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The literature on estimating expectations models is vast and can quickly b
complex. An attempt has been made to explain only the main (limited i
methods currently in use. We shall concentrate only on those problems int
expectations variables and will not analyse other econometric problems that
arise (e.g. simultaneous equations problems). The reader is referred to intermed
metrics text books for the basic estimation methods (e.g. OLS,IV, 2SLS, GL
analysing time series data (e.g. Cuthbertson et a1 (1992) and Greene (1990)).
The rational expectations (RE) hypothesis has featured widely in the literat
begin by discussing the basic axioms of RE which are crucial in choosing an
estimation procedure. We also examine equations that contain multiperiod ex
In the next section, we discuss the widely used ‘errors in variables’ method
estimating structural equations under the assumption that agents have ration
tions. The use of auxiliary equations (e.g. extrapolative predictions) to generat
proxy variable for the unobservable expectations series give rise to two-step
and the pitfalls involved in such an approach are also examined.
Problems which arise when the structural expectations equation has serially
errors will then be highlighted. The Generalised Method of Moments (GMM
of Hansen (1982) and Hansen and Hodrick (1980) and the Wo-Step Wo-S
Squares estimator (Cumby et al, 1983) provide solutions to this problem.

20.4.1 The Economics of Expectations Models and the RE Hypothesis
This section analyses the various ways in which expectations variables are uti
applied literature and the implications of the economic assumptions for the
issues discussed in a later section.
Usually the applied economist is interested in estimating the structural pa
a single equation or set of equations containing expectations terms which form
of a larger model. (In a ‘full’ Muth-RE model (Muth, 1961) we would have
the whole model.) The simplest structural expectations equation can be repre



where:
of exchange is an unbiased estimate of the future spot rate then ylr = fr
the expected future spot rate. In the absence of data on Ex,+, (e.g. quantita
data) we must posit an auxiliary hypothesis for Ex,+,. Whatever expectations
choose, of key importance for the econometrics of the model are
(i) the forecast horizon.
(ii) the dating and content of the information set used in making the foreca
(iii) the relationship between the forecast error and the information set.
To develop these issues further it is useful to discuss the basic axioms of RE

Basic Axioms of RE
If agents have RE they act as if they know the structure of the complete mod
a set of white noise errors (i.e. the axiom of correct specification). Forecasts a
on average, with constant variance and successive (one-step ahead) forecas
uncorrelated with each other and with the information set used in making t
Thus, the relationship between outturn x,+l and the one-step ahead RE fo
using the complete information set 52, (or a subset A,) is:

+
= r$+1
&+l W,+l

where




The one-step ahead rational expectations forecast error @,+I is ‘white noi
‘innovation’, conditional on the complete information set 52, and is orthogona
of the complete information set (A, c 52,).
The k-step RE forecast errors (k > 1) are serially correlated and are MA
demonstrate this in a simple case assume x, is AR(1).




From (20.88) it is easy to see that:


while the two-period ahead forecast error is:
are independent of (orthogonal to) the information set n, (or At). There is
property of RE that is useful in analysing RE estimators and that is the form
to expectations. The one-period revision to expectations


+ 1 and hence from
depends only on new information arriving between t and t
easily seen to be
[t+lxF+j- tx;+j] = @-'wr+l

The two-period revision to expectations


will of course depend on ot+l and and be MA(1): one can generalise th
0t+2
k-period revisions to expectations.

Direct Tests of RE
Direct tests of the basic axioms of RE may involve multiperiod expectatio
immediately raises estimation problems. For example, if monthly quantitative
is available on the one-year ahead expectation, txf+12, test of the axioms oft
a
a regression of the form:
PO+ Pl[tx;+121+ + qr
xr+12 = P2Ar
where
H o : PO = 82 = 0, =1
Under the null, qr+12 is MA(11) and an immediate problem due to RE is the
some kind of Generalised Least Squares (GLS) estimator if efficiency is to be a
course, for one-period ahead expectations where data of the same frequency
the error term is white noise and independent of the regressors in (20.93): OL
provides a best linear unbiased estimator.
An additional problem arises if the survey data on expectations is assu
measured with error. If the true RE expectation is txf+12 and a survey data
measure r.?f+12 where we assume a simple linear measurement model (Pesara
+ Er
+
= a0 Ql[rx;+121
tz;+12
Then substituting for r ˜ f + 1 2from (20.94) in (20.93):


where
able instrument set. However, it is not always simply the case that A t prov
instrument set for the problem at hand.

