LSE approach

4.3.1 Introduction

According to the LSE approach, the failure of Cowles Commission models arises from the lack of attention paid to the statistical model underlying the particular econometric structure adopted to analyze the effect of alternative macroeconomic policies. However, the LSE methodology shares with the traditional Cowles Commission approach the opinion that econometric policy evaluation is feasible. It is only the way how the Cowles Commission approach deals with policy analysis is viewed by the LSE approach as incorrect. The lack of enough interest in the statistical model is thus the source

5 Here the Sims critique applies.

6 It is the Lucas critique.

of the failure of this traditional approach in providing an acceptable answer to the question concerning policy evaluation.

In the Cowles Commission tradition, the starting point of econometric analysis is the belief that the structural form of the process generating the data is known qualitatively. The reduced form is then derived from such a structure. In this framework, the validity of the reduced form is not tested. The lack of validity of the reduced form is thought of by the LSE approach as undermining the credibility of the structural parameter estimates. The LSE methodology recognizes that the economic theory suggests the general specification of the relevant form, but the precise representation of the data generating process (DGP) is always unknown in advance. For this reason, modeling procedures are required to determine the credibility of estimated models.

This means that the prominence of the structural form in the Cowles Commission approach to identification and specification is reversed. In the LSE methodology, the reduced form takes a central role since it represents the crucial probabilistic structure of the data. The traditional logic of Cowles Commission models that the reduced form is derived from the structural model is no longer valid in the LSE approach.

The reduced form is specified in the LSE framework at first. This is realized by defining a system with the set of variables being considered, their classification into modeled and non-modeled variables and the specification of the lag polynomials. The basic principle of econometrics: ’test, test and test’, is then applied to the system. If the system is considered to be a congruent representation of the unknown data generating process, its long-run properties can be identified by implementing cointegration analysis. It should be noted that such analysis is completely implemented on the reduced form. In the next step, a structural model is identified and estimated. Finally, the structural model is used for forecasting and policy evaluation.

4.3.2 The process of reduction

The LSE approach attacks Cowles Commission models by showing that the validity of the reduced form is not properly addressed. By analyzing the

properties of residuals, the LSE diagnosis for the empirical failure of the traditional approach is that structural inference is based on an improper statistical model. Spanos (1990) points out the problems inherent in the Cowles Commission approach by asserting that ‘not only are the statistical assumptions underlying the reduced form not tested, but the reduced form is rarely estimated explicitly.’

To solve the specification problem in the Cowles Commission tradition, the LSE approach puts forward the theory of reduction. Econometric modeling is formalized within the LSE approach as the result of a reduction process. Any econometric model is interpreted as a simplified representation of the unobservable data generating process. A model of the unknown DGP is the starting point in the reduction process. For the representation to be valid or

‘congruent’, the information lost in moving from the DGP to its representation must be irrelevant to the problem at hand. Adequacy of the statistical model can be evaluated through the analysis of the reduced form. Under the ‘general-to-specific’ methodology, the LSE approach starts its specification and identification process from a general dynamic reduced form model. In other words, the reduced form of the structure or the baseline model is generally the earliest stage of the reduction process at the empirical level.

The congruency of such a baseline model can not be directly assessed against the true, unobservable DGP. However, a series of diagnostic tests can be implemented for this purpose. The general idea underlying the application of such criteria is that congruent models should feature true random residuals.

Therefore any departure of the vector of residuals from a random normal multivariate distribution should signal a misspecification. In this way, the empirical analysis begins with the implementation of a battery of diagnostic tests where the null hypothesis of interest is the validity of the baseline model as a simplified representation of the unknown DGP.

Once the baseline model has been validated, the reduction process is carried out by simplifying the dynamics and reducing the dimensionality of the model. The validity of the reduction process can be checked by ensuring that the vector of innovations possesses all the features of true statistical innovations: absence of correlation, heteroscedasticity and non-normality.

Any pattern of this type or any instability in the parameters signalizes a loss of

information that occurred in the reduction from the DGP to the particular specification adopted. Only by implementing diagnostic checks can invalid structural models be discarded. Testing usually concentrates on residuals because any non-randomness in residuals can be interpreted as a signal of incorrect specification of the underlying model.⁷

A further stage in the simplification process can be the imposition of the rank reduction restrictions in the matrix determining long-run equilibriums of the system and the identification of cointegrating vectors. The product of this stage is a statistical model describing the data, possibly distinguishing between short-run dynamics and long-run equilibriums.

Only after the validation procedure is the structural model identified and estimated. No further validation is possible for a just-identified model because its implicit reduced form does not impose any further restrictions on the baseline statistical model. The validity of over-identified specification can be tested by evaluating the validity of the over-identifying restrictions implicitly imposed on the general reduced form. After this last diagnostic check for the validity of the reduction process, the structural model is used for practical purposes.

4.3.3 An assessment

In short, the major strength of the LSE methodology is a careful diagnosis of the problems of the Cowles Commission approach and in the attempt to give

‘scientific dignity’ to the specification of dynamic econometric models.

The concept of cointegration fits naturally in the context of dynamic specification of ECM models. This research strategy implies a multi-step framework: specification of the VAR and its deterministic component, identification of the number of cointegrating vectors, identification of the parameters in cointegrating vectors, tests on the speed of adjustment with respect to disequilibria. The final results depend on the outcome of previous stages which is not established so easily and uniquely empirically.

7 The residuals of a statistical model are generated by the specification adopted and are combined results of omitted variables (both in the sense of omitted variables and of omitted lags of included variables) and errors-in-included-variables of several types (measurement or expectational errors).

Macroeconomists have criticized the reduction process in the LSE approach by arguing that the preferred specification which this process delivers is inclined to be ‘a bit over-cooked’ and this process tends to loosen the link between econometric models and economic theory considerably. The achievement of data congruency means some evident cost regarding the parsimony of the specification and economic interpretability of the results.

Moreover, the LSE approach is not easily applied to systems of equations, even of very limited dimensions. The ‘general-to-specific’ methodology is usually applied in single-equation specification, extensions to systems become very complicated when the system exceeds only a small dimension.