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A linear regression analysis of ocean tramp rates
Transpn Res. Vol. 3, pp. 377-395. Pergamon Press 1969. Printed in Great Britain
A LINEAR REGRESSION ANALYSIS OF OCEAN TRAMP RATES THOMAS H. BATES Center for World Business, San Francisco State College San Francisco, California, U.S.A.
(Received 11 February 1969; in revisedform 23 April 1969) 1. I N T R O D U C T I O N SHIPS that ply the liner trades and are members of the various steamship conferences operate under rate structures that are relatively fixed and are somewhat insensitive to changes in supply and demand. On the other hand, tramp freight rates are, in principle, determined by supply and demand. As a consequence tramp rates are both more sensitive to changes in supply and demand and more unstable than are liner rates. Because tramp rates are less administratively determined than are liner rates they are more amenable to the type of analysis undertaken here. The purpose of this inquiry is through a multivariate regression analysis to better understand the nature of ocean tramp shipping rates and how these rates are influenced by various important factors such as distance of haul, volume of shipment, trade route, season, year (i.e. the forces of demand that existed in a given year), and the terms upon which a rate is quoted. The original research for this study was undertaken by the author during the period 1964-65 at the University of California, Berkeley, as part of a spatial equilibrium analysis of the world sugar economy. Therefore, our interest will be in analyzing the rates for a specific dry, bulk cargo--raw sugar. The years 1959 and 1963 were used in the original study as the basic years for investigation. Consequently, the reported rates used for this study were taken for these two years. The nature of the tramp trade and how rates are determined in this market are discussed in Section 2. This is followed by an analysis of reported rates in Section 3 and an interpretation of our findings in Section 4. Section 5 contains some closing remarks. 2. THE METHOD OF T R A N S P O R T A T I O N 2.1. The nature of the tramp fleet Classified in the ocean shipping trade as a dry, bulk cargo, sugar is usually carried in tramp ships. Generally speaking, a tramp ship can be defined as a freight vessel which does not run on a regularly scheduled line, usually has lower cost of operation and takes cargo in large lots. In fact, some liner companies keep their smaller, older and slower vessels on a stand-by basis for use at times on tramping junkets. Since the same ships are also used in liner services, it is not always easy to distinguish between tramp and liner shipping. Further, at times sugar is available at many large ports which are served by liners. Rather than having to sail with some unutilized capacity, the liners take on partial loads at much lower than prevailing general cargo rates. In terms of operation schedules, the world's nonmilitary freight-carrying fleets may be subdivided (Thoman, 1962) into liners, tramps and private carriers, viz. : 1. Liners maintain regularly scheduled service for passengers, passengers and cargo, and cargo only. They usually are the largest and fastest civilian ships in existence (except 377
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THOMASH. BATES
for the super-tankers) and, when carrying merchandise, tend to haul the more expensive goods which can stand their higher freighting charges and which are attracted to their fast service. 2. Tramp ships do not maintain regular schedules and carry whatever cargo is available at any port of call--usually bulk freight that is low in value. Compared with liners they tend to be older, smaller, more uncertain in schedule and willing to carry almost any legitimate cargo (usually in large or shipload lots) if time is not a decisive factor as to when that cargo should arrive. 3. Private carriers are used primarily by large manufacturing concerns to deliver raw materials, fuels or finished products. In the sugar trades, vessels are commonly chartered on voyage chartert and are hence actually part of the tramp fleet in a broad sense. These vessels are increasingly becoming specialist carriers. Only in recent years has the need for the specialist carrier developed. The present need is because of the fact that whereas formerly sugar was carried bagged as part of other cargoes, today this practice has all but ceased and sugar has become a bulk cargo. 2.2. Tramp rate determination When the negotiations regarding the chartering of a vessel have been completed, the vessel can be said to b e f i x e d . Most fixtures in the tramp market are made through brokers on markets such as the Baltic Exchange in London. Information about fixtures is then issued to the public through such publications as the Daily Freight Register, Fairplay and Norwegian Shipping News. As a further aid in understanding the overall picture of the freight market, several sources have developed freight rate indices. One of particular interest for our purposes is the Norwegian Shipping News tripcharter freight rate index for dry cargoes. Another, which will be mentioned more fully later, is the Chamber of Shipping of the United Kingdom index of tramp shipping freights. The Norwegian Shipping News tripcharter freight rate index for dry cargoes is a worldwide index covering, at the time of this study, fixtures in 23 different trade routes for coal, grain, iron ore, sugar and miscellaneous. These different commodities were weighted as follows: coal, 8; grain, 5; iron ore, 5; sugar, 2; and miscellaneous, 2. One index was constructed for each of the 23 trade routes, with July-December 1947 equal to 100. The indices for the various trade routes were then combined through simple arithmetic averages into group indices for coal, grain, etc. For this purpose each of the route indices was t For future reference, the following definitions (Bes, 1951) will hold: f.i.o. (free in and out) means that the cost of loading and discharging the cargo are not for the account of the vessel (it is for the account of the charterer). Further, the term free in andout, stowed and trzmmed, signifies that stowing is also for the account of the charterer. The alternative to fa.o. or f.i.o., s. and t. is gross terms or gross charter. These terms signify that the cost of loading, stowing, and discharging are for the account of the vessel. The expression berth terms is used for shipments under a charter party, the principal terms of which correspond with the regular terms for shipment of the commodity concerned by the regular lines operating m the particular trade. Generally speaking, the term implies that loading and discharging expenses will be for the ship-owners' account. A charter vessel is one which has been contracted for under a contract of affreightment in the form of a charter-party between a ship-owner and a charterer. On a voyage charter (trip charter) a ship-owner undertakes to put a vessel at a charterer's disposal for the carriage of a full cargo or part cargo from one or more ports to named port(s) of destination at rates and conditions mutually agreed upon. Alternatively, on a time charter, the ship-owner undertakes to put the vessel out on mutually agreed terms for a stated period of time (e.g. 1 year) or she may be let on time charter for one or more consecutive voyages between certain territories.
A linear regression analysis of ocean tramp rates
379
given the weight 1. The resulting five group indices were combined into the tripcharter index using Laspeyres' formula and the weights quoted above. Unfortunately for our purposes, this index had not been published for individual commodities and, therefore, an index for sugar alone was not available. Following the usual reasoning (Thorburn, 1960), ocean freight rates are determined by supply and demand. On the demand side, a freight-owner generally needs transport between two definite ports, and can choose between large and small consignments at a time. On the other hand, on the supply side, a ship-owner has a vessel with a definite cargo capacity and has a choice of allowing it to perform transports over different distances. Therefore, the ship-owner is interested in freight rates over different transport distances for a certain ship, the freight-owner in freight rates over the same distance for vessels of different sizes. If the shipping tonnage available is more than required for servicing tonnage demand, freight rates will fall to a relatively low level. As rates fall, ship-owners will, in the short run, keep their ships in operation as long as freight revenues cover variable costs. This occurred frequently in 1959 when supply or available tonnage was high relative to demand. As rates continue to fall, more and more tonnage is laid up. The supply of available tonnage is thus restricted and the fall in rates dampened. Similarly, an increase in demand will bring tonnage out of lay-up, starting with the most economic. As rates rise, more and more tonnage is made available, thus checking the rise in rates. These conditions are illustrated in Fig. 1. We have been talking about the area on the supply curve SS between demand functions DD and D"D". Note that with low demand the supply of tonnage is rather elastic with changes in the freight market not being reflected so much by changes in freight rates as by changes in tonnage available. Increasing demand brings out more and more tonnage until the point is reached where the only tonnage left in Frelght Rate
D~
\\
___
R
-- J \ \
\
Q'~
il
Q Qt
°
Tonnage Avaxlable
FIG. 1. The demand for and supply of tramp tonnage.
380
THOMAS H. BATES
lay-up are ships under repair or undergoing inspection or maintenance. Thus at some point, A on our diagram, the supply of tonnage becomes very inelastic to changes in rates. Depending on the state of the ship-building art and the availability of competitive modes of transportation (only a limited part of the ocean freight market is affected by competitive forms of transport), a rather small increase in demand now can have quite magnified effects on rates in the short run. Figure 2 shows the Norwegian Shipping News index of freight rates over the period 1947-61 plotted against tonnage laid-up in British and Irish ports over the same period to indicate the nature of short-run supply that was expressed theoretically in Fig. 1, with allowance for the fact that "laid-up" tonnage reflects excess supply rather than total supply.-~ The almost vertical section to the left of the diagram corresponds to the relatively inelastic section of the SS curve in Fig. 1 and represents the short-run supply when demand presses on available ships. The nearly horizontal section is the more elastic section of SS in Fig. 1 and represents short-run supply when demand is actually less than available ships. When the rate index drops to around 60-75, the ships go into storage, but higher Index of Freight Rates 300
X= Trxp C h a r t e r I n d e x • = Time Charter Index 250
$
m
$ 200
15C
x
i00 X
50
0
I
I
0.5
1.0 Laid-Up
I
i 5
Tonnage-Mzlhon
I
2.0
,
21.5
I
3 0
Gross Tons
FIG. 2. Laid-up tonnage against trip- and time-charter rate indices. (From Norwegian Shipping News.) t Figure 2 gives rise to an identification problem. Since each observation is the function of different values of the underlying parameters we cannot be sure whether we have identified a supply curve, a demand curve or some mixture of both. However, over the relevant period 1947-61 demand was much more unstable than supply. Beginning particularly with the Suez crisis in 1956 new ships were ordered and the supply has been increasing since. At the same time demand forces have fluctuated relatively more and it is suggested that the data displayed in Fig. 2 reveal a rough supply curve traced out by a relatively rapidly fluctuating demand schedule moving up and down a slower shifting supply schedule.
