methodological unification - uh
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METHODOLOGICAL UNIFICATION*
JIM GRANATO
Center for Public Policy and Department of Political Science, University of Houston, USA
MELODY LO
Department of Economics, College of Business, University of Texas at San Antonio, USA [email protected]
SUNNY M. C. Wong
Department of Economics, University of San Francisco, USA [email protected]
* Versions of this paper have been presented at the 2004 EITM Summer Program (Duke University), the annual meeting of the Southern Political Science Association (January 6-8, 2005 in New Orleans, Louisiana), the annual meeting of the Canadian Political Science Association (June 2-4, 2005 in London, Ontario), Ohio State University, Penn State University, the University of Texas at Austin, the 2006 EITM Summer Program (University of Michigan), and the 2007 Essex Summer School in Social Science Data Analysis and Collection Program (University of Essex, Colchester, UK). We thank Jim Alt, Mary Bange, Harold Clarke, Michelle Costanzo, John Freeman, Mark Jones, Skip Lupia, David Primo, and Frank Scioli for their comments and assistance.
Abstract:An important disconnect exists between the current use of formal analysis and applied statisticaltechniques. In general, a lack of linkage between formal analysis and applied statistical proceduresleads to a failure to identify invariant parameter estimates. Consequently, current methodologi-cal practice can produce statistically significant parameters of ambiguous origin that fail to assistin falsifying theories and hypotheses. We demonstrate that methodological unification, because itleverages the mutually reinforcing properties of formal and applied statistical analysis, contributesto identified and invariant parameter estimates. These estimates are suitable for hypothesis test-ing and enabling scientific cumulation. A framework for methodological unification is proposed.This framework includes: 1) connecting behavioral and applied statistical concepts; 2) developingand relating formal and applied statistical analogues of these concepts, and 3) linking the ana-logues. We demonstrate the various elements of this framework with examples from development,voting behavior, and the political economy of macroeconomic policy. We contrast this unifiedframework with common applied statistical procedures and demonstrate the added value method-ological unification possesses for achieving scientific cumulation.
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“Empirical observation, in the absence of a theoretical base, is at best descriptive. It tells one whathappened, but not why it has the pattern one perceives. Theoretical analysis, in the absence ofempirical testing, has a framework more noteworthy for its logical or mathematical elegance thanfor its utility in generating insights into the real world. The first exercise has been described as“data dredging,” the second as building “elegant models of irrelevant universes.” My purpose is totry to understand what I believe to be a problem of major importance. This understanding cannotbe achieved merely by observation, nor can it be attained by the manipulation of abstract symbols.Real insight can be gained only by their combination.” (Aldrich 1980, 4).
“...there is still far too much data analysis without formal theory – and far too much formal theorywithout data analysis.” (Bartels and Brady 1993, 148).
1. IntroductionAn important disconnect exists between the current use of formal analysis and applied statistical
techniques.1 This discontinuity contributes to an overemphasis on attaining statistical significance
through the manipulation of standard errors, exercises in data mining, and overall inattention in
relating theoretical specifications to applied statistical tests (Achen 2002, 2005). It can also be
demonstrated that decoupling formal analysis from applied statistical procedures results in a fail-
ure to identify invariant parameter estimates or contributing to the falsification of theories and
hypotheses.2
1 We center the discussion on formal analysis and applied statistical analysis. Formal analysis refers to deductivemodeling that can include a theorem and proof presentation or computational modeling that requires the assistance ofsimulation. Applied statistical analysis involves data analysis using statistical tools. We use the terms analysis andmodeling interchangeably.
In addition, the linkage of formal and applied statistical analysis — the form of methodological unification wedevelop in this paper — possesses important attributes that aid in falsification and, ultimately, scientific cumulation.Formal models, for example, force clarity about assumptions and concepts; they ensure logical consistency, and theydescribe the underlying mechanisms, typically behavioral, that lead to outcomes (Powell 1999, 23-39). The other com-ponent part of methodological unification — applied statistical models and tests — provide generalizations and ruleout alternative explanations through multivariate analysis. Applied statistics assist in distinguishing between causesand effects, allow for reciprocal causation, and also help assess the relative size of the effects. When these respectiveapproaches are unified a researcher has the opportunity to use their scientific attributes in mutually reinforcing waysto aid in developing transparent relations between theory and test.2 The intuition behind the terms identification and invariance is as follows. For applied statistical models identifi-cation relates to model parameters (e.g., bβ) and whether they indicate the magnitude of the effect for that particularindependent variable. Or, in more technical terms, “A parameter is identifiable if different values for the parameterproduce different distributions for some observable aspect of the data” (Brady and Collier 2004, 290).
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Current practice, particularly applied statistical practice, is based in part on a tradition that
borrows and applies statistical tools that improve upon the use of older techniques. But, as this
process of replacing old with new technique took hold, the search for causal mechanisms was
largely ignored. In more technical language, the creation of methodologies that isolated structural
parameters, for the identification of these parameters, became secondary to the use of hand-me-
down applied statistical techniques that end up doing things such as manipulating standard errors
and their associated t-statistics.3 In this methodological environment we find ourselves with “re-
sults” that include statistically significant parameters of ambiguous origin — and little in the way
of scientific cumulation.
The scientific consequences of this methodological status quo are far reaching. Because
the usual methodological approach cannot produce identified and invariant parameter estimates,
policy recommendations, for example, lack a scientific basis since there is no useful information
regarding the mechanism(s) on policy and treatment effectiveness. Among other things, current
practices do not typically model an agent’s behavior and responses to alternative policies as well
as other social, political, and economic factors. As a result, there is no way of knowing how
citizens’ behavior may affect the estimate of structural parameters when the behavioral response
In applied statistical practice, invariance refers to the (non)constancy of the parameters of interest. More gener-ally, “the distinctive features of causal models is that each variable is determined by a set of other variables througha relationship (called “mechanism”) that remains invariant when those other variables are subjected to external influ-ences. Only by virtue of its invariance do causal models allow us to predict the effect of changes and interventions...”(Pearl 2000, 63). In short, the terms invariant or invariance, when applied to applied statistical models, centers onwhether a relation (signified by a parameter) remains constant in the face of a treatment (or policy) shift.
The argument made here is that identification and invariance are not guarantees that a model is “correct;” rather,the point is the analytical transparency produced by models that meet these conditions have falsifiable properties thataid in cumulation.3 We adopt Heckman’s (2000, 59) terminology below:
Structural causal effects are defined as the direct effects of the variables in the behavioral equations...When theseequations are linear, the coefficients on the causal variables are called structural parameters (emphasis added), andthey fully characterize the structural effects.
Heckman also notes there is some disagreement about what constitutes a structural parameter. The disagreementcenters on whether one uses a linear model, a non-linear model or, more, recently a fully parameterized model. Inthe latter case, structural parameters, can also be called “deep” to distinguish between “the derivatives of a behavioralrelationship used to define causal effects and the parameters that generate the behavioral relationship” (page 60).
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of citizens can influence the success or failure of a policy or treatment. The reason, as Lucas (1976)
has argued, is that in-sample estimation provides little guidance to policymakers in predicting the
effects of policy changes because the parameters of current econometric models are unlikely to
remain stable under alternative policies.4
In this paper we argue for methodological unification between formal and empirical analysis
to help ensure that identified and invariant parameter estimates are the consequence.5 We propose
a unified approach that combines formal and empirical analysis — which is consistent with what
has been termed empirical implications of theoretical models (EITM).6
Methodological unification is not new. In its earlier versions, scholars from organizations
such as the Cowles Commission unified formal and empirical analysis to identify causal mech-
anisms through the use of structural parameters. What this version of EITM does is build on
the Cowles Commission approach by placing an emphasis on developing behavioral and applied
statistical analogues and linking these analogues.7 We argue that this version of methodologi-
cal unification would further assist in scientific cumulation because it emphasizes operationalizing
(modeling) behavioral mechanisms to foster a more transparent linkage between theory (predic-
tion) and test. In sum, the methological unification proposed here also places a focus on parameter
identification and parameter invariance but it leverages key aspects of human behavior in this mod-
eling and testing process.
