Charles Bean: Monetary policy after the fall
Paper written by Messrs Charles Bean, Matthias Paustian, Adrian Penalver and Tim Taylor
and presented by Mr Charles Bean, Deputy Governor of the Bank of England, at the Federal
Reserve Bank of Kansas City Annual Conference, Jackson Hole, Wyoming, 28 August 2010.
* * *
The assistance of Alina Barnett, Lavan Mahadeva, Clare Macallan, Haroon Mumtaz and Ryland Thomas was
invaluable. Helpful comments and suggestions from Ed Nelson and numerous Bank of England colleagues are
also gratefully acknowledged. The views expressed do not necessarily reflect those of either the Bank of England
or the Monetary Policy Committee.
1. Introduction: the consensus before the crisis
The Great Financial Crisis that began in August 2007 and the associated Great Contraction
in global economic activity that took place after the collapse of Lehman Brothers in
September 2008 have presented central bankers and finance ministers in the advanced
economies with one of the toughest challenges that they are ever likely to face. While no-one
can claim to have done it perfectly, by dint of aggressive, and in many cases innovative,
policy actions they have collectively succeeded in preventing the collapse of financial
markets, arresting the contraction in activity and putting their economies on the path to
recovery. Even so, the de-leveraging process is incomplete, the recovery remains fragile and
a considerable margin of spare capacity is yet to be worked off, while further policy action
may yet be necessary to keep the recovery on track. It may therefore seem premature to
draw lessons from the crisis for the future conduct of monetary policy in normal times. But
normal times will surely return in due course. And it is natural to ask whether the events of
the past three years point to fundamental flaws in our policy frameworks.
The crisis was perhaps all the more remarkable because it occurred after such a long period
of relatively steady growth and low and stable inflation - the Great Moderation. While the
causes of the Great Moderation are open to debate, most policy makers probably put some
of that improved macroeconomic performance down to better policy. That was reflected in a
consensus - at least in the Anglo-Saxon world - as to the ingredients of a successful policy
framework and was mirrored in an equivalent consensus in the academic literature on
monetary policy, synthesising the rigour of dynamic general equilibrium modelling with the
empirical realism of sticky-price Keynesian thinking, best exemplified in the magisterial
contribution of Woodford (2003).
This pre-crisis set of beliefs was reflected in many of the contributions to this annual
conference in the years leading up to the crisis and so might aptly be christened the
New Challenges for Monetary Policy
"Jackson Hole" consensus; the volume from the
conference that took place here eleven years ago represents as good a reflection as any of
that paradigm. Broadly speaking, this Jackson Hole consensus consisted of the following
ingredients:
1. Automatic stabilisers aside, fiscal policy was unsuitable as an instrument of
macroeconomic demand management. That was justified theoretically by appeal to
the comparative advantage of monetary over fiscal policy in controlling nominal
demand or to Ricardian Equivalence or to the argument that fiscal expansions were
harder to reverse than initiate.
2. Monetary policy was therefore assigned the primary role in short-term aggregate
demand management, with policy conducted through the manipulation of a suitable
short-run interest rate.
3. The monetary transmission mechanism operated mainly through longer-term
interest rates, asset prices and expectations of future inflation. Expectations of
future policy rates were central and credibility was key. These channels might be
augmented by a weak credit channel but the banking sector generally was
conspicuous by its absence, particularly in the New Keynesian synthesis models,
which also dominated thinking within central banks. The importance accorded to
expectations led naturally to an increased focus on communication and
transparency.
4. The conduct of monetary policy was best delegated to an independent central bank,
free of short-term political considerations. That was buttressed by academic thinking
which drew attention to the potential time inconsistency of optimal policy when
expectations of future policy mattered and which suggested that monetary policy
was best delegated to conservative central bankers with long horizons.
5. Intermediate monetary targets were not useful, because of their unstable link with
the ultimate objectives of policy (though that did not preclude them being helpful at
times as indicators of future demand and inflation). For jurisdictions with floating
exchange rates, monetary policy should instead be focussed on the only thing it
could reliably determine in the long run, namely the price level. In many countries,
this was codified into an explicit numerical inflation target; in others, the objective
was left somewhat fuzzier. Focusing policy on the ultimate objective of price
stability, rather than some intermediate variable, offered a policy framework that was
both clearer to the public and potentially more durable. But the short-run stickiness
of wages and prices, coupled with the desirability of avoiding excessive fluctuations
in activity, meant that some "constrained discretion" in the pursuit of price stability
was appropriate; this flexibility was usually incorporated explicitly into central bank
mandates in one way or another.
