Economic Valuation of Lake Tana: A Recreational Use Value Estimation through the Travel Cost Method

Abstract

Lake Tana is a well-known tourist spot in northern Ethiopia that lures both domestic and foreign tourists. The lake’s value is still underrated, despite the site’s immense potential for recreation and tourism. In this study, the recreational value of Lake Tana is estimated, and the consumer characteristics associated with recreational demand are analyzed. The study employs a Zero-Truncated Poisson (ZTP) regression model for data generated by the Individual Travel Cost Method (ITCM) and draws information from 1094 on-site surveys. According to ZTP regression results, variables that are significantly and positively associated with demand for Lake Tana recreation include the monthly income and age of the visitors and their preference for other recreation destinations such as Tis-Abay and Gondar Fasiledes Royal Castle. However, respondents’ leisure time, overall cost, and residential distance from the recreational site are all negatively associated with the demand for recreation. It is also evident that Lake Tana is endowed with a wealth of attributes, ranging from natural beauty to ancient religious and cultural heritages, making the lake a highly desirable recreation destination. According to the estimation, Lake Tana has a yearly recreational value of around USD 68.5 million. However, it also demonstrates that if lake settings were to improve in quality, the value of Lake Tana would rise considerably, reaching USD 151 million. The value of sentimental attachment implies that determining Lake Tana’s recreational value is a key element in the resource’s sustainable utilization and management. To make greater use of Lake Tana’s recreational amenities, however, uncontrolled waste disposal, favorable recreation facilities, and the spread of water hyacinth should be addressed immediately. Furthermore, it is imperative to maintain the lake’s diverse attributes, as the integration of these attributes is what gives the lake its primary appeal.

1. Introduction

Lake Tana is included as one of UNESCO’s biosphere reserve sites due to its global significance [1]. Lake Tana’s condition is in rapid decline as it struggles to accommodate population- and climate-driven pressures [2,3,4,5]. Unfortunately, the attention paid to the lake’s overall benefits and sustainability is far from what is expected; research so far has mainly focused on its hydrological and ecological aspects, with much less emphasis being placed upon the lake’s economic aspects and recreational benefits [6,7,8].

A careful assessment of its worth must be considered when making decisions to ensure equitable use in the present and future [9,10,11,12,13]. The multiple benefits that Lake Tana provides include water for agriculture, electricity, transportation, fisheries, ecosystem services, recreational services, and so on [8,14,15,16]. It is critical that Lake Tana remain viable in order to preserve ecological balance and human wellbeing.

The recreational benefit of Lake Tana is a major component of its total value due to its diverse aesthetic attributes, which include not only the lake’s larger body of water but also the crossing of the Blue Nile, island churches and forests, fauna, and wetlands, as well as transportation services available around it [8,14,17,18]. All of these have become increasingly galvanized tourist attractions over time yet remain underappreciated when it comes to their values being incorporated into decisions related to conservation efforts and resource management. This is because traditional market assessment methods place a strong emphasis on directly traded goods or services instead of non-market values, resulting in an underestimation of what a total value would show for this resource [9,19,20]. As a result, traditional market-based models fail to capture all of Lake Tana’s values [20,21,22].

To better support efficient decision making for a more sustainable lake, there is a need to substitute the traditional market-oriented valuation approach for a more inclusive total economic valuation (TEV), which provides an all-round view of the value of resources through non-market resource valuation techniques [9,21,23]. Availing TEV through assessing the lake’s recreational use value will result in a better understanding of the total value provided by the lake [24,25,26], allowing for more effective and sustainable resource use and management [12,15,19]. More importantly, the recreational services related to Lake Tana are non-rivalry services and hence do not compete with other water uses [6,7,27,28,29].

As a result, the study’s objective is to determine consumer characteristics related to recreational visits to Lake Tana and estimate its recreational value through ITCM using actual and hypothetical visitor behavior data [30,31]. According to our knowledge, this is the first study of its kind on Lake Tana and the second in Ethiopia that integrates augmented ITCM with standard ITCM for the assessment of recreational sites after estimating the recreational value of Lake Tana [5,31,32,33].

2. Literature Review

2.1. Economic Valuation Technique

The travel cost method (TCM) is widely applied to determine the economic value of recreational sites because travel costs are one of the main factors affecting a person’s decision to take a trip, among other things [34,35]. TCM is among the earliest-revealed preference approaches and is the most commonly used model of environmental valuation, especially in the valuation analyses of recreational sites [26,34,36,37]. Though its roots can be traced back to Harold Hoteling’s thoughts from 1947, the TCM has been institutionalized since the completion of research undertaken by Trice and Wood [38] and Clawson and Knetsch [39].

The TCM computes the “derived demand” for recreational sites based on the number of visits to a site and the price associated with consumer access to it [9,36,40]. The cost of travel is taken as the revealed WTP of consumers for access to the site and is used as a proxy for the recreational value, assuming that the associated expenditures reflect at least the minimum amount of a visitor’s WTP [9,41]. Some scholars have drawn attention to the possibly weak complementarity relationship between a natural site’s recreational services and the associated cost of using it [42]. Although the approach is primarily linked to the revealed behavior and attitude of visitors in the context of actual visits [30,43], there are numerous empirical frameworks linking the TCM with data from contingent valuation methods in relation to the site’s attribute quality changes [33]. The contingent version of the TCM is an extension of the basic TCM and aims to capture the intended trips visitors would take under hypothetical scenarios, enabling researchers to create both hypothetical (stated) valuation figures as well as revealed WTP estimates using actual travel patterns [33,44,45]. The frequency of trips and the cost of travelling to the site provide information on the “quantity demanded” and the “inherent price” of the site for both actual and stated TCM techniques [11].

The individual and zonal demand approaches (ITCM and ZTCM) are two variants of the TCM. The ITCM assesses the number of recreational trips made by individual users to a recreational area each year, taking into account visitor’s various travel expenses, while the ZTCM examines the number of recreational trips made by the population of a specific region or zone [46]. The ITCM uses a more thorough visitor survey to take into account each visitor’s various travel expenses, which helps account for differences in travel costs among visitors [47,48]. The ITCM is more suitable for distinct visitor behavior and characteristics related to the use of a recreational area [49]. Therefore, the recreation-related use value of Lake Tana is estimated using ITCM.

