Variable Preference, Moral Value Judgment and Social Welfare in China and Japan

Transcription

1 Variable Preference, Moral Value Judgment and Social Welfare in China and Japan Zhijun Zhao -Visiting Scholar of Policy Research Institute, MOF of Japan -Senior Fellow of Chinese Academy of Social Sciences (CASS) Toshiki Kanamori -Managing Director, Daiwa Institute of Research, Daiwa Securities Group

2 2.Main Content 1. Problems Addressed 2. Cardinal Measurability of Tastes and Happiness 3. Randomness of Utility Function and Information Base 4. Representation of Preference 5. Nature of Social Welfare Function 6. Value Judgments and Constraints to Preferences 7. Social welfare Function under Ambiguity 8. Social Welfare Situation Evaluation in China and Japan 9. Concluded Remark 2

3 3. News from China (1) World No. 2 in economic scale. China has maintained 10% economic growth for over past 30 years, China has surpassed Japan become the world No.2 World no.1 in foreign exchange reserve. China has been accumulated $2,800 billion foreign exchange reserve, world No1 Length of high speed railway (bullet train) reached 7000 km now, surpass Japan,. it is expected to reach 16,000 km by Length of express highway has increased to 65,000 kilometers by 2009 from 11,600 Km in 1999, 55,000 billionaires (Yuan) whose per capita consumption is 2.5 million Yuan, 870,000 persons having assets over ten million Yuan, per capita consumption is 1.9 million Yuan. 3

4 4.News from China (2) However, There are 150 million people living under poverty line, or daily expenditure less than $1. it looks economic growth has nothing to do with them. a survey show that many people are not happy about their situation. The number of people unsatisfied with current social situation is increasing. Many people feel that their happiness is deprived, and their social position marginalized, become victim of economic growth. Beijing, Shanghai, Guangzhou and Shenzhen, the richest cities of China, are all excluded from top 10 happiest cities in China. Ordinary people are also suffering from high inflation, property bubble, Cost of economic growth is very serious. Rivers, lakes are polluted, forest coverage is shrinking. Some regions land is being deserted. Food safety is worrying 4

5 5. Something we see about Japan Japan has long been a highly developed economy and a big welfare state, it looks everything is OK. environmental protection pretty good, water and air quality better than before, and land covered by vast forest coverage. Daily life is very convenient, comfortable Good infrastructure. Public transportation system is very perfect. One of the world long-lived country Japan has been experienced 20 year deflation, called lost decades unemployment rate is higher though still moderate Japan possess very high suicide rate Aging population is increasing The world second largest public debt, only next Zimbabwe 5

6 6. Basic Situation Comparison between China and Japan in 2009 Item China Japan Gap land size( thousand km2 9, (China/Japan) population scale (million) 1, (China/Japan) GDP (billion USD) 4,909 5, per capita GDP (USD) 3,636 40, per capita GDP (PPP) 6,539 32,774 5 Beginning of reform (Year) (meiji) -110 (China-Japan) year becoming second largest (China-Japan) 6

7 7. First impression and Inspired Problems China s growth potential is very huge Japan s welfare level is very high, too high to develop. China lags far behind Japan in per capita term. Chinese are confident about future. Japanese face strong competition pressure from China Why the number of people unhappy about their situation are increasing in spite of rapid growth? Why there are so many Japanese committing suicide in Japan? Where does happiness come from? How to evaluate social welfare of China and Japan? Can we get any implications of policy relevance? 7

8 8. Theoretical Difficulties faced What is nature of social welfare function? Is social choice possible, does social welfare function exists? What is nature of utility function? Is utility measurable? Cardinally measurable or ordinally measurable? What is the nature of preference? What kind of information is revealed by preference axioms? What is the relationship between utility function and preference axioms? The conditions for possibility of social welfare function? 8

9 9. Brief look at Utilitarian Philosophy -Every scientific study begins with ignorance and assumptions Economics is a subject studying rational behaviors. Social and economic phenomena are the outcome of rationality and should be explained by rational principle and arithmetic operations. Rational man seeks greatest happiness or following "the greatest happiness principle" ( Bentham). People s happiness can be measured in utility, as thermometer measures temperature. Happiness of individuals can be compared interpersonally. 9

