Assessing Structure in Monetary Policy Models∗
Ragnar Nymoen
University of Oslo
2 May , 2005.
Abstract
Structural models carry positive connotations in economics. Hence proponents of alternative theories and modeling strategies compete about priority to
label their models as structural. When policy decisions hinge on model properties, the debate about ‘structure’ has potentially important consequences.
The consensus view today is to define “structural models” as synonymous with
systems of equations that are lifted from modern Walrasian macroeconomics.
In this paper we discuss a wider operational definition of a model structural
properties. We define structural property as a many faceted model feature,
e.g., theory content, explanatory power, stability and robustness to regime
shifts. It follows that structural properties, and a structural representation of
the economy, are not guaranteed by a close connection to microfoundations. If
the modelling purpose is to assist monetary policy, a stand must be taken on
issues relating to wage and price making behaviour. Therefore, our examples
are i) the New Keynesian Phillips curve, and ii) a non-Walrasian approach
to inflation modelling based on the idea that in modern economies the rents
generated by the operation of the firm is shared between workers and firms.
1
Introduction
Different monetary policy models is often characterized along a (general) theorydata dimensions, as discussed in Pagan (2003). The trade-off at first appears to be
evident: Direct translation of theoretical relationships to econometric specifications
are likely to lead to misspecified models with inefficient estimates and unnecessary
bad forecasts. On the other hand, relevant theory is needed to get a clear interpretation of estimation results and of model properties.
The appeal of the postulated trade-off between theoretical and empirical coherence (Pagan’s terminology) is that both model builders and model consumers
(e.g., those using models as an aid in policy decision making) can recognize the
balance between theoretical input and data instigated formulation of the model’s
∗
This paper is an extension of Nymoen (2002) and builds on a lecture given at the Economic
Research Centre, Department of Economics, Middle East Technical University, Ankara, 7 April
2003. Thanks to Bjørn Naug for comments and discussion. It also draws on joint work with
Gunnar Bårdsen, Øyvind Eitrheim and Eilev S. Jansen, see Bårdsen et al. (2005). The numerical
results were produced by PcGive 10, Doornik and Hendry (2001) and EViews 5 (provided by
Quantitative Micro Software). Please address correspondence to: Ragnar Nymoen, University of
Oslo,Department of Economics, P.O. Box 1095 Blindern, N-0317 Oslo, Norway. Phone: + 47 22
85 51 48. Fax + 47 22 50 35 35. Internet: ragnar.nymoen@econ.uio.no
1
equations. But the intuitive appeal of the Pagan-frontier can also be misleading, for
example if it is used as a rationale for picking a particular model ‘along the frontier’.
After all the Pagan-frontier is just a construction, and there is no practical way of
telling whether a particular structural VAR or a particular dynamic stochastic general equilibrium model, DSGE, are ‘on the frontier’ and that the only difference
between them is the degree of data/theory coherency. In practice, the (real) reasons
for choosing one model or the other is much more complex include both established
knowledge and subjective beliefs about what is the best theories and econometric
techniques to use. Moreover, the preferences that model producers have about the
theory-data balance (and other aspects of the model specification and evaluation)
is general not shared by the consumers of models, see Granger (1990).
A possible side-effect of Pagan’s trade-off figure, is to encourage attitudes
saying that ‘if only my theory model is good enough (state of the art)’ then ‘anything
goes’ in terms of degree of empirical coherence. If the sole purpose of the model is to
clearly express a theory, then perhaps the ‘anything goes’ position is all right, i.e.,
since a theory cannot explain the observational data of the real world (philosophers
of science would replace real world by ‘phenomenal system’, econometricians by data
generating process, DGP), but the counterfactual data of an isolated and idealized
physical system, see Davis (2000, pp. 207–208). However, it is plain that models
used for monetary policy are not developed with pure theory testing in mind, but
instead with the purpose of explaining the current economic situation, and to provide
forecasts of the future rate of inflation in particular as an aid to the policy decisions
process.
From this perspective, it is intriguing to note that a main development in
macroeconomics in recent years is that New Keynesian DSGE models have been
widely adopted as suitable models for monetary policy analysis. These models,
though modified with nominal price rigidity, have a real business cycle model as
its core. This means that what was originally offered as a normative (Ramsey)
model, with infinitely lived representative agents with perfect foresight and perfectly
competitive markets, has been completely “transformed into a model for interpreting
last year’s and next year’s national accounts’ (Hahn and Solow (1997, p 2)).
In this paper, one of the main thesis is that since the New Keynesian models are
now used for explanation of real world observations, they are also open to the full set
of modern econometric valuation methods. However, until recently the evaluation of
for example the New Keynesian Phillips curve, NPC, curve has been fairly limited
and of a corroborative nature. A limited range of goodness-of-fit tests have been
used, and the consensus view on that basis is that the NPC is a success:it provides
economics with a model of inflation dynamic that scores high on both theoretical
coherence (of course), but also reasonably well in terms of degree of data coherence.
In section 3 we review the results of more complete evaluation exercises. We conclude
in a completely different way than the consensus view: the empirical NPCs that
hitherto has been taken as support for the underlying theoretical model, are in fact
without the claimed theoretical content. In terms of a terminology developed in
section 2, the NPC therefore scores low in terms of the structural properties that we
typically want in macroeconometric models (beside theoretical consistency: ability
to explain the data, stability and constancy, and encompassing earlier findings).
2
'Marshall'
Figure 1: A modified Pagan Frontier
The New Keynesian Phillips curve (and full-blown DSGEs), are part of the reductionist programme of microfoundations to macroeconomics which has become so
dominant that it is now ‘mainstream’–first in academic economics and increasingly
also in central banks (and ministries?). This programme is Walrasian in its methodological orientation since it requires the model to be fully and correctly specified in
one step. In section 4 we ask whether it is reasonable to expect that econometric
models stemming from this programme will obtain a ‘high score’ in terms of structural properties. Based on the work of Kevin Hoover and others, the answer seems
to be negative. Thus if structural model properties are wanted, there is reason to
try to develop alternative modelling methodologies.
In section 5 we note that, ever since the invention of macroeconomics (Frisch
(1933)), there are traces of a parallel programme in macroeconomics which can be
labelled Marshallian because of its insistence on a high level of understanding of
the individual markets (detailed sector modelling), price making behaviour, and a
stepwise modelling approach to the (general equilibrium) macro model, cf. Hoover
(2004) and De Vroey (2004). In line with this view, section 6 presents a Marshallian
counterpart to the New Keynesian Phillips curve. It consists of a game theoretic
model of nominal wage setting, together with monopolistic price setting schedule,
and delivers precise hypotheses about cointegration relationships. Given cointegration (and identification) the theoretical framework can be extended to the errorcorrection model of wage-price dynamics, with lines going back to Sargan (1964),
and which has a range of interesting economic properties. For example,it implies
3
a steady state where the real wage is constant at a given level of unemployment,
hence a natural rate of unemployment is not implied (and is not needed to avoid
destabilizing wage inflation), so there is a rationale for a more detailed modelling
of the real economy in addition to a wage-price core model. In an extended empirical example we show that this approach delivers a model with some structural
properties in place. For example, it explains the data reasonably well, and several
important model features in terms of economic interpretation are constant across
identifiable regime-shift. Finally, the post Walrasian model of the inflation spiral
encompasses both old and new (Keynesian) Phillips curves.
We end this introduction by noting how the results and view of this paper could
lead to a modification of Pagan’s figure of modelling-conflicts, which we referred to
at beginning of the Introduction. First, we agree that theoretical interpretation and
clarity are important structural traits, so we would keep the same vertical axis as Pagan, labelled Degree of theoretical coherence in figure 1. But we discard the premise
that there is only one admissible theoretical framework to build macroeconometric
models from–there are at least two and we represent them as Walrasian and Marshallian in the figure. Along the horizontal axis we have what we think of as an index
of score on the difference aspects of structure (apart from theoretical consistency of
course).
The main message is that models that stem from the Walras programme are
likely to score low on the horizontal axis, but by definition they should score high on
theoretical coherence (but see the analysis of the NPC below) Marshallian models,
as we envisage them are bound to take a more eclectic approach to the theoretical
framework of the macro model, so we cut them off from “maxim score” on the
vertical axis. The score of Marshallian models on the horizontal structural property
axis will no doubt depend on the data generating process (some being more difficult
to model than others) and on econometric and statistical methods. It is of practical
importance however, that structural properties are relatively easy to evaluate within
the Marshallian framework, because of the stepwise modelling approach it brings
back into econometrics as a respectable route to model specification.
2
Structural interpretation and structural properties
To newcomers to the discipline, econometrics appears to be filled up with terminology, and even among professionals, confusion is sometimes caused by different
econometricians using different words for the same phenomena. Nevertheless, it
more often happens that, because we are having a relatively limited disciplinary
vocabulary and a wide range of phenomena to describe, very different things pass
under the same name, and therefore we are in danger of considering them as identical. One example is the word structure in relation to macroeconometric models.
For example, as recently as in the 1980s, most economists would associate the term
structural equation, for example, simply with an equation in system of simultaneous equations, as opposed to a reduced form equation in the reduced form (of the
structural model).
Today, when the word structural model is used, the vast majority of economists will think of entirely different models than the systems-of-equations of the
1970s. Most likely the kind of model that springs to ones mind is model made up of
4
equations that are derived from (or at least consistent with) modern macroeconomic
economic theory of the representative agent, intertemporal optimizing type. In such
model, each equation is said to have structural interpretation with ‘deep structural
parameters’) that are immune to the Lucas critique. This is unproblematic when
the data that the model is used with the counterfactual observations of an idealized
theoretical system. Sometimes however–and the current situation in monetary economics is such a time–the usage of theory models is extended to observations of
the real world. In terms of Pagan’s frontier, this is what happens when a monetary
authority chooses a model very close to the theory coherence axis.
We will argue that the new common understanding of the term structural
model represents a wrong-turn in the development of econometrics since it fails to
grasp the distinction between a model’s postulated structural interpretation and its
eventual structural properties, which are essential for understanding and forecasting observations generated by the real world economy (the ‘phenomenal system’ or
DGP). Structural properties are the gold nudged that we hope to sift out by ardent
repeated theory-data confrontations and modelling. They are not established by
decree.
