*4.2. The Models*

Based on the analysis of Stabler et al. (2009), the assumption was that the use of campsites in Norway (V) depends on the exchange rate, GDP, and season.

$$\mathbf{V} = f(\text{Exchange Rate, GDP, seasonality}) \tag{1}$$

Some researchers have analyzed the effect of changes in the exchange rate by using effective exchange rates, which refers to nominal values adjusted for differences in inflation rates among countries Lee et al. (1996). Especially in the long run, it is more accurate to take into account changes in the consumer price index in different countries Stabler et al. (2009); Syriopoulos (1996). In this study, the effective exchange rate (EER) was used:

$$\text{EER}\_{i} = \frac{\text{CPI}\_{i}}{\text{CPI}\_{j} \cdot \text{ER}\_{ji}} = \frac{\text{CPI}\_{i}}{\text{CPI}\_{j}} \cdot \frac{1}{\text{ER}\_{ij}} = \frac{\text{CPI}\_{i}}{\text{CPI}\_{j}} \cdot \text{ER}\_{ji} \tag{2}$$

The logarithmic transformation of EER*<sup>i</sup>* is:

$$\ln(\text{EER}\_{i}) = \ln(\text{CPI}\_{i}) - \ln(\text{CPI}\_{j}) + \ln(\text{ER}\_{ji}) \tag{3}$$

where CPI is the consumer price index, ER is the nominal exchange rate, *i* denotes country *i*, *j* denotes country *j*, and ER*ji* is the nominal exchange rate for country *j* relative to country *i*.

The effective exchange for the country of origin is the consumption price of the origin country divided by the consumption price at the destination, and this price level is multiplied by the exchange rate between the destination country and country of origin. This can be written as the rate between the consumption price at the origin and destination countries multiplied by the exchange rate between origin and destination countries. Tourist inflow is a dynamic process. To capture the dynamic structure of the dependent variable, it is quite common to use autoregressive distributed lag models (ADLs) with lagged dependent and explanatory variables, as in Song et al. (2003); Brooks (2019). In this study, there was a lag of one and two months for overnight stays.

For hotels, German tourists book their visits more than 150 days in advance, while Swedes book their stays less than 100 days before their arrival in Norway Innovation Norway (2019). This effect is at least as likely to apply to overnight stays at campsites. Similar to Aalen et al. (2019), this study used an average of 4–6 months as the time lag before entry for the value of the exchange rate. In line with the international literature Sanchez-Rivero and Pulido-Fernández (2020), the chosen model is presented in logarithmic form:

$$\begin{aligned} \ln(\mathcal{V}\_{it}) &= \pi\_0 + \mathfrak{a}\_1 \ln(\text{GDP}\_{it}) + \mathfrak{a}\_2 \ln(\text{EER}\_{i, t-\log}) + \mathfrak{a}\_3 \ln(\text{EER}\_{ij, t-\log}) \\ &+ \quad \Sigma\_{k=2}^{12} \delta\_k \text{M}\_{kt} + \beta\_1 \ln(\mathcal{V}\_{i, t-1}) + \beta\_2 \ln(\mathcal{V}\_{i, t-2}) + \lambda \text{YEAR2013} + \mathfrak{e}\_{it} \end{aligned} \tag{4}$$

V*it* is the overnight stay in Norway by visitors from country *i* (*i* = 1: Sweden, 2: Germany) in month *t*. GDP*it* is gross domestic product for country *i* in month *t* (GDP is interpolated linearly from a yearly to a monthly basis). EER*i*,*t*−*lag* is the effective exchange rate between the country of origin and Norway. EER*ij*,*t*−*lag* is the effective exchange rate between the country of origin and an alternative destination (country). *k* is a dummy variable for month number k, where January was the reference group in this regression. Due to a change in registration in 2013, the data for 2013 were not comparable to the data for the previous year. This was addressed by using the dummy variable Year 2013. In Equation (5), *t* is the month of arrival (from 2000 to 2019).

We further assumed that the exchange rate in Sweden can influence the tourist inflow from Germany and vice versa. Therefore, the variable ln(EER*ij*) was included in the model.

The model for Sweden and Germany can be formulated based on Equation (5). The model for Sweden (Country 1) is:

$$\begin{aligned} \ln(\mathbf{V}\_{1t}) &= \; \boldsymbol{\mu}\_{0} + \boldsymbol{\mu}\_{1} \ln(\mathbf{GDP}\_{1t}) + \boldsymbol{\mu}\_{2} \ln(\mathbf{EER}\_{\text{SEK,NOK,t-lag}}) + \boldsymbol{\mu}\_{3} \ln(\mathbf{EER}\_{\text{SEK,euro,t-lag}}) \\ &+ \; \boldsymbol{\Sigma}\_{\text{k}=2}^{12} \delta\_{\text{k}} \mathbf{M}\_{\text{kt}} + \beta\_{1} \ln(\mathbf{V}\_{1,t-1}) + \beta\_{2} \ln(\mathbf{V}\_{1,t-2}) + \lambda \mathbf{YEAR2013} + \boldsymbol{\varepsilon}\_{1t} \end{aligned} \tag{5}$$

and the model for Germany (Country 2) is:

$$\begin{aligned} \ln(\text{V}\_{2t}) &= \, \_0\text{a}\_0 + \mathfrak{a}\_1 \ln(\text{GDP}\_{2t}) + \mathfrak{a}\_2 \ln(\text{EER}\_{\text{euro}, \text{NOK}, \text{t-lag}}) + \mathfrak{a}\_3 \ln(\text{EER}\_{\text{euro}, \text{SEK}, \text{t-lag}}) \\ &+ \, \_2\text{\Sigma}\_{\text{k}=2}^{12} \delta\_{\text{k}} \text{M}\_{\text{k}t} + \beta\_1 \ln(\text{V}\_{2, t-1}) + \beta\_2 \ln(\text{V}\_{2, t-2}) + \lambda \text{YEAR2013} + \epsilon\_{2t} \end{aligned} \tag{6}$$

The ADL models were estimated using ordinary least squares (OLS), which leads to consistent estimators under classical OLS assumptions. A move from a static to dynamic model will often result in the removal of residual autocorrelation. To account for autocorrelation, our model is presented with lagged dependent variables for two periods. If there is still autocorrelation in the residuals of the model after including lags, then the OLS estimators will not be consistent Brooks (2019). We tested for autocorrelation by using the Breusch–Godfrey test Brooks (2019).

We further tested for heteroscedasticity using the Breusch–Pagan test Wooldridge (2020). In the presence of heteroscedasticity, the standard errors may be wrong, and hence, any inference made could be misleading. We therefore used heteroscedasticity-consistent robust standard errors in the case of significant heteroscedasticity.

We checked for multicollinearity using bivariate correlations and variance inflation factor (VIF) indices. If VIF indices are above 10, then we often conclude that multicollinearity is a "problem" for the estimated regression coefficients. However, a VIF above 10 does not mean that the standard errors of the estimated regression coefficients are too large. Therefore, the size of the VIF is of limited use Wooldridge (2020).