The E VM and Extrapolative Predictors
In order to motivate our discussion of the estimation problems in the next two
is useful at this stage to summarise some of the problems encountered when e
structural expectations model: problems that arise include serial correlation and
between regressors and the error term. For illustrative purposes assume th
model of interest is:
+ 82[rX;+21+
Yr = 61[rn;+,l ur

ur is taken to be white noise and xr is an exogenous expectations variable
assumption of RE we have
+ wt+j
= tx;+j
xr+j


A method of estimation widely used (and one of the main ones discussed in t
is the errors in variables method (EVM), where we replace the unobservable
realised value xr+,. This method is consistent with agents being Muth rationa
also be taken as a condition of the relationship between outturn and forec
invoking Muth-RE. Substituting from (20.97) in (20.96)




Clearly from (20.97)xt+ j and wt+j are correlated and hence plim [xi+j & r ]/T #
#
and E(&&’) 0:1 because of the moving average error introduced by the
errors Hence our RE model requires some form of instrumental variable
procedure with a correction for serial correlation. These two general problems
focus for this section.

20.4.2 The Errors in Variables Method EVM
The EVM is a form of IV or 2SLS approach. Under RE, the unobservable
variable rxf+j is determined by the full relevant information set 52,. In the EVM
the true information set Ar(C Q r )is sufficient to generate consistent estimate
first it is shown that OLS yields an inconsistent estimator.

One-Period Ahead Expectations: White Noise Structural Error
It is important to note that here we are dealing with a very specific expecta
The simplest structural model embodying one-period ahead expectations is:

+ ur
Yr = Bx,’,,
at (or A
and the RE forecast error wr+l is independent of the information set
E(Q:w+l) = 0
Substituting (20.101) in (20.99) we obtain
+ 4t
Yr = b r + l
4 = (U1 - B W r + l )
1
Consider applying OLS to (20.103) we have:

B = B + (xr+l’xr+l )-l (xr+1’4r)
From (20.101):

+ plim(w,+i’wt+l ) / T
plim(˜r+l’xt+l/ T = plim($+l’xf+l ) / T
)
on rewriting this more succinctly:

+ aw
0 = axe
2 2
;

From (20.101) and (20.104) and noting that xF+l is uncorrelated in the limit w

-w:
plim(xr+l’qr)/T = -B plim(o,+l’w+l)/T =
Substituting these expressions in (20.105):




Thus the OLS estimator for #? is inconsistent and is biased downwards. The bia
the smaller is the variance of the ‘noise’ element 0: in forming expectations.

Instrumental Variables: 2SLS
OLS is inconsistent because of the correlation between the RHS variable x
error term qf which ‘contains’ the RE forecast error or+l. solution to th
The
is to use instrumental variables, IV, on (20.103). However, to illustrate some
nuances when applying IV consider the following model:
+ Bx2t + + ˜r
= Qes
= (YX;,+˜
yr ut


B)’
Q‘ = Ix;r+i, ˜ 2 1 ) 6 = (a,
where x:t+l, x2, are asymptotically uncorrelated with ur. Direct application
(20.110) would require an instrument for xlf+l from a subset of the infor
The researcher is now faced with two options. Direct application of IV would
instrument matrix
w = h + l ’ X2t)
1
Where xa acts as its own instrument, giving




This is also the 2SLS estimator since in the first stage xlr+l is regressed
predetermined (or exogenous variables) in (20.1 10) and the additional instrum
An alternative is to replace in (20.110) by i l , + l and apply OLS to:




This yields a ‘two step estimator’ but as long as xlf+l is regressed on all the pre
variables, then OLS on (20.114) is numerically equivalent to the 2SLS estimat
therefore consistent. However, there is a problem with this approach. The OL
from (20.117) are:
A


e = yr - $ i l t + l - 19x2
but the correct (IV/2SLS) residuals use Xlr+l and not and are:
ilr+l
h



el = y - hXlr+l - BX2r
Hence the variance-covariance matrix of parameters from OLS on (20.117) a
since s2 = e’e/T is an incorrect (inconsistent) measure of cr2 (Pagan, 1984). Th
straightforward, however; one merely amends the OLS programme to produce
residuals el in the second stage.

