Abstract
Based on a timeuse model with a sound theoretical basis and carefully collected data for Austria, the value of leisure (VoL) for different population segments has been estimated. Through the combination of these results with modespecific values of travel time savings from a related study based on the same data, the first modespecific values of time assigned to travel (VTAT) were calculated. Data was collected using a MobilityActivityExpenditure Diary, a novel survey format which gathers all activities, expenditures, and travel decisions from the same individuals for 1 week in a diarybased format. The average VoL is 8.17 €/h, which is below the mean wage of 12.14 €/h, indicating that the value of work is, on average, negative. Regarding the reliability of the VoL, we show its sensitivity to the variance of working time in a sample, something that has been ignored in previous studies and could be used to avoid inadequate segmentation. We controlled this effect in the analysis of the heterogeneity of the VoL across the population by estimating the parameters from the total (unsegmented) dataset with single interaction terms. We find that the VTAT is strictly negative for walking, predominantly negative for cycling and car, and predominantly positive for public transport with 0.27 €/h on average. The positive VTAT for public transport is a strong indication for the importance of travel conditions, in turn suggesting that improvements in travel conditions of public transport might be as important as investing in shorter travel times.
Introduction
JaraDíaz and Guevara (2003) highlighted that a person who makes a travel decision not only maximizes her utility in this particular choice, but also in the surrounding timeexpenditure space. In order to combine both components, they developed a theoretical timeuse framework model which can be applied to obtain values for different aspects of time use. A key output is the value of leisure (VoL) which represents the value of the marginal utility of all activities that are assigned more time than the minimum necessary. Following DeSerpa (1973), the authors show that estimating the VoL permits a deeper examination of the value of travel time savings (VTTS) obtained from travel choice models because the VTTS equals the VoL minus the value of time assigned to travel (VTAT). The intuition behind this is that the VTTS summarizes the value of the liberated time (opportunity cost of travel), while the VTAT represents the ‘loss’ when travel time is reduced—which is why it relates to travel conditions. The VoL is, therefore, a key piece of information for the integration of travel decisions into the framework of consumer home production. Furthermore, the VTAT is also important because it represents the direct utility (or disutility) derived from the time spent in the travel activity. The VTAT may differ between modes and according to specific conditions of travel such as comfort, reliability, crowding, or the possibility to use the invehicle time productively. There is some indication that the increasing availability of mobile devices enables public transport passengers to use the invehicle time more productively, which may yield a higher value of time assigned to public transport (e.g. Litman 2008). In particular, train travel time can be used for many activities (Lyons et al. 2013). Flügel (2014) provided a summary of why public transport travellers may perceive travel as more relaxed than car travellers.
The VTTS is usually obtained from (conditional) indirect utilities estimated using discrete choice models; it represents the total marginal willingnesstopay for a reduction of travel time in the context of travel choices.^{Footnote 1} The VTTS has high practical relevance in transport planning because savings in travel time account for the biggest share of user benefits in most cost–benefit analyses (e.g. JaraDíaz 1990; Wardman and Lyons 2016; Hensher and Wang 2016). Mode choice models are able to estimate the VTTS by travel mode.
Obtaining the VTAT is more difficult: to be computed it requires the VoL and the VTTS. Estimating the VoL requires in turn a large amount of information from each individual, most importantly time assignment patterns, the allocation of expenditures to various commodities, and travel decisions over a period of sufficient length to be considered as the longterm equilibrium of the individual (JaraDíaz and RosalesSalas 2015, 2017). As a consequence, only a few attempts have been made so far to estimate the VoL with the aforementioned model framework. Table 1 lists the results obtained with the original model formulation presented by JaraDíaz and Guevara (2003) and later expanded by JaraDíaz et al. (2008). They reveal a huge variability of VoL estimates ranging from 0.12 to 123 €/h, and the ratio VoL/w ranges between 0.04 and 6.83. Note, however, that the results from JaraDíaz and Guevara (2003) were obtained with a limited preliminary version of the model. Also, the results from the Netherlands reported by JaraDíaz et al. (2016) are rather implausible; this is discussed at the end of “Data preparation” section. If these studies are not considered, the ratio VoL/w moves only from 0.57 to 2.48. Nonetheless, only a small part of this range can be explained by sociodemographic characteristics or structural factors such as survey year or the economic level of the country. Most VoL estimates follow the order of each country’s wellbeing from the World Values Survey (Frey and Stutzer 2002), but the differences are too large to result from this factor alone. The main part of variability remains unexplained; this raises the question how to estimate the VoL to reflect the time and cost preferences of in a reliable manner.
A possible source of unsystematic fluctuations are deficits and gaps in the data. One of the Chilean samples includes a specific population segment (longdistance commuters to downtown Santiago) who completed a 3day activity diary—expenditures were not reported (JaraDíaz et al. 2004; Munizaga et al. 2008). Other Chilean data bases were constructed from origin–destination surveys (JaraDíaz and Guevara 2003; JaraDíaz et al. 2013).
The German and Swiss data are based on a 6week travel diary—expenditures were not reported and nontravel activities were inferred from the trip purposes (for Germany: Axhausen et al. 2002; for Switzerland: Löchl et al. 2005). The Dutch results (JaraDíaz et al. 2016) are based on the LISS panel (Longitudinal Internet Studies for the Social Sciences), which is a retrospective survey of average activity durations and expenditures; trip details such as travel modes are not reported. Finally, the U.S. results are based on a synthetic dataset obtained from a probabilistic merge of participants of a timeuse survey and a consumer expenditure survey (Konduri et al. 2011). The dataset has been used to estimate various timeuse and expenditure models including the multiple discrete–continuous extreme value model (MDCEV, see Castro et al. 2012). Both timeuse and expenditure information is assuredly of high quality, but the probabilistic merge is questionable given that the aim of such models is to estimate tradeoffs between timeuse and expenditures at the individual level. This calls for a simultaneous survey of both components. To our best knowledge, no dataset exists so far with information on time assignment (including travel details) and expenditures, which has been collected from the same individuals at the same time in a diarybased format.
The unavailability of appropriate data to estimate all values of time (leisure, work, VTTS, VTAT) is the starting point of the current study. We are contributing to this aspect of research by using a novel comprehensive dataset for model estimation, which was obtained from a MobilityActivityExpenditure Diary (MAED). This dataset includes information on activity assignment, expenditure allocation, and travel decisions over 1 week (considered as the whole workleisure cycle) in a diarybased survey format, which has been proven reliable and valid in timeuse surveys, consumer expenditure surveys, and travel surveys. Using these data, many objectives can be achieved:

(i)
Estimation of the VoL for different population segments with three alternative approaches:

(1)
A priori segmentation: subdivide the dataset into segments and estimate separate models for each one;

(2)
Expost segmentation: estimate a global model and calculate the VoL from segmented result datasets;

(3)
Expost segmentation with interaction terms: like (i2) but with moderator variables and interaction terms.
Previous research has used a priori segmentation which estimates all parameters groupspecific, for example, the results of JaraDíaz and Astroza (2013) and JaraDíaz et al. (2013) included in Table 1. Expost segmentation is more efficient, as it does not require dividing the sample into small groups. It would be a methodological advance if expost segmentation (without or with interaction terms) proves to be suitable.

