References

R. Ackoff, Scientific Method, Wiley, New York, 1962.

A.N. Afriat, The Price Index, Cambridge University Press, Cambridge, 1977.

K.R. Akkina, 'Application of Random Coefficient Models to the Aggregation Problem,' Econometrica, 42(1974), pp. 369-376.

R.G.D. Allen, Mathematical Economics, Macmillan & Co Ltd, London, 1964-2.

R.G.D. Allen, Macro Economic Theory, Macmillan & Co Ltd, London, 1967.

R.W. Anderson, 'Perfect Price Aggregation and Demand Analysis,' Econometrica, 47(1979), pp. 1209-1230.

A. Ando and F.Modigliani, 'The "Life-Cycle" Hypothesis of Saving: Aggregate Implications and Tests,' American Economic Review, 53(1963), pp. 55-84.

W. Armstrong, 'The Determinateness of the Utility Function,' Economic Journal, 98(1939), pp. 453-467.

K.J. Arrow, Social Choice and Individual Values, Wiley, New York, 1963-2.

S. Barbera, 'Strategy-proofness and Pivotal Voters: a Direct Proof of the Gibbard-Satterthwaite Theorem,' Universidad del Pais Vasco, Bilbao, 1980.

Y. Bard, Nonlinear Parameter Estimation, Academic Press, New York, 1974.

W.A. Barnett, Consumer Demand and Labor Supply, North-Holland Publishing Company, Amsterdam 1981.

A.P. Barten, 'Maximum Likelihood Estimation of a Complete System of Demand Equations,' European Economic Review, (1969), pp. 7-73.

A.P. Barten, 'The Systems of Consumer Demand Functions Approach, a Review,' Econometrica, 45(1977), pp. 23-52.

J.H. Blau, 'A Direct Proof of Arrow's Theorem,' Econometrica, 40(1972), pp. 61-67.

P.M.C. de Boer, Price Effects in Input-Output Relations: a Theoretical and Empirical Study for the Netherlands, 1949-1967, Ph.D. thesis, Erasmus University Rotterdam, 1981.

P.M.C de Boer and J. van Daal, 'Linearization and Estimation of the Addi-log Budget Allocation Model,' Report 8004 of the Econometric Institute of the Erasmus University Rotterdam, Januari 1980.

C. Blackorby, D.Primont and R.R. Russell, Duality, Separability and Functional Structure, North-Holland Publishing Company, Amsterdam etc., 1978.

307

308 REFERENCES

J. Blokland, Continuous Consumer Equivalence Scales, Martinus Nijhoff, the Hague, 1976.

P.J.M. van den Boogaard and G. Arnaiz, 'On the Sensitivity of Committee Decisions under Alternative Quadratic Criteria,' Report 6107, Econometric Institute, Netherlands School of Economies, Rotterdam, 1961.

P.J.M. van den Boogaard and A.P. Barten, 'Macroeconomic Decision Rules,' Report 5915, Econometric Institute, Netherlands School of Economics, Rotterdam, 1959.

J.C.G. Boot and G.M. de Wit, 'Investment Demand, an Empirical Contribution to the Aggregation Problem,' International Economic Review, 1 (1961), pp. 1-30.

W.H. Branson and A.K. Klevorick, 'Money Illusion and the Aggregate Consumption Function,' American Economic Review, 59(1969), pp. 832-849.

A. Brown and A. Deaton, 'Surveys in Applied Economics, Models of Consumer Behaviour,' Economic Journal, 82(1972), pp. 1145-1236.

M. Brown and W.W. Chang, 'Capital Aggregation in a General Equi­librium Model of Production, Econometrica, 44(1976), pp. 1179-1200

M. Brown and D. Heien, 'The S-Branch Utility Tree: a Generalization of the Linear Expenditure System,' Econometrica, 40(1972), pp. 737-747.

J.C. Burkill and H.Burkill, A Second Course in Mathematical Analysis, Cambridge Un. Press, Cambridge (U.K.), 1970.

