Central Asia Railways Telecommunications
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ANNEX 7.1: The updated Work Plan ANNEX 7.2: The updated Resource Schedule ANNEX 7.3: Statistical analyses and estimation techniques used for economic, social and environmental context of TACIS / CART project Central Asian Railways Telecommunications Progress Report Annex 7.3 ANNEX 7.3 7.3.1 STATISTICAL ANALYSES AND ESTIMATION TECHNIQUES USED FOR ECONOMIC, SOCIAL AND ENVIRONMENTAL CONTEXT OF TACIS / CART PROJECT In section A.1.1 and elsewhere in this Report we have a correlation between the “SILK ROUTE REPUBLICS’ GDP RATES” and their “SHARE OF INTERNATIONAL TRADE”. In the analysis we used rates and shares instead of actual absolute values data. The technique used is quite common and, actually, beneficial for analysts and users alike. In many statistical analyses of socio-economic, economic and social phenomena we don’t always have all the data we need in absolute, real-life values. In fact, many absolute-value data are sometimes very hard to come by. Many are either missing or have a huge error in them. The errors are not the random ones, i.e. ones with zero-sum and such that every standard parametric statistical technique can massage without problems. We are talking here about errors due to shortcomings of the statistical reporting, collecting, evaluation and definition. The missing data and information just compound the analytical tasks. Some, sometimes most of the, deficiencies of data-bases (i.e. erroneous or missing data) can be alleviated by several known techniques and procedures. Here, we shall list just some most useful ways of qualitative upgrading of the suspect data. For in-depth discussion see, for instance (M.Karasek, Socio-Economic Modelling and Forecasting in Developing Countries, The Book Guild Limited, Lewes, England, 1988, pp. 17-54), or (L.Moore, Forecasting the Yield…., A.M.Kelley, New York 1967). Our data-improvement technique should always start with “other information”. If we know the events that cause our unknown or suspect data and can assess the trend of these “causal (or explanatory) events”, there is a good chance we can assess also the trend of the unknown or suspect “effects”. Typical example concerns not very well reported data (that were probably deemed politically volatile) of Saudi Arabia GNP. However, it is well known that Saudi GNP is a function of “Oil Sales” and “Price per Barrel”, both of which are well reported in international publications. Hence, the problem of substantial improvement of GNP data was easily sold. Another technique of data- upgrading is the transformation of the absolute data into “growth rates”. There, the trends are much easier to spot and interpolation technique is therefore much easier to apply. Also in the time-series of “growth rates” (or “relative percentage differences”) the missing or suspect data can be easily upgraded by substituting with “instrumental variables” or “proxies”. An example of “proxy” is, for instance, as follows. Assume two adjacent countries and one of them wants to know the rate of change in number of tourist travelling by car from the other country. Problem may be that, because of visa-free entry, the number of tourists is not available. What is available, however, is the number of cars passing the border. Hence, we can use the “number of passenger cars per time-period” as proxy for “number of tourists per the same period” and build the growth trend on that. Granted, the assumption of uniform number of people per car is implicitly used but, in the large number cases, it tends to give reasonably precise growth trend, if not necessarily in precise absolute numbers. Going back to the original problem of economic analysis in section 1.1. we have postulate a high significance of causality between the two functional elements, “INTERNATIONAL TRADE” and “GDP”, which we denote (7.3.1) GDP = function (INT. TRADE) In a statistical test for a significant positive correlation between the “GROWTH in real GDP” (ARRAY Y in TABLE 7.3.1) and the “SHARE OF TRADE WITH NON-TRANSITION COUNTRIES” (ARRAY X in TABLE 7.3.1) there was, indeed, found high significance at probability level P = 0.05. 1 Central Asian Railways Telecommunications Progress Report Annex 7.3 TABLE 7.3.1 SHARE X GROWTH Y 61 16 64.2 9.6 56.7 3.7 28.2 1.7 53.5 4.1 23.6 3.7 72.6 5 38.8 2.5 47.4 4.4 38.8 -5.2 47.3 1.9 56.9 5.1 58.5 5.1 Y = - 4.3 + 0. 17 X Y = 0. 