The World Trade Model: Invisibles

Marian Bond

doi:10.5089/9781451946840.024.A003

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The World Trade Model: Invisibles

Author: Marian Bond

Publication Date:: 01 Jan 1979

eISBN:: 9781451946840

Language:: English

Keywords:: SP; mixed-citation publication-type; excess demand; trend term; inflow equation; rate of return; export price elasticity; outflow equation; Imports; Exports; Wages

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The purpose of this paper is to present a model of imports and exports of invisibles for the 14 major industrial countries: Austria, Belgium (including Luxembourg), Canada, Denmark, France, the Federal Republic of Germany, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the United Kingdom, and the United States. The model is the second of two parts of the world trade model developed by the Fund’s Research Department to explain current account transactions of industrial countries. The first part deals with merchandise trade flows and was presented in Deppler and Ripley (1978). The present model is similar to its counterpart for merchandise trade in that it is essentially short run in nature. Thus, the approach involves attempts to precisely identify cyclical and other short-run factors and to separate them from long-run factors. Applications of the model include short-term forecasting (6 to 18 months ahead) and simulation of the effects of variations in growth rates, rates of inflation, and exchange rates.

Abstract

To our knowledge, no relatively disaggregated world model of flows of invisibles has ever been constructed. Given the important role such flows have come to play in many countries in recent years,¹ this gap can be explained only by the numerous statistical and conceptual difficulties involved. While a number of empirical studies on transactions in invisibles have appeared over the past two decades, these studies have generally focused on international flows of aggregated or disaggregated invisibles for a particular country, or flows of a particular group of invisibles (such as travel or transportation) for one country or a group of countries. ² A complete multicountry analysis of disaggregated groups of services, however, is necessary if the cross-country interdependence of the flows is to be taken into account. Furthermore, a study that applies the same methodology to all countries is also needed if meaningful cross-country comparisons of results are to be made.

The model presented in this paper is currently limited to 14 industrial countries as a consequence of the paucity of the data for the remaining countries. At a later date, the model may be closed by including all countries or country groupings. Two alternative approaches to the specification of export equations for individual invisible items are adopted in the paper. In the first approach, called the unrestricted approach, separate bilateral functions for a country’s exports of invisibles to each importing country are summed over each importing market to obtain an aggregate export equation. This approach is called unrestricted because imports are not predetermined and therefore are not constrained to equal exports. The second approach, called the market shares approach, takes imports of the various countries as predetermined and determines a country’s export share by such factors as relative prices and exchange rates. The market shares approach is used for categories of invisibles for which information on market shares in a base period is available, and for which the market share structure moves slowly over time according to changing factors, such as relative prices. In all other cases, the unrestricted approach is used.

When specifying the model, the serious data constraints that limit any empirical study on invisibles have to be recognized. Thus, invisibles are subdivided into only six broad groups, namely, freight transportation, travel and passenger transportation, other services, investment income, workers’ earnings and remittances, and transfers. These broad groupings of invisibles are thought to be more appropriate than aggregate invisibles for the following reasons: (a) Invisibles can be dichotomized into items for which an income is received (investment income, workers’ earnings and remittances, and transfers) and items that involve an expenditure (freight transportation, travel and passenger transportation, and other services); variables that determine income items will be different from those that determine expenditure items, (b) Within income and expenditure items, imports and exports of the different individual groups considered are likely to be determined by different exogenous variables.

The organization of the paper is as follows. Section I contains the general specification of the model and the individual basic equations for the six groups of invisibles. Section II presents the parameter estimates, together with a discussion of the model results. Section III contains a summary and concluding remarks. The Appendix provides information on data compilation, use of proxy variables, and the arrangement of country data in the standard framework. Complete documentation of the data sources is available upon request from the author, whose address is Research Department, International Monetary Fund, Washington, D.C. 20431.

I. Model Structure

general specification

The invisibles model is a set of equations comprised of behavioral relationships that determine the volume and/or the value for each group of invisibles. The 14 countries and six groups of invisibles are shown in Table 1. The model differentiates between services (including freight transportation, travel and passenger transportation, other services, investment income, workers’ earnings and remittances) and transfers (including private and official transfers). Workers’ remittances ³ are therefore analyzed as a service item, although for balance of payments purposes they are usually defined as a transfer item.

Table 1.

Fourteen Industrial Countries: Specification of Invisibles Model

Table 1.

Fourteen Industrial Countries: Specification of Invisibles Model

Country Disaggregation	Service and Transfer Grouping	Endogenous Variables	Exogenous Variables
Austria	Freight transportation	Import value and export value	Real gross national product
Belgium	Travel and passenger transportation	Import volume and export volume	Import volume of commodities
Canada	Other services Private Government	Import volume and export volume	Import volume of commodities
Denmark	Other services Private Government	Import volume and export volume	Export volume of commodities
France	Investment income	Income inflow and income outflow value for Canada, the United Kingdom, and the United States	Consumer price index
Germany, Fed. Rep.	Direct		Transatlantic airfare index
Germany, Fed. Rep.	Financial		Implicit deflator
Italy	Other		Exchange rates
Japan	or		Freight rates
Netherlands	Net total flows	Net income flow value for remaining 11 countries	Unit labor costs in manufacturing
Norway	Net total flows	Net income flow value for remaining 11 countries	Interest rates
Sweden	Workers’ earnings and remittances	Income inflow and income outflow value for France, the Federal Republic of Germany, and Italy	Foreign assets and liabilities
Switzerland	Workers’ earnings and remittances		Foreign labor
United Kingdom	Transfers Private Official	Income inflow and income outflow value	Normal output per man-hour in manufacturing
United States	Transfers Private Official	Income inflow and income outflow value	Output per man-hour in manufacturing
Rest of the world	Total services and transfers		Output per man-hour in manufacturing

Table 1.

Fourteen Industrial Countries: Specification of Invisibles Model

Country Disaggregation	Service and Transfer Grouping	Endogenous Variables	Exogenous Variables
Austria	Freight transportation	Import value and export value	Real gross national product
Belgium	Travel and passenger transportation	Import volume and export volume	Import volume of commodities
Canada	Other services Private Government	Import volume and export volume	Import volume of commodities
Denmark	Other services Private Government	Import volume and export volume	Export volume of commodities
France	Investment income	Income inflow and income outflow value for Canada, the United Kingdom, and the United States	Consumer price index
Germany, Fed. Rep.	Direct		Transatlantic airfare index
Germany, Fed. Rep.	Financial		Implicit deflator
Italy	Other		Exchange rates
Japan	or		Freight rates
Netherlands	Net total flows	Net income flow value for remaining 11 countries	Unit labor costs in manufacturing
Norway	Net total flows	Net income flow value for remaining 11 countries	Interest rates
Sweden	Workers’ earnings and remittances	Income inflow and income outflow value for France, the Federal Republic of Germany, and Italy	Foreign assets and liabilities
Switzerland	Workers’ earnings and remittances		Foreign labor
United Kingdom	Transfers Private Official	Income inflow and income outflow value	Normal output per man-hour in manufacturing
United States	Transfers Private Official	Income inflow and income outflow value	Output per man-hour in manufacturing
Rest of the world	Total services and transfers		Output per man-hour in manufacturing

Three of the six groups of invisibles (Investment income, Other services, and Transfers) have been divided into subgroups. “Investment income” was subdivided because separate groups of investors are involved whose behavior may be quite different, and because there is evidence of considerable benefit to be gained from disaggregating in terms of increased accuracy of the results. ⁴ “Other services” and “Transfers” were subdivided to isolate government transactions that are treated as exogenously determined.

Services

The model is based mainly on a static partial equilibrium framework, for which behavioral relationships are hypothesized on the demand side between the level of imports and exports of services and the relevant explanatory variables. Import demand functions are estimated in volume terms for travel and passenger transportation, and other private services, and in value terms for freight transportation, investment income, and workers’ earnings and remittances. ⁵ Prices are assumed to be exogenous in the period of observation. ⁶ Where imports of services of a country are a small proportion of world supply, or the price of inputs into the foreign service industry is determined by local demand and supply and the supplier cannot discriminate between domestic and foreign markets, this is a reasonable assumption. To the extent that disequilibrium situations exist because of nonprice factors, such as incomplete adjustment of the optimizing criteria and long lags in buyers’ responses, a disequilibrium approach would be required.

(1) Imports. In our analysis of imports, services are assigned to three main types—general competitive services, specific one-price services, and factor incomes, which are described separately. Specifically, travel and passenger transportation and other private services are assigned to the general competitive service group, freight transportation to the specific one-price service group, and investment income and workers’ earnings and remittances to the factor income group.

For general competitive service imports, product differentiation of the service is assumed, thus requiring separate demand functions for imported and domestically produced services. The volume equations for competitive services are derived on the assumption that the consumer is faced with a “two-stage budgeting decision,” where, at the first stage, expenditure is allocated among broad groups of goods and services with reference to income and prices and, at the second stage, expenditure ⁷ is allocated between the domestic and the foreign service with reference to domestic and foreign prices of the service. For competitive services, we are concerned with the second stage only. We therefore assume that each imported service group is weakly separable from other goods and services (both domestic and imported). This requires strong assumptions about the way in which imported travel services, for example, are substituted for durables. The approach assumes that marginal rates of substitution between any two services in the relevant service group are independent of the quantity consumed of any commodity or service from any other group.

A general import demand function for each competitive service item for country i will therefore contain the relative price of the imported and domestic service item plus total expenditure on the service item. A trend term is also introduced to represent smoothly changing factors, such as tastes and quality changes. The structural import demand for competitive services of the ith country is written as

\begin{matrix} {M V S}_{i} = a_{0} {D S}_{i}^{a_{1}} {R M P S}_{i}^{a_{2}} e^{a_{3} t} & (1) \end{matrix}

In this equation, MVS_i is the volume of imports of the service item by country i; DS_i is real total expenditure of country i on the service item (i.e., both domestic and foreign service items); and RMPSi is an index of the import price of the service (MPS_i) relative to the domestic price of the service (PS_i) and is calculated as RMPS_i = MPS_i/PS_i. The import price, MPS_i, is a weighted average of the export price indices of each country from which country i imports the service item.