6. Asset markets were thought to be efficient at distributing and pricing risk and
financial innovations were normally welfare enhancing. While asset prices might be
subject to bouts of "exuberance" on the part of investors, there was little that
monetary policy could do about them. The best monetary policy could was to limit
the fallout when sentiment turned.
7. Systemic financial crises were seen only in history books and emerging markets;
they were unlikely to happen in advanced economies with their developed and
wellregulated financial markets. Moreover, price stability and financial stability were
natural bedfellows, the successful achievement of one facilitating the attainment of
the other.
Of course, agreement with each and every element of this consensus was not universal. The
European Central Bank, for instance, continued to place great value on the usefulness of a
monetary pillar. And, as discussed below, there were some who believed that central banks
should also use their constrained discretion to lean against incipient asset-price bubbles and
credit growth. But the set of beliefs above were, we believe, held sufficiently widely in
policymaking and academic circles to be described as a consensus.
In the rest of this paper, we re-visit some aspects of this consensus in the light of the crisis. It
is not possible to cover all the elements of the consensus, though we shall offer some more
wide-ranging observations at the end. In particular, we focus on: whether the experience with
unorthodox policies during the crisis has changed our view of the appropriate policy
instruments in normal times; whether the target rate of inflation should be increased or a shift
to price-level targeting is warranted; and what the experience of the crisis has taught us
about how monetary policy should respond to credit/asset-price booms.1 As a precursor to
that discussion, however, we ask whether monetary policy decisions contributed materially to
the crisis.
2. Monetary policy and the crisis
It is worth stressing at the outset that a multitude of factors, both microeconomic and
macroeconomic, played into the crisis. A non-exhaustive list of microeconomic factors
includes: the incentive to shift loans off banks' balance sheets to avoid capital requirements;
the reduced incentive for care in the origination of loans, when those loans are then
securitised; the distorted incentives facing ratings agencies; pay packages encouraging the
pursuit of short-term returns and the adoption of trading positions with the characteristic of a
deeply out-of-the-money option; and the moral hazard arising from financial institutions that
are too big or too systemically important to fail, together with inadequate supervision of the
same. On top of that, the crisis exposed previously unappreciated informational deficiencies
created by the underlying complexity of some asset-backed securities and the high degree of
interconnectedness of financial institutions. Potential macroeconomic factors include the
international payments imbalances, and the side effects of the Great Moderation, as well as
monetary policy. In our view, it would be a mistake to assign a key role to any of these
factors in isolation. On their own, none can surely explain the worst financial crisis in eighty
years. But together they constituted a potent cocktail. Monetary policy makers would
therefore be remiss if they did not re-examine their own decisions in the lead-up to the crisis
and strive to learn the lessons for the future conduct of policy.
In the normal course of events, looser monetary policy boosts asset prices, as lower policy
rates are usually associated with somewhat lower longer-term interest rates too.
Expansionary policy can also be expected to boost activity and profits, which also tends to
raise asset prices. But the case for monetary policy having a role in the run-up to the crisis
comes less from these conventional monetary transmission channels and more from the idea
that loose monetary policy particularly encouraged a shift into riskier asset classes, which
then got out of hand - the so-called "risk-taking channel" of monetary policy (Borio and Zhu,
2008).
There are broadly three ways in which looser monetary policy encourages increased
risktaking. First, and most conventionally, a lower yield on safe assets encourages substitution
into higher-yielding risky assets, in the process driving up their prices. Second, some
investors such as pension funds need to match the returns on their investments to their
commitments. A reduction in the return on safe assets then encourages them to switch into
high-yielding but riskier assets in an attempt to deliver nominal returns which match their
liabilities - a "search for yield" (Rajan, 2005). Executive compensation linked to absolute
returns has a similar effect.
Finally, a slightly more complex mechanism is developed by Adrian and Shin (2009) and
Adrian, Moench and Shin (2010). They argue that financial intermediaries target leverage
ratios which are either constant (commercial banks) or pro-cyclical (investment banks).