A linear regression analysis of ocean tramp rates
381
rates bring out any desired amount until the laid-up tonnage is approximately 500,000 tons --possibly an irreducible minimum. This figure at least suggests that rates tend to settle down to some lower limit which may reflect variable costs. At times of low freight rates, time-charter rates tend to be relatively lower than tripcharter rates. When rates rise, time-charter rates rise more rapidly. There is also a tendency in boom times for time-charter rates to be above trip-charter rates. An explanation of this behaviour has been given (Alexandersson and Norstrom 1963), as follows: harbor charges and fuel are paid for by the charterer in the case of time charter and by the ship-owner in the case of trip charter. These cost items are relatively unaffected by the state of affairs in the freight market. In a situation of surplus tonnage, the charterer will, therefore, have to see time-charter rates reduced to a level lower than that of trip-charter rates, otherwise it would be more economical to charter the ship on a trip-charter basis. In times of very high rates he will, for the same reason, be willing to pay relatively more for a time-chartered vessel, since part of his cost for the shipment will not be affected by the high cost level for transport. As regards liner shipping, both total costs and fixed costs exceed those of the tramps, mainly because additional facilities are required for the handling of passengers and general cargo than for bulk cargoes. The handling of general cargo calls for more powerful machilaery and the addition of passengers usually requires more space, larger crews and more expensive administrative handling. In addition, by the very nature of their operation, liners must make scheduled sailings whether fully loaded or not. They also call at more ports on the average than the tramps. Since a large proportion of the total costs of the regular steamship lines is made up of fixed costs, rigorous price competition is likely to lead to freight rates somewhere below average costs (perhaps even in the long run). Lines have, therefore, practiced several methods of regulating competition among themselves and of minimizing competition from outsiders. The specialist sugar carrier is capable, when necessary, of carrying coal, grain or lumber. Most of the other specialist carriers are equally capable of being adapted to the carriage of other commodities. In the last several years, the shipment of grains by tanker has become common. The semi-liquid quality of grains has made this possible and the changed relations between freight rates for tankers and dry cargo vessels has made it economical. The shift has been brought about by an increase in tanker tonnage that has progressed more rapidly than the demand for oil transportation. Despite the fact that not all ships are interchangeable, there are enough ships with a range of overlapping uses for the freight rates on different trades to follow one another closely. This overlapping also applies to the time-charter vs. trip-charter market, as we have seen, because of the possibilities for both ship-owner and shipper to accept the one offering more favorable terms. Freight rate data generally show considerable seasonal variation, the magnitude of variation depending basically upon the commodity and the trade route. The seasonal character of many important trades results in variations in demand for tonnage which in turn produces these seasonal variations in freight rates. Specifically, sugar shipments have a clearly seasonal component due to the effect of the harvest seasons. The large shipments from the Caribbean determine the variations in total tonnage engagement, which is highest during March-May, later decreasing to low values during September-November. This matter will be discussed further when we turn to a more thorough analysis of freight rates in the sugar trades. The return cargo position is also a factor influencing the rates in a particular trade. If a given trade route is characterized by one-way trade flows, ships will have to move to the ~7
382
THOMASH. BATES
port of loading in ballast. It will, therefore, pay these ships to accept cargo at any rate as long as it covers the extra costs involved in loading and unloading the return cargo and any possible costs which are incurred above those involved in sailing in ballast. Consequently, freight rates in the direction of the ballast trips are lower than in the cargo direction. There are numerous political and legal factors which have effect on some of the freight rates affecting sugar. These are not dealt with specifically here because of their relative unimportance in the case of tramp rates. 3. ANALYSIS OF R E P O R T E D RATES
3.1. Formulation of the problem We will now turn our attention to the specific nature of ocean rates for sugar and the ways in which these rates are influenced by various important factors. At the outset, it was assumed that the distance of a shipment and the size or volume of the shipment both influenced rates. It did not seem unreasonable to expect that the real effect of volume was not additive to distance, but rather was a modifier of a rate-distance regression. I can show what I mean with a simple model. Assume one that suggests that for any size of carrier V the TC (total cost) function might reasonably be
TC = a+bD
(1)
where TC represents total cost, D represents distance and a and b are constants. When we modify the volume both coefficients would be affected. A simple form of such adjustment might be TC= (a+cV)+(b+eV) D (2) where V represents volume. This simply states that the fixed or terminal charges and the variable costs both would increase with volume---and here in linear form. Since we are interested primarily in the costs per ton and hence in the nature of average costs (and this, of course, assumes that costs influence rates), t we can divide through (2) by V and get A C = a~V+ e + bD/V+ eD (3) where AC represents average cost. It was upon this basis that it was assumed that a logical basis for a statistical analysis of rates would be to relate not to D and V but to D and D~ V. Furthermore, it is apparent that D and D/V must be intercorrelated, with this intercorrelation approaching 1.0 as the variance of D increases relative to the variance of V. Upon inspection of distance and volume data (and the following must be remembered: since our rate observations were on trip-charter rates, it has been assumed that the total tonnage carried as reported was equal to the volume of the ship--or, the same thing, the ships were fully laden) for the rates collected it was found that D was in fact highly variable as compared to V. This was confirmed by correlating D and D/V: for 185 observations in 1959, r is 0.737; for 196 observations in 1963, r is 0.899. Apparently the intercorrelation t Costs and rates can be expected to correspond rather closely in a competitive industry and in the long run. However, in the short run rates will reflect short-run supply and demand situations and, as a result, may vary widely around the long-run level. In other words, rates may settle down to levels just adequate to cover direct trip costs (or lower if on a ballast leg of a trip) or could be very much above long-run average costs. However, if the statistical results do not reveal the true importance of numerous short-run factors, they may be accepted as estimates of the long-run situation.
383
A linear regression analysis of ocean tramp rates
was especially pronounced in the gross rates: combining 1959 and 1963 observations, the intercorrelation between D and D/V is 0.955 for gross terms as compared to 0.541 for f.i.o, terms. For the year 1959 gross the intercorrelation was 0.962 as compared to a 1959 f.i.o, intercorrelation of 0.480, and the year 1963 gross was 0.959 as compared to a 1963 f.i.o, intercorrelation of 0.789. Because of this very high intercorrelation, there is every reason to believe that statistical analyses would yield regression coefficients that were unstable (i.e. subject to large errors of estimate) and that chance factors could give rise to marked shifts in the apparent importance of one or the other variable. In order to preclude this happening we did not use the D and D~ V formulation despite the fact that it seemed to be the logical relationship. Instead we fitted a multiple linear form:
AC= a+bV+cD
(4)
While this form seems appropriate in a priori terms for the cost-distance relationship, it is also not inconsistent with reality as can be seen in Fig. 3. The V influence is expected to be negative, even though the linear form must be considered as only an approximation to the logically expected reciprocal form. ÷
Frelgh~ Rate + ÷
1400 ~t
÷ .L +
+
*
%
4:
I000 +
+
+
800
600
+
*~ ~a- "t
2
q"
°+I
e ÷
0
20~0
40~0
60~080001
10~10
120~
DISTANCE -- MILES
FIG. 3. Best fitting linear regression line for 1959 and 1963 f.i.o, and gross data.
384
THOMASH. BATES
Since short-run supply and demand situations can vary from season to season and from trade route to trade route, we expect considerable variation around any D and V regressions; that is, there will be a portion of variance not related to these two main factors. Therefore, in an attempt to hold some of these influences constant, the statistical analysis included shift variables for such elements as year, type, season and route. This was an effort to more accurately identify the net influences of D and V. 3.2. Sources of data Charter fixtures for sugar for both 1959 and 1963 were obtained from the publications; Norwegian Shipping News, Fairplay and Shipping World. Information necessary to calculate other freight rates was found in the United States Department of Agriculture's Sugar Reports and the International Sugar Council's Statistical Bulletin. In the first three publications, actual fixtures are reported and there is information given as to origin, destination, volume of shipment, freight rate per long ton, usually number and names of ports of call, terms (e.g.f.i.o., gross terms, etc.) and name of carrying vessel. Freight rates for the years 1959 and 1963 from the Greater Caribbean Area including Brazil f.o.b, and stowed (1) to North Atlantic ports and (2) to the United Kingdom were calculated from information in the U.S.D.A. Sugar Reports and from the I.S.C. Statistical Bulletins. Freight rates for the 2 years from Hawaii to San Francisco were obtained from the traffic department of Matson Steamship Co. Some 381 rate observations were coUected and classified according to year (1959 and 1963), terms (f.i.o. and gross) origin, destination, rate, distance, volume and season. These data were then submitted to analysis. The results of this analysis now demands our attention. 3.3. Statistical results Based on the functional relationship expressed in equation (4) (p. 383), the following runs were made: (1) rate as linear function of distance and volume, for each of the two types (f.i.o.-gross) and two years (1959, 1963)--these functions are numbered as l(a), (b), (c) and (d); (2) the two types were combined within each year and a shift variable was used for type--these functions are numbered as 2(a) and (b); (3) both types and years were combined and shift variables were used for type and year--numbered 3; (4) the two types were combined within each year, a shift variable was used for type, the seasons were combined within each year, and seasonal shift variables were used --numbered 4(a) and (b); and, (5) the types were combined as well as the two years and the seasons. Shift variables were used for year, type and season--numbered 5. In summation, these relationships appear as follows:
l(a) l(b) l(c) l(d) 2(a) 2(b)
R = f(D, V) f.i.o. 1959 R=f(D, V) f.i.o. 1963 R= f(D, V) gross 1959 R =f(D, V) gross 1963 R = f(D, V) f.i.o, and gross 1959 R =f(D, V) f.i.o, and gross 1963
A linear regression analysis of ocean tramp rates 3
385
R = f ( b o t h years, b o t h types, D, V)
4(a) R = f ( b o t h types, D, V, seasons) 1959 4(b) R = f ( b o t h types, D, V, seasons) 1963 5
R = f ( b o t h years, b o t h types, D, V, seasons)
Table 1 shows the resulting linear rate regressions equations, including the values o f the various year, type and seasonal shifters. We can see that seasonal shift coefficients differ considerably f r o m 1959 to 1963 [as noted under runs 4(a) and 4(b)]. I n 1959 ocean shipping rates were affected considerably less by seasonal variations than in 1963. A t the same time the relative structure o f seasonal shifts changed between the two years. TABLE 1. LINEAR RATE REGRESSION EQUATIONS WITI-I SHIFT VALUES
Shift values? Run
Basic equation
Season¶ Type~
Year§
R~ 1
l(a) ~ll = 337+0.051Dtt+0.008V~:~ . l(b) l(c) l(d) 2(a) 2(b) 3 4(a) 4(b) 5
(11-573)§§ (1-970) R = l159+O'032D-O.O43V (3.852) ( - 5"493) R = l124+0"075D-0.071V (11-297) (-- 5"633) R = 518+0.083D-0.012V (14'039) (-0"719) R = 455+0.053D-0.008V (13.323) ( - 1.467) R = 1063+0.057D-0.049V (11.021) (-- 7.420) R = 614+0.058D-0.030V (17.010) (--5.909) R = 465+0.053D-0.008V (13-044) (-1.514) R = 1167+0.056D-0.050V (11.371) ( - 7.51~) R = 675+0.057D--0.026V (16.982) (--6.105)
.
.
2
. .
3
.
0.67169
.
.
.
.
.
.
0"64275
.
.
.
.
.
0"72027
274.561 . (1 •-786) 79.207 . (2.430) 182.209 148.371 (8-517) (6-789) 280.926 -(11.867) 79.912 -(2.534) 183.610 162"998 (8.639) (7.495)
.