10 10. Logic of new welfare economics -I don t know, so any form will do People are covered by veil of ignorance, implying rationality is limited Every mind is inscrutable to every other mind (Robins, 1938). Utility is interpersonally incomparable. People can give ordering of alternatives, but can not identify strength of preference to alternatives. information about preference intensity is neglected Happiness can not be measured using cardinal utility, so the concept of preference is introduced to replace utility. If utility function exists, it is ordinal, Economics should begins with observable facts. Altogether, a series of conditions called preference axioms are assumed, which rational behaviors have to follow. 10

11 11.Summary of Difference between utilitarianism (left) and new welfarisim (right) Utility function is something introspective, there is a inherent rule in one s mind which dominates decision making. Utility is meaningful for decision makers. Utility function is unique but not known usually. People has ability to order social states, can identify intensity of preference. Diminishing marginal utility rule is usually accepted. Utility function artificially made by external observers to estimate the preference ordering rule, it is only meaningful for observers and researchers. It is not unique and There are many different cardinal utility functions corresponding to one preference ordering. People has ability to order social states, but not enough to identify intensity of preference Diminishing marginal utility rule is denied. 11

12 12.Asymmetric information implied in Preference Axiom preference Ordering rule can be only known by decision maker himself, not others. One person can only observe others action or ordering outcome, rather than action rule. Utility function is unknown variable to observer Only way to know ordering rule or action rule is guessing according to available ordering outcome. 12

13 13. Pleasure based and choice based utility Utility used to measure desire satisfaction or happiness according to hedonic criterion is called pleasure based utility. Utility used to measure outcome of such events as voting that one does not need to take into account the underlining satisfaction, is called choice based utility. Pleasure based utility don t deny that there is a psychological rule to measure utility intensity Choice based utility, the rule is not defined and not known, the only information is the preference ordering outcome. 13

14 14.What s wrong with new welfare economists For new welfare economists, starting point is preference. utility function is based on preference (but in fact, preference orderings are outputs of thinking or preference). Preference ordering is confused with preference rule (actually they are different things.) The logic followed by new welfare economists is that if two persons have the same ordering, then their preference and their utility functions are the same. Counter example, there are two judges scoring two girls A and B, and both think A is preferred to B, but one choice is based on A looks more beautiful than B, the other s choice is based on A more slender than B. their choice rules are totally different. But welfare economists don t differentiate them, and think two preferences are the same. In our view, New welfare economists method is right, but logic is problematic. 14

15 15. Preference axioms is only a mechanism of classification In facts, many example indicates that people having different preferences can give the same ordering to social states. Not 1-1 corresponding relation. For each preference corresponds to a ordering outcome, But each ordering outcome may correspond to more than one preference rule or utility function. This is why new welfare economists regarding utility function as ordinal. Preference axioms provide a mechanism for classification of people. Assume that there are 3 candidates A, B and C in a country running for presidency in general election, 10 million voters take part in for voting, each one has a different utility function, and based on which gives a ranking among three candidates. If only 6 choices are available, A>B>C, A>C>B, B>C>A, B>A>C, C>A>B, or C>B>A. it is clear that the 10 million voters will be divided into 6 groups according to their choices. Assuming that there are 3 million voters who ranks A>B>C, then in our viewpoints, the ordering A>B>C corresponding to 3 million different cardinal utility functions which is classified into the same group. 15

16 16. Introduction of Variable Cardinal Utility In above example, Ordinalists argue that these 3 million utility functions as the same and equivalent, any of them will be good correspondence to preference ordering. But in our views, the 3 million utility functions are different, only one of them is meaningful for each person, it is uncertain about who has which utility function, the only thing we know is that if I were one member of them, then my utility function must be one of the 3 million utility functions. We introduce random cardinal utility function to replaced ordinal utility function. The randomness of utility is meaningful only for observers who have not enough information determine the preference. In short, economic rationality and preference axioms can be completely understood in the framework of random cardinal utility theory without using the ordinal utility concept. One of the benefits to introduce random utility function is that it provide room for mathematical tool to play role in economics. 16