For some service items, only one price exists. The price of such service items is assumed to be determined either by world supply and demand, so that the domestic price does not deviate much from the foreign price, or by monopolistic conference. It is hypothesized here that freight transportation is an example of a one-price service item where prices are determined by world markets. For example, liner prices are determined monopolistically by liner conferences, and tramp prices are determined by a nearly perfect market. Imports of freight transportation are, however, quite likely to be price sensitive, because certain commodities may not be imported if the cost of transporting them becomes too high. The import demand equation for country i for service items with one price may be written

\begin{matrix} {M V S}_{i} = a_{0} {D G S}_{i}^{a_{1}} {W P S}_{}^{a_{2}} e^{a_{3} t} & (2) \end{matrix}

DGS_i is real total expenditure of country i on goods and services; WPS is the world price of the service item; and t is introduced to represent smoothly changing factors, such as changes in domestic supply of the service item.

A full analysis of factor incomes would require a consideration of the determinants of the factor level, that is, international investment behavior and migrant labor behavior. For this study, however, the factor level is taken to be exogenously determined, and the analysis will focus on how particular variables affect the demand for services from these factors. Factor incomes are estimated in value rather than in volume terms because of the difficulty involved in finding the appropriate deflators. The general equation for outflows of factor income (imports of the factor service) takes the form

\begin{matrix} {\begin{matrix} Y O \end{matrix}}_{i} = {R A}_{i} {F L}_{i} & (3) \end{matrix}

where YO_i is the value of the outflow of factor income, RA_i is the return to the factor, and FL_i is the factor level in country i.

(2) Exports. Two approaches to building export functions are used in this paper—the market shares approach and the unrestricted approach. ⁸ The market shares approach to specifying export demand functions is an import allocation approach, where changes in market shares over time are explained by relative prices and trends. To specify export demand in this way, use is made of the theoretical formulation derived by Strotz (1957; 1959) and Gorman (1959), which allows for consistency of the two-stage maximization procedures. At the first stage, total import demand for the service of country j (MVS_j) is determined, and at the second stage it is allocated among the i exporting countries or markets. Here we assume that the first stage of the allocation has already determined total imports for each country, so that we deal only with the decision as to how these imports should be allocated. We also assume that the utility function is homo-thetic, so that market shares depend only on the relative price of the products in the market, not on the size of the market itself.

With 14 countries included in the model, the number of parameters to be estimated is still quite large; to further reduce the number of responses, we use the theoretical formulation derived by Armington (1969) for products distinguished by place of production. This involves two further assumptions. If the elasticities of substitution between any two competing services in the market are the same as those for any other pair of competing services in that market, then all the price parameters can be expressed in terms of one substitution elasticity, σ_j and the share of country i in country j’s imports. The general bilateral export function for the market shares approach can therefore be written as

\begin{matrix} {X V S}_{i j} = {s m}_{i j}^{0} {M V S}_{j} {({P S}_{i} / {M P S}_{j})}^{σ_{j}} e^{v_{i j} t} & (4) \end{matrix}

where XVS_ij is the export volume of the service item from country i to country j; ${s m}_{i j}^{0}$ is the base-year share of the ith country in the jth country’s imports of the service item; PS_i is the price of the export service of country i; and MPS_j is the average price of the export service to country j, calculated as

{M P S}_{j} = \underset{i}{Π} {P S}_{i}^{{s m}_{i j}}

and σ_j is the substitution elasticity in market j. The trend term is added to the equation to account for factors that affect the allocation of imports over time. ⁹ In this equation, exports of country i to country j are determined by the base-period share of country (market) j’s imports, a change in relative competitors’ prices, and a trend term.

Although equation (4) will not hold exactly in the aggregate unless a first-order linear approximation is obtained, it is assumed here that equation (4) can be used as an adequate approximation of the aggregate relationship, in which XVS represents aggregate exports, and the foreign market variable and foreign prices are appropriately weighted averages. The market-shares estimating equation is

\begin{matrix} {X V S}_{i} = b_{0} {F S}_{i}^{b_{1}} {R X P S}_{i}^{b_{2}} e^{b_{3} t} & (5) \end{matrix}

where XVS_i is the volume of exports of the service item of country i; FS_i is the foreign market variable defined as

{F S}_{i} = \underset{j}{Σ} {s m}_{i j}^{0} {M V S}_{j}

and RXPS_i is the relative effective price competitiveness variable calculated as

{R X P S}_{i} = \underset{j}{Π} {({P S}_{i} / {M P S}_{j})}^{s x_{i j}}

where sx_ij is the share of the jth country in country i’s service exports. The market shares approach will be used for the two general competitive service items—travel and passenger transportation, and other private services.

In the unrestricted approach to specifying export demand functions, exports are not simply the allocation of predetermined imports. Exports are explained by taking separate unrestricted bilateral import functions ¹⁰ for the j countries to which country i exports, and weighting and summing across these j countries. Thus, the export function for service items for which only one price exists is specified as

\begin{matrix} {X V S}_{i} = b_{0} {F D G S}_{i}^{b_{1}} {W P S}^{b_{2}} e^{b_{3} t} & (6) \end{matrix}

FDGS_i is foreign real total (domestic and foreign) expenditure on goods and services (i.e., weighted aggregate real total expenditure on goods and services of the j countries importing from country i). All other variables are defined in equations (2) and (5). The unrestricted approach is also used to describe inflows of income (YI) for factor services:

\begin{matrix} {\begin{matrix} Y I \end{matrix}}_{i} = {R A}_{i}^{f} {F L F}_{i} & (7) \end{matrix}

${R A}_{i}^{f}$ is a weighted average of returns to the factor of the j countries importing from country i, and FLF_i is the sum of the factor level in the j foreign countries.

Transfers

Private transfers include transfers between individuals, between nonofficial organizations, or between individuals and nonofficial organizations. ¹¹ Included are gifts, dowries, inheritances, alimony, and other support remittances, such as contributions to religious, scientific, cultural, and charitable associations. All private transfers are unrequited. Private transfers are assigned to the factor income group. Equations (3) and (7) are used to estimate, respectively, outflows and inflows of private transfers.

Official transfers comprise military and economic grants, subscriptions to international organizations, technical assistance, and scholarships and pensions. For the purposes of this paper, official transfers are treated as exogenously determined.

Identities

A complete system of world trade in invisibles would require that all flows of the kth invisible item be completely determined for all η countries that trade in the invisible item, so that world imports are identically equal to world exports. To build such a world model for invisibles would be extremely difficult, however, in view of the paucity of the data, so that for the rest of the world invisible items are taken to be exogenously determined. In the estimation of the model, the constraint that world imports equal world exports is not taken into account.

individual group equations

Freight transportation services

The transportation account of the balance of payments contains three separate items: (i) receipts from and payments for passenger transportation; (ii) receipts from and payments for cargo transportation; and (iii) receipts from and payments for port services. ¹² In addition, the transportation account is defined to include insurance on merchandise trade. ¹³

The first item—passenger transportation—has been separated from the other categories of transportation and is included in the equation for international travel. The second item—receipts from and payments for international cargo transportation—covers international receipts from and payments for all vessels and vehicles used for international transportation of goods, excluding port services. The third item of the transportation account—receipts from and payments for port services—includes charges for landing services, maintenance facilities, fuel charges, and expenditure ashore by crews.

Special allowance must be made for payments and receipts for port services. As a country’s expenditure to foreign carriers for the transportation of its imports and passengers increases, the port services of foreign carriers in the country in question must also rise; these port service receipts are effectively an offsetting exported component of imported cargo transportation and passenger transportation services. Similarly, when transportation receipts from freight earnings on a country’s carriers increase, that country’s payments to foreign countries on port services also increase; these port service payments are therefore an offsetting imported component of exported cargo transportation and passenger transportation services. ¹⁴

For the individual country, imports of freight transportation services (MVFR_i) have two main components: (i) imports of cargo transportation (MVCT_i); and (ii) imports of port services (MVPS_i). A country’s demand for imports of cargo transportation (MVCT_i) is a derived demand, stemming from the demand for imported commodities. The demand for imported cargo transportation is therefore determined by imported commodities (MVG_i) and the price of cargo transportation to country i (MPCT_i).

Country i’s import demand for port services (MVPS_i) is related to country i’s total cargo transportation services abroad and country i’s total passenger transportation services abroad. (Total is defined here to include both exports of these services and services provided for domestic residents by domestic operators.) It is assumed that a country’s total cargo transportation services abroad are proportional to its exports of goods, and that a country’s total passenger transportation services abroad are proportional to its exports of travel services. For the majority of countries in this study, this is a reasonable assumption, since third-country trade (from foreign port to foreign port) in cargo transportation and passenger transportation is negligible. Therefore, country i’s import demand for port services is determined by its exports of goods and travel services (XGTV_i) and the price of port services (MPPS_i).

Country i’s demand for imported freight transportation services (MVFR_i) is the sum of imports of cargo transportation and imports of port services, and may be written as

\begin{matrix} {M V F R}_{i} = a_{0} {M X V T}_{i}^{a_{1}} {M P F R}_{i}^{a_{2}} e^{a_{3} t} & (8) \end{matrix}

where

{M X V T}_{i} = {M V G}_{i}^{{s p m}_{i}} * {X G T V}_{i}^{(1 - {s p m}_{i})}

and spm_i is the share of country i’s spending on cargo transportation in country i’s spending on cargo transportation and port services.

{M P F R}_{i} = {M P C T}_{i}^{{s p m}_{i}} * {M P P S}_{i}^{(1 - {s p m}_{i})}

The trend term is added to the equation to represent factors that change slowly over time. Important factors that may be accounted for by the trend term are technological changes in the shipping industry, commodity and geographic changes in patterns of trade, growth of flag discrimination in some parts of the world, and changing shares in the country’s active world tonnage.