0"25376
.
.
.
.
.
0.76883
.
.
.
0.53767
--
--
--
0.61510
-12.010 19.473 -57.145 0.77627 (0.383) (0.646) (--2.031) --200.493 -131.782 --157.711 0.59068 (--4.029) (--3.456) ( - 4.200)' -105.025 -57.056 --111.310 0.63820 (-3.443) (-2.187) (--4.438)
t Values presented are modifications to the "intercept" value in the basic equation. $ F.i.o. is taken as base. § The base year is 1959. ¶ October-December quarter (4) is the base. [[ Rate (R) is expressed in cents per long ton. tt Distance (D) is expressed in nautical miles. $:~ Volume (V) is expressed in long tons. §§ Figures in ( ) are t ratios. I n 1959, seasons 1 and 3 showed rates below season 4 while season 3 was above; in 1963, seasons 1, 2 and 3 showed rates considerably below season 4. Runs 2 and 4 b o t h indicate, in shifting f r o m f.i.o, to gross in each year, that 1959 showed a greater increase in t h e f i x e d cost portion o f freight costs (rates). This fact would presumably give us an indication o f the cost o f the additional handling services supplied under gross terms over f.i.o, and would partially reflect the facts that in 1963 rates were higher
386
THOMASH. BATES
and firmer than in 1959, particularly in the trades on which f.i.o, terms are traditional (e.g. Cuban trades where ransom rates were being charged). On those trade routes rates may have been driven high enough above average costs to make up for the additional cost involved (and resultant higher rates) under gross terms. Runs 3 and 5 average these deviations out as they do for seasonal variations. Appendix Table 1 shows that the intercorrelation between D and V lies within the range of 0.34 and 0.75. This is in comparison to the degree of intercorrelation between D and D / V reported above. Furthermore, Table 1 shows that over the range of runs from l(a) to 5, D and V coefficients have remained relatively stable as have the t-ratios. Interestingly, run l(a) shows a positive V coefficient. That is to say, an increase in the volume of shipment results in an increase in cost (or rate) per ton. This anomaly, however, does not show up at any other point. Referring still to Table 1, in run 1, including a, b, c and d, we get more variance in D and V. We would expect this, however, since these runs are by type and year, each one a different combination of the two and no two runs including the same data. In these runs we fluctuate from a D coefficient of 3.2c. per ton-mile to 8.3c. per ton-mile. The Vcoefficient, over the same series of runs, fluctuates from +0.8c. per ton to -7.1c. per ton. In runs 2 through 5, however, these coefficients settle down to a D range of 5.3c. per ton-mile to 5.8c. per ton-mile and a V range of from - 0 . 8 c . per ton to -5.0c. per ton. It can be noted that as we proceed from l(a) to 2(a) to 4(a) R ~ increases in value. The same can be said in proceeding from l(b) to 2(b) to 4(b). We would expect this--that is as more independent variables are added we expect more of total variation to be explained. We note with interest that equation l(b) has a very low R ~. However, equation l(d), which is of the same year but uses gross term data rather than f.i.o, data, is considerably higher and explains more variation than do equations 2(b) and 4(b), which contain more variables. The 1959 regressions in all cases, save l(c) and l(d), explain a larger proportion of total variation than do the 1963 regressions. This is not surprising in light of the various pressures placed on freight rates in 1963 as discussed further below. Appendix Table 2 shows the average residuals for each origin of shipment as well as the number of observations from each origin and the sum of the residuals of each origin. Appendix Table 3 shows the grouped residuals for each trade route, the number of observations for each, the average residual of each, and the average absolute residual for each. Also shown are the grouped seasonal residuals. These data might be rather misleading. Some of the large residuals are for instances where there was only one or two observations. We do not know how normal these observations might be because of the lack of any comparable data. However, if we can have more confidence in the reliability of instances or trade routes over which we have a larger number of observations, we can look at those sources for which at least ten observations were made and notice that the foUowing trade routes showed rates considerably below estimated rates: Cuba to London; Cuba to Antwerp, Rotterdam and Amsterdam; Australia to Yokohama; Mauritius to London and to Antwerp, Rotterdam and Amsterdam; Recife (Brazil) to New York; and the Philippines to New York. Those considerably above-estimated rates included: Cuba to New York; and Australia to London and to Antwerp, Rotterdam and Amsterdam. Nothing really significant can be said about these observations except that the rates with the largest discrepancy, the Philippines to New York, was about $3.00 per ton below estimated rates. Otherwise origins which traditionally employ gross terms (Australia) or f.i.o. (Cuba) are found in both groups. For purposes of rate estimation we can employ the general equation (5), properly adjusted for an average volume and season. By shifting equation (5) by year and using
A linear regression analysis of ocean tramp rates
387
f.i.o, only, using the average volume of 9667.8 long tons calculated from the rate data observed, and summing the seasonal variations and dividing by 4 to get an adjustment of - 6 8 . 3 , we get 1959: R = 352.4+0.0571D (5) 1963:
R = 515.4+0.0571D
(6)
4. I N T E R P R E T A T I O N OF F I N D I N G S The tramp market has been characterized, at least from 1959 to 1963, by excess capacity, i.e. potential scrap ships entered into service whenever rates firmed up. In addition, newly emergent nations, as well as the U.S.S.R., have been rapidly building up their fleets. Consequently, world fleets expanded far in excess of needs. Against this background freight rates behaved unevenly, for m a n y reasons. In 1959 freight rates were low. According to the Cham~oer of Shipping of the United Kingdom index of tramp shipping freights the yearly index numbers for sugar rates were 92.1, 93.2, 104.5, 90.5 and 108.9 for 1959-63 respectively.~ A substantial amount of sugar was moved in 1959 at rates which just covered variable or out-of-pocket costs, according to several charter fixture sources of that year. By the last half of 1963 freight rates gained considerable upward m o m e n t u m and the year d o s e d with rates above the levels of the previous 5 years, despite the fact that world laid-up tonnage had been reduced only by about two-thirds. Reasons for the upward pressure on rates included a world-wide series of crop disasters which set off an unprecedented demand for grain imports. The resultant demands for ships to lift grain cargoes from ports in the United States, Canada, Brazil, Argentina and Australia sent rates to profitable levels. At the same time, a long, hard winter in Europe increased the demand for oil and tankers were switched from the dry-cargo trades. For political reasons, there were also differential pressures on certain rates on a few individual trade routes. As an example (Fairplay, 1963): "The Chinese continue actively to solicit tonnage offers and have now been joined by the Russians, who want March/April shipments to the Baltic and Black Sea. Neither of the Charters, however, appear willing to pay the " r a n s o m " rates demanded by foreign-flag owners as compensation against such reprisals that might occur under the United States ban." Effective from 1 January 1963, the Kennedy administration prohibited vessels which had traded with Cuba from carrying U.S. Government aid cargoes. Ship-owners consequently generally avoided the island, taking the view that the U.S. might eventually introduce more sweeping retaliatory measures against Cuban trade. As a result, while our general regression equations, adjusted for volume and season, indicate that the rate shift from 1959 to 1963 was only $1.63, the average rate shift for the same years in the Cuban trades was approximately $4.
t The 1959 and 1960 index numbers are based on 1952 = 100. In the 1961-62 Annual Report of the Chamber of Shipping of the United Kingdom the 1952 base was discontinued. The weights alloted to the commodities and trades used in calculating the revised index (1960 = 100) were determined by the freights earned in 1958 in the carriage of tramp cargoes by United Kingdom ships. The average for 1960 of the index numbers on the old basis (1952 = 100) was 74"2 and an approximate comparison with the old series was therefore made by taking 74"2 per cent of the index numbers on the revised basis. Note that these indexes indicate an increase of 18-2 per cent in 1963 over 1959; this corresponds closely to the results given in equations (5) and (6)--with D set equal to I0,000 miles, for example, the 1959 to 1963 increase is 17.7 per cent.
388
THOMAS H. BATES
Seasonal variation in sugar production and in the demand for tonnage engagement for shipping depend not only on the area of the world in which the sugar is grown but also on whether it is cane or beet. Also, f.i.o, terms and gross terms are characteristics of certain sugar trades and these trades are comprised of production and consumption centers in various different geographical parts of the world. As examples, f.i.o, terms are traditionally characteristic of trade routes out of the Caribbean area, South America and the Philippines. Gross terms are traditional in the sugar trades out of Australia, Mauritius, South Africa and into England. The Caribbean area has been the world's leading sugar-producing area with Cuba alone producing 20 per cent of all centrifugal sugar in 1959. The Caribbean area as a whole accounted for about 55 per cent of internationally traded sugar in 1959 and about 47 per cent in 1963. It is, therefore, not surprising that the large shipments from this area would in most cases determine the seasonal variations in total tonnage engagement. This tonnage engagement is highest during March-April, decreasing to low values during SeptemberNovember. While sugar shipments out of the southern hemisphere are just the opposite (largest shipments from such sources as Australia, Mauritius, South Africa and Brazil are forthcoming during September-October, and lowest activity is during March-April) because of the reversed seasonal pattern, the sheer magnitude of shipments from the Caribbean would logically lead one to expect the northern hemisphere seasonal pattern to show through in the seasonal variations in sugar freight rates, barring other offsetting factors. This is, indeed, the case with our No. 4(a) equation (shifted seasonally and by year) for 1959 as shown in Table 1. According to our findings, the rate function reached its highest valiae in season 2 (April-June) and its lowest value in season 3 (July-September). It should be remembered that freight rates usually reach maxima and minima 1-3 months earlier than the actual tonnage employment because many ships are chartered well ahead of the actual trip. This same pattern does not, however, show up in the 1963 equation [4(b)]. In that equation, the rate rose to a maximum in season 4 while being at its minimum in season 1. As pointed out above, what happened was that the rather strong political and economic pressures placed on the freight market distorted the rates in such a way that the seasonal sugar patterns did not show through. In addition to the distorting effects of the "ransom" rates being charged for sugar shipments out of Cuba, the unusually severe winter in Europe and the series of crop failures throughout the world lead to unusual demand for tonnage to lift grain and fuels. The long, hard winter in Europe increased demand for oil and switched tankers from the dry cargo trade. These unusual changes in the supply of shipping to the sugar trades caused marked changes in pattern of sugar rates over the year. 5. C O N C L U S I O N
In this study we have been interested in the nature of the rates of sugar-carrying vessels and how these rates are influenced by such important factors as distance of haul, volume of shipment, season, terms, trade route and year. Some conclusions that emerge are: 1. The differential between rates quoted on gross terms basis and those quoted on f.i.o, basis was considerably greater in 1959 than in 1963. While this differential would normally measure the additional handling services supplied under gross terms over f.i.o., the large change reflects in some measure the upward pressure on f.i.o, terms in 1963 of certain political and economic forces existing in that year in trades where f.i.o, terms are traditional.
