VI_SIM_EQN_8 23_2011

VI_SIM_EQN_8 23_2011 - VI 1 James B. McDonald Brigham Young...

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VI 1 James B. McDonald Brigham Young University 12/23/2011 VI. SIMULTANEOUS EQUATION MODELS INTRODUCTION There are several problems encountered with simultaneous equations models that which are not generally associated with single equation models. These include (1) the identification problem, (2) inconsistency of ordinary least squares (OLS) estimators, (3) questions about the interpretation of structural parameters, and (4) the validity of the OLS "t statistics" associated with structural coefficients. To introduce these problems, we review two important papers. The paper on identification by E. J. Working [1927, QJE ] is considered in the first section. The work of Haavelmo [1947, JASA ] dealing with alternative methods of estimating the marginal propensity to consume is described in the second section. The third section contains a brief summary of particularly important results. 1. STRUCTURAL AND REDUCED FORM REPRESENTATIONS, IDENTIFICATION, AND INTERPRETATIONS OF COEFFICIENTS Consider the problem of estimating the impact of an increase in the price of crude oil upon the equilibrium price and quantity of gasoline. The corresponding increase in the price of gasoline will depend upon several factors including the slope of the demand curve.

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VI 2 This is illustrated by the following figure: Figure 1 Assume that (Q 0 , P 0 ) denotes the original equilibrium. Assume that the increase in the price of crude oil results in the supply curve shifting from S 1 to S 2 . The associated change in P depends upon the relevant demand schedule, with the more inelastic schedule being associated with the larger price increases. This example clearly indicates the importance of estimating the slope of the demand schedule to make predictions about the impact of changes in factor price upon the equilibrium price. Estimation of the slope of the demand curve might begin by collecting observations on (P, Q), which might appear as in Figure 2.
VI 3 P Q Figure 2 The reader would probably be tempted to draw a line through the points or perform a least squares estimation on p = β 1 - β 2 Q in order to estimate the demand schedule. But how would we estimate the demand curve if a plot of P and Q appeared as in Figure 3 rather than as in Figure 2? P Q Figure 3

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VI 4 The data in Figure 3 appears to define a supply curve rather than a demand curve. Alternatively, how could we estimate a demand curve if the data appeared as in Figure 4? P Q Figure 4 To answer this question, we need to recall that we observe equilibrium prices and quantities in the data; equilibrium price and quantity are determined by supply and demand factors and not supply or demand alone. The observations depicted in Figure 2 could have been generated by either of the following scenarios: P P
VI 5 Q Q Figure 5 If the demand curve is stable and the supply curve shifts, then the demand curve is "traced out." If both curves shift, fitting a relationship to the observed (P,Q) would not correspond to the underlying demand curve(s). Similarly, Figure 3 could correspond to a relatively stable supply curve and a shifting demand curve or both curves shifting.

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This note was uploaded on 02/29/2012 for the course ECON 388 taught by Professor Mcdonald,j during the Winter '08 term at BYU.

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VI_SIM_EQN_8 23_2011 - VI 1 James B. McDonald Brigham Young...

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