One example of the now common use of the terms structural equation and
structural model is found in a review of monetary policy and institutions in Norway, Svensson et al. (2002). The group, named Norges Bank Watch, specifically
recommended that the Norwegian Central Bank invests resources into the building
of structural models of the Norwegian economy, to be used for policy simulation and
forecasting. By structural models Norges Bank Watch means modern open economy
macroeconomics, see for example p. 7 and p. 56 of Svensson et al. (2002). In 2004,
the first version of the Norges Bank structural macroeconomic model was commissioned for use in policy making process. It is a DSGE model, a real business cycle
model with a New Keynesian Phillips curve.
DSGE models are calibrated, or estimated under the assumption that the
theoretical disturbance are identical to the residuals. This claim is never really
argued but reflects an ambition in the radical research program initiated by Lucas,
namely that the goal of economic theory is to produce models that accurately mimics
the economy. However, as argued by David Hendry, Kevin Hoover and (I am sure)
many others, the claim is quite incredible.1 Basically, because economic data are non
experimental, theoretical ceteris paribus clauses and simplifying assumptions cannot
be trusted to carry over to the empirical analysis. As a result, model residuals do
not reflect the assumed properties of the disturbances (making inference difficult),
omitted variables induce bias in the estimates of the parameters of interest, and
the econometric model becomes unstable with respect to extensions of the data
set. Econometric techniques have been invented in order to rectify some of these
problems, but the validity of these correction methods remain dependent on the
initial assumption that the model is basically sound, and that e.g,. autocorrelated
residuals are indeed a sign of autocorrelated disturbance of the true model and not
of misspecification. This is an example of the strategy of handling a violation of an
1
In the terminology of Spanos (1995), Lucas and Kydland and Prescott and their followers
embrace the theory of errors as the basis of econometrics, and abandons the economerics of Fisher’s
experimental methods (and the way it was integrated in the Cowles-Commisions programme), see
Hoover (2004).
5
apriori assumption of the variance of the disturbance by respecifying the variance
and is based on ‘the axiom of correct specification’ (Leamer (1978)) and implicitly
interprets the residual as the disturbance. In section 3 we shows how this problem
goes right to the heart of the new consensus model of monetary policy: the New
Keynesian Phillips curve.
A main thesis of the present paper is that all models that are used for explanation of the observations of the real macroeconomy should be made subject to
a broad evaluation, regardless of whether they originate close to or far from the
theory-axis of Pagan’s diagram. In particular we oppose the view that a model’s
structural interpretation is a valid argument for by-passing the evaluation stage, or
only doing very limited evaluation.
When the model’s purpose is to understand the real world, its eventual structural properties are conceptually different from its structural interpretation. Heuristically, we take a model to have high degree of structural property if it explains the
data well, is robust to shocks, and is able to fence off challenges from rival models.
A model which is a structural representation of the economy does not disintegrate
that easy! Structural properties are nevertheless relative, to the history, nature and
significance of regime shifts. There is always the possibility that the next shocks to
the system may incur real damage to a model with high structural content hitherto.
Our definition implies that a model’s structural properties must be evaluated
along several dimensions, and the following seem particularly relevant
1. Theoretical interpretation.
2. Ability to explain the data.
3. Ability to explain earlier findings, i.e., encompassing the properties of existing
modes.
4. Robustness to new evidence in the form of updated/extended data series and
new economic analysis suggesting e.g., new explanatory variables.
Economic analysis (#1) is a main guidance in the formulation of econometric models. Clear interpretation also helps communication of ideas and results among researchers and it structures the debate. However, since economic theories are necessarily abstract and build on simplifying assumptions, it seems self evident that direct
translation of a theoretical relationship to an econometric model must lead to such
problems as biased coefficient estimates, wrong signs of coefficients, and/or residual
properties that contradict any initial assumption of white noise disturbances. The
main distinction seems to be between seeing theory as representing the correct specification, (a la leaving parameter estimation to the econometrician), and viewing
theory as a guideline in the specification of a model which also accommodates institutional features, attempts to accommodate heterogeneity among agents, addresses
the temporal aspects for the data set and so on, see e.g., Granger (1999).
Arguments against “largely empirical models”, e.g., sample dependency, lack of
invariance (the Lucas-critique), unnecessary complexity (in order to fit the data) and
chance finding of “significant” variables. Yet, ability to characterize the data (#2)
remains an essential quality of useful econometric models, and given the absence
of theoretical truisms, the implications of economic theory have to be confronted
6
with the data in a systematic way. Moreover, the mentioned pitfalls of empirically
based models can avoided, see e.g., Granger (1999), Hendry (2002). Due to recent
advances in the theory and practice of data based model building, we know that
by using general-to-spesific (gets) algorithms a researcher stands a good chance of
finding a close approximation to the data generating process, see Hoover and Perez
(1999), and Hendry and Krolzig (1999), and that the danger of over-fitting is in fact
(surprisingly) low.2 Conversely, acting as if the specification is given by theory alone,
with only coefficient estimates left to “fill in”, is bound to result in the econometric
problems noted above and which section 3 below will demonstrate.
There is usually controversy in macroeconometrics , so a new model’s capability of encompassing earlier findings is an important aspect of structure (#3). There
are many reasons for the coexistence of contested models for the same phenomena,
some of which may be viewed as inherent (limited number of data observations,
measurement problems, controversy about operational definitions, new theories).
Nevertheless, the continued use a corroborative evaluation (i.e., only addressing
goodness of fit or predicting the stylized fact correctly) may inadvertently hinder
cumulation of evidence taking place. One suspects that there would be huge gains
from a breakthrough for new standards of methodology and practice in the profession.
Ideally, empirical modelling is a cumulative process where models continuously
become overtaken by new and more useful ones. By useful we understand in particular models that are relatively invariant to changes elsewhere in the economy,
i.e., they contain autonomous parameters, see Haavelmo (1944), Johansen (1977),
Aldrich (1989), Hendry (1995b). Models with a high degree of autonomy represent
structural properties: They remain invariant to changes in economic policies and
other shocks to the economic system, as implied by #4 above.3 However, structure
is partial in two respects: First, autonomy is a relative concept, since an econometric
model cannot be invariant to every imaginable shock. Second, all parameters of
an econometric model are unlikely to be equally invariant, and only the parameters
with the highest degree of autonomy represent structure. Since elements of structure
typically will be grafted into equations that also contain parameters with a lower
degree of autonomy, forecast breakdown may frequently be caused by shifts in these
non-structural parameters.4
A strategy that puts a lot of emphasis on forecast behaviour, without a careful
2
Naturally, with a very liberal specification strategy, overfitting will result from gets modelling,
but with “normal” requirements of levels of significance, robustness to sample splits etc, the chance
of overfitting is small. Thus the documented performance of gets modelling now refutes the view
that the axiom of correct specification must be invoked in applied economerics, Leamer (1978). The
real problem of empirical modelling may instead be to keep or discover an economically important
variable that has yet to manifest itself stronlgy in the data, see Hendry and Krolzig (2001). Almost
by implication, there is little evidence that Gets leads to models that are prone to forecast failure,
see Clements and Hendry (2002).
3
see e.g., Hendry (1995a, Ch. 2,3 and 15.3) for a concise definition of structure as the invariant
set of attributes of the economic mechanism.
4
This line of thought may lead to the following practical argument against large-scale empirical
models: Since modelling resources are limited, and some sectors and activities are more difficult to
model than others, certain euations of any given model are bound to have less structural content
than others, i.e., the model as a whole is no better than its weakest (least structural) equation.
7
evaluation of the causes of forecast failure ex post, runs a risk of discarding models
that actually contain important elements of structure. Hence, for example Doornik
and Hendry (1997) and Clements and Hendry (1999, Ch. 3) show that the main
source of forecast failure is deterministic shifts in means (e.g., the equilibrium savings rate), and not shifts in such coefficients that are of primary concern in policy
analysis (e.g., the propensity to consume). Therefore it may not be necessary to bin
a whole model even if it has gone to a rough spell in terms of forecasting. However,
failure to adapt to the new regime, may be a sign of a deeper source of forecast
failure, non-constant derivative coefficients is the most common case (the coefficient
of unemployment a Phillips curve equation would be one example).5 Conversely,
models with high structural content will nevertheless lose regularly to simple forecasting rules, see e.g., Clements and Hendry (1999), Eitrheim et al. (1999). Hence
different models may be optimal for forecasting and for policy analysis, which fits
well with the often heard recommendation of a suite of monetary policy models.
Structural breaks are always a main concern in econometric modelling, but
like any hypothesis of theory, the only way to judge the quality of a hypothesized
break is by confrontation with the evidence in the data. Moreover, given that an
encompassing approach is followed, a forecast failure is not only destructive but
represents a potential for improvement, if successful respecification follows in its
wake, cf. Eitrheim et al. (2002).
3
Evaluation a ‘structural’ inflation equation
There is usually a big gulf between measurable complexities of the real economy
and what an econometric model can hope to incorporate. Hence, starting with the
idea that theory is complete (or that we can act as if it is complete) does not solve
any of the problems of empirical modelling in economics, and specifically does not
guarantee a high degree of structural content.
The New Keynesian Phillips Curve, NPC, has emerged as a consensus theory
of inflation in modern monetary economics, largely because of its stringent theoretical derivation, see Galí and Gertler (1999) and Galí et al. (2001), hereafter GG
and GGL. In a short time it has become an integral part of the New Keynesian
Model of monetary policy, as a modernized and state of the art theoretically instigated aggregate supply equation. In terms of the previous section’s list of structural
characteristics, the NPC scores high on theory consistency (#1), as we show below.
However, tests of all the other structural properties show that the NPC has low
structural content.
3.1 The NPC model6
Let pt be the log of a price level index. The NPC states that inflation, defined
as ∆pt ≡ pt − pt−1 , is explained by Et ∆pt+1 , expected inflation one period ahead
conditional upon information available at time t, and excess demand or marginal
5
See Nymoen (2004) for an analysis of a recent failure in inflation forecasting.
6
This part builds on Bårdsen et al. (2004) and Bårdsen et al. (2005, Chapter 7).
8
costs xt (e.g., output gap, the unemployment rate or the wage share in logs):
(1)
∆pt = bp1 Et ∆pt+1 + bp2 xt + εpt ,
where εpt is a stochastic error term. GG have given a specification of the NPC in line
with Calvo’s work: They assume that a firm takes account of the expected future
path of nominal marginal costs when setting its price, given the likelihood that its
price may remain fixed for multiple periods. This leads to a version of the inflation
equation (1), where the forcing variable xt is the representative firm’s real marginal
costs (measured as deviations from its steady state value). They argue that the
wage share (the labour income share) wst is a plausible indicator for the average
real marginal costs, which they use in the empirical analysis. A hybrid version of
the NPC that uses both Et ∆pt+1 and lagged inflation as explanatory variables is
also provided. It’s main rationale is that the hybrid model does not hinge on jumpbehaviour of the rate of inflation for stability (see below). Our impression is that it
is the hybrid version that is found in most DSGE models commissioned for monetary
policy analysis.