The export demand equation is defined in a way that is similar to the import demand equation. Denoting XVFR_i as export volume of freight transportation services of country i, one may write

\begin{matrix} {X V F R}_{i} = b_{0} {X M V T}_{i}^{b_{1}} {X P F R}_{i}^{b_{2}} e^{b_{3} t} & (9) \end{matrix}

where

{X M V T}_{i} = {X V G}_{i}^{{s p x}_{i}} * {M G T V}_{i}^{(1 - {s p x}_{i})}

spx_i is the share of country i’s receipts from cargo transportation services in country i’s receipts from both cargo transportation and port services; XVG_i is the export volume of goods in country i; and MGTV_i is the import volume of goods and travel services in country i.

{X P F R}_{i} = {X P C T}_{i}^{{s p x}_{i}} * {X P P S}_{i}^{(1 - {s p x}_{i})}

For a few countries—such as Denmark, Japan, Norway, and the United Kingdom—the amount of third-country trade transported by domestic carriers is large, so that exports of cargo transportation are likely to be related to world volume of exported goods as well as to domestic exports, and imports of port services are likely to be related to world volume of exported goods and travel services as well as to domestic exports. ¹⁵ For these countries, the trade variables MXVT_i and XMVT_i are defined as

\begin{matrix} {M X V T}_{i} = {M V G}_{i}^{{s p m}_{i}} * {({X G T V}_{i}^{{s d m}_{i}} * {W X V G T V}^{1 - {s d m}_{i}})}^{1 - {s p m}_{i}} \\ {\begin{matrix} X M V T \end{matrix}}_{i} = {({X V G}_{i}^{{s d x}_{i}} * {W X V G}^{1 - {s d x}_{i}})}^{{s p x}_{i}} * {M G T V}_{i}^{1 - {s p x}_{i}} \end{matrix}

WXVGTV is the volume of world exports of goods and travel services, WXVG is the volume of world exports of goods, sdm_i is the share of country i’s port service payments from own country payments in country i’s payments on port services from own country and third-country payments, and sdx_i is the share of country i’s cargo receipts from own country exports in country i’s cargo receipts from own country exports and third-country exports. Import and export prices of freight transportation also include weights for third-country exports.

Equations (8) and (9) are defined in volumes of freight transportation imports and exports. It was decided, however, to multiply both sides of the equation by the price of freight transportation services, so that data on values of freight transportation imports and exports appear on the left-hand side of the equation, as suggested by Hemphill. This is done because XPFR_i and MPFR_i may be subject to larger measurement errors than are deflators for the other service groups. Equations (8) and (9) can therefore be rewritten for estimation purposes as

\begin{matrix} {M F R}_{i} = a_{0} {M X V T}_{i}^{a_{1}} {M P F R}_{i}^{1 + a_{2}} e^{a_{3} t} & (10) \end{matrix}

\begin{matrix} {X F R}_{i} = b_{0} {X M V T}_{i}^{b_{1}} {X P F R}_{i}^{1 + b_{2}} e^{b_{3} t} & (11) \end{matrix}

Travel and passenger transportation services ¹⁶

The international travel item of the balance of payments statistics of a country covers expenditure in the country by nonresidents and payments to foreign countries by residents of the country in question. The passenger transportation item covers passenger fares paid by foreigners to domestic carriers (receipts) and passenger fares paid by domestic passengers to foreign carriers (payments).

It is postulated here that the demand for imports of foreign travel and passenger transportation services for country i (MVTV_i) is determined by the price of domestic travel and passenger transportation services relative to the foreign price of these services plus expenditure on domestic and foreign travel and passenger transportation services. It will also depend upon destinational characteristics, such as climate, cultural attributes, and scenery. ¹⁷

Total expenditure on domestic and foreign travel and passenger transportation services is not generally available as an aggregate variable for the majority of the countries in this study, so that a proxy variable has to be found. It is asserted here that the expenditure variable is closely associated with the permanent component of income. A permanent income index (YP_i) was therefore derived from real gross national product (Y_i), measured in constant 1970 U.S. dollars, through a geometrically declining moving average truncated after six periods, namely,

{Y P}_{i} = λ Σ_{k = 1}^{6} B^{k} Y_{i_{t - k}}

where

λ = 1 / Σ_{k = 0}^{6} B^{k}

and k refers to semiannual frequencies.

The total foreign price variable is a weighted average of the prices of travel and passenger transportation for all j countries that export to country i. Each of these prices should include the price of travel services in country j, PTV_j, ¹⁸ and the price of transportation from country i to country j, T_ij. It is assumed here that the price of transportation services per mile, T, is the same across countries, but that the share of transportation services in each country’s travel and passenger transportation price index may differ from country to country because the distances involved differ. The foreign price of travel services, MPTV_i (which is a weighted average of the travel prices of the j countries that export to country i), and the transportation price variable, T, have been separated for estimation purposes because the weights on each price variable in the total foreign price variable are unknown. The travel price variable also enters the equation in lagged form because knowledge of foreign travel price changes may be acquired by travelers from previous trips to the country. Knowledge of transportation prices, on the other hand, is likely to be more readily available to travelers, so that no lag is involved.

The import equation for travel and passenger transportation flows can be written

\begin{matrix} {M V T V}_{i} = a_{0} {R M P T V}_{i}^{a_{1}} T^{a_{2}} {Y P}_{i}^{a_{3}} e^{a_{4} t} & (12) \end{matrix}

T is the world index of the average price of passenger transportation; and RMPTV_i is the index of import prices of travel services (MPTV_i) relative to domestic prices of travel services (PTV_i, and is calculated as MPTV_i/PTV_i.

Once imports of various countries’ foreign travel and passenger transportation services have been determined, the market shares approach can be used to determine the exports of country i; these are determined by base-period shares in country (market) j’s imports, a change in country i’s travel price relative to competitors’ travel prices, the price of transportation,¹⁹ and a trend term. The export equation for travel and passenger transportation flows for country i is as follows:

\begin{matrix} X V T V_{i} = b_{0} R X P T V_{i}^{b_{1}} T^{b_{2}} F T V_{i}^{b_{3}} e^{b_{4} t} & (13) \end{matrix}

RXPTV_i is a double-weighted index reflecting the relative effective price competitiveness and is calculated as

{R X P T V}_{i} = Π_{j \neq i}^{n} {({P T V}_{i} / {M P T V}_{j})}^{{s t v x}_{i j}}

where stvx_ij is the share of the jth country in country i’s travel and passenger transportation exports, and FTV_i is the foreign market share variable for travel services calculated as

{F T V}_{i} = \underset{j}{Σ} {s t v m}_{i j}^{0} * {M V T V}_{j}

where ${s t v m}_{i j}^{0}$ is the share of the ith country in country j’s travel and passenger transportation imports in the base period.

Flows of investment income ²⁰

These flows arise from international transactions and can be broadly classified into three groups: (i) direct investment, (ii) financial investment, and (iii) other investment. A full model of international investment income flows should consist of the foreign demand for assets and the domestic supply of liabilities for each country for each of the three groups. The factors that influence these supply and demand equations are likely to be complex, so that no attempt has been made to explain them here. Two approaches to the specification of investment income flows are adopted—a gross flows approach and a net flows approach.

(1) Gross flows approach. Separate relations are estimated for three types of income flow—direct investment (DI), financial investment (FI), and other investment (OI). Flows of direct investment income arise from the ownership of direct investment capital. Flows of financial investment income are composed of income from private holdings of foreign bonds, foreign equities, long-term loans to foreigners, and short-term claims on foreigners. Flows of other investment income include official investment income, such as income receivable or payable by the country’s government or central bank, by a foreign government or central bank, or by an international organization. Official investment income includes income received by the official sector on reserve holdings.

The general earnings equation for country i for all three groups—DI, FI, and OI—is given in equation (14). The investment income outflow equation for country i (imports of capital services) is then presented for outflows of direct investment income and for outflows of financial and other investment income. The investment income inflow equation (exports of capital services) is then explained by summing across separate bilateral income outflow equations for the j countries in which country i holds investment assets.

Foreign earnings on liabilities in country i (E $k_{i t}^{h}$ ) during period t on each k-type liability are the product of the average actual rate of return (RA $k_{i t}^{h}$ ) and the average value of the liability holding (LIAk_it) in country i: ²¹

\begin{matrix} E k_{i t}^{h} = R A k_{i t}^{h} * L I A k_{i t} & (14) \end{matrix}

where k refers to the liability type (DI, FI, OI), and h indicates that the earnings and rate of return variables are those appropriate to the home country (i.e., country i). The rates of return, flow of earnings, and income outflows resulting from these earnings are considered separately for direct investment and for financial and other investment.

(a) Outflows of direct investment income. The rate of return on direct investment liabilities in country i (RAD $I_{i t}^{h}$ ) is likely to be related to the long-term interest rate (RPD $I_{i t}^{h}$ ) that should reflect the inflation rate in country i, and to cyclical fluctuations in the level of economic activity (CYD $I_{i t}^{h}$ ) that result in quasirents and losses. The rate of return on direct investment liabilities. in country i is

\begin{matrix} {R A D I}_{i t}^{h} = β_{0} {({R P D I}_{i t}^{h})}^{β_{1}} {({C Y D I}_{i t}^{h})}^{β_{2}} & (15) \end{matrix}

Recorded outflows of direct investment income differ from earnings because the proportion of earnings that is typically retained and reinvested in the host country is not recorded together with income outflows. To determine outflows of direct investment income, it is necessary to determine the factors that affect the proportion of earnings that is reinvested. Important factors that affect the proportion of earnings repatriated include tax policies or restrictions on profit remittances of host countries, the expected exchange rate at which domestic currency earnings will be converted at the time of repatriation, and the relative profitability of domestic investment compared with foreign investment. The first two factors are difficult to model, so that it is assumed here that the proportion of earnings repatriated (resulting in income outflows) will depend upon the relative profitability of domestic and foreign investment (PR_i). Where tax policies, restrictions, and “leads and lags” with respect to exchange rates exist, and are well documented, dummy variables are included in the equation.