(1)

(ii)
Estimation of the value of time assigned to travel (VTAT) with two innovations: (ii1) modespecific estimation, which yields a separate VTAT for each travel mode, and (ii2) estimation based on the complete model framework introduced by JaraDíaz and Guevara (2003), including travel choices, activity assignment, and (for the first time) expenditure allocation. The VTAT requires the VoL and the VTTS to be calculated.^{Footnote 2}
Model
Our model is based on the formulation created by JaraDíaz et al. (2008). We used this model as a benchmark because it has been applied to four countries (Chile, Germany, Switzerland, USA) as well as to many segments within two of those countries (Chile and USA). This allows our estimations to have a basis for comparison (see Table 1). Note that the MAED data that are used in this paper do not provide a onetoone mapping between activities and goods, and accounting for these relations would require assumptions which are not needed in the basic 2008 model.^{Footnote 3} Here we explicitly recognize that activities have a cost through the market goods bought but we do not attempt to find the proportions by which expenses are allocated to individual activities.
Our utility function U is shown in Eq. (1). It is the loglinear version of a Cobb–Douglas function including three terms which relate to the utility gained from time assigned to work, time assigned to leisure, and expenses assigned to freely consumed goods. The logarithms enforce diminishing marginal utility as the consumption level of a particular alternative increases (i.e., satiation). This assumption yields a multiple discreteness model—that is, the choice of multiple alternatives can occur simultaneously (see Bhat 2005, 2008).^{Footnote 4}
The utilitygenerating resources (time T and expenses E) are subject to the following constraints:
\( \theta_{w} \) is the baseline utility of assigning time to work; T_{w} the amount of time assigned to work; \( \theta_{i} \) and T_{i} the baseline utility and amount of time assigned to activity i; \( \varphi_{j} \) and E_{j} the baseline utility and amount of expenses assigned to good j; \( \tau \) the total time constraint; w the wage rate; I fixed income from other sources but work; μ and λ are Lagrange multipliers representing the marginal utility of increasing available time and increasing available income; κ_{i} the Lagrange multiplier representing the marginal utility of reducing the minimum time constraint of restricted activity i ϵ A^{r}; and η_{i} the Lagrange multiplier representing the marginal utility of reducing the minimum expenditure constraint of restricted good j ϵ G^{r}. Committed activities and goods are those which are necessary for personal and household maintenance such as travel, cleaning the house, rental cost, etc. They are limited at the bottom by technical constraints (i.e., people would like to assign less time and money but cannot because of the technical constraints). The amount of time and expenses assigned to these activities and goods is given externally. It is inferred from the observations and included in the equations as T_{C} and E_{c} (see below).
Furthermore, we assume that each individual assigns nonzero amounts of time and money to each unconstrained activity and consumed good because the logarithms in Eq. (1) do not allow zeros. This is reasonable as we are dealing with an aggregated view of activities and expenses assigned to a workleisure cycle (only one category of work, leisure, and expenses during a whole week), which prevents the presence of zero assignments.^{Footnote 5} The original form of the JaraDíaz et al. (2008) model was stated in terms of goods consumption X_{j}, which is represented here by expenses assigned to goods in monetary terms \( E_{j} = P_{j} X_{j} \), where P_{j} is the unit price of good j. This will be shown to be equivalent to the original model in Eq. (15) below.
Following JaraDíaz et al. (2008), we obtain the first order conditions to find the optimal allocation of activities and expenditures. They yield a solution for T_{w}, T_{i}, and E_{j}, which can be used to calculate \( \mu \) and \( \lambda \), and consequently the VoL and VTAT. The first order conditions are:
where A^{f} and G^{f} denote the set of freely chosen activities and freely consumed goods, respectively. Equation (8) is derived from the budget constraint in Eq. (3) which is always binding when maximizing U, such that \( \lambda \) is always positive.
Calculate \( \mu \) and \( \lambda \) from first order conditions:
The parameters Θ and Φ correspond to the sum of individual time coefficients \( \theta_{i} (\varTheta = \sum\nolimits_{{i \in A^{f} }} {\theta_{i} } ) \) and individual expenditure coefficients \( \varphi_{j} (\varPhi = \sum\nolimits_{{i \in G^{f} }} {\varphi_{j} } ) \).
Rewrite (6) to (11) and insert (9) and (10) into (11):
Solve the quadratic Equation in (10) to obtain the optimal working time \( T_{w}^{*} \):
Insert (9) into (7) with \( T_{w}^{*} \) to obtain \( T_{i}^{*} \):
Insert (10) into (8) with \( T_{w}^{*} \) to obtain \( E_{j}^{*} \)^{Footnote 6}:
Please note that there is a difference between our equation system and the one proposed by JaraDíaz et al. (2008). They normalised their parameters to \( 2(\varTheta + \varPhi + \theta_{w} ) \). This yields a simplified equations system (20)–(22), which was used to estimate normalised parameters \( \alpha \) and \( \beta \). We normalised our parameters by setting Θ to one. This enables us to estimate the original parameters directly from Eqs. (13) to (15).^{Footnote 7} The VoL and VTAW are then obtained from the estimated parameters by inserting (9) and (10) into (6):
Data
A relevant new aspect of the paper at hand is the estimation of timeuse models from a dataset in which activities and expenditures are obtained simultaneously from the same individuals in a diarybased survey. The underlying dataset is discussed in detail in papers by Aschauer et al. (2018, 2019). The sample provides information about all activities, expenditures, and travel decisions over a period of 1 week. It is based on a novel survey design, the MobilityActivityExpenditure Diary (MAED), and a survey conducted in spring and autumn 2015. It is a selfadministered mailback survey with a 1week reporting period, including questions concerning trips, activities, and expenditures for each diary day. The trip section resembles the traditional household travel survey format based on the New KONTIV design^{Footnote 8} (Brög et al. 2009; Socialdata 2009), but the trip purpose section is more comprehensive. It resembles a timeuse diary but with predefined activity types instead of open text fields. Each activity type is reported in a separate row along with the start time, end time, and possible expenditures, which are specified by means of their amount and type. The classification of expenses follows the UN standard Classification of Individual Consumption According to Purpose (COICOP; see UN 2018).
Sampling
The sample was based on a random selection of Austrian households for 18 predefined strata defined by region and level of urbanisation as shown in Fig. 1. Only employed persons were selected for participation because a wage rate is required for model estimation. The survey procedure followed the household travel survey tradition with some modifications resulting from the necessity of screening for employed persons and the high respondent burden as explained in detail in Aschauer et al. (2018, 2019), where the MAED data are presented and compared to the latest Austrian travel survey, timeuse survey, and expenditure survey.
Data preparation
Aside from usual plausibility checks, two additional adjustments were necessary in order to reduce the incidental variation in the diary data and to better reflect the longterm equilibrium of the individuals.
Adjustment of activity durations
A key problem with respect to activities is the working time reported in the diary. It can deviate from the usual amount due to incidental events during the reporting week, such as workload peaks, bank holidays, sickness, training courses, etc. The result is an unsystematic variation of the reported working time which causes unrealistic balances of income and expenditures, because the working time (along with the wage) determines the implied income in the timeuse model [see Eq. (3)]. We addressed this problem by asking for the regular hours worked (according to the contract) and the usual hours of overtime in the personal questionnaire which accompanied the diary. For data analysis, we replaced the reported working time in the diary for all respondents with the ‘effective working time’, which is the sum of the regular working time and the usual hours of overtime. The durations of nonwork activities were adjusted accordingly to satisfy the time constraint. We assume an asymmetric adjustment pattern in the sense that an incidental increase of working time (beyond the usual level) causes different rearrangement patterns than an incidental reduction (below the usual level). For this purpose, we estimated two separate models which were used for the adjustment of activities of two different groups:

1.
Persons who worked more than usual in the reporting week: reduce the working time to the ‘usual effective working time’ and increase nonwork activities accordingly in order to meet the time constraint;

2.
Those who worked less than usual: increase the working time and reduce nonwork activities accordingly.
Adjustment of expenditures
Linked to the reporting of expenditures is the large variability of purchase rhythms of goods and services. In line with conventional expenditure surveys, expenditure information was collected in two sections of the questionnaire: frequently purchased items were reported in the diary, whereas longterm expenses were reported in the household section. This requires a procedure of combining both sources in a manner that avoids doublecounting through expenses that occur in both sections. Aschauer et al. (2019) describe the procedures that have been tested and applied in this context. The collection of expenditure data at two levels (personal and household) induces the need of some rule to allocate the expenses to those individuals who generate income (i.e. earners). The default MAED dataset is based on ‘proportional expenses’ according to the labour income of the household members. In order to run a sensitivity analysis we generated an alternative dataset based on ‘equal expenses’ for freely chosen goods. It assumes transfer payments within the household such that all earners have equal amounts available for freely chosen expenses. In “Value of leisure (VoL) and value of time assigned to work (VTAW)” section (Table 3) we provide and discuss the results of both datasets.
A second issue associated with the expenses is the large variation of shortterm expenses in the diary. A randomly selected week can deviate from the longterm equilibrium for two reasons: exceptionally large purchases (onetimebigticket items, e.g. a new car) and implausible zero spending on essential goods such as food or travel. Reported zeros may be reduced by a longer observation period and facetoface support of participants, as is usual for conventional expenditure surveys, but this has not been done in the MAED because of the unacceptable response burden given that the participants also reported their trips and activities. We employed a modelbased smoothing of expenditures with the intention to reduce the large incidental variation caused by the aforementioned problems but to retain the individual variability as much as possible. The applied procedure consisted of three steps:

1.
Predict the total expenditures as the difference between reported income and estimated savings; the monthly savings are estimated by a linear model using personal and household characteristics as predictors.

2.
Predict the expenditure shares by category with a multinomial logit model, again using personal and household characteristics as predictors.

