Estimation of direct net effects of events

We provide three estimation strategies for the estimation of direct net effects of events and the respective substitution effects based on a quantitative model. We apply the strategies to estimate the effect of fairs on overnight stays in Basel. We show that deseasonalizing by year day fixed effects is superior to month and week fixed effects and semi-parametric deseasonalizing. We find that fairs increase the overnight stays in nights during fairs by 17% and by 8% and 4% in the preceding nights. The net effect of fairs on overnight events is only one fourth of the gross effect. These results demonstrate that the distinction between net and gross effects is crucial also for the estimation of direct effects of events. The study therefore contributes to the literature on the estimation of economic effects of events which recently has focused on this distinction for indirect effects. It also contributes to the theoretical an empirical literature of event tourism in cities.


Introduction
Tourism is often subsidized arguing that the economic benefits exceed the private gains of the involved actors (see e.g. European Commission, 2016). This is also the case for events like festivals or fairs. 1 In order to justify such policies, policy makers need reliable estimates of the economic impacts of the subsidized item. There exists a large literature in tourism economics how to estimate such economic effects in general (see e.g. Kronenberg et al., 2018;Martínez-Roget et al., 2013;Tohmo, 2018;Kim et al., 2015). 2 These general methods can also be applied to assess the impacts of events on the local economy (see e.g. Van Wyk et al., 2015). The literature thereby distinguishes direct economic effects of events, that is, effects that are directly generated by the spending of visitors, and indirect economic effects that occur due to trade relations of directly affected actors with other actors in the economy. Thus, indirect effects are always functions of the initial direct economic effects. Furthermore, literature distinguishes between gross and net effects. Gross effects capture the contribution of events to the economy and net effects capture the impact of events on the economy (Dwyer, 2015). Both only equal if there are neither price nor substitution effects.
Recent developments mainly focussed on the distinct estimation of indirect gross and net effects (see e.g. Dwyer, 2015). Despite the importance of distinguishing between gross and net effects (Dwyer, 2015), the initial direct effects are usually estimated only as gross effect by surveys (see e.g. Van Wyk et al., 2015). But survey data neglects any substitution effects and therefore likely overestimates the impact in the presence of substitution effects and price effects. The estimation of direct net effects however demands the estimation of counter-factional scenarios which in the case of events demands also data on all non-event related touristic activities which is naturally not included in surveys gathered at event sites. However, recent developments in digitization make new data sources available that allow a more rigorous estimation of economic net effects. Therefore, we derive three methods based on event study design (see e.g. Schmidheiny and Siegloch, 2019) that allows to study economic net effects of events using high frequency data: A parametric approach with month and week fixed effects, a parametric approach with year day fixed effects and a semiparametric approach with and without year day fixed effects. Additionally, we present a quantitative model of event tourism demand in cities that can distinguish primary motives of tourists while allowing for secondary motives. The model predicts positive overall effects of fairs on overnight stays but a substitution of leisure tourists while the effects on attraction visits depends on the degree of leisure activities of the attracted fair visitors. The combination of the estimation methods with the model allows to estimate the substitution effects.
We test the methods studying the direct net effect of fairs on overnight stays and attraction visits by overnight visitors in Basel. Fairs are of specific interest because they are usually highly subsidized and attract potentially many tourists to a city for a short time period. If the cities are small compared to the number of visitors of a fair, they can even hit capacity limits. It is at least likely that fair overnight visitors substitute some of the tourists usually visiting the city due to increased prices. We show that a sophisticated method of deseasonalizing is needed to estimate direct net effects. The parametric approach with year day fixed effects delivers plausible results under least restrictive assumptions. The parametric approach with month and week fixed effects delivers partly implausible results which are likely caused by endogeneity issues. The semi-parametric approach with month and week fixed effects has strong identifying assumptions but might be suitable also for shorter time-series that do not allow the inclusion of year day fixed effects.
