Does Tourism Contribute to Real Estate Boom? A DSGE Modeling in Small Open Economy

Abstract

This article aims to investigate the relationship between inbound tourism and housing market along with the recent boom in Icelandic real estate sector, in which both house and rental prices have been rising dramatically. To this end, we construct a small open economy dynamic stochastic general equilibrium model enclosing a tourism sector and a housing market with owner-occupied and rental sections. The simulation results unveil a transmission channel that indicates the higher inbound tourism demand raises both house prices and rental prices. Variance decomposition and historical decomposition show that both inbound tourism demand shock and manufacturing technology shock are the key driving forces of the fluctuations of Icelandic house prices, consumption, and investment, whereas housing preference shock plays the most important role in determining the volatility of rental prices. The policy implications indicate that any shocks to tourism could easily spillover to housing market dynamics and aggregate fluctuations.

Keywords

inbound tourism housing market rental market DSGE modeling COVID-19

Introduction

Ever since the 2008 Global Financial Crisis (GFC), house prices have been closely monitored by circles of academics, business, and policy makers because many have witnessed the boom and bust of house prices at least partly contributed to the crisis (Duca et al., 2010). As a typical example in a small open economy, the residential housing market in Iceland was booming between late 1990s and 2007, followed by a bust of the real estate sector and a severe financial crisis, with the currency falling by more than 50% and over 90% of the domestic financial system collapsing (Einarsson et al., 2015). Recently, Iceland’s house prices have been soaring again and the public starts to worry whether it is the signal of another round of housing bubble. Supplement Figure 1 (available online) plots the Statistics Iceland house price index based on actual property transaction prices and actual rentals for housing (in log real terms and normalized) between 2002 and 2018. As shown in Supplement Figure 1, Iceland has experienced two rounds of real estate boom since the turn of the 21st century, one in the early 2000s ended with a bubble burst between 2008 and 2010, and the other from 2011 onward until the present. In contrast, the rate of increase in rentals is much flatter. The divergence between house prices and rentals witnessed the bursting of the last real estate bubble, and now they seem to be gradually diverging again.

Many people have attributed the recent boom and bust cycle in the Icelandic housing sector to the excessive borrowing and tremendous credit expansion (Benediktsdottir et al., 2011; Benediktsdottir et al., 2017). For instance, the financial liabilities to GDP ratio of both the household sector and the nonfinancial corporate sector have experienced a rapid expansion in the years before the GFC and gradually deleveraged after the GFC till present (see Supplement Figure 2, available online). The buildup and deleverage of financial liabilities to GDP ratio is consistent with the previous round of real estate market boom and bust, but the second round of housing market boom seems to be in sync with the market’s ongoing deleveraging process, which is no longer appropriate to be used for explaining the booming house prices again. Under these circumstances, what draws our attention is the surge of inbound tourism in Iceland over recent years, which comes together with the second round of rising house prices. Supplement Figure 3 (available online) plots Iceland’s inbound tourism expenditure to GDP ratio and inbound passengers through Keflavik airport between 2003 and 2018, both of which have a proper indication of the importance of inbound tourism in the Icelandic economy. Apparently, they were relatively flat before the GFC, whereas both have been rising rapidly since 2010/2011. The above three figures imply that the recent rise in house prices should not be related to debt expansion but more plausible to inbound tourism development.

This article aims to shed some lights on the relationship between inbound tourism and housing market along with the most recent boom in Icelandic real estate sector. To this end, we construct a dynamic stochastic general equilibrium (DSGE) model to investigate the transmission channels through which inbound tourism affects the housing markets in Iceland. The selection of DSGE framework to serve our purpose comes from its cutting-edge role in the macroeconomic modelling for studying economic growth, business cycles and the effects of economic policies, through econometric models based on applied general equilibrium theory and microeconomic principles (Christiano et al., 2018). The constructed DSGE model features three main economic decision makers in the economy, namely, foreign inbound tourists, domestic (Icelandic) households, and entrepreneurs. Foreign tourists consume a “tourism bundle” consisting of tourism goods and services (excluding accommodation) and accommodation as complementary to each other. Accommodation typically includes hotels, guest houses, and recent highly appreciated private renting (e.g., Airbnb). Domestic households consume, work, and live either in their own properties (as homeowners) or rented housing units (as tenants). Last, the entrepreneurs are the main suppliers in the economy, producing both tourism and nontourism (i.e., manufacturing) goods, accumulating real estates and renting out properties to households and inbound tourists. In the economy, the competitive equilibrium is reached when all three decision makers optimize their objective functions subject to various constraints. After that, we sequentially obtain the values of key parameters by strategies of calibration, for which we match the unconditional model and data moments (Gomme & Rupert, 2007) and conduct Bayesian estimation with simulation methods using Markov Chain Monte Carlo approach and Metropolis–Hasting algorithm (An & Schorfheide, 2007). After parameterization, we implement several simulation excises to investigate the role of inbound tourism in shaping the housing market volatility in Iceland.

The findings of our novel modeling strategy can be summarized as follows. First, the impulse response analysis shows that both house prices and rentals increase when confronting a positive inbound tourism demand shock. To understand the transmission mechanism, we observe that higher inbound tourism demand raises the consumption of tourism goods as well as complementary accommodation, which pushes up the rentals. Higher rentals induce more real estate purchase by entrepreneurs, driving up house prices as a result. Meanwhile, more properties for the rental will crowd out the supply in the housing market, which leads to a further increase in house prices. This is the main contribution of our study that quantitatively picks up how the effects of tourism activities are transmitted into the housing market in a transparent manner, which distinguishes itself from other econometric studies such as reduced-form methods (Biagi et al., 2012; Biagi et al., 2015). By doing so, we are able to better examine how the effect of tourism is transmitted into the real estate industry. Second, the variance decomposition and historical shock decomposition show that both inbound tourism demand shock and manufacturing technology shock are the key driving forces of the fluctuations of Icelandic house prices, consumption and investment, whereas housing preference shock plays the most important role in determining the volatility of rental prices. As the largest generator of export revenues for the Icelandic economy, the tourism sector tends to generate spillover to other sectors (e.g., through the real estate market) once experiencing any external demand shocks.