In addition to these effects, firms or individuals often adjust their income outflows (YODI_it) slowly to higher or lower levels of earnings. When the change in earnings is accepted as permanent, rather than temporary, adjustment will be complete. Outflows of permanent direct investment income (YOPDI_it) are given by

\begin{matrix} {Y O P D I}_{i t} = {E D I}_{i t}^{h θ} & (16) \end{matrix}

and actual income outflows adjust gradually to permanent income outflows over a period of time. The adjustment process can be explained by a stock adjustment model of the form

\begin{matrix} {\begin{matrix} Y O D I \end{matrix}}_{i t} / {Y O D I}_{i t - 1} = {({Y O P D I}_{i t} / {Y O D I}_{i t - 1})}^{η} {P R}_{i}^{ρ} & (17) \end{matrix}

where η is the coefficient of adjustment. Substituting equation (15) into (14), (14) into (16), and (16) into (17) gives

\begin{matrix} {\begin{matrix} Y O D I \end{matrix}}_{i} = a_{0} {L I A D I}_{i}^{a_{1}} {R P D I}_{i}^{h^{a_{2}}} {C Y D I}_{i}^{h^{a_{3}}} {P R}_{i}^{a_{4}} {Y O D I}_{i - 1}^{a_{5}} & (18) \end{matrix}

The coefficients of equation (18) are related to the underlying parameters in the following manner:

a_{1} = θ_{η}, a_{2} = β_{1} θ_{η}, a_{3} = β_{2} θ_{η}, a_{4} = ρ, a_{5} = 1 - η

(b) Outflows of financial and other investment income. Financial and other investment liabilities are a mixture of longterm and short-term investments, and for these two categories, earnings are

\begin{matrix} \begin{matrix} \begin{matrix} E k_{i t}^{h} = r k_{i t}^{h} L I A k_{i t} \end{matrix} \\ r k_{i}^{h} \cdot L I A k_{i} = {(L I A k_{i} * R P k_{i}^{h})}^{γ k_{i}} * {(L I A k_{i} * R T k_{i}^{h})}^{(1 - γ k_{i})} \end{matrix} & (19) \end{matrix}

γk_i is country i’s share of long-run liabilities of type k (i.e., financial liabilities and other liabilities) in its holdings of both long-run and short-run liabilities of type k; and RPk_i^h is the long-run interest rate, RTk_i^h the short-run interest rate, on liability of type k in country i. ²²

Outflows of financial and other investment income are assumed to be a constant fraction of earnings, so that

\begin{matrix} Y O k_{i} = E k_{i}^{h θ} & (20) \end{matrix}

Many long-run financial and other investment liabilities have fixed rates of return, so that past interest rates have an effect on current income earned. A lagged dependent variable is therefore added to the equation to reflect the effect of past interest rates on outflows of current income. Substituting equation (19) into (20) and adding a lagged dependent variable gives

\begin{matrix} Y O k_{i} = a_{0} {(r k_{i}^{h} \cdot L I A k_{i})}^{a_{1}} {Y O k}_{i - 1}^{a_{2}} & (21) \end{matrix}

Income inflow (YI) equations can be explained in a way that is similar to income outflow equations except that the exogenous variables are weighted and summed across the j foreign countries in which country i holds assets. The income inflow equation for direct investment can be written as

\begin{matrix} {Y I D I}_{i} = b_{0} {A S S D I}_{i}^{b_{1}} {R P D I}_{i}^{f^{b_{2}}} {C Y D I}_{i}^{f^{b_{3}}} {P R}_{i}^{b_{4}} {Y I D I}_{i - 1}^{b 5} & (22) \end{matrix}

and for financial and other investment

\begin{matrix} \begin{matrix} Y I k_{i} = b_{0} {(r k_{i}^{f} \cdot A S S k_{i})}^{b_{1}} Y I k_{i - 1}^{b_{2}} \\ r k_{i}^{f} \cdot A S S k_{i} = {(A S S k_{i} * R P k_{i}^{f})}^{{α k}_{i}} * {(A S S k_{i} * R T k_{i}^{f})}^{(1 - α k_{i})} \end{matrix} & (23) \end{matrix}

αk_i is country i’s share of long-run assets of type k in its holdings of both long-run and short-run assets of type k;RP $k_{i}^{f}$ is a weighted average of foreign long-run interest rates, and RT $k_{i}^{f}$ a weighted average of foreign short-run interest rates, on asset of type k, where the weights are the share of country j in country i’s total direct investment assets; and ASSk_i is the average value of country i’s total holding of assets abroad over the period.

(2) Net flows approach.²³ In this approach, investment income is defined in net rather than in gross terms. The advantages to be gained from using this method to estimate investment income flows is that it eliminates the need for data on stocks of international assets and liabilities. The assumptions on which the approach is based are rather more restrictive than the assumptions in the gross flows approach: (i) For each country, the rate of return on all assets at time t is assumed to be equal to the rate of return on all liabilities at time t. (ii) The parameters for income inflow equations are assumed to be identical to those for income outflow equations, (iii) The current account is assumed to be equal to net capital flows (including reserve changes), (iv) Income inflows and outflows are assumed to be the same as earnings.

For countries with large errors and omissions items representing an error in an item on the current account, the net change in the investment position will be misstated. It will also be misstated where balancing items are funded partly (or totally) by gold, which does not earn a rate of return. Furthermore, for those countries that report income flows rather than earnings, there is no information on what proportion of earnings is actually repatriated.

Using these assumptions, the equation for net flows of investment income (YN) for all categories of investment for country i is

\begin{matrix} {Y N}_{i t} = {Y I}_{i t} - {Y O}_{i t} & (24) \end{matrix}

\begin{matrix} = R A_{i t}^{f} \cdot {A S S}_{i t} - {R A}_{i t}^{h} \cdot {L I A}_{i t} & (25) \end{matrix}

Assuming that ${R A}_{i t}^{f}$ = ${R A}_{i t}^{h}$ = RA_it, equation (25) can be rewritten as

\begin{matrix} {Y N}_{i t} = {R A}_{i t} \cdot {N A S S}_{i t} & (26) \end{matrix}

where NASS_it = ASS_it – LIA_it. NASS_it is the net average value of the foreign asset position of country i at time t, and RA_it is the average rate of return on these net foreign assets. At present, equation (26) is merely a definition. It becomes an estimating equation when we find proxy variables for RA_it and NASS_it. The estimating equation for net flows of investment income can be expressed as

\begin{matrix} {Y N}_{i t} = c_{0} + \hat{{R A}_{i t}} \cdot \hat{{N A S S}_{i t}} & (27) \end{matrix}

where ${\hat{R A}}_{i t}$ and ${\hat{N A S S}}_{i t}$ are proxy variables for RA_it and NASS_it. Clearly, the closer the proxy variables are to the real variables, the closer c0 will be to zero and c₁ to one.

Other services

This category consists of two subgroups: (i) an account that covers transactions in services between private residents of a country and overseas residents that cannot be included in other categories; and (ii) miscellaneous government transactions. The latter subgroup is treated as exogenously determined in this study.

Because it includes items that cannot be identified elsewhere, the group “Other private services” is extremely heterogeneous. For countries for which workers’ earnings are important and can be distinguished separately, this item has been treated separately. The remainder of the other service group is made up of commissions and agency fees connected with selling of imports and exports; professional and technical services; earnings and payments for films and television programs; communications services, including telecommunications and postal and telephone services; financial and allied services, such as nonmerchandise insurance; royalties and management fees; and other property income not included elsewhere. Where the data permit, royalties and management fees are estimated together with direct investment income flows.

Import demand for other private services for country i is postulated to be determined by economic activity of that country as measured by gross national product (GNP), ²⁴ and by the price of domestic other private services relative to the foreign price of these services. Export demand for other private services is explained by the market shares approach. Other private services import and export equations for the ith country are as follows:

\begin{matrix} {M V O P}_{i} = a_{0} {G N P}_{i}^{a_{1}} {R M P O P}_{i}^{a_{2}} e^{a_{3} t} & (28) \end{matrix}

\begin{matrix} {X V O P}_{i} = b_{0} {F O P}_{i}^{b_{1}} {R X P O P}_{i}^{b_{2}} e^{b_{3} t} & (29) \end{matrix}

MVOP_i and XVOP_i are import and export volumes of other private services for country i, GNP_i is real gross national product in country i in constant 1970 U. S. dollars, RMPOP_i is the weighted index of import prices of other private services (MPOP_i) relative to the domestic price of other private services (POP_i) for country i; RXPOP_i is a double-weighted index reflecting the relative effective price competitiveness, and FOP_i is the foreign market share variable for other private services.

Workers’ earnings and remittances

Workers’ earnings are defined as repatriated labor income of seasonal, border, or temporary workers who have been non-residents of the country for less than one year. Labor income includes wages, salaries, and other compensation to these workers on a gross basis without deduction for taxes, pensions, or other contributions that are included as offsets to labor income in unrequited transfers. Worker’s remittances are included in the private transfers group and are defined as unrequited transfers of migrant workers. These migrant workers are persons who stay, or are expected to stay, in the host country for more than one year. In practice, it is often difficult to draw the distinction between workers’ earnings and workers’ remittances.

A full model of workers’ earnings and remittances should consist of the foreign demand for migrant labor and the domestic supply of migrant labor for each country. The factors that influence these supply and demand equations are likely to be complex, however, so that no attempt has been made to explain them here; instead, the level of migrant labor is taken to be exogenously determined.

Earnings of foreign workers in the host country i (EWR_it) during period t are the product of the average wage paid to foreign workers in country i over the period t (WF_it) and the number of foreign workers in country i over period t (FL_it):

\begin{matrix} {E W R}_{i t} = {W F}_{i t} \cdot {F L}_{i t} & (30) \end{matrix}

The average wage paid to foreign workers in country i (WF_i) is the product of the average hourly wage rate in country i (AHW_i) and the number of hours worked in country i (HHW_i). The number of hours worked by foreign workers is likely to be related to the cyclical fluctuations in country i; foreign workers are rarely employed in jobs, such as government employment, that are protected from cyclical movements, and the number of hours worked are quite likely to vary with economic activity in the host country.

