1. Questions

There is a hypothesis that preference for crowding in public transport vehicles (in-vehicle crowding) changed during the COVID-19 pandemic due to an increased risk of getting a viral infection and increased discomfort of sitting or standing close to other persons. For transport planning, a relevant question is if the valuation/marginal costs of crowding in the post-COVID period differs from the pre-COVID period. If costs persist at a higher level, this might indicate long-term changes in preferences that transport planners should account for when designing future public transport supply.

Our research question is therefore: To what degree has public transport user’s aversion to crowding – measured by crowding multipliers on the value of travel time saving (Wardman and Whelan 2011) – changed during and after the COVID-19 pandemic compared to pre-COVID level?

Our empirical evidence are from two Norwegian cities, and adds to a growing literature on COVID-related crowding costs (Cho and Park 2021; Aghabayk, Esmailpour, and Shiwakoti 2021; Basnak, Giesen, and Muñoz 2022; Shelat, Cats, and van Cranenburgh 2022). To our knowledge, this is the first paper that presents comparable results from all three periods, i.e. before, during and after the pandemic.

2. Methods

We estimate crowding multipliers on the value of travel time savings based on binary stated choice data, using mixed logit models. Available information that enters our statistical model is dummy variables for the round of data collection $D_{a}$ with $a = \{1,2,3,4\},$ travel time $T_{i}$ in minutes for alternative $i = \{1,2\},$ and dummy variables indicating the crowding situation $C_{i,s,k}$ where $s = \{sitting, standing\}$ indicates if one sits or stands over the whole trip and $k = \{ \begin{matrix}1,\ldots,10\ for\ s = sitting \\ \ 5,\ldots,10\ for\ s = standing \end{matrix} \}$ indicates the crowding level as illustrated Figure 1.

Figure 1.Illustration of crowding levels (here in the case of train and metro)

Figure 2 shows an example of a choice task. The three attributes travel time, sitting place and crowding level were established based on reported reference values and combined by means of an orthogonal design (Flügel et al. 2020). A variant of the choice experiment, assigned to 50% of the sample, omitted the verbal description of sitting place and instead showed seat position in the illustration of the crowding level.

Figure 2.Example of a task in the choice experiment (translated from Norwegian)

In our model, the utility function of alternative i for respondent n in choice task t is given as

$$U_{n, t, i, a}=\mu_{a} *\bigl(\alpha_{i}+\sum_{a} \sum_{s} \sum_{k}\left(\beta_{a, s, k} * D_{a} * C_{n, t, i, s, k} * T_{n, t, i, a, s, k}\right)\bigr)+\varepsilon_{n, t}$$

with

• $\varepsilon_{n,t}$ being i.i.d. Gumbel distributed error terms

• $\mu_{a}$ being scale parameters for the different data collections a. For normalization, we apply $\mu_{1} \equiv 1$

• $\alpha_{i}$ being constant terms. For normalization, we apply $\alpha_{1} \equiv 0$

• $\beta_{a,s,k}$ being parameters capturing the marginal utility of travel time in different crowding situations. The marginal utility of travel in uncrowded situations, i.e. $\beta_{a,sitting,1},$ is assumed normally distributed over respondents n to account for unobserved taste heterogeneity. For normalization, we set the mean values of $\beta_{a,\ sitting,1}$ to minus 1.

With the applied normalization, the absolute values of $\beta_{a,s,k}$ represent the crowding multipliers in different situations (defined by $s$ and $k)$ given the round of data collection $a.$

Our data collection was done in four rounds (R1 – R4) using different recruitment techniques. Recruitment was concentrated in the area of the Norwegian capital Oslo (the largest urban area in Norway) and Trondheim (the fourth largest urban area in Norway). Table 1 gives an overview over the samples. Note that all respondents in round 4 also participated in round 2 and/or round 3 (mainly round 3).

3. Findings

The last four lines of Table 1 paint a picture of the COVID situation in Norway at the different points in time. Based on this context, we expected crowding multipliers to be greater during the pandemic (April 2021 and November 2021) compared to 2018 values, and 2022 values to be close to 2018 values.

This was largely confirmed as shown in Figure 3.^[1] Looking at the two left-most panels we see that estimated crowding multipliers were significantly higher during the pandemic (November 2021) compared to pre-COVID (November 2018). Our assessment about significance is based on the robust standard errors (and T-values) of the estimated beta-parameters. They are shown in the form of 95% confidence intervals in the Figure 3. The figure also shows that the post-COVID (May 2022) values are significantly lower compared to November 2021. The post-COVID values remain somewhat above the pre-COVID levels, however, here the confidence intervals are largely overlapping.

Figure 3.Estimated crowding multipliers while sitting (upper panel) and standing (lower panel); comparison of selected pairs of data collections. 95% confidence intervals given in dashed lines.

The absolute values of the pre-COVID crowding multipliers seem to compare well against other studies (Wardman and Whelan 2011; Kroes et al. 2014; Hörcher, Graham, and Anderson 2017; Tirachini et al. 2017). While our COVID-related values are rather high, some high values (of up to 5.1) are also found in Basnak, Giesen, and Muñoz (2022).

For context, Table 2 gives the share of respondents agreeing to the statement that they may feel discomfort when standing close to other persons.

We see that the shares increased substantially from round 1 (pre-COVID) to round 2 (April 2021), but has since been on a decline. Still, the 71.7% in round 4 (post-COVID) is substantially above the pre-COVID share, both compared to the 2018-sample and compared to retrospective questions within the 2022-sample (“before COVID”). This indicates that there might be long-term shifts in preferences.

Some caveats should be taken regarding the different samples, e.g. in respect to the age distributions. However, note that the shares in Table 2 for the 2018 sample are rather consistent with the “before COVID” shares from the later samples. This is encouraging with respect to concerns regarding representativity and comparability of the samples. It also seems like the perception of discomfort is less related to age compared to gender.

Acknowledgement

The writing of this paper and data collection 3 and 4 were financed by the Norwegian Research Council trough the CAPSLOCK project (326814). The first data collection was financed by the transport authorities in Norway through the Norwegian Valuation Study 2018-2019. The second data collected was financed by the Norwegian Railway Directorate and supported by the Norwegian Research Council trough the CODAPT project (315679). We want to thank Askill H. Halse and two anonymous reviewers for valuable comments to the manuscript.