We find that fairs in Basel increase the overnight stays in nights between fair days on average by 17% and by 8% and 4% in the preceding nights. They do not affect the overnight stays the nights following fairs. We observe that business tourist also consume a certain amount of leisure activities during and before fairs, thus we can confirm parallel bleisure tourism. However, the observed consumption patterns are not in line with business tourists attending fairs and extending their stay primarily due to leisure motives. Robustness checks indicate that our results are unlikely to be generated by favourable fair dates that accidentally coincide with visitor peaks. Applying two different methods, we show that the gross effect on overnight stays is about four times the estimated direct net effect. This implies a substitution effect of three fourth of the gross effect. Our effects are estimates on quantities. For economic effects, the ratio is likely to be lower due to price effects. Yet, it still illustrates the importance of distinguishing net and gross effects when estimating initial direct economic effects of events.
Therefore, this study contributes to the field of methods estimating economic effects of events by providing estimation strategies and model that allow the identification of direct net and substitution effects. The superior strategy demands high frequency data on the relevant economic outcomes. But such data becomes more and more available offering a chance to use the strategy also for full economic impact analyses (see e.g. Brown et al., 2020). It also contributes to the theoretical literature on event tourism in cities providing a quantitative model that can distinguish primary motives of tourists while allowing for secondary motives. Furthermore, it contributes to the empirical literature on event tourism by showing that business tourist have leisure motives during and prior to fairs but that they do not extend their stays primarily due to leisure motives.

Related literature
Assessing economic effects of tourism and events has a long tradition in the literature (see e.g. Dwyer and Forsyth, 1997). The basic and still popular model for measuring economic effects of tourism or single events is the input-output model (IO) (see e.g. Kronenberg et al., 2018;Martínez-Roget et al., 2013;Tohmo, 2018). Methodological overviews are provided by Dwyer and Forsyth (1997), Mistilis and Dwyer (1999) and Miller and Blair (2009). The method generally involves two steps: The first step is the assessment of the direct effects of a shock on the economy. A shock can for example be an exogenous shock in inbound tourism for a country or an event. Such direct effects are expenditures for overnight stays, restaurants, equipment, etc. induced by the event. They are usually assessed by surveys asking the spending behaviour of tourists or event visitors (see e.g. Kim et al., 2015;Van Wyk et al., 2015). The second step is the assessment of the indirect effects on the economy. These are expenditures of hotels etc. at their suppliers induced by their increased sales and the iteration of them. These indirect effects are not directly measured but estimated using inputoutput tables that link expenditures and trades between industries. Hence, knowing the direct effects on all industries, factors retrieved from these input-output linkages allow calculating overall economic effects including the indirect effects.
The second step using input-output factors in order to estimate indirect economic effect builds on several strong assumptions. Among others the model assumes that the prices of inputs and outputs are fixed, that is, any demand or supply shock will not change the relative prices in the economy. Furthermore, it assumes linear economics of scale and unlimited supply or unlimited capacities (Dwyer, 2015). These assumptions are not very plausible especially when the direct effects are comparably large (Dwyer et al., 2004). Computable general equilibrium (CGE) models can overcome these shortcomings of the IO models but at the cost of much higher complexity (Dwyer, 2015). Unlike the IO models, CGE models allow for flexible prices and do not impose unlimited capacities and supply. An extensive methodological overview is provided by Burfisher (2017). The assessment of the direct effects is step 1 is unaffected by this model change. Generally, the indirect and overall economic effects are lower using the CGE models instead of the IO models (see e.g. Dwyer et al., 2005).
In recent years, these CGE models became more popular (see e.g. Dwyer, 2015;Van Wyk et al., 2015) but did not entirely replace the IO models. Beyond the mentioned higher complexity of the model, there is a second reason for this development: The effects that they measure are different in nature. While the IO models are capable to answer the question which share of the economic activity is due to tourism or a certain event, CGE models answer the question what would happen to the economic activities if there would be no tourism or a certain event had not taken place. Thus, the IO models result in the contribution of tourism or an event to the economy and the CGE models in the impact of tourism or an event on the economy (Watson et al., 2007). Hence, there is not one model that is superior to the other but researches have to choose the correct model to answer the respective question.
Recent developments in estimating indirect and overall economic effects involve dynamic inputoutput tables (Kronenberg et al., 2018) and explicitly modelling and collecting data on the supply side (Kim et al., 2015).
