Docstoc

ECB

Document Sample
ECB Powered By Docstoc
					Forecasting the ECB’s main refinancing rate.

A field experiment.


Michael Berlemann
ifo Institute for Economic Research, Branch Dresden

Dresden University of Technology

CESifo


March 31, 2006
Abstract. When no appropriate markets to derive expectations on economic variables are available often

surveying methods are employed. However, surveys suffer from the problem how to aggregate individual

expectations in a reasonable manner. We show at the example of a market on the ECB’s main refinancing

rate that experimental markets aggregate information quite efficiently and thus are a useful tool in this

respect.


Keywords: expectations, forecasting, field experiments, experimental stock markets, main refinancing

rate, ECB



JEL code: E58
2                             Forecasting the ECB’s main refinancing rate



                                       1. Introduction




Basically, two basic approaches of macroeconomic forecasting can be distinguished. On
the one hand econometric forecasting techniques can be applied to macroeconomic data
in order to construct forecasts. On the other hand the expectations approach of fore-
casting can be employed by measuring market participants’ expectations on the event
or variable to be forecasted. Whenever these expectations are formed rationally they
should provide unbiased and efficient forecasts. The basic problem of the expectations
approach to forecasting (or simply of measuring expectations) is how to uncover market
participants’ expectations.
    Direct methods of measuring expectations typically rely on some sort of survey in
which certain subsamples of the population are asked to reveal their personal expec-
tations (see Croushore [1996] or Thomas [1999]). However, then an appropriate way of
aggregating the individual responses has to be found. In most cases an arbitrary procedure
such as averaging is used for this purpose which is often inappropriate. Besides solving the
aggregation problem the surveyor has to overcome the well documented (see e.g. Aaker
and Day [1990]) sampling-, non-response- and motivation-problems of respondents.
    The indirect approach of measuring expectations is to derive expectations from mar-
ket participants’ behavior on real world (financial) markets. This approach bases on
the idea that markets are the most efficient means of aggregating private information

(see Lioui and Poncet [2002] and Smith [1982]). Various experimental studies (Smith
[1962,1964,1965], Miller, Plott and Smith [1977], Williams [1979,1980], Smith and Williams
[1983]) found that initially dispersed information is quite efficiently disseminated via
prices in market settings. Thus, market prices solve the information aggregation problem
quite efficiently and can therefore be used to to uncover the underlying expectations of
market participants. However, often there are no appropriate markets available which
can be used to extract forecasts. And even if these markets exist, the underlying expec-
                                 Forecasting the ECB’s main refinancing rate                                  3


tations can often be extracted from the market data only when using highly simplifying
assumptions.1
      As an alternative to real-world markets one might use experimental markets to aggre-
gate initially dispersed private information on events to be forecasted. The experimental
approach to forecasting developed in the late 1980s when political stock markets were
employed to generate market data under somewhat controlled circumstances in field
experiments (see Forsythe et al. [1992]). While these markets were initially intended to
allow to study individual market behavior they delivered election-outcome forecasts as
by-products. Since these forecasts have proven to be highly accurate the method has been
used extensively to forecast election results in the aftermath (see e.g. Berg et al. [2000] or
Berlemann and Schmidt [2001]). However, experimental markets can also be employed to
generate forecasts of economic variables. As an alternative to surveys, experts could also
be asked to take part in appropriately designed experimental markets. These markets
aggregate the experts’ expectations in a non-arbitrary way thereby allowing to derive
useful forecasts. As an example we report results from an experimental forecasting market
on the ECB’s main refinancing rate in this paper. In section 2 we describe the conducted
market. Section 3 explains how forecasts can be extracted from the market and presents
some empirical results. In section 4 we study in how far the forecasts derived from the
market are efficient and thus solve the information aggregation problem in a satisfactory
manner. Section 5 concludes.




