An Econometric Analysis of International Travel

Jacques R. Artus

doi:10.5089/9781451969290.024.A004

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An Econometric Analysis of International Travel

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Jacques R. Artus

Jacques R. Artus
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Publication Date:: 01 Jan 1972

eISBN:: 9781451969290

Language:: English

Keywords:: SP; exchange rate; price variable; transportation cost; price term; foreign travel expenditure; foreign exchange; Currencies; Exchange rates; Personal income; expenditure equation

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THE PRESENT STUDY is an attempt to make a systematic analysis of the short-run determinants of international travel flows by specifying and estimating a complete world travel model. International travel is similar to international trade: it can be described by a system of bilateral and multilateral relationships in which an import of foreign travel services by one country corresponds to an export of such services by another country. Thus, the structure of the world travel model presented in this study is to a large extent similar to the structure of existing world trade models.1 General conceptual problems that are met in specifying such models have already been discussed in the economic literature and will not be reviewed here.2 The present model can be employed either for forecasting for one or two years ahead the foreign travel expenditures and the receipts from foreign visitors of certain countries or to analyze the effects of certain policy changes on international travel. Forecasts for 1972 and estimates of the effects of the changes in exchange rates that occurred in 1970 and 1971 are presented in Appendix II.

Abstract

THE PRESENT STUDY is an attempt to make a systematic analysis of the short-run determinants of international travel flows by specifying and estimating a complete world travel model. International travel is similar to international trade: it can be described by a system of bilateral and multilateral relationships in which an import of foreign travel services by one country corresponds to an export of such services by another country. Thus, the structure of the world travel model presented in this study is to a large extent similar to the structure of existing world trade models.¹ General conceptual problems that are met in specifying such models have already been discussed in the economic literature and will not be reviewed here.² The present model can be employed either for forecasting for one or two years ahead the foreign travel expenditures and the receipts from foreign visitors of certain countries or to analyze the effects of certain policy changes on international travel. Forecasts for 1972 and estimates of the effects of the changes in exchange rates that occurred in 1970 and 1971 are presented in Appendix II.

The coverage of the model is limited in two respects: (1) It is a model of travel flows among developed countries simply because international travel flows are highly concentrated in Western Europe and North America. (2) The aim of the model is to explain only the part of any travel spending abroad that is recorded in balance of payments statistics under the heading, “foreign travel.” Payments of transportation costs are not covered by this item and are not considered here.³ No attempt is made to explain the number of foreign travelers.

I. An Overall View of International Travel

In countries with high per capita incomes, foreign travel expenditure has become an important part of the total spending on foreign goods and services (see Table 1). Most of these foreign travel expenditures are made in developed countries; however, it is the less rich countries in this group that are the main beneficiaries. The European countries that border the Mediterranean Sea, in particular, have become dependent on the spending by foreign visitors to meet their foreign exchange needs.

Table 1.

Selected Countries: Expenditure on and Receipts from International Travel, 1970

Source: International Monetary Fund, Balance of Payments Yearbook.

^¹Costs of insurance and freight for imports are not included.

^²Escudo Area.

^³Rest of Western Europe: Finland, Iceland, Norway, and Turkey.

Table 1.

Selected Countries: Expenditure on and Receipts from International Travel, 1970

		Travel Expenditure Abroad			Receipts From Foreign Visitors
			Expressed as a proportion of expenditure on			Expressed as a proportion of receipts from
Country		Amount	All imported services	All imported goods and services	Amount	All exported services	All exported goods and services	Balance
		Million U. S. dollars	Per cent		Million U. S. dollars	Per cent		Million U. S. dollars
Austria		323	37	9	999	69	25	676
Belgium-Luxembourg		492	17	4	348	12	3	−144
Denmark		273	29	5	314	26	7	41
France		1,108	18	5	1,318	22	6	210
Germany		2,493	23	7	1,024	14	3	−1,469
Greece		55	20 ¹	3	194	32	16	139
Ireland		100	41¹	6	186	40	13	86
Italy		727	13	3	1,639	31	10	912
Netherlands		605	18	4	432	12	3	−173
Portugal²		103	25	5	237	37	14	134
Spain		138	12	2	1,681	68	34	1,543
Sweden		482	30	6	144	9	2	−338
Switzerland		427	44 ¹	6	905	36	11	478
United Kingdom		924	10	3	1,039	9	4	115
Yugoslavia		132	27 ¹	4	276	23	10	,44
ROWE ³		301	—	—	343	—	—	42
Canada		1,398	25	7	1,182	29	6	−216
Japan		315	5	2	232	6	1	−83
United States		3,953	27	7	2,319	12	4	−1,634
	Total	14,349			14,812			463

Source: International Monetary Fund, Balance of Payments Yearbook.

^¹Costs of insurance and freight for imports are not included.

^²Escudo Area.

^³Rest of Western Europe: Finland, Iceland, Norway, and Turkey.

Table 1.

Selected Countries: Expenditure on and Receipts from International Travel, 1970

		Travel Expenditure Abroad			Receipts From Foreign Visitors
			Expressed as a proportion of expenditure on			Expressed as a proportion of receipts from
Country		Amount	All imported services	All imported goods and services	Amount	All exported services	All exported goods and services	Balance
		Million U. S. dollars	Per cent		Million U. S. dollars	Per cent		Million U. S. dollars
Austria		323	37	9	999	69	25	676
Belgium-Luxembourg		492	17	4	348	12	3	−144
Denmark		273	29	5	314	26	7	41
France		1,108	18	5	1,318	22	6	210
Germany		2,493	23	7	1,024	14	3	−1,469
Greece		55	20 ¹	3	194	32	16	139
Ireland		100	41¹	6	186	40	13	86
Italy		727	13	3	1,639	31	10	912
Netherlands		605	18	4	432	12	3	−173
Portugal²		103	25	5	237	37	14	134
Spain		138	12	2	1,681	68	34	1,543
Sweden		482	30	6	144	9	2	−338
Switzerland		427	44 ¹	6	905	36	11	478
United Kingdom		924	10	3	1,039	9	4	115
Yugoslavia		132	27 ¹	4	276	23	10	,44
ROWE ³		301	—	—	343	—	—	42
Canada		1,398	25	7	1,182	29	6	−216
Japan		315	5	2	232	6	1	−83
United States		3,953	27	7	2,319	12	4	−1,634
	Total	14,349			14,812			463

Source: International Monetary Fund, Balance of Payments Yearbook.

^¹Costs of insurance and freight for imports are not included.

^²Escudo Area.

^³Rest of Western Europe: Finland, Iceland, Norway, and Turkey.

If the usefulness of a quantitative study of the determinants of international travel is demonstrated clearly by the importance of this item in the balance of payments of many countries, the feasibility of such a study is less obvious. Difficulties arise because of the complexity of the motivations for international travel and the poor quality of available statistical data on travel spending abroad. Both problems have been discussed at length in a recent study by Gray.⁴ Only a brief review of these problems is presented here.

The many motivations for international travel, broadly speaking, can be divided into three categories: tourism, business, and a residual category containing such diverse motivations as visiting relatives, studying abroad, attending international conferences, and shopping across borders. These motivations are not exclusive; tourism, in particular, is often an important secondary motivation for a business or study trip or for a visit to relatives. Such a classification may be too broad. For example, Gray proposes to differentiate between “sunlust” foreign trips made because some conditions are not available locally and “wanderlust” foreign travel for the sake of coming into contact with faraway cultures and places. Other classifications are possible. Each such class of foreign travel can be expected a priori to depend on different factors. Tourism may be influenced by real disposable personal income, prices of foreign travel services abroad and at home, publicity, cost and convenience of means of transportation, location of the home country, and endowment of the home country and neighboring countries with such tourist attractions as sea resorts, sunny skies, mountain resorts, and places of historical or natural interest. Spending owing to business trips abroad may depend upon the factors that influence imports, exports, and foreign investments. Visits to relatives may be influenced by patterns of immigration.

Collecting statistical data on travel spending abroad is not easy. Such spending can be estimated from two sources: sample surveys of returning travelers, and bank returns on foreign exchange transactions. The second method is particularly unreliable because of the extreme difficulty of separating foreign exchange transactions resulting from capital flows or home remittances and those related to travel spending abroad. Furthermore, tourist payments are made more and more with banknotes that are exported directly by tourists, thereby escaping bank records. Although more precise, the first method is not very reliable either, because the sample is often small and the replies of returning travelers often inaccurate. The method of sample surveys may also lead to large errors of measurement in periods of foreign exchange speculation against the home currency or in periods of rationing of foreign exchange for foreign travel; at such times, responses to questionnaires are often systematically biased. In any case, among the member countries in the Organization for Economic Cooperation and Development only Canada, Ireland, Switzerland, the United Kingdom, and the United States use sample surveys.

The position advanced in this paper is that despite all these difficulties much can be learned from a quantitative analysis of the short-run determinants of international travel. In the short run, most of the factors that cannot be measured easily, such as the demonstration effect, convenience of means of transportation, or endowment with tourist attractions, can be assumed to be either constant or changing at a small and regular rate over time. The difficulties owing to the multiplicity of the motivations for foreign travel are also exaggerated. Tourist travel is by far the largest component of foreign travel. For example, for the United Kingdom, tourist, business, and other travel accounted for 67 per cent, 18 per cent, and 15 per cent, respectively, of foreign travel expenditures in 1969.⁵ Furthermore, foreign travel spending for business trips, visits to relatives, and study abroad are likely to be relatively stable over time. Therefore, a study of short-run changes in foreign travel spending can justifiably concentrate on the factors that may influence tourism alone.

Some of the difficulties covered by the poor quality of statistical data can be reduced by considering a large number of samples, that is, by studying many countries rather than a few chosen ones. Furthermore, at least one economic characteristic of international travel facilitates its study: the fact that the supply of foreign travel services to a large extent can be assumed to be perfectly elastic when a whole country is considered, if only because the amount of goods and services consumed by foreign travelers (food, lodging, entertainment) is normally small relative to the amount of these goods consumed by nationals. There seem to be only a few exceptions, for example, Spain and Yugoslavia. This makes it much easier to identify the factors that influence the demand for foreign travel services.

II. A Model of International Travel

The model of international-travel presented here is based on a mixture of “bilateral” and “structural” approaches.⁶ The bilateral approach is employed to estimate flows of travel expenditure between the United States, Canada, and Western Europe. Each flow between two of these regions is assumed to be independent of any other flow of travel expenditure, so that it can be specified separately. On the other hand, intra-European travel flows are more interdependent, because similar foreign travel services are offered by various neighboring countries. Here, a travel structure has been interposed between the aggregate travel expenditures made by country i and the aggregate receipts from foreign visitors obtained by country j. Country i’s aggregate travel expenditures are estimated separately; then, country j’s receipts are specified as a function of a weighted average of the travel spending abroad by other countries, the weights being the shares of the various countries in country j’s receipts during a base year. Relative prices are introduced as explanatory variables in both the expenditure and receipt functions.

A flow chart of the present model is presented in Chart 1. The model includes separately only the main countries of origin or destination of world travel flows. Although Japan is now an important source of travel flows, it has not been included separately because most of Japan’s travel spending abroad occurs in Asia rather than in the main areas of international travel considered here. The model is not completely closed because the travel flows between the rest of the world (defined as the group of countries not included separately in the model) and Western Europe are not considered. These flows are small and difficult to measure and have been neglected in the present model.

Chart 1.

Flow Chart of the Model of International Travel

Citation: IMF Staff Papers 1972, 003; 10.5089/9781451969290.024.A004

Determinants of foreign travel expenditure

The theory of demand suggests that for a country the demand for imports may be written as

\begin{matrix} \frac{M}{P F} = f (\frac{P F}{P Y}, \frac{Y}{P Y}, H, Z), & (1) \end{matrix}

where M = value of imports; PF = price of imports; PY = price of other goods; Y = domestic disposable money income; H = number of residents; and Z = factors changing slowly over time, such as tastes. This form assumes that individual consumers are not subject to money illusion. If the population is assumed to be homogeneous, relationship (1) may be written on a per capita basis, namely,

\begin{matrix} \frac{M}{P F \cdot H} = f (\frac{P F}{P Y}, \frac{Y}{P Y \cdot H}, Z) . & (2) \end{matrix}

The functional form may be assumed to be log-linear. Relationship (2) may be applied to explain a country’s import of foreign travel services; however, here the precise definition of the relative price term and the specification of the time pattern of relationship (2) pose serious problems, which will now be considered.

The relative price term must reflect the main price variables that affect a country’s foreign travel expenditures. One form that this relative price term may take is

\begin{matrix} {\bar{\begin{matrix} R P \end{matrix}}}_{i} = \frac{\underset{j \neq i}{Σ} ω_{i j} {θ F^{i j} ({\bar{P}}_{j} / {\bar{F}}_{j}) + (1 - θ F^{i j}) {\bar{T}}_{i j} / {\bar{F}}_{i}}}{θ Y^{i} ({\bar{P}}_{i} / {\bar{F}}_{i}) + (1 - θ Y^{i}) {\bar{T}}_{i} / {\bar{F}}_{i}}, & (3) \end{matrix}

where

The bar—indicates that a variable is expressed in index form.

Transportation services are considered as a complement to travel services. The cross-price elasticity between the demand for these joint products and the demand for other goods is assumed to be zero; therefore, prices of other goods are not introduced into the equation.

For European and intra-North American foreign travel flows, the short-run influence of domestic and foreign transportation costs may be neglected (that is, θYⁱ = θF^ij = 1), and formula (3) becomes ⁷

\begin{matrix} {\bar{\begin{matrix} R P \end{matrix}}}_{i} = \frac{\underset{j \neq i}{Σ} ω_{i j} {\bar{P}}_{j} / {\bar{F}}_{j}}{{\bar{P}}_{i} / {\bar{F}}_{i}}, & (4) \end{matrix}

with ω_ij equal to the weight of country j in country i’s total spending on foreign travel services alone.