While the distinction between economic impacts and contribution has been acknowledged in estimation indirect and overall economic effects, the assessment of direct economic effects in the tourism literature lacks strict methodological distinction between both although scholars are aware that this distinction is equally valid in this context (see e.g. Dwyer, 2015). Even very recent studies estimating the effects of events on the economy base their effects on survey data collected at the attendees and the organizers (see e.g. Van Wyk et al., 2015). This method captures the contribution, that is, the gross effect of events because it attributes each US dollar spent to the event. It does not ask how would the US dollars have been spent if the event had not taken place. A valid strategy of estimating direct net economic effects of events seems to be missing in the literature. The reason might rather be a historic lack of data availability than an actual lack of methods from the general economic literature. We address this gap by suggesting an empirical framework that allows to estimate direct effects of events on any measure that is available on a daily basis.
There is a very wide range of studies addressing the economic contribution of events or their impacts on the economy. Many of them focus on single events like the London 2012 Olympics (Blake, 2005), the football world cup in South Africa in 2010 (Saayman and Rossouw, 2008;Bohlmann and Van Heerden, 2008) which all were studies predicting the effects using the above mentioned models. Daniels (2004) investigates sport events but focusses on the effects on wages. Dwyer et al. (2005) estimate the economic effects of the Australian Formula One Grand Prix both using IO and GCE models demonstrating that the results can differ by more than the factor of two depending on the model choice. Van Wyk et al. (2015) and Saayman and Rossouw (2011) both investigate festivals in South Africa. Van Wyk et al. (2015) demonstrates the importance of using a CGE model but also relies on survey data for estimating the direct effects. Other studies investigate the MICE sector. Kasagranda et al. (2017) and Celuch and Dziedzic (2018) take a country perspective for Slovakia and Poland. Celuch and Dziedzic (2018) estimate the contribution of the meeting industry on the Polish Economy. Studies focussing on local effects of fairs are rather rare. Penzkofer (2017), AUMA (2018), Penzkofer (2018) and Hochheim and Penzkofer (2019) all estimate economic effects for fairs in Germany using IO models and survey data. Hence, they all estimate the contribution of these fairs to the economy rather than their impact. However, for fairs which are usually highly subsidized, it is rather interesting for policy makers to know what the economy would look like if the fair did not take place. Or speaking differently, what are the economic costs of cutting subsidies? Hence, in our empirical application, we focus on the direct impact of fairs on overnight stays and the usage of local attractions. Thereby, we compare the direct contribution and the direct impact of fairs on overnight stays and demonstrate that the difference is sizeable and the distinction therefore important.
There are also plenty of studies studying event tourism 3 and event tourists' motives in particular (see e.g. Lichy and McLeay, 2018;Lee et al., 2010;Davidson, 2003;Rittichainuwat and Mair, 2012). They point out that the primary motives for attending conventions or fairs are usually networking, gaining knowledge about the market, etc., hence business related reasons. However, they also identify leisure activities that can be done in the destination as important motive for the travel choice. This phenomenon is also called bleisure tourism (Pinho and Marques, 2021). Yet, what seems to be missing in the literature is a quantitative model of tourism demand in a city that incorporates these different kinds of tourists according to their primary motives and allows for secondary motives.
This study contributes to the methodological literature of estimation the impact of events by providing an estimation strategy for direct net economic effects that in combination with CGE models can allow the estimation of the actual impact of events rather than their economic contribution. It also contributes to the theoretical literature on event tourism in cities providing a quantitative model that can distinguish primary motives of tourists while allowing for secondary motives. Furthermore, it contributes to the empirical literature on event tourism demonstrating the existence of leisure motives of business tourists during fairs and rejecting these motives for extending the stay.