The rest of this article is organized as follows. Next section provides a brief review of previous studies mostly related to our work. In Section 3, we construct a small open economy DSGE model for Iceland, featuring tourism and real estate sectors with an owner-occupied market as well as a rental market. Section 4 presents the empirical results with the Icelandic data, where we calibrate and estimate all parameters. In Section 5, we fully explore the economic implications of the model; more specifically, we examine the transmission mechanism of how inbound tourism affects the Icelandic housing market from different simulation exercises. Section 6 concludes the article.

Literature Review

Recent years have witnessed a growing literature on the role of tourism activities in macroeconomic development. Inbound tourism spending is considered an alternative form of export that helps improve a country’s balance of payments, supports employment and generates additional tax revenues (Archer, 1995; Durbarry, 2002). Due to its vital role in international trade for many tourism-specialized economies, international tourism is seen as a key driving force to long-run economic growth (Lanza et al., 2003; Lucas, 1988). This tourism-led growth hypothesis is theoretically derived from the export-led growth hypothesis that economic growth can be generated not only by increasing the amount of labor and capital within the country but also by expanding exports (Balaguer & Cantavella-Jordá, 2002; Balassa, 1978). del P. Pablo-Romero and Molina (2013) and Brida et al. (2014) provide excellent and exhaustive reviews of the literature on tourism-led growth hypothesis.

Tourism has a significant effect on long-term economic growth, and it is also closely related to short-term economic fluctuations. The relevance of irregular trends and cyclical patterns in tourism demand has been long recognized, but there is a lack of literature isolating the cyclical components of tourism, investigating the turning points and directional changes, and attempting a business cycle interpretation until recently (Song & Li, 2008). If the relationship between the tourism cycle and the entire business cycle can be shown, the tourism policy can take advantage of the delay between the two cycles and take countercyclical measures to mitigate the effects of adverse economic conditions (Guizzardi & Mazzocchi, 2010). For example, income elasticities differ depending on the phase of the business cycle, and this fact has been found to be insightful for analyzing demand reactions and for forecasting (Smeral, 2012); detection of the structural break and causality on both directions between tourism cycle and business cycle can help develop new integral plans of tourism quality and economic development (Mérida & Golpe, 2014); a better understanding the tourism spending symmetry and asymmetry along the business cycle can help propose more effective advertising strategies and appropriate tourism policies (Bronner & de Hoog, 2017).

This article is also related to other literature that initializes the buildup of DSGE framework to analyze the role of the tourism industry in a macroeconomic context. The term “DSGE” was originally introduced in the real business cycle model, which is based on a neoclassical framework with micro-founded optimization behavior of economic agents with flexible prices (Kydland & Prescott, 1982). Later generation of DSGE models that enclosed with various nominal and real frictions have shown tremendous improvement in the empirical fit of data (Christiano et al., 2005; Smets & Wouters, 2007). Since the GFC, the DSGE framework has been heavily criticized. Many have put forward the view that DSGE models developed during the “Great Moderation” proved to be of little use when the world entered the Great Recession (Hendry & Muellbauer, 2018; Stiglitz, 2018). Others seem to think that the DSGE framework should be revised to better account for financial frictions, in particular, the housing market dynamics (Iacoviello, 2005; Iacoviello & Neri, 2010). Sun and Tsang (2017) construct a DSGE model that features both an owner-occupied housing market and a rental housing market to account for the volatility of U.S. price–rent ratio over time. Even though the DSGE framework has been comprehensively explored for studying macroeconomic dynamics and analyzing quantitative policy issues, the application of DSGE models in the tourism field is still profoundly underdeveloped. To the best of our knowledge, there are only few papers so far in the literature that examine the tourism issues under the DSGE framework. Liu et al. (2018) propose a DSGE model estimated using the Bayesian method to explore the relationship between tourism development, driven by tourism productivity growth, and economic growth. Zhang and Yang (2018) adopt a small open economy DSGE framework to investigate the effects of inbound tourism boom on the domestic economy in terms of Dutch disease and welfare consequences. Liu and Wu (2019) construct a Bayesian DSGE endogenous growth model to examine the transmission mechanism between tourism productivity and economic growth. The results shed light on the spillover effects between tourism and other sectors caused by the externalities of physical and human capital and public services.

This article is most closely related to the literature on the impact of tourism activities on the local housing markets of tourist destinations. Research both in the fields of tourism economics and housing studies recognizes that tourism and tourist-related activities can affect housing markets directly via the external demand generated by tourists that competes with the local resident communities for land and housing in tourist destinations, and indirectly via the capitalization of tourism-related amenities in the market price and value of housing (Biagi et al., 2012). Early studies are mainly using hedonic method to focus on specific cases like one city or one neighborhood (Nelson, 2010; Vanslembrouck et al., 2005), or on specific amenities such as beaches, parks, golf courses, and so on (Conroy & Milosch, 2011; Nicholls & Crompton, 2007). To overcome the weakness of using single regression models to estimate the impact of tourism on housing prices, later studies follow by applying the latent class model to account for city-specific heterogeneous effects (Biagi et al., 2015), or by using the system generalized method of moments approach to capture the complexity of the tourism market (Biagi et al., 2015). From our perspective, Elíasson and Ragnarsson (2018) is the only recent work to study the impact of inbound tourism on Icelandic housing market through the channel of short-term renting from Airbnb, where the authors find the contribution of the growth in the Airbnb market on real house prices is 2% per year over the past 3 years or about 15% of the total increase in real house prices during the same period. However, they mainly apply the single-equation econometric model, which is not able to capture the fully fledged dynamic and structural relationship as we do in a DSGE framework.