Only a proportion of earnings of foreign workers in country i will be repatriated. To determine the proportion of earnings repatriated, it is necessary to consider changes in the exchange rate, changes in taxation in the host country, and many other factors. Because of numerous difficulties involved in deriving a model for speculative activity, these activities are included as dummy variables where they have been well documented in other sources. Therefore, YOWR_i = EW $R_{i}^{θ}$ where YOWR_i is income outflows, and the estimating equation may be written as

\begin{matrix} {Y O W R}_{i} = a_{0} {F L}_{i}^{a_{1}} {H H W}_{i}^{a_{2}} {A H W}_{i}^{a_{3}} & (31) \end{matrix}

A bilateral outflow of workers’ earnings and remittances from country i to country j represents an inflow of workers’ earnings and remittances for country j, so that the preceding analysis explains both flows. Hence, inflows of workers’ earnings and remittances (YIWR_i) for a particular country is merely the sum of outflows of foreign countries to which the domestic country sends workers, so that the estimating equation for inflows will be

\begin{matrix} {Y I W R}_{i} = b_{0} {F F L}_{i}^{b_{1}} {F H W}_{i}^{b_{2}} {A F W}_{i}^{b_{3}} & (32) \end{matrix}

FFL_i is the number of country i’s workers in the labor force of foreign countries j, calculated as

{F F L}_{i} = Σ_{j = 1}^{n} {F L}_{j}

FHW_i is the number of hours worked by country i’s workers in the labor force of foreign countries j, calculated as

{F H W}_{i} = \underset{j}{Π} {H H W}_{j}^{{s w e}_{i j}}

swe_ij is the share of country j in country i’s total workers abroad, namely, swe_ij = FL_ij/FFL_i; and AFW_i is the average hourly wage rate paid to workers from country i in the labor force of foreign countries j and is calculated as

{A F W}_{i} = \underset{j}{Π} {A H W}_{j}^{{s w e}_{i j}}

Private transfers

Outflows of private transfers of country i (YOTP_i) are generally assumed to be related to the level of GNP in country i, plus a trend factor, and the equation takes the form

\begin{matrix} {Y O T P}_{i} = a_{0} {G N P}_{i}^{a_{1}} e^{a_{2} t} & (33) \end{matrix}

Inflows of private transfers of country i(YITP_i) are related to foreign GNP (FGNP_i). This variable is a weighted average of the GNP of the j countries that send private transfers to country i, where the weights are the share of country j in country i’s private transfer inflows. The inflow equation for private transfers is

\begin{matrix} {Y I T P}_{i} = b_{0} {F G N P}_{i}^{b_{1}} e^{b_{2} t} & (34) \end{matrix}

II. Parameter Estimates

Information on the data compilation, the use of proxy variables, and the arrangement of individual country data in the standard framework is contained in the Appendix. All the variables in equations (8) to (34) are expressed in billions of U. S. dollars. Balance of payments data in nominal (current) dollars are deflated prior to estimation for travel and passenger transportation and for other private services by use of deflators based at 1970 = 1.0. For freight transportation, the dependent variable is in nominal dollars and the deflator is included as an extra variable on the right-hand side of the equation, because doubt exists as to the appropriateness of the deflator. Factor services and private transfers are estimated in current dollars because no appropriate deflator could be found. Import and export volumes of goods are on an f.o.b. basis. All price indices are in U. S. dollars based at 1970 = 1.0.

Estimates of the parameters for the six groups of invisibles were obtained from semiannual data for the 14 industrial countries by means of ordinary least squares. The estimates are shown, together with their standard errors, the R², the Durbin-Watson statistic, and the standard error of the estimate in Tables 2 to 16. The estimation period, determined by the availability of data for each country and category, is shown in column 2 of each table. A seasonal dummy taking the value of one for the first half year and zero for the second was added to the equation where there was an indication of significant seasonal variations. Other dummy variables were included to represent the effects of special factors or events and are documented in the footnotes to the tables.

The model was estimated using the equations as specified in Section I in log-linear form. To check whether the equation should be linear or log-linear, the equations in Section I were also specified in linear form. To choose between the two specifications, the variance of the linear specification (û_t) was compared with the antilog of the variance of the log-linear specification (û_t’). The ratio of these two variances (û_t/û_t’) was greater than one for most invisibles, so that the log-linear specification was preferred, since it predicts more efficiently over the estimation period. Thus, we assume that the elasticities remain constant over the estimation period. ²⁵ The linear specification was used for those invisibles that are estimated as net flows.

It was felt that the neglect of long-run influences on general competitive and specific one-price invisibles would have two effects, (i) A misleading interpretation of the demand parameters—in particular, income and trade elasticities—that would pick up both cyclical and long-run effects. For example, income elasticities for travel and passenger transportation would include the effects of changes in tastes as well as income effects, (ii) The misspecification of the equation because of omitted variables. ²⁶ The addition of a trend term to represent these omitted long-run factors has, however, led to estimation problems; sometimes the short-run variations in the variables are not large enough, and strong interrelationships among the independent variables, particularly the demand and trend variables, make it difficult to disentangle their separate effects on the dependent variable. In several cases, these interrelations have caused severe multicol-linearity problems, and coefficients with “wrong signs” or with magnitudes that are meaningless have resulted. In these cases, two possible solutions can be tried. First, we can look at the linear combination of the coefficients together; unfortunately, this solution does not enable us to separate the long-run and short-run effects. Second, we can use extraneous estimates of one coefficient to correct for variation in one of the variables, and then estimate the parameters on the other variables. That is the approach followed in this study; in the event of severe multicollinearity, the parameter on the trend term in the equation is constrained to equal the average value of the estimated coefficients of the trend term for the 14 industrial countries. The underlying assumption is that long-run factors that influence the dependent variable are the same for all countries but that it is difficult to measure their impact for individual countries with any degree of precision in the presence of multicollinearity. In the tables, the parameters whose values were restricted a priori to assumed values are not given a standard error.

For some countries and categories of invisibles, the number of observations was quite small. For example, there were only 14 observations for several of the industrial countries for freight transportation and other private service flows. Obviously, the point estimates of the coefficients are less likely to be reliable with a small number of observations than if the number were large, and in these cases some caution should be used in attributing accuracy to findings.

A detailed discussion of the empirical results for each of the six groups of invisibles follows.

services

Freight transportation services

The estimates of the parameters for equations (10) and (11) for each of the 14 countries are presented in Tables 2 to 4.

Table 2.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation Services¹

^¹Standard errors are shown in parentheses. All variables except the dummies are in logarithmic form. SEE is the standard error of the estimate. An asterisk indicates that an estimate is significantly different from zero at the 95 per cent confidence level.

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.9028 (0.0379).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

Table 2.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation Services¹

Country	Estimation Period²	Constant	MXVT_i	MPFR_i	Trend	Dummies		R²	D-W	SEE
Austria	1970–76	–3.94^*	0.14	1.04^*	0.072^*			0.988	1.58	0.061
		(0.33)	(0.21)	(0.26)	(0.013)
Belgium	1965–76	–2.07^*	0.53^*	1.54^*	0.015	0.25^*³		0.991	1.47	0.064
		(0.25)	(0.21)	(0.21)	(0.013)	(0.06)
Canada	1964–76	–1.64^*	0.61^*	1.26^*	0.005			0.987	1.91	0.050
		(0.35)	(0.19)	(0.18)	(0.009)
Denmark	1970–76	–1.56^*	0.32	1.47^*	0.017			0.979	1.68	0.062
		(0.48)	(0.45)	(0.21)	(0.012)
France	1968–76	–1.25	0.43	0.44^*	0.056^*	–0.31^*⁴		0.985	1.49	0.094
		(0.98)	(0.36)	(0.12)	(0.020)	(0.10)
Germany, Fed. Rep.	1961–76	–1.98^*	0.82^*	0.62^*	0.003	0.17^*⁵	0.17^*⁶	0.994	1.52	0.051
		(0.46)	(0.20)	(0.10)	(0.010)	(0.04)	(0.06)
Italy	1968–76	0.32	–0.40^*	0.60^*	0.054^*			0.977	2.66	0.054
		(0.35)	(0.18)	(0.09)	(0.007)
Japan	1964–76	–0.15	–0.48^*	0.58^*	0.103^*	0.16^*⁷		0.998	1.37	0.030
		(0.11)	(0.07)	(0.05)	(0.005)	(0.03)
Netherlands	1970–76	–1.17	0.18	1.06^*	0.030^*			0.966	1.36	0.073
		(1.12)	(0.48)	(0.25)	(0.012)
Norway	1970–76	–0.16	–1.64^*	1.25^*	0.074^*	–0.17^*⁸		0.989	2.19	0.044
		(0.33)	(0.36)	(0.20)	(0.010)	(0.05)
Sweden	1970–76	–2.38^*	0.73	0.49	0.043^*			0.957	2.19	0.083
		(1.00)	(0.60)	(0.28)	(0.013)
Switzerland	1970–76	–3.49^*	0.57^*	1.00^*	0.019			0.972	1.81	0.054
		(0.51)	(0.19)	(0.26)	(0.012)
United Kingdom	1961–76	–0.94	0.68^*	0.60^*	0.001	0.36^*⁹	0.16^*¹⁰	0.993	1.39	0.041
		(0.59)	(0.24)	(0.07)	(0.005)	(0.03)	(0.05)
United States¹¹	1961–76	–1.98^*	0.60^*	0.27^*	0.037^*	0.12^*¹²	–0.07^*¹³	0.827	2.05	0.036
		(0.63)	(0.17)	(0.09)	(0.010)	(0.03)	(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.9028 (0.0379).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