4 The Lucas critique is based on the following intuition: “...given that the structure of an econometric model consistsof optimal decision rules ... and that optimal decision rules vary systematically with changes in the structure of seriesrelevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometricmodels” (Lucas 1976, 41).5 There is a large literature devoted to identification problems (see, for example, Fisher 1966; Manski 1995). Someresearchers treat the issue of simultaneity and identification as one and the same. We consider identification in abroader sense that includes simultaneity, but not limited to simultaneity.6 The linking of formal and empirical analysis is part of the Empirical Implications of Theoretical Models (EITM)initiative supported by the National Science Foundation. For more information see:http://www.nsf.gov/sbe/ses/ polisci/ reports/eitmreport.jsp and http://www.nsf.gov/pubs/2003/ nsf03552/nsf03552.pdf.7 An analogue can be thought of as a device in which a concept is represented by continuously variable — andmeasurable — quantities. Analogues serve as analytical devices for behavior and, therefore, provide for changes inbehavior as well as a more transparent interpretation of the formal and applied statistical model. Analogues alsoemphasize measurement validity — the relation between a measure and the (unmeasured) concept it is meant torepresent.
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This paper is organized as follows. In the next section, we first outline how methodologi-
cal unification contributes to a modeling dialogue that can result in scientific cumulation. We also
discuss how some current research practices hinder scientific cumulation because they create sep-
aration between theory and test — and end up being nonfalsifiable. Section 3 contains a macro
political economy example to demonstrate the weaknesses associated with some current method-
ological practices. Specifically, the example relates these practices to the estimated parameters
(inference) and the predictions of variables of interest.8 Section 4 introduces an original and foun-
dational approach to methodological unification — the Cowles Commission. We then introduce
an early example of methodological unification, Robert Solow’s model of economic development
(Solow 1956). A strength of Solow’s model, and methodological unification, is its ability to al-
low for the successive extensions of his initial model and ultimately support subsequent efforts to
achieve scientific cumulation. In Section 5, we introduce an EITM framework. Section 5 provides
a means of accomplishing falsification by treating social, behavioral, political, and economic con-
cepts (analogues) and applied statistical concepts (analogues) as linked entities. Using examples
from voting behavior and macroeconomic policy and outcomes, we show that the properties of the
social, behavioral, political, and economic analogue(s) and the properties of the applied statisti-
cal analogue(s) can be mutually reinforcing. For each example the unifying properties also point
to extensions of the respective models and tests. We discuss extensions or potential extensions
that build on the original work. Section 6 summarizes these results and provides some conclud-
ing comments on how methodological unification, in general, and EITM, in particular, can change
evaluation procedures as well as how it extends to other research areas.
2. Modeling Dialogues and Scientific CumulationAn enormous amount of research has been devoted to what constitutes scientific cumulation.
Methodological unification can assist in scientific cumulation because it creates a dialogue be-
8 We will use the word inference to refer to a parameter in a regression or likelihood (b). We use the word predictionto refer a model’s forecast of a dependent variable (y). For a technical treatment of these two concepts see Engle,Hendry, and Richard (1983).
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tween theory and test. In more recent versions of methodological unification (e.g., EITM) the
dialogue between model and test now takes on the form of exploiting the mutually reinforcing
properties of formal and empirical analogues.
2.1. Non-Cumulative Research Practices
Unfortunately, the methodological status quo is one in which so-called technical work is only
loosely connected to the fundamental scientific considerations of identification, invariance, and
falsification. Current quantitative research practice places an overwhelming focus on whether sig-
nificant results can be found via various applied statistical techniques. The reliance on statistically
significant results means nothing when the researcher makes little attempt to identify the precise
origin of the parameters in question. Absent this identification effort, it is not evident where the
model is wrong.
We can also evaluate current practice in relation to how it contributes to a modeling dialogue.
What we see is that the process of prediction and validation are never directly applied. Instead,
the empirical test(s) remains in a loop or dialogue with itself. An iterative process of data mining,
overparameterization, and the use of statistical patches (Omega matrices) replaces prediction and
validation. This inevitably follows because current practice does not attempt to identify model
parameters (b’s).9
If we narrow research practice to the use of applied statistics, then three common prac-
tices (data mining, overparameterization, and the use of statistical weighting and patching (e.g.,
“Omega Matrices”)) impairs scientific cumulation (Granato and Scioli 2004). We further refine
this discussion by showing how these practices affect a widely used test indicator, the t-statistic,
which is defined as the ratio of an estimated coefficient (b) to its standard error (s.e.(b)), that is,b
s.e.(b). We have argued that falsifiability is imperative to scientific cumulation and that falsifiabil-
ity requires the mechanisms relating cause and effect are identified. In the case of a t-statistic, this
9 While this example uses linear procedures, non-linear procedures are subject to many of the same weaknesses.Achen (2002), for example, raises questions about the forms of statistical patching in various likelihood proceduresand how these practices obscure identification.
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means linking the formal model to the test and focusing on the identification of the parameter b.
Let us now briefly describe these three common practices and whether they have any relation
to identifying b:
(1) Data Mining: Data mining involves putting data into a statistical package with minimal the-
ory. Regressions (likelihoods) are then estimated until either statistically significant coefficients or
coefficients the researcher uses in their “theory” are found. This step-wise search is not random
and has little relation to identifying causal mechanisms (see Lovell 1983; Denton 1985).
(2) Overparameterization: This practice, related to data mining, is where a researcher includes,
absent any systematic specification search, a plethora of independent variables into a statistical
package and gets significant t-statistics somewhere. Efforts to identify an underlying causal mech-
anism are also ineffectual (Achen 2005).10
(3) Omega Matrices: Data mining and overparameterized approaches are virtually guaranteed
to break down statistically. The question is what to do when these failures occur. There are
elaborate ways of using (error) weighting techniques to correct model misspecifications or to use
other statistical patches that influence s.e.(b). Many intermediate econometric textbooks contain
chapters containing the Greek symbol: Omega (Ω) (e.g., Johnston and DiNardo 1997, 162-164).
This symbol is representative of the procedure whereby a researcher weights the data that are
arrayed (in matrix form) so that the statistical errors, ultimately the standard error noted above, is
altered and the t-statistic is manipulated.11
10 In the absence of formal models, purely applied statistical procedures that use systematic rules in a specificationsearch can be cumulative. See Clarke et al. (2004, 79-129) for an example of building composite empirical modelsthat follow a systematic specification search. Composite models can be crucial in the process of methodologicalunification.11 By way of example (using OLS), consider the following model in scalar form (we drop the constant for simplicity):
yt = βxt + ηt,
and assume there is first-order serial correlation:ηt = ρηt−1 + νt,
where νt is a white noise process. With this estimate of ρ a researcher can “remove” the serial correlation:yt − ρyt−1 = β (xt − ρxt−1) + νt.
Alternatively, in matrix form, we can express this transformation as:βGLS =
¡X 0Ω−1X
¢X 0Ω−1Y,
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In principle, there is nothing wrong with knowing the Omega matrix for a particular statisti-
cal model. The standard error(s) produced by an Omega matrix can serve as a check on whether
inferences have been confounded to such an extent that a Type I or Type II error has been commit-
ted. Far too often, however, researchers treat the Omega weights (or alternative statistical patches)
as the result of a true model. Given that the parameter of “ρ” is based on estimating the error of the
regression, researchers that decide to use this weight are taking the mistakes of their model to “fix”
their standard errors. It is akin to painting over a crack on a bridge (Hendry 1995; Mizon 1995).
This attitude hampers scientific progress because it uses a model’s mistakes to obscure flaws.
Another issue is when using a ρ-restriction, researchers are imposing a restriction on variables
in the estimation system. In the time series case, researchers assume all variables in the system
have the same level of persistence. In the time series-cross-section case, the restriction is even
more severe as researchers assume that all the cases and all the independent variables have the
same level of persistence.
A final scientific problem with ρ-restrictions is that the algebraic manipulations involved with
their imposition can fundamentally alter the original model so that there is no longer any relation
between the theory and the test. A theory that assumes, for example, a certain level of persistence
in behavior (e.g., party identification) can be fundamentally altered by tools used to “filter out”
persistence.
3. Non-Cumulative Research Practice: An ExampleWe demonstrate the problem with current practice in the following macro political economy il-
as opposed to the OLS estimator:βOLS = (X 0X)
−1X 0Y.
The difference is the Ω matrix which can be represented as:
Ω =
⎡⎢⎣ 1 ρ ρ2 ...ρ 1 ... ...ρ2 ... 1 ...... ... ... 1
⎤⎥⎦and with the “ρ” correction:
Ω−1 =
⎡⎢⎣ 1 −ρ ... ...−ρ 1 + ρ2 ... ...... ... 1 + ρ2 ...... ... ... ...
