Linking discrete choice to continuous demand within the framework of a computable general equilibrium model

Transportation Research Part B 46 (2012) 1177–1201

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Transportation Research Part B journal homepage: www.elsevier.com/locate/trb

Linking discrete choice to continuous demand within the framework of a computable general equilibrium model Truong P. Truong, David A. Hensher ⇑ Institute of Transport and Logistics Studies, The University of Sydney Business School, The University of Sydney, NSW 2006, Australia

a r t i c l e

i n f o

Article history: Received 4 November 2011 Received in revised form 4 June 2012 Accepted 4 June 2012

Keywords: Bottom-up Top-down Discrete choice Differentiated products Continuous demand Computable general equilibrium (CGE) models

a b s t r a c t Discrete choice (DC) models are commonly used as basic building blocks in ‘bottom-up’ models which seek to describe consumer and producer behaviour at a disaggregate level, in contrast to continuous demand (CD) models which are used to describe behaviour at a more aggregate level. At a disaggregate level, choice behaviour is defined in terms of commodities differentiated by qualities or attributes. In contrast, aggregate demand behaviour is defined in terms of broadly defined and generically different commodities. In a DC model, the main focus of analysis is not the total quantity of demand, but rather the relative shares or substitution between the choice alternatives, in contrast to a continuous demand model where the focus is on the aggregate substitution between groups of commodities as well as on the income effects. Seen in this way, there is scope for complementary usage of DC and CD models within the framework of a CGE model where DC models are used to describe the preferences for a narrowly defined set of commodities belonging to a particular sector of an economy, and CD models are used to describe the interactions between these sectors. In this paper, we describe how DC and CD models can be used in such an integrated fashion in a spatial computable general equilibrium model to inquire into the wider economic impacts of a transport investment project in the Sydney Metropolitan Area. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Discrete choice (DC) models are often used as the basic building blocks in a bottom-up model which seeks to describe consumer and producer behaviour at a disaggregate level. Such models are often rich in details of the choice alternatives, as well as characteristics of the individual decision makers, and therefore can capture the behavioural responses of individuals to economic policies more accurately than can aggregate models of supply or demand. For example, the decision on commuter mode choice in a DC model can be described not only in terms of the attributes of the travel modes (travel time, travel cost, comfort level, convenience, etc.), but also the socio-economic characteristics of each decision maker (income level, age-group, position in family structure, occupation, flexibility of travel time, etc.). Similarly, the decision on workplace or residential location in a DC model can be described in terms of the varied economic characteristics of the location (e.g., average wage paid for a particular type of work in that location, average rental cost for different housing types, transport costs between different origin and destinations, etc.). This means that policies which seek to influence decisions at the disaggregate level on mode choice or locational choice can be more accurately analysed if set within the framework of a disaggregate DC model. At a disaggregate level of choice decision, however, the typical choice set within a DC model often consists of mainly a narrowly-defined set of varieties, or alternatives, of a particular commodity e.g., different modes of travel, different types ⇑ Corresponding author. Fax: +61 2 93510088. E-mail addresses: [email protected] (T.P. Truong), [email protected], [email protected] (D.A. Hensher). 0191-2615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trb.2012.06.001

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of cars. These varieties or alternatives are differentiated mainly by quality attributes rather than simply by market prices (which can be considered as the summary indices for these attributes).1 In contrast, continuous demand (CD) models which look at behaviour at a more aggregate level are concerned only with the demand for groups of commodities which are generically different (transport, food, housing, education, health, etc.). These groups are to be ‘differentiated’ only or mainly via their market prices.2 The choice decision within a DC model is therefore concerned primarily with the ‘fine’ substitution between different alternatives or varieties of a particular commodity (often produced within a particular sector of an economy), rather than with the gross substitution between groups of commodities (belonging to different sectors of an economy) and the effect of income or budget level on their demand. Seen in this way, there is scope for complementary3 usage of DC and CD models within the framework of a CGE model, where DC models can be used to describe the preferences for a narrowly defined set of commodities, while CD models are used to describe the interactions between the demands for different groups of commodities. In this paper, we describe how DC and CD models can be used in such an integrated fashion in a spatial computable general equilibrium model to inquire into the wider economy impacts of a transport investment project. These wider impacts are to be considered in addition to the usual impacts on the users of the transport network as considered in traditional (partial) benefit-cost analysis (Graham (2007a,b). In the past, there have been studies which also looked at the issue of using a DC model within the framework of a CGE framework (see for example, Horridge (1994)). However, the approach so far has been limited to the use of a theoretical functional form (such as the linear logit4) in a CGE model to replace the use of other alternative functional forms (such as CES) to describe demand for different varieties of a particular activity or commodity (such as transport mode choice or location choice). It has not been extended to the use of an actual or true DC model in a CGE framework. Here we can define a ‘true’ DC model as one specified and estimated using individual-specific discrete choice data rather than estimated (or calibrated) using only aggregate or average market share data (as is the case of the linear logit model). The use of such a model in a CGE framework presents both challenges as well as potential advantages which will be explained in this paper. The plan of the paper is as follows. Section 2 introduces the Multinomial Logit (MNL) discrete choice model as the basic structure used in most disaggregate behavioural models of choice behaviour. Sections 3 and 4 explain how a MNL basic structure can be considered as part of a (conditional) demand system for simple and more complex decision structures. Section 5 then illustrates the connection between DC and CD models within a CGE framework, with an empirical example taken from a study of the wider economic impacts of an urban transport investment project, and Section 6 gives some conclusions. 2. Multinomial Logit (MNL) discrete choice model A typical MNL model of discrete choice is specified as follows:

expðV i Þ ; j2I expðV j Þ

Probi ¼ P

i 2 I:

ð1Þ

Probi is the probability of alternative i being chosen from a choice set I, and Vi is the (indirect) utility function of the choice alternative i. The indirect utility function Vi is usually specified as a linear function of all the attributes of the choice alternative as well as the characteristics of the individual who chooses this alternative5:

Vi ¼

X m2M

am Aim þ

X bn Bin ;

i 2 I:

ð2Þ

n2N

Aim stands for the attribute m of alternative i, Bin is the characteristic n of the individual who chooses alternative i; and am and bn are parameters.6 For example, if i is a mode choice alternative (say ‘‘bus’’) then Aim can be variables describing the travel time 1 Using the Lancaster approach to consumer demand based on commodity characteristics or attributes (Lancaster, 1966). Discrete choice models therefore are often used for the study of the demand for quality-differentiated products. See for example Berry, 1994; Berry et al., 1995, 2004. 2 Market price is also often used in a DC model but this plays the role of only one particular attribute among many, while in a continuous demand model it is the main (and often only) ‘attribute’. 3 An alternative approach is to use a DC model in a ‘conditional demand’ mode and then trying to relate the choice elasticities to demand elasticities (see, for example, Smith et al., 2010). Although this approach is not inconsistent with our approach (see, for example, Section 3.2 below), it tends to restrict the usefulness of a DC model because it implies that DC and CD models are merely substitutes which can be used to analyse the same problem, while in fact, DC and CD models are quite fundamentally different and designed to deal with different issues. For example, a CD model is not well designed to handle the issue of consumer heterogeneity or product variety, but strong in dealing with the issue of income and relative price effects. The reverse is true for DC models. Therefore DC and CD are more complements rather than substitutes. 4 That is, a logit model of choice behaviour which is specified and estimated using market shares data rather than discrete individual choice data (see Oum, 1979). 5 Although product variety and consumer heterogeneity can be considered as equivalent from a theoretical viewpoint, if we look only at the aggregate (or average) behaviour of a ‘representative’ consumer, and if the distribution of the heterogeneous consumer preferences can described in terms of symmetrical positions in the attribute space with respect to the various choice alternatives (product varieties) (see for example, Anderson et al., 1988b, 1989), it is still convenient to distinguish between these two concepts from an empirical point of view because in practice, a DC model describes ‘consumer heterogeneity’ in terms of the characteristics of the decision maker, while product variety is specified in terms of the attributes of the choice alternatives. Developments such as mixed logit however allow for heterogeneity on the attributes. 6 In general, the parameters am and bn are assumed to be ‘generic’, i.e., independent of the choice alternatives, except for the parameter of the constant term, which can be assumed to be ‘alternative-specific’, and this parameter can be represented by the symbol li0 where ai0 – aj0 for i – j.

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Residential Location Choice

Residential Location 1

Residential Location r

Dwelling Type Choice in location r

Dwelling Type 1

…

Dwelling Type I (d)

Residential Location I (r)

……

Work Place Choice for residents at r

Work Place Location 1

Mode Choice 1

Work Place Location w

…

……

Work Place Location I (w)

Mode Choice I (t)

Fig. 1. A nested choice structure.

and cost associated with alternative ‘‘bus’’, and Bin are the variables describing the socio-economic characteristics of the individual who chooses this alternative (such as income level, whether owning a car, professional status, and residential location). If we now assume that, because of the existence of other ‘unobserved’ characteristics of the choice alternative, the indirect utility function is a random rather than deterministic variable, consisting of the deterministic part Vi as specified in (2) and a random error term ei; we can define the well known form:

U i ¼ V i þ ei :

ð3Þ

The individual is then said to choose alternative i over all other alternatives j – i if and only if Ui > Uj for all j – i. This means (ei  ej) > (Vj  Vi) for all j – i. Depending on the distribution of the random error term ei, different choice models can be derived. For example, if ei’s are assumed to be independently and identically distributed (i.i.d.) as a Weibull distribution,7 then the probability of condition (ei  ej) > (Vj  Vi) being satisfied is given by the choice probability function (1).8 Often, a (complex) choice decision can involve many different layers or levels of decision; therefore, the basic MNL model can be extended into a nested structure.9 A decision on residential location, for example, can depend not only on the attributes of the residential location choices (such as distances from the Central Business District (CBD), environmental characteristics of the locations) but also on choices regarding the types of dwelling available within each location, and also the decision on work location. The latter in turn can depend on the types of travel mode choices available for journeys to work from each residential location and to each particular work location. These interrelated choice decisions can be represented by a ‘nested’ MNL choice structure as shown in Fig. 1, and the equations for these decisions are described in the Appendix (Eqs. (A1)–(A7)). 7 If the distribution is normal rather than Weibull (also called extreme value type I distribution) then the choice probability function will take on a different form which is referred to as the ‘probit’ model. 8 We limit the discussion to closed form choice models. The literature has advanced significantly with open-form models such as mixed (or random parameter) logit, error components logit, and scaled MNL – see Hensher and Greene, 2003; Train, 2003; Greene and Hensher, 2010. The focus of the current paper is on integration with a computable general equilibrium framework in order to capture economy wide impacts. In principle, more advanced choice models could be included. 9 This is also to avoid one of the weaknesses of the basic MNL choice model, the global assumption of ‘independence from irrelevant alternative’ (IIA) which says that the choice of alternative i over alternative j is independent of the existence of other alternatives. This means the ratio of choice probabilities (Probj/ Probj) is independent of the existence of (and therefore also the levels of the attributes of) other alternatives. To overcome this weakness, the choice set must be defined carefully so as not to contain subsets of alternatives which are more ‘similar’ to each other than are to others in the choice set. This means in general a ‘nested’ or hierarchical structure is unavoidable to group alternatives together according to degrees of ‘similarity’, for example, ‘blue bus’ and ‘red bus’ are grouped together before being compared to ‘train’ and ‘car’, or mode choices are grouped together before looking at location choices.