2.2. Count Data Estimation

Recreational trips generate count data (observations with only nonnegative integer values between zero and a higher unknown number are referred to as count data, resulting from an underlying count procedure that takes place over time [50,51]) with non-negative integer values. Unlike the modeling of continuous data, treating count data with linear modeling results in biased estimation. In order for an estimation to be consistent, efficient, and unbiased, models such as Poisson, negative binomial, Poisson inverse Gaussian, Greene’s three-parameter negative binomial, and generalized Poisson (GP) are frequently taken into account on the basis of the probability distribution function of the specific set of count data. The selection of an appropriate count model depends on the basic assumptions associated with the nature of dispersion, the absence or presence of zeros in the count data, and whether zero counts are more or less frequent than expected [50,51,52].

In cases where there is no possibility of zero counts in the data set and a significant difference between the mean and variance is not achieved (where there is no overdispersion or, in some cases, underdispersion), the normal Poisson and negative binomial models cannot handle the data appropriately. Instead, with a required amendment, a zero-truncated Poisson is a recommended modeling approach [51,53]. Data from on-site surveys of recreation sites often exclude zero counts from the data mix [51,54,55]. As a result, recreational site valuation studies where the data source is based on on-site surveys use ZTP regression analysis [51,55,56,57].

Using ordinary least squares (OLS) to estimate regression parameters for on-site, survey-based recreation modeling is not supported by the literature due to truncation bias. The estimates may overestimate the underlying level of consumer surplus (CS). To handle this issue, the maximum likelihood estimation (MLE) procedure is used to estimate zero-truncated Poisson regression [48,50].

3. Materials and Methods

3.1. Description of the Study Area

Lake Tana is a heart-shaped lake situated in the northwest region of Ethiopia and is the largest and most enormous lake in Africa (Figure 1).

It is a rich sub-basin with abundant water resources and has great potential for hydropower, irrigation, tourism, transportation, and biodiversity [8,58,59]. The lake has over 45 islands, and 19 of them are the home to monasteries and/or churches of the Ethiopian Orthodox Tewahido Church. A thorough description of the lake is provided in

Table 1. Description of Lake Tana with respect to main physical variables (adopted from McCartney et al. [6] and Anteneh et al. [58]).

Description	Magnitude
Location	1203′64.34″ N, 3732′04.88″ E
Altitude	1786 m
Length (Maximum)	84 km
Width (Maximum)	64 km
Depth	8 m mean and 14 m maximum
Volume	Approximately 28 km3 at 1786 m
Surface area	Approximately 3200 km2
Catchment area	Approximately 15,321 km2

.

The local climate is highly influenced by the inter-tropical convergence zone’s movement, which causes a seasonal rainy period between June and September. The lake is a source of the Blue Nile, with nearly 93% of the water coming from four major rivers: the Gilgel Abay, the Ribb, the Gumara, and the Megech. Forty tributaries also feed the lake [6,8,59]. The lake’s water level usually ranges from 1785.75 to 1786.36 m above sea level, with seasonal and annual variations occurring before the Chara-Chara weir was built. There is roughly 1326 mm of rainfall on average per year. Over 1675 mm of water evaporation occurs on the lake’s surface annually. The seasonal variability in flow has been greatly reduced since the dam became fully operational in 2001 [59,60].

Apart from the riparian area’s population, there are thought to be 15,000 people across all the islands of the lake. According to the CSA [61], the majority of the inhabitants’ livelihoods depend largely on agriculture and fish production [8,62]. Due to its high habitat heterogeneity, the lake supports high biodiversity. The lake is designated as a biosphere reserve site by UNESCO due to its rich biodiversity [1]. The lake is home to about 65 different fish species, of which around a quarter are endemic. The lake is thought to host at least 20,000 water birds and is home to at least 217 various bird species [63].

Lake Tana and its surroundings are endowed with many religious, cultural, and natural attractions. These include the monasteries and churches from the thirteenth and fourteenth centuries, which are situated on the lake’s islands and peninsulas and are home to a variety of treasures, including lovely wall paintings, icons, parchment manuscripts, scrolls, and the treasures of the emperors. Even the Ark of the Covenant was once kept temporarily in one of the monasteries. Consequently, these acted as galleries for the artwork of the Ethiopian Church and the emperors’ valuable assets [64].

Lake Tana is also a popular tourist destination, with Tis-Abay waterfall located in close proximity to its outflow [5]. As a result, the site is popular with tourists. According to the recent report (2016–2019) (due to the global COVID-19 pandemics since 2019, followed by the northern-Ethiopian conflict, we did not assume that data from these years reflected the actual image of the site, so we excluded these years’ information from use in our research work) from [64], the estimated average number of visitors of the site is close to 359,066 people each year, generating over USD 15,223,421 in annual revenue, of which the highest number of visitors and highest revenue were recorded to be 453,434 and USD 18,178,464, respectively, during the 2019 fiscal year. The location is also notable for giving local tour guides, craftsmen, and related service providers a way to make a living. The aim of this research is to improve our comprehension of the recreational value of Lake Tana using a mixture of quantitative and qualitative data gathered from site visitors [64].

3.2. Methods

3.2.1. Sample Size and Sampling Technique

Both primary as well as secondary sources of data were employed in this study; however, it focused mostly on using quantitative and qualitative primary data obtained through in-person interviews. Prior to the primary survey, a pilot pretest was conducted on 30 randomly chosen visitors to Lake Tana to improve the draft questionnaire’s clarity and enhance the response rate and accuracy for the entire survey [65,66]. A three-stage sampling procedure was then used to carry out the whole survey [67], sampling over various months of the year, various days of the week, and various subsets of particular respondents [67,68]. Based on how visitors were distributed across the months of 2019, we first divided the year’s months into three groups: the peak period, the middle period, and the low period of visits [64]. Thereafter, we randomly chose one month from each time frame: March for the low, July for the medium, and November for the peak categories. Since there are fewer and less diversified visitors to the lake from Monday through Friday, we only collected data from weekend visitors for the three months. As the anticipated visitor population of Lake Tana is unknown, the minimal necessary sample size “n” was computed using Equation (1) on the basis of the Cochran sampling formula for an infinite population size [68].