Equation (1) is incomplete as a model for inflation, since the status of xt is left
unspecified. In order to analyse the dynamic implication of the NPC we therefore
consider the following completing system of stochastic linear difference equations7
(2)
(3)
∆pt = bp1 ∆pt+1 + bp2 xt + εpt − bp1 η t+1
xt = bx1 ∆pt−1 + bx2 xt−1 + εxt
0 ≤ |bx2 | < 1
The first equation is adapted from (1), utilizing that Et ∆pt+1 = ∆pt+1 − η t+1 , where
η t+1 is the expectation error. Equation (3) captures that there may be feed-back
from inflation on the forcing variable xt (output-gap, the rate of unemployment or
the wage share) in which case bx1 6= 0.
In order to discuss the dynamic properties of this system, re-arrange (2) to
yield
(4)
∆pt+1 =
1
bp2
1
∆pt −
xt −
εpt + η t+1
bp1
bp1
bp1
and substitute xt with the right hand side of equation (3). The characteristic polynomial for the system (3) and (4) is
¸
∙
1
1
2
(5)
p(λ) = λ −
+ bx2 λ +
[bp2 bx1 + bx2 ] .
bp1
bp1
The system has no stationary solution if either of the two roots are one in magnitude.
If neither of the two roots are on the unit circle, unique stationary solutions exists,
and they may be either causal solutions (functions of past values of the disturbances
and of initial conditions) or future dependent solutions (functions of future values of
7
Constant terms are omitted for ease of exposition.
9
the disturbances and of terminal conditions), see Brockwell and Davies (1991, Ch.
3), Gourieroux and Monfort (1997, Ch. 12).
The future dependent solution is a hallmark of the New Keynesian Phillips
curve. Consider for example the case of bx1 = 0, so xt is a strongly exogenous forcing
variable in the NPC. This restriction gives the two roots λ1 = b−1
p1 and λ2 = bx2 .
Given the restriction on bx2 in (3), the second root is always less than one, meaning
that xt is a causal process that can be determined from the backward solution.
However, since λ1 = b−1
p1 there are three possibilities for ∆pt : i) No stationary
solution: bp1 = 1; ii) A backward solution: bp1 > 1; iii) A forward solution: bp1 < 1.
If bx1 6= 0, a stationary solution may exist even in the case of bp1 = 1. This
is due to the multiplicative term bp2 bx1 in (5). The economic interpretation of the
term is the possibility of stabilizing interaction between price setting and product
(or labour) markets–in fact in direct parallel to the (old) accelerationist Phillips
curve which also hinges on the endogeniety of the rate of unemployment (or output
gap) for stability.
If we consider the rate of inflation to be a jump variable, there may be a
saddle-path equilibrium as suggested by the phase diagram in figure 2. The drawing
is based on bp2 < 0, so we now interpret xt as the rate of unemployment. The
line representing combinations of ∆pt and xt consistent with ∆2 pt = 0 is downward
sloping. The set of pairs {∆pt , xt } consistent with ∆xt = 0 are represented by the
thick vertical line (this is due to bx1 = 0 as above). Point a is a stationary situation,
but it is not globally stable. Suppose that there is a rise in x represented by a
rightward shift in the vertical curve, which is drawn with a thinner line. The arrows
show a potential unstable trajectory towards the north-east away from the initial
equilibrium. However, if we consider ∆pt to be a jump variable and xt as a state
variable, the rate of inflation may jump to a point such as b and thereafter move
gradually along the saddle path connecting b and the new stationary state c.
10
b
Figure 2: Phase diagram for the system for the case of bp1 < 1, bp2 < 0 and bx1 = 0
The jump behaviour implied by models with forward expected inflation is at
odds with observed behaviour of inflation. This have led several authors to suggest
a “hybrid” model, by heuristically assuming the existence of both forward- and
backward-looking agents, see for example Fuhrer and Moore (1995).
In the same spirit as these authors, and with particular reference to the empirical assessment in Fuhrer (1997), GG also derive a hybrid Phillips curve that allows
a subset of firms to have a backward-looking rule to set prices. The hybrid model
contains the wage share as the driving variable and thus nests their version of the
NPC as a special case. This amounts to the specification
(6)
∆pt = bfp1 Et ∆pt+1 + bbp1 ∆pt−1 + bp2 xt + εpt .
GG estimate (6) for the U.S. in several variants –using different inflation measures, different normalization rules for the GMM estimation, including additional
lags of inflations in the equation and splitting the sample. They find that the overall
picture remains unchanged. Marginal costs have a significant impact on short run
inflation dynamics and forward looking behaviour is always found to be important.
In the same manner as above, equation (6) can be written as
(7)
∆pt+1
bbp1
1
bp2
1
= f ∆pt − f ∆pt−1 − f xt −
εpt + η t+1
bp1
bp1
bp1
bp1
11
and combined with (3). The characteristic polynomial of the hybrid system is
#
"
¤
bbp1
1 £ b
1
3
2
(8)
p(λ) = λ − f + bx2 λ + f bp1 + bp2 bx1 + bx2 λ − f bx2 .
bp1
bp1
bp1
Using typical results for the expectation and backward-looking parameters, bfp1 =
0.25, bbp1 = 0.75, together with the assumption of an exogenous ws process with
autoregressive parameter 0.7, we obtain the roots {3.0, 1.0, 0.7}.8 Thus, there is no
stationary solution (neither backward nor forward) for the rate of inflation in this
case.
This seems to be a common result for the hybrid model as several authors
choose to impose the restriction
bfp1 + bbp1 = 1,
(9)
which forces a unit root upon the system. To see this, note first that a 1-1 reparameterization of (7) gives
"
#
b
b
bbp1 2
1
bp2
1
p1
2
∆ pt+1 = f − f − 1 ∆pt + f ∆ pt − f xt − f εpt + η t+1 ,
bp1 bp1
bp1
bp1
bp1
so that if (9) holds, (7) reduces to
(10)
2
∆ pt+1
f
−bp0 (1 − bp1 ) 2
bp2
1
= f +
∆ pt − f xt − f εpt + η t+1 .
f
bp1
bp1
bp1
bp1
Hence, the homogeneity restriction (9) turns the hybrid model into a model of the
change in inflation. Equation (10) is an example of a model that is cast in the
difference of the original variable, a so called dVAR, only modified by the driving
variable xt . Consequently, it represents a generalization of the random walk model
of inflation that was implied by setting bfp1 = 1 in the original NPC. The result in
(10) will prove important in understanding the behaviour of the NPC in terms of
goodness of fit, see below.
If the process xt is strongly exogenous, the NPC in (10) can be considered at
its own. In that case (10) has no stationary solution for the rate of inflation. A
necessary requirement is that there are equilibrating mechanisms elsewhere in the
system, specifically in the process governing xt (e.g., the wage share). As noted
above, this requirement parallels the case of dynamic homogeneity in the backward
looking Phillips curve ( i.e., the accelerationist model, with a vertical long run
Phillips curve). In the present context the message is that statements about the
stationarity of the rate of inflation, and the nature of the solution (backward or
forward) requires an analysis of the system.
The empirical results of GG and GGL differ from other studies in two respects.
First, bfp1 is estimated in the region (0.65, 0.85) whereas bbp1 is one third of bfp1 or less.
Second, GG and GGL succeed in estimating the hybrid model without imposing (9).
GGL (their Table 2) report the estimates { 0.69, 0.27} and {0.88, 0.025} for two
different estimation techniques. The corresponding roots are {1.09, 0.70, 0.37} and
{1.11, 0.70, 0.03}, illustrating that as long as the sum of the weights is less than one
the forward solution prevails.
8
The full set of coefficients values is thus: bx1 = 0, bfp1 = 0.25, bbp1 = 0.75, bx2 = 0.7
12
3.2 Evaluating the NPC as a model of observed inflation
The main tools for evaluation of the NPC on‘Euroland’ (and US) data have been
the GMM test of validity of overidentifying restrictions (i.e., the χ2J -test below)
and measures and graphs of goodness-of-fit. In particular the closeness between the
fitted inflation of the NPC and actual inflation, is taken as telling evidence of the
models relevance for understand US and ‘Euroland’ inflation, see GG and GGL. We
therefore start with an examination of what goodness-of-fit can tell us about model
validity in this area. The answer appears to be: ‘very little’. In this section we also
reviews the result of other approaches. The studies we cite employ data both from
the two large economy data sets (euro area and US data), as well as data from two
open economies: the UK and Norway.
As mentioned above, GG and GGL use the formulation of the NPC (1) where
the forcing variable xt is the wage share wst . Since under rational expectations the
errors in the forecast of ∆pt+1 and wst is uncorrelated with information dated t − 1
and earlier, it follows from (1) that
(11)
E{(∆pt − bp1 ∆pt+1 − bp2 wst )zt−1 } = 0
where zt is a vector of instruments.
The orthogonality conditions given in (11) form the basis for estimating the
model with generalized method of moments (GMM). The authors report results
which they record as being in accordance with a priori theory. Using their aggregate data for the Euro area9 1971.3 -1998.1, we replicate the results for Europe in
GGL:10 ,11
(12)
∆pt = 0.914∆pt+1 + 0.088wst + 0.14
(0.04)
(0.04)
(0.06)
χ2J
σ̂ = 0.321
(9) = 8.21 [0.51]
2
χRW (2) = 4.55 [0.10] .
The instruments used are five lags of inflation, and two lags of the wage share, output
gap (detrended output), and wage inflation. σ̂ denotes the estimated residual standard error, and χ2J is the statistics of the validity of the overidentifying instruments
(Hansen, 1982).12
In terms of the dynamic model (3) - (4) the implied roots are {1.08, 0.7} for
the US and {1.09, 0.7} for Europe. Thus, as asserted by GGL, there is a stationary
forward solution in both cases. However, since neither of the two studies contain
9
See the Data Appendix and Fagan et al. (2001).
10
Below, and in the following, square brackets, [..], contain p-values whereas standard errors are
stated in paranthesis, (..).