F. Carlevaro, Sur la Comparaison et 1a Generalisation de Certains Systemes de Fonctions de Consommation Semi-Aggregees, Herbert Lang, Bern, 1975.

Central Bureau of Statistics, 75 Jaar Statistiek in Nederland, State Publishing Company, The Hague, 1975.

M.J. Chossudowsky, The Application of the Social Welfare Function to the Planning of Economic and Social Policy, Ph.D. thesis, University of North Carolina, Ann Arbor, 1971.

M.J. Chossudowsky, 'Optimal Policy Configurations under Alternative Community Group Preferences,' Kyklos, 4(1972), pp. 754-768.

M.J. Chossudowsky, 'Do Political Parties Have Utility Functions?,' Societe Canadienne de Science Economique, Ottawa, 1972.

M.J. Chossudowsky and W. Sellekaerts, 'A Comparison of Optimal and Actual Policies for High Employment and Price Stability under External Inflationary Conditions: the Canadien Experience,' The Southern Economic Journal, 41(1974), pp. 206-217.

w.e. Churchman, Prediction and Optimal Decision, Prentice Hall,

REFERENCES

Englewood Cliffs, 1961.

Marquis de Condorcet, Essai sur l'Application de l'Analyse a la Probabilite des Decisions Rendues a la Pluralite des Voix, Paris, 1785.

J.S. Cramer, The Ownership of Major Consumer Durables, Cambridge Unl.versi ty Press, Cambridge, 1962.

J.S. Cramer, Empirical Econometrics, North-Holland Publishing Company, Amsterdam, 1971.

J.S. Cramer, 'The Effect of Income Redistribution on Consumer Demand,' in Cramer, Heertje, Venekamp(Ed.), Relevance and Precision, Essays in Honour of P. de Wolff, Samson/North-Holland Publ. Cy, Alphen a.d. Rijn/Amsterdam, 1976.

J. van Daal, 'Money Illusion and Aggregation Bias, I De Economist, 128(1980), pp. 86-93.

J. van Daal and A.S. Louter, 'A Quadratic Engel Curve Demand Model (Squaring with the Representative Consumer),' Paper Presented at the European Meeting of the Econometric Society, Athens, September 1979.

J. van Daal and A.H.Q.M. Merkies, 'A Simple Proof of Nataf's Theorem on Consistent Aggregation,' Economics Letters, 7(1981), pp. 441-446.

A.K. Dasgupta and D.W. Pearce, Cost-Benefit Analysis, Theory and Practice, Macmillan & Co Ltd, London, 1972.

A. Deaton and J. Muellbauer, 'An Almost Ideal Demand System,' American Economic Review, 70(1980), pp. 312-326.

G·. Debreu, Theory of Value, Yale University Press, New Haven and Londen, 1973-5(1959).

F. Demeyer and C.R. Plott, 'The Probability of a Cyclical Majority,' Econometrica, 38(1970), pp. 345-354.

F.B. Denizot and V. Levy-Garboua, 'Le Probleme de I 'Aggregation, ' Revue Economique, 23(1973), pp. 20-53.

J. van den Doel, Democratie en Welvaartseconomie, Samson, Alphen aan de Rijn, 1975.

W. Driehuis, Fluctuations and Growth in a Near Full Employment Economy, Rotterdam University Press, Rotterdam, 1972.

W. Driehuis, 'Labour Market Imbalances and Structural Unemployment,' Kyklos, 31(1978), pp. 638-661.

J. van Driel, 'Consumer Expenditure Allocation Models,' Report 7405/E, Econometric Institute, Erasmus University Rotterdam, 1974.

309

310 REFERENCES

w. Eckstein and G. Fromm, 'The Price Equation, I American Economic Revi,ew, 58(1968), pp. 1159-1183.

C.J. van Eijk and J. Sandee, 'Quantitative Determination of an Optimum Economic Policy,' Econometrica, 27(1959), pp. 1-13

B. Eisenberg, 'Aggregation of Utility Functions, I Management Science, 7(1961), pp. 337-350.

R.C. Fair, 'Labor Force Participation, Wage Rates and Money Illusion,' The Review of Economics and Statistics, 53(1971), pp. 164-168.