$$\mathrm{n}=\frac{{\mathrm{Z}}^2\mathrm{P}(1-\mathrm{P})}{{\mathrm{e}}^2};$$

(1)

where “n” denotes the required minimum sample size, Z = 1.96 denotes the Z-score, P = 0.5 denotes the estimated population ratio of the desired attribute, P(1 − P) is the estimated population ratio of the desired attribute, and e = 5% denotes the margin of error. The Cochran sampling algorithm produced a minimum sample size of 385 respondents. However, a small sample size is not advised for regression analysis using the ZTP technique. (A truncated set of data is a piece of a data distribution that is above or below a specific number, and in order to estimate data without zero counts, a zero truncated model is used [51]) [69]. Because of this, we targeted these selected three months separately, resulting in a large sample size [70], and using an on-site random intercept sampling procedure, we selected 385 sample respondents from each month for a total of 1155 sample respondents [71]. After receiving the respondents’ informed consent, the survey was carried out voluntarily. A viable sample size of 1094 survey respondents were left after 61 sample respondents’ questionnaires were ruled invalid due to missing data and consequently excluded from the study. This sample size was used consistently throughout the data analysis process.

A combination of descriptive and inferential statistics was used in the subsequent data analysis process using Stata 16.0. In order to verify the validity and reliability of the data collection instruments, findings from the pretest survey and the full survey were compared [66]. The outcomes demonstrate that the data collection instruments produced consistent results.

3.2.2. Model Specification

Using the principle of consumer utility maximization and inferring a revealed demand curve, TCM estimates the economic value of a resource. The first supposition is that an individual must decide whether to consume non-market environmental products by choosing to pay the market price of travel in order to visit a recreational site. The consumer (i) will therefore have a utility function (U) that contains a market good vector (X) and a non-market environmental goods vector (Q) [42].

U_i = f(X_i, Q_i)

(2)

Equation (2)’s vector of non-market environmental goods may constitute a variety of value elements, including a recreation value (Y) and other non-market values (q). Therefore, the utility maximization function of an individual can be further described as U_i = f(X_i, Y_i, q_i).

However, we place a greater focus on the resource’s recreational value (Y). This value is influenced by the recreational site’s quality, but it may also be related to consumer characteristics such as the value of the traveler’s time, the distance traveled, their income, their access to other recreational options, and so forth.

We assume that each visit to the recreation site is limited by time (T) and income (I) [42,54]. An individual’s income (I) is given by I = I₀ + wT_w, where I₀ = non-wage income, w = wage rate, and T_w = work hours, and it can be used to purchase market goods or to access recreational services. Time (T), which can also be decomposed into two categories, leisure/recreation time (Ty) and work time (Tw), is another constraint on an individual. The wage rate in this case is used to approximate the opportunity cost of recreation time. In order to maximize the utility function within their time and financial constraints, visitors choose from j alternative leisure pursuits. As a result, the utility function Ui = f(Xi, Yi) is optimized under the constraints of total income I = PxX + PyY and time T = Tw + Ty, where Px is the price of market products, Py is the cost of recreation, Tw is the amount of working time, and Ty is the amount of time spent recreating. These limitations can be revised as I₀ + wT − (wT_y + P_y)Y − P_xX = 0 by further rearrangement and simplification.

The partial effects of each variable in the visitor’s utility maximizing equation can be calculated by formulating the Lagrange equation (L) (L = u(X_i, Y_i) $\pm$ λ (I₀ + wT − Y_i(wT_y + P_y) − P_xX_i)) based on the utility and constraint equations. Through the first-order conditions, we can derive the Marshallian demand functions X_i = g(P_x, P_y, I) and Y_i = f(P_x, P_y, I) for market goods (X) and recreational services (Y), respectively [26,42,43,54].

The demand function for recreational services is the observed and relevant Marshallian demand function for our purposes. We can further differentiate between j for various anticipated recreational site quality improvement scenarios (such as improvements to the intrinsically diverse attributes of the resource, associated infrastructure, and services, etc.), resulting in X_i = g(P_x, P_y, I, q_j) and Y_i = f(P_x, P_y, I, q_j).

Hence, the site’s valuation entails estimating the demand and factoring out the associated CS of recreation under the two scenarios of the lake: the status quo level and anticipated quality changes [11,37,43].

3.2.3. Model Estimation: Zero-Truncated Poisson Model

The frequency of visits to the recreation area is an integer that is not negative, and it produces count data that follows the Poisson distribution [46,48,54,72]. Depending on the degree of data dispersion, the two most popular count data models are the Poisson and negative binomial regression models [73]. However, count data, which fundamentally excludes zero counts, are incompatible with standard Poisson and negative binomial distributions and even the Poisson inverse Gaussian distribution, which all include zeros. Surveys conducted “on site,” where respondents are actual visitors and must, by necessity, have at least one trip count in the set of data, are an example of count data that, by their very nature, preclude zero counts.

The zero-truncated count model is an econometric model that accommodates data with missing zero counts [51,52,53]. Given that Pr[Yi > 0] is the probability that an individual has experienced recreational trips, the conditional density function becomes g(Yi/Yi > 0) = (g(Yi))/(Pr[Yi > 0]), where Yi is the number of trips taken for recreation by visitor i. The zero-truncated model’s density function can be integrated into one through normalization by the likelihood of a positive observation [46]. Count data are often found to be over-dispersed in the practical field because the variance of the data is higher than the mean [51,52], which requires an appropriate test of hypothesis. Our count data from Lake Tana recreational trips had a variance of 2.61 and a mean of 2.03 trips per respondent. Statistical tests (the chi-square goodness-of-fit test and Akaike’s and Schwarz’s Bayesian information criteria (AIC and BIC) test) were used to examine the data’s apparent overdispersion. However, the test rejected the over-dispersion hypothesis, and as a result, unbiased estimations were produced using Stata 16.0’s ZTP regression model with the vce (robust) option [43,46,53].