3.
Replace the reported total expenditures with the predicted total expenditures (Step 1) and fix the balance by adjusting individual expenditure categories using the predicted expenditure shares (Step 2) as a benchmark.
This procedure ensured that the reported expenditures were carefully adjusted (1) only to the necessary extent in order to fix the balance between income, savings, and expenditures, and (2) towards a benchmark which is already adapted to individual characteristics by the multinomial logit model.
All models used for the adjustment are provided in the “Appendix” section (Tables 7, 8, 9 and Fig. 10). The models comprise many predictors including insignificant ones. This is in accordance with the purpose of the adjustment: we did not attempt to obtain the most parsimonious model (as usual for prediction models) but a rich model that reproduces the highest possible share of individual variability. Table 2 shows the pairwise correlations between reported and adjusted amounts. The average correlation is 0.94 for activities and 0.85 for expenditures. The lower correlation of expenditures results from their larger variability: the coefficient of variation of reported expenditures is more than two times higher than that of activities. The generally high level of correlations (also for expenses) indicates that the major portion of reported variability could be maintained with the adjusted data.
The MAED data rectify some limitations of existing datasets that include timeuse and expenditures and have been used in previous estimations of timeuse models. Our data were obtained directly from the same individuals in a diary format. This is an advantage over retrospective data collections (such as in the Dutch LISS panel) because retrospective questions can lead to biased mean values (Browning and Gørtz 2006). Moreover, obtaining activities and expenditures simultaneously from the same individuals should be preferred over imputing expenditures from external sources as done by Konduri et al. (2011), because a timeuse model is mainly about individuals’ tradeoffs between timeuse, income, and expenditures. Note, however, that the probabilistic merge of participants of a timeuse survey with those of a consumer expenditure survey has one possible strength: consumer expenditure surveys collect the expenses usually with more effort over a longer time period than combined surveys (such as the MAED survey) which will most likely result in more accurate data (while also requiring some adjustment and averaging). Finally, we believe that any data obtained from a diarybased survey should undergo an adjustment to fix the individual balances between work time, income, and expenses because data used for a timeuse model should represent the longterm equilibrium on individual levels and not simply as an average across the sample.
Data description
Figure 2 shows the average activity duration per activity category during the reporting week. The top two bars compare the MAED with the latest Austrian timeuse survey (ATUS); we included only employed persons of the ATUS to be consistent with the MAED. Apart from minor deviations, the MAED results fit the time distribution of the ATUS very well. The largest difference is a shortfall of leisure activities in favour of travel and personal activities. Both shifts are probably caused by methodological differences. In the MAED we took great care to record all trips, whereas timeuse surveys are well known for underreporting trips (Gerike et al. 2015 as well as Aschauer et al. 2018). The shift from leisure to personal activities in the MAED is very likely caused by different coding schemes. MAED participants coded the activity types themselves (such as personal or leisure) based on our instructions; one instruction was that ‘leisure’ should be coded if the activity was performed voluntarily. ATUS participants stated the specific kind of activity in open text fields (such as reading or playing with the children). The abstract activity types were inferred from these statements during data processing, but, there is a broad overlap between personal and leisure; many activities that were inferred as ‘leisure’ from the ATUS statements could be perceived as duty by the participants—in particular, social activities such as going to church or visiting a hospital patient. MAED participants would have coded ‘personal’ in this case.
The remaining bars in Fig. 2 show the average activity durations across different population segments in the MAED sample; they reveal only small differences. If there is a horizontal shift across the segments, it is in most cases a tradeoff between paid work and unpaid (domestic) work. This shift is most pronounced in the difference between men and women. The particularly high substitution rate between paid work and domestic work is reflected by the largest negative correlation (− 0.93) among all pairwise correlations between activity categories.
Figure 3 shows the total weekly expenses (white dots) and shares of expenditures by category (coloured bars). The total expenses differ greatly between the segments, most of all between low and highincome (as expected) with a ratio of 1.9; but other segments reveal large differences as well: men, older persons, persons with higher education, and persons living in singleworker households spend more money than those in the complementary segments. The two bars at the top compare the MAED sample with the latest Austrian consumer expenditure survey (ACES), including only employed persons to be consistent with the MAED. The differences are larger than those between MAED and ATUS (see Fig. 2), possibly reflecting the difficulties of surveying expenditures (see “Data preparation” section). The largest deviation (4.6%) refers to the share of housing; it has a specific reason: the original ACES includes rental equivalents (instead of reported expenses) of owneroccupied housing. The MAED data include, in contrast, reported mortgage repayments and operating costs, which are not comparable to (on average lower than) the rental equivalents. Since we found no way to match both procedures, we removed the rental equivalents in the ACES, which explains the lower share.
The remaining bars in Fig. 3 show the average shares of expenditures across different population segments in the MAED sample. The variability of the shares across the segments is much smaller than that of total expenses, which means that people with higher income spend more money on all kinds of commodities: they live in more expensive houses, eat more expensive food, wear more expensive clothes, etc. From this pattern we can conclude that the Cobb–Douglas function holds for the expenditures in the sense that “having chosen the ultimately satisfying budget shares at any given set of relative prices, the superlatively wealthy continue to allocate additional income in the same proportions” (Powell et al. 2002).
Results
Value of leisure (VoL) and value of time assigned to work (VTAW)
The model estimation requires to classify the reported activity and expenditure categories into the model variables. The model defines three types of decision variables: (1) duration of paid work [T_{W} in Eq. (6)], (2) duration of freely chosen activities [A^{f} in Eq. (7)] to which people assign more time than the technical minimum, and (3) expenses on freely consumed goods [G^{f} in Eq. (8)] which people consume more than the technical minimum. These three types of variables allow for a closedform solution; the resulting equation system (13)–(15) can be used to estimate the utility parameters and to calculate the marginal values of leisure and work by inserting the estimates in Eqs. (16) and (17). Furthermore, the model defines two types of exogenous variables referred to as committed activities [T_{c} in Eq. (9)] and committed expenses [E_{c} in Eq. (10)]. We assume that the consumption levels of these committed variables are externally determined by technical constraints, which require a certain minimum (JaraDíaz 2003) and leave no choice to the consumers but to stick to this minimum.
Table 3 shows how the reported activity and expenditure categories were assigned to the model variables. The allocation is critical because it is arbitrary (cannot be deducted from the data) but affects the result. Our definition of committed activities (T_{C}) follows the classification of JaraDíaz et al. (2013), who identified six types: household chores, personal care, assisting friends and family (‘other’ in the MAED sample), administrative chores and family finances, commuting, and education. The only exception is ‘sleep’, which JaraDíaz et al. classified as free activity, whereas we belief that most people try to stick to the minimum. Personal care and household chores are typically classified as ‘committed’ because of their maintenanceoriented nature (Bittman and Wajcman 2000; Robinson and Godbey 2010). These activities are driven by a physical need, but, in most cases, people do not want to pay more attention than necessary. Gronau and Hamermesh (2006) classified these activities as ‘goods intensive’, that is, individuals particularly care about the amount of goods assigned to them. Ahn et al. (2004) also found that people try to save money in maintenance activities. Travel time might, in principle, be considered as an endogenous variable, which is related to activity destinations and also to the overall framework of time and budget assignment as shown by JaraDíaz and Guerra (2003). However, in this paper we follow the approach by JaraDíaz et al. (2008) which, in essence, states that ceteris paribus individuals would be willing to reduce travel time but cannot due to the characteristics of the transport system (transit design, road network, etc.).
The classification of committed expenses (E_{C}) follows Aschauer et al. (2019) as well as Mokhtarian and Chen (2004): expenses on goods associated with physical needs or maintenance were classified as ‘committed’. People need to eat (food), take care of their health (personal), and need a dwelling (housing) with equipment (furnishing). Further committed expenses are financing, insurance, services not related to leisure activities, education, and travel. Freely chosen expenses include outofhome accommodation (mainly visiting a restaurant and holidays), leisure and recreational goods, as well as electronics and communication devices, which are mainly used for entertainment. ‘Clothing’ was also classified as ‘noncommitted’ although it is at least partially essential. The reason is that clothing expenses add up to fairly high amounts in our sample, indicating that the ‘technical minimum’ is exceeded.
Those activity and expenditure categories which have been classified as ‘freely consumed’ as described above were further subdivided into two groups:

1.
Categories that are entirely or at least predominantly freely consumed were classified as T_{1} and E_{1}. T_{1} includes leisure; E_{1} includes leisure, accommodation (mainly eat outside), and electronic.

