0.924
24
6.0
6.4
DW = 1.92
Table 4. Results with Flexible Inflation Targeting
(Unemployment Gap)
it = α [δ0 +δ1rt + πtT + β (πte - πtT) + γ(u_gapt)] + (1-α) it-1
Parameter
α
β
γ
δ0
δ1
Coefficient
Std. Error
0.57
0.11
1.35
0.02
-2.59
1.71
0.25
0.31
1.48
0.34
Sample: 93:1-01:4
Adjusted R2 = 0.918
t- Statistic
5.1
5.3
0.1
-1.7
5.0
DW = 1.85
it = α [δ1rt + πtT + β (πte - πtT) + γ(u_gapt)] + (1-α) it-1
Parameter
α
β
γ
δ1
Coefficient
Std. Error
0.48
1.41
-0.06
1.11
Sample: 93:1-01:4
t- Statistic
0.09
0.30
0.36
0.09
Adjusted R2 = 0.920
5.1
4.6
-0.2
11.7
DW = 1.85
it = α [rt + πtT + β (πte - πtT) + γ(u_gapt)] + (1-α) it-1
Parameter
α
β
γ
Coefficient
Std. Error
0.41
1.67
-0.05
Sample: 93:1-01:4
t- Statistic
0.06
0.26
0.42
Adjusted R2 = 0.919
25
6.1
6.4
-0.1
DW = 1.89
Table 5. Monthly Equation Results
it = α [δ0 +δ1rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
α
β
δ0
δ1
Coefficient
Std. Error
0.18
1.50
-0.65
1.23
Sample: 93:01-01:12
t- Statistic
0.03
0.24
1.60
0.37
4.8
6.1
-0.4
3.3
Adjusted R2 = 0.97 0
DW = 1.38
it = α [δ1rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
Coefficient
Std. Error
t- Statistic
0.03
5.1
0.18
α
1.52
0.25
6.0
β
1.07
0.08
13.0
δ1
2
Sample: 93:01-01:12 Adjusted R = 0.970
DW = 1.385
it = α [rt + πtT + β (πte - πtT)] + (1-α) it-1
Parameter
α
β
Coefficient
Std. Error
0.16
1.68
Sample: 93:01-01:12
0.02
0.22
R2 = 0.970
26
t- Statistic
6.2
7.5
DW = 1.39
Table 6. Estimation Results Using CGG Method
A. it = α [5.6 + τ + β (πt - τ)+ γ(u_gapt)] + (1-α) it-1
Parameter
Coefficient
α
β
τ
γ
Sample: 93:1-01:4
Std. Error
t- Statistic
0.11
0.04
2.7
1.25
0.53
2.4
12.2
11.4
1.1
-0.53
2.47
-0.2
Adjusted R2 = 0.840
DW = 1.81
Method: GMM
B. it = α [δ +7 + β (πt -7)+ γ(u_gapt)] + (1-α) it-1
Parameter
Coefficient
α
β
δ
γ
Sample: 93:1-01:4
C.
Std. Error
t- Statistic
0.11
0.04
2.7
1.25
0.53
2.4
4.28
0.68
6.3
-0.53
2.47
-0.2
Adjusted R2 = 0.840
DW = 1.81
Method: GMM
it = α [δ + πtT + β(πt - πtT)] + (1-α) it-1
Parameter
α
β
δ
Sample: 93:1-01:4
Coefficient
Std. Error
t- Statistic
0.16
0.03
4.5
0.54
4.92
0.27
0.42
2.0
11.8
Adjusted R2 = 0.848
27
DW = 1.56
Method: GMM
Figure 1: 10-year real rate and 9-10 year implied
forward rate: time series plot
6
5
4
3
2
1
92
93
94
95
96
97
B10
98
99
FW9_10
28
00
01
Figure 2: Interest Rate Paths for Alternative "Identifying
Assumptions" and Actual Path
20
18
16
Eq. 6A
14
Eq. 6 B
12
Eq. 3C (EKO)
10
Actual
8
6
4
2
1
III
- 01
I- 0
0
III
- 00
I- 0
9
III
- 99
I- 9
8
III
- 98
I- 9
7
III
- 97
I- 9
6
III
- 96
I- 9
5
III
- 95
I- 9
4
III
- 94
I- 9
I- 9
3
III
- 93
0
Endnotes
a
Another direction of criticism of CGG’s work is that it does not use the data that
were actually available to policy makers at the time decisions were taken, using
instead currently available data that have been substantially revised. See, for
example Orphanides (2001).
b
See Cochrane and Piazessi (2002) for an alternative approach to addressing this
issue using high frequency interest rate data.
29