Table 2.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation Services¹

Country	Estimation Period²	Constant	MXVT_i	MPFR_i	Trend	Dummies		R²	D-W	SEE
Austria	1970–76	–3.94^*	0.14	1.04^*	0.072^*			0.988	1.58	0.061
		(0.33)	(0.21)	(0.26)	(0.013)
Belgium	1965–76	–2.07^*	0.53^*	1.54^*	0.015	0.25^*³		0.991	1.47	0.064
		(0.25)	(0.21)	(0.21)	(0.013)	(0.06)
Canada	1964–76	–1.64^*	0.61^*	1.26^*	0.005			0.987	1.91	0.050
		(0.35)	(0.19)	(0.18)	(0.009)
Denmark	1970–76	–1.56^*	0.32	1.47^*	0.017			0.979	1.68	0.062
		(0.48)	(0.45)	(0.21)	(0.012)
France	1968–76	–1.25	0.43	0.44^*	0.056^*	–0.31^*⁴		0.985	1.49	0.094
		(0.98)	(0.36)	(0.12)	(0.020)	(0.10)
Germany, Fed. Rep.	1961–76	–1.98^*	0.82^*	0.62^*	0.003	0.17^*⁵	0.17^*⁶	0.994	1.52	0.051
		(0.46)	(0.20)	(0.10)	(0.010)	(0.04)	(0.06)
Italy	1968–76	0.32	–0.40^*	0.60^*	0.054^*			0.977	2.66	0.054
		(0.35)	(0.18)	(0.09)	(0.007)
Japan	1964–76	–0.15	–0.48^*	0.58^*	0.103^*	0.16^*⁷		0.998	1.37	0.030
		(0.11)	(0.07)	(0.05)	(0.005)	(0.03)
Netherlands	1970–76	–1.17	0.18	1.06^*	0.030^*			0.966	1.36	0.073
		(1.12)	(0.48)	(0.25)	(0.012)
Norway	1970–76	–0.16	–1.64^*	1.25^*	0.074^*	–0.17^*⁸		0.989	2.19	0.044
		(0.33)	(0.36)	(0.20)	(0.010)	(0.05)
Sweden	1970–76	–2.38^*	0.73	0.49	0.043^*			0.957	2.19	0.083
		(1.00)	(0.60)	(0.28)	(0.013)
Switzerland	1970–76	–3.49^*	0.57^*	1.00^*	0.019			0.972	1.81	0.054
		(0.51)	(0.19)	(0.26)	(0.012)
United Kingdom	1961–76	–0.94	0.68^*	0.60^*	0.001	0.36^*⁹	0.16^*¹⁰	0.993	1.39	0.041
		(0.59)	(0.24)	(0.07)	(0.005)	(0.03)	(0.05)
United States¹¹	1961–76	–1.98^*	0.60^*	0.27^*	0.037^*	0.12^*¹²	–0.07^*¹³	0.827	2.05	0.036
		(0.63)	(0.17)	(0.09)	(0.010)	(0.03)	(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.9028 (0.0379).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

(1) Imports. Table 2 shows that 13 of the 14 countries have more than 95 per cent of the variance of their imports explained as measured by the R² statistic. The Durbin-Watson test rejected the hypothesis of serial independence in the residuals for the U. S. equation, and this equation was re-estimated using the Cochrane-Orcutt correction method.

The results for this category of invisibles are rather disappointing for some countries because it was not possible to identify both short-term and long-term influences with as much precision as one would like. As a result of interrelationships between the trade variable (MXVT) and the time trend, the estimates of the coefficient for the trade variable are poorly determined and are significant at the 95 per cent level for only 9 of the 14 countries; of these 9 countries, only 6 (Belgium, Canada, the Federal Republic of Germany, Switzerland, the United Kingdom, and the United States) have the predicted positive sign. All the coefficients are less than one; use of fleets at less than capacity during a depression and economies of scale during a boom could account for these coefficients being less than one. The values and signs of the coefficients on the trade variable for Austria, France, Italy, Japan, the Netherlands, and Norway, and the fact that a low or negative estimated coefficient for the trade variable is accompanied by a high coefficient on the trend term, lead one to conclude that the multicollinearity between the trade variable and the trend term may be the reason for the poor results for these countries. ²⁷ The cycle in the trade variable and the dependent variable is not measured with sufficient accuracy by the data, and these variables are strongly trended. The large positive coefficient on the trend term for the United States could be due to the effects on freight imports of a long-run decline in the size of the shipping fleet.

The estimates of the effects of changes in tramp, liner, tanker, and surface rates (MPFR) are rather more satisfactory, as they are of the expected sign, and are significant at the 95 per cent level for 13 of the 14 countries. The estimated price coefficients are close to unity only for Austria, the Netherlands, and Switzerland; most of the other countries have coefficients that are significantly less than one. This would indicate that imports of freight transportation services are price sensitive. ²⁸ The results may be biased, however, because of the likely existence of large errors of measurement in the price series used, and because of the effects of nonprice factors, such as maintenance time, loading and unloading time, and safety factors, which are omitted from the equation. The low price coefficient for the United States could be the result of measurement errors in the form of omitted labor costs. The coefficients on the price term for Belgium and Denmark appear larger than one; the size of these coefficients may also reflect errors in data measurement.

To increase the precision of the trade variable for six countries for which multicollinearity was a problem (Austria, France, Italy, Japan, the Netherlands, and Norway), the coefficient on the trend term was constrained to be 0.013. This value is the average value of the estimated coefficients for six countries (Belgium, Canada, the Federal Republic of Germany, Switzerland, the United Kingdom, and the United States) for which multicollinearity problems did not seem to be too severe. ²⁹ The new results are presented in Table 3. The estimates of the trade coefficients have gained in precision and are now significant at the 95 per cent level for Austria, France, Italy, and Japan; the imposed restriction has led to little difference in the R² statistic except for Italy, where it has fallen from 0.977 to 0.880. The freight price coefficient for Norway, however, remained much larger than one, while the coefficient on the trade variable remained negative. The results were more reasonable when the freight price coefficient was constrained to equal 1.0. The equation with the added constraint gave a coefficient on the trade variable that is reasonable in size and sign; unfortunately, this was at the cost of a drastically reduced R² statistic.

Dummy variables were included in 7 of the 14 country equations and are described in the footnotes to Table 3. A shift dummy variable was included in the equations for France, the Federal Republic of Germany, and the United Kingdom because the data definition changed during the period of estimation. The dock strike in the United States in the first half of 1969 was captured with a dummy variable; the full impact of the strike was not reflected in imports and exports because the strike led to substantial rerouting of goods through Canada. The Middle East crisis and the closing of the Suez Canal in 1967 had an unfavorable influence on imports by the United Kingdom. The equations for several countries included a dummy variable to account for the impact of the oil crisis on freight-transportation imports. The oil embargo affected countries’ imports at different periods, depending on the length of the lag involved.

Table 3.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation with Trend Coefficient Constrained to 0.013 for Six Countries¹

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.983 (0.008).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

Table 3.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation with Trend Coefficient Constrained to 0.013 for Six Countries¹

Country	Estimation Period²	Constant	MXVT_i	MPFR_i	Trend	Dummies		R²	D-W	SEE
Austria	1970–76	–3.08^*	0.53^*	1.96^*	0.013			0.955	0.94	0.100
		(0.42)	(0.13)	(0.24)
Belgium	1965–76	–2.07^*	0.53^*	1.54^*	0.015	0.25^*³		0.991	1.47	0.064
		(0.25)	(0.21)	(0.21)	(0.013)	(0.06)
Canada	1964–76	–1.64^*	0.61^*	1.26^*	0.005			0.987	1.91	0.050
		(0.35)	(0.19)	(0.18)	(0.009)
Denmark	1970–76	–1.56^*	0.32	1.47^*	0.017			0.979	1.68	0.063
		(0.48)	(0.45)	(0.21)	(0.012)
France	1968–76	–1.43	0.95^*	0.59^*	0.013	–0.40^*⁴		0.975	1.54	0.107
		(1.11)	(0.32)	(0.11)		(0.10)
Germany, Fed. Rep.	1961–76	–1.98^*	0.82^*	0.62^*	0.003	0.17^*⁵	0.17^*⁶	0.994	1.52	0.051
		(0.46)	(0.20)	(0.10)	(0.010)	(0.04)	(0.06)
Italy	1968–76	–0.89	0.44^*	0.73^*	0.013			0.880	1.31	0.096
		(0.50)	(0.19)	(0.17)
Japan	1964–76	–1.66^*	0.89^*	1.03^*	0.013	–0.01⁷		0.957	0.68	0.132
		(0.29)	(0.10)	(0.22)		(0.12)
Netherlands	1970–76	–1.62	0.52	1.19^*	0.013			0.947	1.37	0.076
		(1.12)	(0.44)	(0.23)
Norway	1970–76	–0.84^*	0.42	1.00	0.013	0.14⁸		0.411	1.49	0.094
		(0.26)	(0.23)			(0.10)
Sweden	1970–76	–2.38^*	0.73	0.49	0.043^*			0.957	2.19	0.083
		(1.00)	(0.60)	(0.28)	(0.013)
Switzerland	1970–76	–3.49^*	0.57^*	1.00^*	0.019			0.972	1.81	0.054
		(0.51)	(0.19)	(0.26)	(0.012)
United Kingdom	1961–76	–0.94	0.68^*	0.60^*	0.001	0.36^*⁹	0.16^*¹⁰	0.993	1.39	0.041
		(0.59)	(0.24)	(0.07)	(0.005)	(0.03)	(0.05)
United States¹¹	1961–76	–1.98^*	0.60^*	0.27^*	0.037^*	0.12^*¹²	–0.07^*¹³	0.827	2.05	0.036
		(0.63)	(0.17)	(0.09)	(0.010)	(0.03)	(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.983 (0.008).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

Table 3.