11
i.e., equation (13) in GGL01. We are grateful to J. David López-Salido of the Bank of Spain,
who kindly provided us with the data for the Euro area and a RATS-program used in GGL01.
12
GGL01 report estimates of (1) for the US as well as for Euroland. Using US data for 1960:1
to 1997:4, they report
(13)
∆pt = 0.924 ∆pt+1 + 0.250 wst .
(0.029)
(0.118)
13
any information about temporal properties of the observed wage share data, the
roots obtained are based on the additional assumption of an exogenous wage share
(bx1 = 0) with autoregressive coefficient bx2 = 0.7.
The statistic χ2RW (2) reports the outcome of testing the joint hypothesis
bp1 = 1 and bp2 = 0,
and we see that the hypothesis that the model can be reduced to a random walk
cannot be rejected. Hence, although the point estimates give a unique solution,
there is no significant support for that claim once we take into account estimation
uncertainty. The insignificant χ2RW (2) statistic has another implication too, namely
that in terms of fit, the Euro-area NPC does as good (or bad) as a simple random
walk.
We dwell on the NPC’s inability to explain inflation observations better than
a random walk exactly because several papers place conclusive emphasis on the
(reasonably) good fit of the NPC. Using US data, GG, though rejecting the pure
forward-looking model in favour of a hybrid model, nonetheless find that the baseline
model remains predominant. In the Abstract of GGL the authors state that “the
NPC fits Euro data very well, possibly better than US data”. Even more recently,
Galí (2003) writes
...while backward looking behaviour is often statistically significant,
it appears to have limited quantitative importance. In other words,
while the baseline pure forward looking model is rejected on statistical
grounds, it is still likely to be a reasonable first approximation to the
inflation dynamics of both Europe and the U.S. (Gali (2003, section
3.1).
We think that this is unconditional declaration of success is completely unwarranted–
the only thing that can be said is that the NPC fits about as well as a random walk
(not always an easy model to beat of course, but we don’t think that this is what
Gali had in mind.). Figure 3 illustrates the point by showing actual and fitted values
of (12) together with the fit of a random walk in the left-hand panel. The similarity
between the series is obvious, and the right-hand panel shows the cross-plot with
regression line of the fitted values.
14
Fitted values from NPC vs.
fitted values from random walk
Actual inflation and fit from the NPC
3.5
3.0
3.0
2.5
2.5
NPC-FIT
3.5
2.0
1.5
2.0
1.5
1.0
1.0
0.5
0.5
0.0
1975
1980
1985
1990
NPCRATSFIT
1995
0.0
0.0
0.5
1.0
DP
1.5
2.0
2.5
3.0
3.5
RW-FIT
Figure 3: Actual and fitted values of equation (14) together with the fit of a random
walk.
Our replication of the Euro-inflation hybrid NPC is given in (14):
∆pt =
0.681 ∆pt+1 + 0.281 ∆pt−1 +
(0.073)
(14)
(0.072)
0.19 wst
(0.026)
+ 0.063
(0.069)
GMM, T = 107 (1971 (3) to 1998 (1))
χ2J (8) = 8.01 [0.43]
Perhaps surprisingly, the same regress (from a structural model to a random walk)
applies to the hybrid model. The main intuition is that, since the coefficients of the
two inflation terms are close to unity (0.96) and the coefficient of the wage share is
neither statistically nor numerically significant, equation (14) is practically speaking
indistinguishable from a pure time series model of the dVAR type. From equation
(10), using the estimation results of the euro-area hybrid NPC the fitted rate of
inflation (∆p̂t ) is given by
∆p̂t = 0.09 + 1.06∆pt−1 + 0.41∆2 pt−1 + 0.02wst−1 .
Note first, that since the variance of ∆2 pt−1 is of a lower order than ∆pt−1 , the sum
1.06∆pt−1 +0.41∆2 pt−1 is dominated by the first factor. Second, since the coefficient
of the forcing variable wst is only 0.02, the variability of wst−1 must be huge in order
to have a notable numerical influence on ∆p̂t . But remember that wst is the wageshare (or its log), which means that its variability is relatively small (for example a
change of more than 0, 01 most be counted as quite big) in normal times.
15
It is interesting to note that when the NPC is applied to other data sets, i.e.,
to such diverse data as US, UK and Norwegian inflation rates, very similar parameter estimates are obtained, see Bårdsen et al. (2002). Is this a sign of structure?
GG and GGL, and other proponents of the NPC claim so. But a the correct interpretation seems to be that the NPC is almost void of explanatory power, and that
it captures only one common feature among different countries data sets, namely
autocorrelation.
Hence, the NPC (as an empirical) model fails to corroborate the theoretical
message: that rational expectations transmits the movements of the forcing variable strongly onto the observed rate of inflation. Recently, it has been shown by
Fuhrer (2005) that the typical NPC fails to deliver the expected result that inflation persistence is ‘inherited’ from the persistence of the forcing variable. Instead,
the derived inflation persistence, using estimated NPCs, turns out to be completely
dominated by ‘intrinsic’ persistence (due to the accumulation of disturbances of the
NPC equation). Quite contrary to the consensus view, Fuhrer shows that the NPC
fails to explain actual inflation persistence by the persistence that inflation inherits
from the forcing variable. Fuhrer summarizes that the lagged inflation rate is not a
‘second order add on to the underlying optimizing behaviour of price setting firms,
it is the model’.
More evaluation of the NPC is provided by e.g., Bårdsen et al. (2004) and
Bårdsen et al. (2005, Ch. 7) which also includes testing of parameter stability (over
sample periods), sensitivity (wrt estimation methodology), robustness (e.g., moving
one variable such as the output-gap from the set of overidentifying instruments to
the ‘structural’ part of the model) and encompassing (preexisting models (on UK
and Norwegian data).13 Expect for recursive stability, the results are disheartening
for those who believe that the NPC represent a data coherent and theory driven
model of price setting. As for recursive stability, it is more apparent than real since
the inherent fit of the model is so poor that statistical stability tests have low power
, and graphs of the sequence of recursive coefficient estimates of the forcing variable
show ‘stability around zero’.
Hence, after evaluation, the structural content of the NPC ‘disappears out
of the window’ leaving a huge question mark hovering over the New Keynesian
modelling programme paradigm: namely how to model inflation? In terms of the
Pagan Frontier, the NPC model (and therefore also the DSGE model) are misplaced
by earlier authors who place it high up on the frontier. On the basis of the results
reviewed here, the relevant position is well inside the frontier and close to origo
(since the fit there intrinsic persistence should not have been there, according to
theory).
Luckily, if the task of modelling real world inflation is started from another position, with a theoretical framework that incorporates some important traits of real
life wage setting for example, no such “puzzles” arise. Section 6 below elaborates.
13
See also Bårdsen et al. (2002) which includes Norwegian data.
16
4
Can we expect structural properties from microfoundations?
The DSGE models in macroeconomics, of which NPC is an integral part, is a continuation of the microfoundations programme in macroeconomics that started with
new classical macro models, rational expectations and the real business cycle model.
Macroeconomics as a discipline of economics was defined in the 1930s by Ragnar Frisch and others. In his paper on business cycles, Frisch was the first to use
the word “microeconomics” to refer to the study of single firms and industries and
“macroeconomics” to refer to the study of the aggregate economy.14 Interestingly,
according to De Vroey (2004), Frisch viewpoint was that macroeconomics belongs
to the domain of general equilibrium because macroeconomics is concerned with the
“whole economics system in its entirety”.15
Today, it is almost universally accepted among economists that macroeconomics is methodologically and ontologically reducible to microeconomics. This is
the essence of the program of microfoundations which aims to explain all macroeconomic phenomenon of the economy, in principle as least, by reference to the
behaviour of rational economic agents as postulated by microeconomics. Nevertheless, those who have reflected at all deeply on the matter often express a scepticism
to the program of microfoundations, and take an anti-reductionist position on the
basis that macroeconomic institutions and variables can fruitfully be viewed as real
entities and that causal structures between macroeconomic variables for example
lay can be disclosed by the systematic application of macroeconomics methodology
and econometrics for example.
A non-reductionist position is a potential starting point for setting up alternatives to the current dominance of representative agent macromodels. It can perhaps
be best presented by first considering the logical near impossibility and the practical
failures of the program of microfoundations (in a rather literal meaning). Microfoundations is typically associated with methodological individualism. Mark Blaug 1992
defines methodological individualism as the principle that “asserts that explanation
of social, political, or economic phenomena can only be regarded as adequate if they
run in terms of beliefs, attitudes and decisions of individuals”. Hence methodological individuals is a doctrine about the priority of intentional (and hence individual)
explanations in economics, as opposed to causal and functional explanations, and
it is widely accepted, almost by default. However there is gulf between theory and
practice, since methodological individualism is not widely practised. The simple
reason is what Kevin Hoover (e.g., Hoover (1988, p. 135)) has dubbed the “Cournot
problem” after the nineteenth mathematician and economist: There are too many
individuals (firms and consumers) and to many goods to be handled by direct modelling. Consequently, we observe that few explanations macroeconomic phenomena
14
In few memorable pharagrams early in his acclaimed paper Frisch states that
15
After ’propagation’, Frisch worked hard on business-cycles right up to the war. But he never
managed to formulate his paradigm as a set of equations, and in a way his macro economic research
programme became a failure, see Bjerkholt and Lie (2001). We can only speculate why he fell short
of formulating a macroeconimic system. Although Frisch of course knew Marshall very well, he
also knew Walras (his formative stay in France), and Frisch seems to have ’chosen’ Walras as his
ideal for a macroeconomic system. (But this is my speculation.)
17
have been successfully reduced to their microfoundations, see Blaug (1992, p. 46).
In fact, one example of the failure of microfoundations is provided by our review
of the poor structural properties of NPC model of (real world) inflation dynamics.