                                       2. Market description


The experimental market we report on was intended to forecast the main refinancing rate
of the European Central Bank (ECB) on 15th January 2003. The market opened up on
  1
     For example, inflation expectations can be derived from the prices of CPI futures (see Lovell and
Vogel [1973] or Lioui and Poncet [2002]). Since CPI futures markets did not develop in most countries,
several authors (see e.g. Fama [1975] or Mishkin [1990]) tried to gauge inflation expectations from the
term structure of interest rates. While this type of data is typically available, generating inflation forecasts
from it is far from being easy. Often a number of simplifying assumptions, e.g. on the behavior of the
real interest rate over time, have to be made.
4                                 Forecasting the ECB’s main refinancing rate



13th October 2002 and closed on 14th January 2003. The market was fully computerized.
In order to be allowed to take part in the market, participants had to register in a market
software via Internet. The market participants were recruited from a university course
in macroeconomics. Altogether 51 students took part in the market. After registrating
participants got trader-IDs and passwords to login the market. Trader accounts for the
participants were created and 100 virtual Euro were transferred to the accounts. These
virtual funds could be used by the participants to organize market transactions. The
three participants with the highest returns on investment were finally rewarded by the
market organizer with 75, 50 and 25 Euro.2
        The market made use of a winner-takes-all design. In the market a set of binary lock-in
options were traded. The underlying of these options was the main refinancing rate of
the ECB on 15th January 2003. The traded options had a fixed, predetermined payoff of
1 virtual Euro if the underlying was inside the strike range at expiration.3


          Table I. Traded contracts in ECB market.

           Contract number    Contract name     Interval middle/border    Pays off 1 virtual Euro, if

                  1              r(2.25−)                2.250                    r   ≤ 2.25
                  2               r(2.50)                2.500                    r   = 2.50
                  3               r(2.75)                2.750                    r   = 2.75
                  4               r(3.00)                3.000                    r   = 3.00
                  5               r(3.25)                3.250                    r   = 3.25
                  6               r(3.50)                3.500                    r   = 3.50
                  7               r(3.75)                3.750                    r   = 3.75
                  8               r(4.00)                4.000                    r   = 4.00
                  9              r(4.25+)                4.250                    r   ≥ 4.25




        The set of binary lock-in options traded in the market is shown in table I.4 The
contracts were designed symmetrically around the main refinancing rate prevailing when
    2
     Since the market was conducted with students at a university, we decided not to use a real-money
setting. As a consequence we can not rule out that at least some players engaged in more risky strategies
than he or she would have done under real-money trading.
   3
     Thus, the type of lock-in options traded in the market were formally identical to what is called pure,
Arrow- or Arrow-Debreu securities in financial markets literature. See e.g. Copeland and Weston [1992].
   4
     To understand the design of the contracts it should be noted that the ECB’s main refinancing rate is
varied only in multiples of 0.25 percent. During the market period the main refinancing rate was changed
once. On 6th December 2002 the rate was lowered by 0.5 percentage points from 3.25 to 2.75 percent.
                                 Forecasting the ECB’s main refinancing rate                                5


the market opened up (3.25 percent).5 The strike ranges of these options did not overlap
and covered the whole range of possible outcomes of the underlying. Since the number
of unique linearly independent securities was equal to the total number of alternative
states of nature we dealt with a complete market (Copeland and Weston [1993], p. 112).
Regardless of the initial distribution of securities it was thus possible to reduce the
uncertainty about the value of future wealth to zero by holding unit portfolios consisting
of one of each option type.
   Upon entering the market and any time thereafter participants could buy unit port-
folios from the market organizer for the price of 1 virtual Euro until the market closed.
Complete unit portfolios could be sold back to the market organizer during the market
period for the same price. Market participants could also buy or sell contracts from
or to other market participants. This “secondary market” was organized as a double
auction market. Market participants could issue offers to buy (bids) or offers to sell
(asks) contracts. When using a first type of transactions, so-called “limit orders”, traders
had to choose the order type (bid or ask), the contract type, the number of contracts he
or she wanted to trade, the desired transaction price and finally the order’s expiration
date. Limit orders were maintained in separate bid and ask queues ordered first by offer
price and then by the time of issuance. Whenever an offer entered one of the queues it
remained there until the offer turned out to be unfeasible (e.g. because of a lack of liquidity
to realize a buying transaction), was withdrawn by the trader, reached its expiration date
or was carried out. Orders were carried out whenever bid- and ask-prices overlapped. The
second type of transactions available, the so-called “market orders”, were orders to buy
or sell at current market prices which were carried out immediately. Different from real
world stock markets, short sales and purchases on margin were disallowed. No transaction
costs were levied by the market organizer.