Model
In order to study the effect of fairs on the visiting quantities, we first provide a simple model, that embodies the general distinction between business tourists and leisure tourists while allowing the business tourist having some leisure demand. Let the overall demand for overnight stays at day t be It depends on the general price level in the destination p t and an indicator M t that equals one if a fair takes place and zero else. The price p t is the price for the bundle of products consumed during the stay. For locations like our empirical case, it makes sense to split this overall demand in leisure tourists' demand Q O t ðp t , M t , k ¼ 0Þ and business tourists' demand Q O t ðp t , M t , k ¼ 1Þ because cities very often attract these two kinds of tourists with different preferences and reasons for stay. In Basel, for example, business tourists account for 65% of the overnight stays while leisure tourists account for only 35%. Hence, we can write Thus, the effect of a fair on the overnight stays is The effect for business tourists is In our model, the business tourist are attracted by fairs, hence the first addend is strictly positive. With fixed supply capacities and without price changes, the demand for business tourists and hence, the overall demand will increase. But this increases the price level in cities with fixed capacities. Hence, the second addend will be negative but not outweigh the first. Thus, the quantity of business tourists will increase during fairs. Considering the empirical case Basel, we would expect to see these effects because the fair tourists account for about 21% of all overnight stays. This is even more pronounces during very large fairs that absorb a substantial amount of the bed capacities like the Art Basel.
The effect for leisure tourist is The leisure tourists in this model are not interested in the fairs, thus the first addend is zero. Yet, due to the overall increase in demand the price level increases due to fixed capacities and hence, we should observe a negative substitution effect of leisure tourist (second addend). Thus, the quantity of leisure tourists will decrease during fairs. We expect this effect to be pronounced in Basel because the fair site is close to the city centre. Thus, there exists a substantial amount of accommodation that is equally attractive to fair visitors and leisure tourists.
If we assume that a share α(k) of both kind of tourists consume leisure attractions during their stay, we can express the attraction demand as The overall effect of fairs on these quantity of attraction visits is unclear It is composed of a negative effect due to the decrease in demand by leisure tourist and a positive effect due to the increase in demand by business tourists. Which of both dominates depends on the relative effects on the overnight stays and the relative sizes of α(k). Note if we assume that there is nothing like bleisure tourism, we would set α(k = 1) = 0 and the effect would clearly be negative. Yet, this is not very plausible in our empirical example since there is for example the art fair Art Basel which is always accompanied by special exhibitions in the city's art museums and galleries.
Note that due to the constant factor α(k) the elasticity of attraction visits with respect to fairs η A (k) of each group equals the elasticity of overnight stays η O (k) This equality is crucial since it allows us to draw conclusions on substitution effects of overnight stays from estimated effects on attraction visits without observing if a tourist is a business tourist or a leisure tourist. Hence, we can overcome the most evident disadvantage of administrative data compared to survey that usually lacks information about the visiting reason of the visit.
The presented model is a static model in the sense that there is no effect of fairs on overnight stays before or after the fair. But if fair visitors and especially exhibitors arrive early to prepare the fair or arrange business meetings, we would expect an increased demand already prior to the fair or thereafter. In cities like Basel that are also attractive to leisure tourism, fair visitors might arrive early or stay longer in order to attend some leisure activities. We can generalize the model above to this case and investigate the effects of a fair on the nights leading the fair, nights during the fair and nights following the fair. We can denote the elasticity of overnight stays by tourist category k in nights between two fair days as η O 0 ðkÞ. This definition assumes constant effects during fairs but is entirely flexible with respect to the length of each fair. This is important since the fairs vary substantially in their length in our empirical example. The elasticities for nights leading fairs by l nights are then denotes η O Àl ðkÞ, that is, for the night before a fair, the elasticity is η O À1 ðkÞ. The elasticities for nights following fairs by f nights are then denotes η O f ðkÞ, that is, for the night after a fair, the elasticity is η O 1 ðkÞ. The same holds for the attraction visits. Figure 1 presents the timing graphically.
This model allows us to study the effect of fairs on overnight stays, the substitution effects and the effects on attraction visits. It is applicable to nights and days during fairs as displayed above but can easily be generalized to other events and tourist groups by altering the interpretation of M t and k.