Extrapolative Predictors
Extrapolative predictors are those where the information set utilised by the econ
is restricted to be lagged values of the variable itself, that is an AR ( p ) mode




The maximum value of p is usually chosen so that er is white noise. OLS
(20.121) yields one-step ahead predictions
x:t+l or to replace x;r+l in (20.110). Using iTr+l an instrument for x;r+l an
as
˜ 2 in the instrument matrix W1 gives consistent estimates. Now consider the
t
method. Having obtain i;t+l the ‘first stage’, the second-stage regression
in
OLS on:
+ Bx2r + 4:
Yr = a?i:r+I
+ a(Xfr+I - x l r + l ) - a?(?lt+l - x1r+1)
4r = ur
Compared with the EVM/IV approach (see equations (20.103) and (20.104))
additional term ( i l t + l -xlt+1) in the error term of our second-stage regressio
The term (xlt+1- is the residual from the first-stage regression (20.12
The variable xzt is part of the agent’s information set, at time t , and may t
used by the agent in predicting x1r+1. If so, then (Xlr+l - and the ‘omitt
from the first-stage regression, namely X Z ˜ are correlated. Thus in (20.124) the
,
between the RHS variable x2t and a component of the error term q: implies t
(20.124) yields inconsistent estimates of (a?, B) (Nelson, 1975). This is usuall
in the literature as follows: if ˜ 2 rGranger causes Xlt+l then the two-step
inconsistent. This illustrates the danger in using extrapolative predictors an
xf+l in the second-stage OLS regression, rather than using 2Tr+l as an inst
applying the IV formula. Viewed from the perspective of 2SLS, the inconsis
second stage (20.124) arises because in the first-stage regression, the research
use all the predetermined variables in the model, he erroneously excludes ˜ 2
paradoxically then, even if ˜2˜ is not used by agents in forecasting Xlt+l it must
in the first-stage regression if the two-step procedure is used: otherwise (Xlr
may be correlated with x;?t. Of course, if the two-step procedure is used and
B)
estimates (&, are obtained, the correct residuals calculated using Xlr+l and n
in equation (20.120)) must be used in the calculation of standard errors.

20.4.3 Serially Correlated Errors and Expectations Variables
Up to this point in our discussion of appropriate estimators we have assumed
errors in the regression equation. We now relax this assumption. Serially corre
may arise because of multiperiod expectations or because of serially correlate
errors. In either case, we see below that two broad solutions to the problem a
The first method uses the Generalised Method of Moments (GMM) approach
(1982) and ‘corrects’ the covariance matrix to take account of serially correl
The second method is a form of Generalised Least Squares estimator under
known as the Two-Step Two-Stage Least Squares estimator (2s-2SLS) (Cu
1983). These two solutions to the problem are by no means exhaustive but
widely used in the literature.

The GMM Approach
This approach is demonstrated by first considering serial correlation that arises i
with multiperiod expectations and then moving on to consider serial correla
structural error.
+ ur
+
Yr = B1x,4tl B2xt4t2

= E(xr+jIQt) ( j = 1,2)
-$+j

RE implies:
+ qt+j
= -$+j ( j = 192)
xt+j

and substituting (20.128) in (20.126) we have our estimating equation:
+ + qr
Yr = B l X r + l B2Xr+2

qr = ur - Bl%+l - B2%+2
2SLS on (20.129) with instrument set A, will yield consistent estimates
However, the usual formula for the variance of the IV estimator is inco
presence of serial correlation and qr is MA(1). Hansen and Hodrick (1980
‘correction’ to the formula for the variance of the usual 2SLS estimator. Putti
in matrix notation:
Y=XP+q
The 2SLS estimator for is equivalent to OLS on
+q
y = Xb*
2 = (%+lc %+2)

= 1,2) on A r
and i t + j are the predictions from the regression of Xr+j(j
estimator is:
b* = ( X X ) - ’ ( X y )
with residuals:
e*=y-m*