The reason for this assumption is that here the average costs of transportation to go abroad and to go to domestic vacation centers have the same relative magnitude and are affected by the same factors, so that they are not an essential element, at least in the short run, in the choice between the two kinds of tourism. Obviously, this assumption is not always realistic; for example, the recent availability of low-price charter flights between England and Spain has certainly influenced many Englishmen to spend their vacation in Spain rather than in England. However, it would be a highly complex, and perhaps impossible, task to take these factors into account.

The previous remarks certainly do not apply to the large travel flows from North America to Europe, where the domestic cost of transportation may still be neglected (that is, θYⁱ = 1), but the cost of trans-Atlantic transportation is likely to play an important role and must be included in the equation. In order to simplify the problem, the cost of transportation across the Atlantic, T_ij, and the corresponding weights, θF_ij, have been assumed to be the same, independently of the European country visited. Thus, even here, the weight ω_ij is identical to the weight of country j in country i’s spending on foreign travel services alone.

For purposes of statistical analysis, it is preferable to separate as much as possible the exchange rate variables from the other price factors included in equation (2). The reason is that exchange rates are known precisely, while the data on the local currency prices of travel services and the costs of transportation may contain large errors of measurement. If a composite variable containing errors of measurement were introduced into the equation, the estimate of its coefficient could be biased significantly.⁸ By introducing both sets of variables separately, it can be shown that under certain conditions, which are likely to be met in this case, the estimate of the coefficient of the relative exchange rate variable will be an unbiased estimate of the price elasticity. A technical discussion of this question is presented in Section III.

To separate, as much as possible, exchange rate variables from local currency price variables, it is assumed that the weighted average of the indices of prices expressed in foreign currency

(\underset{j \neq i}{Σ} ω_{i j} {\bar{P}}_{j} / {\bar{F}}_{j})

can be approximated by the ratio of the weighted average of indices of local currency prices to the weighted average of indices of foreign exchange rates ⁹

(\underset{j \neq i}{Σ} ω_{i j} {\bar{P}}_{j} / \underset{j \neq i}{Σ} ω_{i j} {\bar{F}}_{j}) .

From this assumption and from the assumption that the weights θYⁱ and θF^ij are always equal to unity except for trans-Atlantic travel flows, where the weights θF^ij all have the same value (hereinafter referred to as θF^Atl., smaller than unity), it follows that the relative price term may be written as

\begin{matrix} {\bar{R P}}_{i} & = & \frac{\begin{matrix} θ F^{A t l .} \underset{j \neq i}{Σ} ω_{i j} {\bar{P}}_{j} + [(1 - θ F^{A t l .}) \underset{j \neq i}{Σ} ω_{i j} {\bar{T}}_{i j} / {\bar{F}}_{i}] (\underset{j \neq i}{Σ} ω_{i j} {\bar{F}}_{j}) \end{matrix}}{P_{i}} \\ \times & \frac{{\bar{F}}_{i}}{\underset{j \neq i}{Σ} ω_{i j} {\bar{F}}_{j}} & {(3)}^{'} \end{matrix}

for the trans-Atlantic travel flows, and as

{\bar{R P}}_{i} = \begin{matrix} \frac{\begin{matrix} \underset{j \neq i}{Σ} ω_{i j} {\bar{P}}_{j} \end{matrix}}{{\bar{P}}_{i}} \times \frac{{\bar{F}}_{i}}{\begin{matrix} \underset{j \neq i}{Σ} ω_{i j} {\bar{F}}_{j} \end{matrix}} & (\begin{matrix} 4^{'} \end{matrix}) \end{matrix}

for all other travel flows. The first term of RP_i, relating mainly to relative local currency prices and transportation costs, will hereinafter be referred to as PR_i and the second term, relating to relative exchange rates, as FR_i.

A second reason to consider local currency prices and exchange rates separately is that in the short run the time pattern of the adjustment may be different for each of them because buyers of foreign travel services will be informed faster and more precisely of exchange rate changes than of changes in local currency prices in foreign countries. In the present model, the time pattern of the adjustment is derived from the following set of propositions. Foreign travelers are mainly tourists on an annual trip either in their home country or abroad but always in the same season (mainly summer). Spendings abroad are financed from an annual budget and can be influenced by the relative prices of travel services and the relative exchange rates both at the time when the trip is taking place and at the time when the decision is taken to go to a particular place in the home country or abroad. This decision is taken in the three quarters preceding the time of the trip. During that decision period, travelers have at all times a precise knowledge of exchange rates; however, their knowledge of foreign prices is limited to the memory that they may have of these prices from the time of their previous trip.

The following specification of foreign travel expenditure equations reflects these propositions. Country i’s real per capita spending on foreign travel in a given quarter is expressed as a function of the sum of (i) real per capita disposable personal income received by country i’s residents over the previous four quarters; (ii) the relative local currency prices of travel services in country i and abroad, not corrected for exchange rate changes, in the current quarter and in the corresponding quarter of the previous year; (iii) the relative prices of foreign exchange in country i and abroad in the current quarter and in the previous three quarters; (iv) a time trend representing long-run factors; and (v) a seasonal coefficient. Formally,

\begin{matrix} \begin{matrix} M R_{i, t} / {\bar{P F}}_{i, t} = A {(Σ_{π = 0}^{π = 3} Y R P_{i, t - π - 1})}^{α} {\bar{P R}}_{i, t}^{β_{1}} {\bar{P R}}_{i, t - 4}^{β_{2}} {\bar{F R}}_{i, t}^{γ_{1}} \\ (Σ_{τ = 1}^{τ = 3} {\bar{F R}}_{i, t - τ} / 3) γ_{2} e^{r t} S_{i, t} e^{ε_{t}}, \end{matrix} & (5) \end{matrix}

where

A, α, β₁, β₂, γ₁, γ₂, r = various parameters; and t refers to the quarterly time period.

The main advantage of a quarterly foreign travel model is that it allows for a relatively precise estimation of both the time path of the effect of a discrete change in the exchange rate and the magnitude of the final effect after all adjustments have taken place. However, for many countries, no quarterly data are available on foreign travel spending or on disposable personal income, so that this quarterly model normally cannot be applied directly; nevertheless, equation (5) can be aggregated into a yearly function from which all its parameters can be estimated. Although the rigorous aggregation of equation (5) over four successive quarters yields an extremely complex formula, it can be assumed for the purpose of simplification that S_i is the only variable the magnitude of which changes drastically from quarter to quarter, so that equation (5) can be rewritten on a yearly basis as

\begin{matrix} \frac{\begin{matrix} M R_{i, T} \end{matrix}}{{\bar{P F}}_{i, T}} = A \cdot Y R P_{i, T}^{α} {\bar{P R}}_{i, T}^{β_{1}} {\bar{P R}}_{i, T - 1}^{β_{2}} {\bar{F R}}_{i, T}^{γ_{1}} {\bar{FR}}_{i, TL}^{γ 2} e^{4 γ . T} e^{εT}, & (6) \end{matrix}

where (MR_i,T/PF_i,T) is country i’s per capita real spending abroad during year T, while for each independent variable the observation corresponding to year T is defined as a weighted average of the four corresponding quarterly observations, the weights being the seasonal factors ss_{1, i}, ss_{2, i}, ss_{3, i}, and ss_{4, i}.¹¹ The variable FR_i,TL corresponds to the weighted average of the lagged values of FR_i,t in equation (5).

When quarterly observations on foreign travel spending are not available, equation (6) can be substituted for equation (5). If quarterly observations on real per capita disposable personal income are not available either, simple yearly estimates of this variable can be introduced into equation (6) instead of the correct weighted average of quarterly observations. The error of measurement made in this case is normally small because of the slow fluctuations in income variables.

In bilateral flows, the expressions of variables PR and FR are greatly simplified because only the price and exchange rate variables of the spending and receiving countries are relevant; except for that difference, the specifications of equations (5) and (6) apply to bilateral flows.

Determinants of receipts from foreign visitors

Obviously, for the bilateral flows, the equations for expenditures explain also the receipts from foreign visitors obtained by each country. However, for the multilateral part of the model, the expenditures by one country remain to be allocated among receiving countries. In the present model, this allocation is made by employing a share approach. A country’s real receipts from foreign visitors, X_i, are explained as a function of a market variable, D_i, defined as a weighted average of the foreign travel expenditures made by other countries; relative local currency prices, PC_i; relative exchange rates, FC_i; and various long-run factors represented by a time trend, T. The elasticity of real receipts with respect to the weighted average of other countries’ expenditures is normally assumed to be equal to 1. The methods to specify lag adjustments and to differentiate between the effects of local currency prices and exchange rates are similar to the methods employed for travel expenditures. Formally,

\begin{matrix} \frac{\begin{matrix} X_{i, T} \end{matrix}}{{\bar{P}}_{i, T} / {\bar{F}}_{i, T}} = A \cdot {\bar{D}}_{i, T}^{α = 1} {\bar{P C}}_{i, T}^{β_{1}} {\bar{P C}}_{i, T - 1}^{β_{2}} {\bar{F C}}_{i, T}^{γ_{1}} {\bar{F C}}_{i, T L}^{γ_{2}} e^{4 γ . T} e^{ε T}, & (7) \end{matrix}

where X_i,T is country i’s real receipts from foreign visitors during year T and where the market variable D_i,T is defined as

\begin{matrix} {\bar{D}}_{i, T} = \underset{j \neq i}{Σ} ξ_{i j} ({\bar{M}}_{j, T} / {\bar{P F}}_{j, T}) {\bar{H}}_{j, T,} & (8) \end{matrix}

where H_j,T is the population in year T and ξ_ij is the weight of country j in country i’s receipts in the base year, 1965.

For each other variable contained in equation (7), the observation corresponding to year T is defined as a weighted average of the four corresponding quarterly observations, the weights being the seasonal factors sr_{1, i}, sr_{2, i}, sr_{3, i}, and sr_{4, i}. The definitions of the relative local price variables on a quarterly basis are

\begin{matrix} {\bar{P C}}_{i, t} = \underset{l \neq i}{Σ} ξ_{i l} \frac{θ F^{A t l .} {\bar{P}}_{i, t} + (1 - θ F^{A t l .}) {\bar{T}}_{i j, t}}{\underset{j}{Σ} ω_{l j} {\bar{P}}_{j, t}} & (9) \end{matrix}

in the equations for the receipts of the United States and Canada from Western Europe, and

\begin{matrix} {\bar{P C}}_{i, t} = \underset{l \neq i}{Σ} ξ_{i l} ({\bar{P}}_{i, t} / \underset{j}{Σ} ω_{l j} {\bar{P}}_{j, t}) & (10) \end{matrix}

in the equations for the receipts of European countries. The relative exchange rate variables are

\begin{matrix} {\bar{F C}}_{i, t} = \underset{l \neq i}{Σ} ξ_{i l} (\underset{j}{Σ} ω_{l j} {\bar{F}}_{j, t} / {\bar{F}}_{i, t}) & (11) \end{matrix}

and

\begin{matrix} {\bar{F C}}_{i, t L} = Σ_{τ = 1}^{τ = 3} {\bar{F C}}_{i, t - τ} / 3. & (12) \end{matrix}

The variables PC_i and FC_i reflect the average competitiveness of the foreign travel services offered by country i relative to the foreign travel services offered by other countries in the various “foreign markets l.”¹² The coefficients of the variables PC_i and FC_i are elasticities of market shares with respect to relative prices.¹³

III. Empirical Findings

In nearly all cases, the parameters for foreign travel expenditure were estimated from observations for the period 1955-70 by ordinary least-squares multiple regression, using equation (6) and yearly income data. The only exceptions were the parameters for Germany and the intra-North American flows, which were estimated from quarterly observations by employing equation (5). No attempt was made to explain the foreign travel expenditures of Greece, Portugal, Spain, and Yugoslavia, or of the countries, such as Finland, Iceland, Norway, and Turkey, that constitute the category “rest of Western Europe.” Travel abroad by nationals of these countries is on a fairly small scale, and statistical data on these flows are often inaccurate or nonexistent. In most cases, the parameters of the equations for aggregate receipts from foreign visitors were also estimated from observations for the period 1955-70, by applying equation (7) and plugging into it the estimates of foreign travel expenditures obtained from the expenditure equations.¹⁴ For Austria, France, Germany, Spain, and Switzerland, the parameters for receipts were estimated from observations for the period 1960-70. Consumer price indices were used as proxy variables for prices of foreign travel services, except for Yugoslavia, where an index of service prices was employed. The data are presented in Appendix I.

Results for foreign travel expenditure

Because of the high degree of multicollinearity between trends and income variables, the trends had to be deleted from the regression equations. A study of the biases that may result from this procedure are presented below. Other variables were kept in the equations even when their estimated coefficients were not significantly different from zero; however, they were deleted from the regression equations whenever their estimated coefficient had the wrong sign.

The regression coefficients and the goodness-of-fit statistics are presented in Table 2. The antilogs of the standard errors of the regressions are relatively large, with values above 1.05 for all but six countries.¹⁵ However, the Durbin-Watson test leads to the rejection of the hypothesis of autocorrelated residuals in nine countries and is indeterminate in the other eight countries. This absence of a serious autocorrelation problem suggests that no important variable has been omitted and that the large standard errors of the regressions are likely to be due to errors in the measurement of travel expenditure or to the presence of a number of temporary disturbance factors that are not identified.

Table 2.