Empirical strategy Parametric strategy. The final goal of the empirical strategy is to estimate the direct net effect of events on any economic outcome variable. We suggest and adapted version of the event study design approach by Schmidheiny and Siegloch (2019) and estimate the following equation using OLS with daily data Y t is an outcome variable at date t. 4 M t is an indicator that equals one for date t if there is an event on date t and zero else. The coefficient estimate b β 0 will therefore capture the effect of the event on the respective outcome variable. M tÀf is an indicator that equals one for date t if there is an event on date t À f and zero else. The coefficient estimate b β f will therefore capture the effect on the outcome variable on the fth day after the event. M t+l is an indicator that equals one for date t if there is an event on date t + l and zero else. The coefficient estimate b β Àl will therefore capture the effect on the outcome variable on the lth date before the event. X t is a vector of controls. It contains the same set of dummies for other events that we are not interested in capturing extraordinary demands caused by these events. Furthermore, it contains a year fixed-effect capturing the long-run trend, month fixed effects capturing the seasonality and weekday fixed effects capturing the usual pattern during a week. Yet, all these controls cannot mitigate the fact that the timing of events is not random which can cause potential endogeneity issues.
Note that if the outcome variable Y t is the natural logarithm of an underlying variable of interest like the overnight stays

Parametric strategy with year day fixed effects
If researches have multiple years of observations and the events of interest do not always take place at the same day in the year, they can include year day fixed effects, S t , in equation (8) Y Unlike with date fixed effects, these allow us to compare, for example, the first Monday in each year and not the first of January that is in one year a Monday and the next year a Tuesday. All effects are then identified for events that change their year day. The endogeneity issues here are much less severe because the general seasonal timing does not effect the estimates. The identifying assumption is that the date adjustments of events are not related to the expected outcome on the target date. This is clearly the case for regular events that, for example, take place always on the first Sunday in June. Such events jump six days all 5 or 6 years by construction. Note that month or weekday effects drop out by construction and are not contained inX t .

Semi-parametric strategy
Trying to capture the seasonality by month dummies however places parametric restrictions and leads to discontinuities at the start and end of a month. A more sophisticated approach is adjusting the time-series with a local polynomial smooth in principal following the approaches usually used to identify bunching behaviour in densities (see e.g. Kleven and Waseem, 2013). In particular, we estimate the following equation using OLS Y t is the prediction from a local polynomial smooth of Y t on t excluding the b dates before and the five dates after a fair or an event. The advantage is that it captures the usual level of outcome locally around the event date and that there are no discontinuities at the start and end of a month. Formally, we can approximate the outcome variable Y s around date t by a Taylor polynomial of order p t is the pth derivative of Y t with respect to t. Hence, the polynomial captures the level and the curvature of the function locally. This is much more precise and flexible than using month fixed effects. Formally, we solve the following minimization problem for each date t min f X T s ½Y s À mðsjt, fÞ 2 K h ½s À t where K h [s À t] are Epanechnikov kernel weights with bandwidth h if date s is outside the 2b day window around the event dates and zero else. This also allows us to estimate the polynomial for the dates within that window if the bandwidth is larger than the 2b days. The advantage of this method is that it is less restrictive on the demanded data then the year day fixed effects and offers a more sophisticated deseasonalizing of the data than the paramentric strategy. Yet, the identification is similar to the parametric approach, that is, the nonrandom timing of events is more likely to lead to endogeneity issues than in the strategy with year day fixed effects.

Data
We test the three suggested estimation strategies estimating the effect of fairs on overnight stays in Basel (Switzerland) from 01/01/2015 to 12/31/2019. Fairs are often subsidized events and large  Table 1 provides the descriptive statistics about these fairs. Part B of table 1 contains the descriptive statistics for the overnight stays in the respective period in Basel. The overnight stays are composed of hotels (1 to 5 stars) and other accommodations. The overnight stays in other accommodations more than double from 2016 to 2017 due to the registrations of Airbnb apartments. Since all empirical strategies contain year fixed effects, this is not an identification issue.