⎤⎥⎦ 1
1− ρ2.
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lustration. In this example we use a structural model to show a relation between parameters.12
This is contrary to the current practice which typically ignores structural equation systems (and
reduced forms), let alone identification conditions. We then show via simulation how the weak-
nesses of current practices leads to serious scientific consequences such as incorrect inference and
misleading policy advice.
We examine the relation between a particular macroeconomic policy and outcome: counter-
cyclical monetary policy and inflation. To keep things simple in this example, we have left out
various political and social influences on the policy rule. While this research area holds great po-
tential for explaining why policymakers behave certain ways, it does not affect the methodological
point of this example.13
The model incorporates a lagged expectations augmented Phillips curve, an IS curve (aggre-
gate demand), and an interest rate policy rule (Taylor 1993). Each of these structural equations is
a behavioral relation and they can be derived from microfoundations. In this example, however,
we will also abstract out the microfoundations since they are not central to our demonstration.
The model has the following structure:
yt = ynt + γ (πt −Et−1πt) + u1t, γ > 0, (1)
yt = λ1 + λ2 (it −Etπt+1) + λ3Etyt+1 + u2t, λ1 > 0, λ2 < 0, λ3 > 0, (2)
it = πt + αy(yt − ynt ) + απ (πt − π∗t ) + r∗t , (3)
where yt is the log of output, ynt is the natural rate of output which follows a linear trend: α + βt,
and πt is price inflation. Et is an conditional expectations operator such that Et−1πt is expected
inflation for period t given the information available up to period t−1, Etπt+1 is expected inflation
one period ahead, and Etyt+1 is expected output one period ahead.14 The variable it is a nominal
interest rate that the policymaker can influence, π∗t is the inflation target, r∗t is the real interest rate,
12 Classic work in macro political economy does not rely on structural models (e.g., Hibbs 1977), but see Chappelland Keech (1983), Alesina and Rosenthal (1995), and Freeman and Houser (1998) as exceptions.13 See Chappell and Keech (1983) for an application of a structural model that incorporates the length of a presidentialterm.14 See Sargent (1979) for the detailed discussion on the rational expectations operator.
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u1t is an iid shock (demand shock), and u2t is an iid shock (supply shock).
At issue is the relation between policy and inflation. The model posits that aggregate supply
and demand depend on the expectations over the course of policy and this policy follows some
stable probability. Furthermore, agents understand the policy rule and augment their behavior to
include the expected gains or losses implied by the policy rule and policymaker behavior (Lucas
1976).
The coefficients αy and απ represent the aggressiveness that policymakers possess in stopping
inflationary pressures. Positive values of αy and απ indicate an aggressive inflation-stabilizing
policy tack. These positive parameter values reflect policymaker willingness to raise nominal
interest rates in response to excess demand (inflation), whether it is when output is above its natural
rate (yt > ynt ), or when inflation exceeds its prespecified target (πt > π∗t ). The coefficients
typically range between [0, 2] (Clarida, Gali, and Gertler 2000).15
With the relation between countercyclical monetary policy and inflation stated, we now solve
for inflation using the method of undetermined coefficients. The minimum state variable solution
(MSV) can be presented as:16
πt =
µJ0
1− J1 − J2+
J2J3β
(1− J1 − J2)2
¶+
µJ3
1− J1 − J2
¶ynt +Xt,
15 Clarida, Gali, and Gertler (2000) refer to (3) as a “backward looking” rule. They estimate αy, απ in (3) for theUnited States (1960:1-1996:4). They find that αy ranges between 0.0 to 0.39 and απ ranges between 0.86 to 2.55.They conclude that the United States monetary authority moved to nearly an exclusive focus on stabilizing inflation.16 The MSV solution is the simplest parameterization one can choose using the method of undetermined coefficients(see McCallum 1983).
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where:
J0 = (λ1 − λ2αππ∗t + λ2r
∗t + λ3β)Θ
−1,
J1 = (γ − λ2αyγ)Θ−1,
J2 = λ2Θ−1,
J3 = (λ3 − 1)Θ−1,
Xt = [(λ2αy − 1)u1t + u2t]Θ−1,
and Θ = γ (1− λ2αy)− λ2(1 + απ).
In more compact form the solution is:
πt = Ξ+Ψynt +Xt, (4)
where:
Ξ =J0
1− J1 − J2+
J2J3β
(1− J1 − J2)2 ,
Ψ =J3
1− J1 − J2.
Equation (4) has the attribute that it can relate parameters (αy, απ)with πt. The problem, however,
is that — absent added information — it is impossible to explicitly relate policy and treatment
changes to outcomes.
3.1. Current Practice and Scientific Cumulation
There are important scientific consequences when we fail to link formal and applied statistical
analysis for purposes of deriving structural parameters. First, consider the utility of a reduced form
— which is usually not derived in the current methodological environment. A reduced form such
as (4) possesses weaknesses when it comes to making inferences. The reduced form parameters
(Ji0s,Ξ,Ψ) cannot strictly identify the parameters that relate cause and effect (i.e., αy, απ). Where
reduced forms have power is not in making inferences but in making predictions: reduced form
estimates provide assistance in ex-ante forecasts.
How useful then are reduced forms in making predictions based on specific values of the
independent variables — the so-called conditional forecast? With a reduced form a researcher
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cannot make conditional forecasts. The reason is that the system (described in equations (1) -
(3)) depends on the behavior of the agents and whether responses from agents are invariant. If
agents’ behavior is not invariant, the parameters (in equations (1) - (3)) are not invariant. Without
a mechanism detailing how structural parameters (and behavior) remain (in)variant as independent
variables change, an applied statistical model fails in assessing alternative independent variable
shifts.
While reduced forms lack inferential power necessary to make conditional forecasts, it still
has a linkage to theoretical foundations. Things can be far worse, however, if we use a single
empirical equation similar to equation (4), with no formal-theoretical linkage, and rely on current
applied statistical practices. The parameter(s) “identified” by these current practices lack any real
meaning or use.
To see the flaws associated with current practice more straightforwardly consider equation (5)
which we treat as a single equation estimate of πt:
πt = d0 + d1ynt + v1t, (5)
where v1t is the error term. If we contrast the similarly situated parameters in equations (4) with
(5), we note that d0 would serve the purpose of Ξ and d1 serves the purpose of Ψ. But, already
we can see that equation (5) fails to make any structural statement about the relation between the
policy rule in (3) and inflation in (5). There is no explicit relation between d0 or d1 with αy or απ.
Assume the researcher chooses to ignore any process of methodological unification. Instead
the analyst tries to estimate a shift in policy regime and reestimates (5) with new variables. One
typical way is to add dummy variables signifying policy shifts due to factors such as partisanship
and other factors (e.g., Hibbs 1977). We keep the empirical model small and rewrite (5) with just
one added variable, a policy shift dummy variable (SHIFTt) signifying a change in the intercept or
the level of inflation:
πt = d0 + d1ynt + d2SHIFTt + v2t, (6)
where v2t is the error term.
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Does this really help with identification and falsification? Notice that the parameter d2 in
(6) does not actually reflect actual policy shifts relating policy parameters to inflation (one such as
equation (3)). This shortcoming is severe. It means we do not know what parameters in the system
can lead to counterintuitive results and, ultimately, incorrect policy or treatment recommendations.
Consider the following simulation of the system expressed in (1) , (2) , and (3). In this sim-
ulation the structural explanation, relating parameters in the system, shows that aggregate demand,
as represented by equation (2), must respond in a certain way to changes in real interest rates and
the expected output level. This relation is represented by the parameter λ3 in equation (2). What
happens to the relation between inflation-stabilizing policy and inflation if λ3 is not invariant and
contains alternative responses?
(Figure 1 About Here)
In Figure 1, Panels 1a, 1b, and 1c report the results in a simulation of the system.17 Changes
in inflation are represented in each panel, given changes to λ3. In Panel 1a, when λ3 > 1, an
aggressive policy (αy, απ = 0.5 > 0) does not reduce inflation. On the other hand, in panel Panel
1b, when 0 < λ3 < 1, inflation falls. It is only in the third case, when λ3 = 1, we find that an
aggressive policy keeps inflation roughly around a 2 percent target (see Panel 1c).