Note that in the calculation of e* we use X and not X. To calculate the corre
of /?in the presence of an MA(1) error, note that the variance-covariance m
.. 0
1 p1 0 .......
P1 1 P 1 0 -.
0 P 1 1 . P1
0
-1 P1
**

0 ...........
0 1
p1

where p1 is the correlation coefficient between the error terms. Since ef ar
the consistent estimator b*, then consistent estimators of oi,0; and p are g
following ‘sample moments:
Knowing I: we can calculate the correct formula for var(b*) as follows. Sub
(20.131) in (20.134):
+
b* = B (XX)-’Xq

Since plim(T-’)(Xq) = 0, then b* is consistent and the asymptotic varian
given by:

[
var(b,) = T-’ plim P 1lX‘ [qq’] X [X’XI-’]
X-

PkX]
var(b,) = 0; [a’X]-’ [XX]-’

Above, we assume that the population moments are consistently estimated by t
equivalents. Note that var(b*), the Hansen-Hodrick correction to the covarianc
b*, reduces to the usual 2SLS formula for the variance when there is no seria
(i.e. I: = 0˜1). The Hansen-Hodrick correction is easily generalised to the cas
have an MA(k) error, we merely have to calculate $s(s = 1,2, . . . k) and sub
estimates in I:.
The Hansen-Hodrick correction to the standard errors can also be applied
mation of /?in (20.131) can proceed using OLS. In this case the Hansen-Hodri
for var(b) is given by (20.141)but with X replacing X and the elements of C ar
using the consistent OLS residuals.
In the above derivation we have assumed that the error term is homoscedastic
if the error term is heteroscedastic, as is usually the case with financial data,
also be recomputed to take account of this problem.

A Two-Step Two-Stage Least Squares (2s-2SLS) Estimator
So far we have been able to obtain a consistent estimator of the structural para
(20.126) under RE by utilising IV/2SLS or the EVM. We have then ‘correcte
formula for the variance of the estimator using the Hansen-Hodrick formula
the Hansen-Hodrick correction yields a consistent estimator of the variance it
to obtain an asymptotically more efficient estimator which is also consistent. C
(1983) provide such an estimator which is a specific form of the class of
instrumental variables estimators. The formulae for this estimator look rather
If our structural expectations equation after replacing any expectations variab
outturn values is:
Y=XB+S
with
E(qq’) = a21:and plim[T-’(X’q)] # 0
Then the 2s-2SLS estimator is:
’ ’ ’
= [X’A (A’ A )- A’XI- [X’A (A’ A )- A ’y ]
I: I:
bg2
the error term. We have already discussed above how to choose an appropriate
set and how a ‘consistent’ set of residuals can be used to form 2. This ‘first-stag
of can then be substituted in the above formulae, to complete the ‘second s
estimation procedure (see Cuthbertson (1990)).
In small or moderate size samples it is not possible to say whether the Hanse
correction is ‘better than’ the 2S-2SLS procedure since both rely on asympt
Hence, at present, in practical terms either method may be used. The one clear
emerges, however, is that the normal 2SLS estimator for var(B) is incorrect an
be taken in utilising Cochrane -0rcutt-type transformations to eliminate AR e
this may result in an inconsistent estimator for B.

Summary
There are two basic problems involved in estimating structural (single) equation
expectations terms (such as equation (20.126)) by the EVM. First, correlatio
the ex-post variables xl+j and the error term means that IV (or 2SLS) estimati
used to obtain consistent estimates of the parameters. Second, the error term is
serially correlated which means that the usual IV/2SLS formulae for the varia
parameters are incorrect. l b o avenues are then open. Either one can use the I
to form the (non-scalar) covariance matrix (a2X) and apply the ‘correct’ IV
var(b*) (see equation (20.141)). Alternatively, one can take the estimate of a2
a variant of Generalised Least Squares under IV, for example the 2S-2SLS es
var(&2) in equation (20.145).