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3. Multinomial Logit for use as part of a complete demand system Although the parameters of the choice probability function in a Multinomial Logit discrete choice model are estimated using individual choice data, once estimated, the model can be used to predict aggregate or ‘representative consumer’ demand.10 This can take two forms: either individual-specific data are fed into the discrete choice model to predict the choice probability for each individual and then aggregated up to a level of continuous demand; or alternatively, ‘representative’ individual data can be fed into the DC model to predict the choice probability for this hypothetical individual, and then using the choice probability to predict market share. Either way, a discrete choice model is now being used to predict continuous (‘representative consumer’) demand, and a question arises: how and when is this approach valid? Demand refers to multiple choices either by many individuals with deterministic but heterogeneous preferences on any single occasion, or by a single (hypothetical ‘representative’) individual with probabilistic preference on many different occasions. Therefore, demand refers to a continuous number (absolute quantity of demand or relative market share) whereas discrete choice refers only to a single discrete (0, 1) decision at any one time.11 Discrete choice, therefore, tends to indicate a preference level rather than demand as such. To arrive at the optimal demand decision requires some trade-off between commodities at the extensive margin with a binding budget constraint, rather than a trade-off between attributes of a particular choice alternative at the ‘intensive’ margin where the budget constraint is often not binding. Therefore it is more appropriate to interpret the use of a DC model as being applied to situations where only the preferences or shares between different alternatives of a specific decision are to be determined while assuming that the total aggregate level of demand for all the choice alternatives is to be determined outside of the choice model.12 Although a DC model is fundamentally different from a CD model,13 they can be regarded as parts of a more complete and accurately specified demand system where ‘demand’ refers to ‘optimal choices’; but choices can only be optimal if (1) the constraint is specified accurately (as in a CD model), and (2) preferences are known with accuracy, taking into account not only market factors (such as price and income level), but also other individual socio-demographic characteristics and commodity quality attributes (as in a DC model). Therefore, in what follows, we consider the issue of how to combine the uses of both DC and DC models to describe consumer behaviour in a more accurate manner in the framework of a CGE model. 3.1. Using a DC model to infer the ‘effective’ or ‘generalised’ price for each choice alternative and to derive an aggregate price index for all choice alternatives The choice probability function in a DC model is often specified in terms of the indirect utility function Vi() which charactertises the (maximum) utility level associated with each particular choice alternative i. This indirect utility function contains not only the ‘characteristics’ of the choice alternative being considered (such as travel time and travel costs, acess time and egress time, comfort and convenience level, in a mode choice model) but also the (socio-economic) characterstics of the decision makers (income level, professional status, age, sex, household characteristic, etc.). Leaving aside the characteristics of the decision makers which are used to account for the heterogeneity of the consumers, the characteristics of the choice alternatives can be considered as different attributes which make up the commodity in question (choice alternative).14 Each of the attributes can be assumed to have a ‘shadow price’, and this shadow price is derived from the parameters of the indiract utility function estimated for each DC model. The indirect utility function in a DC model therefore can be written as:

V i ¼ V i ðpi1 ; . . . ; pik Þ ¼ V i ðPi ðpi1 ; . . . ; pik ÞÞ;

i ¼ 1; . . . ; I;

ð4Þ

where pik’s are the implicit or shadow prices of the k attributes of alternative i, and Pi is an aggregator which combines these attributes and shadow prices into an ‘effective’ or ‘quality-adjusted’ price index for the choice alternative. For example, in a mode choice model, different categories of travel time variables can be combined with travel cost (given a value of travel time savings) to obtain a ‘generalised price’ index for the choice alternative. The concept of generalised price can be extended to include, not only travel time and travel costs, but also reliability, crowding, comfort and convenience levels, etc., as important attributes of a travel mode. Each of these attributes has a shadow price attached to it which is inferred from the parameters of the indirect utility function (e.g., the shadow price of travel times is inferred from the ratio of the coefficients of travel time and travel costs). Therefore, in estimating the price index for each choice alternative, the travel cost (‘market 10

See for example, McFadden and Reid (1975). Even if the decision may involve more than one decision, e.g. mode choice nested into work location choice, this is still not multiple decisions but rather only a single combined decision in a ‘nested’ structure. 12 This suggests that concepts such as ‘demand elasticities’ when applied to a DC model must be appropriately qualified. Schmidheiny and Brülhart (2011) for example, referred to the elasticities estimated from a DC model as ‘semi-elasticities’ to distinguish these from the conventional demand elasticities. Alternatively, elasticities from a DC model can be referred to as ‘conditional’ demand elasticities because the ‘condition’ on these choices is that either total quantity of the demand for all the choice alternatives is fixed, or the budget level for all choices is given. See, for example, Hensher et al., 2005; Smith et al., 2010. 13 See, for example, Anderson et al. (1988a, p. 162) where it is noted that while the (linear logit) discrete choice model is ‘equivalent’ to a (CES) continuous demand model when referring to aggregate representative behaviour, the two models are fundamentally different because in the former case, the individual consumer is assumed to buy only one unit of the differentiated products while in the latter case, he/she is assumed to spend a fixed amount of income (perhaps over time or through repeated exercise) on different varieties of the product. 14 This interpretation is similar to that in the Lancaster characteristics approach to the theory of consumer demand (Lancaster, 1966). 11

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price’) must be combined with the shadow costs of other non-market factors to arrive at an ‘effective’ or ‘generalised’ price for the choice alternative. This generalised price is in fact inferred from the indirect utility function. Seen in this way, the indirect utility function of a DC model (as shown in Eq. (2), (4)) can be rewritten in a ‘reduced-form’ as follows:

V i ¼ ai0 þ ai1 Pi ;

i ¼ 1; . . . ; I;

ð5Þ

where ai0 is the original ‘alternative-specific’ constant, ai1 is the co-efficient of the market price or money cost variable associated with the choice alternative,15 and Pi is the aggregator which combines, not only the market price but also all other nonmarket attributes of the choice alternatives into a ‘generalised price’ for the choice alternative i.16 Given the generalised prices for all the choice alternatives, an aggregate or average price index for all choice alternatives can then be computed, using the logsum function17:

dV ¼ d ln

X

expðV i Þ ¼

i2I

X ½ðProbi ÞðdV i Þ:

ð6Þ

i2I

Substituting (5) into (6), we have18:

dV ¼

X

½ðProbi Þða1 dPi Þ ¼ a1

i2I

X ½ðProbi ÞðdP i Þ ¼ a1 dP;

ð7Þ

i2I

where

dP ¼

X ðProbi ÞðdP i Þ;

ð8Þ

i2I

dP therefore can emerge as the differential change in the aggregate or average price index for all choice alternatives which can be inferred from the differential change in the logsum as shown in Eq. (7). The relationship between the aggregate or average price index and the logsum of the indirect utilites is indeed the value of the marginal utility of money, as represented by the parameter a1. 3.2. DC model as a conditional probabilistic demand model The logsum can be interpreted as the expected indirect utility of demand for all choice alternatives, and therefore, we can apply Roy’s theorem to this expected indirect utility function to get a system of probabilistic demand for each choice alternative as follows:

Xi ¼ 

@V=@P i @V=@M

P

P

¼ P

¼ P

j2I ð@V=@V j Þð@V j =@P i Þ

j2I ð@V=@V j Þð@V j =@MÞ

0 j2I ðProbj ÞV ji 0 j2I ðProbj ÞV jM

;

i ¼ 1; . . . ; I;

ð9Þ

where M refers to total income or expenditure. Here Xi is the probabilistic demand for choice alternative i, V 0ji ¼ @V j =@Pi and V 0jM ¼ @V j =@M; i.e., these are the derivatives of the choice indirect utility function with respect to the generalised price index and with respect to the aggregate expenditure level of demand, respectively. From Eq. (5) we can see that V 0ji ¼ 0 if j – i, and V 0ji ¼ ai1 if j = i. The value of V 0jM , however, cannot be inferred directly from a DC model but must be estimated exogenously of the DC model. Despite the lack of information on the value of V 0jM , Eq. (9) can still be used to estimate the share of demand for each choice alternative if in fact the total level of demand for all choice alternatives is assumed to be given.19 Rewriting Eq. (9) in an alternative form:

X i ðProbi Þai1 ¼ ; X j ðProbj Þaj1

i; j ¼ 1; . . . ; I;

ð10Þ

or, when ai1 is assumed to be constant across all alternatives, i.e. ai1 = a1 for all i’s, this is simplified to:

X i ðProbi Þ ¼ ; X j ðProbj Þ

i; j ¼ 1; . . . ; I:

ð11Þ

Thus, if the total level of demand for all choice alternatives (X) is assumed to be given, then the demand for each choice alternative can be derived from Eq. (11):

X i ¼ ðProbi ÞX;

i ¼ 1; . . . ; I:

ð12Þ

15 The value of ai1 represents (minus) the marginal utility of money (in choice alternative i). Normally, this coefficient is generic, i.e. the same for all choice alternatives, therefore we can set ai1 = a1 for all choice alternatives. 16 Using the shadow prices of the attributes as estimated from the DC model. In fact, the estimation of the shadow prices of these attributes is the strength of a DC model which helps to add to the behavioural accuracy of the (complete) demand system. 17 See Appendix, Eqs. A2, A4, and A6. 18 Henceforth, we will assume that ai1 is generic rather than alternative-specific and therefore will write the coefficient for price variable as a1 rather than ai1for simplicity of notation. 19 To be estimated by the CD model in the complete (general equilibrium) demand system.

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Continuous Aggregate Demand for housing and travel activities CD

Discrete Travel Mode Choices

Discrete Dwelling Type Choices DC

Dwelling type 1

DC

Dwelling type I (d)

…

Travel Mode 1

…

Travel Mode I (t)

Fig. 2. Discrete choice (DC) models of transport modes and dwelling types linked to an aggregate continuous demand (CD) model of transport and housing activities.

Eq. (12) shows that the choice probabilities in a DC model can be used to indicate the demand (quantity) shares20 if the total level of demand for all choice alternatives is assumed to be given. When a DC model is linked to a CD model, this total quantity of demand will no longer be assumed to be ‘given’ but is to be estimated within the CD model given the aggregate price index P as derived from the DC-component. Therefore the combined DC–CD model is now a complete demand system with demand quantity and aggregate price index interconnected, as they should be in the framework of a general equilibrium model. 3.3. Example of a simple linkage between DC and CD models Consider the simple example of Fig. 2 where different mode choice decisions are assumed to be represented by a DC model conditional on a total level of travel demand (say, the total number of work trips originating from zone s and with destination in zone z). Similarly, different dwelling type choices can be regarded as different demands for various housing types conditional on a total level of demand for all housing types. Let the indirect utility function for each choice alternative in the mode choice model be defined in a form similar to Eq. (5), i.e.21: ðtÞ

ðtÞ

ðtÞ ðtÞ

V i ¼ ai0 þ a1 Pi ;

i ¼ 1; . . . ; IðtÞ ;

ð13Þ

where a superscript ‘t’ is used to denote travel mode choice. The logsum for this choice model is given by:

dV ðtÞ ¼ d ln

X

ðtÞ

expðV j Þ ¼

j2IðtÞ

X

ðtÞ

ðtÞ

ðProbj ÞðdV j Þ ¼

j2IðtÞ

X

ðtÞ

ðtÞ

ðtÞ

ðProbj ÞðdPj Þ ¼ a1 dPðtÞ ;

ð14Þ

j2IðtÞ

where

dPðtÞ ¼

X j2I

ðtÞ

ðtÞ

ðProbj ÞðdPj Þ:

ð15Þ

ðtÞ

The value of dPðtÞ can be estimated from the change in logsum of the DC model for mode choice and can be regarded as the change in the aggregate price index for travel by all mode choices. In a similar manner, we can also define the indirect utility function for each choice alternative in a DC model for housing (dwelling type choices) and then estimate the change in the aggregate price index for all dwellings types as follows: ðdÞ

Vi

ðdÞ

ðdÞ ðdÞ

¼ ai0 þ a1 Pi ;

dV ðdÞ ¼ d ln

X j2I

i ¼ 1; . . . ; IðdÞ ; ðdÞ

ðdÞ

expðV j Þ ¼ a1 dPðdÞ ;

ð16Þ ð17Þ

ðdÞ

20 If ai1’s are alternative-specific rather than generic (i.e. constant across all alternatives), then the quantity shares will have to be weighted by these coefficients. The ai1’s being alternative-specific implies that each choice alternative is to be regarded as ‘generically different’ from each other. This is the extreme opposite to the case when they are considered as similar (when ai1is assumed to be constant across all alternatives). In the latter case, the choice alternatives are distinguished only via their ‘qualities’ and once their price indices Pi’s have been ‘adjusted’ for the quality differences (as implied by Eqs. (12) and (13)) the choice alternatives can be considered as ‘perfectly substitutable’ and therefore their demand quantities can be aggregated. If on the other hand, they are regarded as generically different then the weights ai1’s will stand for their relative (shadow) prices and therefore, in aggregating their demand, instead of adding the quantities (which will not be meaningful) one should add their total values or expenditures (given by ai1Pi where Pi is the quality-unadjusted market price and ai1 is the shadow value of the different qualities). 21 For simplicity, we have assumed that the coefficient for the price variable is generic rather than alternative-specific (see also the previous footnote). The analysis can easily be extended to the case where some of these coefficients are assumed to be alternative specific. We have also dropped the ‘conditional’ notation (/wr) for simplicity in this section.