The implication of these simulations has direct significance for both reduced form estimation
and current practice — with the consequences being especially direct for current practice. If a
researcher were to estimate the reduced form of inflation as represented in (4) they would find
this instability in the forecast and forecast error. However, they would have difficulty finding the
source of the instability given the lack of information in identifying the relation(s) between the
parameters in (2) and the remaining parameters (variables) in the model.
Yet, this is far better than what occurs using current practices. Specifically, depending on the
value of λ3, there are alternative outcomes that would not be illuminated using (6) and the practices
17 The simulation parameter values are the following for the AS, IS, and policy rule:AS: α = 5.0;β = 0.05; yn0 = 1.0; γ = 10;σu1 = 1.0.IS: λ1 = 3.0;λ2 = −1.0;λ3 = (0.5, 1.0, 1.5);π∗ = 2.0;σu2 = 1.0.Policy rule: αy = 0.5;απ = 0.5; r∗ = 3.0.
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associated with that equation. But, now assume we estimate (6) and find a significant value for
d2 indicating that when policy shifts in an aggressive manner, the level of inflation falls. Does
this mean that aggressive policy reduces inflation? We do not know using this research practice.
Absent an explicitly posited relation, all we can say is that some parameter, that may or may not
relate the independent variable to the dependent variable, is significant.
What is more important is that a formal model would show the substantive findings are not
generalizable when alternative and relevant exogenous conditions are considered. Indeed, the
indeterminacy result shown in Figure 1 is not robust to the inclusion of nominal variables to the
interest rate rule.18 But, we would not know what we do not know under current practices that give
us estimates of equations (5) and (6).
4. Methodological Unification: The Cowles CommissionFor some social sciences, such as political science, the emphasis on applied statistical technique
as opposed to identifying structural parameters can be traced back to a pedagogical tradition that
involved an aversion to mathematical modeling (Arrow 1948). But, this aversion came with a cost.
Absent mathematical modeling, the discipline lacks a basic tool to identify causal mechanisms.
More importantly, academic research exists that can aid this break with current methodologi-
cal practice. The Cowles Commission, for example, has established conditions in which structural
parameters can be identified.19 It was the Cowles Commission that explored the differences be-
tween structural and reduced-form parameters. Conditions for identifiability were introduced to
aid in this differentiation. Along with their work on structural parameters, the Cowles Commis-
sion also gave formal and empirical specificity to issues such as exogeneity and policy invariance
(Aldrich 1989; Morgan 1990; Christ 1994; and Heckman 2000).20
18 Alternatively, McCallum and Nelson (1999) demonstrate that when output is not modeled as a constant, an IScurve of the form (2) can produce indeterminacies.19 Morgan (1990) provides an extensive historical account of the contributions of the Cowles Commission. Forfurther background on the Cowles Commission consult the following URL: http://cowles.econ.yale.edu/.20 With the passage of time, the Cowles Commission’s approach has been criticized. Ironically, the effort to satisfymathematical conditions for parameter “identification” led to practices that undermined the promise of methodologicalunification. In particular, Sims (1980) pointed out the “incredible” theoretical restrictions that were imposed.
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These contributions rested, in part, on a scientific vision that involved merging formal and
applied statistical analysis. The basis for this linkage was the idea that random samples were
governed by some latent and probabilistic law of motion (Haavelmo 1944; Morgan 1990). Further,
this viewpoint meant that formal models, when related to an applied statistical model, could be
interpreted as creating a sample draw from the underlying law of motion. A well-grounded test
of a theory could be accomplished by relating a formal model to an applied statistical model and
testing the applied statistical model. This methodological approach was seen, then, as a valid
representation and examination of underlying processes in existence.
4.1. Example 1: Development
We demonstrate the process of scientific cumulation using the well-known Solow (1956) model
of economic development. This example shows how the traditional approach to methodological
unification can provide a basis for a modeling dialogue and scientific cumulation.
4.1.1. The Formal Model
In his seminal paper, Solow (1956) argues that capital accumulation and exogenous technological
progress are fundamental mechanisms in economic development. Using a simple Cobb-Douglas
production function with a dynamic process of capital accumulation, Solow concludes that a coun-
try experiences a higher transitory growth rate when the country increases its national saving to
stimulate capital accumulation. The formal model has the following structure:
Yt = BtKαt L
1−αt , 0 < α < 1 (7)
St = sYt, 0 < s < 1 (8)
Kt+1 −Kt = St − δKt, (9)
Lt+1 = (1 + n)Lt, (10)
At+1 = (1 + g)At, (11)
where aggregate production in year t (Yt) is determined by capital (Kt) , labor (Lt), and techno-
logical progress (Bt) which is defined as Bt ≡ A1−αt under the Cobb-Douglas specification. St
15
is gross domestic savings in year t and the savings rate (s) is a constant proportion of total pro-
duction. Equation (9) represents the capital accumulation (Kt+1 −Kt) which equals the domestic
savings minus capital depreciation (δKt) , where δ is the depreciation rate. Equations (10) and
(11) show that both labor and technological progress are exogenously increasing at the rates of n
and g, respectively.
4.1.2. Linkage to an Empirical Test
One important prediction from the Solow model is the conditional convergence hypothesis which
states that countries with lower initial levels of capital and output tend to grow faster when the
countries’ characteristics are held constant. Using the technique of linear approximation, we can
derive the average growth rate of the output per worker level (yt ≡ YtLt) as:
ln yT − ln y0T
≈ g +1− (1− λ)T
T
µlnA0 +
α
1− α(ln s− ln (n+ g + δ + ng))− ln y0
¶, (12)
where λ = (1− α) (n+ g + δ) and (ln yT−ln y0)T
represents the average (annual) growth rate be-
tween period t = 0 and t = T . A0 and y0 are the respective technological level and output per
worker level in the initial period, t = 0. Equation (12) shows that the level of initial output per
worker level y0 is negatively associated with the growth rate of output per worker. It implies that a
country tends to grow faster if the output per worker level in the country is lower initially.
Empirical studies typically use a large sample of cross-country data to regress the average of
the annual growth rate on the initial level of real GDP per capita and other related control variables
suggested in the model, such as the national savings (or investment) rate and the population growth
rate (for country i):
giT,0 = β0 − β1 ln yi0 + β2Z
i, (13)
where Zi ≡ ln si − ln¡ni + gi + δi + nigi
¢, and giT,0 ≡
(ln yiT−ln yi0)T
. From equation (13) the
parameters β0, β1 and β2 correspond to: g + 1−(1−λ)TT
lnA0,1−(1−λ)T
T, and α
1−α
³1−(1−λ)T
T
´, re-
spectively.
4.1.3. Extending the Model
Using equation (13) , a common empirical finding is that the initial level of GDP per capita pos-
16
sesses a significant negative correlation with the economic growth rate in a country. This finding
supports the conditional convergence hypothesis that the country with a lower level of real GDP
per capita tends to grow faster (Barro and Sala-i-Martin 1992; Mankiw, Romer, and Weil 1992).
What role, then, does the Solow model play in cumulation? The typical estimated coefficient of
initial real GDP per capita (bβ1) is significantly less than the Solow model prediction (1−(1−λ)T
T).
In other words, the Solow model theoretically overestimates the speed of convergence.
One theoretical alternative is to relax the assumption that output production depended on
homogeneous labor and capital. Mankiw, Romer and Weil (1992) modify the Solow model by
introducing the stock of human capital in the production function. By controlling for the level
of human capital (education), the authors find that the rate of convergence is approximately two
percent per year which is closer to the prediction in the modified Solow model.
The Solow model and the extensions of it provide an example of a cumulative research pro-
cess. The modifications in the theoretical model were due to the empirical tests, but this is feasible
due to methodological unification. The modeling dialogue here gives the researchers a better un-
derstanding of the regularities in economic development. If researchers do not consider the Solow
model and solely apply an empirical procedure by regressing the average growth rate on the initial
real GDP per capita, they could misinterpret the empirical results and fail to understand the mech-
anism(s) that influence economic development. On the other hand, if the researchers only set up
a theoretical model but do not test it empirically, they would not know that the model is actually
inconsistent with the empirical observations.