P.C. Fishburn, 'Arrow's Impossibility Theorem, Concise Proof and Infinite Voters,' Journal of Economic Theory, 2(1970), pp. 103-106.

P.C. Fishburn, The Theory of Social Choice, Princeton University Press, Princeton, New Jersey, 1973.

P.C. Fishburn, 'Paradoxes of Voting,' The American Political Science Review, 68(1974), pp. 537-546.

F.M. Fisher, 'Embodied Technical Change and the Existence of an Aggregate Capital Stock,' Review of Economic Studies, 32(1965), pp. 263-288.

F.M. Fisher, 'Approximate Aggregation and the Leontief Conditions,' Econometrica, 37(1969), pp. 457-469.

F.M. Fisher, 'The Existence of Aggregate Production Functions,' Econometrica, 37(1969), pp. 553-577.

F.M. Fisher, 'Aggregate Production Functions Revisited,' The Review of Economic Studies, 49(1982), pp. 615-626.

W.D. Fisher, Clustering and Aggregation in Economics, John Hopkins, Baltimore, 1969.

A.F. Friedlaender, 'Macro Policy Goals in the Postwar Period,' Department of Economics, Boston College Discussion Paper No.6, 1970.

A.F. Friedlaender, 'Macro Policy Goals in the Postwar Period: A study in Revealed Preference,' Quarterly Journal of Economics, 87( 1973), pp. 25-43.

R. Frisch, 'The Multiplex Method for Linear and Quadratic Planning,' Economic Institute, University of Oslo, 1957.

T. Gamaletsos, 'Further Analysis of Cross-Country Comparison of Consumer Expenditure Patterns' European Economic Review, 4(1973), pp. 1-20.

W.A. Gamson, 'Experimental Studies of Coalition Formation, I in

REFERENCES

L. Berkowitz(Ed.), Advances in Experimental Psychology, Academic Press, New York, 1964.

M. Garman and M. Kamien, 'The Paradox of Voting: Probability Calculations,' Behavioral Science, 13(1968), pp. 305-316.

R. C. Geary, 'A Note on "A Constant Utility Index of the Cost of Living",' Review of Economic Studies, 18(1950), pp. 65-66.

L.P.J. van der Geest, 'Het Vastleggen van Economisch-Politieke Oordelen in Preferentiefuncties,' Unpublished Master's thesis, Erasmus University Rotterdam, 1976.

A. Gibbard, 'Manipulation of Voting Schemes,' Econometrica, 41(1973), pp. 587-601.

S.M. Goldman and H. Uzawa, 'A Note on Separability in Demand Analysis,' Econometrica, 32(1964), pp. 387-398.

W."l. Gorman, 'Community Preference Fields," Econometrica, 21(1953), pp. 63-80.

W.M. Gorman, 'Separable Utility and Aggregation,' Econometrica, 27(1959), pp. 469-481.

W.M. Gorman, 'On a Class of Preference Fields, I Metronomica, 13( 1961), pp. 53-56.

W.M. Gorman, 'The Structure of Utility Functions,' Review of Economic Studies, 35(1968), pp. 367-390.

J. de V. Graaff, Theoretical Welfare Economics, Cambridge University Press, 1971 (1957).

H.A.J. Green, Aggregation in Economic Analysis, an Introductory Survey, Princeton University Press, Princeton, 1964.

G.Th. Guilbaud, 'Les Theories de l'Interet General et le Probleme Logique de l'Aggregation,' Economie Appliquee, 5(1952), pp. 501-584.

K.L. Gupta, Aggregation in Economics, a Theoretical and Empirical Study, Rotterdam University Press, Rotterdam, 1969.

R. Harkema and S. Schim van der Loeff, 'A Note on Aggregation of C.E.S.-Type Production Functions,' European Economic Review, 6(1975), pp. 97-101.