Regression Coefficients: Annual Real Per Capita Expenditure on International Travel, 1955–70 ¹

^¹The estimated values of the scale and disturbance factors are given directly rather than under their logarithmic forms. Below the point estimate for each factor, a check beside a number indicates the antilog of the standard error of the estimated value of this factor under logarithmic form. Numbers in parentheses are standard errors. Se and D- W refer to the standard errors of the regressions and the Durbin-Watson statistics, respectively. Below the standard error of each regression, a check beside a number indicates its antilog. Standard errors and regression coefficients are corrected for the number of degrees of freedom.

^²Trend, 1955–58.

^³Brussels World’s Fair, 1958.

^⁴Foreign exchange restriction in 1958.

^⁵Foreign exchange restriction in 1959.

^⁶Political disturbances and foreign exchange restriction in 1968.

^⁷Foreign exchange restriction in 1969.

^⁸The period of observation covers only 1960–70.

^⁹The estimation was made from quarterly observations.

^¹⁰A more complete recording than usual of travel debits caused by the discount on Italian banknotes abroad, which led Italian tourists to purchase their currency requirements at home.

^¹¹Foreign exchange restriction in 1966 (one half of the effect), 1967, 1968, and 1969.

^¹²Expo 67 in Montreal, 1967.

^¹³Reduction in duty-free allowances for returning travelers, beginning in September 1961.

^¹⁴Olympic Games in Rome, 1960.

^¹⁵Political crises in Europe (Berlin, 1961, and France, May 1968).

^¹⁶Rest of the world.

^¹⁷Trend, 1955–70.

Table 2.

Regression Coefficients: Annual Real Per Capita Expenditure on International Travel, 1955–70 ¹

		Scale Factor					Elasticities with Respect to					Goodness-of-Fit Statistics
Country		Scale Factor	Disturbance Factors				Y	PR	PR _T-1	FR	FR _L	${\bar{R}}^{2}$	Se	D-W
Austria		45.30					3.84		−0.75	−2.45		0.983	0.0976	1.92
		5.05 √					(0.25)		(1.52)	(1.92)			1.102 √
Belgium-Luxembourg		5.64	0.267 ²		0.485 ³		2.46					0.966	0.1130	1.78
		5.01 √	(0.043)		1.062 √		(0.24)						1.120 √
Denmark		18.00					1.63	−3.20		−2.97		0.996	0.0263	2.02
		2.09 √					(0.10)	(0.29)		(0.55)			1.027 √
France		6.54	0.862 ⁴	0.729 ⁵	0.928 ⁶	0.788 ⁷	3.55		−5.26		−4.69	0.973	0.1080	1.70
		14.90 √	1.228 √	1.161 √	1.145 √	1.144 √	(0.38)		(1.09)		(1.17)		1.114 √
Germany ^8, ⁹		137.00					2.34	−1.82	−1.77	−1.21	−0.67	0.983	0.0590	2.31
		7.54 √					(0.43)	(1.34)	(1.26)	(0.52)	(0.66)		1.061 √
Ireland		43.83					1.66	−2.45		−0.32	−3.80	0.916	0.0758	1.59
		4.82 √					(0.24)	(1.95)		(13.14)	(13.21)		1.079 √
Italy		2.18	0.236 ²		1.466 ¹⁰		1.78	−5.09		−7.63		0.993	0.0653	2.96
		3.89 √	(0.033)		1.085 √		(0.21)	(1.13)		(1.55)			1.068 √
Netherlands		24.30					1.85	−0.14		−4.48	−1.03	0.990	0.0554	2.13
		6.41 √					(0.28)	(0.93)		(2.20)	(2.32)		1.057 √
Sweden		7.07					2.86			−1.32	−2.28	0.962	0.0889	1.41
		5.65 √					(0.24)			(4.17)	(4.43)		1.093 √
Switzerland		22.95					1.36				−1.19	0.998	0.0095	2.31
		1.20 √					(0.03)				(0.12)		1.010 √
United Kingdom		9.73	0.864 ¹¹				2.00		−1.23	−1.78		0.940	0.0380	2.28
		1.26 √	1.026 √				(0.34)		(1.04)	(0.34)			1.039 √
United States
	In Canada ⁹	1.23	1.465 ¹²				1.73	−3.74		−1.40	−0.98	0.988	0.0843	1.76
		2.45 √	1.066 √				(0.14)	(1.03)		(0.68)	(0.77)		1.086 √
	In Western Europe	4.72	0.947 ¹³	1.118 ¹⁴	0.939 ¹⁵			−1.02			−1.01	0.934	0.0330	2.27
		15.25 √	1.035 √	1.051 √	1.030 √			(0.50)			(0.83)		1.033 √
	In ROW ¹⁶				0.0649 ¹⁷							0.987	0.0354	1.08
					(0.0019)								1.035 √
Canada
	In United States ⁹	9.21	0.835 ¹²				0.83		−5.56	−1.42	−1.05	0.897	0.0892	2.15
		2.70 √	1.065 √				(0.17)		(1.47)	(0.73)	(0.83)		1.093 √
	In Western Europe	7.69	0.892 ¹²						−1.56		−0.79	0.928	0.0487	1.80
		1.02 √	1.075 √						(0.12)		(0.26)		1.050 √
	In ROW ¹⁶		0.866 ¹²		0.1133 ¹⁷					−2.73		0.931	0.1020	1.84
			1.118 √		(0.0123)					(1.01)			1.108 √

^²Trend, 1955–58.

^³Brussels World’s Fair, 1958.

^⁴Foreign exchange restriction in 1958.

^⁵Foreign exchange restriction in 1959.

^⁶Political disturbances and foreign exchange restriction in 1968.

^⁷Foreign exchange restriction in 1969.

^⁸The period of observation covers only 1960–70.

^⁹The estimation was made from quarterly observations.

^¹⁰A more complete recording than usual of travel debits caused by the discount on Italian banknotes abroad, which led Italian tourists to purchase their currency requirements at home.

^¹¹Foreign exchange restriction in 1966 (one half of the effect), 1967, 1968, and 1969.

^¹²Expo 67 in Montreal, 1967.

^¹³Reduction in duty-free allowances for returning travelers, beginning in September 1961.

^¹⁴Olympic Games in Rome, 1960.

^¹⁵Political crises in Europe (Berlin, 1961, and France, May 1968).

^¹⁶Rest of the world.

^¹⁷Trend, 1955–70.

Table 2.

Regression Coefficients: Annual Real Per Capita Expenditure on International Travel, 1955–70 ¹

		Scale Factor					Elasticities with Respect to					Goodness-of-Fit Statistics
Country		Scale Factor	Disturbance Factors				Y	PR	PR _T-1	FR	FR _L	${\bar{R}}^{2}$	Se	D-W
Austria		45.30					3.84		−0.75	−2.45		0.983	0.0976	1.92
		5.05 √					(0.25)		(1.52)	(1.92)			1.102 √
Belgium-Luxembourg		5.64	0.267 ²		0.485 ³		2.46					0.966	0.1130	1.78
		5.01 √	(0.043)		1.062 √		(0.24)						1.120 √
Denmark		18.00					1.63	−3.20		−2.97		0.996	0.0263	2.02
		2.09 √					(0.10)	(0.29)		(0.55)			1.027 √
France		6.54	0.862 ⁴	0.729 ⁵	0.928 ⁶	0.788 ⁷	3.55		−5.26		−4.69	0.973	0.1080	1.70
		14.90 √	1.228 √	1.161 √	1.145 √	1.144 √	(0.38)		(1.09)		(1.17)		1.114 √
Germany ^8, ⁹		137.00					2.34	−1.82	−1.77	−1.21	−0.67	0.983	0.0590	2.31
		7.54 √					(0.43)	(1.34)	(1.26)	(0.52)	(0.66)		1.061 √
Ireland		43.83					1.66	−2.45		−0.32	−3.80	0.916	0.0758	1.59
		4.82 √					(0.24)	(1.95)		(13.14)	(13.21)		1.079 √
Italy		2.18	0.236 ²		1.466 ¹⁰		1.78	−5.09		−7.63		0.993	0.0653	2.96
		3.89 √	(0.033)		1.085 √		(0.21)	(1.13)		(1.55)			1.068 √
Netherlands		24.30					1.85	−0.14		−4.48	−1.03	0.990	0.0554	2.13
		6.41 √					(0.28)	(0.93)		(2.20)	(2.32)		1.057 √
Sweden		7.07					2.86			−1.32	−2.28	0.962	0.0889	1.41
		5.65 √					(0.24)			(4.17)	(4.43)		1.093 √
Switzerland		22.95					1.36				−1.19	0.998	0.0095	2.31
		1.20 √					(0.03)				(0.12)		1.010 √
United Kingdom		9.73	0.864 ¹¹				2.00		−1.23	−1.78		0.940	0.0380	2.28
		1.26 √	1.026 √				(0.34)		(1.04)	(0.34)			1.039 √
United States
	In Canada ⁹	1.23	1.465 ¹²				1.73	−3.74		−1.40	−0.98	0.988	0.0843	1.76
		2.45 √	1.066 √				(0.14)	(1.03)		(0.68)	(0.77)		1.086 √
	In Western Europe	4.72	0.947 ¹³	1.118 ¹⁴	0.939 ¹⁵			−1.02			−1.01	0.934	0.0330	2.27
		15.25 √	1.035 √	1.051 √	1.030 √			(0.50)			(0.83)		1.033 √
	In ROW ¹⁶				0.0649 ¹⁷							0.987	0.0354	1.08
					(0.0019)								1.035 √
Canada
	In United States ⁹	9.21	0.835 ¹²				0.83		−5.56	−1.42	−1.05	0.897	0.0892	2.15
		2.70 √	1.065 √				(0.17)		(1.47)	(0.73)	(0.83)		1.093 √
	In Western Europe	7.69	0.892 ¹²						−1.56		−0.79	0.928	0.0487	1.80
		1.02 √	1.075 √						(0.12)		(0.26)		1.050 √
	In ROW ¹⁶		0.866 ¹²		0.1133 ¹⁷					−2.73		0.931	0.1020	1.84
			1.118 √		(0.0123)					(1.01)			1.108 √

^²Trend, 1955–58.

^³Brussels World’s Fair, 1958.

^⁴Foreign exchange restriction in 1958.

^⁵Foreign exchange restriction in 1959.

^⁶Political disturbances and foreign exchange restriction in 1968.

^⁷Foreign exchange restriction in 1969.

^⁸The period of observation covers only 1960–70.

^⁹The estimation was made from quarterly observations.

^¹⁰A more complete recording than usual of travel debits caused by the discount on Italian banknotes abroad, which led Italian tourists to purchase their currency requirements at home.

^¹¹Foreign exchange restriction in 1966 (one half of the effect), 1967, 1968, and 1969.

^¹²Expo 67 in Montreal, 1967.

^¹³Reduction in duty-free allowances for returning travelers, beginning in September 1961.

^¹⁴Olympic Games in Rome, 1960.

^¹⁵Political crises in Europe (Berlin, 1961, and France, May 1968).

^¹⁶Rest of the world.

^¹⁷Trend, 1955–70.

Estimated income elasticities are high with small standard errors for nearly all countries. Two noticeable exceptions are the expenditures made by U.S. nationals and Canadians in Europe, which do not seem to be affected by income; in both equations, the income variables were deleted after their estimated coefficients had been found small, not significantly different from zero, and with a negative sign. A possible reason is that the short-run variations in the aggregate disposable personal income of these countries do not reflect closely the variations in the income of the members of the professions, businessmen, and students, who represent a large fraction of the U.S. nationals and Canadians traveling in Europe.¹⁶

As could be expected, the multicollinearity among successive values of the local currency price and exchange rate variables is so high that most of the time the partial elasticities with respect to lagged and unlagged variables cannot be estimated with any precision. However, the estimates of the sums of the coefficients of the lagged and unlagged variables are more precise. These estimates, which express the estimated “total” elasticities of foreign travel expenditure with respect to local currency prices or with respect to exchange rates, are presented in Table 3 for the European countries. (This table also gives some results corresponding to an assumed long-run trend of +5 per cent a year for per capita real travel expenditure (that is, 4r = 0.05); their meaning will be explained below.) The estimates of the total elasticities with respect to exchange rates are reasonably precise and less dispersed than the estimates of the total elasticities with respect to local currency prices. Only four local currency price elasticities are significantly different from zero, in contrast to most foreign exchange rate elasticities. The estimated values of these total elasticities are high. The average total elasticities for European countries are −2.71 (0.42)¹⁷ for local currency prices and −3.58 (0.52) for exchange rates.¹⁸

Table 3.

Total Elasticities of Real Per Capita Expenditure with Respect to Income, Local Currency Price, and Foreign Exchange Rate for European Countries, With and Without Trend¹

^¹An asterisk indicates that an estimate is significantly different from zero at the 95 per cent confidence level. Columns headed by 4r = 0.0 refer to the regression equations assuming no trend factor. Columns headed by 4r = 0.05 refer to the regression equations where the annual trend coefficient is constrained to 0.05.

Table 3.