The likelihood of a zero count, according to the Poisson log-likelihood function L (μ; y) $={\sum }_{\mathrm{n}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{i}}\mathrm{l}\mathrm{n}({\mathsf{\mu }}_{\mathrm{i}})-{\mathsf{\mu }}_{\mathrm{i}}-\mathrm{l}\mathrm{n}\left({\mathrm{y}}_{\mathrm{i}}!\right)$ is exp (−μ), where µ is the intensity or rate parameter [51,52]. The value of a zero-count probability (exp (−μ)) is subtracted from 1 to exclude the probabilities of zero counts from the probability distribution function, and by dividing the probability distribution function by 1−exp(−μ), the residual probabilities are rescaled.

$$\mathrm{F}(\mathrm{y};\mathsf{\mu })=\frac{{\mathrm{e}}^{-{\mathsf{\mu }}_{\mathrm{i}}}{{\mathsf{\mu }}_{\mathrm{i}}}^{{\mathrm{y}}_{\mathrm{i}}}}{1-\exp (-{\mathsf{\mu }}_{\mathrm{i}})){\mathrm{y}}_{\mathrm{i}}!}$$

(3)

Equation (3) allows the exclusion of zero counts from each portion of the Poisson probability distribution function. By using μ = exp(xβ), the resulting log-likelihood function is displayed in Equation (4).

$$\mathrm{L}(\mathsf{\mu };{\mathrm{y}}_{\mathrm{i}}/{\mathrm{y}}_{\mathrm{i}}>0)=\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)={\sum }_{\mathrm{n}=1}^{\mathrm{n}}\left\{{\mathrm{y}}_{\mathrm{i}}\right({\mathrm{x}}_{\mathrm{i}}^{\prime }\mathsf{\beta })-\mathrm{e}\mathrm{x}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}^{\prime }\mathsf{\beta }\right)-\mathrm{l}\mathrm{n}\mathsf{\Gamma }\left({\mathrm{y}}_{\mathrm{i}}+1\right)-\mathrm{l}\mathrm{n}[1-\exp \left(-\exp ({\mathrm{x}}_{\mathrm{i}}^{\prime }\mathsf{\beta }\right))]\}$$

(4)

Thus, the ZTP model is estimated by the full maximum likelihood algorithm of the xβ parameterization instead of the $\mathsf{\mu }$ parameterization of a General Linear Model (GLM) [51,52].

3.2.4. Model Variables: Variable Description and Expected Signs

Among the variables in our model are a combination of respondents’ socioeconomic variables and site-related variables.

In our ITCM regression analysis, the dependent variable is the count of trips made for recreation to the lake by each respondent (Yi). This reflects people’s willingness to travel to use a recreational service while keeping their budget constraints in mind [46]. The number of recreation trips that visitors take at a specific price level is the quantity demanded of the site’s recreation service and is often known as “recreation demand.”

Travel cost (Tc), which is the total of all expenses for the recreational trip from the outset of the journey to the end of the visit and vice versa, is the primary explanatory variable in the analysis. It includes several cost elements such as travel, lodging, and the opportunity costs of time. For round trips to and from Lake Tana, significant transportation costs are involved, including boat transportation along the entire body of the lake. Additional accommodation expenses include those for hotel lodging and meals, as well as admission fees for the lake itself and other associated services. The opportunity cost of time is evident, and it may be roughly calculated by dividing the round-trip travel time by one third of the respondent’s projected hourly salary [71,74]. The aggregate of all estimated and measured costs is the total travel cost. According to Poor and Smith [75] and a number of other, later studies, the demand for recreation is inversely related to recreation costs, as indicated by the travel cost estimate. Consequently, its sign is anticipated to be negative and significant [25,55,75,76,77].

Our model also takes into account the visitors’ age, sex, location in relation to the site, level of income and education, travel history, free time, and access to alternative recreation sites as potential extra-explanatory variables (

Table 2. Descriptions and expected effects of explanatory variables.

Variable	Description	Measure	Expected Effect
Travel cost (Tc)	Visitor’s travel cost, measured and treated in a continuous form	Total cost of visitation expenditure in USD	−
Age (Ag)	Age of visitors, measured and treated in a continuous form	Visitor’s age in number of years	−/+
Sex (Sx)	Visitors’ sex as a dummy variable	0 = female, 1 = male	−/+
Distance (Dst)	Visitors’ distance from the site, measured and treated in a continuous form	Distance of visitor’s residence to the lake in kilometers	−
Income (I)	Visitors’ monthly income, measured and treated in a continuous form	Monthly income in USD	+
Education (Educ)	Visitors’ education status, measured and treated in a categorical form	0 = basic, 1 = intermediary, 2 = advanced	+
Trip experience (Te)	Visitors’ trip experience, measured and treated in a continuous form	Frequency of trips to the site throughout a visitor’s lifetime	+
Leisure time (Lt)	Leisure time of visitors, measured and treated in a continuous form	Free/leisure time of a visitor in number of days per year	+
Alternative recreation site (Ars)	Access to alternative recreation site measured through access cost: Tis-Abay waterfall (Ars-Tawf), Gondar fasiledes royal heritage (Ars-Gfrh), Saint lalibela rock church (Ars-Slrc) and Semein mountain national park (Ars-Smnp)	Total expenditure of visitor to these alternative sites in USD	+
Attribute (Atr)	Distinguishing features or characteristics of the lake: attribute diversity (the monasteries, churches and forests of the islands and Peninsulas, birds, hippos, availability of cultural handcrafts, the moment of Abay River flowing across the lake, etc. = Atr-Diversity) Recreation facility (availability of transport access, hoteling service, beaches, etc. = Atr-Facility) Relative proximity with alternative sites (Tis-Abay, Gondar, Lalibela, Semien mountain = Atr-Proximity)	0 = Atr-facility, 1 = Atr-diversity, 2 = Atr-proximity	+

).

With the factors taken into account in the model, the Lake Tana’s recreation trip function adopts a log-link functional form, and since the log-link exponentiates the linear predictors, Equation (5) can be applied to express this function in natural logarithmic forms.

ln (Y_i) = β₀ + β₁Sx + β₂Ag + β₃Educ + β₄Dst + β₅I + β₆Te + β₇Ars + β₈Lt + β₉Atr + β₁₀Tc + e_i

(5)

The demand equation can also be expressed in exponential form, as shown in Equations (6) and (7) for the initial lake level and following some quality improvements.