   5
     In order to get a forecast as precise as possible the set of traded options can be increased during the
market period. This can easily be done by splitting options into two (or more) contracts with smaller
strike ranges (given that the options do not overlap and all possible outcomes of the underlying are still
covered). In order not to influence the values of the participants’ portfolios by contract splits, each holder
of a split contract is supplied with one of each newly issued contract in exchange.
6                                Forecasting the ECB’s main refinancing rate



        All primary and secondary market transactions were organized via a market software.
Besides serving as a market platform the software provided several facilities for the traders
to obtain information on the market. A trader could access personal information on his
market account, current portfolio or already submitted orders. The software also delivered
information about the highest bids to buy and lowest asks to sell for each contract type
or the last prices for which a certain share was traded.
        The ECB market got liquidated as soon as the realization of the underlying was known.
The individual payoff of each participant in virtual Euro consisted of (i) the virtual money
the trader held on his market account when the market closed and (ii) the liquidation
value of the portfolio of contracts the trader held at the end of the market.




              3. Density forecast, mean forecast and forecast uncertainty


Using Arbitrage Pricing Theory it can be easily shown that the prices of the pure secu-
rities traded in the market are equal to the probabilities, market participants attach to
the different states of nature.6 Thus, the described experimental stock market directly
generates a density forecast for the ECB’s main refinancing rate. However, it does not
                                                            f
directly deliver a mean forecast. The mean market forecast rt at time t can be constructed
by multiplying the normalized7 last observed market prices8 with the the middles of the
    6
     According to Arbitrage Pricing Theory the equilibrium price of a pure security principally depends
on three factors: the risk-free rate of return, individuals’ attitudes towards risk and expectations as to the
probability that a particular state will occur (Copeland and Weston [1993], p. 116). Since the risk-free
rate of return is zero in the described market and there is no non-diversifiable risk, the prices of the
traded contracts solely depend on market participants’ expectations on the probabilities with which the
various states of nature occur. However, this is true only if the market is in equilibrium. It is then when
all available information is reflected in the current market prices.
   7
     Experience from previous experimental markets shows that last traded prices do not always add
up to one. A possible reason for this observation is that traders in most markets are cash-restrained.
Thus, even if some traders would have perfect information on the fair prices of all contracts they will
typically not have enough funds to fix the prices to their fair values. While this problem should diminish
in markets with a high number of traders it can hardly be ignored in smaller markets. To deal with this
problem most market organizers normalize the sum of last traded prices to unity before calculating the
mean market forecast.
   8
     Besides last observed prices (last traded prices (LTP)) market organizers often report daily volume-
weighted prices (average traded prices (ATP)). While from a theoretical point of view last observed prices
should be superior since they belong to the most actual, marginal transactions, we nevertheless report
both sorts of forecasts in the following.
                               Forecasting the ECB’s main refinancing rate                              7


strike ranges of the referring options and summing up for all traded contracts,9 i.e.

                          f      pr(2.25−),t            pr(2.50),t
                         rt =                 · 2.25 +             · 2.50 + . . .
                                     Pt                    Pt
                                   pr(4.00),t           pr(4.25+),t
                                 +             · 4.00 +               · 4.25.
                                       Pt                    Pt

with

                               Pt := pr(2.25−),t + . . . + pr(4.25+),t .