Total Elasticities of Real Per Capita Expenditure with Respect to Income, Local Currency Price, and Foreign Exchange Rate for European Countries, With and Without Trend¹

		Income			Local Currency Price			Foreign Exchange Rate
		Point estimate		Standard	Point estimate		Standard	Point estimate		Standard
Country		4r = 0.0	4r = 0.05	error	4r = 0.0	4r = 0.05	error	4r = 0.0	4r = 0.05	error
Austria		3.84*	2.71*	0.25	−0.75	−1.24	1.52	−2.45	−1.93	1.92
Belgium-Luxembourg		2.46*	1.13*	0.24	—	—	—	—	—	—
Denmark		1.63*	0.70*	0.10	−3.20*	−1.73*	0.29	−2.97*	−2.25*	0.55
France		3.55*	2.44*	0.38	−5.26*	−4.87*	1.09	−4.69*	−4.87*	1.17
Germany		2.34*	2.03*	0.43	−3.59*	−5.26*	1.10	−1.88*	−1.90*	0.53
Ireland		1.66*	0.27	0.24	−2.45	−0.73	1.95	−4.12	−0.45	3.87
Italy		1.78*	0.79*	0.21	−5.09*	−4.33*	1.13	−7.63*	−6.94*	1.55
Netherlands		1.85*	1.14*	0.28	−0.14	−0.04	0.93	−5.51*	−3.04*	1.11
Sweden		2.86*	1.36*	0.24	—	—	—	−3.60*	−1.74	1.61
Switzerland		1.36*	0.11*	0.03	—	—	—	−1.19*	−0.31*	0.12
United Kingdom		2.00*	0.09	0.34	−1.23	−1.13	1.04	−1.78*	−2.67*	0.34
	Average	2.30*	1.16*	0.08	−2.71*	−2.42*	0.42	−3.58*	−2.61*	0.52

Table 3.

Total Elasticities of Real Per Capita Expenditure with Respect to Income, Local Currency Price, and Foreign Exchange Rate for European Countries, With and Without Trend¹

		Income			Local Currency Price			Foreign Exchange Rate
		Point estimate		Standard	Point estimate		Standard	Point estimate		Standard
Country		4r = 0.0	4r = 0.05	error	4r = 0.0	4r = 0.05	error	4r = 0.0	4r = 0.05	error
Austria		3.84*	2.71*	0.25	−0.75	−1.24	1.52	−2.45	−1.93	1.92
Belgium-Luxembourg		2.46*	1.13*	0.24	—	—	—	—	—	—
Denmark		1.63*	0.70*	0.10	−3.20*	−1.73*	0.29	−2.97*	−2.25*	0.55
France		3.55*	2.44*	0.38	−5.26*	−4.87*	1.09	−4.69*	−4.87*	1.17
Germany		2.34*	2.03*	0.43	−3.59*	−5.26*	1.10	−1.88*	−1.90*	0.53
Ireland		1.66*	0.27	0.24	−2.45	−0.73	1.95	−4.12	−0.45	3.87
Italy		1.78*	0.79*	0.21	−5.09*	−4.33*	1.13	−7.63*	−6.94*	1.55
Netherlands		1.85*	1.14*	0.28	−0.14	−0.04	0.93	−5.51*	−3.04*	1.11
Sweden		2.86*	1.36*	0.24	—	—	—	−3.60*	−1.74	1.61
Switzerland		1.36*	0.11*	0.03	—	—	—	−1.19*	−0.31*	0.12
United Kingdom		2.00*	0.09	0.34	−1.23	−1.13	1.04	−1.78*	−2.67*	0.34
	Average	2.30*	1.16*	0.08	−2.71*	−2.42*	0.42	−3.58*	−2.61*	0.52

The bilateral flows between the United States and Canada are found to be sensitive to local currency prices and exchange rates, while the expenditures made by these countries in Western Europe seem to be rather insensitive to these factors. The total elasticities of U. S. expenditures in Canada are -3.74 (1.03) for local currency prices and -2.38 (0.35) for exchange rates. For Canada’s expenditures in the United States, the total elasticities are -5.56 (1.47) for local currency prices and -2.47 (0.34) for exchange rates. The estimates of the elasticities of Canadian and U. S. expenditures in Western Europe with respect to relative local currency prices, exchange rates, and transportation costs are derived from the estimates of the coefficients of the relative exchange rate variables and the coefficients of the variables PR_T and PR_T-1, which, here, are composite variables. The elasticity with respect to exchange rates is only -0.50 (0.87) for U.S. expenditures and -0.39 (0.27) for Canada’s expenditures. Elasticities with respect to domestic prices are larger: -1.02 (0.50) for the United States and -1.56 (0.12) for Canada. Elasticities with respect to foreign prices and transportation costs are equal to half the values of the elasticities with respect to domestic prices because both foreign prices and transportation costs have a 50 per cent weight in the definition of the PR_T and PR_T-1 variables.

Disturbance factors, such as foreign exchange restrictions, reduction in duty-free allowance for returning travelers, and international fairs, had a large impact on foreign travel flows (see Table 2). In particular, foreign exchange restrictions were found to have reduced France’s expenditure by 13.8 (19.6) per cent in 1958, 27.1 (11.7) per cent in 1959, 7.2 (13.4) per cent in 1968,¹⁹ and 21.2 (11.3) per cent in 1969, compared with what it would have reached without exchange restrictions. In the United Kingdom, foreign exchange restrictions cut foreign travel expenditure by an average of 13.6 (2.0) per cent from mid-1966 to the end of 1969.

Analysis of possible bias

Several sources of bias need to be investigated. First, there is not much doubt that European foreign travel flows have been increasing over the past 15 years under the influence of such long-run factors as the development of means of communication, in particular the increase in the number of private automobiles. The trends having been deleted from the regression equations, the influence of these long-run factors is now picked up by the remaining variables, and this may cause relatively large bias in the estimates of their coefficients. The precise values of this bias can be determined only if the true values of the coefficients of the trend variables are known.²⁰ Obviously these true values are unknown; however, it is most unlikely that they could be larger than 0.05 (that is, a compounded rate of increase of 5 per cent a year for per capita real spending on foreign travel) if only because in most countries such a trend would already account for the bulk of the observed increases in foreign travel, leaving only small increases to be explained by growth in real income. To have an indication of the maximum value of this bias, all estimates of income, local currency prices, and exchange rate elasticities for European countries have been re-estimated under the assumption of a 5 per cent positive trend. The results are presented in Table 3. Estimated income elasticities are cut in half, on average, from 2.30 (0.08) to 1.16 (0.08). The average of the estimated local currency price elasticities is reduced from −2.71 (0.42) to −2.42 (0.42), while the average of the estimated exchange rate elasticities is reduced from −3.58 (0.52) to −2.61 (0.52).

Another source of bias is the use of consumer price indices as proxy variables for local currency prices of travel services. Such proxy variables are certainly imperfect. To the extent that the average of local currency prices of foreign countries is the source of error, both the dependent variable, which is in real terms, and the independent relative local currency price variable will contain a similar error of measurement, and the estimate of the coefficient of the local currency price elasticity will be biased toward −1.²¹ However, this is not likely to be an important source of error because the averaging procedure employed to derive the relevant index of local currency prices in foreign countries should tend to reduce the importance of these random errors. The main source of error is probably the domestic price variable, which enters only the relative price term, so that the estimate of the elasticity is more likely to be biased toward zero.²² These errors of measurement may also cause some bias in the estimates of the coefficients of the other variables present in the equation. However, this is not likely. In general, this should not result in serious bias for the exchange rate elasticities because there is no reason, at least in the short run, to expect a high correlation between either the errors of measurement or the true local currency prices and the variations in the exchange rates.²³ Exceptions are the equations for U. S. and Canadian expenditures in Western Europe, where the PR and FR variables are not independent because they both contain the same foreign exchange rates. In these cases, errors of measurement in the local currency price variables may also cause some bias in the estimates of the exchange rate elasticities. Furthermore, this dependence increases the indeterminacy of the estimates.

Results for receipts from foreign visitors

First, the parameters of the receipts equations were estimated without imposing the constraint that the elasticity, α, of receipts with respect to the market variable is equal to 1. The estimated value for α was found significantly different from unity in only two countries: Spain and Swizerland. To decrease the high degree of multicollinearity present in most equations, all equations except those for Spain and Switzerland were re-estimated after imposing a constraint that α is equal to unity and transferring the market variables to the left-hand side of the equations.²⁴ The equations for the receipts of the United States and Canada from the “rest of the world” are specified on an ad hoc basis; real receipts are explained by a trend.

The regression coefficients and goodness-of-fit statistics are presented in Table 4. The standard errors of the estimated values of travel receipts are large, with values above 1.05 in ten countries. Here also the main reason is likely to be the poor quality of the data. Receipts from foreign visitors in countries such as Greece, Portugal, and Yugoslavia are not measured with much precision; and it is probably no coincidence that it is for these countries that the standard errors of the regressions are the largest. The Durbin-Watson statistics lie in the indeterminate zone in all cases except for the United Kingdom and for the receipts of the United States from the rest of the world, where it leads to accepting the hypothesis of autocorrelated residuals.

Table 4.

Regression Coefficients: Annual Real Receipts from Foreign Visitors, 1955–70¹

^²The period of observation covers only 1960–70.

^³Brussels World’s Fair, 1958.

^⁴Underrecording of receipts in 1970; see footnote 25.

^⁵Events in France, May 1968. These events were a deterrent to North American tourism in most of northern Europe.

^⁶Underrecording of receipts because of the discount on Italian banknotes abroad, which led foreign tourists to purchase their currency requirements before entering Italy.

^⁷Expo 67 in Montreal, 1967.

^⁸Rest of the world.

Table 4.

Regression Coefficients: Annual Real Receipts from Foreign Visitors, 1955–70¹

Country		Scale Factor	Factors		Trend	D	PC	PC _T-1	FC	FC _L	${\bar{R}}^{2}$	Se	D-W
		Scale Factor	Disturbance			Elasticities with Respect to					Goodness-of-Fit Statistics
Austria ²		351.4			0.0379	1.0				−4.16	0.772	0.0393	1.74
		1.03 √			(0.0070)					(1.32)		1.040 √
Belgium-Luxembourg		178.3	1.572 ³		−0.0101	1.0					0.824	0.0610	1.38
		1.03 √	1.069 √		(0.0034)							1.063 √
Denmark		113.4			0.0228	1.0	−2.82				0.826	0.0403	1.39
		1.05 √			(0.0052)		(0.40)					1.041 √
France ²		716.3	0.821 ⁴	0.905 ⁵	−0.0066	1.0	−1.99				0.793	0.0400	1.08
		1.03 √	1.056 √	1.048 √	(0.0056)		(0.94)					1.040 √
Germany ²		642.3			−0.0509	1.0	−1.87			−0.828	0.964	0.0233	2.11
		1.06 √			(0.0196)		(1.37)			(0.357)		1.023 √
Greece		49.4			0.0611	1.0			−3.68	−1.61	0.764	0.0832	2.49
		1.09 √			(0.0106)				(3.21)	(3.35)		1.085 √
Ireland		142.0			0.0035	1.0	−1.78	−0.78	−1.70	−0.72	0.697	0.0490	1.95
		1.07 √			(0.0058)		(1.55)	(1.43)	(1.79)	(2.08)		1.050 √
Italy		843.1	0.780 ⁶		0.0192	1.0	−3.64		−4.68		0.699	0.0515	2.23
		1.06 √	1.062 √		(0.0090)		(1.18)		(1.70)			1.053 √
Netherlands		131.4			0.0504	1.0	−4.95	−1.12	−1.95	−3.15	0.816	0.0414	1.97
		1.14 √			(0.0139)		(0.82)	(0.85)	(1.52)	(1.75)		1.042 √
Portugal		8.8			0.1986	1.0				−12.76	0.901	0.189	1.07
		1.21 √			(0.0223)					(3.13)		1.209 √
Spain ²		838.0			−0.0388	1.820					0.990	0.049	1.75
		1.10 √			(0.0162)	(0.166)						1.050 √
Sweden ²		92.3			−0.0380	1.0	−0.37	−0.86			0.933	0.0361	1.55
		1.03 √			(0.0051)		(1.24)	(1.12)				1.036 √
Switzerland		578.2			0.0128	0.658	−2.10		−1.06		0.998	0.0135	2.92
		1.06 √			(0.0061)	(0.057)	(0.34)		(0.33)			1.014 √
United Kingdom		651.3	0.919 ⁵		−0.0260	1.0			−1.66		0.727	0.0705	0.54
		1.04 √	1.089 √		(0.0041)				(0.70)			1.073 √
Yugoslavia		38.3			0.0358	1.0	−0.22		−0.21	−0.65	0.745	0.1240	1.44
		1.32 √			(0.0350)		(0.28)		(0.57)	(0.48)		1.133 √
United States
	From Western Europe	280.8	1.064 ⁷		−0.0730	1.0		−2.07			0.650	0.0689	1.17
		1.19 √	1.079 √		(0.0180)			(0.45)				1.071 √
	From ROW ⁸ (less Canada)	249.8			0.0083	—					0.978	0.0596	0.60
		1.03 √			(0.0032)							1.061 √
Canada
	From Western Europe	149.1	1.3077		−0.1553	1.0	−0.48	−2.64			0.735	0.0781	2.16
		1.34 √	1.092 √		(0.0398)		(1.12)	(0.92)				1.082 √
	From ROW ⁸ (less United States)	7.2	1.842 ⁷		0.1021	—					0.933	0.1410	0.98
		1.08 √	1.165 √		(0.0088)							1.152 √

^²The period of observation covers only 1960–70.

^³Brussels World’s Fair, 1958.

^⁴Underrecording of receipts in 1970; see footnote 25.

^⁵Events in France, May 1968. These events were a deterrent to North American tourism in most of northern Europe.

^⁶Underrecording of receipts because of the discount on Italian banknotes abroad, which led foreign tourists to purchase their currency requirements before entering Italy.

^⁷Expo 67 in Montreal, 1967.

^⁸Rest of the world.

Table 4.