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dPðdÞ ¼

  X ðdÞ ðdÞ Probj dPj ;

ð18Þ

j2IðdÞ

dPðdÞ is interpreted as the change in the aggregate price index for housing derived from the change in the logsum of the DC model for dwelling type choices. Both dPðtÞ and dP ðdÞ are then used in an aggregate CD model to estimate the change in the total levels of demand for travel and housing activities (which have been assumed to be fixed or given in the DC models). To illustrate, let the aggregate demand for these activities (X ðtÞ and X ðdÞ ) be described by a constant elasticity of substitution (CES) utility function:

  h  q  q i1=q U ¼ U X ðtÞ ; X ðdÞ ¼ dt X ðtÞ þ dd X ðdÞ :

ð19Þ

Here the parameters dt, dd are referred to as distribution parameters, and r = 1/(1  q) is the elasticity of substitution between these aggregate activities. Maximising the utility function (19) subject to a budget constraint:

X ðtÞ PðtÞ þ X ðdÞ PðdÞ 6 M;

ð20Þ

where M is the total expenditure level on travel and housing activities, will result in a system of demand equations of the following form:

 r h  q  q i1 X ðIÞ ¼ M dI =P ðIÞ dt X ðtÞ þ dd X ðdÞ ;

I ¼ ft; dg:

ð21Þ

Eq. (21) can also be written in the simpler ‘percentage change’ form (using a lower case letter to denote percentage change):

ðIÞ x

X

ðIÞ

¼ m  rp 

J¼ft;dg

!

X

¼

Sj xðJÞ

ðJÞ

SJ ð1  rÞp

"

r

ðIÞ  p

J¼ft;dg

X



m

¼ #

X

! ðJÞ

SJ p

" ðIÞ

r p 

J¼ft;dg

ðIÞ  p ; ðJÞ ¼ x  r½p SJ p

X

# ðJÞ

Sj p

J¼ft;dg

I ¼ ft; dg;

ð22Þ

J¼ft;dg

where

P ðIÞ X ðIÞ ðdI Þr ðPðIÞ Þ1r ¼P r ðJÞ 1r ; M J¼ft;dg ðdJ Þ ðP Þ

SI ¼

X

¼ p

I ¼ ft; dg;

ð23Þ

ðJÞ ; SJ p

ð24Þ

J¼ft;dg

X

x ¼

SJ xðJÞ ;

ð25Þ

J¼ft;dg

m¼

X

  ðJÞ ; SJ xðJÞ þ p

ð26Þ

J¼ft;dg

 xðdÞ , whereas the term x measures the aggregate income effect on the demands for travel and housing activities  xðtÞ and  22 ðIÞ   ðr½p  pÞ measures the (aggregate) substitution effect between these demands. From Eq. (12) we can write: ðtÞ

ðtÞ

X i ¼ ðProbi ÞX ðtÞ ; ðtÞ Xi

ð27Þ ðtÞ

where denotes the level of demand for choice alternative i (i.e., mode i) within the travel branch (t); X is the aggregate ðtÞ level of demand for all modes of travel, and ðProbi Þ is the choice probability for mode i. Taking the differential of the logarithmic function (d ln) or percentage change of both sides of Eq. (27) and using a lower case letter to denote percentage change, we have:

  ðtÞ ðtÞ xi ¼ xðtÞ þ d ln Probi :

ð28Þ

The first term on the right hand side of Eq. (28) is linked to the CD model via Eq. (22), the second term on the right hand side is linked to a DC model.23 Similar analysis can be used to estimate the disaggregate choices and aggregate demand for housing leading to equations similar to Eqs. (27) and (28) but applied to the housing rather than the travel activities In summary, a DC model can be used to estimate the substitution effects between choice alternatives of a narrowly defined class of commodities (travel mode choices, dwelling type choices, etc.). From the indirect utilities of the DC models, price indices of the narrowly defined choice alternatives as well as the aggregate price indices of broadly defined classes 22 23

To be distinguished from the disaggregate substitution effects which describe only the substitution effects between choice alternatives within a DC model. See for example Eq. (A9) in the Appendix.

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of commodities can be estimated. Using these price indices in an aggregate CD model allows one to estimate not only the aggregate income effect due to changes in income level but also the substitution effects. The linkage of DC models to a CD model therefore allows for a wide range of commodities to be considered in demand analysis with a richer analysis. 3.4. Issues of estimations and data consistencies between DC and CD models Discrete choice models are estimated using individual discrete choice data while continuous demand models in a CGE framework are often ‘calibrated’ using aggregate demand shares data contained in the input–output table of a particular year and with certain important parameters (such as elasticities of substitution) being taken from other econometric studies. There are thus issues of data compatibility and parameter consistency when combining the uses of the two types of models that need to be addressed. When a DC model is estimated, there are a large number of attributes (variables and parameters associated with these variables) which need to be identified and estimated. However, when the model is used in a prediction mode, only a smaller set of attributes, which are subject to policy impacts, will change. The rest often remain unchanged and therefore can be ‘absorbed’ into the so-called ‘alternative-specific constants’ (ASCs) of the indirect utility functions during the calibration process.24 Thus when linking a DC model to a CD model in a CGE framework, only a smaller set of key attribute variables and their associated parameters will play an important role, such as travel time or travel costs (for mode choice model), employment, wage or income levels (for work location choice model), and housing prices (for residential location choice model). These variables are often existing in a form which can be used consistently in both DC to CD models in a CGE framework. For example, wage, or income level is determined in the CD models as outcomes of the labour market while in DC models they are used only as ‘attributes’ for a choice decision. Choice decisions (e.g., with respect to residential and work place locations) produce outcomes which affect housing and employment levels in various locations which are then used as impacts on the housing and labour markets to produce outcomes (wages and income levels) which are then fed back into DC models. Therefore, there is no issue of incompatibility of data bases but only the advantage of data complementarity between their uses in DC and CD models. However, one issue which can be important, and that is the question of the appropriate level of aggregation. CD models are often highly aggregate and used to describe the behaviour of a ‘typical’ or ‘representative’ consumer or producer. DC models, on the other hand, are highly disaggregate and used to describe the behaviour of different types of consumers or producers. Therefore, to take full advantage of the different levels of aggregation, first, the rich details of DC models must be preserved as far as possible with data availability. Then, different classes of CD models for different types of consumers or producers will need to be specified in order to be linked to the appropriate outcomes from specific DC models. For example, mode choice or residential location decisions of a particular type of worker can be based on the personal income level of the worker. Hence, in linking these DC models to the labour markets25 in a CD model, different labour markets for these different types of workers (e.g., by occupation and industry) must also be built. This can increase the dimension of the model substantially, but only where necessary and where there are advantages (for policy purposes, as well as for accuracy of the predictions). With the DC model system involving a number of endogenous choice responses in spatial markets, such a household location, dwelling type, fleet size and vehicle type choices, and worker mode, departure time and workplace location choices, careful consideration is given to the conditional relationships between each choice decision. A fully integrated system of nesting of the suite of endogeneous choices as a nested logit model system with linkages via the expected maximum utility or logsum index provides a system compliant with individuals and households acting as if they are utility maximising. There is typically directional linkages dependent of the pre-specified hierarchy (which is correctly defined to accommodate differences in variances associated with the unobserved effects attached to each choice making situation, and is not a decision hierarchy per se. To accommodate market-based feedback, this can be achieved (as in TRESIS – see below) through equilibration of disequilibration in each of the markets of interest such as residential location (using location rents), workplace location (using number of jobs), mode and departure time (using travel time) and vehicle type (using new and used vehicle prices). Importantly a real behavioural strength of a DC model system is the careful selection of the range of choice responses that are likely to be on offer in real markets. DC systems limited to the ‘common’ transport choices of mode, destination and frequency choice are somewhat limited in achieving the objective. 4. More complex linkages between DC models and aggregate demand models within a CGE framework To utilise the strength of each type of model, more complex linkages between DC and aggregate demand models can be assumed, depending on the nature of a particular choice-demand situation. In the previous section, we have considered the simple linkage between housing and travel mode choice activities, with DC models describing the choices within each group of activities and a CD model linking the aggregate demand of these two groups. Consider now a more complex relationship 24 We note that choice decisions are based on differences in (indirect) utilities rather than on their absolute levels, hence only changes in the indirect utilities will affect the change in choice decisions. See for example, Eq. (A9) in the Appendix. This means the alternative specific constants only affect the initial choice probabilities, but not their subsequent changes. 25 Similarly with the housing market; different types of housing markets associated with different types of residential location choices can also be established.

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CES model of Aggregate demand (at residential location)

Housing demand

DC model of dwelling type choices

DC model of residential location choices

Travel demand

Demand for Cars

DC model of departure time & mode choices

DC model of fleet size choices

DC model of work location choices

Housing market (prices)

Housing supply

Demand for Other goods

DC model of automobile technology choices

DC model of employment (work practices) choices

Automobile market Labour market (wages)

Industry production activities Notes:

Income (at work location)

Automobile supply

DC model; aggregate quantities; aggregate CD model; supply activities; market equilibrium. links (e.g., quantities) from continuous demand (CD) modules, links (e.g., prices) from discrete choice (DC) modules. links (e.g., via logsums) between discrete choice modules. general equilibrium links.

Fig. 3. Schematic representation of links from discrete choice (DC) modules to continuous demand (CD) modules within a general equilibrium (GE) framework.

between many activities in a local economy such as described in Fig. 1. In this case, activities such as dwelling type choices and travel mode choices can be linked to a continuous demand model of housing, travel, and other goods. Other activities such as residential and work place location choices can be linked, not only to a demand system but also to production activities (supply of employment opportunities in various locations). Fig. 3 is a schematic representation of all the possible linkages between DC models described in TRESIS (a Transport Environmental Strategy Impact Simulator (see Hensher, 2002; Hensher and Ton, 2002) and a CGE model (SGEM or Sydney General Equilibrium Model) describing the local economy of the Sydney Metropolitan Area (SMA).26 TRESIS and SGEM have been developed at the Institute of Transport and Logistics Studies (ITLS) in Sydney. Some of the DC models contained in TRESIS have been described in detail in Section 1 (see Fig. 1) but in addition, TRESIS also contains DC models of household automobile technology choice, fleet size choice, and employment (or work practices) choice. To link the choice behaviours of these DC models to the SMA economy, we need to extend the aggregate CD demand module within the SGEM model to include not only housing and travel activities (as done in the previous section), but also demand for automobiles and other goods. Secondly, we also need to specify a housing supply function which can be linked to the level of aggregate housing demand as specified by the DC model of housing type choice. The DC model of automobile technology choices can be linked to an automobile supply function.27 Finally, labour markets in various zones also need 26 27

For a description of the integrated TRESIS–SGEM model, see the Appendix. An alternative is to assume that supply is given exogeneously.

