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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
25 An Example of the Use of 2SLS: Modelling
the Bid-Ask Spread and Volume for Options
• George and Longstaff (1993)
- 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
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.
- Summer '13
- Financial Markets