Y₀ = exp (β₀ + β₁Sx + … + β₁₀T_c) + e_0i

(6)

Y₁ = exp (β₁₁ + β₁₂Sx + … + β₂₀T_c) + e_1i

(7)

3.2.5. Welfare Estimation

The distinction between the highest price a person is willing to pay to visit a recreational location and the total associated travel costs is known as the CS [40,78]. CS is calculated by integrating the region of the demand curve lying between the actual travel cost (travel cost at mean) and Tc = ∞ (the choke price, at which trip demand ultimately equals zero) and presented in exponential and indefinite integral form in Equations (8) and (9), respectively [11,32,54,57].

$$\mathrm{C}\mathrm{S}={\int }_{\mathrm{T}\mathrm{c}\mathrm{i}}^{\mathrm{\infty }}{(\mathrm{e}}^{\mathsf{\beta }0+\mathsf{\beta }1\mathrm{S}\mathrm{x}+---+\mathsf{\beta }10\mathrm{T}\mathrm{c}})\mathrm{d}\mathrm{T}\mathrm{c}$$

(8)

$$\mathrm{C}\mathrm{S}={\left[\frac{{\mathrm{e}}^{\mathsf{\beta }0+\mathsf{\beta }1\mathrm{S}\mathrm{x}+---+\mathsf{\beta }10\mathrm{T}\mathrm{C}}}{{\mathsf{\beta }}_{\mathrm{T}\mathrm{c}}}\right]}_{\mathrm{T}\mathrm{c}=\mathrm{T}\mathrm{c}\mathrm{i}}^{\mathrm{T}\mathrm{c}=\mathrm{\infty }}$$

(9)

where $\infty$ = choke price and Tc_i = mean travel cost of visitor i

We estimated two different types of demand for the Lake Tana recreational site. The first is the lake’s status quo-level recreational value using the standard TCM. The second method makes use of the contingent TCM, which estimates the lake’s amenity value in light of four hypothetical scenarios that simulate changes in the levels of some site characteristics ((1) increasing the availability of open space areas in and around the lake by 50%; (2) improving the transportation, infrastructure, and accommodation facilities by 50%; and (3) achieving a 100% improvement in the lake’s and its vicinity’s quality by preventing the expansion of water hyacinth and waste disposal). The contingent TCM’s result can also be referred to interchangeably as the hypothetical TCM or augmented TCM [31,33].

${\mathrm{C}\mathrm{S}}_{\mathrm{Y}0}$ is the CS before the lake’s quality is changed,${\mathrm{C}\mathrm{S}}_{\mathrm{Y}1}$ is the CS after some improvement in the site’s quality, ${\mathrm{C}\mathrm{S}}_{\mathsf{\Delta }}$ is the change in the CS, λ is the predicted number of annual trips taken to the site, β_Tc is the regression coefficient corresponding to the travel cost variable, and n is the overall number of visitors. Given the above, the per-trip average, and total welfare estimations are performed using measures from

Table 3. Recreational value welfare measures of Lake Tana before and after quality changes.

Welfare Measures	Before Change in Lake’s Quality	After Some Improvement in the Lake’s Quality
CS per person per trip	$-\frac{1}{{\mathsf{\beta }}_{0\mathrm{T}\mathrm{c}}}$	$-\frac{1}{{\mathsf{\beta }}_{11\mathrm{T}\mathrm{c}}}$
CS for average trip	$-\frac{\mathsf{\lambda }0}{{\mathsf{\beta }}_{0\mathrm{T}\mathrm{c}}}$	$-\frac{\mathsf{\lambda }1}{{\mathsf{\beta }}_{11\mathrm{T}\mathrm{c}}}$
Total Annual CS	$-\frac{1}{{\mathsf{\beta }}_{0\mathrm{T}\mathrm{c}}}\times \mathrm{n}$	$-\frac{1}{{\mathsf{\beta }}_{11\mathrm{T}\mathrm{c}}}\times \mathrm{n}$
Change in a CS (${\mathrm{C}\mathrm{S}}_{\mathsf{\Delta }}$ = ${\mathrm{C}\mathrm{S}}_{\mathrm{Y}1}{-\mathrm{C}\mathrm{S}}_{\mathrm{Y}0}$)	${\int }_{\mathrm{T}\mathrm{c}\mathrm{i}}^{{\mathrm{\infty }}^{\mathrm{Y}1}}{(\mathrm{e}}^{\mathsf{\beta }11+\mathsf{\beta }12\mathrm{S}\mathrm{x}+---+\mathsf{\beta }20\mathrm{T}\mathrm{c}})\mathrm{d}\mathrm{T}\mathrm{c}-{\int }_{\mathrm{T}\mathrm{c}\mathrm{i}}^{{\mathrm{\infty }}^{\mathrm{Y}0}}{(\mathrm{e}}^{\mathsf{\beta }0+\mathsf{\beta }1\mathrm{S}\mathrm{x}+---+\mathsf{\beta }10\mathrm{T}\mathrm{c}})\mathrm{d}\mathrm{T}\mathrm{c}$

for each site’s condition [31,54,55,70,78,79,80].

4. Results

4.1. Descriptive Analysis

Table 4. Socioeconomic characteristics of respondents (n = 1094).

Variables	Category/Dummy	Frequency	Percent	χ2 (p-Value)
Sex	Female	594	54.30	18.61(0.046) *
	Male	500	45.70
Education	Basic	24	2.19	88.36(0.000) ***
	Intermediary	193	17.64
	Advanced	877	80.16
Alternate Site choice	Ars-Tawf	587	53.66	41.11(0.085) *
	Ars-Gfrh	318	29.07
	Ars-Slrc	98	8.96
	Ars-Smnp	91	8.32
Attribute choice	Attribute proximity	314	28.70
	Attribute diversity	511	46.71	22.10(0.335)
	Attribute facility	269	24.59

Note: *** p < 0.01, and * p < 0.10.

and

Table 5. Respondents’ socioeconomic profile (n = 1094).

Variables	Mean	Std. Deviation	Minimum	Maximum
Age	31.95	9.70	17.00	75.00
Distance (km)	360.17	294.63	3.00	1200.00
Monthly income (USD)	403.77	391.92	10.00	2300.00
Leisure Time	41.29	20.27	5.00	195.00
Trip Experience	40.66	17.58	2.00	180.00
Recreation trip	2.03	16.98	1.00	12.00
Time at the site (days)	1.00	0.00	1.00	1.00
Total cost	153.04	90.31	15.00	620.87

provide information about the sample’s descriptive characteristics. Female respondents were more frequent than male respondents (p < 0.05), which may indicate that more women visit the recreation site. The majority of visitors were younger, with an average age of 31.95 years (Table 5). A significant proportion of visitors (80.16%) had advanced degrees, and those with higher education were substantially more likely to have visited Lake Tana at least once (p < 0.01) (Table 4). On average, visitors visited the site once a year and had a mean monthly income of USD 403.77 (Table 5).