2.
Categories that are committed by their nature, but it seems that most respondents have exceeded the technical minimum, were classified as T_{2} and E_{2}. T_{2} includes eating and shopping; E_{2} includes clothes.
Figure 4 shows the correlation pattern of the model variables (descriptive statistics of these variables are provided in the “Appendix” section, Table 10). T_{W} is positively related with E_{C} and negatively with T_{C}—as assumed in the theory and specified in Eq. (13). Another aspect to be noted is the opposite pattern of timeuse and expenditure variables: all timeuse variables are negatively correlated due to the common time constraint τ, whereas the expenditure variables are positively correlated among each other and also with T_{W}. This follows from the equalizing effect of labour income: it increases with T_{W} and increases in turn the available budget for all kinds of goods.
The model estimation was carried out using a maximum likelihood estimation. It can be used under the normality assumption to estimate the parameters from the nonlinear equation system (13)–(15), which is rewritten as:
where g_{i} denotes a function of parameter vector β and error terms \( \eta_{i} \sim N\left( {\mu_{i} ,\sigma_{i} } \right) \). The joint density of all error terms can be expressed as:
The loglikelihood function of a sample of size J is:
The maximum loglikelihood function in Eq. (20) yields estimates of the parameters in Eqs. (13)–(15). The VoL and VTAW can be calculated by entering these estimates in Eqs. (16) and (17). As stated in “Data preparation” section we tested two assumptions regarding how expenses are shared between members of the same household. The default dataset assumes ‘proportional expenses’ according to the labour income. The alternative dataset assumes ‘equal expenses on freely chosen goods’. This was achieved by allocating all expenses on freely consumed goods (E_{1} and E_{2}) at equal amounts to the household members; the committed expenses (E_{C}) were left unchanged (i.e. proportional to the labour income) to avoid negative disposable incomes (E_{C} > wT_{W}), which can cause negative square roots in Eq. (13).
Table 4 shows the result of the estimation. The default dataset (proportional expenses) yields a VoL of 8.17 €/h, which is below the average wage of 12.14 €/h. As shown by many (see JaraDíaz 2007 for a synthesis) the VoL equals the total value of work given by the wage plus the value of time assigned to work (VTAW). Therefore, the VTAW is negative with an average of − 3.97 €/h; it means that the average person works for the money and dislikes work as an activity. The alternative dataset (equal expenses on freely chosen goods) yields a VoL of 9.68 €/h, which is 18% higher. The difference arises from the lower estimate of Φ (0.308 vs. 0.365). The interpretation is straightforward: the implicit transfer of income between household members causes that the expenses have less statistical influence on the working time T_{W} [the response variable in Eq. (13)], because the expenses are equalised but T_{W} continues to differ between members of the same household. This results in a lower sensitivity of T_{W} with respect to changes in expenses and consequently in a lower value of income (λ and Φ). The sensitivity analysis gives an idea to what extent and in which direction the VoL is influenced by how resources are allocated among household members. Given the importance of this aspect, we consider household models (either in the cooperative or noncooperative version) as an avenue for future work. The remaining results of this paper are based on the dataset with proportional expenses, because it yields a clear balance between labour income and expenses at the individual level and permits comparison with existing studies reported in Table 1, which have used samples of oneworker households (JaraDíaz et al. 2016) or onepersononeworker households (Konduri et al. 2011).
Heterogeneity of the VoL across different population segments
A segmented consideration of the values of time seems to be important given the large differences between VoL estimates of different population segments in previous studies (see Table 1). These studies have consistently used a priori segmentation (i.e., the segments were treated as independent samples and separate models were estimated for each segment), but there are different options how to conduct a segmentation. These options have never been compared to each other, although they have different strengths and weaknesses and might yield different results.
In this section we compare alternative options to capture the heterogeneity in the VoL across seven segmentation variables, each of which was treated as follows: the variable was transformed to a binary variable (if not already binary) in a way that it identifies two groups of similar size (low vs. high age; low vs. high income etc.). Table 5 shows these variables along with their original distribution and binary segments.
Segmentation approaches
The possible influence of the segmentation method on the VoL manifests in Eq. (16): it reveals the VoL as a function of four observed variables and one estimated parameter as follows:

The VoL increases with observed wage rate w, working time T_{W}, and committed time T_{C};

It decreases with observed committed expenses E_{C} and the estimated parameter Φ.^{Footnote 9}
This means that the segmentation method can affect the VoL only through the parameter Φ because this is the only estimated quantity in Eq. (16). We compared three options of how to estimate Φ:

1.
ExPost Segmentation The parameters are estimated from the total dataset using a global model. The VoL is then calculated from the segmented dataset based on the global Φ estimate; the VoL accounts only for differences in the distribution of observed variables, whereas Φ is constant across all segments.

2.
APriori Segmentation The dataset is segmented beforehand; the parameters are estimated for each of the segmented datasets, which implies that all parameters are segmentspecific. The VoL is then calculated from the segmented dataset based on segmentspecific Φ estimates; it accounts for differences in the distribution of observed variables as well as other differences that affect the estimation of Φ.

3.
Interaction terms The parameters are estimated from the total dataset using a model with interaction terms involving the segmentation variables. Each of the four main effect parameters (θ_{w}, θ_{1}, φ_{1}, Φ) can have an interaction term independent from the other parameters. This way, segmentspecific Φ values can be obtained and used to calculate the VoL for each segment. For the sake of comparability, we used the binary grouping variables also for the interaction model, although a moderator variable could, in principle, have a higher scale level (e.g., actual income rather than a binary dummy indicating low and high income).
Expost versus apriori segmentation
Figure 5 compares the segmented VoL estimates from expost segmentation (the most restrictive model where all parameters are estimated from the total sample) with those from a priori segmentation (the least restrictive model where all parameters are segmentspecific); results are provided in the “Appendix” section, Table 11. Both methods yield similar results when segmenting by gender, age, and income—which suggests that these classifications have a consistent impact on the VoL. However, four segmentation variables yield very dissimilar or even reversed effects depending on the method used: urbanity, level of education, presence of children, and number of workers in the household. The reversed effect of the presence of children on the VoL provides no indication of the superiority of either procedure, because this effect can indeed be twofold as pointed out by JaraDíaz et al. (2013): on the one hand, children require a lot of time, which translates into more time pressure compared to childless households; on the other hand, taking care of children can be a pleasurable activity for parents. However, the segmentation with respect to the educational level appears counterintuitive in the a priori case, because the VoL of both low and high education segments deviates in the same direction from the global average.^{Footnote 10}
This raises the question why, in some cases, a priori segmentation causes these problems with reversed effects and counterintuitive results. We found the main reason in the sensitivity of the VoL to the variance of the working time (T_{W}) in each segment, which becomes effective only if the parameters are estimated segmentspecific (i.e. in the case of a priori segmentation). This sensitivity can be intuitively explored from the behaviour of the T_{W} in Eq. (13) during the process of parameter estimation:

A large variability of T_{W} must be reflected by a large variability of the predicted working time T_{W}* to achieve a close fit, which means large responses of T_{W}* to given changes in the explanatory variables^{Footnote 11};

The responsiveness of T_{W}* is larger, if θ_{w} (baseline utility of work) is more negative. The reason is the right term under the square root in Eq. (13) because this term increases linearly with − θ_{w}^{Footnote 12};

A negative θ_{w} enforces a large Φ (baseline utility of freely consumed goods) to satisfy the condition that the marginal utility of work plus labour income equals the marginal utility of leisure as defined in Eq. (6).
In order to verify this in our data, Fig. 6 shows the results of a simulation. We generated a series of datasets based on the total sample (n = 737). In each dataset we pivoted the values of T_{W} symmetrically around the mean, such that the mean does not change, but the variance becomes smaller or larger; the changes in T_{W} were balanced by opposite changes of T_{C} to meet the time constraint; everything else was left unchanged. The result shows the close response of the parameter Φ to changes in the variance of T_{W} in line with the aforementioned description; it
Figure 7 shows how this mechanism affects the segmentation results. The blue and red lines are the same as in Fig. 5; the grey line shows the inverse standard deviation of T_{W} in each segment.^{Footnote 13} The deviation of the a priori segments from the expost segments throughout follows the direction of the grey line, especially in the three cases of reversed results (urbanity, education, and presence of children). The sensitivity to the variance of T_{W} makes a priori segmentation vulnerable to unexpected external influences because the variance of T_{W} can differ for many reasons. An example is the segmentation by gender. Men are more often fulltime employed (high T_{W} but small variance of T_{W}), whereas women have more flexible parttime arrangements (low T_{W} but large variance of T_{W}). The lower T_{W} (and lower wage) of women causes a lower VoL; this is already captured in the expost segment. The a priori segment yields an even lower VoL for women, because it accounts for the larger variance of womens’ T_{W}. Does this really indicate a low value of time? Or rather the opposite: a higher time pressure on women resulting from unpaid duties such as domestic work and child care, which requires more flexibility with paid work? The same pattern applies to the particularly high VoL of single workers in the a priori segment: single workers are in most cases full time workers with large T_{W} and small variance of T_{W} The expost segmentation yields almost no difference, because the larger T_{W} is balanced by a slightly lower wage of single workers, and the influence of the variance of T_{W} disappears.
To summarize, we find that a priori segmentation yields, for some segments, peculiar results and reversed effects compared to those of expost segmentation. We have presented an explanation for these problems based on the role played by the variance of working time within each segment. An additional problem of a priori segmentation can be large standard errors, if the underlying segments have a small sample size.
Interaction terms versus expost segmentation
The problems associated with a priori segmentation call for a parsimonious use of degrees of freedom—such as reflected by the use of interaction terms, which allow for more flexibility from single interaction terms up to a full interaction model.^{Footnote 14} In preparation of this approach we modified the model Eqs. (13–15) by replacing each instance of the main effect parameter with an interaction term of the form \( \beta_{i} Z^{{y_{i} }} \), where \( \beta_{i} \) denotes the main effect parameter, Z the segmentation variable, and \( y_{i} \) the interaction parameter, which gives the sensitivity of \( \beta_{i} \) with respect to changes in Z. We estimated all 15 possible interaction models for each segmentation variable, but only 5 models are shown in the “Appendix” section (Table 11): four ‘single interaction models’ with one interaction term on one of the four main effect parameters and a ‘full interaction model’ with interaction terms on all four parameters.
The full interaction model has the same degrees of freedom as a priori segmentation; it yields indeed very similar results. The single interaction models are more similar to expost segmentation. Those models with an interaction term on another parameter than Φ can only change the magnitude of the VoL in both segments but not the ratio between the two segments, unless Φ has also an interaction term. An interaction term on Φ causes the largest deviation from expost segmentation. Figure 8 compares the Φinteraction model with expost segmentation. It reveals only one noticeable (but still insignificant) difference for households with and without children.
Since the VoL is a latent variable which cannot be observed, there is no basis for comparison across models based on the VoL estimates themselves. However, from the analysis above, we conclude that a priori segmentation and the full interaction model are not appropriate in our case. The large number of degrees of freedom makes the estimation process sensitive to the variance of working time within each segment, to which expost segmentation is not sensitive. This difference is evident in the simulation results (Fig. 6), empirical results (Fig. 7), and in the behaviour of Eq. (13). We recommend a limited number of degrees of freedom to make the estimation process more robust against the influence of the workingtime variance. The most restrictive option is expost segmentation which supresses this influence entirely. From our results, however, it seems that a single interaction term on the parameter Φ can be used to account for heterogeneity in the sample without seriously affecting the robustness of the model.
Value of travel time saving (VTTS) and value of time assigned to travel (VTAT)
As explained earlier, the value of travel time savings (VTTS)—estimated from travel choice models—represents the willingnesstopay to diminish travel time by one unit. As originally shown by DeSerpa (1971), the VTTS has two components: the opportunity cost regarding other activities (leisure or work) and the value of a reduction of the travel activity by itself. The first component is the value of leisure (VoL). The secondcalled the value of time assigned to travel (VTAT)—depends on the travel conditions. Analytically, the formula is
where VTTS_{m} is the (modespecific) value of travel time saving estimated from a travel choice model, VoL is the (individualspecific) value of leisure, and VTAT_{m} is the value of time assigned to travel, driven by modespecific characteristics such as comfort and how productively invehicle time can be used for secondary activities (for a general derivation see JaraDíaz 2007, Chapter 2). Equation (21) shows that unless one has an estimate of the opportunity cost of travel given by the VoL, the VTAT_{m} simply cannot be estimated. As explained earlier, this is exactly the reason why a timeuse model is needed. The VoL estimates were presented in “Results” section of this paper, while the modespecific VTTS_{m} were estimated in a parallel effort by Schmid et al. (2018) from a model which combines different data types (RP, SP) and experiment types (mode, route, and shopping destination choice) using 21,681 choice observations of 744 respondents. The data used for the travelchoice model originates from the same MAED survey, which was used for the continuous choice models in this paper.^{Footnote 15} The SP data were collected by a followup survey from a subsample of 504 respondents. A mixed logit model was estimated, which accounts for unobserved heterogeneity in the VTTS and the availability of the different modes and includes scale parameters for the different data and experiment types (see e.g. Train 2009).
The common data source makes the VoL and VTTS_{m}, although estimated separately, compatible to each other. However, a consequence of the independent estimation is that possible correlations between the error terms of continuous decisions and discrete mode choices are not considered. Munizaga et al. (2008) tested the effect of a joint estimation of both types of decisions using full information maximum likelihood (FIML) in comparison to an independent estimation of both types. They had very large correlations between continuous and discrete choices (up to 0.676), possibly because they used a sample of longdistance commuters, for whom the chosen travel mode can make a substantial difference on how their day is organised. Despite the large correlations, they found only small differences between the parameters from joint and independent estimations. Table 6 shows the correlations between the error terms of the continuous equations and the mode choice probabilities estimated from the MAED sample.^{Footnote 16} They are much smaller than those reported by Munizaga et al. (2008); the largest is 0.108 between the error term of working time and the choice probability of public transport. It indicates that the bias from ignoring the correlations between continuous and discrete decisions is likely to be small. Future work might include a joint estimation of continuous and discrete decisions.
Figure 9 shows the VoL, VTTS, and VTAT estimates for different population segments; the VTTS and VTAT also for different travel modes (results are provided in the “Appendix” section, Table 12). The VTTS related to public transport is throughout lower than that of other modes including the car, which confirms a common finding (see Table 1 in Schmid et al. 2018). From Eq. (21) one can see that, for a given individual (i.e. a given value of leisure), the low willingness to pay to reduce travel time in public transport is caused by a large (predominantly nonnegative) value of time assigned to public transport, as shown on the right hand side of Fig. 9. Another important aspect is the large difference between the VTAT of car and public transport (4.4 €/h on average), which persists even after controlling for user characteristics. The smallest difference arises in the urban segment with 2.2 €/h.
The findings regarding VTAT are indeed novel and interesting. They emerge exactly due to the possibility of disentangling the two components behind the VTTS. The main finding is that travel conditions in public transport (captured only by VTAT) are perceived more pleasant than those in a car, which seems to capture well the quality of service of public transport in Austria, contradicting the common opinion that traveling by car is generally more pleasant. We have no basis for comparison, because these are the first modespecific VTAT estimates. But there are reasonable arguments why public transport users might perceive the time assigned to travel more pleasant than car drivers (and are therefore less timesensitive): they are released from the driving task and can engage in many kinds of secondary activities, which makes the time assigned to travel more comfortable, entertaining, and useful. Flügel (2014) provides a summary of why public transport travellers may be less timesensitive than car travellers.
Synthesis and conclusions
The aim of this study was to obtain representative estimates for the value of leisure (VoL), value of time assigned to work (VTAW), and (for the first time) modespecific values of time assigned to travel (VTAT) of Austrian workers. VTAT have been obtained by comparing the VoL with modespecific values of travel time savings (VTTS) from a related study based on the same data source (Schmid et al. 2018).
The average VoL in the population was estimated at 8.17 €/h. This is considerably less than the average wage rate of 12.14 €/h; the result is a negative VTAW of − 3.97 €/h, indicating that time assigned to work is valued negatively on average and people work mainly for the salary. The result seems reasonable in the sense that the VoL is not too far away from (but also not identical to) the wage rate. In their estimations of the VTTS, Schmid et al. (2018) found that the modeeffect dominates over the effect of user characteristics; the average VTTS estimates for walk, bike, car, and public transport are 12.30, 11.20, 12.40, and 7.90 €/h, respectively. An important implication is that the direct utility of time assigned to travel, expressed by the VTAT, has inverse signs for different modes: it is strictly negative for walking, cycling and car driving, and close to zero (predominantly positive) for public transport with an average of 0.27 €/h. The clear priority of public transport has not been identified in previous studies (e.g. Wardman 2004; Shires and De Jong 2009). It may indicate that the public transport benefits more than other modes from technological innovations and mobile devices such as smartphones, etc. These devices affect the perceived comfort and how invehicle time can be used for secondary activities such as work, communication, or entertainment. From a transport planning perspective, the results support those who claim that the conditions of travel matter greatly (e.g. Litman 2008; Lyons et al. 2013; Flügel 2014) and investments in better travel conditions are as important as investments in higher speed to attract customers to public transport.
An important finding with respect to the reliability of the VoL is its sensitivity to the variance of working time in the sample: a high variance causes a low VoL and vice versa. This has not been noted in previous studies, possibly because it is not visible in the equations but results from a specific behaviour of the equations during parameter estimation. This has several implications:

It might be responsible for some of the fluctuations of VoL estimates in previous results (see Table 1).

It can cause biased VoL estimates of population segments if the variance of working time in the segment deviates from the global average. This problem appears only if a priori segmentation is used (i.e., if separate models are estimated for each segment). To be on the safe side, we recommend using expost segmentation (i.e., estimation of global parameters and calculation of the VoL in the segmented data with these parameters). In our sample it seems that single interaction terms in the global model do not seriously affect the robustness.

It might affect the comparison of countries with different degrees of regulation of the labour market. Parttime workers exhibit a large variability in any labour market, but the variability of fulltime workers depends on the degree of regulation. Fulltime workers in a strongly regulated market (as in Austria and many other European countries) exhibit a low variance in working time because the maximum is limited by collective agreements, whereas fulltime workers in a deregulated market may exhibit a larger variability.
To the best of our knowledge, this is the first study that uses a data source which has been collected with the explicit intention to estimate all components of the timeuse framework introduced by JaraDíaz and Guevara (2003): a representative sample, where all information required for modelling has been collected from the same individuals at the same time in a diarybased format. Given the high data quality and the fact that we obtained reasonable results (in terms of a plausible size and moderate variability of VoL estimates) we conclude:

Going ahead towards practical usability of the values of time obtained from the timeuse framework model not only requires advanced models, but (possibly even more so) advanced data.

