The disturbances in the structural equations are

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Unformatted text preview: imates also need to be modified compared with their OLS counterparts, but once this has been done, we can use the usual t- and F-tests to test hypotheses about the structural form coefficients. 22 Instrumental Variables • Recall that the reason we cannot use OLS directly on the structural equations is that the endogenous variables are correlated with the errors. • One solution to this would be not to use Y2 or Y3 , but rather to use some other variables instead. • We want these other variables to be (highly) correlated with Y2 and Y3, but not correlated with the errors - they are called INSTRUMENTS. • Say we found suitable instruments for Y2 and Y3, z2 and z3 respectively. We do not use the instruments directly, but run regressions of the form (27) & (28) 23 Instrumental Variables (cont’d) • Obtain the fitted values from (27) & (28), Y3 with these in the structural equation. and , and replace Y2 and • We do not use the instruments directly in the structural equation. • It is typical to use more than one instrument per endogenous variable. • If the instruments are the variables in the reduced form equations, then IV is equivalent to 2SLS. 24 Instrumental Variables (cont’d) • What Happens if We Use IV / 2SLS Unnecessarily? The coefficient estimates will still be consistent, but will be inefficient compared to those that just used OLS directly. • The Problem With IV What are the instruments? Solution: 2SLS is easier. Other Estimation Techniques 1. 3SLS - allows for non-zero covariances between the error terms. 2. LIML - estimating reduced form equations by maximum likelihood 3. FIML - estimating all the equations simultaneously using maximum likelihood 25 An Example of the Use of 2SLS: Modelling the Bid-Ask Spread and Volume for Options • • George and Longstaff (1993) Introduction - Is trading activity related to the size of the bid / ask spread? - How do spreads vary across options? • How Might the Option Price / Trading Volume and the Bid / Ask Spread be Related? Consider 2 possibilities: 1. Market makers equalize spreads across options. (fees important) 2. Spread is a constant proportion of the option value. (inventory) . 26 Market Making Costs • The S&P 100 Index has been traded on the CBOE since 1983 on a continuous open-outcry auction basis. • Transactions take place at the highest bid or the lowest ask. • Market making is highly competitive. 27 What Are the Costs Associated with Market Making? • For every contract (100 options) traded, a CBOE fee of 9c and an Options Clearing Corporation (OCC) fee of 10c is levied on the firm that clears the trade. • Trading is not continuous. • Average time between trades in 1989 was approximately 5 minutes. 28 The Influence of Tick-Size Rules on Spreads • The CBOE limits the tick size: $1/8 for options worth $3 or more $1/16 for options worth less than $3 • The spread is likely to depend on trading volume ... but also trading volume is likely to depend on t...
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This note was uploaded on 09/20/2013 for the course FINA 5170 taught by Professor Janebargers during the Summer '13 term at Greenwich School of Management.

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