5. Methodological Unification: EITMWe have been arguing that scientific cumulation is more likely to occur when efforts are made to
identify parameters in the model. An emphasis on parameter identification, structural parameters,
provides more transparent interpretation and allows for refutation. However, if one were to strictly
adhere to the Cowles Commission approach we would, for example, forego the chance of modeling
new uncertainty created by shifts in behavioral traits (e.g., public tastes, attitudes, expectations, and
17
learning). The scientific consequence of this omission directly affects the issues of identification
and invariance because these unaccounted behavioral shifts of variables would not be linked with
the other variables and specified parameters.
An EITM framework addresses these issues through the unification of formal and empirical
analysis. This framework takes advantage of the mutually reinforcing properties of formal and
empirical analysis to address the challenge(s) above. Another attribute of this framework is the
emphasis on concepts that are quite general and integral to many fields of research but that are
seldom modeled and tested in a direct way. EITM places emphasis on finding ways to model
human behavior and action and, thereby, aids in developing realistic representations that improve
upon simple socio-economic categorization.
Recall that we accept the Cowles Commission’s focus on identification of structural param-
eters. We add the emphasis on modeling behavior to the Cowles Commission approach so that
new uncertainty created by shifts in behavioral traits such as public tastes, attitudes, expectations,
learning, and the like can be properly studied.
The framework we develop also can address the critique of the structural approach leveled by
Sims (1980). It is well known that reduced form estimates are not identified. The practice of finding
ways to identify models can lead to “incredible” theoretical specifications (Sims 1980; Freeman,
Lin, and Williams 1989). Our framework, by way of adding behavioral concepts and analogues,
holds the potential to strengthen the credibility for various identification restrictions. Analogues,
in particular, have important scientific importance since they hold the promise of operationalizing
mechanisms.21
This framework is summarized as follows:
21 We argue that operationalizing mechanisms can be thought of in much broader terms than having a variable “de-termined by a set of other variables” (see Footnote 2). This is particlarly true in trying to use analogues for behavior.An example of operationalizing a mechanism can be seen in the work of Converse (1969). He advanced the theorythat strength of party identification (and voting behavior) is primarily a function of intergenerational transmission plusthe number of times one had voted in free elections. To operationalize his proposed mechanism — intergenerationaltransmission — and the number of times one voted, he made use of the following analogue: the Markov chain. Thisparticular analogue allowed for a particular dynamic prediction that he tested against actual voting data.
18
1. Unify Theoretical Mechanisms and Applied Statistical Concepts
Given that human beings are the agents of action, mechanisms should reflect overarching social
and behavioral processes. Examples include (but are not limited to):
• decision making
• bargaining
• expectations
• learning
• social interaction
It is also important to find an appropriate statistical concept to match the theoretical concept. Ex-
amples of applied statistical concepts include (but are not limited to):
• persistence
• measurement error
• nominal choice
• simultaneity
2. Develop Behavioral (Formal) and Applied Statistical Analogues
To link concepts with tests, we need analogues. An analogue can be thought of as a device in which
a concept is represented by continuously variable — and measurable — quantities. Analogues
serve as analytical representations for behavior and, therefore, provide for changes in behavior as
well as a more transparent interpretation of the formal and applied statistical model. Analogues
also emphasize measurement validity, the relation between a measure and the (unmeasured) con-
cept it is meant to represent. Examples of analogues for the behavioral (formal) concepts such as
expectations, nominal choice, and learning include (but are not limited to):
• conditional expectations procedures
• decision theory
• Bayesian and adaptive learning procedures
On the other hand, examples for the applied statistical analogues for the applied statistical
concepts of persistence, measurement error, nominal choice, and simultaneity include:
19
• autoregressive estimation
• error-in-variables regression
• discrete choice modeling
• multi-stage estimation (e.g., two-stage least squares)
3. Unify and Evaluate the Analogues
The third step uses the mutually reinforcing properties of the formal and empirical analogues and
helps identify the parameters of interest. Examples of this linkage exist in social science disci-
plines such as political science and economics. In political science, Kramer (1983) focuses on
economic voting where he makes the assumption that voters would respond to changes in their
income. He further assumes that voters respond to government induced changes in income, but
researchers only see total changes in income. This “signal extraction” problem creates a mea-
surement error challenge. The applied statistical consequence (error-in-variable result) is that
aggregate level data can mitigate this measurement error, but individual level data still possesses
the error.
In economics, one can also find a “behavioral” argument linking expectations (uncertainty)
and measurement error. On different substantive topics, both Friedman (1957) and Lucas (1973)
unify “error in variables” regressions with formal models involving expectations and uncertainty.
Their linkage provides a behavioral explanation on why parameters in their empirical model mimic
error-in-variables regressions.
5.1. Example 2: Voting with Compensational and RepresentationalPreferences
The act of voting provides a useful window into methodological unification. Hotelling (1926) and
Downs (1957) argue that voters choose one party over the others based on the relative political
positions of parties – proximity voting theory. Voters are more likely to vote for a political party if
the position of the party is closer to voters’ ideal position. As the party’s position further deviates
from a voter’s ideal position, the voter receives less utility and is less likely to vote for it.22
22 Applications of this particular utility function abound. Erikson, Mackuen and Stimson (2002), for example,
20
5.1.1. The Relation Between Decision Theory and Discrete Choice Models
Kedar (2005) questions the validity of the assumption. She argues that, besides the proximity of
parties’ positions, voters are also concerned about each party’s contribution to the aggregate policy
outcome. Kedar (2005) starts with the proximity model:
Uij = −β1 (vi − pj)2 , (14)
where Uij is the disutility of voter i for party j0s policy position, vi is the ideal point of voter i, pj is
the policy position of party j, and β1 is a scalar. Equation (14) states that voter i perceives disutility
for party j when the position of party j deviates from voter i0s ideal point. On the other hand, if
the position of party j is equivalent to his ideal point (i.e., vi = pj), no disutility is perceived to
result from party j.
Assuming that party positions can affect policy outcomes, Kedar (2005) argues that the policy
outcome is the weighted average of policy positions of the respective parties:
P =mXj=1
sjpj, (15)
where 0 < sj < 1 is the relative share of party j in the legislature andPm
j=1 sj = 1 for all j.
If voters are policy-outcome oriented, and concerned that the policy outcome may deviate
from their ideal point if party j is not elected, then the utility of voter i pertaining to party j
becomes:
Uij = −β2h(vi − P )2 −
¡vi − P−pj
¢2i, (16)
and
P−pj =
Ã1P
k 6=j sk
!Xk 6=j
skpk, (17)
where β2 is a scalar. Equation (17) represents the policy outcome if party j is not in the legislature.
Equation (16) provides an important insight on how voters view the contribution of party j to the
policy outcome affecting their utility. If party j takes part in policy formulation and makes the
policy closer to voter i’s ideal point vi, then¡vi − P−pj
¢2> (vi − P )2 . Therefore, voter iwill gain
positive utility to have party j to be in the process of policy formation (i.e., Uij > 0). However,
assume that voters’ utility is an inverse function of the squared distance of party political position and the voters’ idealposition.
21
if the inclusion of party j makes the policy outcome increase in distance from voter i’s idea point
such that¡vi − P−pj
¢2< (vi − P )2 , then the utility of voter i for party j is negative.
Now assume that voter i has expectations concerning party j that are based on the weighted
average of both the party’s relative position and its contribution to policy outcomes. Voter i’s
utility for party j can now be written as:
Uij = θn−γ (vi − pj)
2 − (1− γ)h(vi − P )2 −
¡vi − P−pj
¢2io+ δjzi, (18)
where θ is a scalar, δj is a vector of coefficients on voter i’s observable variables zi for party j,
and β1 and β2 correspond to γ and 1 − γ, respectively, such that β1 + β2 = γ + (1− γ) = 1.
When γ → 1, it implies that voters are solely concerned with a party’s positions. This situation is
called representational voting behavior. On the other hand, γ → 0 implies that voters vote for a
party such that the policy outcome can be placed at the voter’s desired position(s). This outcome
is called compensational voting behavior.
