Car Ownership? Evidence from the Copenhagen Metropolitan Area

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In this equation the levels of , and , that occur in the numerator refer to the situation before the extension of the metro network. 25 corresponds with the change ∆ln ,, in log income can be determined as: The change in income itself that ∆ ,, 1 ∆ ,, (A5) If households would not change their location, housing type or car ownership position, this would suffice to compute the welfare impact of the change in the metro network. However, the changes in the utilities of the choice alternatives that occur as a consequence of the extension of the metro network will induce some households to change their residential location, car ownership position or perhaps even their housing type. To take this into account as well, we use the results of De Palma and Kilani (2003). We start by defining ∆ as the largest of the conditional compensating variations: ∆ max ,, ∆ ,, (A6) DePalma and Kilani (2003) show that the unconditional compensating variation is always between the minimum and the maximum of the conditional compensating variations. To be able to compute it exactly we define functions ,, as follows: ,, ,, , , , , , , ; , (A7) where the values of , and , refer to the situation with the extended metro network. Clearly, if ∆ ,, , ,, is equal to the utility household I experienced before the ∗ extension of the metro network. Now define: ,, max ,, , ,, ∆ ,, and let ∗ denote the logit choice probabilities defined on the basis of these utilities: 26 25 The income level that occurs in the denominator refers (from the derivation of (A.3)) to the situation after the extension of the metro network, but we assume throughout that household income does not change because of the extension of the metro network. 26 This equation is analogous to (2) for the generator function of the multinomial logit model. 50
,, ∗ ∗ ,, ∑ ∑ ∑ ∗ ,, (A8) This brings us – finally – in the position to define the expected value of the unconditional expected value of the compensating variation : 27 ∆ ∆ ∑ ∑ ∑ ,, ∗ (A9) ∆ ,, De Palma and Kilani (2003) suggest to evaluate this expression through simulation. Since the integral has to be computed is one-dimensional, Gaussian quadrature is also feasible and we used this technique (see Judd, 1999, chapter 7). 27 It can be shown that (A8) reduces to the change in the logsum when utility is linear in income. 51
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TI 2015-139/VIII Tinbergen Institut
Page 3: Does improving public transport dec
Page 6 and 7: even in transportation the impact o
Page 8 and 9: It is a fair simplification to clai
Page 10 and 11: of owner-occupied residences consti
Page 12 and 13: 3. The model This section presents
Page 14 and 15: ∑ ∑ ∑ ,, , which implie
Page 16 and 17: holds for the unconditional compens
Page 18 and 19: sum of the average utility of the a
Page 20 and 21: characteristics that make an area a
Page 22 and 23: the last six are characterizing the
Page 24 and 25: determined by the demographic compo
Page 26 and 27: second stage we put the estimated v
Page 28 and 29: Table 4.a First step estimation pro
Page 30 and 31: preferred to apartments and a highe
Page 32 and 33: Map 5. Metro system extension 6.1.
Page 34 and 35: Map 7. Change in relative house pri
Page 36 and 37: demographic composition of neighbou
Page 38 and 39: Table 6: Compensating variations of
Page 40 and 41: area. Since it is difficult to choo
Page 42 and 43: Judd, K. 1998. Numerical Methods in
Page 44 and 45: Table A.1.2. Hedonic price equation
Page 46 and 47: Table A.2.2 First step IV estimatio
Page 48 and 49: Map A.2. Pct. change in population
Page 50 and 51: Map A.4. Pct. change in the share o
Page 52 and 53: Map A.6. Pct. change in the number
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Car Ownership? Evidence from the Copenhagen Metropolitan Area

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