A linear regression analysis of ocean tramp rates
389
2. There are more questions raised than are answered regarding the effects of trade routes on rates. Since all rate observations are "lumped" together for analysis such interesting questions as: " W h a t is the difference in rate if a ship moves in trades where a two-way flow of bulk commodities occurs against where it moves in ballast in order to take a load ?" and " W h a t was the effect of the U.S.A. embargo on Cuban sugar on sugar rates ?" are difficult to answer. More specifically, combining data that relate to trade routes with two-way cargo movements with data that relate to trades where there are negligible bulk cargo movements in one direction (so backhauls are rare or non-existent) masks the fact that these two kinds of data probably have very different coefficients of distance and would affect the slope of the regression line differentially rather than just shift the Y intercept. A different research design would be required and was beyond the purpose of this study. What data are brought out in this study on the effect of trade routes on rates are really not conducive to m a n y justifiable conclusions because of the relatively few observations on most of the trade routes. 3. Seasonal variations in sugar shipments showed through in the form of rate changes more clearly in 1959 than in 1963. This, again, can at least partially be explained by the rather severe distorting effects on rates in 1963 of various political and economic developments (particularly in Europe and the Caribbean). Our analysis of reported rates has allowed us to note the combined effect on average carriage rates for sugar of such unusual occurrences as the United States trade embargo on Cuba (viz. through the payment of ransom rates), the severe winter in Europe and the series of crop failures throughout the world in 1963. Acknowledgment--The author wishes to express his debt to the late Professor Raymond Bressler, Jr., of the University of California, Berkeley, for his interest in this study and for his many useful suggestions, and to the referee for his pertinent and helpful criticism. Of course, any shortcomings of the study are the responsibility of the author.
REFERENCES ALEXANDERSSONG. and NORSTROMG. (1963). World Shipping: An Economic Geography of Ports and Seaborne Trade. John Wiley, New York. ANOrCVMOUS(1963). Fairplay p. 17. Bns J. (1951). Chartering and Shipping Terms, C. DeBoer Jr., Den Helder, Holland. THOMANR. S. (1962). The Geography of Economic Actwity. McGraw-Hill, New York. THORBURNT. (1960). Supply and' Demand of Water Transport. Stockholm, Sweden.
390
THOMAS H . BATES
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A hnear regression analysis of ocean tramp rates
391
APPENDIX TABLE 1--continued
Equation
Variable
Coefficient
Standard error
t-ratio
l(a)
02 03 02 03 02 03 02 03 01 03 04 01 03 04 01 02 04 05 01 03 04 05 06 07 01 03 04 05 06 07 01 02 04 05 06 07 08
0.05078 0.00849 0-03168 -0.04254 0.07467 -0.07147 0.08334 -0.01164 274.56116 0-05290 - 0 00791 79 20662 0 05701 -0.04877 148.37072 182.20947 0 04817 -0.02616 280.92583 0.05283 -0.00811 - 12.00983 19 47313 -57-14478 79-91165 0-05591 -0.04696 -200"49281 - 131"78190 - 157.71144 162-99773 183"61024 0.05721 -0.02634 - 105"02507 -57"05607 - 111"31016
0-00438 0.00431 0.00822 0-00774 0 00661 0 01268 0.00593 0.01618 23.29649 0.00397 0.00539 32.59345 0.00517 0.00657 21.85525 21.39315 0.00342 0.00442 23.67342 0-00405 0-00535 31.39361 30.15225 28"14045 31-53207 0'00491 0'00625 49.76392 38.13260 37.55430 21.74679 21.25376 0 00336 0 00431 30'50586 26'08284 25.08144
11.57372 1.97003 3-85200 -5.49298 11.29719 -5.63336 14.03920 -0.71949 11.78551 13.32323 - 1.46721 2.43013 11-02058 -7-41994 6.78878 8.51718 17.00990 -5.90853 11"86671 13"04388 - 1"51379 -0-38255 0 64582 - 2 03069 2 53429 11.37135 -7.51317 -4"02887 -3"45588 -4.19955 7.49525 8 63895 16.98212 - 6-10480 -3"44278 -2"18749 -4"43794
l(b) l(c) l(d) 2(a)
2(b)
3
4(a)
4(b)
5
Dependent variable 01 01 01 01 02
02
03
02
02
03
392
THOMAS H. BATES
APPENDIX TABLE 2. AVERAGE RESIDUALS FOR EACH ORIGIN (U.S. CENTS)
Origin*
A v e r a g e residual
No. of observations
Sum of residuals
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
38.15934800 112.20161000 69.13520000 - 101.22905000 0.83615620 -026.62785000 22-36084500 -300.08796000 -95.57081700 31.61526200 40.16997500 -4.23690000 -219'02570000 - 195-97309000 --32.16743500 160-90667000 - 144"18310000 161"54700000 308"38614000 41"69880000 117"13020000 -84"89210000 233"34120000
103 15 79 43 10 19 2 17 23 11 2 4 1 5 6 4 2 1 5 1 1 6 2
3930.41290000 1683.02420000 5461-68080000 -4352-84950000 8-36156200 -505"92916000 44.72169000 -5101.49540000 -2198.12880000 247-76789000 80-33995000 - 16.94760000 -219"02570000 -979"86549000 - 193'00461000 643'62670000 -288"36620000 161"54700000 1541"93070000 41.69880000 117"13020000 -509"35260000 466 68240000
* See n o t e to A p p e n d i x T a b l e 3.
A linear regression analysis of ocean tramp rates
393
APPENDIX TABLE 3. AVERAGEAND AVERAGEABSOLUTERESIDUALSGROUPED BY TRADE ROUTE AND SEASONS(U.S. CENTS)
Destination
Average residual
Average absolute residual
No. of observations
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 18 19 20 21 22 27
-8-62963780 -88-30744300 -32.11403500 66"72854000 59"84540500 2"26717000 57-50336600 - 136"39357000 -51-49534000 -51-38430000 -133-46704000 102.82830000 125"65120000 346"16771000 67"81030000 204-66057000 176.24396000 208.48530000 --82.08357000
151"22592000 162.89884000 141"29975000 91"20656000 85"46333100 2"26717000 150.74891000 136.39357000 51"49534000 51.38430000 133.46704000 134-63710000 125"65120000 346"16771000 67.81030000 204"66057000 176"24396000 208"48530000 82"08357000
19 16 17 2 19 1 18 1 2 1 4 6 1 7 1 2 3 1 1
2 2 2 2 2
2 3 5 9 14
136"20919000 118.93378000 3-21892000 610"70370000 77"29390000
136.20919000 188.93378000 17.31456000 610"70370000 77"29390000
4 3 5 1 2
3 3 3 3 3 3
2 3 5 7 10 28
104"06784000 55.87618700 -55-48390000 134-09830000 270"50645000 119.13200000
175.97375000 158.45932000 140"53206000 134.09830000 270"50645000 119-13200000
33 32 10 1 2 1
4 4 4 4 4
2 3 6 7 29
-65.74260700 --156-80778000 -- 109"75500000 -369-77970000 --62"80380000
76-46392300 156"80778000 142"37460000 369"77970000 62"80380000
26 12 3 1 1
5 5 5 5 5 5
1 2 5 7 11 13
1.04511000 88"86128000 110"48850000 --64"01883300 42"23516000 - 14"07066600
1"04511000 88"86128000 110.48850000 64"01883300 42"23516000 14"07066600
1 1 1 3 1 3
6 6 6 6 6 6 6
2 3 7 11 13 15 16
354"94330000 326"86650000 --127-71914000 108"57631000 5"61680000 76-81033000 45.31089000
354.94330000 326.86650000 176"44195000 108-57631000 5.61680000 76.81033000 45.31089000
1 1 12 2 1 1 1
Origin*
394
THOMAS H. BATES APPENDIX TABLE 3--continued No. of observations
Destination
7 7 7 7
1 3 5 30
139.36859000 517-93570000 --94-64690000 -51"25330000
139"36859000 517"93570000 94"64690000 51-25330000
1 1 1 1
8
7
-300'08797000
300"08797000
17
9 9 9 9 9
2 3 5 6 7
- 9 1 62111200 - 167"03955000 -53"50287500 79"92330000 2"62230000
116"84843000 167"03955000 53"50287500 79"92330000 7"50000000
8 8 4 1 2
10 10
2 3
20"16398300 43"35680000
71.95891600 87.91468000
6 5
11
7
40.16997500
40'16997500
2
12
17
-4"23690000
4.23690000
4
13
13
-219"02570000
219"02570000
1
14 14 14
6 7 21
-189"60790000 -215.59673000 -143"46740000
189.60790000 215.59673000 143"46740000
1 3 1
15 15 15 15
2 3 7 23
-50'83450000 -97"15230000 -74.30095000 154"41859000
50'83450000 97"15230000 74"30095000 154.41859000
2 1 2 1
16 16
4 13
39"74641000 201-29343000
39"74641000 201"29343000
1 3
17
6
-144.18310000
144"18310000
2
18
13
161.54700000
161"54700000
1
19 19 19
7 13 25
37"49963300 894"52110000 534"91080000
37.49963300 894"52110000 534'91080000
3 1 1
20
14
41.69880000
41"69880000
1
21
24
117"13020000
117"13020000
1
22 22 22 22 22
2 3 13 23 26
29.26290000 35"87560000 -463"99130000 -61"86370000 -77"89900000
114"00000000 35"87560000 463"99130000 61"86370000 77"89900000
2 1 1 1 1
-45"65143000 3.84165150
136-15006000 148-02870000
55 95
Season No. 1 2
Average residual
Average absolute redual
Origin*
A linear regression analysis of ocean tramp rates
395
APPENDIX TABLE 3--contmued
Origin*
Destination
Season No. 3 4
Average residual
Average absolute residual
No. of observations
-51'10519300 57.04338800
126"62316000 165.98557000
102 129
Sum of Residuals 0'00370000 -
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Origm Nos. Cuba Santo Domingo Austraha Mauritius Santos Recife Peru Phlhppines South Africa Fiji Mexico Hawaii Constanza Madras Bombay Poland Lourenco Marques Odessa Argentina Rostov Hamburg Indonesia
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
Destination Nos. Casablanca London, Liverpool Antwerp, Rotterdam, Amsterdam Plraeus Yokohama Montreal New York Benghazi Beirut Hong Kong Bordeaux Odessa Colombo Iran Turns Uruguay San Francmco Shanghai Danzig Cadiz Lubeck Alexandria Saigon A1 Basrah Genoa Chile Leningrad New Orleans St. John Vancouver
* The numbers referring to origins and destinations are those assigned for purposes of programming.