Regression Coefficients: Annual Real Receipts from Foreign Visitors, 1955–70¹

Country		Scale Factor	Factors		Trend	D	PC	PC _T-1	FC	FC _L	${\bar{R}}^{2}$	Se	D-W
		Scale Factor	Disturbance			Elasticities with Respect to					Goodness-of-Fit Statistics
Austria ²		351.4			0.0379	1.0				−4.16	0.772	0.0393	1.74
		1.03 √			(0.0070)					(1.32)		1.040 √
Belgium-Luxembourg		178.3	1.572 ³		−0.0101	1.0					0.824	0.0610	1.38
		1.03 √	1.069 √		(0.0034)							1.063 √
Denmark		113.4			0.0228	1.0	−2.82				0.826	0.0403	1.39
		1.05 √			(0.0052)		(0.40)					1.041 √
France ²		716.3	0.821 ⁴	0.905 ⁵	−0.0066	1.0	−1.99				0.793	0.0400	1.08
		1.03 √	1.056 √	1.048 √	(0.0056)		(0.94)					1.040 √
Germany ²		642.3			−0.0509	1.0	−1.87			−0.828	0.964	0.0233	2.11
		1.06 √			(0.0196)		(1.37)			(0.357)		1.023 √
Greece		49.4			0.0611	1.0			−3.68	−1.61	0.764	0.0832	2.49
		1.09 √			(0.0106)				(3.21)	(3.35)		1.085 √
Ireland		142.0			0.0035	1.0	−1.78	−0.78	−1.70	−0.72	0.697	0.0490	1.95
		1.07 √			(0.0058)		(1.55)	(1.43)	(1.79)	(2.08)		1.050 √
Italy		843.1	0.780 ⁶		0.0192	1.0	−3.64		−4.68		0.699	0.0515	2.23
		1.06 √	1.062 √		(0.0090)		(1.18)		(1.70)			1.053 √
Netherlands		131.4			0.0504	1.0	−4.95	−1.12	−1.95	−3.15	0.816	0.0414	1.97
		1.14 √			(0.0139)		(0.82)	(0.85)	(1.52)	(1.75)		1.042 √
Portugal		8.8			0.1986	1.0				−12.76	0.901	0.189	1.07
		1.21 √			(0.0223)					(3.13)		1.209 √
Spain ²		838.0			−0.0388	1.820					0.990	0.049	1.75
		1.10 √			(0.0162)	(0.166)						1.050 √
Sweden ²		92.3			−0.0380	1.0	−0.37	−0.86			0.933	0.0361	1.55
		1.03 √			(0.0051)		(1.24)	(1.12)				1.036 √
Switzerland		578.2			0.0128	0.658	−2.10		−1.06		0.998	0.0135	2.92
		1.06 √			(0.0061)	(0.057)	(0.34)		(0.33)			1.014 √
United Kingdom		651.3	0.919 ⁵		−0.0260	1.0			−1.66		0.727	0.0705	0.54
		1.04 √	1.089 √		(0.0041)				(0.70)			1.073 √
Yugoslavia		38.3			0.0358	1.0	−0.22		−0.21	−0.65	0.745	0.1240	1.44
		1.32 √			(0.0350)		(0.28)		(0.57)	(0.48)		1.133 √
United States
	From Western Europe	280.8	1.064 ⁷		−0.0730	1.0		−2.07			0.650	0.0689	1.17
		1.19 √	1.079 √		(0.0180)			(0.45)				1.071 √
	From ROW ⁸ (less Canada)	249.8			0.0083	—					0.978	0.0596	0.60
		1.03 √			(0.0032)							1.061 √
Canada
	From Western Europe	149.1	1.3077		−0.1553	1.0	−0.48	−2.64			0.735	0.0781	2.16
		1.34 √	1.092 √		(0.0398)		(1.12)	(0.92)				1.082 √
	From ROW ⁸ (less United States)	7.2	1.842 ⁷		0.1021	—					0.933	0.1410	0.98
		1.08 √	1.165 √		(0.0088)							1.152 √

^²The period of observation covers only 1960–70.

^³Brussels World’s Fair, 1958.

^⁴Underrecording of receipts in 1970; see footnote 25.

^⁵Events in France, May 1968. These events were a deterrent to North American tourism in most of northern Europe.

^⁶Underrecording of receipts because of the discount on Italian banknotes abroad, which led foreign tourists to purchase their currency requirements before entering Italy.

^⁷Expo 67 in Montreal, 1967.

^⁸Rest of the world.

The long-run factors represented by trends seem to play an important role. The countries bordering the Mediterranean Sea and located relatively far from the center of industrial Europe, such as Greece, Portugal, and Yugoslavia, benefit from large positive trends, which probably represent the progressive decrease in transportation costs. However, some countries, such as the Netherlands and Austria, seem also to benefit from favorable trends. International travel to Germany and from Western Europe to the United States and Canada are suffering from large long-run unfavorable trends.

The partial estimated share elasticities with respect to the local currency prices and the exchange rates, lagged and unlagged, vary greatly from country to country and have large standard errors. The total elasticities for European countries are presented in Table 5. Only five of the total local currency price elasticities are significantly different from zero. The results for the exchange rate elasticities are more satisfactory; ten of these elasticities are significantly different from zero. Furthermore, in nearly all cases where the exchange rate elasticity is not properly identified, there are strong reasons to assume that the data on receipts are not precise, particularly in the periods where the exchange rates changed.²⁵ Nevertheless, the results indicate clearly that receipts from foreign visitors are price sensitive. The average of the identified share elasticities for European countries are −2.51 (0.34) for local currency prices and −2.89 (0.35) for exchange rates. The unrealistically high value of the estimated exchange rate elasticity for Portugal is not included in the average. The elasticities for Germany are relatively low, namely, −1.87 (1.37) for local currency prices and -0.83 (0.36) for foreign exchange rates. This can be explained by the exceptionally high proportion of business travel and transit travel in the receipts of this country.

Table 5.

Total Share Elasticities of Real Receipts with Respect to Local Currency Prices and Foreign Exchange Rates for European Countries¹

^¹An asterisk indicates that an estimate is significantly different from zero at the 95 per cent confidence level.

Table 5.

Total Share Elasticities of Real Receipts with Respect to Local Currency Prices and Foreign Exchange Rates for European Countries¹

		Local Currency Price		Foreign Exchange Rate
		Point	Standard	Point	Standard
Country		estimate	error	estimate	error
Austria		—	—	−4.16*	1.32
Belgium-Luxembourg		—	—	—	—
Denmark		−2.82*	0.40	—	—
France		−1.99*	0.94	—	—
Germany		−1.87	1.37	−0.83*	0.36
Greece		—	—	−5.29*	1.53
Ireland		−2.56	1.86	−2.42*	0.63
Italy		−3.64*	1.18	−4.68*	1.70
Netherlands		−6.07*	0.78	−5.10*	1.30
Portugal		—	—	−12.76*	3.13
Spain		—	—	—	—
Sweden		−1.23	0.81	—	—
Switzerland		−2.10*	0.34	−1.06*	0.33
United Kingdom		—	—	−1.66*	0.70
Yugoslavia		−0.22	0.28	−0.86*	0.40
	Average	−2.51*	0.34	−2.89*	0.35

^¹An asterisk indicates that an estimate is significantly different from zero at the 95 per cent confidence level.

Table 5.

Total Share Elasticities of Real Receipts with Respect to Local Currency Prices and Foreign Exchange Rates for European Countries¹

		Local Currency Price		Foreign Exchange Rate
		Point	Standard	Point	Standard
Country		estimate	error	estimate	error
Austria		—	—	−4.16*	1.32
Belgium-Luxembourg		—	—	—	—
Denmark		−2.82*	0.40	—	—
France		−1.99*	0.94	—	—
Germany		−1.87	1.37	−0.83*	0.36
Greece		—	—	−5.29*	1.53
Ireland		−2.56	1.86	−2.42*	0.63
Italy		−3.64*	1.18	−4.68*	1.70
Netherlands		−6.07*	0.78	−5.10*	1.30
Portugal		—	—	−12.76*	3.13
Spain		—	—	—	—
Sweden		−1.23	0.81	—	—
Switzerland		−2.10*	0.34	−1.06*	0.33
United Kingdom		—	—	−1.66*	0.70
Yugoslavia		−0.22	0.28	−0.86*	0.40
	Average	−2.51*	0.34	−2.89*	0.35

^¹An asterisk indicates that an estimate is significantly different from zero at the 95 per cent confidence level.

The receipts of the United States and Canada from European visitors seem also to be price elastic. The coefficients of the FC variables could not be estimated reliably; however, the estimates of the coefficients of the composite variables PC have the expected sign and relatively small standard errors. For the United States, the elasticities implied by these estimates are -1.03 (0.22) with respect to domestic local currency prices and transportation costs and −2.01 (0.44) with respect to foreign local currency prices. For Canada, these implicit elasticities are −1.56 (0.56) and −3.07 (1.10), respectively.

Analysis of possible bias

As in the analysis of travel expenditure, errors of measurement in the local currency prices may cause some bias in the estimates of the elasticities of travel receipts with respect to local currency prices. The only difference is that here the bias is more likely to be toward −1 because the dependent variable is deflated by a single local currency price variable, so that there is no averaging of errors as in the deflator of the dependent variable of the expenditure equations. This bias may be the reason why the estimated local currency price elasticities are smaller than the estimated exchange rate elasticities. Thus, these exchange rate elasticities are probably a better indicator of the price sensitivity of receipts from foreign visitors.

IV. Conclusion

The poor quality of the data on foreign travel expenditures, receipts from foreign visitors, and prices of foreign travel services seriously limits the conclusion that can be derived from an econometric analysis of international travel flows. Nevertheless, the results show clearly that most foreign travel flows are influenced significantly by relative prices. The best estimates of price elasticities are probably those obtained from the estimation of the coefficients of the relative exchange rate variables. If these estimates are considered, the estimated average price elasticity for expenditures on foreign travel by European countries is between − 3.58 (0.52) and −2.61 (0.52), depending upon the assumption about long-run trends in expenditures. If, as is likely, these trends are only slightly below +5 per cent a year, the estimated average elasticity may be close to −2.61 (0.52). Travel flows between the United States and Canada are also price elastic. The elasticities with respect to exchange rates are −2.38 (0.35) for the U. S. spending in Canada and −2.47 (0.34) for Canada’s spending in the United States. Expenditures made by the United States and Canada in Western Europe seem rather insensitive to exchange rates. Relative prices were also found to influence the choice of the foreign country visited. The estimated average price elasticity of market share for European countries is −2.89 (0.35).

Most international travel flows seem also to be highly income elastic, although the high multicollinearity between the income variables and simple trend factors prevents a precise estimation of income elasticities. The estimated average income elasticity for Western European countries varies between 2.30 (0.08) and 1.16 (0.08), depending upon the assumption about long-run trends in expenditures. Travel flows from North America to Western Europe do not seem to be influenced by income factors in the short run; however, this result may be caused by the use of national aggregate income data in the statistical analysis rather than data on the income of the main social groups from which North American tourists in Europe come.

APPENDICES

I. Sources of Data

Receipts and expenditures, X_i and M_i

Data on total receipts from foreign visitors and total expenditures on foreign travel in terms of U. S. dollars were obtained from the International Monetary Fund’s Balance of Payments Yearbook, various issues. Quarterly data on Germany’s foreign travel expenditure were taken from Statistische Beihefte zu den Monatsberichten der Deutschen Bundesbank, Reihe 3, various issues. Quarterly data on North American travel flows can be found in the Survey of Current Business, published by the U. S. Department of Commerce. Expenditures series were expressed on a per capita basis by employing the population series published by the UN Statistical Office in the Demographic Yearbook, various issues.

Real per capita disposable personal income, YRP_i

Data on yearly current values of the disposable income of households in all countries included in the model, except Germany, Canada, and the United States, were obtained from the UN Yearbook of National Accounts Statistics, various issues. Data on quarterly current values of the disposable personal income in Germany, Canada, and the United States came from various issues of the Monthly Report of the Deutsche Bundesbank, the National Income and Expenditure Accounts issued by Statistics Canada, and the Survey of Current Business, respectively. These current series were deflated by the consumer price indices and were expressed on a per capita basis.

Consumer price indices, P_i

Quarterly data on each country’s consumer price index can be found in the Fund publication, International Financial Statistics (IFS), various issues. The only exception is Yugoslavia, where a price index for services was substituted for the overall consumer price index; this price index for services was obtained from Indeks, published by Yugoslavia’s Federal Institute for Statistics, various issues.

Exchange rates, F_i

Quarterly series of official (end-of-period) exchange rates were taken from the Fund’s IFS, various issues. For France, Spain, Turkey, and Yugoslavia, quarterly series of black market rates for U. S. banknotes were used instead of the series of official exchange rates. Series of black market rates were obtained from Pick’s Currency Yearbook, various issues.

Regional classification of receipts and expenditures, W_ij and ξ_ij

Data on the regional classification of receipts and expenditures in 1965 for France, Germany, the United Kingdom, and the United States came from Tourism in OECD Member Countries, 1969, published by the Organization for Economic Cooperation and Development (OECD). Data on the regional classification of receipts and expenditures of other countries were taken from the Fund’s Balance of Payments Yearbook, 1965. The regional classification given in this Fund publication is not very detailed; it was completed by using the data available on balances of foreign travel for the four countries just mentioned and also the data given by the OECD publication on the number of nights spent by citizens of country i in country j in 1969.

Cost of trans-Atlantic transportation

Data on the annual average cost of trans-Atlantic transportation can be found in the yearly surveys of international travel published in the Survey of Current Business, usually in the June or July issues. The cost of this transportation was assumed to represent half of the average cost of a trip to Europe (North America) for North American (European) nationals in 1965.

Seasonal coefficients, SS_i and SR_i

In most cases, the relative importance of each quarter in the expenditures and receipts of each country in the base year (1965) was derived from the quarterly balance of payments statements made available to the Fund. However, as no quarterly statements were available for Greece, Ireland, Portugal, Spain, Switzerland, and Turkey, an estimate was made from the monthly data on the number of nights spent by foreign visitors obtained from the OECD publication, Tourism in OECD Member Countries, 1966.