J. Hartog and J.G. Veenbergen, 'Dutch Treat: Long Run Changes in Personel Income Distribution,' De Economist, 126(1978), pp. 521-549.

J.R. Hicks, Value and Capital, Clarendon Press, Oxford, 1937.

J.R. Hicks, A Revision of Demand Theory, Oxford University Press, Oxford, 1956.

311

312 REFERENCES

H.S. Houthakker, 'The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis,' Review of Economic Studies, 23(1955), pp. 27-31.

H.S. Houthakker, 'Additive Preferences,' Econometrica, 28(1960», pp. 224-257.

H.S. Houthakker and L.D. Taylor, Consumer Demand in the United States, 1929-1970, Cambridge University Press, Cambridge Mass. ,1970-2.

H. Howe, R.A. Pollak and T.J. Wales, 'Theory and Time Series Estimation of the Quadratic Expenditure System,' Econometrica, 47(1979), pp. 1231-1248.

A.P. Huyser and W.H. Somermeyer, 'Elasticidades Ingreso y Cualitativas en Mexico, una Aplicacion del Modelo de Asignacion del Gasta,' Demagrafia y Economica, 7(1973), pp. 203-237.

Y. Ijiri, 'The Linear Aggregation Coefficients as the Dual of the Linear Correlation Coefficient,' Econometrica, 36(1968), pp. 252-259.

Y. Ijiri, 'Fundamental Queries in Aggregation Theory, I Journal of the American Statistical Association, 66(1971), pp. 766-782.

M.D. Intriligator, 'A Probabilistic Model of Social Choice,' Review of Economic Studies, 40(1973), pp. 553-560.

M.D. Intriligator, Mathematical Optimization and Economic Theory, Prentice Hall, Englewood Cliffs, New Jersey, 1971.

L. Johansen, Production Functions, North-Holland Publishing Company, Amsterdam, 1972.

L. Johansen, 'Establishing Preference Function for Macroeconomic Decision Models. (Some Observations on Ragnar Frisch's Contributions),' European Economic Review, 5(1974), pp. 41-66.

D.W. Jorgenson, L.J. Lau and T.M. Stoker, 'The Transcendental Logaritmic Model of Consumer Behavior, I Discussion Paper, Harvard University, January 1981.

A. Kapteyn, A Theory of Preference Formation, Ph.D. thesis, University of Leyden, 1977.

W.J. Keller, 'A Nested C.E.S.-Type Utility Function and its Demand and Price-Index Functions,' European Economic Review, 7(1976), pp. 175-186.

W.J. Keller, 'Savings, Leisure, Consumption and Taxes; The Household Expenditure System,' European Economic Review, 9(1977), pp. 151-167.

W.J. Keller, Private Communication, 1979.

REFERENCES

W.J. Keller, 'Aggregation of Economic Relations, a Note,' De Economist, 128(1980), pp. 558-562.

J.M. Keynes, The General Theory of Employment, Interest and Money, Macmillan & Co Ltd, London, 1936.

P. Kirman and D. Sonderman, 'Arrow's Theorem, Many Agents, and Invisible Dictators,' Journal of Economic Theory, 4(1972), pp. 267-279.

D. Klahr, 'A Computer Simulation of the Paradox of Voting,' The American Political Science Review, 6(1966), pp. 384-390.

L.R. Klein, 'Remarks on the Theory of Aggregation,' Econometrica, 14(1946), pp. 303-312.

L.R. Klein, A Textbook of Econometrics, Row, Peterson & Co., Evanston, Illinois, 1953.

L.R. Klein and H. Rubin, 'A Constant-Utility Index of the Cost of Living,' The Review of Economic Studies, 15(1947), pp. 84-87.

T. Kloek, 'Note on Convenient Matrix Notations in Multivariate Statistical Analysis and in the Theory of Aggregation,' International Economic Review, 2(1961), pp. 351-360.

313

P. Kooiman and T. Kloek, 'Aggregation of Micro Markets in Disequilibrium. Theory and Application to the Dutch Labour Market 1948-1975,' Paper Presented at the European Meeting of the Econometric Society, Athens, September, 1979.