A LINEAR REGRESSION ANALYSIS OF OCEAN TRAMP RATES THOMAS H. BATES Center for World Business, San Francisco State College San Francisco, California, U.S.A.
(Received 11 February 1969; in revisedform 23 April 1969) 1. I N T R O D U C T I O N SHIPS that ply the liner trades and are members of the various steamship conferences operate under rate structures that are relatively fixed and are somewhat insensitive to changes in supply and demand. On the other hand, tramp freight rates are, in principle, determined by supply and demand. As a consequence tramp rates are both more sensitive to changes in supply and demand and more unstable than are liner rates. Because tramp rates are less administratively determined than are liner rates they are more amenable to the type of analysis undertaken here. The purpose of this inquiry is through a multivariate regression analysis to better understand the nature of ocean tramp shipping rates and how these rates are influenced by various important factors such as distance of haul, volume of shipment, trade route, season, year (i.e. the forces of demand that existed in a given year), and the terms upon which a rate is quoted. The original research for this study was undertaken by the author during the period 1964-65 at the University of California, Berkeley, as part of a spatial equilibrium analysis of the world sugar economy. Therefore, our interest will be in analyzing the rates for a specific dry, bulk cargo--raw sugar. The years 1959 and 1963 were used in the original study as the basic years for investigation. Consequently, the reported rates used for this study were taken for these two years. The nature of the tramp trade and how rates are determined in this market are discussed in Section 2. This is followed by an analysis of reported rates in Section 3 and an interpretation of our findings in Section 4. Section 5 contains some closing remarks. 2. THE METHOD OF T R A N S P O R T A T I O N 2.1. The nature of the tramp fleet Classified in the ocean shipping trade as a dry, bulk cargo, sugar is usually carried in tramp ships. Generally speaking, a tramp ship can be defined as a freight vessel which does not run on a regularly scheduled line, usually has lower cost of operation and takes cargo in large lots. In fact, some liner companies keep their smaller, older and slower vessels on a stand-by basis for use at times on tramping junkets. Since the same ships are also used in liner services, it is not always easy to distinguish between tramp and liner shipping. Further, at times sugar is available at many large ports which are served by liners. Rather than having to sail with some unutilized capacity, the liners take on partial loads at much lower than prevailing general cargo rates. In terms of operation schedules, the world's nonmilitary freight-carrying fleets may be subdivided (Thoman, 1962) into liners, tramps and private carriers, viz. : 1. Liners maintain regularly scheduled service for passengers, passengers and cargo, and cargo only. They usually are the largest and fastest civilian ships in existence (except 377
378
THOMASH. BATES
for the super-tankers) and, when carrying merchandise, tend to haul the more expensive goods which can stand their higher freighting charges and which are attracted to their fast service. 2. Tramp ships do not maintain regular schedules and carry whatever cargo is available at any port of call--usually bulk freight that is low in value. Compared with liners they tend to be older, smaller, more uncertain in schedule and willing to carry almost any legitimate cargo (usually in large or shipload lots) if time is not a decisive factor as to when that cargo should arrive. 3. Private carriers are used primarily by large manufacturing concerns to deliver raw materials, fuels or finished products. In the sugar trades, vessels are commonly chartered on voyage chartert and are hence actually part of the tramp fleet in a broad sense. These vessels are increasingly becoming specialist carriers. Only in recent years has the need for the specialist carrier developed. The present need is because of the fact that whereas formerly sugar was carried bagged as part of other cargoes, today this practice has all but ceased and sugar has become a bulk cargo. 2.2. Tramp rate determination When the negotiations regarding the chartering of a vessel have been completed, the vessel can be said to b e f i x e d . Most fixtures in the tramp market are made through brokers on markets such as the Baltic Exchange in London. Information about fixtures is then issued to the public through such publications as the Daily Freight Register, Fairplay and Norwegian Shipping News. As a further aid in understanding the overall picture of the freight market, several sources have developed freight rate indices. One of particular interest for our purposes is the Norwegian Shipping News tripcharter freight rate index for dry cargoes. Another, which will be mentioned more fully later, is the Chamber of Shipping of the United Kingdom index of tramp shipping freights. The Norwegian Shipping News tripcharter freight rate index for dry cargoes is a worldwide index covering, at the time of this study, fixtures in 23 different trade routes for coal, grain, iron ore, sugar and miscellaneous. These different commodities were weighted as follows: coal, 8; grain, 5; iron ore, 5; sugar, 2; and miscellaneous, 2. One index was constructed for each of the 23 trade routes, with July-December 1947 equal to 100. The indices for the various trade routes were then combined through simple arithmetic averages into group indices for coal, grain, etc. For this purpose each of the route indices was t For future reference, the following definitions (Bes, 1951) will hold: f.i.o. (free in and out) means that the cost of loading and discharging the cargo are not for the account of the vessel (it is for the account of the charterer). Further, the term free in andout, stowed and trzmmed, signifies that stowing is also for the account of the charterer. The alternative to fa.o. or f.i.o., s. and t. is gross terms or gross charter. These terms signify that the cost of loading, stowing, and discharging are for the account of the vessel. The expression berth terms is used for shipments under a charter party, the principal terms of which correspond with the regular terms for shipment of the commodity concerned by the regular lines operating m the particular trade. Generally speaking, the term implies that loading and discharging expenses will be for the ship-owners' account. A charter vessel is one which has been contracted for under a contract of affreightment in the form of a charter-party between a ship-owner and a charterer. On a voyage charter (trip charter) a ship-owner undertakes to put a vessel at a charterer's disposal for the carriage of a full cargo or part cargo from one or more ports to named port(s) of destination at rates and conditions mutually agreed upon. Alternatively, on a time charter, the ship-owner undertakes to put the vessel out on mutually agreed terms for a stated period of time (e.g. 1 year) or she may be let on time charter for one or more consecutive voyages between certain territories.
A linear regression analysis of ocean tramp rates
379
given the weight 1. The resulting five group indices were combined into the tripcharter index using Laspeyres' formula and the weights quoted above. Unfortunately for our purposes, this index had not been published for individual commodities and, therefore, an index for sugar alone was not available. Following the usual reasoning (Thorburn, 1960), ocean freight rates are determined by supply and demand. On the demand side, a freight-owner generally needs transport between two definite ports, and can choose between large and small consignments at a time. On the other hand, on the supply side, a ship-owner has a vessel with a definite cargo capacity and has a choice of allowing it to perform transports over different distances. Therefore, the ship-owner is interested in freight rates over different transport distances for a certain ship, the freight-owner in freight rates over the same distance for vessels of different sizes. If the shipping tonnage available is more than required for servicing tonnage demand, freight rates will fall to a relatively low level. As rates fall, ship-owners will, in the short run, keep their ships in operation as long as freight revenues cover variable costs. This occurred frequently in 1959 when supply or available tonnage was high relative to demand. As rates continue to fall, more and more tonnage is laid up. The supply of available tonnage is thus restricted and the fall in rates dampened. Similarly, an increase in demand will bring tonnage out of lay-up, starting with the most economic. As rates rise, more and more tonnage is made available, thus checking the rise in rates. These conditions are illustrated in Fig. 1. We have been talking about the area on the supply curve SS between demand functions DD and D"D". Note that with low demand the supply of tonnage is rather elastic with changes in the freight market not being reflected so much by changes in freight rates as by changes in tonnage available. Increasing demand brings out more and more tonnage until the point is reached where the only tonnage left in Frelght Rate
D~
\\
___
R
-- J \ \
\
Q'~
il
Q Qt
°
Tonnage Avaxlable
FIG. 1. The demand for and supply of tramp tonnage.
380
THOMAS H. BATES
lay-up are ships under repair or undergoing inspection or maintenance. Thus at some point, A on our diagram, the supply of tonnage becomes very inelastic to changes in rates. Depending on the state of the ship-building art and the availability of competitive modes of transportation (only a limited part of the ocean freight market is affected by competitive forms of transport), a rather small increase in demand now can have quite magnified effects on rates in the short run. Figure 2 shows the Norwegian Shipping News index of freight rates over the period 1947-61 plotted against tonnage laid-up in British and Irish ports over the same period to indicate the nature of short-run supply that was expressed theoretically in Fig. 1, with allowance for the fact that "laid-up" tonnage reflects excess supply rather than total supply.-~ The almost vertical section to the left of the diagram corresponds to the relatively inelastic section of the SS curve in Fig. 1 and represents the short-run supply when demand presses on available ships. The nearly horizontal section is the more elastic section of SS in Fig. 1 and represents short-run supply when demand is actually less than available ships. When the rate index drops to around 60-75, the ships go into storage, but higher Index of Freight Rates 300
X= Trxp C h a r t e r I n d e x • = Time Charter Index 250
$
m
$ 200
15C
x
i00 X
50
0
I
I
0.5
1.0 Laid-Up
I
i 5
Tonnage-Mzlhon
I
2.0
,
21.5
I
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FIG. 2. Laid-up tonnage against trip- and time-charter rate indices. (From Norwegian Shipping News.) t Figure 2 gives rise to an identification problem. Since each observation is the function of different values of the underlying parameters we cannot be sure whether we have identified a supply curve, a demand curve or some mixture of both. However, over the relevant period 1947-61 demand was much more unstable than supply. Beginning particularly with the Suez crisis in 1956 new ships were ordered and the supply has been increasing since. At the same time demand forces have fluctuated relatively more and it is suggested that the data displayed in Fig. 2 reveal a rough supply curve traced out by a relatively rapidly fluctuating demand schedule moving up and down a slower shifting supply schedule.