Mean forecasts do not provide any information on the uncertainty underlying the fore-
cast. Since one and the same mean forecast can principally result from many different
probability distributions information about the uncertainty surrounding a mean inflation
forecast is important in addition to the forecast itself. A measure of forecast uncertainty
helps to qualify a forecast and gives a richer picture of the expected range of likely
outcomes (Ericsson [2001], pp. 88-89). The described experimental market setting allows
to assess the mean forecast’s uncertainty directly. Since the normalized market prices
can be interpreted as the market’s aggregated evaluation of the probabilities of different
scenarios, these probabilities can be used to calculate the empirical variance of the daily
mean forecast as

               2         pr(2.25−),t             f      pr(2.50),t            f
                                                                                2
              σrf ,t =                · (2.25 − rt )2 +            · 2.50 − rt + . . .
                             Pt                            Pt
                           pr(4.00),t              f
                                                      2  pr(4.25+),t            f
                         +             · 4.00 − rt +                 · (4.25 − rt )2 .
                               Pt                             Pt

The market allowed to extract forecasts and to assess their empirical variances at any
point in time during the market period. The market thus delivered a time-series of fixed-
event forecasts. The mean forecasts of the ECB’s main refinancing rate on 15th January
2003 are shown in figure 1. It is easy to see that the market performed quite well. From
the beginning of the market period on the market predicted a decreasing refinancing rate.
  9
     Most of the strike ranges in the ECB market consisted of only one outcome of the main refinancing
rate. However, there are two options in the market which have infinitely large strike ranges (r(2.25−),
r(4.25+)). To deal with this problem we use the (lower respectively the upper) bounds of these infinitely
large intervals instead of the class middles. Doing so is unproblematic as long as the prices for these
contracts are comparatively low. Whenever the market prices for these intervals are high, thus indicating
that market participants attach a significant probability to the case that the underlying will fall into
the contracts’ strike range, the market organizer can easily solve this problem by the earlier described
splitting procedure.
8                                                                                         Forecasting the ECB’s main refinancing rate



Initially, the market predicted a decrease by some 0.25 percent. However, well before the
refinancing rate was in fact lowered the market forecast further decreased to around 2.90
percent indicating that ECB might take two steps down on the ladder. After the factual
change of the refinancing rate on 6th December the market forecast converged quickly to
2.75 percent and remained there until the market closed.

                                            3.300

                                            3.200

                                            3.100
         Main refinancing rate in percent




                                            3.000

                                            2.900

                                            2.800

                                            2.700

                                            2.600

                                            2.500

                                            2.400
                                                     02



                                                                   02



                                                                                 02



                                                                                               02



                                                                                                             02



                                                                                                                           02



                                                                                                                                         02



                                                                                                                                                       02



                                                                                                                                                                     02



                                                                                                                                                                                   02



                                                                                                                                                                                                 02



                                                                                                                                                                                                               02



                                                                                                                                                                                                                             03



                                                                                                                                                                                                                                           03
                                                   20



                                                                 20



                                                                               20



                                                                                             20



                                                                                                           20



                                                                                                                         20



                                                                                                                                       20



                                                                                                                                                     20



                                                                                                                                                                   20



                                                                                                                                                                                 20



                                                                                                                                                                                               20



                                                                                                                                                                                                             20



                                                                                                                                                                                                                           20



                                                                                                                                                                                                                                         20
                                                 0.



                                                               0.



                                                                             0.



                                                                                           1.



                                                                                                         1.



                                                                                                                       1.



                                                                                                                                     1.



                                                                                                                                                   2.



                                                                                                                                                                 2.



                                                                                                                                                                               2.



                                                                                                                                                                                             2.



                                                                                                                                                                                                           2.



                                                                                                                                                                                                                         1.