Fourteen Industrial Countries: Regression Coefficients for Imports of Freight Transportation with Trend Coefficient Constrained to 0.013 for Six Countries¹

Country	Estimation Period²	Constant	MXVT_i	MPFR_i	Trend	Dummies		R²	D-W	SEE
Austria	1970–76	–3.08^*	0.53^*	1.96^*	0.013			0.955	0.94	0.100
		(0.42)	(0.13)	(0.24)
Belgium	1965–76	–2.07^*	0.53^*	1.54^*	0.015	0.25^*³		0.991	1.47	0.064
		(0.25)	(0.21)	(0.21)	(0.013)	(0.06)
Canada	1964–76	–1.64^*	0.61^*	1.26^*	0.005			0.987	1.91	0.050
		(0.35)	(0.19)	(0.18)	(0.009)
Denmark	1970–76	–1.56^*	0.32	1.47^*	0.017			0.979	1.68	0.063
		(0.48)	(0.45)	(0.21)	(0.012)
France	1968–76	–1.43	0.95^*	0.59^*	0.013	–0.40^*⁴		0.975	1.54	0.107
		(1.11)	(0.32)	(0.11)		(0.10)
Germany, Fed. Rep.	1961–76	–1.98^*	0.82^*	0.62^*	0.003	0.17^*⁵	0.17^*⁶	0.994	1.52	0.051
		(0.46)	(0.20)	(0.10)	(0.010)	(0.04)	(0.06)
Italy	1968–76	–0.89	0.44^*	0.73^*	0.013			0.880	1.31	0.096
		(0.50)	(0.19)	(0.17)
Japan	1964–76	–1.66^*	0.89^*	1.03^*	0.013	–0.01⁷		0.957	0.68	0.132
		(0.29)	(0.10)	(0.22)		(0.12)
Netherlands	1970–76	–1.62	0.52	1.19^*	0.013			0.947	1.37	0.076
		(1.12)	(0.44)	(0.23)
Norway	1970–76	–0.84^*	0.42	1.00	0.013	0.14⁸		0.411	1.49	0.094
		(0.26)	(0.23)			(0.10)
Sweden	1970–76	–2.38^*	0.73	0.49	0.043^*			0.957	2.19	0.083
		(1.00)	(0.60)	(0.28)	(0.013)
Switzerland	1970–76	–3.49^*	0.57^*	1.00^*	0.019			0.972	1.81	0.054
		(0.51)	(0.19)	(0.26)	(0.012)
United Kingdom	1961–76	–0.94	0.68^*	0.60^*	0.001	0.36^*⁹	0.16^*¹⁰	0.993	1.39	0.041
		(0.59)	(0.24)	(0.07)	(0.005)	(0.03)	(0.05)
United States¹¹	1961–76	–1.98^*	0.60^*	0.27^*	0.037^*	0.12^*¹²	–0.07^*¹³	0.827	2.05	0.036
		(0.63)	(0.17)	(0.09)	(0.010)	(0.03)	(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in payments on bunkering in Belgium, first half and second half 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Shift dummy, second half 1971 to first half 1976.

^⁶Temporary increase in imports of raw materials, first half 1975.

^⁷Oil crisis, first half and second half 1974.

^⁸End of period of long-term contracts, second half 1975.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Middle East crisis, second half 1967.

^¹¹Corrected for first-order autocorrelation. The first-order autoregressive coefficient was 0.983 (0.008).

^¹²Oil crisis, second half 1974.

^¹³Dock strike in the United States, first half 1969.

(2) Exports. The parameter estimates for exports of freight transportation derived from equation (11) are presented in Table 4, and these results in general support the hypothesized relationships that freight transportation exports depend on exports of goods and port disbursements and on freight rates. The coefficients on the long-run trend term are also significant in 7 of the 14 equations; for the United Kingdom, the coefficient is negative and could represent supply factors that have a depressing influence on exports, such as the growth in the number of ships operating under flags of convenience to take advantage of lower operating costs. The large positive coefficient on the trend term for Japan can be explained by the considerable expansion of the Japanese fleet, particularly in the early 1970s. The trend term for Japan is also thought to reflect the increase in receipts from leasing domestically owned ships to foreign operators. The increase in transshipment from Rotterdam to the Rhine and other river ports and increased road haulage activity may explain part of the large positive coefficient on the time trend for the Netherlands equation.

Table 4.

Fourteen Industrial Countries: Regression Coefficients for Exports of Freight Transportation Services¹

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in receipts on bunkering in Belgium, 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Increased exports of investment goods to members of the Organization of Petroleum Exporting Countries, first half 1975.

^⁶Shift dummy, second half 1971 to first half 1976.

^⁷Oil crisis, second half 1974.

^⁸Devaluation of sterling, second half 1967.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Dock strike in the United States, first half 1969.

Table 4.

Fourteen Industrial Countries: Regression Coefficients for Exports of Freight Transportation Services¹

Country	Estimation Period²	Constant	XMVT_i	XPFR_i	Trend	Dummies			R²	D-W	SEE
Country	Estimation Period²	Constant	XMVT_i	XPFR_i	Trend	Seasonal	Other		R²	D-W	SEE
Austria	1970–76	–3.50^*	0.68	1.43^*	0.019	–0.10			0.943	1.29	0.103
		(0.61)	(0.54)	(0.37)		(0.07)
Belgium	1965–76	–2.01^*	0.60^*	1.66^*	0.005		0.21^*³		0.995	1.89	0.045
		(0.18)	(0.17)	(0.18)	(0.012)		(0.04)
Canada	1964–76	–1.67^*	0.45^*	0.43^*	0.026^*	–0.09^*			0.993	1.72	0.035
		(0.25)	(0.12)	(0.07)	(0.004)	(0.02)
Denmark	1970–76	–3.31	0.44	1.20^*	0.027	–0.06^*			0.985	1.47	0.060
		(2.74)	(0.60)	(0.24)	(0.162)	(0.05)
France	1968–76	–1.38^*	0.49^*	1.16^*	0.019		–0.36^*⁴		0.989	2.15	0.061
		(0.60)	(0.20)	(0.16)			(0.06)
Germany, Fed. Rep.	1961–76	–1.43^*	0.65^*	1.04^*	–0.004		0.21^*⁵	0.06^*⁶	0.994	1.88	0.042
		(0.40)	(0.17)	(0.11)	(0.009)		(0.05)	(0.03)
Italy	1968–76	–1.06^*	0.34	0.98^*	0.012		–0.16^*⁷		0.988	2.23	0.042
		(0.36)	(0.22)	(0.14)	(0.011)		(0.05)
Japan	1964–76	–3.84^*	0.84^*	1.52^*	0.029				0.995	2.14	0.059
		(1.09)	(0.33)	(0.17)	(0.017)
Netherlands	1970–76	–3.68^*	0.73 [-1]	0.46^*	0.053^*		0.09⁷		0.990	1.52	0.049
		(1.80)	(0.51)	(0.19)	(0.013)		(0.06)
Norway	1970–76	–5.15	1.22	0.48^*	–0.003				0.928	1.41	0.084
		(2.88)	(0.66)	(0.22)	(0.019)
Sweden	1970–76	–1.56^*	0.66	0.54^*	0.015	–0.28^*			0.968	1.80	0.063
		(0.67)	(0.35)	(0.18)	(0.012)	(0.03)
Switzerland	1970–76	–2.86^*	0.58^*	1.21^*	–0.017				0.984	1.60	0.035
		(0.33)	(0.22)	(0.19)	(0.011)
United Kingdom	1964–76	–3.74^*	1.14^*	0.85^*	–0.029^*		0.19^*⁸	0.25^*⁹	0.990	1.58	0.047
		(1.10)	(0.29)	(0.12)	(0.013)		(0.05)	(0.04)
United States	1961–76	–0.13	0.29^*	1.08^*	0.010^*		–0.11^*¹⁰		0.996	1.48	0.028
		(0.36)	(0.12)	(0.07)	(0.004)		(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in receipts on bunkering in Belgium, 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Increased exports of investment goods to members of the Organization of Petroleum Exporting Countries, first half 1975.

^⁶Shift dummy, second half 1971 to first half 1976.

^⁷Oil crisis, second half 1974.

^⁸Devaluation of sterling, second half 1967.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Dock strike in the United States, first half 1969.

Table 4.

Fourteen Industrial Countries: Regression Coefficients for Exports of Freight Transportation Services¹

Country	Estimation Period²	Constant	XMVT_i	XPFR_i	Trend	Dummies			R²	D-W	SEE
Country	Estimation Period²	Constant	XMVT_i	XPFR_i	Trend	Seasonal	Other		R²	D-W	SEE
Austria	1970–76	–3.50^*	0.68	1.43^*	0.019	–0.10			0.943	1.29	0.103
		(0.61)	(0.54)	(0.37)		(0.07)
Belgium	1965–76	–2.01^*	0.60^*	1.66^*	0.005		0.21^*³		0.995	1.89	0.045
		(0.18)	(0.17)	(0.18)	(0.012)		(0.04)
Canada	1964–76	–1.67^*	0.45^*	0.43^*	0.026^*	–0.09^*			0.993	1.72	0.035
		(0.25)	(0.12)	(0.07)	(0.004)	(0.02)
Denmark	1970–76	–3.31	0.44	1.20^*	0.027	–0.06^*			0.985	1.47	0.060
		(2.74)	(0.60)	(0.24)	(0.162)	(0.05)
France	1968–76	–1.38^*	0.49^*	1.16^*	0.019		–0.36^*⁴		0.989	2.15	0.061
		(0.60)	(0.20)	(0.16)			(0.06)
Germany, Fed. Rep.	1961–76	–1.43^*	0.65^*	1.04^*	–0.004		0.21^*⁵	0.06^*⁶	0.994	1.88	0.042
		(0.40)	(0.17)	(0.11)	(0.009)		(0.05)	(0.03)
Italy	1968–76	–1.06^*	0.34	0.98^*	0.012		–0.16^*⁷		0.988	2.23	0.042
		(0.36)	(0.22)	(0.14)	(0.011)		(0.05)
Japan	1964–76	–3.84^*	0.84^*	1.52^*	0.029				0.995	2.14	0.059
		(1.09)	(0.33)	(0.17)	(0.017)
Netherlands	1970–76	–3.68^*	0.73 [-1]	0.46^*	0.053^*		0.09⁷		0.990	1.52	0.049
		(1.80)	(0.51)	(0.19)	(0.013)		(0.06)
Norway	1970–76	–5.15	1.22	0.48^*	–0.003				0.928	1.41	0.084
		(2.88)	(0.66)	(0.22)	(0.019)
Sweden	1970–76	–1.56^*	0.66	0.54^*	0.015	–0.28^*			0.968	1.80	0.063
		(0.67)	(0.35)	(0.18)	(0.012)	(0.03)
Switzerland	1970–76	–2.86^*	0.58^*	1.21^*	–0.017				0.984	1.60	0.035
		(0.33)	(0.22)	(0.19)	(0.011)
United Kingdom	1964–76	–3.74^*	1.14^*	0.85^*	–0.029^*		0.19^*⁸	0.25^*⁹	0.990	1.58	0.047
		(1.10)	(0.29)	(0.12)	(0.013)		(0.05)	(0.04)
United States	1961–76	–0.13	0.29^*	1.08^*	0.010^*		–0.11^*¹⁰		0.996	1.48	0.028
		(0.36)	(0.12)	(0.07)	(0.004)		(0.03)

^²The period covers the first half of the first year indicated to the first half of 1976.