A linear regression analysis of ocean tramp rates
381
rates bring out any desired amount until the laid-up tonnage is approximately 500,000 tons --possibly an irreducible minimum. This figure at least suggests that rates tend to settle down to some lower limit which may reflect variable costs. At times of low freight rates, time-charter rates tend to be relatively lower than tripcharter rates. When rates rise, time-charter rates rise more rapidly. There is also a tendency in boom times for time-charter rates to be above trip-charter rates. An explanation of this behaviour has been given (Alexandersson and Norstrom 1963), as follows: harbor charges and fuel are paid for by the charterer in the case of time charter and by the ship-owner in the case of trip charter. These cost items are relatively unaffected by the state of affairs in the freight market. In a situation of surplus tonnage, the charterer will, therefore, have to see time-charter rates reduced to a level lower than that of trip-charter rates, otherwise it would be more economical to charter the ship on a trip-charter basis. In times of very high rates he will, for the same reason, be willing to pay relatively more for a time-chartered vessel, since part of his cost for the shipment will not be affected by the high cost level for transport. As regards liner shipping, both total costs and fixed costs exceed those of the tramps, mainly because additional facilities are required for the handling of passengers and general cargo than for bulk cargoes. The handling of general cargo calls for more powerful machilaery and the addition of passengers usually requires more space, larger crews and more expensive administrative handling. In addition, by the very nature of their operation, liners must make scheduled sailings whether fully loaded or not. They also call at more ports on the average than the tramps. Since a large proportion of the total costs of the regular steamship lines is made up of fixed costs, rigorous price competition is likely to lead to freight rates somewhere below average costs (perhaps even in the long run). Lines have, therefore, practiced several methods of regulating competition among themselves and of minimizing competition from outsiders. The specialist sugar carrier is capable, when necessary, of carrying coal, grain or lumber. Most of the other specialist carriers are equally capable of being adapted to the carriage of other commodities. In the last several years, the shipment of grains by tanker has become common. The semi-liquid quality of grains has made this possible and the changed relations between freight rates for tankers and dry cargo vessels has made it economical. The shift has been brought about by an increase in tanker tonnage that has progressed more rapidly than the demand for oil transportation. Despite the fact that not all ships are interchangeable, there are enough ships with a range of overlapping uses for the freight rates on different trades to follow one another closely. This overlapping also applies to the time-charter vs. trip-charter market, as we have seen, because of the possibilities for both ship-owner and shipper to accept the one offering more favorable terms. Freight rate data generally show considerable seasonal variation, the magnitude of variation depending basically upon the commodity and the trade route. The seasonal character of many important trades results in variations in demand for tonnage which in turn produces these seasonal variations in freight rates. Specifically, sugar shipments have a clearly seasonal component due to the effect of the harvest seasons. The large shipments from the Caribbean determine the variations in total tonnage engagement, which is highest during March-May, later decreasing to low values during September-November. This matter will be discussed further when we turn to a more thorough analysis of freight rates in the sugar trades. The return cargo position is also a factor influencing the rates in a particular trade. If a given trade route is characterized by one-way trade flows, ships will have to move to the ~7
382
THOMASH. BATES
port of loading in ballast. It will, therefore, pay these ships to accept cargo at any rate as long as it covers the extra costs involved in loading and unloading the return cargo and any possible costs which are incurred above those involved in sailing in ballast. Consequently, freight rates in the direction of the ballast trips are lower than in the cargo direction. There are numerous political and legal factors which have effect on some of the freight rates affecting sugar. These are not dealt with specifically here because of their relative unimportance in the case of tramp rates. 3. ANALYSIS OF R E P O R T E D RATES
3.1. Formulation of the problem We will now turn our attention to the specific nature of ocean rates for sugar and the ways in which these rates are influenced by various important factors. At the outset, it was assumed that the distance of a shipment and the size or volume of the shipment both influenced rates. It did not seem unreasonable to expect that the real effect of volume was not additive to distance, but rather was a modifier of a rate-distance regression. I can show what I mean with a simple model. Assume one that suggests that for any size of carrier V the TC (total cost) function might reasonably be
TC = a+bD
(1)
where TC represents total cost, D represents distance and a and b are constants. When we modify the volume both coefficients would be affected. A simple form of such adjustment might be TC= (a+cV)+(b+eV) D (2) where V represents volume. This simply states that the fixed or terminal charges and the variable costs both would increase with volume---and here in linear form. Since we are interested primarily in the costs per ton and hence in the nature of average costs (and this, of course, assumes that costs influence rates), t we can divide through (2) by V and get A C = a~V+ e + bD/V+ eD (3) where AC represents average cost. It was upon this basis that it was assumed that a logical basis for a statistical analysis of rates would be to relate not to D and V but to D and D~ V. Furthermore, it is apparent that D and D/V must be intercorrelated, with this intercorrelation approaching 1.0 as the variance of D increases relative to the variance of V. Upon inspection of distance and volume data (and the following must be remembered: since our rate observations were on trip-charter rates, it has been assumed that the total tonnage carried as reported was equal to the volume of the ship--or, the same thing, the ships were fully laden) for the rates collected it was found that D was in fact highly variable as compared to V. This was confirmed by correlating D and D/V: for 185 observations in 1959, r is 0.737; for 196 observations in 1963, r is 0.899. Apparently the intercorrelation t Costs and rates can be expected to correspond rather closely in a competitive industry and in the long run. However, in the short run rates will reflect short-run supply and demand situations and, as a result, may vary widely around the long-run level. In other words, rates may settle down to levels just adequate to cover direct trip costs (or lower if on a ballast leg of a trip) or could be very much above long-run average costs. However, if the statistical results do not reveal the true importance of numerous short-run factors, they may be accepted as estimates of the long-run situation.
383
A linear regression analysis of ocean tramp rates
was especially pronounced in the gross rates: combining 1959 and 1963 observations, the intercorrelation between D and D/V is 0.955 for gross terms as compared to 0.541 for f.i.o, terms. For the year 1959 gross the intercorrelation was 0.962 as compared to a 1959 f.i.o, intercorrelation of 0.480, and the year 1963 gross was 0.959 as compared to a 1963 f.i.o, intercorrelation of 0.789. Because of this very high intercorrelation, there is every reason to believe that statistical analyses would yield regression coefficients that were unstable (i.e. subject to large errors of estimate) and that chance factors could give rise to marked shifts in the apparent importance of one or the other variable. In order to preclude this happening we did not use the D and D~ V formulation despite the fact that it seemed to be the logical relationship. Instead we fitted a multiple linear form:
AC= a+bV+cD
(4)
While this form seems appropriate in a priori terms for the cost-distance relationship, it is also not inconsistent with reality as can be seen in Fig. 3. The V influence is expected to be negative, even though the linear form must be considered as only an approximation to the logically expected reciprocal form. ÷
Frelgh~ Rate + ÷
1400 ~t
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+
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4:
I000 +
+
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800
600
+
*~ ~a- "t
2
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0
20~0
40~0
60~080001
10~10
120~
DISTANCE -- MILES
FIG. 3. Best fitting linear regression line for 1959 and 1963 f.i.o, and gross data.
384
THOMASH. BATES
Since short-run supply and demand situations can vary from season to season and from trade route to trade route, we expect considerable variation around any D and V regressions; that is, there will be a portion of variance not related to these two main factors. Therefore, in an attempt to hold some of these influences constant, the statistical analysis included shift variables for such elements as year, type, season and route. This was an effort to more accurately identify the net influences of D and V. 3.2. Sources of data Charter fixtures for sugar for both 1959 and 1963 were obtained from the publications; Norwegian Shipping News, Fairplay and Shipping World. Information necessary to calculate other freight rates was found in the United States Department of Agriculture's Sugar Reports and the International Sugar Council's Statistical Bulletin. In the first three publications, actual fixtures are reported and there is information given as to origin, destination, volume of shipment, freight rate per long ton, usually number and names of ports of call, terms (e.g.f.i.o., gross terms, etc.) and name of carrying vessel. Freight rates for the years 1959 and 1963 from the Greater Caribbean Area including Brazil f.o.b, and stowed (1) to North Atlantic ports and (2) to the United Kingdom were calculated from information in the U.S.D.A. Sugar Reports and from the I.S.C. Statistical Bulletins. Freight rates for the 2 years from Hawaii to San Francisco were obtained from the traffic department of Matson Steamship Co. Some 381 rate observations were coUected and classified according to year (1959 and 1963), terms (f.i.o. and gross) origin, destination, rate, distance, volume and season. These data were then submitted to analysis. The results of this analysis now demands our attention. 3.3. Statistical results Based on the functional relationship expressed in equation (4) (p. 383), the following runs were made: (1) rate as linear function of distance and volume, for each of the two types (f.i.o.-gross) and two years (1959, 1963)--these functions are numbered as l(a), (b), (c) and (d); (2) the two types were combined within each year and a shift variable was used for type--these functions are numbered as 2(a) and (b); (3) both types and years were combined and shift variables were used for type and year--numbered 3; (4) the two types were combined within each year, a shift variable was used for type, the seasons were combined within each year, and seasonal shift variables were used --numbered 4(a) and (b); and, (5) the types were combined as well as the two years and the seasons. Shift variables were used for year, type and season--numbered 5. In summation, these relationships appear as follows:
l(a) l(b) l(c) l(d) 2(a) 2(b)
R = f(D, V) f.i.o. 1959 R=f(D, V) f.i.o. 1963 R= f(D, V) gross 1959 R =f(D, V) gross 1963 R = f(D, V) f.i.o, and gross 1959 R =f(D, V) f.i.o, and gross 1963
A linear regression analysis of ocean tramp rates 3
385
R = f ( b o t h years, b o t h types, D, V)
4(a) R = f ( b o t h types, D, V, seasons) 1959 4(b) R = f ( b o t h types, D, V, seasons) 1963 5
R = f ( b o t h years, b o t h types, D, V, seasons)
Table 1 shows the resulting linear rate regressions equations, including the values o f the various year, type and seasonal shifters. We can see that seasonal shift coefficients differ considerably f r o m 1959 to 1963 [as noted under runs 4(a) and 4(b)]. I n 1959 ocean shipping rates were affected considerably less by seasonal variations than in 1963. A t the same time the relative structure o f seasonal shifts changed between the two years. TABLE 1. LINEAR RATE REGRESSION EQUATIONS WITI-I SHIFT VALUES
Shift values? Run
Basic equation
Season¶ Type~
Year§
R~ 1
l(a) ~ll = 337+0.051Dtt+0.008V~:~ . l(b) l(c) l(d) 2(a) 2(b) 3 4(a) 4(b) 5
(11-573)§§ (1-970) R = l159+O'032D-O.O43V (3.852) ( - 5"493) R = l124+0"075D-0.071V (11-297) (-- 5"633) R = 518+0.083D-0.012V (14'039) (-0"719) R = 455+0.053D-0.008V (13.323) ( - 1.467) R = 1063+0.057D-0.049V (11.021) (-- 7.420) R = 614+0.058D-0.030V (17.010) (--5.909) R = 465+0.053D-0.008V (13-044) (-1.514) R = 1167+0.056D-0.050V (11.371) ( - 7.51~) R = 675+0.057D--0.026V (16.982) (--6.105)
.
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0.67169
.
.
.
.
.
.
0"64275
.
.
.
.
.
0"72027
274.561 . (1 •-786) 79.207 . (2.430) 182.209 148.371 (8-517) (6-789) 280.926 -(11.867) 79.912 -(2.534) 183.610 162"998 (8.639) (7.495)
.
0"25376
.
.
.
.
.
0.76883
.
.
.