Consequently an increase in the value of a bank's equity resulting from, say, a rise in the
value of its (risky) assets will lead it to expand its debt (through deposit or wholesale funding)
and a corresponding increase in its assets, either through extending new loans or acquiring
additional securities. So as looser monetary policy boosts asset prices, it encourages an
expansion in banks' balance sheets, putting further upward pressure on asset prices.
Leverage targets therefore act as an amplification mechanism. But the number of relatively
safe borrowers/projects is limited. So the extension in the volume of loans is also likely to
involve moving along the risk spectrum towards more risky borrowers.
Looser monetary policy is not the only factor operating through these channels. Two other
macroeconomic factors are potentially relevant. First, a number of authors have focussed on
the role of international payments flows in the crisis, with capital flowing "uphill" from
emerging economies, such as China, into the United States and some other advanced
economies (see, for instance, Obstfeld and Rogoff, 2009, and the references therein).
Bernanke (2005) attributes this to a "savings glut" in the surplus countries. Possible drivers
include: an inadequate household safety net and restricted capital market access for
enterprises in China; the accumulation of precautionary holdings of international reserves by
emerging economies following the Asia crisis; and rational savings of the windfall gains from
higher oil prices on the part of oil producers. A perceived comparative advantage of the
United States in creating "high quality" financial assets from real investments may also have
played a part (Caballero, Farhi and Gourinchas, 2008). This resulted in downward pressure
on the yields on government bonds and other safe assets, and upward pressure on asset
prices generally. Low long-term safe interest rates would also have encouraged the shift into
riskier assets through the risk-taking channel described above.
Second, the lead-up to the crisis was also a long period of steady growth coupled with low
and stable inflation (the Great Moderation).2 Households, businesses and market participants
were consequently faced with a complex signal-extraction problem: how much of this
reduction in economic volatility was permanent? Whereas many economic signal extraction
problems involve learning about the first moments of a distribution, this involves making
inferences about higher moments. The longer such a period of low volatility lasts, the more
reasonable it is to assume that it is permanent. But given the necessary infrequency with
which tail events occur, there may be a natural tendency for people erroneously to conclude
that they could never happen simply because none have materialised recently. Certainly
market measures of uncertainty are consistent with this idea, as measures of volatility
implied from options prices (such as the VIX) suggest that the perceived risks in financial
markets had shrunk to extremely low levels by 2006. This reduction in the perceived
riskiness of the environment is also likely to encourage financial market participants to
increase their holdings of riskier assets and to drive up their prices.
A key piece of evidence suggesting that excessively loose monetary policy might have had a
part to play in generating the preconditions for the crisis is provided by comparisons of policy
rates with the policy settings generated by a benchmark Taylor rule (Taylor, 2007). Chart 1
shows the difference between the policy rate and benchmark estimates of the appropriate
policy rate derived from a Taylor rule for the United States, the euro area and the United
Kingdom. Notwithstanding the usual caveats about the construction of such benchmarks, the
very low level of the Federal Funds rate relative to the Taylor rule from 2001 to 2005 in the
aftermath of the collapse of the dot-com bubble is striking.
Of course, the Federal Open Market Committee (FOMC) set its target Federal Funds rate at
unusually low levels for a reason, namely concerns that the United States might find itself
mired in deflation of the sort experienced by Japan during its "Lost Decade". Bernanke
(2010) provides a vigorous defence of Federal Reserve policy over this period, arguing that
evidence from a comparison of guideline policy rates from conventional Taylor rules with
actual policy rates is unpersuasive. Central banks usually set policy not on the basis of past
inflation but rather their expectations of future inflation, looking through temporary
movements in inflation that result from shocks to commodity prices or indirect tax rates.
During 2002-5, the FOMC judged that prospective underlying ("core") inflation was
considerably weaker than realised headline inflation, and that the latter would move down
towards the former in the medium term once the temporary effects of one-off disturbances
had passed through. Bernanke finds that merely substituting Greenbook inflation forecasts
for actual inflation in an otherwise standard Taylor rule eliminates much of the discrepancy
with the target Federal Funds rate.
