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There are four tasks for macroeconometricians: describe and summarise macroeconomic data; make forecasts; quantify the structure of the macroeconomy; and undertake policy analysis (Stock & Watson, 2001). Before the 1970s these four tasks were done using a variety of approaches, from single-equation models to large models with hundreds of equations.. Simultaneous Equation Methodology (SEM) was conceived at the Cowles Commission (Malinvaud, 1983).

Gujarati (2003) said about the SEM:

In such models there is more than one equation – one for each of the mutually, or jointly, dependent or endogenous variables. And unlike the single-equation models, in the simultaneous-equation models one may not estimate the parameters of a single equation without taking into account information provided by other equations in the system. (pp. 717–718)

As a result, in this model variables are divided into endogenous variables, whose values are determined within the model, and exogenous variables, whose values are determined outside the model (Gujarati, 2003). An independent variable is a variable that influences other variables, while a dependent variable is expressed as a linear function of one or more explanatory or independent variables. In SEM, exogenous variables are not determined by any variables in the model, but other variables are determined by them, so they can be considered

only as independent variables. However, endogenous variables can be considered to be either dependent or independent variables, because an independent variable in one equation may be a dependent variable in other equations.

SEM evolved through economists in the Cowles Commission (Malinvaud, 1983; Tinbergen, 1939), who focused on the statistical testing and measurement of business-cycle theories: Dresch (1940), who studied the impact of several taxation devices using a 15-equation model, and Haavelmo (1940), who considered the problem of solving a set of structural equations in a general simultaneous-equation setting. According to Karayiannis (2004), Klein constructed a new method for estimating econometric relationships called two-stage least squares (2SLS), which was considered by Kang (1995) to be unbiased when the sample size is infinitely large but substantially biased for a typical sample size used in practice.

A large number of studies employed SEM during the late 1960s and early 1970s (Malinvaud, 1983). Many employed SEM to study the effect of fiscal policy. Grossman (1988) used U.S. data to study the relationship between the size of government and economic growth. He expected that the provision of public goods should raise the productivity of the private sector and bring about growth in output; however, a problematic public decision-making process results in an inefficient quantity of public goods and an increase in taxes. These problems become bigger when the size of the government is larger.

Karikari (1995) also who found a negative effect from an expansionary fiscal policy in Ghana. However, Croushore (1989) and Croushore, Koot and Walker (1990) found a positive effect from an expansionary fiscal policy on private consumption in the U.S. In the studies that focus on taxes, Modigliani, Steindel, Hymans and Juster (1977), using U.S. data, discovered that a decrease in taxes temporarily increases private consumption. Jha (1999), employing Indian and Chinese data, found that an increase in taxes can be an obstacle to economic growth. Some studies compare the effect of fiscal policy and monetary policy. Morishima and Saito (1964) found that the effect of fiscal policy is more important during high unemployment. Moroney and Mason (1971) also argued that fiscal policy is more effective than monetary policy.

However, Lucas (1976) criticised SEM for not representing theory and for being ineffective in policy analysis, as pointed out by Sims (2002, p. 1):

appear, via expectations, in many equations of the model, not just in the “policy equations”. Thus an attempt to predict the effects of a policy change by changing only the policy equation, holding other equations in the model fixed as in SEM, will fail, because the other equations will in fact change when the policy changes. Sargent (1979) claimed that using structural econometric models such as SEM involves employing a large number of restrictions. In the same vein, Sims (1980) claimed that:

Because existing large models contain too many incredible restrictions, empirical research aimed at testing competing macroeconomic theories too often proceeds in a single- or few-equation framework. For this reason alone, it appears worthwhile to investigate the possibility of building large models in a style which does not tend to accumulate restrictions so haphazardly. (pp. 14–15)

Moreover, in SEM, identification can be obtained without the assumption of the orthogonality of structural disturbances. If the component is correlated with other components, an isolated change in a single component residual is unlikely to occur (Lutkepohl, 2006). Further, no variable can be considered to be exogenous in a world of rational, forward-looking agents (Bjornland, 2006). As a result, the model is not good for policy analysis if the policy variables that are assumed to be exogenous variables react endogenously to macroeconomic variables. After the Lucas critique, the Dynamic Stochastic General Equilibrium (DSGE) approach was developed (Cogley & Yagihashi, 2010). However, Lui and Theodoridis (2010) criticised the DSGE as follows:

Economic theory is used to define all the linkages between variables. The tight economic structure solves the identification problem, but at a cost. As theory is never able to fully explain the data, an agnostic VAR will almost certainly ‘fit’ the data better. (p. 3)

Dungey and Pagan (2008) explained this as follows:

Investigation of this feature shows that the way many DSGE models are implemented on such data fails to adequately reflect this feature. …When implemented on data it is often the case that DSGE models are simply estimated using data that has been transformed to I(0) form through some filtering operation, which generally does not reproduce the model-consistent estimate of the permanent component. (pp. 1–2)