The visitors most frequently (46.71%) cited the lake’s diverse attractions, such as the monasteries, churches, forests of the islands and peninsulas, birds, hippopotamuses, cultural handicrafts, and the Abay River’s flow across the lake, as their favorite feature of the site. A smaller percentage of visitors (28.70%) also cited the nearby tourist attractions, such as the Tis-Abay Waterfall, Gondar Fasiledes Royal Heritage, Saint Lalibela Rock Church, and Semein Mountain National Park, as a factor in their decision to visit Lake Tana. The infrastructure and services of the site were the least important factors for visitors (Table 4).

The average distance traveled by visitors to Lake Tana was 360.17 km, though visitors never stayed more than one day at the lake. The average cost of visiting the site was USD 153.04 (Table 5).

The majority (59%) of visitors had taken a single trip (Figure 2), whereas respondents visited the recreational site on average 2.03 times per year (Table 3).

4.2. Econometric Analysis

Based on the visitors’ socioeconomic profile and other recreation-related data, we estimated the yearly number of recreational trips.

4.2.1. Model Comparison and Statistical Tests

Aside from the important recommendations regarding the suitability of the ZTP regression model for count data, which excludes zero counts by definition, the study used the chi-square goodness-of-fit test and alternative model comparisons based on the Akaike and Bayesian information criteria (AIC and BIC). The results of the chi-square goodness-of-fit test indicated that the overdispersion hypothesis was rejected at a significant level of p < 0.01.

According to the AIC and BIC criteria [51], the efficiency of the model’s parameter estimation was inversely proportional to the estimated values of both the AIC and the BIC, which means that the model was more effective at estimating parameters, as the estimated values of AIC and the BIC decreased, as shown in

Table 6. Model comparisons using Akaike and Bayesian information criteria.

Model	Obs	11 (Null)	11 (Model)	df	AIC	BIC
Poisson Regression Model (Poisson)	1094	−1882.769	−1513.761	15	3057.521	3132.485
Generalized Poisson Regression Model (GP)	1094	−1869.835	−1362.562	16	2757.125	2837.086
Zero-Truncated Poisson Regression Model (ZTP)	1094	−1728.005	−1115.103	15	2260.205	2335.169
Zero-Truncated Negative Binomial Regression Model (ZTNB)	1094	−1514.973	−1115.103	16	2262.205	2342.167
Generalized Negative Binomial Regression Model (GNB)	1094	−1870.868	−1513.76	16	3059.519	3139.481
Zero-truncated Poisson inverse Gaussian (ZTPIG)	1094	-	−1519.931	15	3069.862	3144.826

.

4.2.2. Determinants of Recreation Demand/Trip

Table 7. Regression results of a ZTP model of individuals’ recreation demand at a status quo level and hypothetical quality change.

Trip Frequency	At Status Quo Level		With Quality Improvements
	Coefficient	Robust Std. Err	Coefficient	Robust Std. Err
Sex (Female = 0)
Male (1)	−0.16195 **	0.05902	−0.12803 **	0.04343
Ag	0.02379 ***	0.00312	0.01371 ***	0.00234
Educ (Basic = 0)
Intermediary	−0.07960	0.07804	0.04284	0.05515
Advanced	0.15652 *	0.08907	0.15780 **	0.06929
Dst	−0.00077 ***	0.0002	−0.00246 ***	0.00021
Te	−0.00247 **	0.00128	−0.00311 **	0.00107
Lt	−0.00008	0.00028	0.00018	0.00029
I	0.00059 ***	0.00006	0.00024 ***	0.00005
Ars-Smnp (0)
Ars-Tawf (1)	0.25588 ***	0.05707	0.16157 ***	0.04181
Ars-Gfrh (2)	0.27313 **	0.13060	0.24154 *	0.12790
Ars-Slrc (3)	−0.05720	0.09908	−0.04962	0.07706
Atr (Atr-Facility = 0)
Atr-Diversity	0.12718 *	0.06940	0.02814	0.05377
Atr-Proximity	0.09487	0.0696	0.06060	0.05088
Tc	−0.00662 ***	0.00107	−0.00301 ***	0.00061
Constant	0.13126	0.17029	0.90483 ***	0.12804
Number of obs (n)	1094		1094
Pseudo R2	0.3547		0.3216
Log-likelihood	−1115.1025		−1220.1365
Wald chi2(14)	1192.58		1138.22
Prob > chi2	0.0000		0.0000

Note: *** p < 0.01, ** p < 0.05, and * p < 0.10.

shows the results of ZTP regression, which indicate that a number of explanatory variables significantly predict visitors’ decisions to take recreational trips to Lake Tana.

Our findings revealed that women are more likely than men to take recreational visits (p < 0.05).

The visitor’s age is statistically significant (p < 0.01) and positively correlated with the frequency of recreation trips. For every year that the respondent’s age rises, the number of annual recreational trips taken increases by a factor of 1.0241. (If Y and X represent outcome and explanatory variables in the expression of Y = exp(β₀ + β₁X_i …) or Ln(Y) = β₀ + β₁X_i…, the change in Y as a result of a change in X is exp(β) ×Y.).

Visit frequency is inversely correlated with respondents’ geographical distance from the recreation site (p < 0.01). The predicted coefficient (−0.0008) suggested that for every additional kilometer situated away from Lake Tana, the frequency of recreational trips made by visitors drops by a factor of 0.9992.

The respondents’ monthly income was significantly and positively correlated with recreation trips (p < 0.01). For every dollar increase in the income, the log count of recreational trips rises by 0.0006.

The variable for spending on alternative recreation locations (Ars) showed mixed findings in affecting recreation trips to Lake Tana. Spending money at alternative recreation destinations such as Tis-Abay Waterfall (p < 0.01) and Gondar Fasiledes Royal Heritage (p < 0.05) was significantly and positively associated with taking recreational trips to Lake Tana. For every dollar increase in money spent accessing the Tis-Abay Waterfall, the predicted number of recreational trips to Lake Tana increases by 1.2916. The number of recreational visits to Lake Tana increases by 1.3141 for every additional dollar spent on the Gondar Fasiledes Royal Heritage site.