                                                                                                                                                                                                                                       1.
                                              .1



                                                            .1



                                                                          .1



                                                                                        .1



                                                                                                      .1



                                                                                                                    .1



                                                                                                                                  .1



                                                                                                                                                .1



                                                                                                                                                              .1



                                                                                                                                                                            .1



                                                                                                                                                                                          .1



                                                                                                                                                                                                        .1



                                                                                                                                                                                                                      .0



                                                                                                                                                                                                                                    .0
                                            15



                                                          22



                                                                        29



                                                                                      05



                                                                                                    12



                                                                                                                  19



                                                                                                                                26



                                                                                                                                              03



                                                                                                                                                            10



                                                                                                                                                                          17



                                                                                                                                                                                        24



                                                                                                                                                                                                      31



                                                                                                                                                                                                                    07



                                                                                                                                                                                                                                  14
                                                                             Last Traded Prices Normalized Forecast                                           Average Traded Prices Normalized Forecast
                                                                             Actual interest rate                                                             Last observed interest rate


Figure 1. Mean forecast of ECB’s main refinancing rate on 15th January 2003.


    Whenever the ECB’s main refinancing rate has some predictable component we should
expect empirical variances of the forecasts to decrease in the course of time since the
market participants are getting more information over the market period. In figure 2 we
show the variances of the mean forecasts during the market period. In fact, the uncertainty
surrounding the forecast showed a decreasing tendency throughout the market period (see
figure 2).




                                                                                                       4. Forecast efficiency


While it is hardly possible to judge the absolute accuracy of the derived forecasts, we
can study in how far the used methodology is efficient in aggregating individual informa-
tion. As outlined earlier, the aggregation problem of individual expectations, based on
                                                                            Forecasting the ECB’s main refinancing rate                                                                                                           9




                              0.14


                              0.12


                              0.10
         Forecast variance




                              0.08


                              0.06


                              0.04


                              0.02


                              0.00
                                      02



                                                    02



                                                                  02



                                                                                02



                                                                                              02



                                                                                                            02



                                                                                                                          02



                                                                                                                                        02



                                                                                                                                                      02



                                                                                                                                                                    02



                                                                                                                                                                                  02



                                                                                                                                                                                                02



                                                                                                                                                                                                              03



                                                                                                                                                                                                                            03
                                    20



                                                  20



                                                                20



                                                                              20



                                                                                            20



                                                                                                          20



                                                                                                                        20



                                                                                                                                      20



                                                                                                                                                    20



                                                                                                                                                                  20



                                                                                                                                                                                20



                                                                                                                                                                                              20



                                                                                                                                                                                                            20



                                                                                                                                                                                                                          20
                                  0.



                                                0.



                                                              0.



                                                                            1.



                                                                                          1.



                                                                                                        1.



                                                                                                                      1.



                                                                                                                                    2.



                                                                                                                                                  2.



                                                                                                                                                                2.



                                                                                                                                                                              2.



                                                                                                                                                                                            2.



                                                                                                                                                                                                          1.



                                                                                                                                                                                                                        1.
                               .1



                                             .1



                                                           .1



                                                                         .1



                                                                                       .1



                                                                                                     .1



                                                                                                                   .1



                                                                                                                                 .1



                                                                                                                                               .1



                                                                                                                                                             .1



                                                                                                                                                                           .1



                                                                                                                                                                                         .1



                                                                                                                                                                                                       .0



                                                                                                                                                                                                                     .0
                             15



                                           22



                                                         29



                                                                       05



                                                                                     12



                                                                                                   19



                                                                                                                 26



                                                                                                                               03



                                                                                                                                             10



                                                                                                                                                           17



                                                                                                                                                                         24



                                                                                                                                                                                       31



                                                                                                                                                                                                     07



                                                                                                                                                                                                                   14
                                                                                        ATP normalized forecast                               LTP normalized forecast


Figure 2. Variance of ECB market forecasts.