P. Kooiman, 'Using Business Survey Data in Empirical Disequilibrium Models,' International Centre for Economics and Related Disciplines, London School of Economics, 1982.

S.K. Kuipers and F.H. Buddenberg, 'Unemployment on Account of Market Imperfections in the Netherlands Since the Second World War,' De Economist, 126(1978), pp. 390-412.

E. Kuh, 'Aggregation Theory and Practice,' in W. Sellekaerts(Ed.), Econometrics and Economic Theory, Essays in Honour of Jan Tinbergen, Macmillan & Co Ltd, London, 1974.

L.J. Lau, 'Existence Conditions for Aggregate Demand Functions, I

Technical Report No. 248, Institute for Mathematical Studies in the Social Sciences, Stanford University, 1977 (rev. 1980).

W.W. Leontief, 'A Note on the Interrelation of Subsets of Independent Variables of a Continuous Function wi th Continuous Fi rat Deriva ti ves, ' Bulletin of the American Mathematical Society, 53(1947), pp. 343-350.

W.W. Leontief, 'Introduction to a Theory of the Internal Structure of Functional Relationships,' Econometrica, 15(1947), pp. 361-373.

D.Levhari, 'A Note on Houthakker's Aggregate Production Function

314 REFERENCES

in a Multifirm Industry,' Econometrica, 36(1968), pp. 151-154.

C. Lluch, 'The Extended Linear Expenditure System,' European Economic Review, 4(1973), pp. 21-32.

H. Luetjohann, Linear Aggregation in Linear Regression, University of Stockholm (Institute of Statistics), 1974.

E. Malinvaud, 'L'Aggregation dans les Madeles Economiques, I Cahiers du Seminaire d'Econometrie, 4, Centre National de la Recherche Scientific, Paris, 1956.

E. Malinvaud, Methodes Statistiques de l'Econometrie, Dunod, Paris, 1969-2.

E. Malinvaud, Profitability and Unemployment, Cambridge University Press, Cambridge (U.K.), 1980.

A.H.Q.M. Merkies, 'Van Prognoses naar Programma's, I Inaugural Address, Vrije Universiteit, Amsterdam, 1973.

A.H.Q.M. Merkies and J.A. Bikker, 'Aggregation of Lag Patterns with an application in the Construction Industry, I European Economic Review, 15(1981), pp. 385-405.

A.H.Q.M. Merkies and T.E. Nijrnan, 'Preference Functions of Dutch Political Parties,' Economie Applique, 34(1981), pp. 785-818.

A.H.Q.M. Merkies and A.J. Vermaat, 'Sociaal-Economische Doelstellingsfuncties. Rapportage Eerste Verkennende Enquete,' Faculty of Actuarial Sciences and Econometrics, Vrije Universiteit, Amsterdam, 1977.

A.H.Q.M. Merkies and T Nijman, 'The Maesurement of Quadratic Preference Functions with Small Samples,' Research Paper 68, Faculty of Actuarial Sciences and Econometrics, Vrije Universiteit, Amsterdam, 1983.

A.H.Q.M. Merkies and A.J. Vermaat, 'Preferentiefuncties van een Aantal Politieke Partijen en Maatschappelijke Organisaties,' Research Paper No. 53, Faculty of Actuarial Sciences and Econometrics, Vrije Universiteit, Amsterdam, 1980.

A.H.Q.M. Merkies and A.J. Vermaat, 'De Onmacht van een Kabinet: een Empirisch Onderzoek naar Sociaal-Economische Preferentie Functies en hun Gebruik als Welvaartsindicator,1 Maandschrift Economie, 45(1981), pp. 101-118.

O. Morgenstern and G.L. Thompson, Mathematical Theory of Expanding and Contracting Economies, Lexington Books, Lexington, 1976.

J. Muellbauer, 'Aggregation, Income Distribution and Consumer Demand,' Review of Economic Studies, 62(1975), pp. 525-543.

J. Muellbauer, lCommunity Preferences and the Representative

REFERENCES 315

Consumer,' Econometrica, 44(1976), pp. 979-1000.