From equation (18) , we obtain voter i’s optimal or “desired” position for party j by solving
the first order condition of Uij with respect to pj:
p∗j = vi
"γ (1− sj) + sj
γ¡1− s2j
¢+ s2j
#−(1− γ)
³sjPm
k=1,k 6=j skpk
´γ¡1− s2j
¢+ s2j
. (19)
When γ → 1 (representational voting), we have:
p∗j = vi for γ → 1. (20)
When γ → 0 (compensational voting), we have:
p∗j =vi −
Pmk=1,k 6=j skpk
sjfor γ → 0, (21)
and the policy outcome would be:
P¯γ→0,pj=p∗j =
mXk=1
skpk = sjpj +mX
k=1,k 6=jskpk
= sjp∗j +
mXk=1,k 6=j
skpk
= sjvi −
Pmk 6=j skpk
sj+
mXk=1,k 6=j
skpk
= vi. (22)
22
For (20)— (22), we see that voters make an optimal voting decision based on representational
(proximity) and compensational voting considerations. Kedar (2005) argues that the representa-
tional and compensational voting considerations can reflect the levels of political bargaining in
different institutional systems. In majoritarian systems, where the winning party is able to im-
plement its ideal policy with less need for compromise, voters would place greater value on γ so
that they would vote for the party positioned closest to their ideal position. However, in the case
where institutional power sharing (γ is small) exists, voters would vote for a party whose position
is further from their ideal positions to draw the collective outcome closer to their, the voter’s, ideal
point. While the voting literature generally supports the proximity model, where voters choose
the party which is closer to their political positions, Kedar (2005) argues that such a consideration
would be reduced if the institutional environment involves more power-sharing.
5.1.2. Unifying and Evaluating the Analogues
Kedar (2005) tests the folllowing two hypotheses with voting survey data from Britain, Canada,
Netherlands, and Norway:
Hypothesis 1: Voters’ behavior in the countries with a majoritarian system follows the proximity
model more closely (larger γ) than those in the countries with a consensual system (smaller γ).
Hypothesis 2: The pure proximity model (γ = 1) does not sufficiently represent voting behavior.
To test Hypothesis 1, Kedar (2005) first identifies the institutional features of Britain, Canada,
Norway and the Netherlands. Using the indicators of majoritarianism and power-sharing in Li-
jphart (1984), she concludes that Britain and Canada are more unitary whereas the Netherlands
and Norway are more consensual. Methodological unification occurs when Kedar derives the log-
likelihood multinomial model based on equation (18) and estimates issue voting in four political
systems using three measures: (i) seat shares in the parliament; (ii) vote shares; and (iii) portfolio
allocation in government. The empirical results support the first theoretical hypothesis: voting be-
havior in the majoritarian systems (i.e., Britain and Canada) is more consistent with the proximity
model relative to that in the consensual systems (i.e., the Netherlands and Norway). Hypothesis 2
is tested using the likelihood ratio test. The results show that, in all four political systems, com-
23
pensational voting behavior exists in the survey data. The pure proximity model is an insufficient
explanation.
5.1.3. Extending the Model
The model and tests that Kedar presents provide the foundation for extensions that can examine
the robustness of her findings. One way to build on her formal model is to relax the assumption
that voters’ expectations are error free. It is well known that equilibrium predictions change or are
fragile when expectations are based on imperfect or limited information. In addition, to this ex-
tension on expectations is a determination of whether voters (in Kedar’s model) learn equilibriums
consistent with rational expectations.
5.2. Example 3: Economic Voting
Starting with Kramer (1983) and continuing with work that includes (but is not limited to) Alesina
and Rosenthal (1995), Suzuki and Chappell (1996), and Lin (1999) there is a substantial liter-
ature on how the economy affects voting behavior. For our purposes we demonstrate how the
combined work of Alesina and Rosenthal, Suzuki and Chappell, and Lin have in their own way
contributed constituent parts that allow for the study of economic voting within a unified method-
ological framework.
5.2.1. The Relation Between Expectations, Uncertainty, and Measurement Error
We first start with the formal model that has behavioral attributes of expectations and uncertainty.
Of the studies of economic voting mentioned above, Alesina and Rosenthal (1995) provide the
formal model (pages 191-195). Their model of economic growth can be derived using an expec-
tations augmented aggregate supply curve (see equation (1)):
yt = yn + γ (πt − πet) + εt, (23)
where yt represents the rate of economic growth (GDP growth) in period t, yn is the natural level
of the economic growth rate23, πt is the inflation rate at time t, and πet is the expected inflation rate
23 This variable has similar properties to equation (1) where the natural rate of output (ynt ) is assumed to grow at aconstant rate of β. This follows from yn = ynt − ynt−1 = β.
24
at time t formed at time t− 1.
With voter expectations over inflation established we now turn to uncertainty in those ex-
pectations. Let us assume that voters want to determine whether to attribute credit or blame for
economic growth (yt) outcomes to the incumbent administration. Yet, voters are faced with the
challenge in determining what part of the economic outcomes is due to incumbent “competence”
(i.e., policy acumen) or simply good luck. Based, in part on equation (23), equation (24) presents
this “signal extraction” or measurement error problem:
εt = ηt + ξt. (24)
The variable εt represents the shock that is comprised of the two unobservable characteristics noted
above. The first, represented by ηt, reflects “competence” that can be attributed to the incumbent
administration. The second, symbolized as ξt, are shocks to growth that are beyond administration
control (and competence). Both ηt and ξt have zero mean and have second moments σ2η and σ2ξ
respectively.
Note also that competence is argued to have a persistent property, which can allow for reelec-
tion. This feature can be characterized as an MA(1) process:
ηt = μt + ρμt−1, 0 < ρ ≤ 1 (25)
where μt is iid¡0, σ2μ
¢. The parameter ρ represents the strength of the persistence. The lag or lags
allow for retrospective voter judgements.
Next, let us assume that voters’ judgements include a general sense of the average rate of
growth (yn) and that they also observe actual growth (yt). Equation (23) implies that when voters
predict inflation with no systematic error (i.e., πet = πt), the result is non-inflationary growth that
does not adversely affect real wages. Now we can link economic growth performance with voter
uncertainty at the source. We formalize how economic growth rate deviations from the average
can be attributed to administration competence or fortuitous events:
yt − yn = εt = ηt + ξt. (26)
Equation (26) shows that when the actual economic growth rate is greater than its average or
25
“natural rate” (i.e., yt > yn), then εt = ηt + ξt > 0. Yet, voters are unable to distinguish the
incumbent’s competence (ηt) from the stochastic economic shock (ξt) as they can and do make
forecasts.
Because competence can persist, voters use this property to make forecasts, thereby providing
greater or less weight to competence over time. To demonstrate this behavioral effect, substitute
equation (25) in (26):
μt + ξt = yt − yn − ρμt−1 (27)
With these equations in place, we can now determine the optimal estimate of competence, ηt+1,
when the agents only see yt. We demonstrate this result by making a one-period forecast of
equation (25) and then solve for its expected value (conditional expectation) at time t:
Et
¡ηt+1
¢= Et
¡μt+1
¢+ ρE (μt|yt) = ρE (μt|yt) , (28)
where Et
¡μt+1
¢= 0. In equation (28), we see that competence, ηt+1, can be forecasted by pre-
dicting μt+1 and μt. Since there is no information available for forecasting μt+1, voters can only
forecast μt based on observable yt (at time t) from equation (27) .
Using the method of recursive projection and equation (27) we demonstrate how the be-
havioral analogue for expectations is linked to the empirical analogue for measurement error (an
error-in-variables “equation”24):
Et
¡ηt+1
¢= ρE (μt|yt) = ρ
σ2μσ2μ + σ2ξ
¡yt − yn − ρμt−1
¢, (29)
where 0 < ρσ2μ
σ2μ+σ2ξ< 1. Equation (29) shows that voters can forecast competence using the
difference between yt − yn, but also the “weighted” lag of μt¡i.e., ρμt−1
¢.
In equation (29), the expected value of competence is positively correlated with the economic
24 The traditional applied statistical view of measurement errors is that the correlated signs of the measurementerrors among independent variables can lead to inappropriate signs for regression coefficients. This is exactly whatmethodological unification accomplishes. The theory — the formal model — implies an applied statistical modelwith measurement error. Consequently, one can examine, with a unified approach, the joint effects and identify thecause. Applied statistical tools cannot untangle conceptually distinct effects on a dependent variable.
We also hasten to add that Friedman (1957) and Lucas’s (1973) substantive findings would not have been achievedhad they just treated their research question as a pure measurement error problem requiring only an applied statisticalanalysis (and “fix” for the measurement error) that focused on a significant t-statistic.