17 17. The meaning of interpersonal comparability implied in preference axioms Since preference comparison is a classification mechanism, Utilities are partially compared in light of classification mechanism provided by preference ordering. People classified in the same group can be called to have similar preference. The people classified in different groups is called not to have similar preference. The preference axioms imply that the same conclusion could be drawn from different decision rule under uncertainty and imperfect information. Great minds think alike. ( 君子所见略同 ) Different roads lead to the same goal.( 殊途同归 ) 17

18 18. Analogical example 1: possibility of social choice. L1 L2 Maximum point Two different curves have the same maximum point. But we could not say that the two curves are the same one 18

19 18. Analogical example 2: possibility of social choice O Supply curve Demand curve Supply curve represents preference of a producer, demand curve represents preference of consumer, they both maximize their utility and equilibrium O Supply side and demand side are different in preference to goods, but they all reached the happiest at the equilibrium O. 19

20 19. Analogical example 3: possibility of social choice-great minds think alike According to Arrow,, there is no social welfare function satisfying all his five conditions. But if dropping one or more of Arrow s conditions, then social choice is possible. If a society is made up of people of similar preferences, social agreement is easily reached and social choice will be possible. 20

21 21. Analogical example 4: possibility of social choice-optimal choice is a set of alternatives A C B for lack of information and limitation of rationality, an individual s optimization choice is not necessarily a single point but a set of points (one can not identify which one is the best). Set A is X s optimal choice Set B is Y s optimal choice Set C, the intersection of A and B, is optimal for both A and B. Set C is the social choice 21

22 22. Preference axioms without uncertainty (Deaton, 1987) Axiom 1: reflexivity: Preference is reflexive if for any x belongs S, x~x. Axiom 2: completeness: exactly one of the following is true: (1) x is preferred to y, (2) y is preferred to x, or (3) x is indifferent to y. Axiom 3: transitivity: if x is preferred to y and y is preferred to z, then x is preferred to z. Axiom 4: continuity:if x is preferred to y, and if z is sufficiently close to y, then x is preferred to z. Axiom 5: Preferences are not saturated. (increasing) Axiom 6: Preferences are convex. 22

23 23. Existence of utility function under Preference axioms without uncertainty There is a utility function satisfying all above axioms Such a utility function is not unique, that information is not enough above axioms do not include information about preference intensity and diminishing marginal utility law can not be derived from axioms. further information is needed to determine a unique utility function. 23

24 24. Concept of Uncertainty, Risk and Ambiguity Uncertainty is a general expression of random phenomenon. Some uncertain phenomena are relatively simple and can be represented by probability measure, this type of uncertainty is called risk; some uncertain phenomena are rather complex and cannot be expressed in one probability measure, this type of uncertainty is called ambiguity. Since the world we face is basically uncertain, it would be better to ground choice to social states and social welfare function on the framework of uncertainty. 24

25 25. Preference Axioms under Risk Assume that Social states is represented by a series of probability distribution p in set P Axiom 7: completeness: if p1,p2 are in P, then either, P1 is preferred to P2, or P1 is indifference to P2, or P2 is preferred to P1. Axiom 8: transitivity: if P1 is preferred to P2, and P2 is preferred to P3, then P1 is preferred to P3, Axiom 9: if P2 is indifference to P1, for any t in [0,1] and p3 t*p1+(1-t)p3< t*p2+(1-t)p3 are in P. Axiom 10: if p3 is preferred to p2 preferred to p1, then there are numbers t1 and t2, such that p3 t1*p1+(1-t1)p3<p2 and p2< t2*p1+(1-t2)p3. 25

26 26. Representation of preference under risk (von Neumann and Morgenstern) there is expected utility function of P in P, such that Expected utility U(P)= Ep(X)= V(xi)*Pi, v is value function under certainty 26