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to be linked to the work location choice of workers as described in the DC model of work location choice, and with the actual employment opportunities within each zone of the local economy (see Appendix). 5. An Illustrative experiment To illustrate the applicability of the approach described in this paper for linking DC models to CD model within a CGE framework, we consider a simple experiment. In this experiment, we investigate the impacts of a transport investment project in the Sydney Metropolitan Area (SMA) on transport users and on the local economy. The impacts on transport users are traditionally estimated within the TRESIS module using the various DC models which are shown in Fig. 1. TRESIS, however, only captures the ‘conventional’ impacts as considered in standard cost-benefit analysis, i.e., direct impacts on the users of the transport network, but not the indirect impacts on the wider economy which can be measured only if TRESIS is linked to a demand/supply system and imbedded within a CGE framework such as described in Fig. 3. In the experiment, we assume that the New South Wales (NSW) Government will spend money to upgrade a particular rail link in the SMA transport network. This is the so-called North-West Rail Link (NWRL) which is a 23-kilometer rail line between Epping and Rouse Hill. The project involves the construction of six new rail stations along this railway line, with approximately 3000 park and ride spaces and bus interchange facilities to provide rail access for commuters living in the growing North West region to major employment centres in Norwest Business Park, Macquarie Park, St Leonards, Chatswood, North Sydney and the CBD. It is suggested that by providing rail access through to Rouse Hill, the new line will also support future residential and commercial development in the North West growth centre. The rail link will serve a population of 360,000, which is expected to grow to 485,000 by 2021, and by 2036 the new rail link is expected to service a region with more than 145,000 jobs (see Hensher et al., in press for further details). The purpose of our illustrative experiment is to estimate what will be the economic impacts of the investment projects, not only on potential transport users of the network, but also on employment opportunities in the SMA.28 5.1. Conventional cost benefit analysis Using DC models, conventional cost benefit analysis (CBA) looks at the impacts of a transport investment project on users of the transport network. Assume that as a result of the investment projects, users of the transport network experience some welfare improvement in their activities associated with the transport projects (for example, an increase in comfort and convenience level while travelling, and/or a reduction in total travelling time) which can be quantified by a willingness to pay (WTP) measure. In a DC model of transport mode choice, for example, the WTP measure is captured by the value of the maximum (indirect) utility associated with each choice alternative which will change when the transport project is implemented. The expected value of the maximum utility associated with all choice alternatives is captured by the logsum value. Therefore, the change in the logsum value (from ‘before’ to ‘after’ the project) will indicate the extent to which the transport project impacts on all users of the transport neworks travelling in all modes. This change in logsum value can then be converted into dollar terms by dividing it by the marginal utility of money, and this is then referred to as the ‘compensating variation’ of the transport project (for mode choice activities only)29:

CV

ðtÞ

2 3 Z     X 14 X 1 ðtAÞ ðtBÞ 5 ¼ ln exp V j exp V j  ln ¼

a1

j2I

ðtÞ

j2I

ðtÞ

a1

tA

tB

d ln

X j2I

ðtÞ

Z   1 ðtÞ exp V j ¼

a1

tA

dV ðtÞ :

ð29Þ

tB

Here a1 is the estimated coefficient of the money cost attribute in the joint departure time and mode choice (DTMC) mode in TRESIS which is assumed to represent the marginal utility of money, the superscripts ‘A’ and ‘B’ in the utility functions are used to indicate the situation ‘After’ and ‘Before’ the projects are implemented, and the superscript ‘t’ refers to the travel (i.e. DTMC) model.30 Since joint departure time and mode choice is only a ‘short run’ decision which has the capacity to influence medium and long run decisions such as work place location and also residential locations, to measure the welfare change of transport investment, it is important to look also at other welfare changes associated with other medium run and long run decisions 28 We confine the analysis of the ‘wider economic impacts’ of the project to only employment opportunities because we want to illustrate the simple links between DC models (of transport mode choice, work and residential location choices) to economic activities in the local areas using the methodology presented in this paper for linking DC to CD models. The purpose of the exercise is not to conduct an exhaustive cost-benefit analysis of the transport projects, which is beyond the scope of the present paper. 29 The use of Eq. (38) as a measure of CV in a DC model is conditional on the assumption that there is no or negligible income effect (and is often referred to as Consumer Surplus). In a general equilibrium approach, the income effect is then taken into account via the measure of ‘wider economic impacts’ as will be considered in the next section. CV is a concept first introduced by Hicks (1939). It refers to the amount of money which must be taken away from the users in the ‘new state’ (i.e., after a project) to make him/her indifferent between the new and old (i.e. before the project) states. After the project, the ‘real income’ of the user is indicated by the logsum measured at the new attribute levels. This is normally greater than the ‘real income’ of the user at the old state (i.e., logsum value at the old attribute levels). Therefore, the difference (as indicated by the right hand side of Eq. (38)) must be a measure of the CV. Eq. (29) can also be seen to be related to Eq. (7), (14) and (17) where the (change in) the value of the logsum is related to (change in) the aggregate ‘price index’ of each DC model which represents the welfare change where only the price or substitution effect is dominant (i.e., when the income effect is negligible). 30 Eq. (29) is in fact is related to the change in logsum of DTMC which is shown in Eq. (A2) of the Appendix.

T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201

1187

Source: Vickerman (2011) Fig. 4. Net gains from transport improvement – monocentric city. (See for example Vickerman (2007).

such as those associated with work location and residential location choices31. An important question, therefore arises, and that is to what extent are these welfare changes interconnected, and whether there are any risks of underestimation or double counting of the overall benefits of a particular transport project if we focus attention only on one or some of the welfare changes and neglecting others. This question has long been a vexing issue in transport economic analysis and is now also widely discussed in the transport literature in recent years, under the heading of ‘wider economy impacts’ (WEIs) of transport projects.32 5.2. Wider economy impacts Conventional CBA of a transport project does not usually include many of the ‘wider economy impacts’ (WEIs) of a transport project on the rest of the local and national economies, partly because it often relies on a partial equilibrium33 approach which focuses attention mainly on the transport sector only. This does not necessarily mean that transport benefits do not include other benefits (such as those accruing to final consumption and production activities at origins and destinations) since transport is a ‘derived’ activity, and hence its benefits are also derived from (i.e., transferred to) other benefits.34 However, due to a combination of many factors (from market imperfections, to the limited or partial equilibrium nature of the framework of analysis) there may be underestimation (and in some cases, double counting) of the overall benefits if we look only at the benefits accruing to the transport sector activities and neglect the WEIs on other sectors of the economy. For example, Venables (2007) shows that following an improvement in the transport network, workers wage level in certain locations may rise (or fall) to take account of the so-called ‘agglomeration (dis-agglomeration)35 effects’, employment level and housing rent may also change. All this implies that the benefits (and costs) of a transport invetment projects will consist in this case of the impacts accruing, not only to transport activities, but also to employment and housing activities. Therefore, neglecting the latter impacts may render the conventional measurements of the transport benefits (which are confined to transport activities only) inaccurate. In this section we focus attention on two important aspects of the WEIs following from a transport network improvement project: (1) the general equilibrium effects, and (2) the ‘agglomeration (dis-agglomeration) effects’. The former concerns the issue of general economic efficiency (including spatial efficiency) of an economy which only a modelling and measurement methodology that can capture these general effects (rather than partial effects) such as the one proposed in this paper can 31

In addition, there are also welfare changes associated with other decisions such as on vehicle type choice and fleet size choice in TRESIS. The concept of ‘wider economy impacts’ has a long history tracing back to many earlier attempts by transport economists and engineers trying to identify not only the short term direct impacts of a transport project on a particular link in the transport network but also the overall long term impacts for the network as a whole (see for example, Dodgson, 1973; Jara-Díaz, 1986; Williams et al., 1991; Martinez and Araya (2000); Mohring, 1993). 33 The term ‘partial equilibrium’ is a relative term. For example, a model which looks at the impacts of a transport investment project on users of the transport network only is a partial equilibrium model, compared to one which includes the impacts on the surrounding housing market, labour markets. However, even here, the approach can still be considered as ‘partial’ if it neglects the important impacts of the transport infrastructure project on regional and international migration and trade, etc. 34 See for example Jara-Díaz (1986); Jara-Diaz (1989). 35 In general, impacts of a project can go two ways: positive (benefits, agglomeration) or negative (costs, dis-agglomeration, etc.) therefore, to avoid having to mention both of these impacts, we refer to only the positive aspect and let the negative impacts be implied. 32

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T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201

Old transport system

New transport system

A

w2

β

B w1

N1

N2

Fig. 5. Net gains from transport improvement – multi-zonal city.

quantify more fully and accurately.36 The latter concerns the issue of productivity improvement following a transport infrastructure investment project.37 Following from the improvement in a transport network, users of the network (assumed to be mainly workers in our study, which focuses attention only on journeys to work) can benefit in the form of improved departure time and mode choice decisions. These benefits are captured in the logsum of the DTMC model in conventional analysis as explained in the previous section. Some part of these benefits is ‘transferred’ or linked to the benefits of work location choice and residential location choice. TRESIS. Locational choice decisions will impact on the housing market, while work location choice can impact on employment activities in various locations. In the general equilibrium framework which is considered in our study, the ultimate benefits and costs of the tranport project therefore can be summarised in the benefits accruing to the housing and labour market. Using the framework of analysis of Venables (2007) as shown in Fig. 4, we can say that the WEIs of a transport project can consist of: (1) a, standing for the benefits accruing to existing employment activities, (2) b, being the benefits accruing to new employment activities, and (3) (d + b0 ) representing the benefits arising from improved labour productivity (agglomeration effects). Assuming that ‘conventional’ transport benefits analysis only focuses attention on a (which are the benefits accruing to mode choice activities and/or residential location choice activities only)38 it can then be said that our general equilibrium modelling framework extends this analysis to consider the measurement of b, b0 , and d in a multi-zonal spatial economy. If we assume for simplicity that transport improvement only leads to a redistribution39 of a given level of housing and emploment activities within a multi-zonal city (such as the Sydney Metropolitan Area) rather than altering this total level, then following a transport network improvement which allows some workers to change the place of employment to take advantage of a higher wage level in another zone, the net benefits/costs of this redistribution of employment activities will include the gains in total employment wage bill (representing increase in value added) in some zones (such as the one shown in Fig. 5) where employment has increased from N1 to N2 and therefore with a total net gain40 in workers wage bill of b. Summing up all the values of b’s. over all zones will give us the total ‘general equilibrium’ (GE) impacts of the transport improvement project. This GE impact can be considered as representing the improvement in spatial economic efficiency of the local economy arsing from the transport network improvement. In addition to this improvement in spatial

36 Because it will allow for feedback and forward linkage effects, and also avoid the problem of double counting, since it will focus only on the ultimate ‘final’ outcome, rather than on intermediate outcomes. 37 Although this issue is beyond the scope of our paper, it can still be considered here to illustrate the usefulness of our modelling framework to allow even for this wider issue to be considered in the model. 38 In the original Venables (2007) model there is only one location (city centre) to consider, hence locational choice benefits simply imply the benefit accruing either to the users of the transport network (in the form of the value of travel time savings) and/or the landlord (in the form of increased housing rent). The model does not show the break up of a into these two components because the model does not consider the issue of interactions between transport sector and housing market. Also, in conventional analysis, even if work location choice can be considered (e.g. in TRESIS in stand alone mode) the issue of labour market readjustment taking into account wage differentials between different locations (i.e. the value of b in Fig. 5) are not often explicitly considered. 39 The issue of growth in these activities can also be considered using our modeling framework, but for reasons of simplicity and clarity of analysis, we have simply chosen to ignore the question of growth. To consider growth would involve extending the analysis to include issues such as interregional and international trade and macroeconomic policies which is beyond the scope of our paper. 40 Conversely, some workers may have to switch employment to locations where the existing wage level is lower, in which case there will be a net loss to workers wage bill rather than a net gain. This may sound unrealistic, but workers may choose to suffer from a lower wage in return for lower transport and/or housing costs.