The Model

Based on Sun and Tsang (2017) and Zhang and Yang (2018), we construct a small open economy DSGE model that features tourism good sector and housing market. There are two types of final goods: tourism good $Y_{T, t}$ , and a manufacturing good, $Y_{M, t}$ . This dichotomy helps model the resource allocation between sectors. The housing market is divided between an owner-occupied section and a rental section that serves both domestic households and foreign tourists. Tourism goods and rental housing, though technically nontradable, can bring foreign reserve earnings to the destination country when consumers are foreign visitors (Copeland, 1991).

There are three groups of decision makers in the economy: foreign tourists, domestic households, and entrepreneurs. Foreign tourists, endowed with a tourism budget, decide how to allocate complementary consumption between tourism goods and accommodation. Domestic households derive utility from consumption, housing services, and leisure time (disutility from working). Consumption is a composite of tourism and manufacturing goods. Housing services are from owner-occupied housing and rental housing. Labor supply goes to both the tourism sector and manufacturing sector. Entrepreneurs are the main suppliers in the economy, producing both tourism and manufacturing goods, accumulating real estates and renting out to households and tourists. All three agents maximize their objective functions subject to specific budget constraints, where the optimization problems are defined later. Figure 1 summarizes the circular flow of the model economy.

Figure 1

Circular Flow of the Model Economy

Foreign Tourists

Foreign tourists enter the tourism destination (Iceland) with a particular amount of spending budget $Y_{t}^{F}$ , determined stochastically, and derive utility from consuming a bundle of tourism related goods and services. The spending budget will be affected partially by the exogenous movement of exchange rate, as studied in Tang et al. (2014). The bundle $X_{t}$ is assumed to be divided between the accommodation $H_{R, t}^{F}$ and the rest tourism-related consumption $C_{T, t}^{F}$ , including both air and land transportation, food and beverage services and fee of travel agencies, and so on, and aggregated by a constant elasticity of substitution (CES) function. The utility maximization problem for foreign tourists is given by

V^{F} = E_{0} \sum_{t = 0}^{\infty} {(β^{F})}^{t} (\ln X_{t})

(1)

X_{t} = {[φ^{f} \frac{1}{χ^{f}} {(C_{T, t}^{F})}^{\frac{χ^{f} - 1}{χ^{f}}} + {(1 - φ^{f})}^{\frac{1}{χ^{f}}} {(H_{R, t}^{F})}^{\frac{χ^{f} - 1}{χ^{f}}}]}^{\frac{χ^{f}}{χ^{f} - 1}}

subject to the budget constraint

p_{T, t} C_{T, t}^{F} + r_{t}^{H} H_{R, t}^{F} = Y_{t}^{F}

(2)

where $β^{F}$ is foreign tourists’ subjective discount factor. For parameters, $φ^{f}$ is the share of tourism consumption in the bundle and $χ^{f}$ is the elasticity of substitution between tourism consumption and accommodation in the bundle; for variables, $p_{T, t}$ is the (relative) price of tourism goods and $r_{t}^{H}$ stands for the (real) rent of accommodation. From common experiences, tourists enjoy tourism related activities during the daytime and stay in hotels or rented places overnight; they consume tourism goods and accommodation together while travelling. Therefore, we assume $C_{T, t}^{F}$ and $H_{R, t}^{F}$ are complementary to each other. Since foreign tourists rarely work or invest, or prohibited to do so by law, during their stay in the destination country, we leave the utility function and the budget constraint as simple as they look like. The optimality condition for foreign tourists states that foreign tourists’ relative demand for tourism goods and accommodation, depending on the two alternatives’ relative prices and their shares in the utility function.

Domestic Households

The economy is populated by identical and infinitely-lived households, who derive utility from consumption $C_{t}^{H}$ , housing $H_{t}^{H}$ and leisure (disutility of working $N_{t}$ ). Total consumption consists of tourism goods $C_{T, t}^{H}$ and manufacturing goods $C_{M, t}^{H}$ . For housing, the households can choose to live either in owner-occupied residences $H_{P, t}^{H}$ or rental housing $H_{R, t}^{H}$ . The two options are substitutes to each other. Last, the households can work either in the tourism sector $N_{T, t}$ or in the manufacturing sector $N_{M, t}$ . Consumption, housing and labor are all aggregated by CES functions, where the specifications are shown shortly. The household’s lifetime utility function is given by

V^{H} = E_{0} \sum_{t = 0}^{\infty} {(β^{H})}^{t} (\ln C_{t}^{H} + j_{t} \ln H_{t}^{H} - \frac{N_{t}^{1 + η}}{1 + η})

(3)

C_{t}^{H} = {[φ^{h} \frac{1}{χ^{h}} {(C_{T, t}^{H})}^{\frac{χ^{h} - 1}{χ^{h}}} + {(1 - φ^{h})}^{\frac{1}{χ^{h}}} {(C_{M, t}^{H})}^{\frac{χ^{h} - 1}{χ^{h}}}]}^{\frac{χ^{h}}{χ^{h} - 1}}

H_{t}^{H} = {[ω^{h} \frac{1}{ϕ^{h}} {(H_{P, t}^{H})}^{\frac{ϕ^{h} - 1}{ϕ^{h}}} + {(1 - ω^{h})}^{\frac{1}{ϕ^{h}}} {(H_{R, t}^{H})}^{\frac{ϕ^{h} - 1}{ϕ^{h}}}]}^{\frac{ϕ^{h}}{ϕ^{h} - 1}}