27 27. Representation of preference under Ambiguity There are many formulations about Ambiguity, the most famous intuitive one is The Multiple Priors Model, a generalization of von Neumann and Morgenstern expected utility function. The multiple priors model is proposed by Gilboa and Schmeidler (1989) postulates the following utility function on the set of Anscombe-Aumann (1963) (AA) acts, and first introduced to solve income based social welfare function by Zhao (2010). It can be show that a kind of sub linear expectation (Peng,1997,and Artzner et all (1999 Artzner et al, 1999) U MP ( ) min u( ) dp min u( ( x)) df( x) p P p P R 27

28 28. Nature of Social Welfare Function Social welfare function is a concept associated with personal value judgments, on which economists have never reached agreement, thus, it is impractical to find a definition that every one agrees. Nevertheless, as a scientific method of evaluating social states, social welfare function should be discussed in depth. The word social in term social welfare function has two different meanings: One, word social is reflected in social state, the inputs of social welfare function, then social welfare function is a function of social states The second meaning is that social welfare function is reflected in social opinion, outputs of social welfare function. Social opinions is aggregated from different opinion of social states. 28

29 29. SWF Sen and Buchanan s definition Social welfare function is a process or rule that is used to rank social states from highest to lowest. This definition exhibits an inclusiveness of the definition of social welfare function. According to this definition, social welfare function is seen as a process or rule to rank social states, and any function that complete ordering social states following rationality can be called a social welfare function, no matter it is formulated individualistically or collectively. In this definition, there is no impossibility theorem. 29

30 30. SWF: Arrow s Impossibility Theorem Social welfare function must be individualistic, that is, a social welfare function has to be derived from aggregation of individual welfare functions. Arrow listed 5 conditions (see right side), which he believed necessary for social welfare function (Arrow, 1970, 1986). Condition 1: Unrestricted domain: For any set of individual voter preferences, the social welfare function should yield a unique and complete ranking of social choices. Condition 2: Positive association: social welfare function is such that social ordering responds positively or at least not negatively with individual values (orderings). Condition 3: Independence of irrelevant alternatives: The social preference between x and y should depend only on the individual preferences between x and y, regardless of how z is ordered. 30

31 31. SWF: Arrow s Definition (continued) Condition 4: Non-imposition (or citizen sovereignty): the social welfare function is not to be imposed. This condition implies that every possible social preference order should be achievable by some set of individual preference orderings. Condition 5: Non-dictatorship: The social welfare function is not to be dictatorial. This means that social welfare function should account for the wishes of multiple voters. Conclusion: there is no social welfare function satisfying all above five conditions. 31

32 32. Our overall views on Arrow s conditions Positive association is relevant. Impossibility is artificially made. It is a result of putting five conflicting conditions together. Arrow s universal axiom is not line with social practice, ignore the force of morality and law. morality and law restricts scope of choices, therefore some choice are not arbitrary, but imposed. We strongly oppose Arrow s assumption of independence of irrelevant alternative, which is impractical because it eliminates comparable information Thanks to imperfect information and uncertainty, optimal choice may not be a single point, it may be a set of alternatives Drop any of arrow s conditions, social welfare choice may be possible (Sen s view) Preferences are not independent and at least partially comparable. There are lots of similarity between behaviors. 32

33 33. Our overall views continued Social welfare function is not individualistic Any social welfare function is a projection relative to a specific reference frame, it is only meaningful for specific reference frame. every one can give a evaluation of social welfare states, but only government evaluation is policy relevant. Different reference frame induces different social welfare function. Social welfare function in general is dictatorial or oligarchy (a small group or committee determined) In the real world, social decision process is classified as voting process (elected leader or president), policy making process (make my president and his team), and policy revision process reflecting public opinions. Arrow s definition is only relevant for voting process. 33

34 34. Another version of Arrow Definition: the possibility theorem (Arrow,1976): if there are more than one commodity and if every set of individual orderings each of which satisfies individualistic assumptions is admissible, then every social welfare function satisfying condition 2 and 3 is either imposed or dictatorial. Note;Arrow here confesses that social welfare function may be dictatorial, imposed, not necessarily aggregated from individuals 34