Eastern_Subs

Inner_Sydney

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong Average over all origins

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.04 0.00 0.00 0.00 0.01 n.a. n.a. 0.02 n.a. n.a. 0.07 0.03 n.a. n.a. 0.02

StGge_Suther

3

n.a: not applicable because there are no train trips along these routes.

0.04 0.00 0.00 0.00 n.a. 0.00 0.19 0.02 0.01 n.a. 0.07 0.03 n.a. n.a. 0.02

2

1

Name

No.

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 4.68 0.07 0.03 0.00 0.00 0.23

Destination zone no.

Origin zone

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 n.a. 2.21 0.07 0.03 n.a. n.a. 0.03

Canter_Banks

4

0.04 n.a. 0.00 0.00 0.01 0.00 0.19 0.02 n.a. 18.23 0.07 n.a. n.a. n.a. 0.70

Fairfd_Livrp

5

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 n.a. n.a. 0.07 n.a. n.a. n.a. 0.00

Outer_SW_Syd

6

0.04 0.00 n.a. 0.00 0.01 0.00 0.19 0.02 n.a. 15.24 0.07 0.03 0.00 0.00 0.83

Inner_W_Syd

7

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 18.75 0.07 0.03 n.a. n.a. 0.88

Centrl_W_Syd

8

0.04 0.00 n.a. n.a. n.a. n.a. n.a. 0.02 0.01 18.90 n.a. 0.03 n.a. n.a. 2.70

Outer_W_Syd

9

Table 1 Percentage change in the total number of work trips by TRAIN between Origin–Destination zones following the improvement in the rail link between zone 1 and zone 10.

4.82 n.a. n.a. 2.30 18.55 n.a. 15.85 19.62 19.69 13.09 5.72 9.43 n.a. n.a. 4.07

Blck_Baulk_H

10

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 n.a. 6.15 0.07 0.03 0.00 0.00 0.46

Lower_N_Syd

11

0.04 0.00 0.00 0.00 n.a. n.a. 0.19 0.02 0.01 9.36 0.07 0.03 n.a. 0.00 0.19

Horns_Kuring

12

0.04 n.a. n.a. n.a. n.a. n.a. 0.19 0.02 n.a. n.a. n.a. n.a. n.a. n.a. 0.00

Nth_Beaches

13

0.04 n.a. n.a. n.a. n.a. n.a. 0.19 n.a. n.a. n.a. 0.07 0.03 n.a. 0.00 0.02

Gosfrd_Wyong

14

0.32 0.00 0.00 0.01 0.53 0.00 0.52 0.29 1.10 5.59 0.40 0.13 0.00 0.00 0.52

Average over all destinations

T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201 1189

Eastern_Subs

Inner_Sydney

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong Average over all origins

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 0.08 0.07 0.03 0.00 n.a. 0.00

StGge_Suther

3

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 0.13 0.07 0.03 0.00 n.a. 0.02

Canter_Banks

4

n.a: not applicable because there are no CAR (Drive_alone) trips along these routes.

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 0.08 0.07 0.03 0.00 n.a. 0.00

2

1

Name

No.

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 3.90 0.07 0.03 0.00 0.00 0.11

Destination zone no.

Origin zone

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 1.74 0.07 n.a. 0.00 0.00 0.09

Fairfd_Livrp

5

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 0.08 0.07 n.a. n.a. n.a. 0.00

Outer_SW_Syd

6

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 4.73 0.07 0.03 0.00 0.00 0.25

Inner_W_Syd

7

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 1.22 0.07 0.03 0.00 0.00 0.18

Centrl_W_Syd

8

0.04 n.a. 0.00 0.00 0.01 0.00 0.19 0.02 0.01 1.07 0.07 0.03 0.00 0.00 0.18

Outer_W_Syd

9

3.78 0.00 0.00 0.05 1.44 0.00 4.09 0.36 0.30 0.29 3.44 0.52 0.00 0.00 0.34

Blck_Baulk_H

10

Table 2 Percentage change in the total number of work trips by CAR (Drive_alone) between Origin–Destination zones following the improvement in the rail link between zone 1 and zone 10.

0.04 0.00 0.00 0.00 0.01 0.00 0.19 0.02 0.01 3.01 0.07 0.03 0.00 0.00 0.16

Lower_N_Syd

11

0.04 0.00 0.00 0.00 n.a. n.a. 0.19 0.02 0.01 0.58 0.07 0.03 0.00 0.00 0.08

Horns_Kuring

12

0.04 0.00 0.00 0.00 0.01 n.a. 0.19 0.02 0.01 0.08 0.07 0.03 0.00 0.00 0.01

Nth_Beaches

13

0.04 n.a. n.a. n.a. 0.01 n.a. n.a. 0.02 0.01 n.a. 0.07 0.03 0.00 0.00 0.00

Gosfrd_Wyong

14

0.05 0.00 0.00 0.00 0.07 0.00 0.37 0.04 0.05 0.63 0.20 0.08 0.00 0.00 0.12

Average over all destinations

1190 T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1 Inner_Sydney

Name

No.

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 Eastern_Subs

Destination zone no.

Origin zone

0.06 0.03 0.02 0.16 0.19 0.09 0.52 0.64 0.07 0.14 0.04 0.12 0.06 0.18

3 StGge_Suther 0.55 0.38 0.44 0.37 0.56 0.43 1.19 0.02 0.45 0.60 0.44 0.40 0.46 0.44

4 Canter_Banks 0.56 0.47 0.85 0.92 0.46 0.77 0.22 1.25 0.76 0.91 0.77 0.88 0.79 0.74

5 Fairfd_Livrp 0.06 0.30 0.04 0.02 0.27 0.09 0.35 0.44 0.16 0.30 0.35 0.04 0.03 0.08

6 Outer_SW_Syd 1.87 1.73 2.16 2.25 2.08 2.16 0.93 2.81 2.34 3.10 2.06 2.15 2.12 2.23

7 Inner_W_Syd 1.51 1.41 1.56 1.46 1.69 1.55 2.02 1.02 1.56 1.66 1.48 1.54 1.62 1.62

8 Centrl_W_Syd 0.07 0.52 0.14 0.09 0.36 0.08 0.77 0.20 0.07 0.15 0.05 0.00 0.18 0.04

9 Outer_W_Syd 0.80 0.55 0.98 0.90 1.01 0.85 1.46 1.38 0.91 0.53 1.06 1.10 0.70 0.90

10 Blck_Baulk_H

Table 3 Percentage change in choice probability for a work place location (destination zone) given a residential location (origin zone) following the improvement in the rail link between zone 1 and zone 10.

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

11 Lower_N_Syd

0.23 0.13 0.10 0.11 0.27 0.11 1.08 0.49 0.16 0.28 0.25 0.08 0.12 0.09

12 Horns_Kuring

0.06 0.05 0.00 0.12 0.26 0.01 0.97 0.18 0.04 0.16 0.06 0.03 0.00 0.04

13 Nth_Beaches

0.25 0.01 0.04 0.03 0.16 0.06 0.18 0.66 0.03 0.30 0.56 0.03 0.08 0.01

14 Gosfrd_Wyong

T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201 1191

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Table 4 Changes in places of residence and places of work following from the improvement in the rail link between zone 1 and zone 10. Place of residence

Place of work

Zone no.

Work place

Before project

After project

Absolute change

Before project

After project

Absolute change

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong Total

134,084 94,872 14,6105 89,397 102,038 84,876 66,453 100,141 119,499 164,031 125,692 103,884 94,391 92,887 1,518,350

134083.9 94871.95 146,105 89397.31 102,037 84876.76 66452.5 100142.7 119498.8 164029.5 125,692 103884.1 94390.98 92887.02 1,518,350

0 0 0 0 1 1 1 2 0 1 0 0 0 0 0

387,740 62,106 86,702 72,075 83,642 52,089 56,965 143,849 80,119 116,909 175,129 61,777 65,415 73,833 1,518,350

387739.9 62105.94 86683.2 72429.73 83056.27 52141.35 55799.71 146106.8 80169.23 115906.7 175,129 61838.66 65419.58 73823.45 1,518,350

0 0 19 355 586 52 1165 2258 50 1002 0 62 5 10 0

efficiency, there may also be an improvement in economies of scale in some parts of the city which will result in improvements in labour productivity (and hence wages – assuming that (labour) productivities will flow onto wage improvement).41 This is the so-called agglomeration (AG) effects, which can be added to the GE impacts to arrive at the total WEIs. 5.3. Results First, we consider the transport and land use impacts of the NWRL Project as described by the various DC models belonging to the TRESIS part of the integrated model system. Tables 1 and 2 show the effect of the transport improvement in the rail link between zone 1 (Inner Sydney) and zone 10 (Blacktown Baulkham Hills) (see Fig. A1 for zone locations) resulting from the NWRL investment project on mode choice decisions of workers living, not only in these two zones, but also in all other zones. Quite clearly, the probability of a worker living in zone 10 choosing rail as the preferred mode of transport (to travel outside of zone 10) will increase following the improvement in this rail link, which allows them to go to and from, not only the inner city (zone 1) but also all other zones (see column and row 10 of Table 1). Network equilibrium analysis implies that workers living in zones other than zone 10 will also be affected (although to a lesser degree). For example a comparison of row 1 (Inner_Sydney) and row 11 (Lower_N_Syd) shows that workers from Inner Sydney are now more likely to use trains than those from Lower North Sydney (to go to zones other than zone 10). On average, however, the last column and row of Table 1 shows that there are increases in train trips to and from most zones, with a total net increase of 0.52% of all train trips for the network as a whole. Table 2 shows the percentage change in choice probability for the car (Drive_alone) mode of transport42 between different zones following the improvement in the rail link between zones 1 and 10. Quite clearly, trips by car (and other non-train) modes to and from zone 10 will decrease substantially, but interestingly, although car trips between zones 1 and zone 10 will decrease (by about 3.9%), car trips from zone 1 to other zones are not affected (the small increase of about 0.04% of car trips from zone 1 to other zones reflect the general increase in total number of work trips from this zone rather than due to substitution effects between modes – hence see also row 1 of Table 1). In general, there is an overall decrease of 0.12% in car trips to and from other zones as a result of the NWRL project.43 Work location choice decisions are affected by the transport network improvement, and this is shown in Table 3. Here it is interesting to observe that as a result of the transport improvement between zone 1 and zone 10, workers may now prefer to work in zones other than zones 1 and 10. In fact, zone 10 is now not preferred as a work place as compared to, say zone 8 (Central West Sydney) or zone 4 (Canterbury_Bankstown). Other zones (5, 7) also lose preference as a work place in addition to zone 10. This shows that the impacts of an investment in a particular link in a transport network may have the potential to flow onto other links. The residential location decision is also affected by the transport improvement but to a much smaller extent than the work location decision. This is shown in Table 4 where it can be seen that as a result of the NWRL Project, very few workers will change their place of residence, but many more are taking advantage of improved transport to change their place of work.44 41 Agglomeration effects will result in increases in existing wage level just as dis-agglomeration effects can result in a wage reduction. This is in addition to the existing wage gaps between different locations which may arise from accumulated historical agglomeration or due to other factors such as natural resource endowments associated with different locations. 42 Because of the symmetry in the MNL choice functional form, all other modes besides TRAIN will experience the same substitution effect (percentage change in choice probability) following the shock to train characteristics. Therefore, Table 2 will also represent other modes (except TRAIN). However, because of the different number of trips originally by these modes. The last row and column of Table 2 will be different for other modes implying the average changes will be different although the probabilistic changes are the same for different non-train modes. 43 And an overall decrease of 0.25 for bus trips to and from all zones as a result of the NWRL project. 44 This will also be reflected in the results for housing and labour market where the WEIs on the former is minimal whereas those impacts on the latter are more substantial (see below).

