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  • 11/23/2015

    ANKITA MANDAL 001400302024

    SAYANTAN BAIDYA 001400302042

    SOUMI BHATTACHARYYA 001400302043







    PG II



    Equation System

  • Simultaneous Equation System November 23, 2015

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  • Simultaneous Equation System November 23, 2015

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    We are grateful to the faculty of Department of Economics (Jadavpur University) for

    their unwavering support and cooperation. Working on this project has given us the

    opportunity to gather immense knowledge regarding econometric tools and

    economic analysis that will surely benefit us significantly in our careers in the future.

    We thank our professor Dr. Arpita Dhar immensely for setting us this task of

    preparing and presenting this project. We are extremely grateful and thankful to her

    for her tireless guidance without which it would not have been possible for us to

    make progress in our endeavour. We also take this opportunity to thank our

    department for providing us with a functioning computer laboratory and library

    facilities which helped us to fulfil all our needs regarding our project. Moreover, we

    are also grateful to our friends and families for their constant support and help.

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    A casual look at the published empirical work in business and economics will reveal that many economic relationships are of the single-equation type.In such models,

    one variable (the dependent variable Y) is expressed as a linear function of one or more

    other variables (the explanatory variables, the Xs). In such models an implicit

    assumption is that the cause-and-effect relationship, if any, between Y and the Xs is

    unidirectional: The explanatory variables are the cause and the dependent variable is

    the effect.

    However, there are situations where there is a two-way flow of influence among

    economic variables; that is, one economic variable affects another economic variable(s)

    and is, in turn, affected by it (them). Thus, we need to consider twoequations. And this

    leads usto consider simultaneous-equation models, models in which there is morethan

    one regression equation, one for each interdependent variable.

    Keywords: Nonseparablemodels,simultaneousequations, multicollinearity.

    JEL classification. : C3.

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    Single equation models, i.e., models in which there was a single dependent variable Y and one or more explanatory variables, the Xs, the emphasis was on

    estimating and/or predicting the average value of Y conditional upon the fixed values of

    the X variables. The cause-and-effect relationship, if any, in such models therefore ran

    from the Xs to the Y.

    But in many situations, such a one-way or unidirectional cause-and-effect

    relationship is not meaningful. This occurs if Y is determined by the Xs, and some of the

    Xs are, in turn, determined by Y. In short, there is a twoway, or simultaneous,

    relationship between Y and (some of) the Xs, which makes the distinction between

    dependent and explanatory variables of dubious value. It is better to lump together a set

    of variables that can be determined simultaneously by the remaining set of variables

    precisely what is done in simultaneous-equation models. In such models there is

    more than one equationone 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.

    In quite a similar view as of our single equation models , our conventional

    Classical Linear Model Assumption , is that all the explanatory variables of an

    equation are strictly unrelated. But when we start dealing with Simultaneity Bias it

    very likely gives rise to the problem of related explanatory variables, precisely the

    problem of Multicollinearity. In this particular problem the individual regression

    parameters are not estimable with sufficient precision because of high standard errors

    which often occurs due to highly intercorrelated regressors. In econometric literature

    Multicollinearity is one of the misunderstoood conceptions since high

    intercorrelations among the explanatory variables are neither necessary nor

    sufficient to cause the multicollinearity problem rather the best indicators of the

    problem are the t-ratios of the individual coefficients.

    Thus our endeavour is to resolve the problem of simultaneity, if present , as well

    as to emphasise on the fact that intercorrelation between explanatory variables is

    neither necessary nor sufficient for the existence of Multicollinearity rather we should

    concentrate more on the models significance.

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    An obvious reason for the endogeneity of explanatory variables in a regression model is simultaneity: that is, one or more of the \explanatory variables are jointly determined with the \dependent variable. Models of this sort are known as simultaneous equations models (SEMs), and they are widely utilized in both applied microeconomics and macroeconomics. Each equation in a SEM should be a behavioral equation which describes how one or more economic agents will react to shocks or shifts in the exogenous explanatory variables, ceteris paribus. The simultaneously determined variables often have an equilibriuminterpretation, and we consider that these variables are only observed when the underlying model is in equilibrium.

    For instance, a demand curve relating the quantity demanded to the price of a good, as well as income, the prices of substitute commodities, etc. conceptually would express that quantity for a range of prices. But the only price-quantity pair that we observe is that resulting from market clearing, where the quantities supplied and demanded were matched, and an equilibrium price was struck. In the context of labor supply, we might relate aggregate hours to the average wage and additional explanatory factors:

    where the unit of observation might be the county. This is a structural equation, or behavioral equation, relating labor supply to its causal factors: that is, it reacts the structure of the supply side of the labor market. This equation resembles many that we have considered earlier, and we might wonder why there would be any difficulty in estimating it. But if the data relate to an aggregate such as the hours worked at the county level, in response to the average wage in the county this equation poses problems that would not arise if, for instance, the unit of observation was the individual, derived from a survey. Although we can assume that the individual is a price- (or wage-) taker, we cannot assume that the average level of wages is exogenous to the labor market in Suffolk County. Rather, we must consider that it is determined within the market, affected by broader economic conditions. We might consider that the z variable expresses wage levels in other areas, which would cet.par. have an effect on the supply of labor in Suffolk County; higher wages in Middlesex County would lead to a reduction in labor supply in the Suffolk County labor market, cet. par. To complete the model, we must add a specification of labor demand:

    where we model the quantity demanded of labor as a function of the average wage and additional factors that might shift the demand curve. Since the demand for labor is a

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    derived demand, dependent on the cost of other factors of production, we might include some measure of factor cost (e.g. the cost of capital) as this equation's z variable.

    In this case, we would expect that a higher cost of capital would trigger substitution of labor for capital at every level of the wage, so that

    Note that the supply equation represents the behavior of workers in the aggregate, while the demand equation represents the behavior of employers in the aggregate. In equilibrium, we would equate these two equations, and expect that at some level of equilibrium labor utilization and average wage that the labor market is equilibrated. These two equations then constitute a simultaneous equations model (SEM) of the labor market. Neither of these equations may be consistently estimated via OLS, since the wage variable in each equation is correlated with the respective error term. How do we know this? Because these two equations can be solved and rewritten as two reduced form equations in the endogenous variables hi and wi. Each of those variables will depend on the exogenous variables in the entire system-z1 and z2-as well as the structural errors ui and vi:

    In general, any shock to either labor demand or supply will affect both the equilibrium quantity and price (wage). Even if we rewrote one of the