0.53767
--
--
--
0.61510
-12.010 19.473 -57.145 0.77627 (0.383) (0.646) (--2.031) --200.493 -131.782 --157.711 0.59068 (--4.029) (--3.456) ( - 4.200)' -105.025 -57.056 --111.310 0.63820 (-3.443) (-2.187) (--4.438)
t Values presented are modifications to the "intercept" value in the basic equation. $ F.i.o. is taken as base. § The base year is 1959. ¶ October-December quarter (4) is the base. [[ Rate (R) is expressed in cents per long ton. tt Distance (D) is expressed in nautical miles. $:~ Volume (V) is expressed in long tons. §§ Figures in ( ) are t ratios. I n 1959, seasons 1 and 3 showed rates below season 4 while season 3 was above; in 1963, seasons 1, 2 and 3 showed rates considerably below season 4. Runs 2 and 4 b o t h indicate, in shifting f r o m f.i.o, to gross in each year, that 1959 showed a greater increase in t h e f i x e d cost portion o f freight costs (rates). This fact would presumably give us an indication o f the cost o f the additional handling services supplied under gross terms over f.i.o, and would partially reflect the facts that in 1963 rates were higher
386
THOMASH. BATES
and firmer than in 1959, particularly in the trades on which f.i.o, terms are traditional (e.g. Cuban trades where ransom rates were being charged). On those trade routes rates may have been driven high enough above average costs to make up for the additional cost involved (and resultant higher rates) under gross terms. Runs 3 and 5 average these deviations out as they do for seasonal variations. Appendix Table 1 shows that the intercorrelation between D and V lies within the range of 0.34 and 0.75. This is in comparison to the degree of intercorrelation between D and D / V reported above. Furthermore, Table 1 shows that over the range of runs from l(a) to 5, D and V coefficients have remained relatively stable as have the t-ratios. Interestingly, run l(a) shows a positive V coefficient. That is to say, an increase in the volume of shipment results in an increase in cost (or rate) per ton. This anomaly, however, does not show up at any other point. Referring still to Table 1, in run 1, including a, b, c and d, we get more variance in D and V. We would expect this, however, since these runs are by type and year, each one a different combination of the two and no two runs including the same data. In these runs we fluctuate from a D coefficient of 3.2c. per ton-mile to 8.3c. per ton-mile. The Vcoefficient, over the same series of runs, fluctuates from +0.8c. per ton to -7.1c. per ton. In runs 2 through 5, however, these coefficients settle down to a D range of 5.3c. per ton-mile to 5.8c. per ton-mile and a V range of from - 0 . 8 c . per ton to -5.0c. per ton. It can be noted that as we proceed from l(a) to 2(a) to 4(a) R ~ increases in value. The same can be said in proceeding from l(b) to 2(b) to 4(b). We would expect this--that is as more independent variables are added we expect more of total variation to be explained. We note with interest that equation l(b) has a very low R ~. However, equation l(d), which is of the same year but uses gross term data rather than f.i.o, data, is considerably higher and explains more variation than do equations 2(b) and 4(b), which contain more variables. The 1959 regressions in all cases, save l(c) and l(d), explain a larger proportion of total variation than do the 1963 regressions. This is not surprising in light of the various pressures placed on freight rates in 1963 as discussed further below. Appendix Table 2 shows the average residuals for each origin of shipment as well as the number of observations from each origin and the sum of the residuals of each origin. Appendix Table 3 shows the grouped residuals for each trade route, the number of observations for each, the average residual of each, and the average absolute residual for each. Also shown are the grouped seasonal residuals. These data might be rather misleading. Some of the large residuals are for instances where there was only one or two observations. We do not know how normal these observations might be because of the lack of any comparable data. However, if we can have more confidence in the reliability of instances or trade routes over which we have a larger number of observations, we can look at those sources for which at least ten observations were made and notice that the foUowing trade routes showed rates considerably below estimated rates: Cuba to London; Cuba to Antwerp, Rotterdam and Amsterdam; Australia to Yokohama; Mauritius to London and to Antwerp, Rotterdam and Amsterdam; Recife (Brazil) to New York; and the Philippines to New York. Those considerably above-estimated rates included: Cuba to New York; and Australia to London and to Antwerp, Rotterdam and Amsterdam. Nothing really significant can be said about these observations except that the rates with the largest discrepancy, the Philippines to New York, was about $3.00 per ton below estimated rates. Otherwise origins which traditionally employ gross terms (Australia) or f.i.o. (Cuba) are found in both groups. For purposes of rate estimation we can employ the general equation (5), properly adjusted for an average volume and season. By shifting equation (5) by year and using
A linear regression analysis of ocean tramp rates
387
f.i.o, only, using the average volume of 9667.8 long tons calculated from the rate data observed, and summing the seasonal variations and dividing by 4 to get an adjustment of - 6 8 . 3 , we get 1959: R = 352.4+0.0571D (5) 1963:
R = 515.4+0.0571D
(6)
4. I N T E R P R E T A T I O N OF F I N D I N G S The tramp market has been characterized, at least from 1959 to 1963, by excess capacity, i.e. potential scrap ships entered into service whenever rates firmed up. In addition, newly emergent nations, as well as the U.S.S.R., have been rapidly building up their fleets. Consequently, world fleets expanded far in excess of needs. Against this background freight rates behaved unevenly, for m a n y reasons. In 1959 freight rates were low. According to the Cham~oer of Shipping of the United Kingdom index of tramp shipping freights the yearly index numbers for sugar rates were 92.1, 93.2, 104.5, 90.5 and 108.9 for 1959-63 respectively.~ A substantial amount of sugar was moved in 1959 at rates which just covered variable or out-of-pocket costs, according to several charter fixture sources of that year. By the last half of 1963 freight rates gained considerable upward m o m e n t u m and the year d o s e d with rates above the levels of the previous 5 years, despite the fact that world laid-up tonnage had been reduced only by about two-thirds. Reasons for the upward pressure on rates included a world-wide series of crop disasters which set off an unprecedented demand for grain imports. The resultant demands for ships to lift grain cargoes from ports in the United States, Canada, Brazil, Argentina and Australia sent rates to profitable levels. At the same time, a long, hard winter in Europe increased the demand for oil and tankers were switched from the dry-cargo trades. For political reasons, there were also differential pressures on certain rates on a few individual trade routes. As an example (Fairplay, 1963): "The Chinese continue actively to solicit tonnage offers and have now been joined by the Russians, who want March/April shipments to the Baltic and Black Sea. Neither of the Charters, however, appear willing to pay the " r a n s o m " rates demanded by foreign-flag owners as compensation against such reprisals that might occur under the United States ban." Effective from 1 January 1963, the Kennedy administration prohibited vessels which had traded with Cuba from carrying U.S. Government aid cargoes. Ship-owners consequently generally avoided the island, taking the view that the U.S. might eventually introduce more sweeping retaliatory measures against Cuban trade. As a result, while our general regression equations, adjusted for volume and season, indicate that the rate shift from 1959 to 1963 was only $1.63, the average rate shift for the same years in the Cuban trades was approximately $4.
t The 1959 and 1960 index numbers are based on 1952 = 100. In the 1961-62 Annual Report of the Chamber of Shipping of the United Kingdom the 1952 base was discontinued. The weights alloted to the commodities and trades used in calculating the revised index (1960 = 100) were determined by the freights earned in 1958 in the carriage of tramp cargoes by United Kingdom ships. The average for 1960 of the index numbers on the old basis (1952 = 100) was 74"2 and an approximate comparison with the old series was therefore made by taking 74"2 per cent of the index numbers on the revised basis. Note that these indexes indicate an increase of 18-2 per cent in 1963 over 1959; this corresponds closely to the results given in equations (5) and (6)--with D set equal to I0,000 miles, for example, the 1959 to 1963 increase is 17.7 per cent.
388
THOMAS H. BATES
Seasonal variation in sugar production and in the demand for tonnage engagement for shipping depend not only on the area of the world in which the sugar is grown but also on whether it is cane or beet. Also, f.i.o, terms and gross terms are characteristics of certain sugar trades and these trades are comprised of production and consumption centers in various different geographical parts of the world. As examples, f.i.o, terms are traditionally characteristic of trade routes out of the Caribbean area, South America and the Philippines. Gross terms are traditional in the sugar trades out of Australia, Mauritius, South Africa and into England. The Caribbean area has been the world's leading sugar-producing area with Cuba alone producing 20 per cent of all centrifugal sugar in 1959. The Caribbean area as a whole accounted for about 55 per cent of internationally traded sugar in 1959 and about 47 per cent in 1963. It is, therefore, not surprising that the large shipments from this area would in most cases determine the seasonal variations in total tonnage engagement. This tonnage engagement is highest during March-April, decreasing to low values during SeptemberNovember. While sugar shipments out of the southern hemisphere are just the opposite (largest shipments from such sources as Australia, Mauritius, South Africa and Brazil are forthcoming during September-October, and lowest activity is during March-April) because of the reversed seasonal pattern, the sheer magnitude of shipments from the Caribbean would logically lead one to expect the northern hemisphere seasonal pattern to show through in the seasonal variations in sugar freight rates, barring other offsetting factors. This is, indeed, the case with our No. 4(a) equation (shifted seasonally and by year) for 1959 as shown in Table 1. According to our findings, the rate function reached its highest valiae in season 2 (April-June) and its lowest value in season 3 (July-September). It should be remembered that freight rates usually reach maxima and minima 1-3 months earlier than the actual tonnage employment because many ships are chartered well ahead of the actual trip. This same pattern does not, however, show up in the 1963 equation [4(b)]. In that equation, the rate rose to a maximum in season 4 while being at its minimum in season 1. As pointed out above, what happened was that the rather strong political and economic pressures placed on the freight market distorted the rates in such a way that the seasonal sugar patterns did not show through. In addition to the distorting effects of the "ransom" rates being charged for sugar shipments out of Cuba, the unusually severe winter in Europe and the series of crop failures throughout the world lead to unusual demand for tonnage to lift grain and fuels. The long, hard winter in Europe increased demand for oil and switched tankers from the dry cargo trade. These unusual changes in the supply of shipping to the sugar trades caused marked changes in pattern of sugar rates over the year. 5. C O N C L U S I O N
In this study we have been interested in the nature of the rates of sugar-carrying vessels and how these rates are influenced by such important factors as distance of haul, volume of shipment, season, terms, trade route and year. Some conclusions that emerge are: 1. The differential between rates quoted on gross terms basis and those quoted on f.i.o, basis was considerably greater in 1959 than in 1963. While this differential would normally measure the additional handling services supplied under gross terms over f.i.o., the large change reflects in some measure the upward pressure on f.i.o, terms in 1963 of certain political and economic forces existing in that year in trades where f.i.o, terms are traditional.
