ńňđ. 14 |

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 â€˜errors in variablesâ€™ 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 â€˜fullâ€™ 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 â€˜white noi

â€˜innovationâ€™, 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(&&â€™) 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,â€™,,

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+lâ€™xr+l )-l (xr+1â€™4r)

From (20.101):

+ plim(w,+iâ€™wt+l ) / T

plim(˜r+lâ€™xt+l/ T = plim($+lâ€™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+lâ€™qr)/T = -B plim(o,+lâ€™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 â€˜noiseâ€™ element 0: in forming expectations.

Instrumental Variables: 2SLS

OLS is inconsistent because of the correlation between the RHS variable x

error term qf which â€˜containsâ€™ 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)â€™

Qâ€˜ = 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 â€™ 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 â€˜two step estimatorâ€™ 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 = eâ€™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 â€˜first stageâ€™, 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 agentâ€™s information set, at time t , and may t

used by the agent in predicting x1r+1. If so, then (Xlr+l - and the â€˜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 â€˜correctsâ€™ 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

â€˜correctionâ€™ 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 ) - â€™ ( 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 â€˜sample moments:

Knowing I: we can calculate the correct formula for var(b*) as follows. Sub

(20.131) in (20.134):

+

b* = B (XX)-â€™Xq

Since plim(T-â€™)(Xq) = 0, then b* is consistent and the asymptotic varian

given by:

[

var(b,) = T-â€™ plim P 1lXâ€˜ [qqâ€™] X [Xâ€™XI-â€™]

X-

PkX]

var(b,) = 0; [aâ€™X]-â€™ [XX]-â€™

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 â€˜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(qqâ€™) = a21:and plim[T-â€™(Xâ€™q)] # 0

Then the 2s-2SLS estimator is:

â€™ â€™ â€™

= [Xâ€™A (Aâ€™ A )- Aâ€™XI- [Xâ€™A (Aâ€™ A )- A â€™y ]

I: I:

bg2

the error term. We have already discussed above how to choose an appropriate

set and how a â€˜consistentâ€™ set of residuals can be used to form 2. This â€˜first-stag

of can then be substituted in the above formulae, to complete the â€˜second s

estimation procedure (see Cuthbertson (1990)).

In small or moderate size samples it is not possible to say whether the Hanse

correction is â€˜better thanâ€™ 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 â€˜correctâ€™ 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 â€˜standard econometricsâ€™ and a

clear presentation and exposition is given in Greene (1990). More advanced

provided in Harvey (1981)â€™ 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)â€™ albeit somewhat tersely. A useful basic introduction to

â€˜general to specificâ€™ 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

Gordonâ€™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

Winnerâ€™s curse, 172, 173

discount rate, 140, 346, 348, 354, 368

Woldâ€™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

Tobinâ€™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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