FURTHER READING
There are a vast number of texts dealing with ‘standard econometrics’ and a
clear presentation and exposition is given in Greene (1990). More advanced
provided in Harvey (1981)’ Taylor (1986) and Hamilton (1994) and in the latt
larly noteworthy are the chapters on GMM estimation, unit roots and changes
Cuthbertson et a1 (1992) give numerous applied examples of time series tec
does Mills (1993)’ albeit somewhat tersely. A useful basic introduction to
‘general to specific’ methodology is to be found in Charemza and Deadman (
a more advanced and detailed account in Hendry (1995). ARCH and GARCH
in a series of articles in Engle (1995).
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Index
Akaike information criterion, 339 Box Jenkins methodology, 422, 43
Anomalies, 169, 185 Bretton Woods, 255, 256, 290, 299
Anti-inflation policy, 207, 250 Bubble, 156-168, 193, 195, 301, 3
Arbitrage, 63, 172, 259, 268-271 collapsing, 157, 162, 163, 167,
Arbitrage pricing theory (APT), 61-67, 74, 75, exogenous, 157, 161, 302
129, 401 explosive, 156, 162
Arbitrageurs, 174, 179 intrinsic, 157, 163- 167, 360
ARCH model, 43-45, 183, 202, 375-380, rational, 156-163, 167, 195, 30
389, 398-415,438-442 Budget constraint, 49, 223, 391, 39
ARIMA models, 286, 287, 398, 420-442 Budget deficit, 393
ARMA models, 117, 126-127, 151-153, 161, Bullish, 182, 183, 203
339, 382, 421, 422, 426-437 BZW equity index, 367
Asset demand, 54-57
Augmented Dickey Fuller test (see Dickey-
Fuller test) Capital asset pricing model (CAPM
Autocorrelation, 421, 422, 426 82-88, 96, 97, 103, 122, 127
Autocovariance function, 422, 426 177, 178, 190, 221, 222, 248,
Autoregressive models (see ARMA models) 373-377,381-412
consumption (see consumption
post-tax, 72, 73
Bankruptcy, 177, 201 zero beta, 48-54, 69, 234, 248,
Bearish, 182, 183, 203, 204 Capital gaidloss, 345, 363, 364, 3
Beta, 24, 41-46, 57-61, 70-73 Capital market, 19, 187
Bid-ask spread (see also spread), 124, 173 Capital market line (CML), 37-39,
Big-Bang, 174 Capital mobility, 291 -293
Black Wednesday, 256, 257 Central bank, 207, 266, 271, 280,
Bond, 3-10, 178, 208, 211-227, 234, 250, Chaos, 169, 176, 195, 196, 205-29
297, 309, 311, 313, 375, 401, 402, Chartists, 174, 179, 194, 198-201,
407-41 331
corporate, 207, 212, 237, 272, 379, 392, Chi-squared distribution (see distri
393 Closed end fund, 170-173, 185
coupon paying, 8, 212, 246, 249 Cochran-Orcutt transformation, 452
government, 189, 207, 212, 326, 392, 393, Cointegration, 162, 302, 328, 329,
434 -438
397, 398
zero coupon, 212, 229, 234, 340, 402, 413, Commercial paper, 353, 356
414 Consol (see Perpetuity)
pure discount, 7, 212, 213, 241, 245, 249, Consumer Price Index, 368
331, 402 Consumption, 294, 353, 355, 368,
Bond market, 207-214, 234, 249, 315, 332, 408
344, 374,376,402-411 Consumption CAPM (CCAPM), 7
Bond price, 211-218,246-247 128, 133-140, 408
Cost mark up equation, 431 Ordinary least squares (OLS), 1
Covariance conditional, 409-413, 438 242, 244, 253, 272, 276, 27