If highquality data is used for parameter estimation, the data collection effort seems to be rewarded by more reliable results. This interpretation should be confirmed by further efforts into gathering of highquality data.
A datacollection technique that is likely to become more important in the future is probabilistic merging. It would thus be a promising option for further research to compare the MAED data with an artificial dataset in which the expenses are imputed from the latest Austrian consumer expenditure survey. This might answer the question how much is lost by probabilistic merging compared to simultaneous collection—which is indeed more burdensome.
Notes
 1.
For the VTTS to represent the opportunity cost of travel, it must include all utility components, which are experienced while travelling, e.g. more comfortable seats or the availability of WIFI—but no oneoff effects such as the possibility of online reservation. The respective timedependent variables should either be multiplied by travel time (and the coefficient is added to the travel time coefficient), or they are omitted in the utility function (and the corresponding utility is implicitly included in the travel time coefficient by its average value).
 2.
To obtain VTAT we use the VTTS estimates obtained by Schmid et al. (2018), which are based on the same data source.
 3.
There is only one experimental attempt in the literature which introduces (technical) relationships between goods and time (JaraDíaz et al. 2016); this model yields rather implausible results which underlines the experimental character of this branch of research. Also, the MAED data do not include expenses for external service providers, which prevents the use of another recent experimental extension: the introduction of domestic activities as a decision of households which are hiring external providers (RosalesSalas and JaraDíaz 2017).
 4.
The logarithm in Eq. (1) corresponds to the \( \alpha_{k} \) parameter in Bhat's model. A difference, however, is that the logarithm has a predefined curvature, whereas \( \alpha_{k} \) can be estimated.
 5.
In an empirical survey it can still happen that zero assignments occur, in particular, if more detailed activity classifications are used. In this case we suggest imputing reasonable values using methods available in the literature.
 6.
 7.
The change in normalization was done for analytical convenience only; it does not affect the results. Please note that α and β are derived from the exponents of the Cobb–Douglas function and are therefore adimensional—as the original parameters.
 8.
'KONTIV' is the name of a travel survey design and instrument developed in the seventies by Werner Brög and associates for the German national travel diary. It has become the standard of selfadministered travel surveys in German speaking countries.
 9.
Φ captures the utility associated with freely consumed goods; the remaining two input quantities in Eq. (16) are constants and do not affect the VoL: the time constraint τ and the parameter Θ, which is set to one for normalisation.
 10.
Another problem associated with a priori segmentation are the large confidence intervals of 'urban residents' and 'single workers'; they are a result of the low sample size of these segments (see Table 5).
 11.
 12.
The respective term is \(  4E_{c} /w\left( {\tau  T_{c} } \right)\theta_{w} \left( {\varTheta + \varPhi + \theta_{w} } \right) \). All other terms in Eq. (13) respond in the opposite direction to changes of θ_{w}, but these responses are smaller in size and are therefore outperformed by the former.
 13.
The standard deviation of T_{W} was rescaled to fit in the VoL scale of Fig. 7. The rescaled values can be perceived as 'predicted VoL' from a model with the segmentspecific standard deviation of T_{W} as sole predictor: \( y =  12.36 + 239/stdev\left( {T_{W} } \right) \).
 14.
Each of the four main effect parameters can have an interaction term independent from the other parameters, which yields 15 possible models according to permutation rules: four models with one interaction term, six models with two interaction terms, four models with three interaction terms, and one model with four interaction terms.
 15.
The continuous choice models presented in this paper include the reported trips as part of the committed time and the travel cost as part of the committed expenses (see Table 3).
 16.
The choice probabilities are assumed to distribute logistically and were subject to a Leetransformation in order to obtain normally distributed variables. Lee (1983) proposed a method to account for correlations in a discrete–continuous model system by transforming apriori assumed marginal distributions for each error term into the standard normal and generating a joint multivariate normal distribution of the resulting transformed error terms. Lee’s method has been applied by many authors, e.g., Bhat (1998) and Habib (2013).
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Acknowledgements
Open access funding provided by Austrian Science Fund (FWF). Reinhard Hössinger, Regine Gerike, and Florian Aschauer gratefully thank to Austrian Science Fund (FWF) for funding the research project Valuing (Travel) Time (Award Number I 1491G11), from which this article arises. Sergio JaraDíaz would like to thank funding by Fondecyt, Chile, Grant 1160410, and the Complex Engineering Systems Institute, ISCI, Grant CONICYT: FB0816. We also thank Friedrich Leisch, head of the Institute of Applied Statistics and Computing at the University of Natural Resources and Life Sciences Vienna, for his statistical advice, as well as Ashleigh Möller from the Institute of Transport Planning and Road Traffic at the TU Dresden for proofreading the manuscript.
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RH: literature review, data analysis, manuscript writing. FA: data collection, data description, manuscript writing. SJD: theoretical model, interpretation, manuscript editing. SJ: software development for data analysis, manuscript editing. BS: provision of choice data and models, manuscript editing. SP: introduction, conclusions, manuscript editing. KWA: content planning, interpretation, manuscript editing. RG: project leader, research approach, sample design, manuscript editing
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Appendix
Appendix
The two models in Table 7 correspond to our assumption that an incidental increase of working time beyond the usual level (left model) causes different rearrangement patterns than an incidental reduction below the usual level (right model). Furthermore, we assume strictly substitutional relationships between work and other activities, such that an increase of working time causes a reduction of other activities and vice versa. This was informed by restricting the lower bound of the parameters to zero. In three cases, we obtained parameters at the lower bound, because the estimated values were negative, although they did not significantly differ from zero: (1) Domestic work is not reduced as the working time increases. This might indicate that domestic activities cannot be reduced easily due to their strongly committed nature. (2) Travel is not increased as the working time decreases. This makes sense due to the complementary relationship between work and the travel to work. The parameter might indeed be negative, but it is fixed here to zero because of the insignificant deviation. (3) Personal activities are also not increased as the working time decreases. This might indicate that an additional demand for personal activities is usually not the reason why the working time is reduced below its usual level.
Figure 10 illustrates by means of an example (a particular person) how the reported expenses were adjusted to match the balance between income and expenses, while keeping the interperson variability of expenses. The aim of the adjustment is to equal the total expenses (sum of reported expenses) to the predicted expenses such that the ratio reported/predicted is one, irrespective of whether or not the reported expenditure shares match the predicted shares. The person in Fig. 10 reported only 85.5% of predicted expenses (obtained as income minus predicted savings from the savings model in Table 8). The missing 14.5% were imputed by increasing those expenditure shares that were below the predicted shares obtained from the expenditure shares model in Table 9 (in this case: Housing, Food, Accommodation, Clothes etc.). The remaining shares, which equal or exceed the predicted shares, were not increased (Health, Electronic, Financing, Other). Please note that the predicted shares (grey line) are already adapted to the individual’s household and personal characteristics. The adjustment works inversely for persons whose reported income exceeds the predicted income (ratio reported/predicted > 1).
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Hössinger, R., Aschauer, F., JaraDíaz, S. et al. A joint timeassignment and expenditureallocation model: value of leisure and value of time assigned to travel for specific population segments. Transportation 47, 1439–1475 (2020). https://doi.org/10.1007/s1111601910022w
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DOI: https://doi.org/10.1007/s1111601910022w
Keywords
 Value of leisure
 Value of time assigned to travel
 Time use
 Expenditure allocation
 Segmentation