That, of course, still leaves open the possibility that the FOMC's fears that inflation would
turn out too low were, at least with hindsight, exaggerated. Whether or not policy was
appropriate ex ante will always be difficult to answer because we do not know what would
have happened under a different policy path. One can, however, answer a slightly different
and more straightforward question, namely what impact the accommodative policy stance
had on asset prices and credit growth. Bernanke goes on to provide time-series and
crosscountry evidence, which suggests that monetary policy played a relatively modest role in the
boom in house prices in the United States and a number of other countries.
Chart 1 shows that both UK and euro-area policy rates were less noticeably out of line with
their respective Taylor benchmarks. That too is striking. Indeed, in the United Kingdom, they
were actually above the benchmark for much of the relevant period, even though the United
Kingdom saw one of the larger run-ups in debt and house prices during this period. And, in
the euro area, countries such as Spain experienced substantial house price booms, while
countries such as Germany did not. That need not imply that monetary policy was innocent in
the run-up to the crisis, as the equilibrium real interest rate could have been higher in the
United Kingdom than in the calibrated Taylor rule. And differences in equilibrium real interest
rates across countries can in principle explain the heterogeneity in the euro area. But this is
hardly compelling evidence for assigning the central role to monetary policy, suggesting that
other factors were more important.
To complement Bernanke's analysis, we provide some further evidence on the impact of
policy on credit and asset prices, obtained from estimated vector auto-regressions for the
United States and the United Kingdom. The model includes the standard macroeconomic
variables appearing in New Keynesian descriptions of monetary policy: real GDP growth, CPI
inflation and a short-term nominal interest rate. In addition, the model also includes a set of
variables relating to credit and asset prices: total credit growth; the spread of
investmentgrade corporate bonds over government bonds, as a general indicator of credit spreads; and
house price inflation. To capture the potential impact of the Great Moderation on perceptions
of the riskiness of the environment, we also include a measure of macroeconomic volatility.
This is generated from an auxiliary factor stochastic-volatility model, which estimates the
common time-varying volatility in a set of key macroeconomic variables (GDP, consumption,
investment, exports, imports and inflation). The resulting series are shown in Chart 2,
together with estimated one standard deviation confidence intervals, and have the
characteristics that one would expect: high in the Seventies and early Eighties, then falling
back as the period of the Great Moderation wears on, and rising sharply with the onset of the
financial crisis and the Great Contraction.
We envisage a set of seven underlying fundamental shocks driving these seven variables: an
aggregate demand shock; an aggregate supply shock; a monetary policy shock; a
macroeconomic volatility shock; a credit demand shock; a credit supply shock; and a house
price shock. The first three of these are conventional in nature. The fourth captures changes
in the riskiness of the macroeconomic environment. The credit demand and credit supply
shocks are intended to capture movements in credit resulting from other factors, while the
house price shock captures movements in house prices attributable to factors not elsewhere
accounted for. Other factors driving both credit and house prices will include the low level of
long-term real interest rates and associated international current account imbalances.
The identification scheme employs a combination of ordering assumptions and theoretical
sign restrictions on the impulse responses (see Uhlig, 2005). Macroeconomic volatility should
be a slowly moving variable that is little affected by contemporaneous developments in the
economy. One would expect that most of the variance in macroeconomic volatility - a
second moment - is not well explained by the other shocks; that is borne out in the results,
especially for the United Kingdom. Macroeconomic volatility is therefore assumed to be
contemporaneously unaffected by any of the other shocks. The aggregate demand/supply
block comes next, affecting credit and housing markets and monetary policy
contemporaneously, but not being affected by contemporaneous developments in them; an
aggregate demand shock affects inflation and growth in the same direction, while an
aggregate supply shock drives them in different directions. That is followed by the credit
market block: again, a credit demand shock drives credit growth and the bond spread in the
same direction, while a credit supply shock drives them in different directions. Then comes
monetary policy; policy makers are therefore assumed to be able to react to movements in
the real economy and in credit markets within the quarter, which does not seem
unreasonable. House prices come last.