Credit limit, 271 324, 325, 373, 435, 443-45
Currency, 255, 261, 292, 305-307, 376, 444 Seemingly unrelated regression
(SURE), 276, 324, 334, 39
Euler equation, 77-85, 138, 154- 1
Data, 237, 277-284, 302, 328, 403, 444
302
Debt-equity ratio, 379
Eurocurrency market, 268
Detrending, 344, 425, 426
Eurocurrency rate, 269, 271, 397
Devaluation, 270, 282, 283
European Monetary System (EMS)
Diagnostic test, 129, 342, 351, 430
Excess holding period yield (see H
Dickey Fuller test (DF test), 435
Excess volatility (see volatility)
Discount factor, 136, 344, 373, 380, 381
Exchange rate, 194, 200-207, 255
Discount rate, 346-350, 360-367, 378
290-307, 376,417
Discounted present value (DPV), 3-21, 76-88,
fixed/floating, 255-257, 271, 28
104- 112, 136- 147, 178, 188, 208-216,
real, 262-265, 292, 298
311, 350, 363-365, 378-381
Exchange Rate Mechanism (ERM)
Distribution, 58, 71, 100, 111, 126, 152, 168,
290, 300
182, 183, 321, 386, 392, 418, 419, 434,
Exchange rate overshooting, 256, 2
441
291 -295
Dividend, 9, 10, 346-352, 359-368, 372,
Expectations
380-387, 434
mathematical, 100- 102, 114
Dividend price ratio, 346-354, 359, 360,
Rational (see Rational expectati
366-369, 375, 377, 387
Dornbusch overshooting model, 293-295 revision to, 363, 364
Dow Jones index, 130, 161 Expectations hypothesis (EH), 208
Duration, 217 219-232, 237, 240-252, 309-
339-340, 348, 403-408, 443
Extrapolative predictor, 447-449
Earnings, 360
Earnings price ratio, 355
Economic fundamentals (see fundamentals)
Factor analysis see APT)
Economic model, 417, 427, 431, 432
Fads, 175, 183, 185, 202, 342, 360
Economic theory, 417, 431 -433
Fair game, 77, 94, 96, 100-104, 15
Economic time series (see time series)
Federal Reserve, 244, 404
Efficiency (see informational efficiency)
Feedback trader, 118-120, 179, 38
Efficient frontier, 25, 29-33, 37
Fisher hypothesis, 226, 265, 292, 2
Efficient markets hypothesis (EMH), 44,
Flex-price monetary model, 290-30
93-100, 105-129, 134, 143-152,
Forecast, 311-316, 323-335, 346-3
169-181, 194, 201, 208-215, 231-234,
359, 360, 380, 410, 424, 425,
249,265, 269-288,309-315,338-368,
444,449
377, 387,438
conditional, 422-426
Efficient portfolio (see portfolio)
multiperiod, 320, 334, 339, 342
EMU 257
unconditional, 415
Employment, 207, 256, 293, 294, 303
Forecast error, 242, 250, 283, 310,
Error correction model, 306, 342, 343,
434-437 341,353,363,365,377-391,40
Errors in variables method (EVM), 443-452 422,427,438-447
Estimation Forecasting
2 stage least squares (2SLS), 272, 275, 403, chain rule of forecasting 311, 32
443-452 Forecasting equation, 311, 312, 318
Generalised least squares, 443, 445, 452 359, 364
281-288, 293-300,304-30
288, 334, 337
397
Forward premium, 252, 253, 275-278, 289,
testing, 268-289
303, 305, 334-340
Internal rate of return, 6-21
Forward rate, 251, 252, 259-268, 273-280,
International Fisher hypothesis (se
288, 334-340
hypothesis)
Forward rate unbiasedness (FRU), 264-268,
International Monetary Fund (IMF
272-289,334-342
Investment appraisal 6, 15-20