II. Forecasts of Foreign Travel Flows in 1972 and Estimates of the Effects of the Exchange Rate Changes of 1970–71

Flora J. Higgins ^*

The model described in the body of this paper was employed to forecast foreign travel expenditures and receipts of the OECD countries (excluding Japan) for 1972. The forecasts took into account all exchange rate changes during 1970–71, including the currency realignment of December 1971. To estimate the impact of these changes on travel flows in 1972, the set of forecasts for that year was compared with an estimate of what these flows would have been had there been no exchange rate changes after 1969. To determine the ultimate (equilibrium) effects of the realignment of December 1971, travel flows of 1972, calculated on the assumption that exchange rates had not changed since 1969, were compared with corresponding flows, calculated on the assumption that the realignment rates of December 1971 had been in effect from 1969.

Forecasts of Foreign Travel Flows in 1972

In these forecasts, quarterly values of the exogenous variables for the first quarter of 1971 through the fourth quarter of 1972 were inserted into the model described above. For 1971 the values are actual, although sometimes preliminary, data; for 1972 they are forecasts. Changes from 1971 to 1972 in the average annual values are indicated in Table 6.

Table 6.

Assumed Changes of the Exogenous Variables in 1972

(In per cent)

^¹Annual values are derived by averaging quarterly data.

^²Measured in terms of U.S. dollars.

^³The rate for the pound sterling for the whole of 1972 is the rate that was included in the agreement on the currency realignment in December 1971.

^⁴Percentage change in the price index for services.

^⁵Rest of Western Europe. Average of the values for Finland, Iceland, Norway, and Turkey. The weight of each country is the sum of its expenditures and receipts from foreign travel.

^⁶The Canadian dollar is assumed to stay at par with the U. S. dollar during 1972.

Table 6.

Assumed Changes of the Exogenous Variables in 1972

(In per cent)

	Change from 1971 to 1972¹			Change in Exchange Rates from Parity of December 31, 1970^1, ²
	Consumer prices	Real disposable income	Exchange rates²
Austria	4.8	3.8	6.1	11.59
Belgium-Luxembourg	4.8	3.8	7.9	11.57
Denmark	5.3	2.5	5.8	7.45
France	5.7	5.0	7.9	8.57
Germany	4.7	2.9	6.8	13.58
Greece	4.8		0.0	0.0
Ireland	7.9	3.8	6.2	8.57
Italy	4.6	2.9	6.2	7.48
Netherlands	6.9	2.8	7.2	11.57
Portugal	9.9	…	3.3	5.50
Spain	6.6	…	6.8	8.57
Sweden	4.8	2.4	6.0	7.49
Switzerland	4.6	3.4	5.8	13.58
United Kingdom	6.1	4.8	6.2 ³	8.57
Yugoslavia	16.0 ⁴	…	−11.8	−11.76
ROWE ⁵	6.5	…	4.1	5.55
Canada	4.4	6.1	0.3 ⁶	8.11 ⁶
United States	3.5	4.2	0.0	0.0

^¹Annual values are derived by averaging quarterly data.

^²Measured in terms of U.S. dollars.

^³The rate for the pound sterling for the whole of 1972 is the rate that was included in the agreement on the currency realignment in December 1971.

^⁴Percentage change in the price index for services.

^⁵Rest of Western Europe. Average of the values for Finland, Iceland, Norway, and Turkey. The weight of each country is the sum of its expenditures and receipts from foreign travel.

^⁶The Canadian dollar is assumed to stay at par with the U. S. dollar during 1972.

Table 6.

Assumed Changes of the Exogenous Variables in 1972

(In per cent)

	Change from 1971 to 1972¹			Change in Exchange Rates from Parity of December 31, 1970^1, ²
	Consumer prices	Real disposable income	Exchange rates²
Austria	4.8	3.8	6.1	11.59
Belgium-Luxembourg	4.8	3.8	7.9	11.57
Denmark	5.3	2.5	5.8	7.45
France	5.7	5.0	7.9	8.57
Germany	4.7	2.9	6.8	13.58
Greece	4.8		0.0	0.0
Ireland	7.9	3.8	6.2	8.57
Italy	4.6	2.9	6.2	7.48
Netherlands	6.9	2.8	7.2	11.57
Portugal	9.9	…	3.3	5.50
Spain	6.6	…	6.8	8.57
Sweden	4.8	2.4	6.0	7.49
Switzerland	4.6	3.4	5.8	13.58
United Kingdom	6.1	4.8	6.2 ³	8.57
Yugoslavia	16.0 ⁴	…	−11.8	−11.76
ROWE ⁵	6.5	…	4.1	5.55
Canada	4.4	6.1	0.3 ⁶	8.11 ⁶
United States	3.5	4.2	0.0	0.0

^¹Annual values are derived by averaging quarterly data.

^²Measured in terms of U.S. dollars.

^³The rate for the pound sterling for the whole of 1972 is the rate that was included in the agreement on the currency realignment in December 1971.

^⁴Percentage change in the price index for services.

^⁵Rest of Western Europe. Average of the values for Finland, Iceland, Norway, and Turkey. The weight of each country is the sum of its expenditures and receipts from foreign travel.

^⁶The Canadian dollar is assumed to stay at par with the U. S. dollar during 1972.

The exchange rates projected for 1972 are those agreed on in the realignment of December 1971.²⁶ Consumer prices are estimates that take into account the expected effects of the exchange rate changes of 1970-71. These effects, estimated from a model designed to determine the equilibrium effects of exchange rate changes on trade flows and prices, were assumed to be distributed evenly over the 18 months following the change in exchange rates.²⁷

The projected growth of real disposable income of the various countries for the first half of 1972 was based on the OECD forecasts of the growth in real consumption and in real gross domestic product for that period, published in the OECD’s Economic Outlook, December 1971. For the second half of 1972, estimates were made. Population forecasts were based on linear extrapolations of the trends observed during 1965-70. The average U. S. dollar cost of trans-Atlantic transportation in 1972 has been estimated to decrease by 3 per cent, reflecting (1) a “normal” decrease of 10 per cent as a result mainly of the progressive shift to charter flights ²⁸ and (2) an offsetting increase of 7 per cent in air fare instituted by the International Air Transport Association to compensate for the depreciation of the U. S. dollar.

Because of the existence of delayed price and income effects and the high concentration of tourism during the summer, the forecasts for travel flows were determined mainly by the values of the exogenous variables during 1971 and the first two quarters of 1972. These values were either observed or the result of projections over the near future; thus, the risk of errors resulting from incorrect data for the exogenous variables is minimal. On the other hand, because no travel data were available for 1971, it was necessary to make forecasts for 1972 with equations estimated over a period extending only to 1970.²⁹ Therefore, the possibility of errors owing to a change in the structure of the model must be reckoned with.

Forecasts of foreign travel flows in 1972 are presented in Table 7. The size of most travel flows is expected to increase greatly. However, an important part of this increase reflects higher local currency prices in Europe and in North America and the depreciation of the U. S. dollar, in which the values of the flows are expressed.³⁰

Table 7.

Forecasts of Foreign Travel Flows in 1972¹

^¹After each point estimate and in the same unit as the estimate, a confidence interval of one standard error, representing a significance level of approximately 60 per cent, is indicated.

^²Transactions with non-franc countries.

^³There is no expenditure equation for this country in the model. The forecast for expenditure presented here is obtained from an extrapolation of a log-linear trend estimated from observations on real expenditure over the period 1965-70 and a separate forecast for the average change in dollar prices in the foreign countries visited.

^⁴The unusually heavy recording of expenditure and the exceptionally light recording of receipts in 1970 as a result of hidden capital movements have been assumed to continue in 1972; see footnote 10 to Table 2 and footnote 6 to Table 4.

^⁵Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

^⁶For these countries, the travel account has been divided into several bilateral flows.

Table 7.

Forecasts of Foreign Travel Flows in 1972¹

		Forecast Values for 1972			Forecast Changes From 1970 (Observed Values)
		Expenditure	Receipts	Balance	Expenditure	Receipts	Balance
		Million U. S. dollars			per cent		Million U. S. dollars
Austria		658 ± 93	1,479 ± 100	821 ± 137	103.7 ± 28.8	48.0 ± 10.0	145 ± 137
Belgium-Luxembourg		780 ± 116	503 ± 37	−277 ± 122	58.5 ± 23.6	44.5 ± 10.6	−133 ± 122
Denmark		319 ± 11	433 ± 21	114 ± 23	16.8 ± 4.0	37.9 ± 6.7	73 ± 23
France ²		1,755 ± 390	1,813 ± 114	58 ± 406	66.7 ± 37.0	59.9 ± 10.0	−23 ± 406
Germany		4,053 ± 179	1,278 ± 57	-2,775 ± 188	62.6 ± 7.2	24.8 ± 5.6	−1,306 ± 188
Greece ³		72 ± 4	378 ± 65	306 ± 65	30.9 ± 7.2	94.8 ± 33.5	167 ± 65
Ireland		169 ± 22	290 ± 52	121 ± 57	69.0 ± 22.0	55.9 ± 28.0	35 ± 57
Italy ⁴		801 ± 87	2,420 ± 207	1,619 ± 224	10.2 ± 12.0	47.7 ± 12.6	707 ± 274
Netherlands		903 ± 70	562 ± 35	−341 ± 79	49.3 ± 11.6	30.1 ± 8.1	−168 ± 79
Portugal ³,⁵		122 ± 17	544 ± 134	422 ± 135	25.8 ± 17.5	139.6 ± 59.0	292 ± 135
Spain ³		192 ± 4	2,931 ± 192	2,739 ± 192	39.1 ± 2.9	74.4 ± 11.4	1,196 ± 192
Sweden		524 ± 55	165 ± 8	−359 ± 55	8.7 ± 11.4	14.6 ± 5.6	−21 ± 55
Switzerland		577 ± 8	1,235 ± 28	658 ± 29	35.1 ± 1.9	36.5 ± 3.1	180 ± 29
United Kingdom		1,259 ± 84	1,284 ± 119	25 ± 145	36.3 ± 9.1	23.6 ± 11.4	−90 ± 145
Yugoslavia ³		256 ± 43	517 ± 93	261 ± 102	93.9 ± 33.1	87.3 ± 33.7	117 ± 102
Canada ⁶		1,544 ± 70	1,357 ± 74	−187 ± 102	10.4 ± 5.0	14.8 ± 6.3	29 ± 102
	United States	977 ± 59	1,175 ± 72	198 ± 93	10.4 ± 6.6	13.5 ± 7.0	48 ± 93
	Western Europe	420 ± 26	121 ± 13	−299 ± 29	23.2 ± 7.6	72.8 ± 18.6	−13 ± 29
	Others	147 ± 28	61 ± 11	−86 ± 30	27.8 ± 24.3	45.2 ± 26.2	−5 ± 30
United States ⁶		4,457 ± 152	2,963 ± 129	-1,494 ± 199	12.7 ± 3.8	27.8 ± 5.6	140 ± 199
	Canada	1,175 ± 72	977 ± 59	−198 ± 93	13.5 ± 7.0	10.4 ± 6.6	−48 ± 93
	Western Europe	1,509 ± 112	462 ± 40	-1,047 ± 119	15.2 ± 8.5	45.3 ± 12.6	−55 ± 119
	Others	1,773 ± 74	1,524 ± 108	−249 ± 131	11.2 ± 4.6	36.6 ± 9.7	243 ± 131

^¹After each point estimate and in the same unit as the estimate, a confidence interval of one standard error, representing a significance level of approximately 60 per cent, is indicated.

^²Transactions with non-franc countries.

^⁵Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

^⁶For these countries, the travel account has been divided into several bilateral flows.

Table 7.