Following the innovative work of Clarida et al. (1999) and others, the NPC has
quickly acquired a position of a (new) consensus model of inflation dynamics, for
example as the model of the supply side of dynamic stochastic general equilibrium
models.16 This wide acceptance no doubt reflects the belief that the NPC represents
the end of the profession’s decade long quest for a data-consistent, micro-based,
rational expectations model of price-setting. Alas, as we have seen that even on its
own premises, the NPC is a complete failure. 17
The fate of the NPC illustrates that the commitment among economists to
methodological individualism is not grounded in successful applications, see Hoover
(2001, p 111). Rather, it appears to be based on an a instinctive or habitual belief
that methodological individualism is the only way “to do” macroeconomic research
properly. As already hinted above, the approach underlying our modelling programme is non-reductionist and is founded on the view that macroeconomic variables
are “real” entities with an external objective existence and that a goal of modelling
is to chart-out the causal structures (which need not be constant or invariant) between them. This view has recently been convincingly developed by Hoover (2001),
which we have made several references too already. A strong motivation of taking
a macroeconomic reality as a premise for a macro modelling is the noted failures of
the reductionistic programme. The reductionist programme does not seem tenable,
and we regard the Cournot problem as its fundament obstacle. Despite paying lipservice to methodological individualism, the closest that macroeconomics has come
to microfoundations is the representative agent model. However, the representative
agent side-steps the whole problem of representing the behaviour of each individual
and build up macroeconomic aggregates from there. Hence the representative agent
is framework can be seen as a concession to the impossibility of overcoming the central problem of the microfoundations program, namely how to link the postulated
behaviour of microeconomic agents to the measured behaviour of macroeconomic
variables, see Hoover (2001, page 285).
A commitment to a macroeconomic reality does not justify (or force upon
us) an atheoretical or wholly empirical and/or mechanical approach to macroeconometric modelling.18 To deny an essential connection between individual economic
16
The original NPC seems to have lost its credentials very quickly, the following remarks apply
to the hybrid NPC, where the lagged rate of iflation is included.
17
In addition economic theory develops over time, so the hallmark of structural interpretation
changes its valour over time, and the theory instigated macro models face the possibility of nonconstancy and regime shifts from within so to say. For example, DSGE models build on Ricardian
equivalence, and therefore imply that increased government expenditure reduce privare consumption. In new DSGE models, a proportion of households are assumed to be non-Ricardian. This
brings the models predictions closer to the evidence, but it also represents a regime shift in the
model.
18
In Hoover (2001), the coexistence of a macroeconomic and microeconomic reality is sought
established by the use of the philosophical theory of supervenience, see Chapter 5 in particular.
Supervenience allows a macroeconomic configuration to be derived from a given configuration of
microeconomic elements. But starting from a descpription of the macro level, there is no determined
(unique) corresponding constellation of micro elements.
18
behaviour and macroeconomics aggregates would be quite absurd. The general point
is that we regard that the right level for both specification and evaluation of any
formulated relationship is the macroeconomic level. below discusses some of the
specific issues that figure prominently in the ‘theory’ versus ‘data’ debate.
5
Back to square one: A Marshallian approach to macromodelling
Criticism of the reductionists approach to macroeconomics is usually met with the
answer that there are no alternatives–unless one want to stay forever with the ISLM model. Clearly, this is not true, and other macroeconomic programmes are now
being developed. Although the approaches differ in detail, there is also a wide common ground. For example: i) A resistance of the almost casual transformation of
a normative perfect foresight, intertemporal substitution perfect competition model
into a model for interpreting real world macroeconomic observations. ii) A focus
in the large-scale economic pathologies (prolonged depression, mass unemployment,
persistent inflation), which are strictly speaking unmentionable in the new consensus model. iii) A clear stand in the behaviour of the labour market, which is
modelled consequently as noncompetitive and with information asymmetries, and
non-market clearing. Consequently these “non-consensus” macro models do not accept the natural rate hypothesis in the form of an accelerationist Phillips curve for
example. iv) The alternative (new) macroeconomic models are non-Walrasian in
that they account for why the labour market fails to clear in particular, and that
they are critical to the postulate of a complete set of Arrow-Debreu markets in
general (again once the purpose is explanation).
The new alternative macro theory is also characterized by what we can call a
stepwise modelling. A good example is the essay by Hahn and Solow (1997) where a
model of wage and price setting and the labour market is developed first, and then
it is grafted into what the authors refer to as a ‘prototype macroeconomic model’.
Apparently, this stepwise approach to macroeconomic modelling flies in the
face of current new classical macroeconomics, of which DSGE models are the latest
and most popular development. These models adhere to the Walrasian principle that
one need to consider an entire economy at once, rather than a section of it. However,
if we imagine for a second that Walras never wrote his Elements and that, in the inter
war years, those who wanted to build macroeconomic general equilibrium models
only had Marshall’s writings available.19 In such a setting, Walras’ principle about
studying an entire economy on one go would be counter-intuitive. Intuitively, one
would rather take a stepwise approach consisting of studying the functioning of one
isolated market (Model A in our terminology) in the first stage, and piecing together
the results of the practical analysis to a complete model (Model B) in the second
stage. This two-tier general equilibrium methodology can according to De Vroey
(2004) be considered as typically Marshallian in contrast to the one-shot Walrasian
methodology. The gist of the approach was often expressed by ‘the Keynesians’ for
example by Hicks:
19
This analysis is due to De Vroey (2004), section 3.2.
19
If a model of the whole economy is to be securely based, it must be
grounded in an intelligible account of how a single market is supposed
to work, Hicks (1965, p. 78)20
In our view, one interesting topic to discuss is whether a modernized Marshallian approach to macroeconometric modelling is capable of establishing structural
properties in model that are intended for explanation and to aid policy. Of course
it has been a long standing task of model builders to establish good practice and
develop operational procedures for econometric model building which secures that
the end product of piecewise modelling is tenable and useful. Important contributions in the literature include Klein (1983), Klein et al. (1999), Christ (1966), and
the surveys in Bodkin et al. (1991) and Wallis (1994).
In Bårdsen et al. (2005) we supplement the existing literature by suggesting
the following stepwise operational procedure:21
1. By relevant choices of variables we define and analyse subsectors of the economy (correspond to marginalisation in econometrics).
2. By distinguishing between exogenous and endogenous variables we construct
(by conditioning) relevant partial models, which we will call models of type A
3. Finally, we need to combine these submodels in order to obtain a model B for
the entire economy.
Our thesis in the book is that, given that Model A is a part of Model B, it is
possible to learn about Model B from Model A. Of course this stepwise approach to
macroeconoming modelling flies in the face of current new classical macroeconomics,
of which DSGE models are the latest and most popular development. However,
given the failure of that programme to establish structural properties to the model
of inflation dynamics for example, a radically different approach may be needed.
Examples of properties that can be discovered using the stepwise procedure
includes cointegration in Model B. This follows from a corollary of the theory of
cointegrated systems: any non-zero linear combination of cointegrating vectors is
also a cointegrating vector. In the simplest case, if there are two cointegrating vectors in Model B, there always exists a linear combination of those cointegrating
vectors that “nets out” one of the variables. Cointegration analysis of the subset of
variables (i.e., Model A) excluding that variable will result in a cointegrating vector
corresponding to that linear combination. Thus, despite being a property of Model
B, cointegration analysis of the subsystem (Model A) identifies one cointegration
vector. Whether that identification is economically meaningful or not remains in
20
In this Hick’s would find himself in agreement with Milton Friedman is seems. In an interview
Friedman, Snowdon and Vane (1997), was asked specifically about his methodological position:
Question [to Friedman]: Kevin Hoover has drawn a methodological distinction between your work
as Marshallian and that of Robert Lucas as Walrasian. Is that distinction valid? Answer: There
is a great deal to that. On the whole I believe that it is probably true. I have always distinguished
between the Marshallian approach and the Walrasian approach. I have been personally always a
Marshallian (p. 202).
Maybe De Vroy is right, and that a Marshallian approach was ‘in the air’ ?
21
See Jansen (2002), reply to Søren Johansen (Johansen (2002)).
20
general an open issue, and any such claim must be substantiated in each separate
case. Our experience is that there is relatively few problems connected with identification of equilibrium relationships in subsectors (model A). For example, having
completed the macro model, it is possible to check the validity of the implicit assumption underlying the cointegration analysis of the consumption function. Other
important properties of the full model that can be tested from subsystems include
the existence or not of a natural rate of unemployment, see Bårdsen and Nymoen
(2003) and the relevance or not of forward looking terms in wage and price setting,
e.g. Bårdsen et al. (2004).
As pointed out by Johansen (2002), there is a Catch 22 to the above procedure: a general theory for the three steps will contain criteria and conditions which
are formulated for the full system. This seems to cut post-Walrasian econometrics
off from anything but VARs with only a few variables, so that the full Johansen
procedure can be applied. However, piecewise modelling can in practice be seen as
a sort of gradualism - seeking to establish sub-models that represents partial structure: i.e., partial models that are invariant to extensions of the sample period, to
changes elsewhere in the economy (e.g., due to regime shifts) and remains the same
for extensions of the information set. The alternative to this thesis amounts to a
kind of creationism, i.e., unless macroeconometrics should be restricted to aggregate
models, see Bårdsen et al. (2005, Chapter 2).
A separate reason to focus on sub-models is that the modellers may have good
reasons to study some parts of the economy more carefully than other parts. For
a central bank that targets inflation, there is a strong case for getting the model
of the inflationary process right. This calls for careful modelling of the wage and
price formation conditional on institutional arrangements for the wage bargain, the
development in financial markets and the evolving real economy in order to answer
a number of important questions: Is there a natural rate (of unemployment) that
anchors unemployment as well as inflation? What is the importance of expectations
for inflation and how should it be modelled? What is role of money in the inflationary
process? In line with this, next section evaluates a post-Walrasian alternative to the
NPC.
6
Evaluating the structural properties of an econometric
wage-price model
The modelling of inflation dynamics is important for monetary policy models, and
requires not only theoretical models, good data and efficient estimation routines.
One also needs to draw on knowledge about the characteristics of the labour market,
wage-setting and of other institutional traits that are specific to the economy under
study. If there is a trade off between estimation efficiency and the issue of getting the
economic institutions and mechanisms right, the practitioners of macroeconometric
modelling should give priority to the latter.
The clearest alternative to the NPC makes use of a framework that focuses on
wage setting, along with the price making of firms. An important underlying idea
is that workers and firms bargain over the distribution of rents created within the
firm. Although this is an almost trivial starting point, following the implications
leads to models that are quite unlike the NPC, or the conventional backward looking
21
Phillips curve for that matter. For example, there is no ‘need’ for unemployment
to stay close to a natural rate in order to avoid an accelerating price level (refuting
Phillips curve models), hence the average rate of unemployment is not pinned down
from wage and price setting alone (refuting a Layard-Nickell model); in the medium
run, real wages predicted to be positively linked to productivity.