GARCH model, 183, 301, 377, 383-389, 400, January effect, 123, 129, 169-173
406, 415, 438-442, 452 Johansen procedure, 434, 437
Gaussian error, 418, 426
Gearing, 190, 389, 393
Geometric random walk (see random walk) Lag operator, 418-421
Gordon’s growth model, 135, 164, 347, 359 Leverage, 379
Granger causality, 325-330, 348-354, Likelihood ratio test, 309, 315-31
433-438, 449 336, 396,411
Linear combination
Linearisation, 363, 368
Herding, 156, 175, 176, 190, 202 Liquidity preference hypothesis, 2
Holding period return yield (HPY), 9, 10, 219-221, 228, 231-237, 252
208-253, 331, 345, 353, 358, 368, 376, Liquidity premium (see risk prem
397-414 London Interbank Rate (LIBOR, L
Hyperinflation, 262, 292, 298, 300 326-328

MA process (see also ARIMA mo
Indifference curve, 3, 10-18, 38, 39, 50, 55-57
123, 420-423,437
Inflation, 54, 108, 130, 207, 218, 226, 252,
Maastricht Treaty, 288
256, 263-267, 272, 295, 300-307, 378, Marginal rate of substitution (MR
393, 400-406, 431 Market psychology, 156, 285
Information set, 261, 312, 327, 330-341, Market segmentation hypothesis,
348-369,386,396,404-411,423,426, 219-223, 231, 243, 331, 404
433, 443-452 Markov switching model, 127, 16
Informational efficiency, 105- 117, 138- 142, Martingale, 94, 99-104, 113, 159
147-150, 159,265, 283, 309-310, 315, 244, 249, 250, 301
368, 404, 406 Matrix
semi strong form, 105 companion, 322, 372
strong form, 105 variance-covariance, 227, 242,
weak form, 105, 117, 128, 133 321-325, 365, 373, 396, 4
Insider information, 105 Maturity spectrum, 213, 245-249
Integrated GARCH (IGARCH) (see GARCH 326, 331, 332, 402
model) Mean reversion, 172, 178-185, 2
Interest rate, 3-20, 33-73, 130, 207-212, 243, Mean variance criterion, 26, 30
244, 259-269, 290-298, 309, 315-333, Mean variance model, 179, 375,
375 -409 399, 405
continuously compounded, 3-8, 20, Measurement error, 397, 401, 407
211-233, 251, 414 Merger, 19, 93, 105, 113
Modigliani-Miller theorem, 99, 1
real, 104, 257, 290-293,
Money market, 293, 294
risk free, 10-25, 33, 34, 48-65, 82-116,
Money market line, 17
121, 146, 214, 220-237
Pure expectations hypothesis (PEH
expectations hypothesis)
NAIRU, 431
Net present value (see discounted present
Random walk, 94, 104, 105, 122-1
value) 143-150, 162, 183, 194, 195,
Neural network, 202, 205, 302 299-306, 342,400,419-426
Neutrality of money, 291 -294 Rate of return, 3-5, 49, 98, 235-24
Noise trader, 118-128, 169-204, 258, 282, Rational expectations, 94- 123, 145
284, 288, 299-307, 375-377, 380, 201, 227-232, 242, 243, 250,
387-390 302-332,350-355,402-406,4
Non-stationarity (see stationarity) Rational valuation formula (RVF),
NYSE, 129, 133, 172, 365, 384,400 116-118, 143-155, 162, 179,
211-215, 220, 223, 311-313,
353-367
OECD, 300,326 Real interest differential model (RI
Omitted variables, 149, 399, 436, 437, 449 295 -298
Orthogonality condition, 94- 110, 138- 141, Real interest rate parity (see intere
147-154, 167, 248, 272, 281, 319, 323, parity)
325, 336, 444 Real interest rate (see interest rate)
Output, 256, 378-380, 431 Redemption yield (see yield to ma
Restriction
cross equation restriction, 298, 3
Pension fund, 170, 173, 176, 207, 332 315-323, 335-344, 353,35
Perfect foresight linear restriction, 349
rate, 224, 228-234 non-linear restriction, 324, 349,
regression, 331 Return (see also rate of return)
price, 178, 215, 240, 311, 344, 345, 350, excess, 41-112, 128-135, 159,
351, 358, 360 222, 345,349-357,383-407
spread, 208, 225, 227, 231, 237, 242, 245, expected, 23-104, 124, 149, 152
246, 319, 325-330 260,352,363-374,387-400
Performance index, 25, 47, 57-61, 131, 132 linearisation, 368, 369
Perpetuity, 9, 212, 216, 240 multiperiod, 358-368
Persistence, 176, 183, 344, 352, 361-390, 400, Risk, 20-45,54-67, 259,270,357