For the United States, the variables in the vector auto-regression are: CPI inflation; GDP
growth; the effective Federal Funds rate; the difference between the Merrill Lynch corporate
BAA and 10-year Treasury yields; the growth in total private credit market debt outstanding
deflated by CPI; the rate of change of house prices (the National Association of Realtors
existing homes price index to 1975 linked to the Federal Housing Finance Agency thereafter)
deflated by CPI; and the macroeconomic volatility index. For the United Kingdom, the
equivalent variables are: CPI inflation; GDP growth; Bank Rate; the difference between the
investment-grade corporate bond and 10-year government bond yields; the growth in M4
lending (excluding securitisations and loans to intermediate OFCs) deflated by CPI; the rate
of change of house prices (the Nationwide house price index to 1983 linked to the Halifax
measure thereafter) deflated by CPI; and the macroeconomic volatility index. The data are
quarterly, there are two lags of each variable, and the sample runs from 1966 Q3 to 2010
Q1. A good case can be made for employing only more recent data, on the grounds that
monetary policy reaction functions have evolved during this time. But the cost of that is
reduced precision and estimates over just the latter part of the period turn out to be rather
less well defined. The model is estimated using Bayesian methods to facilitate imposition of
the sign restrictions and the construction of confidence intervals on convolutions of the
parameters.
The impulse responses are shown as four-quarter growth rates in Charts 3a (United States)
and 3b (United Kingdom), where the dark blue lines are the posterior median responses and
the blue swathes provide one standard deviation confidence intervals. For the most part
these look sensible, though, as is usually the case in such exercises, there are one or two
responses that look a little odd. In particular, both sets of estimates exhibit the oft-observed
"price puzzle", whereby the immediate impact of a monetary policy tightening is to increase,
rather than decrease, the rate of inflation. A number of explanations for this price puzzle
have been advanced in the literature, including the reaction of the monetary policy maker to
information on inflation prospects not incorporated in the model, and a monetary policy
reaction function that is insufficiently sensitive to inflation over part of the sample period.
Because of the presence of the price puzzle, we do not to focus on the behaviour of inflation
in the simulations reported below.
Aside from the initially perverse inflation response, the impact of an unexpected monetary
tightening is as one would expect, in both the United States and the United Kingdom: output
growth falls, the bond spread rises, real credit growth falls and real house price inflation falls.
The impact of an increase in macroeconomic volatility (i.e. an increase in general riskiness)
is also worth highlighting: output growth falls, credit spreads rise, real credit growth falls, and
real house price inflation falls. This is all as one would expect from the discussion above
regarding the risk-taking channel. In both countries, inflation also rises when macroeconomic
volatility increases.
Charts 4a and 4b show historical decompositions derived using the posterior means of the
distribution of the coefficient estimates. As there is rather a lot of information to digest in
these decompositions, we show just the main variables of interest: the policy rate, and the
four-quarter growth rates of output, real credit and real house prices. We also combine the
impact of the aggregate demand and supply shocks into a single composite factor, and do
the same with the credit demand and credit supply shocks so as to focus more clearly on the
impact of monetary policy and macroeconomic volatility. There are a number of points to be
made.
First, monetary policy (the green bars) during the 2002-5 period is loose relative to the
estimated historical reaction function not only in the United States - as might be expected
given the evidence from Chart 1 - but also, more surprisingly, in the United Kingdom. In the
United States, the Federal Funds rate is, on average, 1.5 percentage points below the rate
that would have obtained if the estimated reaction function had applied. In the United
Kingdom, the corresponding figure is 2.1 percentage points. There is, however, a simple
explanation for the apparent looseness relative to the estimated reaction function in the
United Kingdom, namely the change in the policy regime associated with the adoption of
inflation targeting and the subsequent credibility gain from giving operational responsibility for
monetary policy to the Bank of England. This represented a sharp change in regime after a
somewhat chequered history of inflation control and probably contributed to a lower
equilibrium real policy rate because of the associated reduction in the inflation risk premium.
Second, those monetary policy deviations can explain only part of the excess credit growth
and house price inflation in the two countries over 2002-5. In the United States, the
monetary policy shocks are associated with, on average, an extra 0.6 percentage points on
annual real credit growth and an extra 1.5 percentage points on annual real house price
inflation. That is to be compared with average actual annual real credit growth over the
period of 5.6 per cent and average annual real house price inflation of 5.8 per cent. For the
United Kingdom, the corresponding figures are an average 1.3 percentage points on annual
real credit growth and 6.0 percentage points on annual real house price inflation, compared
with average annual real actual credit growth of 8.9 per cent and average annual real house
price inflation of 13.0 per cent. In both countries, an important driver of house price inflation
over the period is house price shocks, though a wider range of influences appear to have
been involved in driving the expansion in credit. The moral from these results would appear
to be that although monetary policy may have played a role in fuelling the credit/house-price
boom that preceded the crisis, it is rather more Rosencrantz than Hamlet. We return in
Section 5 to the question of whether these findings suggest that policy should be set
differently in future.