This approach to inflation modelling has a relative long history and has been
tested repeatedly tested against real world data.22 . The structure and theoretical
content has not been destroyed by testing, but it has evolved in the process.
6.1 Wage bargaining theory
A main advance in the modelling of labour markets rests on the perception that
firms and their (organized or unorganized) workers are engaged in a partly cooperative and partly conflictual sharing of the rents generated by the operation of the
firm. In line with the assumptions, nominal wages are modelled in game theoretic
framework which fits the comparatively highly level of centralization and coordination in Norwegian wage setting, (e.g., Nymoen and Rødseth (2003a) and Barkbu
et al. (2003) for a discussion of the degree of coordination).
Our ability to model nominal wage setting in game theoretic terms is a main
advance in terms of theoretical underpinnings of macro model, and as one would
expect of such a revolution, the approach has profound implication. Linked up with
an assumption of monopolistically competitive firms, it represents a satisfactory
theory of the supply-side in the medium run. However, in applications we must
bridge the gap between the formal relationships of the model, and the empirical
relationship that may be present in the data. The main step here is to invoke the
assumptions of stochastic trends and to interpret the theoretically derived equations
as hypothesized cointegration relationships. From that premise, a dynamic model
of the inflation spiral in error-correction form follows logically.
There is a number of specialized models of “non competitive” wage setting.
Our aim in this chapter is to represent the common features of these approaches in a
model of theoretical model of wage bargaining and monopolistic competition, building on Rødseth (2000, Ch. 5.9) and Nymoen and Rødseth (2003a). We start with
the assumption of a large number of firms, each facing downward-sloping demand
functions. The firms are price setters and equate marginal revenue to marginal costs.
With labour being the only variable factor of production (and constant returns to
scale) we obtain the following price setting relationship
Qi =
ElQ Y Wi (1 + τ 1i )
ElQ Y − 1
Zi
where Zi = Yi /Ni is average labour productivity Yi is output and Ni is labour input.
Wi is the wage rate in the firm, and τ 1i is a payroll tax rate. ElQ Y > 1 denotes the
absolute value of the elasticity of demand facing each firm i with respect to the firm’s
22
In particular Sargan (1964), 1980. Bårdsen et al. (2005, Ch 3) trace the kind of model we use
below, with an explicit distinction between theoretical relationships that apply to the steady state,
and other dynamic equations that are intended to explain actual inflation, back to the Norwegian
model of inflation, see Aukrust (1977).
22
own price. In general ElQ Y is a function of relative prices, which provides a rationale
for inclusion of e.g., the real exchange rate in aggregate price equations. However, it
is a common simplification to assume that the elasticity is independent of other firms
prices and is identical for all firms. With constant returns technology aggregation
is no problem, but for simplicity we assume that average labour productivity is the
same for all firms and that the aggregate price equation is given by
(15)
Q=
ElQ Y W (1 + τ 1)
ElQ Y − 1
Z
The expression for real profits (π) is therefore
π=Y −
W (1 + τ 1)
W (1 + τ 1) 1
N = (1 −
)Y.
Q
Q
Z
We assume that the wage W is settled in accordance with the principle of maximizing
of the Nash-product:
(ν − ν 0 )f π1−f
(16)
where ν denotes union utility and ν 0 denotes the fall-back utility or reference utility.
The corresponding break-point utility for the firms has already been set to zero in
(16), but for unions the utility during a conflict (e.g., strike, or work-to-rule) is nonzero because of compensation from strike funds. Finally f is represents the relative
bargaining power of unions.
Union utility depends on the consumer real wage of an unemployed worker and
the aggregate rate of unemployment, thus ν( W
, U, Aν ) where P denotes the consumer
P
23
price index. The partial derivative with respect to wages is positive, and negative
with respect to unemployment (ν 0W > 0 and ν 0U ≤ 0). Aν represents other factors
in union preferences. The fall-back or reference utility of the union depends on the
overall real wage level and the rate of unemployment, hence ν 0 = ν 0 ( W̄
, U) where
P
W̄ is the average level of nominal wages which is one of factors determining the size
of strike funds. If the aggregate rate of unemployment is high, strike funds may run
low in which case the partial derivative of ν 0 with respect to U is negative (ν 00U < 0).
However, there are other factors working in the other direction, for example that
the probability of entering a labour market programme, which gives laid-off workers
higher utility than open unemployment, is positively related to U. Thus, the sign
of ν 00U is difficult to determine from theory alone. However, we assume in following
that ν 0U − ν 00U < 0.
With these specifications of utility and break-points, the Nash-product, denoted N , can be written as
or
23
½
¾f ½
¾1−f
W
W (1 + τ 1) 1
W̄
N = ν( U, Aν ) − ν 0 ( )
(1 −
)Y
P
P
Q
Z
½
N = ν(
¾f ½
¾1−f
1
W̄
Wq
(1 − Wq )Y
, U, Aν ) − ν 0 ( )
Pq (1 + τ 1)
P
Z
We abstract from a proportional income tax rate.
23
where Wq = W (1 + τ 1)/Q is the producer real wage and Pq (1 + τ ) = P (1 + τ 1)/Q
is the so called real wage wedge (between the consumer and producer real wage).
It might be noted that the income tax rate is omitted from the analysis since
it plays no role in the empirical model This simplification is in accordance with
previous studies of aggregate wage formation, see e.g. Calmfors and Nymoen (1990)
and Nymoen and Rødseth (2003b), where no convincing evidence of important effects
from the average income tax rate τ 2 on wage growth could be found. Note also that,
that unlike many expositions of the‘bargaining approach’, for example Layard et al.
(1991, Chapter 7), there is no aggregate labour demand function (employment as a
function of the real wage), subsumed in the Nash-product. In this we follow Hahn
and Solow (1997, p 32), who point out that bargaining is usually over the nominal
wage and not over the number of employment.24
The first order condition for a maximum is given by NWq = 0 or
(17)
f
Wq
, U, Aν )
ν 0W ( Pq (1+τ
1)
Wq
ν( Pq (1+τ
, U, Aν ) − ν 0 ( W̄
, U)
1)
P
= (1 − f)
1
Z
(1 − Wq Z1 )
.
q
In a symmetric equilibrium, W = W̄ , leading to W
= W̄
in equation (17), and the
Pq
P
b
aggregate bargained real wage Wq is defined implicitly as
(18)
Wqb = F (Pq (1 + τ 1), Z, f, U ).
A log-linearization of (18), using the property of homogeneity of degree 1 in prices,
and with subscript t for time period added, gives:25
(19)
w = mw + q + (1 − δ 12 ) (p − q) + δ 13 z − δ 15 u + δ 16 τ 1.
0 ≤ δ 12 ≤ 1, 0 < δ 13 ≤ 1, δ 15 ≥ 0, 0 ≤ δ 16 ≤ 1
Equation (19) is a general proposition about the bargaining outcome and its
determinants, and can serve as a starting point for describing wage formation in any
sector or level of aggregation of the economy.
Equation (15) already represents the normal price setting rule, and upon
linearization we have
(20)
q = mq + (w + τ 1 − z) .
24
They also make the point that such a demand function represents and internal inconsistency,
since the firms are price makers, not price takers, in the model.
25
Ideally, from the defintion of the wedge, (1 − δ 12 ) = δ 16 . However, in light of entirely different
time series properties of the empirical counterparts to p − q and τ 1, this restriction is not imposed.
The role of the wedge as a source of wage pressure is contested in the literature. In part, this
is because theory fails to produce general implications about the wedge coefficient ω–it can be
shown to depend on the exact specification of the utility functions ν and ν 0 , see e.g., Rødseth
(2000, Chapter 8.5) for an exposition.
24
6.2 How does the theory apply in a macro model?
At this point we must ask how the two theoretical relationships can be translated
into hypothesized relationships holding between actual time series? The answer is
that we interpret (19) and (20) as two cointegration relationships. Equation (19)
is then a hypothesis about how the wage rate the total economy, when measured
by an aggregated wage index wt (where t denotes quarters), cointegrates with the
empirical counterparts (time series) of p − q, z, u and τ 1. To be more precise,
we assume that wt , pt , qt and zt are I(1), and cointegrated. ut and τ 1t are I(0) by
assumption, and affect the mean of the cointegration relationship.26
Hence, as a first step, we re-write (19) and (20) as two hypothesised cointegration relationships:
(21)
(22)
wt = mw + q + (1 − δ 12 ) (pt − qt ) + δ 13 zt − δ 15 ut + δ 16 τ 1t + ecmb,t
qt = mq + (wt + τ 1t − zt ) + ecmf,t
where the subscript t for time period has been introduced, and where the two disturbances ecmb,t and ecmf,t are both I(1) if the theory is correct.
At this stage it is worth mentioning one interpretation of (21) and (22) which
is frequently made in the literature, but which represents a wrong turn: By making
use the homogeneity property, the two equations can be written as two conflicting
equations of the real wage wt − qt :
(23)
(24)
b
wq,t
= mw + qt + (1 − δ 12 ) (pt − qt ) + δ 13 zt − δ15 ut + δ 16 τ 1t + ecmb,t
f
wq,t
= −mq − τ 1t − zt − ecmf,t
Next, take the mathematical expectation on both sides of both equations. The
f
b
addition requirement of E[wq,t
] = E[wq,t
], then allows us to solve for the ‘natural
rate’ of unemployment (or ‘wage-curve’ NAIRU) from this partial system (of wag
and price setting). If δ12 = 1 the wedge drops out and the ‘natural rate’, call it uw is
seen to depend only on factors from the supply side of the economy. However, from
the dynamic model below it is straight forward to established the general result that
ut → uss 6= uw , where uss denotes the the rate of unemployment in a steady state
of a dynamic wage and price model, see Kolsrud and Nymoen (1998). Thus, there
is in general no correspondence between the wage curve NAIRU uw and the steady
state of the dynamic wage-price system which we develop next.27
26
Real-world data of the rate of unemployment has also non-linear traits, such as shifts in mean,
but this non-linearity is probably better represented by regime shift dummies than by a unit-root.
Hence we regard data on u as representing an underlying I(1) process, although it may be subject
to deterministic shifts.