The results related to the attributes of the lake indicate that the diverse nature of the site, which comprises both natural and heritage components, is positively associated with the number of recreation trips (p < 0.1). However, travel cost negatively and significantly influences respondents’ number of trips to the Lake Tana recreation site (p < 0.01). The estimated total cost coefficient indicates that a one dollar increase in travel expenses results in a 0.9934 reduction in the annual number of recreational trips.

4.2.3. Consumer Surplus Analysis under Normal Lake Conditions

The frequency of visitors’ trips to the Lake Tana recreation site (Yi) and their travel expenses (Tc) were taken into account while estimating individual visitors’ demand functions for the site. According to the estimation, the estimated demand function is ln(Yi) = −0.1313–0.0066 Tc. Using an integration of the inverse demand function between 1.00 and 2.03 (the estimated mean trip), Lake Tana’s recreational value is calculated to be USD 306.52 for an average number of trips, and it is calculated to be USD 151 for each individual visit. Consequently, Lake Tana’s estimated yearly recreational value is USD 68.5 million (based on the total number of visitors who registered during the study’s survey period, which was the 2019 fiscal year).

4.2.4. Consumer Surplus Analysis under Hypothetical Quality Change

The potential of the Lake Tana recreation site is not being fully utilized due to several factors, and this is impacting its attractiveness to potential visitors as well as its recreational opportunities. Table 7 displays the results of a regression analysis that investigated two different dependent variables. The first variable was based on their actual visits to the lake in its current state, while the second variable was generated by asking visitors about their expected number of visits to Lake Tana per year if its quality improved. According to the findings, there were no significant differences in the regression outcomes between these two situations.

Based on the results of the regression analysis, the coefficient for total cost (Tc = −0.003) has a significant and adverse impact on how often visitors would want to return to the site after improvements are made to the lake’s quality. A similar conclusion was also drawn from the regression analysis of the number of times visitors have already visited the site in its current state.

According to the estimates in

Table 8. Overview of recreational values “with” and “without” attribute quality changes.

Values	$\mathbf{CS}\mathbf{without}\mathbf{Quality}\mathbf{Changes}\left({\mathbf{C}\mathbf{S}}_{\mathbf{Y}0}\right)$	$\mathbf{CS}\mathbf{with}\mathbf{Quality}\mathbf{Changes}\left({\mathbf{C}\mathbf{S}}_{\mathbf{Y}1}\right)$	$\mathbf{Change}\mathbf{in}\mathbf{CS}\left({\mathbf{C}\mathbf{S}}_{\mathsf{\Delta }}\right)$
CS per trip per person	151.00	333.33	182.33
CS for average number of trips	306.52	676.67	370.15
CS for annual visitors	68,468,534.00	151,143,155.20	82,674,621.20

, upgrading the quality of Lake Tana’s site would raise the recreational value per visit to USD 333. By enhancing the site quality, the total recreational value for the site is expected to reach USD 676.67 based on the average number of visits, resulting in an annual recreational value exceeding USD 151.1 million. Consequently, it is anticipated that the lake’s worth would rise by USD 182.33 per person per trip and by USD 370.15 overall for the average number of trips due to the improvements in quality.

5. Discussion

5.1. Determinants of Recreation Demand/Trip

The results of the study suggest that Lake Tana holds significant value for recreational service, both currently and potentially with improvements to the site’s quality.

The lake has a diverse array of attractive features, such as natural qualities and nearby attractions, and cultural and religious values, which are highly favored by visitors. According to qualitative interviews, visitors value the site’s diversity, which includes monasteries, churches, forests on the islands and peninsulas, birds, hippopotami, cultural handicrafts, and the sight of the Abay River flowing across the lake. On the other hand, they are less interested in recreation facilities such as transportation access, lodging options, beaches, and site infrastructure. This implies that investments in site development initiatives and infrastructure upgrades are necessary [81,82]. However, recreation facilities such as the availability of transport access, lodging options, beaches, and other infrastructure for accessing the site appear less preferred, which highlights the need for interventions such as investment in site development initiatives, services, and infrastructure upgrades. These findings are substantiated by earlier studies by Tardieu and Tuffery [81], White et al. [83], Mäntymaa et al. [31], Kaya [84], and Matthew et al. [23], which highlight the importance of a recreation site’s biophysical characteristics and the need to enhance access and amenities. Mäntymaa et al. [31] found that nature-based attributes such as trees and water are frequently connected with recreation trips, while Kaya [84] and Matthew et al. [23] found that only the stand structure of a forest in Turkey and a park’s facilities in the Keroh recreational forest of Malaysia, respectively, were associated with recreation trips. Thus, the diverse attributes of Lake Tana make it a highly attractive recreational site, appealing to a broad range of visitors.

In this study, we compared the number of stay days and trip frequency at Lake Tana with those at other, similar recreational sites, and we found that visitors to other sites—for example, Maasai Mara Park in Kenya and Kalam Valley in Pakistan—stayed for longer periods than visitors to Lake Tana [85,86]. These sites had visitors who stayed for up to 16 days, while at Lake Tana, most visitors stayed for only one day, suggesting that Lake Tana is a less preferred destination for long-term stays. On the other hand, the annual trip frequency at Lake Tana and other sites was found to be similar. For example, findings from Kongar Lake in Indonesia (61.3%) [87] and Nagarhole National Park and Nandi Hills in India (70%) [86] revealed that the visitors only made a single visit.

The frequency of visits to Lake Tana is related to various factors, such as visitor income, distance to the lake, alternative tourist destinations expenditure, and total travel cost. These estimates align with prior study regarding their significance and correlation with recreational trips. Individuals with higher monthly income are more likely to visit Lake Tana more frequently, indicating that they can afford the cost of the trip [57,76,88,89]. As predicted, there is a significant negative correlation between the number of recreation trips and the respondent’s distance from the site [90,91]. This finding supports the notion that distance and visit frequency have a negative relationship in studies that use TCM [37,90,91,92,93].

Travelling to Tis-Abay Waterfall and Gondar Fasiledes Royal Heritage was found to have a positive relationship with visits to Lake Tana, meaning that as the amount spent on recreation at those sites increased, and as did the demand for recreation at Lake Tana. This was supported by both theoretical and empirical evidence [76,94].