N_{t} = {[{(ω^{n})}^{- \frac{1}{ϕ^{n}}} {(N_{T, t})}^{\frac{1 + ϕ^{n}}{ϕ^{n}}} + {(1 - ω^{n})}^{- \frac{1}{ϕ^{n}}} {(N_{M, t})}^{\frac{1 + ϕ^{n}}{ϕ^{n}}}]}^{\frac{ϕ^{n}}{1 + ϕ^{n}}}

where $β^{H}$ is households’ subjective discount factor, $j_{t}$ captures the stochastic housing preference shock. For consumption bundle, $φ^{h}$ is the share of tourism goods, $χ^{h}$ is the elasticity of substitution between tourism goods and manufacturing goods; for housing, $ω^{h}$ is the share of owner-occupied housing, $ϕ^{h}$ is the elasticity of substitution between owner-occupied and rented housing; for labour, $ω^{n}$ is the share of tourism sector labour, $ϕ^{n}$ represents the elasticity of substitution between tourism labour and manufacturing labour. The flow of funds constraint is given by

\begin{array}{l} p_{T, t} C_{T, t}^{H} + p_{M, t} C_{M, t}^{H} + q_{t} [H_{P, t}^{H} - H_{P, t - 1}^{H}] + r_{t}^{H} H_{R, t}^{H} + B_{t} \\ = w_{T, t} N_{T, t} + w_{M, t} N_{M, t} + r_{t - 1}^{B} B_{t - 1} \end{array}

(4)

where $p_{M, t}$ is the (relative) price of manufacturing goods, $q_{t}$ is the real house price, $B_{t}$ is the bond issued by entrepreneurs and $r_{t}^{B}$ is the corresponding interest rate, $w_{T, t}$ and $w_{M, t}$ are the real wages in the tourism sector and manufacturing sector, respectively. The optimality conditions for domestic households shows that the households’ relative demand of tourism goods and manufacturing goods, depending on the two alternatives’ relative prices and their shares in the CES aggregation function; implies that households would equalize the marginal cost and marginal benefit of housing investment, where the benefit includes the capital gain and utility of housing; indicates that the optimal condition for renting decision, in which the marginal utility of renting houses is equal to the rent; presents that the households’ relative labor supply, depending on the shares and relative wages in the two sectors.

Entrepreneurs

There is a continuum of entrepreneurs who accumulate capital $K_{T, t}$ , $K_{M, t}$ , and housing, $H_{R, t}^{E}$ . They hire labor $N_{T, t}$ , $N_{M, t}$ and combine with their own capital to produce tourism goods $Y_{T, t}$ and manufacturing goods $Y_{M, t}$ . Another role that entrepreneurs play is to provide rental services with their holding of housing stock $H_{P, t}^{E}$ . Their lifetime utility is as follows:

V^{E} = E_{0} \sum_{t = 0}^{\infty} {(β^{E})}^{t} (\ln C_{t}^{E})

(5)

where $β^{E}$ is entrepreneurs’ subjective discount factor, $C_{t}^{E}$ is their consumption of manufacturing goods. Entrepreneurs do not consume tourism goods to simplify the size of the model. Allowing consumption of both goods certainly complicates the model setup without providing additional analytical insights. Entrepreneurs optimize subject to the following flow of funds constraint

\begin{array}{l} p_{T, t} Y_{T, t} + p_{M, t} Y_{M, t} + r_{t}^{H} H_{P, t}^{E} + B_{t} \\ = p_{M, t} C_{t}^{E} + r_{t - 1}^{B} B_{t - 1} + w_{T, t} N_{T, t} + w_{M, t} N_{M, t} + q_{t} (H_{P, t}^{E} - H_{P, t - 1}^{E}) \\ + K_{T, t} - (1 - δ_{T}) K_{T, t - 1} + K_{M, t} - (1 - δ_{M}) K_{M, t - 1} \end{array}

(6)

moreover, a collateral constraint

B_{t} \leq m_{t} E_{t} (q_{t + 1} \frac{H_{R, t}^{E}}{r_{t}^{B}})

(7)

where $δ_{T}$ and $δ_{M}$ are depreciation rates of tourism and manufacturing capital, respectively. Also, $m$ is the loan-to-value ratio in the collateral constraint. Equation (7) states that due to the limited commitment problem (Kiyotaki & Moore, 1997), the maximum amount that the entrepreneur can borrow is bound by a fraction (determined by the stochastic process $m_{t}$ ) of the expected value of collateral (housing stock). Entrepreneurs use Cobb–Douglas technologies with constant returns to scale in both sectors. The production functions follow:

Y_{T, t} = A_{T, t} {(N_{T, t})}^{α^{T}} {(K_{T, t - 1})}^{1 - α^{T}}

(8)

Y_{M, t} = A_{M, t} {(N_{M, t})}^{α^{M}} {(K_{M, t - 1})}^{1 - α^{M}}

(9)

where $A_{T, t}$ and $A_{M, t}$ measure stochastic productivity shocks in the tourism sector and the manufacturing sector, respectively, and the parameters $α^{T}$ and $α^{M}$ capture the labour income share in the two sectors. The optimality conditions for entrepreneurs equals the increase in entrepreneurs’ utility that would stem from borrowing additional unit; states that the marginal benefit of consumption today equals marginal benefit of consumption next period less the cost of tightening collateral constraint; implies that the marginal benefit of consumption today less renting cost equals marginal benefit of housing investment and loosing collateral constraint next period.

Market Clearing Condition

The market clearing conditions for the goods markets (tourism and manufacturing), the housing market and renting market are given by

C_{T, t}^{F} + C_{T, t}^{H} = Y_{T, t}

(10)

\begin{array}{l} p_{M, t} (C_{M, t}^{H} + C_{t}^{E}) + K_{T, t} - (1 - δ_{T}) K_{T, t - 1} \\ + K_{M, t} - (1 - δ_{M}) K_{M, t - 1} = p_{M, t} Y_{M, t} + Y_{t}^{F} \end{array}

(11)

H_{P, t}^{H} + H_{R, t}^{E} = \bar{H}

(12)

H_{R, t}^{F} + H_{R, t}^{H} = H_{R, t}^{E}

(13)

Equation (10) states that the demand for tourism goods from foreign and domestic tourists equals to tourism production. Equation (11) indicates that manufacturing production plus inbound tourism revenue is used for consumption and investment. Equation (12) shows the equality between housing stock from households and entrepreneur and total housing supply (fixed in our setup). Last, Equation (13) displays that the renting demand from foreign tourists and domestic tenants equal to renting supply by entrepreneurs.