27
The heuristic explanation usually given after the NAIRU has been established from the two
f
b
static relationships is that excessive real wage claims on the part of the workers, i.e., wq,t
> wq,t
,
2
b
∗
result in increasing inflation (e.g. ∆ pt > 0), while wq,t < wq,t goes together with falling inflation
(∆2 pt > 0). The only way of maintaining a steady state with constant inflation is by securing
f
b
= wq,t
holds, and the function of unemployment is to reconcile the claims,
that the condition wq,t
see Layard et al. (1994, Ch. 3). There are really two additional doctrines of the Layard-Nickell
model. First, that no equilibrium with a constant rate of inflation is possible without the condition
f
b
wq,t
= wq,t
. Second, the adjustment of the rate of unemployment is the singular equilibrating
mechanism that brings about the necessary equalization of the competing claims. Neither of these
doctrines are needed to justify the use of bargaining theory in a cointegration context.
25
A second important step in making the wage setting model operation is identification. While the two cointegrating relationships are not identified in general, there
are several interesting special cases where identification is unproblematic, Bårdsen
et al. (2005, p. 81). For example, for the modelling of aggregated (rather than sectoral) wages and prices which is our concern identification is achieved by combining
(21) and (22) with a definition of the consumer price index pt ,
(25)
pt ≡ (1 − ζ) qt + ζpbt + ητ 3t , 0 < ζ < 1,
0 < η ≤ 1,
where the import price index pbt naturally enters. The parameter ζ measures of
the openness of the economy. Also, the size of the parameter η will depend on how
much of the retail price basket is covered by the indirect tax-rate index τ 3t . By
substitution of (22) in (25) the system is now in terms of wt and pt and this system
is usually identified, as we will see an example of in the next section.
The third stage in the operationalization of is the error-correction system. In
brief, we allow wage growth ∆wt to interact with current and past price inflation,
changes in unemployment, changes in tax-rates, and previous deviations from the
desired wage level consistent with (19)
(26)
∆wt − α12,0 ∆qt = c1 + α11 (L) ∆wt + α12 (L) ∆qt + β 12 (L) ∆zt
− β 14 (L) ∆ut − β 15 (L) ∆τ 1t
− γ 11 ecmw,t−r + β 18 (L) ∆pt + 1t ,
where ∆ is the difference operator, the α1j (L) and β 1j (L) are polynomials in the
lag operator L:
α1j (L) = α1j,1 L + · · · + α1j,(r−1) Lr−1 , j = 1, 2,
β 1j (L) = β 1j,0 + β 1j,1 L + · · · + β 1j,(r−1) Lr−1 , j = 2, 4, 5, 6.
The β−polynomials are defined so that they can contain contemporaneous effects.
The order r of the lag polynomials may of course vary between variables and is
to be determined empirically. This specification is a generalization of the typical
European wage curve, where the American version is derived by setting γ 11 = 0–see
Blanchard and Katz (1999)
Any increase in output above the optimal trend exerts a (lagged) positive pressure on prices, measured by the output gapt , as in Phillips-curve inflation models. In
addition, product price inflation interacts with wage growth and productivity gains
and with changes in the payroll tax-rate, as well as with corrections from an earlier
period’s deviation from the equilibrium price (as a consequence of e.g., information
lags, see Andersen (1994, Chapter 6.3)):
(27)
∆qt − α21,0 ∆wt = c2 + α22 (L) ∆qt + α21 (L) ∆wt + β 21 (L) gapt
− β 22 (L) ∆prt + β 25 (L) ∆τ 1t − γ 22 ecmf,t−r + 2t ,
where
α2j (L) = α2j,1 L + · · · + α2j,(r−1) Lr−1 , j = 1, 2,
β 2j (L) = β 2j,0 + β 2j,1 L · · · + β 2j,(r−1) Lr−1 , j = 1, 2, 5.
26
Solving (25) for qt and substituting out in equations (19), (26), (20), and (27), the
theoretical model condenses (19)—(27) to a wage-price model suitable to estimation
and similar to the early equilibrium-correction formulation of Sargan (1980):
¸
¸
∙
¸∙
¸∙
∙
1
−a12,0
∆w
∆w
α11 (L) −a12 (L)
=
+
∆p t
∆p t
−a21 (L) α22 (L)
−a21,0
1
(28)
∙
−
∙
γ 11 0
0 γ 22
⎡
⎢
¸⎢
⎢
−β 14 (L) −β 15 (L)
0
β 12 (L)
⎢
b21 (L) −b22 (L) ζα22 (L)
0
b25 (L) ηα22 (L) ⎢
⎢
⎣
12 (L)
−ζ α1−ζ
¸
×
∙
+
where
12 (L)
−η α1−ζ
1
− (1 + ζd12 ) −δ 13 ζd12 δ 15
− (1 − ζ)
1
(1 − ζ) −ζ 0
∙
e1
e2
¸
,
gap
∆z
∆pb
∆u
∆τ 1
∆τ 3
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎡t
⎢
⎢
¸⎢
δ 16
ηd12 ⎢
⎢
− (1 − ζ) −η ⎢
⎢
⎢
⎣
w
p
z
pb
u
τ1
τ3
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
t−r
t
α12,0
+ β 18,0 ,
1−ζ
a21,0 = (1 − ζ) α21,0 ,
α12 (L)
+ β 18 (L),
a12 (L) =
1−ζ
a21 (L) = (1 − ζ) α21 (L) ,
b2j (L) = (1 − ζ) β 2j (L) , j = 1, 2, 5,
δ 12
,
d12 =
1−ζ
e1 = 1 ,
e2 = (1 − ζ) 2 .
a12,0 =
(29)
map from the theoretical parameters in (26) and (27) to the coefficients of the
model (28). The validity of these parameter restrictions are tested in the evaluation
process.
The model (28) contains the different channels and sources of inflation discussed so far: Imported inflation ∆pbt , and a range of domestic channels: the output
gap, changes in the rate of unemployment, in productivity, and in tax rates. Finally
the model includes deviations from the two steady-state equations
¶
µ
η
(30)
w = const + p + δ 13 z + δ 15 u + δ 16 τ 1 + d12 ζ p − pb − τ 3
ζ
(31)
p = const + (1 − ζ) (w − z + τ 1) + ζpb + ητ 3
27
Table 1: Diagnostics for the unrestricted I(1) wage-price system , the restricted I(0)
system, and the final model .
Panel 1
Unrestricted system, 48 parameters
σ̂ ∆w = 0.83%,
σ̂∆p = 0.32%
HQ = −14.54,
SC = −13.82
ARv 1 − 5 F (20, 178) = 0.75[0.77]
Normality v χ2 (4) = 7.48[0.11]
Heteroscedasticity v F (66, 224) = 1.06[0.37]
Panel 2
Restricted I(0) system, 30 parameters
σ̂ ∆w = 0.86%,
σ̂∆p = 0.33%
HQ = −14.81,
SC = −14.41
ARv 1 − 5 F (20, 202) = 0.89[0.60]
Normality v χ2 (4) = 4.86[0.30]
Heteroscedasticity v F (75, 251) = 1.02[0.25]
Panel 3
Final model, 17 parameters
σ̂ ∆w = 0.85%,
σ̂∆p = 0.35%
HQ = −15.06,
SC = −14.83
Overidentification χ2 (13) = 9.47[0.74]
ARv 1 − 5 F (20, 216) = 0.96[0.52]
Normality v χ2 (4) = 2.26[0.69]
Heteroscedasticity v F (75, 272) = 1.15[0.22]
The sample is 1972(4) to 2004(2), 127 observations.
The numbers in [..] are p-values.
References: Overidentification test (Anderson and Rubin (1949, 1950),
Koopmans et al. (1950), Sargan (1988)),
AR-test (Godfrey (1978) and Doornik (1996)),
Normality test (Doornik and Hansen (1994)), and
Heteroscedasticity test (White (1980) and Doornik (1996)).
as Equilibrium Correction Mechanisms (EqCMs), which have weights γ 11 and γ 22
respectively. The expressions in (30) and (31) are the econometric model’s counterparts to the theoretical wage and price equations, equation (19) and (20) above.
Consistency with the assumed cointegration implies that the joint hypothesis
of γ 11 = γ 22 = 0 can be rejected. Tests of cointegration and possible simplifying
restrictions on the EqCMs are conducted in the next section.
The dynamic model has a steady-state solution with ∆2 pt = 0, also when dynamic homogeneity is imposed as a set of restrictions. The steady state is conditional
on any given rate of unemployment, which amounts to saying that the wage-price
subsystem does not tie down the equilibrium rate of unemployment. This is a similar property to the fair wage model in Hahn and Solow (1997). Instead, there is a
stalemate in the dynamic “tug-of-war” between workers and firms that occurs for a
given rate of unemployment, see Kolsrud and Nymoen (1998) and Bårdsen and Nymoen (2003) for discussion. We next shows that there is a similar stability property
28
for our extended version of the model.
6.3 Evaluation of the wage-price model’s structural properties
In this evaluation we use Norwegian seasonally unadjusted data for the period
1972(4)-2004(2), which is adds 11 quarters to the version of this model in Bårdsen et al. (2005, Ch. 9). This is not a large number of observations, but the period
includes one a notable change in Norwegian economic policy in March 2001, when
inflation targeting became official.
The variables
that contain ¤the long-run wage-price equations are collected in
£
0
the vector wt pt zt pbt ut . All variables are in logs. The wage variable
w, is average hourly wages in the mainland economy, excluding the North-Sea oil
producing sector and international shipping. The productivity variable z is defined
accordingly–as mainland economy value added per man hour at factor costs. The
price index p is measured by the official consumer price index. Import prices pb are
measured by the official index. The unemployment variable u is defined as a “total”
unemployment rate, including labour market programmes.
We also include, as non-modelled variables, the payroll-tax τ 1, indirect taxes,
τ 3 and real GDP y - the changes in which represent changes in the output gap,
if total capacity follows a trend. Institutional variables are also included. Wage
compensation for reductions in the length of the working day is captured by changes
in the length of the working day –see Nymoen (1989). Composite dummies are
used to capture the impact of incomes policies and direct price controls. The rate
of change of energy prices is also includes as exogenous, since the p is the log of the
headline CP I in this model.
In the estimated VAR wages and prices enter with three lags and the other
main variables enter with one or two lags. The diagnostics of the VAR show no
problems in the residuals, see Panel 1 of Table 1 below. This is accordance with
earlier modelling of this data set.
Since there are non-modelled I(1) and I(0) in the VAR, the canonical correlations are very high, so we proceed to the identification stage assuming that there are
two cointegrating relationships. Panel 1 of Table 2 uses normalization together with
the theoretical exclusion restriction on q, and a non-linear constraint on the effect
of indirect taxes. The resulting 6 overidentifying restrictions are not significant on
the χ2 (6) test. Panel 2 adds two more restrictions, in accordance with theory and
then panel 3 goes all the way to a fixed set of parameter values. Clearly all three
identifying steps are acceptable, the theoretical steady-state relationships appears
to be well identified in the data.