Forecasts of Foreign Travel Flows in 1972¹

		Forecast Values for 1972			Forecast Changes From 1970 (Observed Values)
		Expenditure	Receipts	Balance	Expenditure	Receipts	Balance
		Million U. S. dollars			per cent		Million U. S. dollars
Austria		658 ± 93	1,479 ± 100	821 ± 137	103.7 ± 28.8	48.0 ± 10.0	145 ± 137
Belgium-Luxembourg		780 ± 116	503 ± 37	−277 ± 122	58.5 ± 23.6	44.5 ± 10.6	−133 ± 122
Denmark		319 ± 11	433 ± 21	114 ± 23	16.8 ± 4.0	37.9 ± 6.7	73 ± 23
France ²		1,755 ± 390	1,813 ± 114	58 ± 406	66.7 ± 37.0	59.9 ± 10.0	−23 ± 406
Germany		4,053 ± 179	1,278 ± 57	-2,775 ± 188	62.6 ± 7.2	24.8 ± 5.6	−1,306 ± 188
Greece ³		72 ± 4	378 ± 65	306 ± 65	30.9 ± 7.2	94.8 ± 33.5	167 ± 65
Ireland		169 ± 22	290 ± 52	121 ± 57	69.0 ± 22.0	55.9 ± 28.0	35 ± 57
Italy ⁴		801 ± 87	2,420 ± 207	1,619 ± 224	10.2 ± 12.0	47.7 ± 12.6	707 ± 274
Netherlands		903 ± 70	562 ± 35	−341 ± 79	49.3 ± 11.6	30.1 ± 8.1	−168 ± 79
Portugal ³,⁵		122 ± 17	544 ± 134	422 ± 135	25.8 ± 17.5	139.6 ± 59.0	292 ± 135
Spain ³		192 ± 4	2,931 ± 192	2,739 ± 192	39.1 ± 2.9	74.4 ± 11.4	1,196 ± 192
Sweden		524 ± 55	165 ± 8	−359 ± 55	8.7 ± 11.4	14.6 ± 5.6	−21 ± 55
Switzerland		577 ± 8	1,235 ± 28	658 ± 29	35.1 ± 1.9	36.5 ± 3.1	180 ± 29
United Kingdom		1,259 ± 84	1,284 ± 119	25 ± 145	36.3 ± 9.1	23.6 ± 11.4	−90 ± 145
Yugoslavia ³		256 ± 43	517 ± 93	261 ± 102	93.9 ± 33.1	87.3 ± 33.7	117 ± 102
Canada ⁶		1,544 ± 70	1,357 ± 74	−187 ± 102	10.4 ± 5.0	14.8 ± 6.3	29 ± 102
	United States	977 ± 59	1,175 ± 72	198 ± 93	10.4 ± 6.6	13.5 ± 7.0	48 ± 93
	Western Europe	420 ± 26	121 ± 13	−299 ± 29	23.2 ± 7.6	72.8 ± 18.6	−13 ± 29
	Others	147 ± 28	61 ± 11	−86 ± 30	27.8 ± 24.3	45.2 ± 26.2	−5 ± 30
United States ⁶		4,457 ± 152	2,963 ± 129	-1,494 ± 199	12.7 ± 3.8	27.8 ± 5.6	140 ± 199
	Canada	1,175 ± 72	977 ± 59	−198 ± 93	13.5 ± 7.0	10.4 ± 6.6	−48 ± 93
	Western Europe	1,509 ± 112	462 ± 40	-1,047 ± 119	15.2 ± 8.5	45.3 ± 12.6	−55 ± 119
	Others	1,773 ± 74	1,524 ± 108	−249 ± 131	11.2 ± 4.6	36.6 ± 9.7	243 ± 131

^¹After each point estimate and in the same unit as the estimate, a confidence interval of one standard error, representing a significance level of approximately 60 per cent, is indicated.

^²Transactions with non-franc countries.

^⁵Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

^⁶For these countries, the travel account has been divided into several bilateral flows.

The comparison between travel flows in 1970 and the forecasts for 1972 shows that large changes are foreseen in the balances of some countries, particularly the projection of an increase of $1,306 million (±$188 million)³¹ in the German travel deficit. However, these forecasts of German travel flows do not take into account the fact that Munich would be the site of the Olympic Games in the summer of 1972. Because of these games, German travel receipts may be slightly larger and German travel expenditures slightly smaller than forecast herein.

A fall in the net receipts of Belgium-Luxembourg, France, and the Netherlands is also forecast. However, for the first two, the range of possible error of the forecast is very large. Large increases are forecast in the surpluses of most Mediterranean countries: for Italy and Spain, the projected increases are $707 million (±$224 million) and $1,196 million (±$192 million), respectively; for Greece and Portugal, $167 million (±$65 million) and $292 million (±$135 million), respectively.

The overall trade balance of the United States is not expected to change significantly. The forecast is for an improvement of $151 million (±$199 million). Its travel balance with Western Europe may deteriorate slightly, despite an expected increase of 45.3 per cent (±12.6 per cent) in receipts from this region, and its travel expenditures in Canada may grow slightly faster than its receipts from Canada. However, these developments are more than compensated for by the large increase foreseen in U. S. receipts from Japan and non-OECD countries.

Estimates of the Impact of the Exchange Rate Changes of 1970–71 on Travel Flows in 1972

To determine the influence of the exchange rate changes in 1970 and 1971 on foreign travel flows in 1972, the model was employed to estimate the expected values of these flows, assuming no changes in exchange rates after 1969. The difference between these simulated values and the previous forecasts for the year—representing the expected impact of the exchange rate changes on travel flows for 1972—is presented in Table 8.

Table 8.

Estimated Effects of the Currency Realignment in 1970–71

^¹Transactions with non-franc countries.

^²It has been assumed that the real expenditure of this country is not affected by changes in relative prices. Changes in nominal expenditures reflect the average changes in dollar prices in the foreign countries visited.

^³Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

Table 8.

Estimated Effects of the Currency Realignment in 1970–71

		Effects on the 1972 Foreign Travel Flows					Final Effects Evaluated at the Size of World Travel in 1972
		Expenditure	Receipts	Balance	Expenditure	Receipts	Expenditure	Receipts	Balance	Expenditure	Receipts
		Million U. S. dollars			Per cent		Million U. S. dollars			Per cent
Austria		123	13	−110	23.0	0.9	116	−22	−138	21.7	−1.5
Belgium-Luxembourg		61	61	0	8.5	13.8	60	60	0	8.3	−15.6
Denmark		21	26	5	7.0	6.4	20	29	9	6.7	7.1
France ¹		43	151	108	2.5	9.1	206	141	−65	12.0	8.5
Germany		526	136	−390	14.9	11.8	391	158	−233	11.1	13.9
Greece ²		5	116	111	7.5	44.3	5	136	131	7.5	51.1
Ireland		13	18	5	8.3	6.6	13	18	5	8.3	6.6
Italy		53	244	191	7.1	11.2	64	238	174	8.6	10.9
Netherlands		158	19	−139	21.2	3.7	161	9	− 152	21.6	1.7
Portugal ^2, ³		9	36	25	8.0	7.1	9	72	63	8.0	14.2
Spain ²		14	193	179	7.9	7.0	14	345	331	7.9	12.6
Sweden		28	11	−17	5.6	7.1	34	11	−23	6.9	7.1
Switzerland		69	110	41	13.6	9.8	63	124	61	12.4	11.0
United Kingdom		97	66	−31	8.3	5.4	98	72	−26	8.4	5.9
Yugoslavia ²		19	35	16	8.0	7.3	19	66	47	8.0	13.7
Canada		146	17	−129	10.4	1.3	71	39	−32	5.1	2.9
	United States	110	0	−110	12.7	0.0	40	20	−20	4.6	1.7
	Western Europe	12	18	5	3.2	17.5	5	20	15	1.2	19.4
	Others	24	−1	−25	19.5	−3.2	26	−1	−27	21.1	−1.6
United States		−13	131	144	−0.3	3.9	20	70	50	0.4	2.5
	Canada	0	110	110	0.0	12.7	20	40	20	1.7	4.6
	Western Europe	−13	11	24	−0.8	2.4	0	10	10	0.0	2.2
	Others	0	10	10	0.0	0.7	0	20	20	0.0	1.3

^¹Transactions with non-franc countries.

^³Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

Table 8.

Estimated Effects of the Currency Realignment in 1970–71

		Effects on the 1972 Foreign Travel Flows					Final Effects Evaluated at the Size of World Travel in 1972
		Expenditure	Receipts	Balance	Expenditure	Receipts	Expenditure	Receipts	Balance	Expenditure	Receipts
		Million U. S. dollars			Per cent		Million U. S. dollars			Per cent
Austria		123	13	−110	23.0	0.9	116	−22	−138	21.7	−1.5
Belgium-Luxembourg		61	61	0	8.5	13.8	60	60	0	8.3	−15.6
Denmark		21	26	5	7.0	6.4	20	29	9	6.7	7.1
France ¹		43	151	108	2.5	9.1	206	141	−65	12.0	8.5
Germany		526	136	−390	14.9	11.8	391	158	−233	11.1	13.9
Greece ²		5	116	111	7.5	44.3	5	136	131	7.5	51.1
Ireland		13	18	5	8.3	6.6	13	18	5	8.3	6.6
Italy		53	244	191	7.1	11.2	64	238	174	8.6	10.9
Netherlands		158	19	−139	21.2	3.7	161	9	− 152	21.6	1.7
Portugal ^2, ³		9	36	25	8.0	7.1	9	72	63	8.0	14.2
Spain ²		14	193	179	7.9	7.0	14	345	331	7.9	12.6
Sweden		28	11	−17	5.6	7.1	34	11	−23	6.9	7.1
Switzerland		69	110	41	13.6	9.8	63	124	61	12.4	11.0
United Kingdom		97	66	−31	8.3	5.4	98	72	−26	8.4	5.9
Yugoslavia ²		19	35	16	8.0	7.3	19	66	47	8.0	13.7
Canada		146	17	−129	10.4	1.3	71	39	−32	5.1	2.9
	United States	110	0	−110	12.7	0.0	40	20	−20	4.6	1.7
	Western Europe	12	18	5	3.2	17.5	5	20	15	1.2	19.4
	Others	24	−1	−25	19.5	−3.2	26	−1	−27	21.1	−1.6
United States		−13	131	144	−0.3	3.9	20	70	50	0.4	2.5
	Canada	0	110	110	0.0	12.7	20	40	20	1.7	4.6
	Western Europe	−13	11	24	−0.8	2.4	0	10	10	0.0	2.2
	Others	0	10	10	0.0	0.7	0	20	20	0.0	1.3

^¹Transactions with non-franc countries.

^³Transactions of metropolitan Portugal with the rest of the world, including its overseas territories.

For this simulation, the previous data on consumer prices for 1971 and 1972 were corrected by removing the estimated influence of the exchange rate changes. Data on real disposable income were not changed because it was assumed either that the currency changes would have little effect on real disposable income or that any such effect would be offset by use of monetary or fiscal policy. Because of the no-change-in-exchange-rates assumption, the U. S. dollar price of trans-Atlantic transportation has been adjusted to reflect only the estimated decrease of 10 per cent resulting from the progressive shift to charter flights.

The deficits estimated for the 1972 travel balances of Germany and the Netherlands under the no-change-in-exchange-rates assumption are $390 million and $139 million, respectively, smaller than the ones forecast for these countries after taking into account the exchange rate changes of 1970–71. Similarly, the Austrian surplus in this simulation will be $110 million smaller than the surplus previously forecast. France, Greece, Italy, and Spain—all of whose currencies experienced relative depreciations—are expected to benefit in 1972 from the exchange rate changes of 1970–71. For the other European countries, the simulated results for 1972 indicate that their travel balances should not be affected much by the changes in exchange rates of 1970–71. In North America, the impact of these changes on the travel balances of Canada and the United States in 1972 is expected to be, respectively, a deterioration of $129 million and an improvement of $144 million.

Estimates of the Ultimate Effects of the Currency Realignment of December 1971 at the Size of World Travel in 1972

To isolate the influence of the currency realignment of December 1971, the model has been employed to simulate 1972 travel flows under the assumption that the realignment rates were in effect from 1969.^32, ³³ In this simulation, the projections of consumer prices in 1972 were adjusted to include fully the estimated effects of the exchange rate changes on prices shown in Table 9. Comparison of this new simulation of 1972 travel flows with the simulated flows under the no-change-in-exchange-rates assumption indicates the ultimate effects of the realignment on travel flows at the size of world travel in 1972; these effects are shown in Table 8.

Table 9.

Estimate of the Final Effect of the Exchange Rate Changes of 1970–71 on Consumer Prices

(In per cent)

Source: Simulation of a model designed to determine the equilibrium effects of exchange rate changes on trade flows and prices.

For most countries, the estimated effect of the realignment, while significant, is not large. For Germany, the final effect—a worsening of its travel balance by $233 million—is smaller than the previously estimated impact of the exchange rate changes in 1970-71 on the 1972 travel balance. The explanation for this difference may lie partly in the fact that the final realignment rate for the deutsche mark was less appreciated, relative to other currencies, than its peak rate during 1971 and partly in the fact that the decline in German consumer prices resulting from the realignment is taken fully into account.³³ For France, in contrast to the improvement in its 1972 travel balance that was estimated as a result of the impact of the exchange rate changes in 1970-71, the ultimate effect of the realignment is estimated to be a worsening of its balance. The fact that the final realignment rate for the French franc appreciated more, relative to other currencies, than its average rate during 1970-71 may explain this difference. The final effect for Austria and the Netherlands is also estimated to be unfavorable; these countries had quite large relative revaluations. The ultimate effect of the currency realignment will be an increase of $174 million, $331 million, and $131 million in the travel surpluses for Italy, Spain, and Greece, respectively.

The ultimate effect of the December 1971 currency realignment on the overall balance of the United States is small. The effect on travel flows of changes in the local currency prices of the United States and Canada, particularly Canada, is expected to offset the effect of the change in the exchange rate. Furthermore, the U. S. travel balance with Western Europe is not affected significantly. U. S. expenditures in Western Europe should not decrease because of their relatively low price elasticity, and U. S. receipts from Western Europe should rise by only a small amount because the U.S. dollar cost of trans-Atlantic transportation was raised by 7 per cent to reflect the depreciation of the U. S. dollar.

Conclusion

It is obvious that the results presented in this Appendix must be interpreted with much caution. The model of foreign travel from which they are derived rests on many simplifying assumptions, and only a few of the many variables that may affect foreign travel have been introduced explicity into its equations. Moreover, irregularities in the recording of foreign travel flows of most countries could not be eliminated. Nevertheless, the results seem reasonable a priori and may be considered as an indication of the order of magnitude of the foreign travel flows in 1972 and of the effects of the currency realignment on these flows.

Analyse économétrique des voyages internationaux

Résumé

Cette étude présente un modèle économétrique complet des flux de voyages internationaux. Son objectif principal est d’évaluer dans quelle mesure les recettes et dépenses figurant au compte voyages de divers pays développés sont à court terme sensibles aux prix. Ce modèle peut être également utilisé pour prévoir un ou deux ans à l’avance le compte voyages de certains pays ou pour simuler les effets sur les voyages internationaux de certaines mesures prises par les autorités. Des applications concrètes sont données en annexe, notamment des prévisions pour 1972 et une estimation des effets des modifications des taux de change qui se sont produites en 1970 et 1971.