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T.P. Truong, D.A. Hensher / Transportation Research Part B 46 (2012) 1177–1201 Table 5 Fleet size choice for households living in different zones before and after the NWRL Project. Residential zone

Before project shares of fleet sizes

After project shares of fleet sizes

Absolute change in shares of fleet sizes

No.

Name

Single car

Multi-cars

Single car

Multi-car

Single car

Multi-car

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong

0.990 0.983 0.807 0.818 0.759 0.608 0.774 0.733 0.596 0.711 0.783 0.661 0.716 0.596

0.010 0.017 0.193 0.182 0.241 0.392 0.226 0.267 0.404 0.289 0.217 0.339 0.284 0.404

0.999 0.983 0.807 0.820 0.779 0.608 0.989 0.720 0.437 0.939 0.908 0.557 0.716 0.597

0.001 0.017 0.193 0.180 0.221 0.392 0.011 0.280 0.563 0.061 0.092 0.443 0.284 0.403

0.009 0 0 0.001 0.02 0 0.215 0.013 0.159 0.228 0.125 0.104 0 0.001

0.009 0 0 0.001 0.02 0 0.215 0.013 0.159 0.228 0.125 0.104 0 0.001

Table 6 Vehicle type choice before and after the NWRL Project. Residential zone

Before project shares of vehicle types

After project shares of vehicle types

Absolute change in shares of vehicle types

No.

Name

Small

Medium

Large

Small

Medium

Large

Small

Medium

Large

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Inner_Sydney Eastern_Subs StGge_Suther Canter_Banks Fairfd_Livrp Outer_SW_Syd Inner_W_Syd Centrl_W_Syd Outer_W_Syd Blck_Baulk_H Lower_N_Syd Horns_Kuring Nth_Beaches Gosfrd_Wyong

0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202 0.202

0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455 0.455

0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343 0.343

0.121 0.202 0.202 0.202 0.198 0.202 0.127 0.206 0.217 0.068 0.163 0.218 0.202 0.202

0.492 0.455 0.455 0.455 0.456 0.455 0.489 0.453 0.447 0.517 0.473 0.447 0.455 0.455

0.387 0.343 0.344 0.343 0.346 0.343 0.384 0.341 0.335 0.416 0.364 0.335 0.343 0.343

0.081 0 0 0 0.004 0 0.075 0.004 0.015 0.134 0.039 0.016 0 0

0.038 0 0 0 0.002 0 0.034 0.001 0.007 0.062 0.018 0.008 0 0

0.043 0 0 0 0.003 0 0.041 0.002 0.008 0.072 0.021 0.009 0 0

Table 5 shows the changes in fleet size for households living in different zones following the improvement in the rail link between zones 1 and 10 as a result of the NWRL project. It can be seen that households residing in zones 7, 10 and 11 will now prefer a single car fleet rather than multi-car fleet, while the opposite is true for households residing in zones 8, 9, and 12. This can partly be explained by the fact that following the improvement in public transport (rail link), people travelling to work and residing in zones 7, 10 and 11 (see last column of Table 1) will now tend to switch to train and therefore there is less need for the ownership of a second vehicle for travelling to and from work. This encourages a switch to a single-car fleet size.45 Consistent with this switch to single-car fleet size is a switch also to larger-sized car, as seen from Table 6, for people living in zones 1, 7, 10–11. Table 7 shows the values of various types of impacts (general equilibrium (GE) and agglomeration (AG) impacts) resulting from the NWRL project. To facilitate the identification and measurement of these separate impacts, we first define a ‘reference’ scenario where we assume that the impacts of the NWRL Project will be measured under the assumption that there are no linkages or feedback effects between DC decisions (mode choice, residential location and work location choices) and the general economy (housing and labour markets). The GE and AG impacts in this case will be zero because under the assumption that there are no linkage from DC decisions to the wider economy (and also assuming that there are no other macroeconomic impacts on the housing and labour markets)46 the net results is that there will be no change in employment and/or wage levels, hence no change in total income for commuters (workers) as a whole. Next, we defined a ‘general equilibrium’ (GE) scenario where we allow for linkage between residential location choices and housing market equilibrium as well as 45 TRESIS uses a dynamic heuristic to apportion behavioural response over a 5 year period, depending in the nature of the response. Some responses are almost instantaneous such as adjustments in kilometers, whereas others take time, with residential location possibly being the slowest to fully adjust. In TRESIS these annual adjustments can be chosen by the analyst or the defaults of 0.5 adopted. 0.5 indicates that half of the probability choice response is adjusted in a year and the residual is carried forward for an agreed number of years as 0.5 per annum of the balance of the probability response. See Hensher, 2002 for more details. 46 Such as arising from the supply side (i.e., resource utilisation to finance the Project). This assumption is for convenience only and is reasonable when the project is only a small undertaking compared to the overall economy.

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Table 7 Different components of the wider economic impacts (WEIs) of the NWRL transport improvement project. (in 2006 AUD$ million/per annum). Type of impacts

Description

GE

General equilibrium or spatial economic efficiency effects arising from transport system improvement and resulting in a net change in total wage income for all workers

AG

Agglomeration effects arising from changes in employment densities in various zones which lead to productivity improvement and hence wage level changes, and a resulting net change in total wage income for all workers (over and above the GE impacts).

WEIs

Sum of the above

Scenarios (*) GE20

GE20AG

GE20AG2

GE10AG

GE2AG

3.46

3.46

3.46

3.06

1.11

(92.3%) 0.29

(85.6%) 0.58

(91.3%) 0.29

(79.3%) 0.29

(7.7%) 3.75

(14.4%) 4.04

(8.7%) 3.35

(20.7%) 1.40

3.46

*

Notes: GE20: General equilibrium scenario, implying linkage between DC decisions and housing and labour markets. Wage elasticity of labour demand set equal to 20 GE10: General equilibrium scenario with wage elasticity of labour demand set equal to 10.0. GE2: General equilibrium scenario with wage elasticity of labour demand set equal to 2.0. AG: Agglomeration scenario, implying linkage between effective employment densities and wage level. Agglomeration elasticities set equal to the actual empirically estimated values for the SMA. AG2: Agglomeration scenario with agglomeration elasticities set equal to 2 times the actual estimated values for the SMA.

between work location decisions and labour markets in various zones. These linkages take the form of housing prices and wage levels in different zones now being endogenously determined by both DC decisions as well as aggregate supply–demand conditions in the wider economy. The results from this scenario can be referred to as ‘‘GE’’ impacts.47 Finally, we consider a third scenario (agglomeration (AG) scenario) where we assume a transport improvement and the resultant employment opportunities redistribution will affect effective employment densities in various zones which can then impact on labour productivity and the level of wages. This will produce an additional impact on the wage level and therefore on total income for all workers. The difference between the results for this scenario and the results for GE scenario can be assumed to come from the agglomeration effect. From Table 7, it can be seen that the GE impacts of the NWRL project (when wage elasticity of labour demand is assumed to be equal to 20, i.e., ‘‘GE20’’ scenario)48 can amount for a WEI of about 3.46 million per annum49 (see column 1 of Table 7). This can constitute nearly 92.4% of the total WEIs, leaving only about 7.6% to the agglomeration impacts if both the GE and AG impacts are assumed to be present for a particular scenario (see the combined GE20-AG scenario in column 2 of Table 7). The agglomeration effects, however, will be greater if the agglomeration elasticities are assumed to be higher, essentially the effect can vary almost linearly with the magnitude of the agglomeration elasticities (comparing columns 2 and 3 of Table 7). The GE impacts are naturally reduced if the magnitude of the wage elasticity of labour demand is assumed to be smaller, implying that firms have difficulties in adjusting labour demand to the level of labour supply and may have to resort to the clearing mechanism of real wage to achieve equilibrium in the labour market, rather than adjusting the level of output and/or moving the place of production. In the last column of Table 7, for example, we see that the GE impacts would be reduced to almost onethird of its original (column 2) value if in fact the wage elasticity of labour demand is equal (in magnitude) to only one tenth of the assumed value (i.e., 2 instead of 20). This shows the extreme sensitivity of the WEIs measurement with respect to some crucial parameters such as the wage elasticity of labour demand50 and this is a signal to policy makers that nothing can be taken for granted when planning a transport investment project, because the outcome can also depend critically on ‘complementary’ policies such as incentives for firms to relocate, in addition to incentives for workers to change their places of residence and employment. In summary, the lesson that can be learned from the experiment carried out in this study is that there can be no clear cut ‘rule of thumb’ when it comes to the determination of the magnitudes of the so-called WEIs (or their ‘mark-up’ over conventional measure of benefits) of a transport project.51 What is required instead is a clear methodology and modelling framework 47 Note that the equilibrium housing prices and wage levels determined in the wider economy now also feedback to the original DC decisions hence the DC outcomes for the reference scenario and the GE scenario may not necessarily be the same. 48 See Appendix for an explanation of why wage elasticity of labour demand assumed for a transport and urban policy context is different (and much larger) than wage elasticity assumed for national aggregate labour demand analysis. 49 All values are in 2006 Australian dollar. 50 This finding is consistent with the finding in Vickerman (2007), for example, where the labour market is mentioned as a crucial factor in determining the magnitude of WEIs. 51 This is consistent with conclusions from other studies in this area; see for example Oosterhaven and Elhorst (2003). To determine the ‘mark up’ of WEIs over the ‘conventional’ measure of the benefits, one must define what is a ‘conventional’ measure. In our case, if we use TRESIS in a stand-alone mode rather than combine it with SGEM, then the ‘conventional’ estimate of the benefits of the NWRL Project (based on an estimate of the change in logsum of residential location choices for all the different households in the sample data base for the SMA) amount to some $25.486 million in AUD$2006 per annum. When comparing this figure with the results from the GE20-AG scenario, this implies a ‘mark-up’ of WEIs over conventional benefits of some 14.7%. However, when using the results of other scenarios, this figure can range from a low value of 5.5% (based on GE2-AG scenario) to a high value of 15.9% (using scenario GE20AG2), Therefore, there is no hard and fast rule for describing the WEIs but only a recognition that it can vary greatly, depending on many assumptions particularly those relating to the labour market.