dispersed information, is one of the major problems within the expectations approach of
forecasting.
   A concept for studying the efficiency of fixed-event forecasts has been developed by
Nordhaus [1987]. Efficiency of fixed-event forecasts requires that forecast errors should
be uncorrelated with past forecast revisions since such a correlation could be used to
decrease forecast errors. Moreover efficient time series of fixed-event forecasts should not
show any autocorrelation in forecast revisions. Such an autocorrelation could indicate
that newly arriving information is not incorporated into the market prices immediately.
   However, up to now the concept has rarely been applied since most time series of

forecasts are rolling-event forecasts. Nordhaus [1987] himself studied the efficiency 4 time
series (oil prices, nuclear capacity, energy and real GNP) of fixed-event forecasts. He found
significant autocorrelation of forecast revisions and thus empirical evidence in favor of
the hypothesis of social psychologists that people tend to hold on to prior views too long
(see Tversky and Kahneman [1981]). More recently, Bakshi, Kapetanios and Yates [2003]
studied the efficiency of 7 time series of fixed event inflation forecasts of surveys of fund
managers conducted by Meryll Lynch. The authors had to reject the hypothesis that the
10                             Forecasting the ECB’s main refinancing rate



forecast errors are uncorrelated with past revisions for 5 out of 7 time series of fixed event
forecasts. Similarly, 2 of the time series exhibited autocorrelation of forecast revisions.
     In order to study the efficiency of the ECB main refinancing rate forecasts derived
from the market we first analyze in how far the forecast errors are correlated with past
forecast revisions. We therefore run the OLS-regression

                     f               f      f              f      f
               rτ − rt = α0 + α1 · (rt−1 − rt−2 ) + α1 · (rt−2 − rt−3 ) + t .            (1)

The results of regression 1 are shown in table II. We find positive constants for both
forecasts. However, there is no significant correlation between past forecast revisions and
forecast errors.

                   Table II. Correlation between forecast errors and past forecast
                   revisions (OLS).
                                                      f      f         f      f
                    Market    Forecast   Constant    rt−2 − rt−1      rt−3 − rt−2
                                type     (t-value)    (t-value)        (t-value)

                     ECB       LTP          0.19         -1.22               -1.54
                                         (6.83)∗∗∗      (-1.01)             (-1.27)
                     ECB       ATP          0.17         -1.18               -1.53
                                         (6.11)∗∗∗      (-0.85)             (-1.10)

                    Significance levels are reported as follows: * for a 90%-
                    significance-level, ** for 95% and *** for more than 99%.




     In a second step we study in how far the forecast revisions are autocorrelated. We
therefore run the OLS regression

                               f    f           f      f
                              rt − rt−1 = β · (rt−1 − rt−2 ) + t .                       (2)

The estimation results are shown in table III. While the LTP forecast revisions show no
serial correlation the hypothesis of autocorrelated forecast revisions can not be rejected on
a 90-percent confidence level for the ATP forecasts. However, past ATP forecast revisions
only explain a minimal part of the observed forecast revisions. Nevertheless it seems that
forecasts based on last observed prices generate slightly more efficient forecasts than those
based on average figures.
                              Forecasting the ECB’s main refinancing rate                        11


              Table III. First-order autocorrelation of ECB main refinancing rate
              forecast revisions.

                  Market       Forecast type    Coefficient    T-statistic    p     r2

                ECB market         LTP             0.12          1.23      0.22   0.00
                ECB market         ATP             0.17          1.67      0.09   0.01




   Altogether, we can conclude that the ECB market performed quite well in efficiently
aggregating individual information. Thus, the experimental markets methodology delivers
a highly useful and efficient solution to the information aggregation problem.




                                        5. Conclusions


Initially, political stock markets were used to generate market data in field experiments
in order to study how individual market participants behave in market settings. The high
accuracy of the forecasts of election results derived from these markets indicate that the
experimental markets methodology also provides a useful tool for forecasting. The results
presented in this paper indicate that it might be useful to employ this methodology for
example to extract market expectations on the future use of monetary policy instruments
by the central bank.