35 35. three principles of Social Value Judgments as Constraints to Preferences Principle 1: Justice and equity Principle. Justice Principle here has two implications: first, every person in a society has sympathy to the weak and the poor, and to protect sanctity of life and dignity of humankind, minimum wage and living standard for basic needs should be guaranteed. Income distribution should be prone to the poorest if income is redistributed, and income of the poorest should increase with social mean income. Principle 2: Efficiency Principle. Interpersonal difference in ability is accepted as an objective social existence and it is necessary for a society to accept interpersonal difference in ability and ensure everybody in a society gets what he deserves from market. To accept and protect difference in income distribution is a premise of efficiency. Principle 3: Relativity and maximization principle: social welfare is relative concept to specific reference frame. each member of the society has his own preference pattern and his own standard to evaluate social states. Whoever evaluates social states follows the principle of expected utility maximization. 35

36 36. Income distribution and Social Welfare Function: individual welfare and reference point Reference frame is represented individual utility function U(x,F(x)) X: is individual income level F(x): income distribution function; U(x,F(x)) :is utility function that is bounded, monotonous increasing and concave. Note: (1) The boundedness of utility function is assumed to ensure that expected utility or the expectation of the value function exists; (2) F(x) is increasing function, the higher the income level compared with others, the higher the social position; and the higher the position the happier. Which mean individual utitilty is increasing function of social position 36

37 37. Constraint 1: minimum income wage income is distributed on x m, x m 0 Note: this condition reflects Justice principle: government is obligated to consider basic needs of every people of the society, and ensure everyone to live with a dignity life. therefore, a reasonable assumption is that the minimum income is guaranteed as a major consideration of policy making. 37

38 38. Income distribution and Social Welfare Function: Ambiguous Distribution Within multiple priors framework, income distribution can not be represented by a single probability measure, but can be represented by a set of continuously differentiable probability distributions: P F( x x, m, G ( G, G)) is mean income (expected), G denotes Gini coefficient. Government want to keep Gini coefficient at moderate level, not too large, not too small. If it is too small efficiency is impacted. 38

39 39. Social Welfare Objective Function : Social welfare is measured and evaluated by government in terms of expected utility in her reference frame. social objective is to find F* such that: W ( F * ) Max E F F U ( X ), F( X ) Max F P x m U ( x, F( x)) F ( x) dx 39

40 40. Variational Structure of Social Welfare Problem W Objective: Constraints: U ( X, F( X ) U ( x, F( x)) F ( x) dx ( F) Max E F F 2 x m Ex x x m xf ( x) dx x m n 1 1 F( x) F ( x) dx (1 G ) n Boundary conditions: F( ) 0 F( ) 1 y m 40

41 41. Proposition 1:(Representation of the optimal income distribution) If utility function U U (x) is a continuously differentiable, bounded and concave, then there must be a distribution F* which maximizes social welfare. F U (, ( )) y y F ym ( y) 1 U y ( ym, F( ym)) 1 ( n 1) optimal distribution is determined by government preference (utility) and it decreases with marginal utility of income. Once the utility function is known, a specific expression of optimal distribution function is obtained. 41

42 42. Proposition 2 (Representation of social welfare function under concave utility) n=2, If utility function is a continuously differentiable, bounded and concave, then there must be a distribution which maximizes social welfare. the social welfare function is a function of minimum income, average income and Gini mean difference. W ( F ) R( x ) U ( x ) (1 G) R ( x ) U ( x ) U ( x ) x m m m m m m 42

43 43. Proposition 3: (Sen welfare function) Sen s social welfare function is a special case of the social welfare function obtained here. However, Sen s Function is derived in different framework, Deaton get Sen s function by imposing some homogenous assumptions on individuals preferences under certainty. here we demonstrate that social welfare function can be derived in the framework of rational optimization behavior. W sen ( F * ) (1 G) 43

44 44. Invariance of social welfare function Any social welfare function is invariant up to a increasing transformation. This implies that any standardized social welfare function can be transformed into Sen s social welfare function by a increasing transformation g. g ˆ U ( x) = (1 G) The binary social welfare function looks independent of the form of U. 44