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which can be set up to estimate the WEIs for each specific geographical and economic situation and to take into account the nature of different policies which can affect certain important parameters which have been used in the analysis to estimate these WEIs. 6. Conclusion In this paper we have presented a methodology for linking a disaggregate discrete choice (DC) model to an aggregate continuous demand (CD) model, and integrated both types of models into a common framework of a computable general equilibrium (CGE) model. The methodology is important and useful because, from a theoretical viewpoint as well as in practice, both types of models are often designed and estimated to deal with different issues or in different areas of study. For example, a DC model is often designed to look at heterogeneous consumer preferences for a variety of products which are to be differentiated mainly by quality attributes rather than just simple market price, while the CD model is better suited to deal with the question of ‘representative’ consumer demand for aggregate commodities which can be ‘distinguished’ only through aggregate market prices. DC models are often used to deal with disaggregate or intra-sectoral decisions (such as decisions on mode choices in the transport sector, or land uses in the housing sector), whereas CD models are better suited to handle the issue of aggregate income and substitution effects in demand decisions for different groups of commodities in different sectors of an economy. Both types of models are therefore necessary and useful for the study of policy issues which require a detailed look at the individual behavioural responses (such as in the transport land use activities), while at the same time keeping track of the wider economy impacts of these decisions and feedback from the wider economy to individual decisions. Although in our experiments we illustrate the usefulness of the methodology mainly in the context of some transport issues (such as how to measure the wider economy impacts of a transport infrastructure investment project), and confine the analysis to this simple exercise, the methodology is potentially applicable to other issues such as how to link transport decisions and policies to the wider environmental objective of greenhouse gas emissions reduction and mitigation of climate change. Significant policy impacts are often evaluated mostly at the aggregate economy wide level, yet effective policy instruments are often designed only at the disaggregate individual consumer or producer level. Therefore, to be able to combine both a study of effective policy instruments with an investigation of practical policy impacts, it is important to be able to combine the use of both DC models and CD models (or bottom-up and top-down models) within a common framework, such as that of a computable general equilibrium model. Acknowledgement We thank two referees for very insightful comments that have materially improved the paper. Appendix A A.1. The structure of TRESIS-SGEM TRESIS-SGEM model – as the name suggests – consists of two parts: (1) the TRESIS module which is a series of nested discrete choice models specifying departure time and mode choice, work location choice, dwelling type choice and residential location choice behaviour for different types of workers-cum-commuters/consumers distinguished by occupations and industries (see Tables A2 and A3), vehicle type choice and fleet size choice,52 and (2) the SGEM module which is a spatial general equilibrium model describing some of the basic economic activities within the different geographical zones of the Sydney Metropolitan Areas (Table A1). The Sydney Metropolitan Area is divided into 14 different zones (see Fig. A1 and Table A1), each zone is characterised by the total number of dwellings of different types, population and employment of various occupations and in different industries. As well, there is journey to work information on commuters travelling from each particular zone to a specific work destination with income level, occupation and employment industry specified (the Australian Bureau of Statistics (ABS), 2006). When TRESIS is used on its own, many of the economic variables relating to these activities are assumed to be given ‘exogenously’ in the TRESIS module; for example, housing prices, total level of demand for housing and for travel activities, total employment. The DC models then simply ‘distribute’ these total level of economic activities among the various ‘alternatives’ such as departure time and mode choice (given total number of trips between any origin–destination pair), dwelling types choices (given total level of demand for housing in each residential location), work place location choices (given the total level of employment). When TRESIS is combined with SGEM in the integrated model, these total level variables are now endogenously estimated, with the aggregate price indices to be determined within the various DC models while the equilibrium quantities are to be determined within the SGEM module. 52 A full blown TRESIS will also include DC modules of work practice choice and vehicle kilometer driven (seeHensher, 2002; Hensher and Ton, 2002). However, in this version of TRESIS which is to be linked to a CGE model, these two modules are not necessary and can be replaced by other structures within the CGE model (such as the labour market and demand for aggregate transport).

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Table A1 Geographical zones in the Sydney Metropolitan Area with employment levels and journeys to work in 2006. Zone number

Short name

Long name

Employment number in 2006

Journeys to work (daily) in 2006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total

Inner Sydney Eastern Suburbs StGrge Sutherlnd Canter. Bankstwn Fairfld Liverpl Outer SW Syd. Inner W Syd. Central W Syd. Outer W Syd. Blcktwn Blk Hills Lower N Shore Hornsby Kuringai Northern Beaches Gosford Wyong SMA

Inner Sydney Eastern Suburbs St George Sutherland Canterbury Bankstown Fairfield Liverpool Outer South West Sydney Inner West Sydney Central West Sydney Outer West Sydney Blacktown Baulkham Hills Lower North Shore Hornsby Kuringai Northern Beaches Gosford Wyong Sydney Metropolitan Area

396,498 63,497 88,236 73,698 85,463 52,938 58,332 147,300 81,518 119,490 180,611 63,148 67,010 74,950 1,552,689

324,963 84,867 161,571 111,422 133,351 76,538 75,597 153,270 119,032 155,674 176,070 83,344 77,238 90,778 1,823,716

Source: TRESIS (Hensher, 2002; Hensher and Ton, 2002) and ABS (2006).

Table A2 Different labour occupations considered in TRESIS-SGEM. Occupation number

Short name

Long name

1 2 3 4 5 6 7 8 9

Managers Professionals TechTrades CommPersServ ClericlAdmin SalesWorkers MachOperDriv Labourers Others

Managers Professionals Technicians and trades workers Community and personal service workers Clerical and administrative workers Sales workers Machinery operators and drivers Labourers Others

Source: ABS (2006).

A.2. TRESIS module A.2.1. Theoretical structure First a departure time and mode choice (DTMC) model is constructed. Let a superscript ‘t’ denote travel mode choice, ‘w’ to denote work location choice, ‘r’ to denote residential location choice, and ‘d’ to denote housing or dwelling type choice. Each travel model choice decision (t) is assumed to be conditional (/) on a particular work-residence locations pair (wr). Therefore we can write: ðt=wrÞ

ðt=wrÞ

Vi

expðV i

Þ ; i 2 Iðt=wrÞ ; ðt=wrÞ expðV Þ j2I j X X ðtÞ ðt=wrÞ ðt=wrÞ ¼ aðtÞ þ bn Bin ; m Aim

ðt=wrÞ

Probi

¼P

ðt=wrÞ

m2M ðtÞ

dV ðt=wrÞ

ðA1Þ

n2N ðtÞ

  ðt=wrÞ        exp V i X X ðt=wrÞ ðt=wrÞ ðt=wrÞ   d ln exp V jðt=wrÞ ¼ d ln exp V j Probj dV j ¼ ¼ ; P ðt=wrÞ j2Iðt=wrÞ i2Iðt=wrÞ j2Iðt=wrÞ j2I exp V j X

ðt=wrÞ

ðA2Þ

where I(t/wr) is the set of departure time and mode choices, Aim are attribute variables of these choice alternatives (access, ðt=wrÞ egress, in-vehicle travel times, travel costs, toll charges, frequencies (of public transport modes), etc.), Aim are attribute ðtÞ variables of the commuters (socio-economic status, income variable, etc.), am and bðtÞ are empirical coefficients for these n variables.53 V ðt=wrÞ is referred to as the ‘logsum’ or ‘inclusive value’ (Ben Akiva and Lerman, 1979; McFadden, 2001; Hensher et al., 2005) of all the travel mode choice decisions (conditional on a particular work-residence locations pair). The logsum can be used to indicate the expected maximum utility (EMU) of all choices for a particular choice set and can be shown to 53

For full details of these variables and coefficients, their estimations and all related issues see Hensher, 2002; Hensher and Ton, 2002.

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Table A3 Industries in TRESIS-SGEM. Industry number

Short name

Long name

1 2 3 4 5 6 7 8 9 10

Agr_For_Fish Mining Manufacturing ElyGasWatWst Construction Wholes_Trade Retail_Trade Accom_Food TranPostWare InfoMediaTel

11 12 13

FinanceInsur RentHirRealE ProfSciTech

14 15 16 17 18 19 20

Admin_Supprt PubAd_Safety Edu_Training HlthC_SoAstn Arts_Recrtn OthServcs Others

A, ‘‘Agriculture, Forestry and Fishing’’ B, ‘‘Mining’’ C, ‘‘Manufacturing’’ D, ‘‘Electricity, Gas, Water and Waste Services’’ E, ‘‘Construction’’ F, ‘‘Wholesale Trade’’ G, ‘‘Retail Trade’’ H, ‘‘Accommodation and Food Services’’ I, ‘‘Transport, Postal and Warehousing’’ J, ‘‘Information Media and Telecommunications’’ K, ‘‘Financial and Insurance Services’’ L, ‘‘Rental, Hiring and Real Estate Services’’ M, ‘‘Professional, Scientific and Technical Services’’ N, ‘‘Administrative and Support Services’’ O, ‘‘Public Administration and Safety’’ P, ‘‘Education and Training’’ Q, ‘‘Health Care and Social Assistance’’ R, ‘‘Arts and Recreation Services’’ S, ‘‘Other Services’’ Inadequately described or not stated

Source: ABS (2006).

represent the total consumer surplus associated with these choices.54 The logsum for mode choice is then used as an explanatory variable in the work place location (WLC) choice to indicate the interrelationship between these decisions: ðw=rÞ Probi

  ðw=rÞ exp V i  ; ¼ X ðw=rÞ exp V j

i 2 Iðw=rÞ :

ðA3Þ

j2Iðw=rÞ ðw=rÞ

Vi

¼

X m2M ðwÞ

dV

w=rÞ

¼ d ln

X

amðwÞ Aðw=rÞ þ im

ðw=rÞ

bðwÞ n Bin

þ cðwÞðtÞ ; V ðt=wrÞ ;

n2NðwÞ

X

exp



ðw=rÞ Vi

i2Iðw=rÞ



  ðw=rÞ    i exp V i X h ðw=rÞ ðw=rÞ   d ln expðV ðw=rÞ Þ ¼ Probi ¼ dV i : X i ðw=rÞ exp V j i2Iðw=rÞ i2Iðw=rÞ X

ðA4Þ

j2I

Note that the decision on work location is conditional on a given residential location choice. Finally, the residential location choice is assumed to depend not only on work place location (w) but also on dwelling type choice (‘d’). The decision on dwelling type choice is given by: ðdÞ Probi

  ðdÞ exp V i  ; ¼X ðdÞ exp V j

i 2 IðdÞ ;

ðA5Þ

j2IðdÞ ðdÞ

Vi

¼

X m2M

ðdÞ aðdÞ im Aim þ

ðdÞ

dV ðdÞ ¼ d ln

X n2N

X i2IðdÞ



ðdÞ

exp V i

ðdÞ ðdÞ

bin Bin ;

ðdÞ



  3 ðdÞ    i exp V i Xh ðdÞ ðdÞ 4   d ln exp V iðdÞ 5 ¼ Probi dV i ; ¼ P ðdÞ i2IðdÞ n2N ðdÞ j2I exp V j X

2

ðA6Þ

54 See, for example, Ben Akiva and Lerman, 1979. Note that for reason of brevity, we refer to ‘the logsum’ i.e. V ðt=wrÞ in the text, but in mathematical expressions, it is more convenient to express this concept in terms of its differential i.e. dV ðt=wrÞ rather than in its absolute level form. The reason is partly because in a multinomial discrete choice model, the logsum (and the indirect utility functions which are used to define it) is identified only up to an arbitrary constant, therefore, taking the differential will eliminate this arbitrary constant.