26
growth rate deviations. Voter assessment is filtered by the coefficient, σ2μσ2μ+σ
2ξ, which represents a
proportion of competence that voters are able to interpret and observe. The behavioral implications
are straightforward. If voters interpret that the variability of economic shocks solely comes from
the incumbent’s competence (σ2ξ → 0), then σ2μσ2μ+σ
2ξ→ 1. On the other hand, the increase in the
variability of uncontrolled shocks, σ2ξ , confounds the observability of incumbent competence since
the signal coefficient σ2μσ2μ+σ
2ξ
decreases. In this case, voters assign less weight to the economic
performance in assessing the incumbent’s competence.
5.2.2. Unifying and Evaluating the Analogues
Alesina and Rosenthal (1995) test the empirical implications of their model with data on economic
outcomes and political parties for the period 1915 to 1988. To perform these tests, they first
estimate the theoretical specification for economic growth in equation (23) and collect the esti-
mated exogenous shocks (εt) in the economy. With these estimated exogenous shocks, they then
construct their variance-covariance structure. Since competence (ηt) in equation (25) follows an
MA(1) process, they hypothesize that a test for incumbent competence, as it pertains to economic
growth, can be performed using the covariances between the current and preceding year. The spe-
cific test centers on whether the changes in covariances with the presidential party in office are
statistically larger than the covariances associated with a change in presidential parties. They re-
port null findings (e.g., equal covariances) and conclude that there is little evidence to support that
voters are retrospective and use incumbent competence as a basis for support.
5.2.3. Extending the Model
Alesina and Rosenthal use equations (23) and (25) to form their tests. However, the empirical
models of both Suzuki and Chappell (1996) and Lin (1999) provide alternative tests. While
neither Suzuki and Chappell or Lin provide formalization, their results clearly could be linked
with the formalization set forth by Alesina and Rosenthal. The key attributes of both Suzuki
and Chappell (1996) and Lin (1999) is that they treat economic voting as having a dynamic or
episodic nature. Parameters fluctuate based on changes in circumstance — depending (in this line
27
of research) on how much variability there is in economic growth.
The “separate” studies of Alesina and Rosenthal (1995), Suzuki and Chappell (1996), and
Lin (1999) all focus on the issue of economic voting. These studies have addressed the matter
with alternative approaches. With a unified approach, the potential linkage between these studies
would lead to direct relation between the parameters of the formal and empirical models. An
EITM version of such work is to test the competence equation (29), which ultimately would unify
the formal model of Alesina and Rosenthal with the empirical tests of Suzuki and Chappell and
Lin.
5.3. Example 4: The Political Economy of Monetary Policy
In the past twenty five years, due in part to social, political, and economic factors, there has been
a regime shift in monetary policy. Monetary authorities now place greater emphasis on stabiliz-
ing domestic price levels than during the advent of the Phillips curve (e.g., inflation targeting).
Accompanying this regime shift has been a renewed emphasis on the study of overall policy ef-
fectiveness (see Bernanke et al., 1999 and Taylor 1999) and the use of interest rate rules in new
Keynesian models (see Clarida, Gali, and Gertler 2000). More recently, Granato and Wong (2006)
have used a model with new Keynesian properties to determine the relation between inflation sta-
bilizing policy, inflation persistence and volatility, and business cycle fluctuations.
5.3.1. The Relation between Expectations, Learning, and Persistence
In this example we establish a relation between expectations, learning, and the persistence of a
variable of interest (inflation). Substantively speaking, we demonstrate how the implementation
and aggressiveness of maintaining an inflation target affects inflation persistence. The intuition
of the model is as follows: policy influences public expectations by encouraging the public to
substitute an inflation target for past inflation. Therefore, a negative relation should exist between
periods of aggressive inflation-stabilizing policy and inflation persistence.25
The model has two components. As in the example in Section 3, we rely on a standard model
25 We define an aggressive inflation-stabilizing policy as one that includes a willingness to respond forcefully todeviations from a prespecified implicit or explicit inflation target.
28
of macroeconomic outcomes and policy. The second component assumes that agents learn in an
adaptive manner and that they form expectations as new data becomes available over time. The
model, containing behavioral analogues for expectations and learning, contains a unique and stable
rational expectations equilibrium (REE) (Evans and Honkapohja 2001). The stability (E-stability)
conditions have direct implications for the relation between agents and policymakers.26 Under the
REE, aggressive implementation of an inflation target guides agents to the stable equilibrium and
reduces inflation persistence.
The model assumes a two-period contract. For simplicity, prices reflect a unitary markup
over wages. The price at time t, pt, is expressed as the average of the current (xt) and the lagged
(xt−1) contract wage:27
pt =1
2(xt + xt−1) , (30)
where pt is the logarithm of the price level, and xt is the logarithm of the wage level at period t.
In addition, agents are concerned with their real wages over the lifetime of the contract:
xt − pt =1
2[xt−1 − pt−1 +Et (xt+1 − pt+1)] + θzt, (31)
where xt − pt represents the real wage rate at time t, Et (xt+1 − pt+1) is the expectation of the
future real wage level at time t + 1 formed at time t, and zt = yt − ynt is the excess demand for
labor at time t. The inflation rate (πt) is defined as the difference between the current and lagged
price level (pt − pt−1). With this definition we substitute equation (31) into equation (30) and
obtain:
πt =1
2(πt−1 +Etπt+1) + θzt + u3t. (32)
where Etπt+1 is the expected inflation rate over the next period and u3t is iid¡0, σ2u3
¢. Equation
26 Adaptive learning allows agents to achieve the REE within the context of a stochastic (updating) process that istypically represented via adaptive learning. Agents do not initially obtain the REE, but they attempt to learn thestochastic process by updating their forecasts (expectations) over time as new information becomes available.
In more technical terms, adaptive learning is used so that agents update parameters of a forecasting rule — per-ceived law of motion (PLM) — associated with the stochastic process of the variable in question to learn an REE.This process requires a condition establishing convergence to the REE — the E-stability condition. The E-stabilitycondition determines the stability of the equilibrium in which the PLM parameters adjust to the implied actual law ofmotion (ALM) parameters. See Evans and Honkapohja (2001) for details.27 See Wang and Wong (2005) for the details of the general theoretical framework.
29
(32) captures the main characteristic of inflation persistence. Since agents make plans about their
real wages over both past and future periods, the lagged price level (pt−1) is taken into considera-
tion as they adjust (negotiate) their real wage at time t. This model feature allows the inflation rate
to depend on both the expected inflation rate as well as past inflation.
Similar to equation (2) , equation (33) represents a standard IS curve where the quantity
demanded on output relative to natural output (zt) is negatively associated with the changes in real
interest rates:
zt = −ϕ (it − Etπt+1 − r∗) + u4t, (33)
where it is nominal interest rate, r∗ is the target real interest rate, u4t is iid¡0, σ2u4
¢, and ϕ > 0.
As in equation (3) , we assume that policymakers use an interest rate rule — the Taylor rule
— when conducting monetary policy:
it = πt + αyzt + απ (πt − π∗) + r∗, (34)
where positive values of απ and αy indicate a willingness to raise (lower) nominal interest rates
in response to the positive (negative) deviations from either the target inflation rate (πt − π∗), the
output gap (zt), or both.
The equilibrium inflation rate can be found by taking the reduced form of the system. It is
derived by substituting equation (34) into equation (33). Next solve for zt and then put that result
into equation (32). If we solve that expression for πt we have:
πt = Γ0 + Γ1πt−1 + Γ2Etπt+1 + ξt, (35)
where:
Γ0 = (θϕαππ∗)Φ−1,
Γ1 = (1 + ϕαy) (2Φ)−1 ,
Γ2 = (1 + ϕαy + 2θϕ) (2Φ)−1 ,
ξt = [θu4t + (1 + ϕαy)u3t]Φ−1,
and Φ = 1 + ϕαy + θϕ (1 + απ) .
30
Equation (35) shows that current inflation depends on the first-order lag of inflation and also ex-
pected future inflation. When we “close” (35) we find the MSV can be expressed as an AR(1)
process, thereby establishing methodological unification.
Methodological unification occurs when we solve for the REE since this will involve merging
the behavioral analogue of expectations with the empirical analogue for persistence. Simply take
the conditional expectations at time t + 1 of equation (35) and substitute this result into equation
(35) :
πt = A+Bπt−1 + ξt, (36)
where A = Γ0 (1− Γ2B − Γ2)−1 , B =
¡1±√1− 4Γ1Γ2
¢(2Γ2)
−1, and ξt ≡ ξt (1− Γ2B)−1 .