What about the empirical counterpart to the dynamic wage-price system in
equation (28)? To answer that question, we start with a reduced form EqCM which
includes the same information as on the original VAR, but of course all the I(1)
levels variables are now restricted by the two equilibrium correction terms given by
Panel 3 in Table 2. Hence we now seek identification in this I(0) system. We don’t
show the details of this restricted (i.e., by the cointegrating vectors) reduced form
here, but the associated diagnostics are shown in Panel 2 in Table 1.
We then “model the system”, using FIML estimation and seeking a parsimo-
29
Table 2: Testing steady-state hypotheses.
Panel 1: No effect from producer prices and imposed effect of indirect taxation
w = p + 0.86 z − 0.14u + 2.03τ 1
(0.08)
(0.02)
(1.11)
p = 0.58 (w + τ 1 − z) + 0.42pb + 0.5τ 3
(0.06)
2
χ (6) = 10.35[0.11]
Panel 2: Full effect of productivity and no effect of payroll-tax
w = p + z − 0.15 u
(0.02)
p = 0.58 (w + τ 1 − z) + 0.42pb + 0.5τ 3
(0.06)
2
2
χ (8) = 15.19[0.06], χ (2) = 4.84[0.09]
Panel 3: Imposed long-run solution
w = p + z − 0.15u
p = 0.6 (w + τ 1 − z) + 0.4pb + 0.5τ 3
2
χ (10) = 15.32[0.12], χ2 (2) = 0.13[0.94]
The sample is 1972(4) to 2004(2), 127 observations.
nious model in terms of parameters.
⎤
⎡
#
"
1 + 0.26L
0
(0.06)
d
¶
⎥ ∆w
⎢ µ
=
⎦ c
⎣
∆p
1 − 0.11L2
− 0.21 + 0.18 L
t
(0.03)
(0.03)
(0.05)
⎡
⎤
⎤⎡
∆2 y
0
0.09
0
(0.015)
⎣
⎦
⎣
∆z ⎦
(32)
0.03L − 0.03 0.025
∆pb t
(0.01)
(0.006) (0.008)
⎡
−⎣
0.12
(0.01)
0
0
0.06
(0.008)
⎤
⎦
∙
L2
−0.6L2
⎡
⎢
⎢
¸⎢
⎢
−1 −1
0
0.15L
0
0
⎢
L2 0.6 −0.4
0
−0.6 −0.5 ⎢
⎢
⎢
⎣
w
p
z
pb
u
τ1
τ3
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
t−1
The final model is shown in equation (32) and the diagnostics of this ‘structural
model’ is reported in Panel 3 of Table 1. Note in particular the statistic Overidentification χ2 (13) which is the joint test of all the overidentifying restrictions that
are separating the final model from the restricted I(0) system in Panel 2 of Table 1.
The statistic is insignificant, meaning that the final model encompasses the system,
hence relative to the overparameterized system in Panel 2, the final model has good
degree of fit. The two equilibrium terms are highly significant in their respective
equations. Hence, unlike was the case for the PCM (also on Norwegian data) there
is no ‘regress’ to a random walk (dVAR) model in this case. Our economic theory
of wage and price making behaviour stays in the model!
Apart from the ecm-terms, we have first the half-year growth rate of real
GDP which represent demand pressure on CPI inflation in the model (but no direct
influence on nominal wage growth). Productivity growth has a negative impact
30
0.02
0.01
r Dw
0.00
0.00
−0.02
−0.01
2005
1.0
1990
1.0
1up Dw
1995
2000
1%
0.5
0.5
0.0
0.0
1990
1.0
1up CHOWs
1995
2000
2005
2000
2005
r Dp
1990
1up Dp
1990
1995
2000
2005
1995
2000
2005
1%
1%
0.5
1990
1995
Figure 4: Model (32): Recursive residuals and sequences of Chow tests
and import price growth is estimated to have a small positive short run effect.
Both of these two effects are as expected, and we note that the import price effect
implies that the pass-through of transitory changes in the rate of foreign exchange
is negligible A permanent shock to the exchange rate will have a noticeable effect
on the CPI level after some time though. In principle, because of the homogeneity
restriction on the cointegration relationships long run pass-through is 100%. In the
wage growth equation only the productivity term is included. Again, the size of the
estimated coefficient is reasonable: Although the effect of a permanent change in z
on wages is one, the impact effect of the quarterly rate of change ∆z is much lower,
after all most of the quarterly variation is purely short-term.28
From model (32) we see that the short-run wage-price interactions are quite
28
s mentiioned we also control for changes in energy prices, indirect taxes and of changes in the
length of the working week. The estimated coefficients of these variables are omitted in order to
save space.
31
important in the model, which of course is an expected feature of a model of the
inflation spiral. Inflation depends on ∆wt and ∆wt−1 with almost equal coefficients
(again, this can represent that prices adjust more strongly to relatively permanent
changes in wage costs). In the wage equation, ∆pt does not enter at all, so wage
growth adjust to price increases only trough the ecm-term in this model. In earlier
specifications we have used a simultaneous equation model, which gave the same
residual standard errors. Hence, the simultaneous equation specification and the
recursive model are difficult to separate, and do represent structural properties it
seems. As pointed out by Nymoen (1991) on a related data set, both model specification of are consistent with the view that prices react somewhat faster to changes
in wages than vice versa.
So far we have discussed the theory consistency (identification!) and ability
to explain the data, and the results show that there are no particular problems (or
modelling conflicts) between these two structural properties. Encompassing of other
models is another structural property, and we note directly from model (32) that our
model of the inflation spiral is cannot be reduced to a conventional Phillips-curve
system. This is due to the significance of the ecm-terms in both equations. What
about the New Keynesian Phillips curve? According to that model, the (lagged)
cointegration terms for example might be due to omitted forward looking terms. It
is possible to test this, and we refer to the exposition in Bårdsen et al. (2005, p.
141–145) which shows that the opposite is observed: By inclusion of the ecm-term
of the price equation in a Norwegian NPC, the estimated coefficient of ∆pt+1 in the
NPC is reduced to zero.
7
Conclusions
To both producers and users of macroeconomic models the word “structure” has a
positive ring to it. For that reason, the terms structural equation and structural
model are likely to stay in the disciplines’ vocabulary. Yet the meaning of structural
model has changed dramatically in the course of a few decade. The ‘big structural
econometric models’ of the 1970s, or the text-book simultaneous equations model
are not recognized as structural models by modern mainstream macroeconomists.
Instead, structural models (with deep structural parameters) delineates the class of
models that adhere to microfoundations with infinitely lived representative agents
and rational expectations, and a good deal of market perfections. In line with other
authors we refer to the consensus approach to macro modelling as Walrasian. It
is characterized by a belief in one-step specification of the whole model, and that
the goal of theory is to provide an economic model that accurately reflects the realworld macroeconomy. Thus the realm of theory has been moved from the stylized
counterfactual systems to the real world.
Monetary policy has become an important area of demand for macroeconomic
analysis, and Walrasian modelling methodology has moved in quickly and with great
force. The spearhead is the New Keynesian DSGE models which are presented as
structural models because of their theory underpinnings. Nevertheless, it is unclear if
any DSGE model are structural in the sense of being invariant under extensions over
time, across regimes and to additional information sources, Hendry (1995b). Failure
on any of these requirements reveal a non-structural equation in a wider meaning
32
of the term. In line with this, we propose that to use ‘structural interpretation’
to denote ‘derived form theory’ and to treat it as one of many dimensions of the
operational concepts of ‘structural property’ and ‘structural representation’. Hence
a model that achieves the ideal of a structural representation of the macroeconomy
embodies not only theoretical coherency but also explanatory power, stability and
robustness to regime shifts.
Like beauty in people, the elegance of theoretically derived economic models is
only skin deep, and does not guarantee that their econometric counterparts have the
structural properties discussed above (explanatory power, constancy and autonomy
of parameters; encompassing). These hallmarks of useful econometric models cannot
be postulated, but are likely to be hard earned features of models that have been
developed and tested over time with the aim of maximizing their degree of structural
content. Of course, it is understood that every model is a simplification of reality
and inherently ‘false’. Nevertheless, our definition allows us to talk about degrees of
structural content. We believe that the degree of structural property of an equation
(or a complete model) is well worth assessing, also from a model users’s point of
view.
The empirical sections above show that a model with structural interpretation,
the New Keynesian Phillips curve, NPC, fails on each other measurable structural
property when applied to euro-area data. Even more radically, as shown by Jeff
Fuhrer (2005), the New Keynesian Phillips curve when estimated on US data, fails
to meet its own criteria of success: instead of explaining inflation persistence in
terms of the persistence inherited from the forcing variables, the intrinsic persistence
due to lagged inflation is the model. In our analysis, this internal inconsistency is
created by the low explanatory power of the US inflation NPC. Our review of NPC
estimation results on several other data sets show that the NPC fits no better than
a random-walk type of time series model. Hence, the internal inconsistency pointed
out by Fuhrer is likely to prevail. DSGEs, which uses the New Keynesian Phillips
curve, can therefore not claim to be structural representations of the macroeconomy.
As noted by Fuhrer, the proponents of the DSGE model now have to come up with
a new way of modelling inflation.
The failure of the Walrasian approach to econometric modelling of the rate
of inflation is contrasted with a Marshallian methodology, (Hoover (2004)). This
methodology has achieved some success in establishing structural representations of
the inflation spiral in for example Norway and the UK. In general terms, Marshallian macroeconomic methodology combines theory (we provide an example where
theory is used to define identifiable steady-state relationships clearly), with qualitative and quantitative information about the specific market or economy that is
analysed. A modernized Marshallian methodology can for example draw on the cointegration approach to non-stationary systems, and general-to-specific model specification. The role of forward looking behaviour can be assessed, and expectations
can be represented in the specified model. When the purpose is to specify a full
macroeconometric model, Marshallian methodology is open to stepwise modelling,
whereby econometric modules for single markets are grafted into the larger (complete) macro model. If it gains acceptance, Marshallian methodology may reinstate
stepwise and sectorial modelling as respectable activities in macroeconomics, a research programme that was stopped dead in its tracks by Lucas’ reorientation of
33
macroeconomics.
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