The third point of note is the significant role played by shocks to macroeconomic volatility
(blue bars), particularly in regard to credit growth, with noticeably more rapid expansion in
credit taking place during tranquil periods. In particular, over the period 2002-5,
macroeconomic volatility accounts for, on average, an extra 0.7 percentage points on US
annual real credit growth and 0.5 percentage points on US annual real house price growth. In
the United Kingdom, the corresponding effects are even larger: 2.1 percentage points on
annual real credit growth and 2.0 percentage points on annual real house price inflation. A
reduction in volatility also confers a sizeable "growth dividend", suggesting that the stability of
the Great Moderation period boosted the sustainable rate of growth, while the current period
of high volatility has had the opposite effect; that is consistent with the cross-country
evidence of Ramey and Ramey (1995), who find that higher volatility tends to be associated
with lower growth.
The idea that periods of economic stability encourage exuberance in credit markets, thus
sowing the seeds of their own destruction, is a key part of Minsky's theory of recurring
financial crises (see e.g. Minsky, 1982). The results here provide some empirical evidence
for such a dynamic process. Moreover, to the extent that better policy accounted for the
Great Moderation, it provides a second, indirect, channel whereby policy may have
contributed to creating the conditions conducive to a subsequent financial bust. But it would
clearly be a mistake to conclude that policy should aim to induce fluctuations in the
macroeconomy in order to prevent financial market participants becoming too confident about the
outlook! The right moral is surely that policy makers need to be most vocal about the risks to
the outlook when things appear to be going well, and to take appropriate restraining action if
needed.
3. The instruments of monetary policy
Dealing with the fallout from the banking crisis has pushed central banks in the affected
jurisdictions into uncharted waters. The top panel of Table 1 summarizes the wide variety of
measures adopted by some of the major central banks, while Chart 5 illustrates the
associated expansion in the balance sheets of the Federal Reserve, the European Central
Bank and the Bank of England.
The most immediate response was to offer liquidity support to the banking sector, especially
as the crisis intensified in the wake of the collapse of Lehman Brothers and the rescue of
American International Group. Measures adopted included widening access to Discount
Window Facilities, expanding the range of eligible collateral and counterparties, extending
loan tenors and introducing foreign currency swap lines. As the lending in these operations is
normally over-collateralised, there is essentially negligible credit risk to the central bank. In
addition to these classical, if somewhat expanded, central banking support operations, a
number of central banks - most especially the Federal Reserve, but also the European
Central Bank and the Bank of England - undertook less conventional actions aimed at
improving the operation of particular, temporarily dysfunctional, markets. For instance, the
Federal Reserve and the Bank of England both bought high-quality Commercial Paper,
reducing the risk that a borrower could not raise new funds to repay maturing paper and thus
also encouraging private investors to lend. This exposes the central bank to some credit
risk,3 but the short tenor and restriction to high-quality companies makes the risk slight.
The Federal Reserve's Term Asset-Backed Securities Loan Facility (TALF) represented a
rather more radical departure. Under the TALF, the Federal Reserve made medium-term
loans to investors against highly-rated securities backed by consumer and business debt,
with the aim of increasing the availability of consumer and business credit. Even though
there is a haircut on the securities, the credit risk to the central bank is potentially higher
under this programme; that risk was effectively underwritten through the provision of credit
protection by the US Treasury.
Many of these extraordinary actions were designed to be self-liquidating as conditions
normalise: central bank or government support becomes more expensive than market
finance, or else is specifically time-limited. A central bank should not offer special support to
particular private institutions or markets indefinitely, unless it is seeking to offset an
identifiable market failure. Otherwise, it just ends up distorting the market structure.
Moreover, to the extent that there is a market failure or distortion present, in the first instance
it is surely the job of government, rather than the central bank, to address that market failure.
In addition, anything that involves the central bank favouring particular businesses or sectors
of the economy or exposing the consolidated public sector balance sheet to credit risk takes
it into territory that is inherently political and risks inviting political intervention or limitations to
its independence.
While there should be little need for extraordinary liquidity and credit support once normal
ti