Equation (36) is the MSV solution of inflation — which depends solely on the lagged inflation
rate. Because we are using a formal model one complication we are alerted to, with important
empirical implications, is the nature of the coefficient of lagged inflation, B. This parameter is a
quadratic where the two values are defined as:
B+ =1 +√1− 4Γ1Γ22Γ2
,
B− =1−√1− 4Γ1Γ22Γ2
.
Based on the behavior of the model’s parameters, we determine the properties of the quadratic
solutions and solve for the relation between aggressive inflation-stabilizing policy (απ) and infla-
tion persistence (B). Granato and Wong (2006) show thatB− is a unique stationary solution when
απ ≥ 0. When policymakers adopt an aggressive inflation-stabilizing policy, a stationary AR(1)
solution can be obtained (i.e., B−) while an explosive AR(1) solution (i.e., B+) would also be pos-
sible. However, the technique of adaptive learning (McCallum 2003) serves an important selection
criteria (i.e., determining stable solutions) where only the stationary solution (i.e., B−) is attain-
able and that the explosive solution (i.e., B+) is not possible. In other words, if agents learn the
equilibrium in an adaptive manner and they form expectations as new data becomes available over
time, B− is the only learnable (E-stable) equilibrium when policymakers aggressively stabilize in-
flation (i.e., απ > 0). Finally Granato and Wong (2006) point out that equation (36) represents
the AR(1) process of the inflation rate. The empirical implications of the model as represented in
31
equation (36) shows that an increase in απ reduces persistence under B−.
5.3.2. Unifying and Evaluating the Analogues
To test the relation between the policy parameter(s) and inflation persistence — the equilibrium
predictions — we use quarterly United States data (for the period 1960:I to 2000:III). According
to the model, inflation persistence should be reduced significantly under an aggressive inflation-
stabilizing policy. From equation (36)we estimate a first-order autoregressive process (i.e., AR(1))
of the United States inflation rate. As a consequence of the more aggressive inflation-stabilizing
policy stance during the Volcker-Greenspan period (August, 1979 through August, 2000), we ex-
pect that the inflation-persistence parameter (Bt) in the Volcker-Greenspan period to be smaller
(statistically) relative to the pre-Volcker period.
(Figure 2 About Here)
The formal model predicts that a positive inflation stabilization policy parameter (απ) re-
duces inflation persistence, Bt. We also estimate equation (34) in order to contrast the parameter
movements in απ and αy.28 Figure 2 provides point estimates of inflation persistence (Bt) and
policy rule parameters, απ and αy, for a 15-year rolling sample starting in the first quarter of 1960
(1960:I). The results show that after 1980, inflation persistence starts falling. Figure 2 also shows
that both απ and αy de-emphasize inflation and output stability in approximately 1968. Prior to
1968, countercyclical policy emphasize output stability (αy > 0). Aggressive inflation stabilizing
policy occurrs only after 1980, when απ > 0.
5.3.3. Extending the Model
The model presented here, in some respects, is a mirror of the model proposed by Kedar. Kedar’s
model emphasizes micro foundations but makes assumptions about voter expectations. In this
example, the behavioral concepts and analogues focus on expectations and learning, but there is
little in the way of microfoundations or in the strategic interaction between policymakers and the
public. These extensions would help determine the robustness of the equilibrium predictions
28 See also Granato and Wong (2006, 198–211).
32
pertaining to inflation persistence and inflation volatility.
6. Summary and DiscussionIn this paper we describe the weaknesses of current research practices and how their nonfalsifiable
nature fail in building a cumulative science. We argue that identifying causal mechanisms can
be achieved through a modeling dialogue that harnesses the unification of formal and empirical
analysis. In particular, we share the Cowles Commission emphasis on structural parameters and
devising ways to identify these structural parameters. We build on the Cowles Commission’s
work to recover a model’s parameters, but we also offer an alternative framework that can help
address the Sims (1980) critique of conventional structural estimation practice. In sum, our goal
is to develop a framework to provide a behavioral explanation on why parameters in an applied
statistical model act the way they do.
The EITM examples illustrate the way methodological unification can be extended beyond
more traditional approaches. We use analogues, work through the properties of the analogues,
and focus on the relation between the formal-theoretical parameter(s) and the applied statistical
parameter(s). Explicit emphasis on the parameters allows for greater likelihood of knowing what
is being tested. We account for the problems faced when using a reduced form and we know that
the reduced form is far superior to the current practices of data mining, overparameterization, and
Omega matrices.
Having said this, it is also clear that there are further challenges dealing with establishing
linkages from parameters to tests. One ongoing issue is how to deal with overparameterization.
In our policy example, we work out a mechanism between the policy parameter (απ) and the
persistence parameter (Bt), but also note there are other free parameters in the expression for the
persistence parameter. The potential shifts in the remaining free parameters may be influencing
the results.
The fact that we are now focused on overparameterization and the issue of free parameters
as opposed to unscientific diversions is indicative of the scientific potential of methodological
33
unification. And yet, the existence of free parameters means that nonfalsification is still a threat.
Consider the policy example again. Because we have not worked out the behavior of certain
parameters in the system, we are open to the criticism that an autonomous shift in one of the free
parameters confounds the link between theory and test. Moreover, the policy example suggests
the framework must be extended to include a means “to fix” as many parameters in the system as
possible. The framework is flexible enough to accomplish this task. The issue will be making
appropriate use of additional formalization — informed by empirical and contextual evidence —
to provide greater specificity on the range of magnitudes that the previously free parameters take
and whether all free parameters are subject to some restriction.
From this we conclude that methodological unification can be thought of as having two lev-
els, one level involving results that are consistent with the formal and applied statistical analogues’
predictions.29 But, a second level requires even greater emphasis on identifying every structural
relation in the formal model and analogue so that every estimate in the reduced form and applied
statistical analogue are isolated. It follows from the inferential challenges posed by overparam-
eterization that efforts be directed to developing metrics on the degree to which free parameters
can confound the results. Our conjecture is to think along the lines of creating some “tolerance”
criteria on the relation between the structural equations, the number of free parameters, and the po-
tential to maximize falsification. One could envision a mix of rank and order type conditions in
conjunction with Extreme Bounds Analysis (EBA) (see Leamer 1983 and Bamber and van Santen
1985, 2000).
The framework we use is part of an ongoing process geared toward methodological unification
(see Morton 1999). What we describe can be extended in many ways. Unified methodological
frameworks that foster links to different levels of analysis (Kydland and Prescott 1982; Freeman
and Houser 1998) or make explicit use of game theory (Signorino 1999; Mebane and Sekhon
2002) are just two more examples. We also think the use of Bayesian analysis is a promising route
29 Analogues are central to our framework. Some have been created but others will have to be invented as the researchquestions demand them. For example, one can have a model and test that has changing parameters, but not follow thepath of Lucas (1973).
34
for unification (Achen 2006). Experiments, too, provide a rich alternative or compliment to the
secondary data analysis we use in this paper and are a natural outlet for methodological unification.
People can sit in different pews but still be members of the same congregation.
Ultimately, what methodological unification means — whether by using our framework or
some alternative — is a clean break from current practices such as data mining, overparameter-
ization, and Omega matrices. No half-measures will suffice if the goal is to build a cumulative
science that rests on falsifiable research practices. The usual conception of treating applied sta-
tistical problems as simply requiring statistical patches will need to give way to viewing these
nuisances as having a theoretical basis. With that new viewpoint a researcher can take advantage
of the mutually reinforcing properties of both formal and applied statistical analysis, and test the
linkage with data.
35
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Figure 1
0 10 20 30 40 50 60 70 80 90 100
4
6
8
Time
Infla
tion
Panel 1a: 3 = 1.5 > 1
Panel 1b: 3 = 0.5 < 1
Panel 1c: 3 = 1
0 10 20 30 40 50 60 70 80 90 100
-4
-2
0
Time
Infla
tion
0 10 20 30 40 50 60 70 80 90 1001
1.5
2
2.5
3
Time
Infla
tion
λ
λ
λ
Figure 2
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
75:1 80:1 85:1 90:1 95:1 00:1
(Inflation Aggressiveness Parameter) (Output Aggressiveness Parameter)Inflation Persistence Coefficient
1960:I|
1975:I
1965:I|
1980:I
1970:I|
1985:I
1975:I|
1990:I
1980:I|
1995:I
1985:I|
2000:I