412,413, 440, 442 402-414
Peso problem, 147-252, 258, 279, 282-284, default, 212
288, 299, 301 fundamental, 174
Phillips curve, 266, 267, 291-294 idiosyncratic/specific, 62, 63
Plaza and Louvre accord, 256, 301 market price of, 20, 38, 39, 384
Portfolio, 24-89, 121, 172- 178,381-399 409
efficienthefficient, 26 measures of, 45, 394, 404-408
market, 24, 40, 44, 73, 121, 178, 381, 399 reinvestment, 214
optimal, 22, 35 risk averse, 3-24, 55, 58, 86, 87
Portfolio balance model (PBM), 296-298 140, 181, 185, 199, 203, 27
Portfolio diversification, 22, 25 -31 391-405
Predictability, 122, 184, 358, 361-372 risk lover, 10-20
Preferred habitat hypothesis, 208, 219, 223 risk neutral, 10-20, 76, 82-87,
Present value (PV) (see discounted present 242, 261-305, 334, 342, 40
risk premium, 7, 214-232, 237,
value)
245-253, 272-279, 289, 33
Price competitiveness, 255
375-390,402-411
Price index, 128, 139, 267, 384
svstematichnsvstematic. 41 -43
Principle agent problem, 20 . ,
d
Separation principle, 16, 20, 23, 37, 50, 53 403, 404
Short termism, 98, 113, 185-190, 204 Trend
Single index model (SIM), 67-69, 204 deterministic, 139, 143, 144, 16
Small fr effect, 170, 173 426, 435
im
Smart money, 169, 173-204, 243, 303-307, stochastic, 143, 415, 425, 426,
377, 380,388-389
Spread, 226-245, 309-333, 348, 350, 402-411
Spurious regression, 426, 434 Utility, 3, 10-20, 55, 58, 84-88,
Stability, 353, 430, 438 391-394
Standard and P w r s composite share index,
122, 123, 128-130, 161-166, 357, 359,
380-382 Value line investment survey (VLI
Standard deviation ratio, 138, 139, 325, 350, VAR, 227, 268, 286, 287, 298, 30
353, 354 402, 428-438, 449
Stationarity, 141, 142, 162, 193, 418-437 advantageldisadvantage, 323-32
Statistical model, 417, 431, 432 cross equation restriction, 309-
Sticky price monetary model, 290-303 336-342, 350
Stock return predictability, 122- 134, 184, multivariate, 339, 365
353- 357 Variance conditionaVunconditiona1
Stock market, 116-156, 176, 351, 377 373, 383-389, 402, 405-413
Stock price, 116-155, 344-373, 380-390 438, 439, 442
Structural model, 431-438 Variance bounds test, 116, 136, 13
Sunspots, 156 208, 215, 226-234, 246-249
344, 351, 360, 361, 368
Variance decomposition, 352, 365
Takeover, 19, 93, 98, 105, 113, 148, 149, 186, Variance ratio, 116, 117, 125, 138
188, 202-204 160, 178, 229, 246, 248, 309
Tax, 52-54, 72, 73, 97, 99, 169, 170, 189, 324-330,337,353-361
271,401 Variance-covariance matrix (see m
Term premium (see risk premium) VARMA model, 428-437
Term structure, 5-7, 209, 216-230, 249, 251, Volatility, 134- 146, 169, 178, 183
312, 315-340, 345, 348, 402-414, 437 249, 258, 279-282,300, 327
empirical evidence, 234-253 404,406, 413
Term to maturity, 213, 214, 226, 247-250, Volatility tests (see variance boun
402,408,409
Terms of trade, 292
Time series
Wald test, 315-361
stationaryhon-stationary,419, 425, 426, 434
Weekend effect, 96, 123, 169, 170
univariate/multivariate,415, 417-438
White noise, 143, 274, 275, 334, 3
Time varying
419,427-429,437,446-449
beta, 402, 406
Winner’s curse, 172, 173
discount rate, 140, 346, 348, 354, 368
Wold’s decomposition theorem, 42
real interest rates, 139
risk/term premia, 152, 209, 219-222,
227-231, 246-249,276, 277, 342-348,
Yield (see interest rate)
355, 375-377, 387-391,401-414,438
dividend, 348, 387, 388
variances/covariances, 221, 368, 375, 376,
spot, 7, 212, 213, 223-234
383,387-390, 398-401,409-415,442
Yield curve, 7, 207, 226, 231, 250
Tobin’s risk aversion model, 54-57
Yield spread (see spread)
Trading rule (see trading strategy), 124,
Yield to maturity, 8, 208-217, 22
130-135, 202, 309, 380, 385
240, 246, 249, 402
Transformation line, 25, 33-36, 55

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