Competitive Equilibrium

The competitive equilibrium of the model is defined by a sequence of prices ${p_{T, t}$ , $p_{M, t}$ , $q_{t}$ , $r_{t}^{H}$ , $r_{t}^{B}$ , $w_{T, t}$ , $w_{M, t}}$ and real allocations ${C_{T, t}^{F}$ , $C_{T, t}^{H}$ , $C_{M, t}^{H}$ , $C_{t}^{E}$ , $C_{t}^{H}$ , $C_{t}$ , $H_{P, t}^{H}$ , $H_{P, t}^{E}$ , $H_{R, t}^{H}$ , $H_{R, t}^{F}$ , $Y_{T, t}$ , $Y_{M, t}$ , $K_{T, t}$ , $K_{M, t}$ , $N_{T, t}$ , $N_{M, t}$ , $B_{t}}$ that satisfy the following: (a) the optimization problems of foreign tourists, (b) the optimization problems of domestic households, (c) the optimization problems of entrepreneurs, and (d) all markets clear.

Empirical Results

Data

We choose three Icelandic data observables between 2002 and 2018: real consumption, real investment, and real house prices. All data series are obtained from Statistics Iceland. We refrain from using a series of tourism expenditure because there was a significant change of data compiling process by Statistics Iceland in 2009, and the data before and after are inconsistent. We do not use housing rentals because the data series is not consistent with our model measurement, which also includes hotel and guesthouse charges. The solution of our model takes the form of a state-space representation that is used to compute the likelihood function (Smets & Wouters, 2004). To make the data observables consistent with our model measurements, we log-linearize the equilibrium system in the model and make the corresponding transformation of the three data series by taking logarithms and then HP-filter (Hodrick & Prescott, 1997), as shown in Supplement Figure 4 (available online).

Model Calibration

The calibration procedure involves assigning values to some parameters of the model based on either micro-evidence from previous studies or long run steady state facts of the economy we study (Gomme & Rupert, 2007). We calibrate parameters in our model based on Iceland’s annual data over the past decade or so. These statistics can provide us a steady state ratio to match and pin down some parameter values. For the rest parameters, we rely on Bayesian estimation described in the next subsection.

Since the model is specified on an annual basis, the discount factor $β^{H}$ is set to 0.966, corresponding to a steady-state real interest rate of 3.5% (Seneca, 2010). We fix the discount factor of the entrepreneurs $β^{E}$ at 0.932. This value has a limited effect on the dynamics, but guarantees an impatience motive for entrepreneurs large enough that their borrowing limit is always binding (Iacoviello & Neri, 2010). The weight on housing in the households’ utility $j$ is set at 0.71, to pin down the average ratio of housing stock to consumption for domestic households. Regarding the inverse of Frisch elasticity of labor supply $η$ , we follow Seneca (2010) to set it at 3. Steady state entrepreneurial loan-to-value ratio $m$ is set to 0.7 to account for the average downpayment requirement for mortgage loans (Elíasson & Pétursson, 2009). The capital depreciation rate in the tourism sector is assumed to be higher than that in the manufacturing sector to account for the intensive utilization of facilities in tourism and hospitality-related activities during peak seasons (Turner & Hesford, 2018). This difference implies the tourism sector is more labor intensive than manufacturing sector (higher labor share in tourism production function), which is consistent with the general empirical fact (Chen et al., 2016). Therefore, we set $δ_{T} = 0.2$ , and $δ_{M} = 0.1$ , wheares the equilibria imply $α^{T} = 0.66$ , and $α^{M} = 0.55 >$ . These values are plausible comparing with that in Seneca (2010). Table 1 summarize the calibrated parameters as well as the steady-state ratios of the model (see the appendix for the derivation of the steady state, available online).

Table 1

Calibrated Parameters and Steady-state Ratios

Parameter	Description	Value	Source
$β_{H}$	Domestic HHs’ discount factor	0.966	Seneca (2010)
$β_{E}$	Entrepreneurs’ discount factor	0.932	Iacoviello and Neri (2010)
$j$	Weight on housing	0.71	Iacoviello and Neri (2010) and the authors’ calculation
$η$	Inverse of Frisch elasticity of labor supply	3	Seneca (2010)
$m$	Entrepreneurial loan-to-value ratio	0.7	Elíasson and Pétursson (2009)
$α_{T}$	Labor share in tourism production	0.66	Seneca (2010) and the authors’ calculation
$α_{M}$	Labor share in manufacturing production	0.55	Seneca (2010) and the authors’ calculation
$δ_{T}$	Tourism capital depreciation rate	0.2	Seneca (2010) and the authors’ calculation
$δ_{T}$	Manufacturing capital depreciation rate	0.1	Seneca (2010) and the authors’ calculation
Variable
$Y^{F} / Y$	Inbound tourism expenditure output ratio	11.8%	Statistics Iceland
$p_{T} Y_{T} / Y$	Tourism production output ratio	17.7%	Statistics Iceland
$C / Y$	Consumption output ratio	68.1%	Statistics Iceland
$N_{T} / N$	Tourism share of employment	11.0%	Statistics Iceland
$p_{T} C_{T}^{H} / C$	Domestic tourism expenditure consumption ratio	8.7%	Statistics Iceland
$I_{T} / I$	Share of investment in tourism sector	19.5%	WTTC T&T Iceland
$r^{H} H_{R}^{F} / Y^{F}$	accommodation expenditure for inbound tourists	21.1%	Statistics Iceland
$H_{P}^{H} / H$	Home ownership rate	80%	Statistics Iceland

Note: HH = household.