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Fig. 6. A1 TRESIS-SGEM zones for the SMA.

and the decision on residential location choice is defined to be dependent on both the logsum of dwelling type choice V ðdÞ and the logsum of work location choice V ðw=rÞ : ðrÞ

expðV i Þ ðrÞ ; Probi ¼ X ðrÞ expðV j Þ

i 2 IðrÞ ;

ðA7Þ

j2IðrÞ

ðrÞ

Vi ¼

X

ðrÞ aðrÞ im Aim þ

m2M ðrÞ

dV ðd=rÞ ¼ d ln

X

ðrÞ ðrÞ

ðr=dÞ

bin Bin þ ci

n2N ðrÞ ðd=rÞ

expðV j

j2Iðd=rÞ

dV ðw=rÞ ¼ d ln

X

X

Xh

Þ¼

dV

¼ d ln

X j2IðrÞ

ðd=rÞ

Probj

V ðw=rÞ

 i ðd=rÞ d Vj

j2Iðd=rÞ

   i Xh ðw=rÞ ðw=rÞ ðw=rÞ exp V j Probj d V j ¼

j2Iðw=rÞ

ðrÞ

ðr=wÞ

V ðd=rÞ þ ci

ðA8Þ

j2Iðd=rÞ

  Xh  i ðrÞ ðrÞ ðrÞ exp V j Probj d V j ¼ : j2IðrÞ

A.2.2. Calibration and estimation of changes in choice behaviour Consider, for example, the choice behaviour in the DTMC model. First, the initial choice probabilities can be ‘calibrated’ (see Section 3.4 in the text) to fit with the initial number of work trips between any origin–destination (O–D) zonal pairs (r–w) using the Australian Bureau of Statistics (ABS) journey to work data (ABS, 2006). The change in choice probabilities are then estimated using Eq. (A1): taking the differential logarithm of both sides of Eq. (A1) gives:

  2 3 ðt=wrÞ   exp V i ðt=wrÞ  5 ¼ dV iðt=wrÞ  dV ðt=wrÞ : d ln Probi ¼ d ln 4P ðt=wrÞ V ðt=wrÞ exp j2I j

ðA9Þ

The left hand side of Eq. (A9) gives the ‘percentage change’ in choice probabilities. The first term on the right hand side is the change in indirect utility caused by the changes in the levels of attributes (see Eq. (A1) (following from the implementation

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of a particular policy). The second term on the right hand side is the change in the logsum, which results from the changes in indirect utilities of all choice alternatives (Eq. (A2)). Similar calibration and estimation procedures apply to other choice models such as dwelling type (DwT) choice, work location choice (WLC) and residential location choice (RLC) choice models. By firstly matching the initial choice probabilities with aggregate share data in the initial data base, and then taking the differential logarithm of Eqs. A3, A5, A7 we obtain the changes in these choice probabilities in a form similar to Eq. (A9). A.3. SGEM module The SGEM module consists mainly of an aggregate continuous demand (CD) model describing the aggregate quantities of demand for various commodities referred to by the discrete choice models, such as aggregate demand for housing, for travel activities, and for other goods:

  r½p ðcÞ  p ; xðcÞ ¼ y

c ¼ ft; d; og:

ðA10Þ

Here  xðcÞ stands for (the percentage change in aggregate demand for)55 commodity (c) where c = t (travel), d (housing, and o ðcÞ is the corresponding percentage change in aggregate price, p  is the share weighted average of all p ðcÞ ; y  stands (other goods); p for the percentage change in income or after tax wage level, and r is a CES substitution elasticity. For travel activity, xðtÞ is related to departure time and mode choice (DTMC) decisions via equation such as (27), (28) as described in the text, and similarly ðcÞ are inferred from the values of the indirect utilities of the DC models as described by Eqs. (13) and (16) for housing activities; p in the text. On the supply side, housing supply in SGEM is represented by a constant elasticity of supply function:

di ¼ d þ edi pdi ;

i 2 IðdÞ :

ðA11Þ pdi

Here di stands for the percentage change in the supply of dwellings of type i, stands for the percentage change in the price of dwellings of type i, d is a constant which can be used to simulate any exogenous shocks, and edi is the elasticity of dwelling supply.56 Equilibrium condition in the dwelling market requires:

di ¼ xdi ;

i 2 IðdÞ ;

ðA12Þ

and this will allow housing prices to be endogenised in the model. Similar assumptions can be made for the labour market although this will be more complex than the housing market. Traditional neoclassical analysis of the aggregate labour market starts with some theories about labour supply (work-leisure choice) and labour demand (marginal productivity theory of labour), assuming that real wage can act as a market clearing mechanism. In our disaggregate approach, we can use a DC model of work location decision to describe the distribution of a given volume of labour supply57 to various locations following from a transport system improvement. The DC model of work location choice therefore can act as a ‘conditional’ labour supply model (‘conditional’ on a given level of total employment for the SMA as a whole) which then acts to distribute this total level of aggregate supply to various zones. Demand for labour (by firms) in different zones is then assumed to match with this labour supply via two mechanisms. Firstly, firms can vary the level of employment by substituting labour for other factors of production such as capital. This implies a movement along a labour demand curve (which is downward sloping with respect to the wage rate due to decreasing marginal productivity of labour when labour is expanded while capital is held fixed). Secondly, firms can also vary employment by changing the scale of production58 which implies a shift in the firm’s demand curve for labour. A combination of the above two actions by various firms will produce an aggregate outcome for labour demand curve which is either highly elastic with respect to the level of wage rate (if the second mechanism dominates) or highly inelastic (if the first mechanism dominates). It can be said that when comparing labour demand in a transport and urban policy context with labour demand in a macroeconomic context, we can assume that the latter mechanism dominates. This implies labour demand can be assumed to be highly flexible and elastic with respect to 55 See also Eq. (20) in the main text. Note the convention that a lower case letter is used to denote percentage change and a bar on top of a letter is used to denote aggregate level of demand, or average price, hence from here on we will drop reference to these terms wherever this can be implied. Eq. (A3) is an extension of Eq. (20) where we include ‘other goods’. This goods can also be disaggregated or extended into various types of commodities (such as demand for automobiles) if a DC model (for vehicle type choice for example) specifically requires reference to such an aggregate commodity. 56 Taken from Gitelman and Otto (2010) which is a recent study on the supply of housing for the various local government areas of Sydney. 57 The determination of this ‘given’ total volume of labour supply (as well as total volume of labour demand) is to be determined by aggregate macroeconomic factors such as international trade, migration, investment, and technological change. Transport and urban planning policies are often concerned mainly with a ‘redistribution’ of this total volume to various locations, although they may have a (small) linkage effect with the aggregate level of GDP growth and aggregate labour supply and demand conditions. 58 Firms can change the scale of production also by shifting production activities between different locations. Oosterhaven and Elhorst (2003) for example, also consider the response of firms’ demand for labour following an improvement in the transport system in terms of shifts in the demand curve rather than movements along the curve. Assuming that different areas can be characterised either as labour surplus or labour deficit, shifts in the labour demand curve can cause either an increase in the quantity of labour employed without any change in the level of wage rate (as in the area of labour surplus) or conversely, a change in the level of wage rate without any change in the level of labour demand (because labour supply is fixed in labour deficit area). Our analysis is consistent with the analysis given in Oosterhaven and Elhorst, although we assume labour supply can vary (following work location decision changes) rather than remaining fixed, and hence demand can simply shift to ‘accommodate’ for these supply changes without significant change in wage level – in contrast to a conventional labour market analysis in a macroeconomic context.

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the level of wage rate than is the case of national labour demand.59 As a result, for our study, we assume that the wage elasticity of labour demand (following from the changes in labour supply caused by changes in work location choices) is much higher than that often assumed for the case of macroeconomic analysis.60 A.3.1. Agglomeration effects Despite our assumption that labour demand in a spatial redistribution context is fairly elastic, implying that (initial) wage levels do not need to change significantly to allow for labour demand to adjust to labour supply to accommodate work location changes, the wage levels in SGEM, however, can still be impacted upon, but this time by a different factor, and that is, the so-called agglomeration effect (Venables, 2007). To define and measure this effect, first, we introduce the concept of effective employment density (see Graham, 2007a; Mare and Graham, 2009):

s–z X Eiz Eis ; U iz ¼ pffiffiffiffiffiffiffiffiffiffiffi a þ ðdzs Þa ð Az =pÞ s

i ¼ 1; . . . ; I;

z; s ¼ 1; . . . ; Z:

ðA13Þ

Here, Uiz is a measure of employment density for industry i in zone z, Eiz is the level of employment in industry i in zone z, dzs pffiffiffiffiffiffiffiffiffiffi is the distance between zone z and zone s, Az is the land area of zone z, so that Ai =p is an estimate of the average distance between jobs within zone z, a is a ‘distance decay’ parameter which can be empirically estimated, but often assumed to be =1 (see Graham, 2007a; Mare and Graham, 2009). Assuming that increases in employment density (agglomeration) can generate economies of scale in production activities which are external to firms but internal to a particular location (see Graham (2007b)). These economies of scale arise from the increased size of the market (for intermediate inputs, labour inputs, as well as knowledge and other resources) which will allow for further specialisation and hence improvement in output and labour productivity for existing as well as new activities. To quantify these improvements, we use a measure called agglomeration elasticity, which is the percentage change in (labour or output) productivity following from a one percentage change in effective employment density. Empirically, this elasticity can be estimated from a statistical relationship of the following form:61

lnðW izo Þ ¼ bi þ ci lnðU izo Þ z ¼ 1; . . . ; Z;

o ¼ 1; . . . ; O:

ðA14Þ

where (Wizo) is the wage level for workers of occupation o in industry i located in zone z, and (Uizo) is the employment density for this particular occupation o in industry i and zone z, bi is an industry specific constant term, and ci is a measure of the agglomeration elasticity. Following from an improvement in the transport system and with redistribution of employment opportunities around the SMA, effective employment densities in various zones can change, and therefore, if we assume that agglomeration effects exist, then labour productivity and hence wages62 (for different occupations and industries) in various locations will also change,63 which then lead to changes in the income level of workers (after taking account of income tax):

izo lnðW izo ½1  sÞ ¼ y

z ¼ 1; . . . ; Z;

o ¼ 1; . . . ; O:

ðA15Þ

izo is the (percentage change in) the income level of worker of occupation o in industry i Here (s) is the income tax rate, and y and zone z. Any change in after-tax income level as described by Eq. (A15) then has a potential to affect the levels of demand for housing and transport activities as described by Eq. (A10). References Anderson, S., De Palma, A., Thisse, F., 1988a. The CES and the logit – two related models of heterogeneity. Regional Science and Urban Economics 18 (1), 155–164. Anderson, S., De Palma, A., Thisse, F., 1988b. A representative consumer theory of the logit model. International Economic Review 29 (3), 461–466. Anderson, S., De Palma, A., Thisse, F., 1989. Demand for differentiated products, discrete choice models, and the characteristics approach. Review of Economics Studies 56 (1), 21–35. 59 After all, if one of the main objective of urban planning and transport improvement is to effect a redistribution of residential and employment opportunities to increase the spatial economic efficiency of an urban economy, then allowing a highly inelastic labour demand curve to exist (because firms are constrained by physical as well as institutional constraints to move production to where there are plenty of labour supply) will render this objective ineffective. 60 Wage-elasticity of labour demand in a macroeconomic context is often estimated to range from a low value of 0.5 in the short run to a maximum value (in terms of magnitude) of 2.0 in the long run (see, for example, Lewis and MacDonald (2002); Mowbray et al.(2008)). In our simulation experiment, we assume that wage elasticity of labour demand is 20 for the ‘reference’ case, but we also carry out sensitivity tests for the case when this elasticity is assumed to take on smaller values of 10, or even 2. Note that in other studies on labour market and transport or migration policies (see Oosterhaven and Elhorst (2003) for example) labour demand curve is often assumed to shift in response to changes in these policies, with no change in wage level (which is assumed to be determined nationally). This implies infinite wage elasticities. 61 The discussion of the appropriateness of this empirical form as well as other empirical issues in the measurement of the agglomeration elasticities for the SMA is fully documented in Hensher et al. (2012). Here we are only making use of these estimated parameters to implement the concept of agglomeration effects in our SGEM model and use this in our simulation exercises. 62 i.e., assuming that wage level will follow productivity level. 63 In a CGE context, it does not matter if we assume changes in employment densities (in various locations) follow from or are caused by changes in the levels of productivity and wages in these locations, because they are in fact interrelated. For example, initial differences in the levels of wages in different locations may have been caused by the initial differences in productivity levels between these areas. However, following from improvement in the transport system, workers may begin to change work locations not only to take advantage of the existing wage differentials, but in so doing can also contribute to further agglomeration and productivity improvement. Hence the distinction between ‘cause’ and ‘effect’ can become blurred due to interrelationships and feedback effects.

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