                                           References

Aaker, D. A. and G. S. Day (1990):
   Marketing Research; 4th Edition, New York.
Bakshi, H., G. Kapetanios and A. Yates (2003):
   Rational Expectations and Fixed-event Forecasts: An Application to UK Inflation; Bank of England
   Working Paper, No. 176, Bank of England, London.
Berlemann, M. and C. Schmidt (2001):
   Predictive Accuracy of Political Stock Markets - Empirical Evidence from a European Perspective;
   Dresden Discussion Paper Series in Economics, Dresden 5/01, University of Technology.
Berg, J., R. Forsythe, F. Nelson and T. Rietz (2000):
   Results from a Decade of Election Futures Markets Research; Working Paper, College of Business
   Administration, University of Iowa.
12                            Forecasting the ECB’s main refinancing rate



Copeland, T. E. and J. F. Weston (1992):
   Financial Theory and Corporate Policy; 3rd Edition, Reading/Mass.
Croushore, D. (1996):
   Inflation Forecasts: How Good Are They?; Federal Reserve Bank of Philadelphia Business Review,
   May/June, pp. 1-11.
Ericsson, N. R. (2001):
   Forecast Uncertainty in Economic Modeling; in: D. H. Hendry and N. R. Ericsson (Eds.), Understand-
   ing Economic Forecasts, Cambridge/Mass, pp. 68-92.
Fama, E. F. (1975):
   Short-term Interest Rates as Predictors of Inflation; American Economic Review, Vol. 65 (3), pp.
   269-282.
Forsythe, R., F. Nelson, G. R. Neumann and J. Wright (1992):
   Anatomy of an Experimental Political Stock Market; American Economic Review, Vol. 82 (3), pp.
   1142-1162.
Lioui, A. and P. Poncet (2002):
   Revealing Inflation Expectations : Let the Market Do It; Working Paper, Bar Ilan University, Ramat
   Gan.
Lovell, M. C. and R. C. Vogel (1973):
   A CPI-Futures Market; Journal of Political Economy, Vol. 81 (2), pp. 1009-1012.
Miller, R. M., Ch. R. Plott and V. Smith (1977):
   Intertemporal Competitive Equilibrium: An Experimental Study of Speculation; Quarterly Journal
   of Economics, Vol. 91, pp. 599-624.
Mishkin, F. S. (1990):
   What Does the Term Structure Tell us About Future Inflation?; Journal of Monetary Economics, Vol.
   25, pp. 77-95.
Nordhaus, W. D. (1987):
   Forecasting Efficiency: Concepts and Applications; Review of Economics and Statistics, Vol. 69, pp.
   667-674.
Smith, V. (1962):
  An Experimental Study of Competitive Market Behavior; Journal of Political Economy, Vol. 70, pp.
  111-137.
Smith, V. (1964):
  Effect of Market Organization on Competitive Equilibrium; Quarterly Journal of Economics, Vol. 78,
  pp. 181-201.
Smith, V. (1965):
  Experimental Auction Markets and the Walrasian Hypothesis; Journal of Political Economy, Vol. 73,
  pp. 387-393.
Smith, V. (1976):
  Experimental Economics: Induced Value Theory; American Economic Review, Vol. 66, pp. 274-279.
Smith, V. (1982):
  Markets as Economizers of Information: Experimental Evidence on the ”Hayek Hypothesis”; Economic
  Inquiry, Vol. 20, pp. 165-179.
Smith, V. and A. W. Williams (1983):
  An Experimental Comparison of Alternative Rules for Competitive Market Exchange; reprinted in V.
  Smith (Ed.), Papers in Experimental Economics, Cambridge (1991).
Thomas, L. B. (1999):
  Survey Measures of Expected U.S. Inflation; Journal of Economic Perspectives, Vol. 13 (4), pp. 125-
  144.
                               Forecasting the ECB’s main refinancing rate                       13


Tversky, A. and D. Kahneman (1981):
   The framing of decisions and psychology of choice; Science, Vol. 211, pp. 453-458.
Williams, A. W. (1979):
   Intertemporal Competetive Equilibrium: On further Experimental results, Research in Experimental
   Economics, Vol. 1, pp. 255-278.
Williams, A. W. (1980):
   Computerized Double Auction Markets: Some Inital Experimental Results, Journal of Buisness, Vol.
   53, pp. 235-258.

				
DOCUMENT INFO