Prior and Posterior Distribution for Bayesian Estimation

For parameters that are specific to our model without insights from past research, we rely on the Bayesian method to estimate their values based on our sample (An & Schorfheide, 2007). The Monte Carlo-based optimization routine with Metropolis–Hasting algorithms is used to estimate the posterior mode and we generate two Markov chains with 20,000 draws in each chain to simulate the posterior distribution of the parameters. Supplement Figure 5 (available online) displays the multivariate convergence diagnostic test, reflecting the reliability of the estimation results (Brooks & Gelman, 1998). The upper, middle, and lower figures refer to the raw sequences and the corresponding second and third central moments, which all show closer or horizontally stable between the blue line and red dashed line, implying the two drawn chains converge and good reliability of the estimation. The acceptance ratio of the two chains are 0.59 and 0.53, respectively. This type of diagnostic test is also used in Liu and Wu (2019).

The parameters needing Bayesian estimation include foreign tourists’ elasticity of substitution between tourism consumption and accommodation $χ^{f}$ , households’ elasticity of substitution between tourism and manufacturing goods $χ^{h}$ , between houses of owner occupy and renting $ϕ^{h}$ , labour between tourism and manufacturing $ϕ^{n}$ , and the share parameters $φ^{f}$ , $φ^{h}$ , $ω^{h}$ , and $ω^{n}$ . The parameters governing the five shock process also require estimation, including AR(1) correlation coefficients $ρ_{f}$ , $ρ_{T}$ , $ρ_{M}$ , $ρ_{m}$ , and $ρ_{j}$ , and standard deviations $σ_{f}$ , $σ_{T}$ , $σ_{M}$ , $σ_{m}$ , and $σ_{j}$ , specified as follows:

\ln Y_{t}^{F} = ρ_{f} \ln Y_{t - 1}^{F} + e_{f, t} e_{f, t} ~ N (0, σ_{f}^{2})

\ln A_{T, t} = ρ_{T} \ln A_{T, t - 1} + e_{T, t} e_{T, t} ~ N (0, σ_{T}^{2})

\ln A_{M, t} = ρ_{M} \ln A_{M, t - 1} + e_{M, t} e_{M, t} ~ N (0, σ_{M}^{2})

\ln m_{t} = ρ_{m} \ln m_{t - 1} + e_{m, t} e_{m, t} ~ N (0, σ_{m}^{2})

\ln j_{t} = ρ_{j} \ln j_{t - 1} + e_{j, t} e_{j, t} ~ N (0, σ_{j}^{2})

Regarding the prior means, foreign tourists’ elasticity of substitution between tourism consumption and accommodation $χ^{f}$ can be jointly determined by the share of accommodation in inbound tourists’ expenditure of 33%, and the tourists’ price elasticity of accommodation demand of 0.6 (Masiero et al., 2015). Similarly, households’ elasticity of substitution between tourism and manufacturing goods $χ^{h}$ , is pinned down by combining the average share of Icelanders’ tourism consumption in their total consumption basket of 8.7% and Icelanders’ price elasticity of tourism demand of 0.5 (Song et al., 2010). It is difficult to obtain the substitutional elasticity between homeownership and rental due to the absence of prior information. We assume that the substitution is very elastic and we follow Sun and Tsang (2017) to assign the value of $ϕ^{h}$ to 6.5. For the elasticity of substitution of labor between tourism and manufacturing production, there is also of limitted prior information. We generally conjecture that tourism is still characterized by a workforce with a relatively lower level of skills and substitution between tourism and manuthe facturing sector is not very easy (Marchante et al., 2007). Therefore, we set the value of $ϕ^{n}$ to 0.8 for prior the mean. The prior means for the four shares are all set at 0.5 to account for generic situations. The prior distributions of the structural parameters and shock processes are presented in the left panels of Table 2.

Table 2

Prior and Posterior Distribution for Bayesian Estimation

Prior and Posterior Distribution of the Structural Parameters
Parameter	Prior Distribution			Posterior Distribution
Parameter	Distribution	M	SD	M	10%	90%
$χ^{f}$	Beta	0.5	0.1	0.4734	0.1309	0.7711
$χ^{h}$	Gamma	5	1	4.9051	3.4999	6.3831
$ϕ^{h}$	Gamma	6.5	1	6.1769	4.5608	7.6457
$ϕ^{n}$	Beta	0.8	0.1	0.8158	0.6837	0.9659
$φ^{f}$	Beta	0.5	0.1	0.5144	0.1892	0.8435
$φ^{h}$	Beta	0.5	0.1	0.4986	0.3345	0.6607
$ω^{h}$	Beta	0.5	0.1	0.5185	0.1917	0.8432
$ω^{n}$	Beta	0.5	0.1	0.6418	0.3986	0.9203
Prior and Posterior Distribution of the Shock Processes
$ρ_{f}$	Beta	0.7	0.1	0.7053	0.6031	0.8287
$ρ_{T}$	Beta	0.7	0.1	0.7017	0.5482	0.8656
$ρ_{M}$	Beta	0.7	0.1	0.7120	0.5694	0.8606
$ρ_{m}$	Beta	0.7	0.1	0.6919	0.5405	0.8572
$ρ_{j}$	Beta	0.7	0.1	0.7810	0.6611	0.9054
$σ_{f}$	Inverse gamma	0.1	0.1	0.9504	0.6119	1.3255
$σ_{T}$	Inverse gamma	0.1	0.1	0.0832	0.0301	0.1372
$σ_{M}$	Inverse gamma	0.1	0.1	0.0506	0.0347	0.0657
$σ_{m}$	Inverse gamma	0.1	0.1	0.0867	0.0334	0.1403
$σ_{j}$	Inverse gamma	0.1	0.1	0.3533	0.1912	0.5224