Travel cost, which includes travel, lodging, and opportunity cost of time, was identified as the key explanatory factor in a ZTP regression analysis. The model assumed a relationship between trip frequency and travel costs as a proxy for the price of accessing the site [46]. The estimated travel cost coefficient was found to be significant and negative, indicating an inverse association with the frequency of recreational visits [25,55,76,77]. This is consistent with the theory of consumer behavior, which suggests that higher travel costs result in lower trip frequency, and vice versa [25,76,95].

5.2. Consumer Surplus

We also estimated the prospective Lake Tana’s recreational value using the travel cost coefficient, the mean number of recreational trips made by sample respondents, and the records of the total annual visitor count for the site [78]. An estimated value attachment to the lake in terms of an annual recreation value of USD 68.5 million, an average visitation rate of USD 306.52 per tourist, and an average trip rate of USD 151 per visitor imply that the lake is an important and economically significant recreation site [55,80]. In contrast, the revenue generated from admission fees and related services in 2019 was only approximately USD 15.2 million, which is significantly lower than the predicted yearly recreational value [64,96].

Based on methodological and site-characteristic relatedness and geographical proximity, we compared our findings regarding both current and hypothetical results with previous studies based on methodological and site characteristic relatedness as well as geographical proximity [5,71,85,97]. Our analysis showed that Lake Tana’s estimated annual recreational value of USD 68.5 million is much lower than that of Kenya’s Mara National Parks (USD 73.1 million per year) [85] and Turkey’s Lake Manyas (USD 103 million per year) [98]. Lake Tana’s estimated annual recreational value (USD 68.5 million per year) is higher than the estimated annual recreational value of Ifrane National Park (USD 13.2 million) in Morocco [71], Lake Ziway (USD 3.2 million) in Ethiopia [99], and Tis-Abay Waterfall (USD 9.5 million) in Ethiopia [5]. The stated empirical results are, of course, subject to a specific methodological approach, estimation techniques, assumption variations, and—most importantly—an annual number of visitors to the specific site. Thus, it is impossible to anticipate that comparisons of CS estimates will be exactly equal, even though our results fall within the acceptable bounds of estimated values [100].

The results from the hypothetical TCM, which considered the value appraisal of Lake Tana under several potential resource management scenarios, formed the other significant finding of our study. This revealed that Lake Tana is expected to cost USD 333 per visit per person and to have an annual economic benefit of USD 151 million under hypothetical quality enhancements. The results of this hypothetical analysis revealed that the site’s worth could grow by more than a twofold increase if the lake’s qualities were improved.

The differential arises from the anticipated total yearly recreational value under the imagined improvement scenario and the existing condition, which shows a potential efficiency loss brought on by poor resource management [49,101]. The economic worth of the lake for recreational use could have be as high as USD 151 million, a more than 100% increase from the actual estimated value, if decisions about resource usage and management had taken the economic value flows of Lake Tana into account [11,43]. In light of this, the projected yearly recreational value from the ITCM is a reflection of how much money would have been lost if less focus had been placed on the lake’s recreational potential.

We compared the contingent ITCM scenario results with similar studies that incorporated the standard and contingent ITCM, including studies in Switzerland by Filippini et al. [33], in Spain by Pueyo-Ros et al. [102], in Finland by Lankia et al. [103], and in Wales by Anciaes [104]. In comparison, our estimated recreational value attained using the contingent ITCM increases by a greater percentage (more than 100%) from its estimated value at the status quo level than the findings of Anciaes [104] in Wales, where the improved water quality of a beach resulted in a 52% increase from its status quo value. The impacts of water quality change in Finland’s lakes resulted in an annual value increment of 53–80% [103], which is still short of the findings from Lake Tana. The significant difference in results could show how Lake Tana’s site quality improvement is responsive to a higher estimated recreational value.

Nevertheless, since on-site data results cannot provide information on potential new visitors brought on by the hypothetical quality adjustment, the appraised CS result from the hypothetical ITCM in this study only reflects the lower bound of the real change in welfare [33,105].

In the pursuit of resource sustainability, effective resource usage, and management, it is required to understand the whole economic worth of a lake. Thus, it is necessary to make a comprehensive effort to account for all multivariate values in order to estimate the lake’s entire worth. The primary focus of this study was to evaluate Lake Tana’s recreational use value, although this is only one aspect of the lake’s overall economic impact, which encompasses a variety of values such as use and non-use, direct and indirect values, and economic and non-economic benefits. To assess the total economic worth of Lake Tana and minimize needless inefficiency in the usage of the resource’s potential, it is crucial to conduct additional research on the remaining values [106,107,108,109].

While acknowledged for its effectiveness in assessing recreational benefits, the TCM can be challenging [34,46]. The influence of multipurpose travel, estimating travel times, and how locals and visitors from a distance are treated are significant issues. The credibility of the research findings will therefore be determined by how the valuation framework is used and how these issues are handled [24,74]. Nonetheless, the current study provides insightful information about the significant economic worth of Lake Tana’s recreational services in the context of an LMIC that has not received enough attention.

6. Conclusions

The study reveals that Lake Tana holds significant recreational value for visitors. The estimated annual total value indicates a high value placed on the site, with women and higher-educated visitors being more likely to visit. The ZTP modeling result shows that the decision to visit more often is also significantly correlated with the visitor’s age, monthly income, and access to alternative recreation sites. The distance and total cost of visitation, on the other hand, are significantly and negatively related to visitors’ decisions to engage in recreation on the site, implying that demand for recreation at Lake Tana is inversely related to travel costs.

The substantial association between visitors’ recreational trips, the number of days stayed, and the lake’s attributes suggests that visitors have placed a high value on the site’s wide range of features, mixing natural and historical heritages, forest ecosystems, and water bodies. Maintaining all of the lake’s diverse attributes is, therefore, necessary to increase both the yearly trip frequency and the number of days of stay at the site and thereby to maximize its potential recreational value.

Although Lake Tana has enormous recreational value, visitors’ short stays at the site, the unremarkable annual mean trip frequency, and the contingent ITCM’s result revealed a limitation in fully exploiting the resource’s potential for recreation. By paying closer attention to the nonmarket values of Lake Tana and making investments in the infrastructure and accompanying services needed to accommodate more visitors and longer stays, it is possible to improve the overall economic gains from this magnificent and iconic natural resource. Hence, we urge the authorized managers, planners, and policymakers to consider Lake Tana’s estimated recreational use value at all stages of the planning and decision-making processes and to ensure its sustainability.