45 45. Social Welfare Situations in Japan and China Above theoretical discussion indicates that social welfare function could be any function that follows preference axioms and ranks social states rationally, social welfare function is not necessarily individualistic, it could be approved by every member of society, or it could be dictatorial or team determined depending on rules and restrictions imposed. Social welfare function could be regarded as projection of social states on a specific reference frame denoted by utility function. Given utility function, restrictions imposed on preference, social welfare function can be represented by average income multiplied by measure index of income disparity, such as Social welfare =average income*(1- generalized Gini coefficient). Some indexes reflecting social welfare can not be measured in money 45

46 46 46: Human Development Indicators Germany France US UK Japan India Russia China Brazil Rank

47 47: Japan's Land and Tokyo Stock Indexes land Tokyo stock

48 48. Public debt-gdp ratios Rank Country % of GDP Date 1 Zimbabwe Japan (210) 2009 (2010) 6 Italy Iceland Greece Canada France Germany United Kingdom Brazil India United States China Russia

49 49 49 Unemployment Rate (% of labor force) Germany France US UK Japan 4.3 India Russia China Brazil Year

50 50. Japan s Net GNI (2008 ) GNI 28,213 31,433 33,654 34,506 35,500 35,188 33,790 GDP 28,152 31,037 32,878 33,553 34,352 34,129 32,774 GNI-GDP , , ,016.5 (GNI-GDP) *100/GDP

51 Gini Coefficients(%) Russia Brazil India China US UK Germa ny Japan France Country

52 52. GNI per capita (2008 PPP US$) Times of 2009/1990 Brazil China France Germany India Japan Russia UK US

53 53 53: Economic Welfare index India China Brazil Russia Japan UK France US Germany Countries

54 54. Feeling of happiness(china 07, Japan 05) Very happy Quite happy Not very happy Not at all happy Sum China (100%) Japan (100%) 54

55 55. Lowest Homicide Rate in Japan in Japan Germany China France India UK US Russia Brazil

56 56. Lowest Robbery Rate France Germany India Japan Russia UK US 56

57 57. Suicide Rate (every 100, 000 persons) Nation Male Female Total Year Russia Japan Korea France China Germany US India UK

58 Life expectancy at birth (years) India Russia Brazil China US UK Germany France Japan

59 59. Overall impressions about Japan social welfare It is too developed to develop further. the so called lost two decades is not appropriate for Japan. its economic growth rate in past ten years is only little lower than other developed countries mentioned in the paper. Japan s economic welfare index is at the same level as other developed countries mentioned. Good infrastructure and convenient daily life. Japan s jobless rate is in better condition than other countries. Japan is ranked among the longest lived countries Japan also has lowest homicide rate Japan also has lowest robbery rate water, and air quality improved, and environment is better, thanks to shifting of industrial production bases to overseas. 59

60 60. Take steps to handle challenges to Japan Japan s college students are now hard to find job. Second highest public debts and possibility of suffering debt crises Have to face competition from emerging China and India, which might push up energy price in global market and have cheap labor. Reestablish family value, take care of suicides. Immediately take steps to recover balance of government fiscal deficit. Simplify entrance procedure, Strengthen and stabilize economic ties with China, share benefit of china fast economic growth, Attract more rich Chinese to come to Japan 60

61 61. Overall impressions about Chinese social welfare Fast growth, confident about future, per capita GDP Still low and lags far behind Japan Social welfare is increasing but it is tremendously discounted by increasing regional, rural-urban disparity and bad income distribution. Very bad air and water pollution Inflation and property bubble. Bad corruption 61

62 62. Take steps to Eradicating corruption and maintaining political stability should be given top priority. Slowdown economic growth, Curb Inflation and property bubble, encourage to efficiently use natural resources and energy. Reform tax system to narrow income disparity. Perfect social safety net, improve rural people s health care, strengthen rural infrastructure. More public expenditure should be used in environmental protection and water resources, promote environmental protection awareness of ordinary. Expanding forest coverage 62

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