The right panels of Table 2 report the posterior mean, and 90% probability intervals. The estimate of $χ^{f}$ , inbound tourists’ elasticity of substitution between tourism consumption and accommodation, is 0.47, implying the complemetary relationship between the two. The three elasticities of substitution for domestic households, $χ^{h}$ , $ϕ^{h}$ , and $ϕ^{n}$ , are esitmated to be 4.91, 6.18, and 0.82, respectively. Therefore, it is quite clear that households demonstrate strong elasticities of substitution between tourism and manufacturing consumption, and between owner-occupied housing and rented properties (substitutes), reflecting easy movements in between; but weak substitutability of labor across sectors, implying difficulties when workers want to switch between different jobs. The estimates of three of the four shares, $φ^{f}$ , $φ^{h}$ , and $ω^{h}$ , are quite close to 0.5, whereas that of $ω^{h}$ is equal to 0.64. All AR(1) shocks are quite persistent, where the posteriors are close to their priors. The disturbances of inbound tourism demand shock and domestic house preference shock are extremely volatile.

Model Implications

In this section, we consider the economic implications of the model and examine the role of the tourism sector in explaining the fluctuation of housing price in Iceland. First, we use impulse response functions (IRFs) to illustrate how inbound tourism demand shock and other structural shocks shape the housing market dynamics (Cogley & Nason, 1995). Second, we rely on the unconditional forecast error variance decomposition to show the relative importance of different shocks in explaining the volatility of Icelandic housing market and the general economy (Lanne & Nyberg, 2016). Last, we conduct historical shock decomposition to show the driving force disturbance in our sample (Hasumi et al., 2018).

Impulse Responses

We simulate and plot the IRFs of 18 key variables to the inbound tourism demand shock, tourism sector productivity shock, and manufacturing sector productivity shock. Figure 2 plots the IRFs to inbound tourism demand shock. It indicates that a positive shock to foreign tourists’ demand, due to changes of preference or income, induces directly higher tourism goods consumption and rental together by foreign tourists, driving up prices of tourism goods and rentals. Higher rental prices motivate entrepreneurs to accumulate more housing stock for renting, which cut down the supply of owner-occupied housing (not shown), and push up house prices. Higher prices of tourism goods and house rental force domestic households to cut demand of tourism consumption and rental. Moreover, higher tourism production demands more employment in tourism industry, which raises sectoral wages. There is a flow of labour from the manufacturing sector to the tourism sector. Overall, aggregate output, consumption and investment all increase. These results are consistent with the results from (Zhang & Yang, 2018).

Figure 2

Impulse Responses to the Inbound Tourism Demand Shock

Supplement Figure 6 (available online) plots the IRFs to tourism sector productivity shock. As the figure shows, higher tourism sector productivity directly raises tourism production and wages and lowers the prices of tourism goods. Cheaper tourism goods induce increased consumption by foreign and domestic tourists. Due to complementarity, foreign tourists demand more housing rental (i.e., short-term vacation rentals) as well, driving up rental prices. House prices increase along with rental prices, though the effects are indirect and weak. A booming tourism sector indicates surging sectoral employment and wages. The aggregate economy, therefore, goes up with a higher level of output, consumption, and investment. The results are in line with that of Liu et al. (2018).

Supplement Figure 7 (available online) shows the IRFs to manufacturing sector productivity shock. The transmission channel is similar to that of tourism sector productivity shock but located in the manufacturing sector. Higher productivity in manufacturing industry induces higher manufacturing production, whereas lower prices of manufacturing goods. Lower cost boosts the demand for manufacturing consumption, crowding out tourism consumption of domestic and foreign tourists. Foreign tourists’ rental also declines due to complementarity to tourism consumption. Rental prices increase because tourism goods prices are higher and the decline of foreign tourism consumption is not as strong as a foreign rental (as shown in Equation [2]). As usual, the aggregate output, consumption, and investment all rise.

Variance Decomposition

We rely on forecast error variance decomposition to measure the relative importance of different shocks in shaping the aggregate fluctuations in Iceland. The idea is to determine the proportion of the variability of the errors in forecasting the endogenous variables that is due to variability in the structural shocks (Lanne & Nyberg, 2016). We mainly focus on six variables of most interest—real house prices, real rental prices, tourism production, manufacturing production, consumption, and investment, where the rest are available on request from the corresponding author. Supplement Table 1 (available online) presents the results on variance decomposition. The inbound tourism demand shock, $σ_{f}$ , drives over 40% of the variance in house prices, the variable of major interests. Manufacturing sector technology shock, $σ_{M}$ , drives a large amount (over 40%) of variance in house prices. Besides, housing preference shock, $σ_{j}$ , plays a significant role while tourism sector technology shock, $σ_{T}$ , and loan-to-value ratio shock, $σ_{m}$ , play a minor role. The other variable in the housing market is the rental prices, more than two thirds of which is driven by housing preference shock (69%). Inbound tourism demand shock ranks second, explaining almost 16% of the volatility. By contrast to house prices, rental prices have more say from shock to loan-to-value ratio, for almost 10%. Both manufacturing and tourism sector productivities have little contribution to the variance of rental prices.

For quantities produced by the two industries, we find that the sectoral factors have major influences over their corresponding sectors. For instance, inbound tourism demand shock and tourism technology shock combined account for almost all the variation of tourism production, though inbound tourism demand alone contributes nearly 70%. To understand the fluctuations in the tourism sector, the demand and supply shocks in the tourism sector are the key. Regarding the manufacturing sector, we find that manufacturing productivity alone explains 89% of the variation in production, whereas the rest four shocks together account for only 11%. This result is in line with the real business cycle literature that the total factor productivity shock accounts for the bulk of aggregate fluctuations (Prescott, 2016).