L’étude démontre clairement que la plupart des flux de voyages internationaux sont influencés de façon significative par les prix relatifs. Ceci vaut des flux de voyages intra-européens comme de ceux qui ont lieu entre les Etats-Unis et le Canada. Les prix relatifs influencent aussi bien le choix entre les voyages à l’intérieur ou à l’étranger que celui des pays étrangers visités. Les flux de voyages entre l’Amérique du Nord et l’Europe occidentale semblent moins sensibles aux taux de change ou au prix des services de voyage dans les deux régions, exprimés en monnaie locale, probablement à cause de l’importance relative du coût du transport transatlantique.

Análisis econométrico de los viajes internacionales

Resumen

En este artículo se presenta un modelo econométrico completo de las corrientes de viajes internacionales. Se hace especial referencia a la estimación de la sensibilidad a corto plazo con respecto a los precios de los gastos e ingresos en la cuenta de viajes de varios países desarrollados. El modelo también puede servir para prever con antelación de uno a dos años la cuenta de viajes de ciertos países o para simular los efectos de determinadas modificaciones de la política de viajes internacionales. En un Apéndice se presentan como aplicaciones prácticas previsiones para 1972 y estimaciones del efecto de las modificaciones de los tipos de cambio ocurridas en 1970 y 1971.

Los resultados del estudio indican claramente que casi todas las corrientes de viajes internacionales reflejan bastante la influencia de los precios relativos. Así ocurre tanto en lo que se refiere a las corrientes de viajes intra-europeos como a los que se efectúan entre el Canadá y los Estados Unidos. Los precios relativos afectan la elección entre viajes internos y viajes al extranjero, así como la selección de los países extranjeros visitados. Las corrientes de viajes entre América del Norte y Europa occidental parecen menos sensibles frente a los tipos de cambio o los precios de los servicios de viaje en moneda nacional en ambas regiones, debido probablemente a la importancia relative de los costos del transporte transatlántico.

Mr. Artus, economist in the Special Studies Division of the Research Department, has degrees from the Faculty of Law and Economics in Paris and from the University of California at Berkeley.

For example, see F. G. Adams, H. Eguchi, and F. Meyer-zu-Schlochtern, An Econometric Analysis of International Trade, Organization for Economic Cooperation and Development (January 1969).

See Grant B. Taplin, “Models of World Trade,” Staff Papers, Vol. XIV (1967), pp. 433-55, and Rudolf R. Rhomberg, “Possible Approaches to a Model of World Trade and Payments,” Staff Papers, Vol. XVII (1970), pp. 1-28.

This principle is not always respected, because it is often difficult to isolate nontransportation expenditures. For example, funds paid abroad on transportation within a foreign country or between foreign countries are nearly always included in balance of payments statistics under the item, “foreign travel.”

H. Peter Gray, International Travel-International Trade (Lexington, Massachusetts, 1970).

See “Record Year for Tourism in 1969,” Board of Trade Journal, Vol. 199 (September 23, 1970), pp. 656-63.

For a discussion of these two approaches, see Rhomberg, op. cit.

The influence of the cost of trans-Atlantic transportation is also neglected as a determinant of the aggregate expenditure of European countries because of the small weights of the United States and Canada in these expenditures.

On the bias caused by the existence of errors of measurement in the exogenous variables, see Edmond Malinvaud, Statistical Methods of Econometrics (Chicago, 1966), pp. 326-35.

Here, the two weighting schemes were found to yield similar results.

All indices are defined with the first quarter of the base year (1965) = 1.0.

The trend coefficient in the yearly function is approximately equal to four times the trend coefficient r in the quarterly function.

The expression “foreign markets l” refers to the aggregate expenditure on foreign travel by residents of country l.

The share elasticity E₈ for a product exported by a given country can be expressed as a function of the elasticity of substitution E, namely,

E_{8} = \frac{1 - s (1 - P)}{1 + s (1 - P) E} E,

where s is the share of the import market of this product and P is the ratio of the price of this product to the average price of all products available in the market. In the present case, s is always relatively small and P is not likely to be too far from unity, so that E₈ can be considered a good proxy for E.

For the countries for which expenditure equations had not been estimated, observed rather than estimated values were used. However, the weights of these countries in the receipts of other countries are quite small.

Each regression equation being in log form, the upper and lower boundaries for an a confidence interval for the estimated expenditures in U. S. dollars are obtained by multiplying and dividing, respectively, the point estimate for these expenditures by the antilog of the standard error of the regression with the t statistic as exponent. Therefore, the degree of precision of the estimated expenditures is conveniently expressed by the antilog of the standard error of the regression. A value of 1.05 for this antilog corresponds to a standard error of 5 per cent for the estimated expenditures in U. S. dollars.

In both equations, there is a high degree of multicollinearity between real disposable personal income and the variable PR, which, in these two cases, reflects mainly the progressive decrease in the average cost of transportation across the Atlantic. All these variables are dominated by their trend component. This also may explain why it has been impossible to identify income elasticities for these two travel flows.

Numbers in parentheses are standard errors.

The averages are computed over the identified negative elasticities. The assumption is that the true values of the elasticities, the estimates of which were initially found with the wrong sign, must be considered as unknown rather than as equal to zero. This procedure may result in a small negative bias to the extent that the elasticities that are not identified may be those of the smallest absolute magnitude.

The estimate for 1968 is probably biased upward because a part of the decrease in expenditures may have resulted from the events in May rather than from the exchange restrictions.

If r is the true value of the trend coefficient omitted from the regression equation, the bias in the estimates of the coefficients of the other variables Z present in the equation is given by the following formula,

E (B * - B) = r \cdot M_{T Z} M_{Z Z,}^{- 1}

where B is the vector of the true values of the coefficients of the variables Z, B* is the vector of estimated values of these coefficients when the trend is omitted, the operator E indicates that the mathematical expectation of the variables B* -B is considered, and $M_{T Z} M_{Z Z}^{- 1}$ is defined as the vector of regression coefficients of the trend T on the variables Z. For a proof of this formula, see Malinvaud, op. cit., p. 263.

This assumes that the error with which price is measured is independent of the true price. For a proof, see Murray C. Kemp, “Errors of Measurement and Bias in Estimates of Import Demand Parameters,” The Economic Record, Vol. 38 (1962), pp. 369-72.

This assumes that the error is not highly and negatively correlated with the true value of the price variable. See Guy H. Orcutt, “Measurement of Price Elasticities in International Trade,” The Review of Economics and Statistics, Vol. XXXII (1950), pp. 117-32.

The effect of an error of measurement in an independent variable can be analyzed by considering this random error as an omitted variable. The relationship

MR/PF = A · YRP^α (PR · V)^β FR^γ e^γ.T e^ε,

where V is a multiplicative random error, is misspecified; it should be written

MR/PF = A · YRP^α (PR · V)^β V^-β FR^γ e^γ.T e^ε.

By applying the formula presented in footnote 20, we have

E (γ * - γ) = - β \cdot M_{V F R} M_{F R F R}^{- 1};

that is, the bias of the estimated exchange rate elasticity γ* depends upon the regression coefficient of the random error variable V on the exchange rate variable FR in the regression of V on FR and other variables present in the equation.

For a discussion of the advantages of such a constraint, see Adams, Eguchi, and Meyer-zu-Schlochtern, op. cit., p. 35.

This is particularly true for France where, at the time of the devaluations of 1957 and 1958 and again after the devaluation of 1969, the receipts from foreign visitors indicated in the French balance of payments did not reflect the large increases in the imports of French travel services indicated by other countries.

Miss Higgins, research assistant in the Special Studies Division of the Research Department, is a graduate of the University of Missouri and the School of Advanced International Studies of the Johns Hopkins University.

As no central rate was set for the Canadian dollar, it has been assumed to remain at par with the U. S. dollar in 1972.

Because some exchange rate changes occurred before December 1971, it was assumed that some of these effects on consumer prices had already occurred in 1970 and 1971.

This decrease is estimated by fitting a log-linear trend to the series for the period 1965–70.

Exceptions are the equations for (1) intra-North American flows and German expenditure, which were estimated from a period extending to the first quarter of 1972, and (2) French expenditure and Italian receipts, which were estimated for a period up to 1971.

These local currency prices are expected to rise by an average of 13 per cent between 1970 and 1972; the U. S. dollar was depreciated by about 10 per cent against the European currencies.

A confidence interval of ± 1 standard error, representing a significance level of approximately 66 per cent, is indicated in parentheses after the point estimate.

The realignment refers to the rates agreed upon during meetings at the Smithsonian Institution in Washington in December 1971.

Making the realignment effective from 1969 ensures that all adjustments will have taken place by 1972.

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IMF Staff papers: Volume 19 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1972: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969290

ISSN:: 1020-7635

Pages:: 202

DOI:: https://doi.org/10.5089/9781451969290.024

Keywords
I. An Overall View of International Travel
II. A Model of International Travel
- Determinants of foreign travel expenditure
- Determinants of receipts from foreign visitors
III. Empirical Findings
- Results for foreign travel expenditure
- Results for receipts from foreign visitors
IV. Conclusion
APPENDICES
- I. Sources of Data
- II. Forecasts of Foreign Travel Flows in 1972 and Estimates of the Effects of the Exchange Rate Changes of 1970–71
Analyse économétrique des voyages internationaux
- Résumé
Análisis econométrico de los viajes internacionales
- Resumen

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Chart 1.

Flow Chart of the Model of International Travel

RP _i	=	relative price term;
P _i	=	price of travel services in country i, expressed in country i’s currency;
F _i	=	price of the U. S. dollar in terms of country i’s currency;
T _ij	=	average transportation cost of a round trip between country i and country j, expressed in country i’s currency;
T _i	=	average transportation cost within country i, expressed in country i’s currency;
θF ^ij	=	weight of country i’s spending on foreign travel services in country j in country i’s spending on both foreign travel services in country j and transportation to and from country j;
θY ⁱ	=	weight of country i’s spending on domestic travel services in country i’s spending on both domestic travel services and domestic transportation;
ω _ij	=	weight of country j in country i’s total spending on foreign travel services and foreign transportation.

RP _i	=	relative price term;
P _i	=	price of travel services in country i, expressed in country i’s currency;
F _i	=	price of the U. S. dollar in terms of country i’s currency;
T _ij	=	average transportation cost of a round trip between country i and country j, expressed in country i’s currency;
T _i	=	average transportation cost within country i, expressed in country i’s currency;
θF ^ij	=	weight of country i’s spending on foreign travel services in country j in country i’s spending on both foreign travel services in country j and transportation to and from country j;
θY ⁱ	=	weight of country i’s spending on domestic travel services in country i’s spending on both domestic travel services and domestic transportation;
ω _ij	=	weight of country j in country i’s total spending on foreign travel services and foreign transportation.

MR_i	=	value of country i’s per capita spending on foreign travel services, expressed in U.S. dollars;
${\bar{P F}}_{i}$	=	weighted average of the indices ¹⁰ of local currency travel service prices in foreign countries, expressed in U.S. dollars, the weight of each country being the share of that country in country i’s tourist expenditure in 1965;
YRP_i	=	real per capita disposable personal income in country i, expressed in constant 1965 U.S. dollars;
S_i	=	a seasonal variable taking the value ss_{1, i}, ss_{2, i}, ss_{3, i}, and ss_{4, i}, in the first, second, third, and fourth quarter of each year, with ss_{1, i} + ss_{2, i} + ss_{3, i} + ss_{4, i} = 1;
e	=	base of natural logarithms;
ε	=	a stochastic disturbance term;

MR_i	=	value of country i’s per capita spending on foreign travel services, expressed in U.S. dollars;
${\bar{P F}}_{i}$	=	weighted average of the indices ¹⁰ of local currency travel service prices in foreign countries, expressed in U.S. dollars, the weight of each country being the share of that country in country i’s tourist expenditure in 1965;
YRP_i	=	real per capita disposable personal income in country i, expressed in constant 1965 U.S. dollars;
S_i	=	a seasonal variable taking the value ss_{1, i}, ss_{2, i}, ss_{3, i}, and ss_{4, i}, in the first, second, third, and fourth quarter of each year, with ss_{1, i} + ss_{2, i} + ss_{3, i} + ss_{4, i} = 1;
e	=	base of natural logarithms;
ε	=	a stochastic disturbance term;

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Abstract

I. An Overall View of International Travel

II. A Model of International Travel

Determinants of foreign travel expenditure

Determinants of receipts from foreign visitors

III. Empirical Findings

Results for foreign travel expenditure

Analysis of possible bias

Results for receipts from foreign visitors

Analysis of possible bias

IV. Conclusion

APPENDICES

I. Sources of Data

Receipts and expenditures, Xi and Mi

Real per capita disposable personal income, YRPi

Consumer price indices, Pi

Exchange rates, Fi

Regional classification of receipts and expenditures, Wij and ξij

Cost of trans-Atlantic transportation

Seasonal coefficients, SSi and SRi

II. Forecasts of Foreign Travel Flows in 1972 and Estimates of the Effects of the Exchange Rate Changes of 1970–71

Forecasts of Foreign Travel Flows in 1972

Estimates of the Impact of the Exchange Rate Changes of 1970–71 on Travel Flows in 1972

Estimates of the Ultimate Effects of the Currency Realignment of December 1971 at the Size of World Travel in 1972

Conclusion

Analyse économétrique des voyages internationaux

Résumé

Análisis econométrico de los viajes internacionales

Resumen

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Inter-American Development Bank

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Table of Contents

Headings

Figures

Metrics

Receipts and expenditures, X_i and M_i

Real per capita disposable personal income, YRP_i

Consumer price indices, P_i

Exchange rates, F_i

Regional classification of receipts and expenditures, W_ij and ξ_ij

Seasonal coefficients, SS_i and SR_i