14 X PEARSON CORRELATION COEFFICIENT = 0.54 Significant at 0.05 Probability Level NOTE: The Pearson correlation coefficient is usually used for non-parametric statistics. These are the cases where the errors in variables are not randomly distributed, which perhaps involves over 80 percents of all data-series from all the spheres of technical, social, and economic life on this planet. 7.3.2 SOME OTHER ESTIMATION TECHNIQUES BASED ON SMALL SAMPLES Assume that we have no technical data on an important railway line in any of the Central Asian republics. These technical data are absolutely essential for preparing studies on optimum regional compatibility of telecommunication and signalling equipment and protocols to speed-up of the regional and international railway transit system and substantially increase its capacity well into the 21st century. Assume also that we have a small sample of the required data for the investigated railway. A sample that covers, perhaps, 10 percents of the length of the line we want to map. Let us denote the whole railway line or network, we want to map in so far the technical equipment, procedures etc. …… RL and the known content of the information from the sample (of the line)……SL. 2 Central Asian Railways Telecommunications Progress Report Annex 7.3 Consider possibilities: (1) If the sample SL is in all major operational, technical, technological and procedural criteria identical to RL then the problem is simple. Correcting for the number of main stations and other important crossings and loops, we consider the sample SL to be a typical sub-interval of the whole network RL. Then we can use a simple multiplier to estimate the whole RL. The principle here is the same as in a standard survey technique. (2) Sample SL is not a typical sub-interval. It contains, however, all the segments (of various technical, technologic and operational specifications) the investigated line (or network) RL consists of. Then, we have to use a multidimensional qualitative multiplier that would capture individual segments of the investigated net. The final estimated picture emerges by setting together all the pieces of the mosaic. This technique is not as straightforward and simple as the first one. With the help of railway transportation experts it should lead to reasonably precise estimate all the same. Example: Assume that each station on the line for which we don’t have any other technical information is known. Assume also that the standard equipment of every station of certain size and importance is known. Then pairing the similarly sized stations and summing them up gives us the first iteration of the estimates and a piece of the mosaic. Two theorems on fitting averages of the parts of the whole picture into the average of the whole picture (no matter if the “whole” consists of mosaic like pieces or their multiplication) is listed below. It should make the relationship between SL (an average of the part in the first case and an average multiplier in the second case) and RL (and average of the “whole” no matter how built) clearer. THEOREM 7.3.1: E (x1 + x2 +……xn) = E (x1) + E (x2) +…….E (xn) or E (a1x1 + a2x2 + …..anxn) = a1E (x1) + a2E (x2)……. anE (xn) THEOREM 7.3.2: E (x1x2. ……..xn) = E(x1) E(x2)………E(xn) (xi …..independent) Bibliography: Rektorys, K., Survey of Applicable Mathematics, 1969 ILIFFE BOOKS Ltd. London,pp. 1036-1037 3 ANNEX 7.4: Decision making methodology for the TACIS / CART project Central Asian Railways Telecommunications Progress Report Annex 7.4 ANNEX 7.4 – DECISION-MAKING METHODOLOGY FOR THE CART / TACIS PROJECT 7.4.1 FORMULAS, THEOREMS & AXIOMS USED IN ECONOMIC & TECHNICAL ANALYSES DEFINITION 7.4.1: Let us graphically express two real numbers a, b, (i.e. positive, negative, rational, and irrational and also zero) as the points on the X-axis (see EXHIBIT 7.4.1) b a ______|_____|__|___|_____|_____|_____|____|_|__________ -3 -2 -1 0 1 2 3 EXHIBIT 7.4.1 Then we say that a > b (or b < a) when and only when the point a lies on the right-hand side (RHS) of the point b. DEFINITION 7.4.2: Let a and b be two arbitrary real numbers (on the X-axis). Then a > b ( or b < a) when and only when the number {a - b} is a positive number. With any two real numbers, a and b, the two operations + and . each associate unique real numbers, denoted by a + b and a . b, respectively, in such a way that, if a, b, c, etc. are real numbers, the following axioms hold: AXIOM 7.4.1 (of Archimedes): Between any two real numbers, there is a rational number AXIOM 7.4.2: If a and b are the arbitrary real numbers, only one of the following relations holds: a = b , a > b , b > a THEOREM 7.4.1: If a > b and b > c , then a > c. Proof: to be found in [1: Chapter II, par.2] THEOREM 7.4.2: If a > b and c > 0 (i.e.