For aggregate variables like consumption and investment, the two most important shocks are found to be inbound tourism demand and manufacturing productivity. More specifically, 46% variation of consumption is attributed to inbound tourism demand shock, and another equal 46% is to manufacturing technology. When we turn to the variation of investment, manufacturing productivity is the most important shock, accounting for 55%. The rest is mostly contributed by inbound tourism demand (35%). Overall, we observe that the inbound tourism demand shock plays key role in determining the fluctuations of Icelandic house prices and aggregate economic quantities.

Historical Decomposition

For each of the four variables of most interest—real house prices, real rental prices, real consumption, and real investment, we conduct a historical shock decomposition, as shown in Supplement Figure 8 (available online), which shows the historical contribution of each type of structural shock to the variability of the endogenous variables over the sample period (Hasumi et al., 2018). Due to space limitation, the detailed results for all variables are available on request from the corresponding author. As Panel (a) shows, the inbound tourism demand shock and the house preference shock are the primary driving forces of the fluctuations in real house prices. Besides, manufacturing productivity shock also plays a significant role, confirming earlier result from variance decomposition. Panel (b) shows that house preference is the most important driving force determining the fluctuation of rental prices and inbound tourism demand shock ranks second, whereas the rest shocks only play a minor role. Panels (c) and (d) present that most of the fluctuations in consumption and investment are driven by the inbound tourism demand shock and manufacturing productivity shock. Overall, the estimated variance decomposition and the historical shock decomposition results show that the inbound tourism demand shock explains the very large amount of variation in house prices, rental prices, and aggregate quantities such as consumption and investment in Iceland.

Conclusion

Although the role of tourism in local economic growth has been widely investigated in the current tourism literature, the impact of tourism activities on the real estate market has not been fully studied. The majority of existing research is based on either hedonic method or traditional single regression econometric model with house price as a function of tourism, largely discarding the dynamics of the tourism–house price relationship from a broader macro context. The ongoing Icelandic housing market boom provides a perfect case to study, and the surging housing demand is companied with an explosion of inbound visitors and private renting to tourists, which inspires an exploration of the dynamic relationship between tourism and real estate markets. With a DSGE model, the article investigated this relationship with both an owner-occupied housing market and a rental market for inbound tourists renting.

We utilized the model by using Bayesian econometric technique and conducted several simulation exercises to examine how the shock to inbound tourism shapes the dynamics of the Icelandic housing market and the aggregate economy. The impulse response analysis demonstrated that both housing prices and rentals increase after a positive shock to inbound tourism demand. Higher inbound tourism demand raises the consumption of tourism goods as well as complementary accommodation, which pushes up the rentals. Higher rentals induce more real estate purchase by entrepreneurs, driving up house prices. Meanwhile, more properties in the rental market will crowd out the supply in the housing market, which leads to a further increase of house prices. The variance decomposition and historical shock decomposition show that both inbound tourism demand shock and manufacturing technology shock are the key driving forces of the fluctuations of Icelandic house prices, consumption and investment, whereas housing preference shock plays the most important role in determining the volatility of rental prices.

In terms of the policy implications, we are aware that the tourism sector in Iceland has grown to surpass all other sectors as the largest generator of export revenues for the Icelandic economy and any disturbances to tourism sector could easily spillover to housing market dynamics and aggregate fluctuations. Stabilizing tourism sector has the potential not only to stabilize foreign exchange earnings but also enable the macroeconomy to develop steadily. Since inbound tourism very likely synchronizes with the world business cycles, the countercyclical policy is needed for tourism management in Iceland. Gil-Alana and Huijbens (2018) show that the intensity of tourism development policy depends on the degree of persistence in the shock to the tourism sector. Our results are consistent with their argument that strong measures should be taken, given the facts of a very persistent shock to inbound tourism and a significant spread of tourism activities to the aggregate economy in Iceland.

During the recent COVID-19 pandemic, Icelandic inbound tourists shrank dramatically as nearly six thousand people, mostly in the tourism and transport industry, have been laid off by the end of April. As shown in our earlier simulation, a persistent negative shock to inbound tourism induced by the COVID-19 pandemic would spill-over and result in a dramatic decline in the real estate price and a slump in consumption, investment, and output. To stabilize the negative cycle, our analysis implies that some kind of response policy, such as government stimulus package or a tax cut, is needed to restore the housing sector and overall economy. As expected, we do see the economic actions in the wake of the COVID-19 pandemic, including measures to present Reykjavik as a viable tourist destination undertaken as soon as the situation allows. It is expected that we will continue to see related strong actions to ensure the recovery of the tourism sector and aggregate economy in Iceland.

Our work provided an initial attempt to analyze the relationship between tourism activities and house prices under the DSGE framework. As a preliminary research endeavor, this article did not embrace a detailed analysis of policy implementation such as tax levies in the tourism industry to compromise between raising the government revenue and promoting domestic tourism service to foreign visitors. Meanwhile, we modeled the rental market for inbound tourists in a relatively rough fashion that we did not further divide the total market into hotels, guesthouses, and private rentals to capture the sectoral effects, possibly neglecting the heterogeneous impacts. We consider these important extensions and leave for future research efforts.

Supplemental Material

Supplemental_material – Supplemental material for Does Tourism Contribute to Real Estate Boom? A DSGE Modeling in Small Open Economy

Supplemental material, Supplemental_material for Does Tourism Contribute to Real Estate Boom? A DSGE Modeling in Small Open Economy by Hongru Zhang and Yang Yang in Journal of Hospitality & Tourism Research

Footnotes

Authors’ Note:

This work was supported by the [National Social Science Foundation of China] under Grant [17AJY030]; [Jiangxi University of Finance and Economics Faculty Research Seed Fund] under Grant [K62192012].

ORCID iD

Yang Yang

Supplemental Material

Supplemental material for this article is available online.

Hongru Zhang (e-mail: zhanghongru@jxufe.edu.cn) is an assistant professor at the School of Economics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China. Yang Yang (corresponding author; e-mail: yangy@temple.edu) is an associate professor at the School of Tourism and Hospitality Management at Temple University.

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