A linear regression analysis of ocean tramp rates
389
2. There are more questions raised than are answered regarding the effects of trade routes on rates. Since all rate observations are "lumped" together for analysis such interesting questions as: " W h a t is the difference in rate if a ship moves in trades where a two-way flow of bulk commodities occurs against where it moves in ballast in order to take a load ?" and " W h a t was the effect of the U.S.A. embargo on Cuban sugar on sugar rates ?" are difficult to answer. More specifically, combining data that relate to trade routes with two-way cargo movements with data that relate to trades where there are negligible bulk cargo movements in one direction (so backhauls are rare or non-existent) masks the fact that these two kinds of data probably have very different coefficients of distance and would affect the slope of the regression line differentially rather than just shift the Y intercept. A different research design would be required and was beyond the purpose of this study. What data are brought out in this study on the effect of trade routes on rates are really not conducive to m a n y justifiable conclusions because of the relatively few observations on most of the trade routes. 3. Seasonal variations in sugar shipments showed through in the form of rate changes more clearly in 1959 than in 1963. This, again, can at least partially be explained by the rather severe distorting effects on rates in 1963 of various political and economic developments (particularly in Europe and the Caribbean). Our analysis of reported rates has allowed us to note the combined effect on average carriage rates for sugar of such unusual occurrences as the United States trade embargo on Cuba (viz. through the payment of ransom rates), the severe winter in Europe and the series of crop failures throughout the world in 1963. Acknowledgment--The author wishes to express his debt to the late Professor Raymond Bressler, Jr., of the University of California, Berkeley, for his interest in this study and for his many useful suggestions, and to the referee for his pertinent and helpful criticism. Of course, any shortcomings of the study are the responsibility of the author.
REFERENCES ALEXANDERSSONG. and NORSTROMG. (1963). World Shipping: An Economic Geography of Ports and Seaborne Trade. John Wiley, New York. ANOrCVMOUS(1963). Fairplay p. 17. Bns J. (1951). Chartering and Shipping Terms, C. DeBoer Jr., Den Helder, Holland. THOMANR. S. (1962). The Geography of Economic Actwity. McGraw-Hill, New York. THORBURNT. (1960). Supply and' Demand of Water Transport. Stockholm, Sweden.
390
THOMAS H . BATES
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A hnear regression analysis of ocean tramp rates
391
APPENDIX TABLE 1--continued
Equation
Variable
Coefficient
Standard error
t-ratio
l(a)
02 03 02 03 02 03 02 03 01 03 04 01 03 04 01 02 04 05 01 03 04 05 06 07 01 03 04 05 06 07 01 02 04 05 06 07 08
0.05078 0.00849 0-03168 -0.04254 0.07467 -0.07147 0.08334 -0.01164 274.56116 0-05290 - 0 00791 79 20662 0 05701 -0.04877 148.37072 182.20947 0 04817 -0.02616 280.92583 0.05283 -0.00811 - 12.00983 19 47313 -57-14478 79-91165 0-05591 -0.04696 -200"49281 - 131"78190 - 157.71144 162-99773 183"61024 0.05721 -0.02634 - 105"02507 -57"05607 - 111"31016
0-00438 0.00431 0.00822 0-00774 0 00661 0 01268 0.00593 0.01618 23.29649 0.00397 0.00539 32.59345 0.00517 0.00657 21.85525 21.39315 0.00342 0.00442 23.67342 0-00405 0-00535 31.39361 30.15225 28"14045 31-53207 0'00491 0'00625 49.76392 38.13260 37.55430 21.74679 21.25376 0 00336 0 00431 30'50586 26'08284 25.08144
11.57372 1.97003 3-85200 -5.49298 11.29719 -5.63336 14.03920 -0.71949 11.78551 13.32323 - 1.46721 2.43013 11-02058 -7-41994 6.78878 8.51718 17.00990 -5.90853 11"86671 13"04388 - 1"51379 -0-38255 0 64582 - 2 03069 2 53429 11.37135 -7.51317 -4"02887 -3"45588 -4.19955 7.49525 8 63895 16.98212 - 6-10480 -3"44278 -2"18749 -4"43794
l(b) l(c) l(d) 2(a)
2(b)
3
4(a)
4(b)
5
Dependent variable 01 01 01 01 02
02
03
02
02
03
392
THOMAS H. BATES
APPENDIX TABLE 2. AVERAGE RESIDUALS FOR EACH ORIGIN (U.S. CENTS)
Origin*
A v e r a g e residual
No. of observations
Sum of residuals
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
38.15934800 112.20161000 69.13520000 - 101.22905000 0.83615620 -026.62785000 22-36084500 -300.08796000 -95.57081700 31.61526200 40.16997500 -4.23690000 -219'02570000 - 195-97309000 --32.16743500 160-90667000 - 144"18310000 161"54700000 308"38614000 41"69880000 117"13020000 -84"89210000 233"34120000
103 15 79 43 10 19 2 17 23 11 2 4 1 5 6 4 2 1 5 1 1 6 2
3930.41290000 1683.02420000 5461-68080000 -4352-84950000 8-36156200 -505"92916000 44.72169000 -5101.49540000 -2198.12880000 247-76789000 80-33995000 - 16.94760000 -219"02570000 -979"86549000 - 193'00461000 643'62670000 -288"36620000 161"54700000 1541"93070000 41.69880000 117"13020000 -509"35260000 466 68240000
* See n o t e to A p p e n d i x T a b l e 3.
A linear regression analysis of ocean tramp rates
393
APPENDIX TABLE 3. AVERAGEAND AVERAGEABSOLUTERESIDUALSGROUPED BY TRADE ROUTE AND SEASONS(U.S. CENTS)
Destination
Average residual
Average absolute residual
No. of observations
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 18 19 20 21 22 27
-8-62963780 -88-30744300 -32.11403500 66"72854000 59"84540500 2"26717000 57-50336600 - 136"39357000 -51-49534000 -51-38430000 -133-46704000 102.82830000 125"65120000 346"16771000 67"81030000 204-66057000 176.24396000 208.48530000 --82.08357000
151"22592000 162.89884000 141"29975000 91"20656000 85"46333100 2"26717000 150.74891000 136.39357000 51"49534000 51.38430000 133.46704000 134-63710000 125"65120000 346"16771000 67.81030000 204"66057000 176"24396000 208"48530000 82"08357000
19 16 17 2 19 1 18 1 2 1 4 6 1 7 1 2 3 1 1
2 2 2 2 2
2 3 5 9 14
136"20919000 118.93378000 3-21892000 610"70370000 77"29390000
136.20919000 188.93378000 17.31456000 610"70370000 77"29390000
4 3 5 1 2
3 3 3 3 3 3
2 3 5 7 10 28
104"06784000 55.87618700 -55-48390000 134-09830000 270"50645000 119.13200000
175.97375000 158.45932000 140"53206000 134.09830000 270"50645000 119-13200000
33 32 10 1 2 1
4 4 4 4 4
2 3 6 7 29
-65.74260700 --156-80778000 -- 109"75500000 -369-77970000 --62"80380000
76-46392300 156"80778000 142"37460000 369"77970000 62"80380000
26 12 3 1 1
5 5 5 5 5 5
1 2 5 7 11 13
1.04511000 88"86128000 110"48850000 --64"01883300 42"23516000 - 14"07066600
1"04511000 88"86128000 110.48850000 64"01883300 42"23516000 14"07066600
1 1 1 3 1 3
6 6 6 6 6 6 6
2 3 7 11 13 15 16
354"94330000 326"86650000 --127-71914000 108"57631000 5"61680000 76-81033000 45.31089000
354.94330000 326.86650000 176"44195000 108-57631000 5.61680000 76.81033000 45.31089000
1 1 12 2 1 1 1
Origin*
394
THOMAS H. BATES APPENDIX TABLE 3--continued No. of observations
Destination
7 7 7 7
1 3 5 30
139.36859000 517-93570000 --94-64690000 -51"25330000
139"36859000 517"93570000 94"64690000 51-25330000
1 1 1 1
8
7
-300'08797000
300"08797000
17
9 9 9 9 9
2 3 5 6 7
- 9 1 62111200 - 167"03955000 -53"50287500 79"92330000 2"62230000
116"84843000 167"03955000 53"50287500 79"92330000 7"50000000
8 8 4 1 2
10 10
2 3
20"16398300 43"35680000
71.95891600 87.91468000
6 5
11
7
40.16997500
40'16997500
2
12
17
-4"23690000
4.23690000
4
13
13
-219"02570000
219"02570000
1
14 14 14
6 7 21
-189"60790000 -215.59673000 -143"46740000
189.60790000 215.59673000 143"46740000
1 3 1
15 15 15 15
2 3 7 23
-50'83450000 -97"15230000 -74.30095000 154"41859000
50'83450000 97"15230000 74"30095000 154.41859000
2 1 2 1
16 16
4 13
39"74641000 201-29343000
39"74641000 201"29343000
1 3
17
6
-144.18310000
144"18310000
2
18
13
161.54700000
161"54700000
1
19 19 19
7 13 25
37"49963300 894"52110000 534"91080000
37.49963300 894"52110000 534'91080000
3 1 1
20
14
41.69880000
41"69880000
1
21
24
117"13020000
117"13020000
1
22 22 22 22 22
2 3 13 23 26
29.26290000 35"87560000 -463"99130000 -61"86370000 -77"89900000
114"00000000 35"87560000 463"99130000 61"86370000 77"89900000
2 1 1 1 1
-45"65143000 3.84165150
136-15006000 148-02870000
55 95
Season No. 1 2
Average residual
Average absolute redual
Origin*
A linear regression analysis of ocean tramp rates
395
APPENDIX TABLE 3--contmued
Origin*
Destination
Season No. 3 4
Average residual
Average absolute residual
No. of observations
-51'10519300 57.04338800
126"62316000 165.98557000
102 129
Sum of Residuals 0'00370000 -
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Origm Nos. Cuba Santo Domingo Austraha Mauritius Santos Recife Peru Phlhppines South Africa Fiji Mexico Hawaii Constanza Madras Bombay Poland Lourenco Marques Odessa Argentina Rostov Hamburg Indonesia
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
Destination Nos. Casablanca London, Liverpool Antwerp, Rotterdam, Amsterdam Plraeus Yokohama Montreal New York Benghazi Beirut Hong Kong Bordeaux Odessa Colombo Iran Turns Uruguay San Francmco Shanghai Danzig Cadiz Lubeck Alexandria Saigon A1 Basrah Genoa Chile Leningrad New Orleans St. John Vancouver
* The numbers referring to origins and destinations are those assigned for purposes of programming.