^³Increase in receipts on bunkering in Belgium, 1974.

^⁴Shift dummy, first half 1968 to second half 1970—these observations are not reconcilable with series after first half 1971.

^⁵Increased exports of investment goods to members of the Organization of Petroleum Exporting Countries, first half 1975.

^⁶Shift dummy, second half 1971 to first half 1976.

^⁷Oil crisis, second half 1974.

^⁸Devaluation of sterling, second half 1967.

^⁹Shift dummy, second half 1970 to first half 1976.

^¹⁰Dock strike in the United States, first half 1969.

For some countries, the trade variable did not fluctuate widely enough over the cycle, with the result that the trade variable and the trend term are highly collinear. This lowered the precision of the estimates, particularly for Austria and France, and for these 2 countries the trend term was constrained to be equal to the average value of the coefficients of the trend term (0.019) for 12 of the 14 countries; Japan and the United Kingdom were excluded because of their large, changing shares in active world tonnage. The unconstrained results for Austria and France are recorded in footnote 30; ³⁰ these can be compared with the more precise constrained results in Table 4. Of the 14 countries, 8 show estimated coefficients for the trade variable (XMVT) that are significant at the 95 per cent level; these coefficients range in size between 0.29 and 1.14. In general, one would expect the elasticity of freight transportation exports with respect to the volume of trade to be unity; however, the average elasticity for all 14 countries here is 0.65. More efficient use of the fleet during a boom and inefficient use during a depression could account for this average elasticity measurement.

The results show that for all countries freight rates are significant at the 95 per cent level and that for three countries (the Federal Republic of Germany, Italy, and the United States) the coefficients on the price term are close to unity. Results for the other countries are widely distributed on both sides of one, so that no clear conclusion can be reached as to the price sensitivity of freight transportation exports with respect to freight rates.

The seasonal dummy variables indicate a strong negative seasonal pattern for the first half year for Austria, Canada, and Sweden. Dummies for other disturbances had an important impact for Belgium, the Federal Republic of Germany, Italy, the Netherlands, the United Kingdom, and the United States. The sign of the coefficient on the dummy for the oil embargo is not uniform; the coefficient is positive for the Netherlands and negative for Italy. The difference in signs is thought to be due to the different impact that oil prices had on different sectors of the shipping market; transportation credits rose as a result of the impact of the oil crisis on the tramp and liner market, but fell as a result of the impact on the tanker market. The positive coefficient on the oil crisis dummy for the Netherlands, for example, is due largely to higher values of bunker deliveries. The dummy for the devaluation of sterling was included in the equation for the United Kingdom, because freight rates on third-country trade were set in terms of the sterling value of foreign goods.

Travel and passenger transportation services

Equations (12) and (13) were fitted to data on travel and passenger transportation flows for 14 industrial countries. Direct estimation of the distributed lags on the relative price variable is not possible because of the collinearity of the lagged values, and an indirect method using a polynomial distributed lag was used. A polynomial of degree two gave the best results in terms of minimum standard error criteria. The length of the lag was also determined by minimum standard error criteria, and in some instances a zero constraint was imposed on the value of the end-period coefficient. ³¹

(1) Imports. The estimates of the parameters for equation (12) are presented in Table 5. For all of the countries, more than 96 per cent of their variance is explained by the chosen variables as can be seen from the R² statistic, and there was no evidence of serial autocorrelation in the residuals.

Table 5.

Fourteen Industrial Countries: Regression Coefficients for Imports of Travel and Passenger Transportation Services¹

^²The period covers the first half of the first year indicated to the second half of 1976.

^³The length of the lag is indicated in square brackets.

^⁴The mean lag is in half-year units.

^⁵Corrected for first-order autocorrelation. The first-order autoregressive coefficient was -0.768 (0.166).

^⁶Speculative flows in Belgium, first half and second half 1973.

^⁷Speculative flows in Belgium, first half and second half 1969.

^⁸Shift in seasonal pattern as follows—Canada: S1, first half 1960 to second half 1973; S2, first half 1974 to second half 1976; France and the United Kingdom: S1, first half 1960 to second half 1971; S2, first half 1972 to second half 1976.

^⁹Bicentennial year in the United States, first half and second half 1976.

^¹⁰Expo in Canada, first half and second half 1967.

^¹¹Shift dummy, first half 1960 to second half 1967.

^¹²Political disturbances and strikes in France, first half and second half 1968.

^¹³Foreign exchange restrictions in France, first half 1968 to second half 1972.

^¹⁴Austrian Olympics and backlog of delayed travel plans, second half 1975 to first half 1976.

^¹⁵Speculative flows in Italy, first half and second half 1971.

^¹⁶Speculative flows in Italy, first half and second half 1972.

^¹⁷Speculative flows in Italy, first half and second half 1974.

^¹⁸Foreign exchange restrictions in Japan, first half 1967 to second half 1970.

^¹⁹Temporary increase in direct and indirect taxation in the Netherlands, first half and second half 1971.

^²⁰Rapid expansion of organized flights abroad from Sweden, first half and second half 1970.

^²¹Shift dummy, first half 1960 to second half 1966.

^²²Foreign exchange restrictions in the United Kingdom, first half 1967 to second half 1969.

^²³Political disturbances in Europe, first half and second half 1968.

Table 5.

Fourteen Industrial Countries: Regression Coefficients for Imports of Travel and Passenger Transportation Services¹

Country	Estimation Period²	Constant	YP_i	RMPTV_i		T	Trend	Dummies					R²	D-W	SEE
				Long-run elasticity³	Mean lag⁴			Seasonal		Other
				Long-run elasticity³	Mean lag⁴			S1	S2	Other
Austria⁵	1967–76	3.24^* (1.17)	–2.56^* (0.59)	–0.83 [4] (0.97)	0.70 (3.18)	0.13 (0.18)	0.112^* (0.017)	–0.33^* (0.07)					0.988	2.51	0.035
Belgium	1964–76	–6.69^* (1.60)	2.06^* (0.63)	–4.85 [4] (2.75)	2.19^* (1.06)	–0.12^* (0.06)	–0.020 (0.019)	–0.22^* (0.01)		0.14^*⁶ (0.04)	0.10^*⁷ (0.04)		0.994	2.21	0.034
Canada	1960–76	–13.35^* (4.92)	3.50^* (1.31)	–1.35^* [4] (0.41)	2.08 (1.09)	–0.51^* (0.14)	–0.077 (0.037)	–0.05^* (0.02)	0.10^*⁸ (0.04)	0.35^*⁹ (0.09)	–0.13^*¹⁰ (0.05)		0.973	1.44	0.061
Denmark	1961–76	–5.65^* (1.62)	1.79^* (0.69)	–2.76^* [6] (0.41)	2.10^* (0.73)	–0.03 (0.14)	–0.023 (0.015)	–0.28^* (0.02)					0.987	1.42	0.046
France	1960–76	–14.17^* (4.04)	3.13^* (0.92)	–2.93^* [4] (0.52)	1.01^* (0.37)	–0.14 (0.22)	–0.017 (0.025)	–0.37^* (0.02)	–0.29^*⁸ (0.04)	–0.71^*¹¹ (0.08)	0.33^*¹² (0.06)	0.19^*¹³ (0.06)	0.989	1.48	0.063
Germany, Fed. Rep.	1960–76	–4.34^* (1.80)	1.04^* (0.38)	–2.78^* [4] (0.42)	0.25 (0.47)	–0.22 (0.13)	0.013 (0.009)	–0.33 (0.18)		0.13^*¹⁴ (0.05)			0.993	1.46	0.052
Italy	1961–76	–8.09^* (3.06)	1.85^* (0.76)	0.71 [4] (0.47)	2.63 (1.33)	–1.96^* (0.23)	–0.014 (0.016)	–0.28^* (0.02)		0.16^*¹⁵ (0.06)	–0.14^*¹⁶ (0.07)	–0.21^*¹⁷ (0.06)	0.993	1.50	0.058
Japan	1961–76	–14.04^* (2.68)	2.67^* (0.61)	–0.71 [4] (0.78)	3.81 (3.73)	0.17 (0.27)	–0.016 (0.026)	–0.09^* (0.03)		–0.19^*¹⁸ (0.04)			0.996	1.32	0.071
Netherlands	1960–76	–4.25 (2.40)	0.65 (0.85)	4.47^* [4] (1.30)	1.47^* (0.59)	0.27 (0.21)	0.078^* (0.027)	–0.22^* (0.02)		–0.16^*¹⁹ (0.06)			0.992	1.58	0.054
Norway	1964–76	–7.08 (6.22)	2.78 (3.44)	–0.35 [4] (1.84)	0.54 (2.70)	0.40^* (0.10)	–0.039 (0.089)	–0.21^* (0.02)					0.969	1.83	0.052
Sweden	1961–76	–5.34^* (1.73)	1.25^* (0.57)	–1.39 [4] (0.87)	0.34 (1.54)	–0.43^* (0.17)	0.018 (0.011)	–0.16^* (0.01)		0.11^*²⁰ (0.06)			0.995	2.11	0.040
Switzerland	1960–76	–2.56^* (0.57)	0.55^* (0.25)	–1.88^* [6] (0.42)	1.86^* (0.86)	–0.63^* (0.13)	0.007 (0.009)	–0.26^* (0.08)		0.09^*²¹ (0.02)			0.997	1.66	0.023
United Kingdom	1961–76	–4.50 (3.60)	1.03 (0.80)	–0.66^* [4] (0.26)	0.51 (1.31)	–0.34^* (0.07)	0.012 (0.012)	–0.43^* (0.13)	–0.28^*⁸ (0.02)	–0.12^*²² (0.02)	–0.10^*²³ (0.03)		0.994	2.32	0.031
United States	1960–76	–3.74 (2.24)	0.72^* (0.34)	–1.26^* [3] (0.26)	2.20^* (0.60)	0	0.021^* (0.008)	–0.17^* (0.02)		0.07^*¹⁰ (0.03)			0.978	2.55	0.049