Bringing the fair data and the overnight stay data together, we can plot the daily overnight stays as in panel (a) of Figure 2 for 2019. The dark gray bars mark fair dates while the light gray bars mark dates with other events that are likely to influence the number of overnight stays. The solid black lines are the daily overnight stays. One can clearly see that they fluctuate a lot. On the one hand, there is a seasonality, that is, there are more overnight stays in summer than in the winter. Second, there are typically more overnight stays during the week than on weekends. Obviously, there are several peaks of which most seem to coincide with fairs or events. Thus, we have first visual evidence that the fairs actually increase the overnight stays, as do the events. The same holds if we consider the occupancy rate as depicted in panel (b) of Figure 2. We also see that several fairs coincide with occupancy rates above 90% where the overnight stays are close to the overall capacity limit of Basel's accommodation.

Net effects
Panel (a) of Figure 3 presents the results for equation (8) using the natural logarithm of daily overnight stays as dependent variable and with only event controls and a time window of +/À10 days around fairs. The estimate for 0 is b β O 0 and estimates the average percentage effect of fairs on overnight stays for nights between fair days. Hence, it estimates that in these nights the overnight stays increase by 20% compared to nights without fairs. The estimates are also significantly positive up to three days before fairs and as of the third night after a fair. The latter seems surprising but might actually be caused by the nonrandom timing of fairs. Panel (b) of Figure 3 shows the results including additionally year fixed effects, month fixed effects and weekday fixed effects. The results do not change very much except that the lead and lag estimates are smoother.
Controlling by month fixed effects might not be enough because it can neither perfectly capture seasonal pattern nor perfectly address endogeneity issues arising from nonrandom fair dates. Therefore, we also estimate the parametric specification in equation (9) which adds season day fixed effects that can account for any seasonality in the data. Panel (c) of Figure 3 presents the results. Indeed, the positive estimates for the days following a fair disappeared while the fair effect stayed almost the same (17%). The two nights before the fairs are also significantly positive with an increase of 7.7% in nights before fairs and of 4.5% two nights before. We find no significant effect after the fair.
The semi-parametric approach using equation (10) leads to very similar results as panel (d) of Figure 3 indicates. The estimated coefficient during fairs is almost the same as in the parametric specifications and we clearly see significantly more overnight stays the nights before fairs. The positive estimates four days after the fair however indicate that also the semi-parametric approach captures a certain timing effect of fairs. If we estimate the effect using equation (10) but with year fixed effect, the estimated effects get very close to the parametric specification with year day fixed effects as panel (e) of Figure 3 shows. Yet, the point estimate for fair nights is slightly lower.
Overall, one can conclude that a sophisticated process of deseasonalizing is demanded to estimate direct net effects of events. 5 In our application, we prefer the parametric specification with season day fixed effects alone because it puts less restrictions on the size of the estimated time window around fairs 6 and has least restrictive identifying assumptions.

Heterogeneity
The data allows to split the effect into different accommodation categories. Hence, we estimated equation (9) using only hotel overnight stays. The estimates are very similar as using all overnight stays (see panel (a) of Figure 4) which is caused by the fact that overnight stays in other accommodation account for less than 10% of all overnight stays. The estimates using only overnight stays in other accommodations are positive for almost the entire time window as indicated in panel (b) of Figure 4. But the confidence bands are very large such that we would not over interpret the significant estimates at the tails. The effect during fairs is very similar to hotels. Thus, there is no specific accommodation category profiting more or less from fairs.

Robustness
The major identification issue is that fairs are not randomly timed within a year which is addressed by the year day fixed effects. But the re-timing of fairs and the introduction and abolishment of fairs that drive the identification when we use year day fixed effects might neither be random but strategic regarding the overnight stays. To test whether the effects are likely caused by favourable re-timing of fairs, we performed a bootstrap analysis: We randomly retimed the fairs within each year keeping their duration constant and estimated equation (9). We repeated this procedure 1000 times and plotted the distribution of the estimates for the nights between fair days, b β 0 , in Figure 5. The effects are centred around zero. The red line plots the actually estimated effect of 17%. All bootstrap effects are far below the estimated effect. Hence, we can rule out that our results are driven by strategic re-timing of fairs.

