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* POLITICAL ECONOMY. 190 POLITICAL ECONOMY. condition in IS'JS should be identical with those in prewUinf; yeais. as their object was to dis- cover the exait effect of the reiluction in hours upon profits and conditions of employment. The chief instrument of the method of difference is thus the experiment, to which may he added in economics the observation of extraordinary in- stances in whieh the conditions of an experiment are closely approximated by some fortuitous or extraordinary event. Thus the Black Dcatli in England furnishes a striking excmplilication of the effect upon wages of a sudden diminution in the supply of labor. In theory the metliod of difference requires that the colhUeral or sur- rounding circumstances shall be absolutely alike. This condition is seldom fulfilled even approxi- mately, and hundreds of instances miglit be cited in which the method has been al)used. To refer to the experiment at the Salford Iron Works, which on the whole constitutes an ideal economic experiment, it is evident that grave doubt is thrown on the results of this experi- ment by the fact that the workmen themselves were interested in the success of the experiment, and probably worked with extraordinary care and diligence to make it a success. Finally, it is to be noted that the nietliod of difference, while entirely satisfactory where the conditions are ])er- fect, is always narrow and restricted. It shows with certainty that a given cause in a certain set of circumstances can produce a certain result, but tells us nothing of what will happen in another set of circumstances. To generalize, to establish uniformities, use is made of the method of agreement. Here we compare circumstances wholly different, with the exception of two iihenomena between which we expect to estalilish a causal connection. The causal connection is indicated by the repeated conjunction of the two ]>henomena. If we ex- amine the movement of exports and the move- ment of the marriage rate, and find that a rise' in the exports per capita is always accompanied by a rise in the marriage rate, we are safe in accepting this connection as an economic uni- formity or law, provided that we have examined a very large number of instances in which the collateral circumstances have been infinitely di- verse and varied. Theoretically this method re- quires that we should exhaust every possible combination of circinistances before concluding that a rise in the exports per capita will always cause an increase of marriages. With respect to the general utility of the inductive method, it is plain that, though little can be done without it, it seldom, if ever, suffices to convince. Take the case of the exports and the marriage rates cited above. Hundreds of instances might be adduced from PInglish statis- tics in which a rise in the per capita exports has been followed by a rise in the marriage rate'. Yet no one believes that a mere increase in exports would cause an increase in marriage. Both are evidently the results of a single cause — active business, etc. Brisk trade, high wages, constant employment, etc, stimulate marriage and show themselves usually in an increased volume of exports, yet if commercial prosperity at any time increased without stimulating ex- ports, we have every reason to believe that the marriage rate would rise irrespective of exports. And in less developed countries where trade and commerce are relatively unimportant no con- nection is observed between exi)orts and marriage. The great dilliculty of induction in economics is due to the complexity of economic phenomena: we are seldom able either to bring about a satisfactOrv ex])eriment or to .secure a sulliciently diverse number of instances of agrcenu^nl. Cur- rent literature is full of sweeping generalizations based upon far less agreement than that ob.served between marriages aiul exports. The twenty-live years preceding the repeal of the corn laws in England were, on the whole, far less [U'ospcrous tluin the twenty-five years which succeeded the lepeal ; er(/o, concluded many writers, free trade would be advantageous to every country of the world. On the other hand, the method nf agree- ment has been e(|uaUy abused. Because tlic crea- tion of the great modern European monarchies was in most instances accompanied liy protective tariffs, colonization schemes, and a certain harsh- ness and brutality toward strangers, therefore, concluded the extremists of the German His- torical 8chool. it is not only expedient, but ethically right, that the German Empire in the last half of the nineteenth century should start in with protective tarill's, colonization schemes, and the policy of the mailed fist. To-day it is universally conceded that both methods must and should be used wherever possible. Otiiek Methods. In actual practice a large number of complicated combinations of the de- ductive and iniluctive methods arc used in economics. Induction in its quantitative aspect gives rise to the statistical method. No school of political economy has ever disputed the im- portance and value of statistics, and in the last few years it has made more ra))id ju'ogress |)er- haps than any other branch of the science. This is due to the increased public expenditures in statistical investigations, and the impetus given to the improvement of the study by such associa- tions as the International Statistical Institute, the Royal Statistical Society, the American Statistical Association. So great has been the development of statistical technique at the hands of such men as Quetelet, Bertillon, Engels. Von Mayr, Edgeworth (to whom should be added from other sciences, Galton, Venn, Karl Pearson, etc), that the technique of quantitative induc- tion constitutes in reality a new branch of science. (See Statistics.) Deduction in its quantitative aspect gives rise to the mathematical method of political economy, which at tlio ])res- ent time is employed to a greater or less extent in all branches of economic theory, particularly in the investigation of prices, incidence of taxa- tion, etc. Opinions ditl'er upon the usefulness of mathematics except in statistics. Mathemat- ical diagrams for purposes of illustration, at least, have undoubtedly made a permanent place for themselves in the science, but the utility of algebraic mathematics, except for him who com- putes them, is doubtful. See Mercantilism: Physiocrats; Interest; Rent; Labor; Finance; SocioLOGy; Protec- tion; Free Trade; Lais.sez-faibe; Socialism; Trade Unions ; Vali'e : Usitry. Bibliography, The most important works of the earlier English economists are: Smith, Wefrlth of Nntimix (London, 1776; many later editions) ; Say, Traits d'fconomie politique (Paris, 1803) ; Rieardo, Principles of Political Economy and Taxation (London, 1817) ; Mal- thus, Political Economy (ib., 1820); Mill,