Substitution effects
The estimated effects in the results section are direct net effects which only equal the gross effects if there are no substitution effects. Our model however suggested a crowding out of leisure tourists during fairs. Hence, in this section, we estimate the magnitude of these substitution effects which allow us to assess the error using direct gross effects as an input for an economic effect analysis instead of direct net effects. First, we annualize the results from estimating equation (9) in levels applying the following calculation The result is a net effect of 66,500 additional overnight stays per year as presented in Table 2. The gross and substitution effects are estimated using two different methods: In method 1, the gross effect is calculated as 21% of the annual overnight visitors following the official statistics (BHP -Hanser und Partner AG, 2016) resulting in 275,415 overnight stays due to fairs. Hence, 208,915 overnight stays only substitute other overnight stays.
In methods 2a) and b), we estimate the substitution effect indirectly by exploiting data of the usage of the Basel Card which each legal overnight guests receives. The Basel Card grants discounts at various attractions in Basel. Each time the card is used it is scanned. The data at hand contains every single use of the Basel Card from 01/01/2018 to 05/14/2019. 7 If we assume that the fair visitors do not have any demand for attraction visits (α(k = 1) = 0) and that the different types of overnight visitors that usually visit Basel are equally likely to be substituted by fair, the effect on attraction visits reflects the substitution effect for overnight stays as derived in equation (7). Panel (a) of Figure 6 presents the results of estimation equation (9) using the natural logarithm of the usage of the Basel Card as dependent variable. Panel (a) of Figure 6 refers to method 2a) and shows that the attraction visits decrease two nights before fairs up to À30% on fair days. Applying equation (13) to the estimates for the attraction visits leads to an estimated substitution effect of À82,384 visitors. This implies that the gross effect is 148,885 which is much lower than the official statistics.
The assumption that fair visitors do not visit attractions does not entirely hold, since for example, during the art fair, museums are rather complements to the fair. Hence, panel (b) of Figure 6 refers to method 2b) and plots the effect only for the zoo, which is least likely to be visited by fair guests, that is, we can assume that (α zoo (k = 1) = 0). This is also reflected in the larger effect on fair days which is almost À50%. 8 Applying equation (13) to the estimates for the zoo visits leads to an estimated substitution effect of À185,032 visitors. This implies that the gross effect is 251,532 which almost matches the official statistics from method 1.
Thus, the direct gross effect of fairs on overnight stays in Basel is about four times the net effect. Three fourth of the overnight stays only substitute other overnight stays. This demonstrates the importance also distinguishing between net effects and gross effects (impact and contribution) when Notes: The net effect is the annualized cumulative net effect over all fairs including the +/À10 days window around the fairs from the estimation of equation (9). Method 1: The gross effect is calculated as 21% of the annual overnight visitors following BHP -Hanser und Partner AG (2016). Method 2a): The substitution effect is the annualized cumulative net effect over all fairs including the +/À10 days window around the fairs from the estimation of equation (9) using the logarithm of attraction visits by overnight guests as dependent variable. Method 2b): The substitution effect is the annualized cumulative net effect over all fairs including the +/À10 days window around the fairs from the estimation of equation (9) using the logarithm of zoo visits by overnight guests as dependent variable.
estimating the direct effect of events. Every CGE model based estimation based on the gross effects would by far overestimate the indirect impact.

Discussion
The empirical results indicate that the overall demand for overnight stays increases during fairs as predicted by the theoretical considerations. The model suggests that the overall effect is combined of a positive effect on the demand of business tourists and a negative effect on the demand of leisure tourists (substitution effect). The empirical results confirm both effects and quantify their relative size. The substitution effect of the leisure tourists is about 75% of the gross effect on business tourists. Hence, we see that during fairs there is a substantial crowding out of leisure tourists in cities. Yet, the empirical results also show that business tourist visiting fairs engage in leisure activities during fairs. This conclusion follows from the fact that we see a drop in the overall attraction visits during fairs that is smaller than the drop in the zoo visits which is arguably a very unlikely activity for business tourists. Hence, we can provide evidence for bleisure tourism taking place during fairs. We can also see that the demand increases prior to the fairs but not thereafter. If we consider the patterns of the effect on the attraction visits, we clearly see that this increase in overnight stays already goes along with a substitution of leisure tourist prior to fairs. The relative sizes prior to fairs are similar to those during fairs although the absolute sizes are smaller. Hence, this increase is caused by business tourists attracted by the fairs 9 that arrive early. The results on attraction visits also show that they engage in leisure activities prior to the fairs. But the fact that the relative sizes of these effects are constant means that they rather have the same share of leisure consumption prior to the fair than during the fair. This means that they do not arrive early in order to consume leisure activities prior to the business activities. Thus, the extension of the stay takes place only prior to fairs and is likely primarily motivated by business motives related to the preparation of the fairs and not by leisure motives alone because otherwise we would also observe positive effects after fairs.

Conclusion
In this paper, we studied the current methodological developments in assessing the economic impacts of tourism and touristic events. We showed that although there has been a lot of progress in estimating the indirect effects in recent years (see e.g. Dwyer, 2015;Kronenberg et al., 2018), there is less progress in the methods estimating the size of the initial shock, that is, the direct economic effect (see e.g. Notes: This table presents the estimates of the average percentage effect of fairs on overnight stays in Basel from 01/01/2015 to 12/31/2019. À1 refers to the night before a fair and +1 to the night following the last fair day. 0 refers to nights between two fair days. Year day clustered standard errors in parentheses. Significance levels: *p < 0.10, **p < 0.05, ***p < 0.01. Figure 7. Further results. Kim et al., 2015). Usually, literature regards gross effects from survey data as the initial shock (see e.g. Kim et al., 2015;Kronenberg et al., 2018;Van Wyk et al., 2015) but if it does not equal the net effect it has the potential to severely overestimate the direct effect and the indirect effect which is a function of the direct effect. Therefore, we present a quantitative model of event tourism demand in cities that can distinguish primary motives of tourists while allowing for secondary motives. The model predicts positive overall effects of fairs on overnight stays but a substitution of leisure tourists while the effects on attraction visits depends on the degree of leisure activities of the attracted fair visitors. Furthermore, we derive three methods based on event study design (see e.g. Schmidheiny and Siegloch, 2019) that allows to study economic net effects of events using high frequency data: A parametric approach with month and week fixed effects, a parametric approach with year day fixed effects and a semi-parametric approach with and without year day fixed effects. The combination of the estimation methods with the model allows to estimate the substitution effects. We test the methods studying the direct net effect of fairs on overnight stays and attraction visits by overnight visitors in Basel. We show that a sophisticated method of deseasonalizing is needed to estimate direct net effects, that is, the specifications with year day fixed effects deliver more plausible results under less restrictive assumptions. While the parametric approach with month and week fixed effects delivers partly implausible results, the semi-parametric approach with month and week fixed effects might be suitable also for shorter time-series.
We find that fairs in Basel increase the overnight stays in nights between fair days on average by 17% and by 8% and 4% in the preceding nights. They do not affect the overnight stays the nights following fairs. We observe that business tourist also consume a certain amount of leisure activities during and before fairs; thus, we can confirm parallel bleisure tourism. However, the observed consumption patterns are not in line with business tourists attending fairs and extending their stay primarily due to leisure motives. Robustness checks indicate that our results are unlikely to be generated by favourable fair dates that accidentally coincide with visitor peaks.
Using two different methods, we demonstrate that the gross effect of fairs on overnight stays in Basel is about four times the net effect depending on the underlying assumptions. This ratio is quite large and might be lower for other direct economic effects like restaurant visit. It is also likely to be lower if one incorporates price effects. But we can clearly reject the assumption of the absence of price and substitution effects is made by traditional approaches for estimation direct economic effects. Thus, a clear distinction between net and gross effects is demanded also in the first stage of the estimation of economic effects of events in the case where events are large compared to the local capacities.
The method introduced in this paper is suitable for studying any direct economic effects of events but it is demanding on the respective data: For a comprehensive economic analysis, one needs daily data on all relevant economic outcomes. Recent developments are in digitization make such data more and more available. Future research therefore should focus on new data sources that can be exploited to more adequately estimate direct economic effects of tourism or events.