J. Muel1bauer, 'Economics and the Representative Consumer 1 I Ch. 2 of L. Solari and J.-N. Pasquier(Ed.), Private and Enlarged Consumption, North-Holland Publishing Company, Amsterdam, 1976.

J. Muellbauer, 'Macrotheory VS. Macroeconometrics: the Treatment of "Disequilibrium" in Macromodels, I Paper Presented at the European Meeting of the Econometric Society, Geneva, September 1978.

J. Muysken, Aggregation of Putty-Clay Production Functions, Ph.D. thesis, University of Groningen, 1979.

E.J. Nanson, 'Methods of Elections,' Trans~ctions of Proceedings of the Royal Society of Victoria, 18(1882).

A. Nataf, 'Sur la Possibilite de Construction de Certains Macromodeles,' Econometrica, 16(1948), pp. 232-244.

J. von Neumann and O. Morgenstern, Theory of Games and Economic Behaviour, Princeton University Press, Princeton, 1944.

R. Niemi and H. Weisberg, 'A Mathematical Solution for the Probability of the Paradox of Voting,' Eehavioral Sciences, 1)(1968), pp. 317-323.

P. Nijkamp and W.H. Somermeyer, 'Explicating Implicit Preference Functions,' Economics of Planning, 11(1971), pp. 101-119.

H. Ninomiya, 'Some Remarks on t~e Existence of Independent Solutions for Homogeneous First Order Differential Equations,' Journal of Mathematics of Kyoto University, 13(1973), pp. 605-610.

G.H. Orcuts, H.W. Watts, J.B. Edwards, 'Data Aggregation and Information Loss,' American Economic Review, 58(1968), 4, pp. 773-787.

D. Patinkin, Money, Interest and Prices, 2nd Ed., Harper and Row, New York, 1965.

I.F. Pearce, A Contribution to Demand Analysis, Oxford, Clarendon Press, 1964.

~.H. Peston, 'A View of the Aggregation Problem,' Review of Economic Studies, 27(1959), pp. 58-64.

L. Phlips, Applied Consumption Analysis, North-Holland Publishing Company, Amsterdam, 1974.

F. Pokropp, Aggregation von Produktionsfunktionen, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1972.

F. Pokropp, 'The Functional Equation of Aggregation,' Chapter 6 of W. Eichhorn, Functional Equations in Economics, Addison-Wesley Publishing Company, London etc, 1978.

316 REFERENCES

F. Pokropp, 'Macroeconomic Production Correspondences and Consistent Aggregation,' OR Verfahren, 19B1.

P. Rietveld, Multiple Objective Decision Methods and Regional Planning, North-Holland Publishing Company, Amsterdam, 1980.

W.H. Riker, 'Arrow's Theorem and Some Exampl es of the Paradox of Voting,' in J.M. Claunch(Ed.), Mathematical Applications in Political Science, The Arnold Foundation, Dallas, 1965.

K. Ringwald, 'Optimal Aggregation in Linear Models: a Generalization,' Paper presented at the World Meeting of the Econometric SOCiety, Aix en Provence, September 1980.

J. Ritzen and D.R. Winkler, 'The Revealed Preferences of a Local Government: Black/White Disparities in Scholastic Achievement,' Journal of Urban Economics, 4(1977) pp. 310-323.

P.A. Samuelson, Foundations of Economic Analysis, Harvard University Press, Cambridge, 1966(8th ed.).

P. A. Samuelson, I Some Implications of "LineA.ri ty", I The Review of E:conomic Studies,' 1 5( 1947), pp. 88-90.

K. Sato, Production Functions and Aggregation, North-Holland Publishing Company, Amsterdam, 1975.

M. Satterthwaite, 'Strategy Proofness and Arrow's Condition: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions,' Journal of Economic Theory, 10(1975), pp. 187-217.

S. Schim van der Loeff and R. Harkema, 'A Multiperiod Revealed Preference Approach to Estimating Preference Functions under Rational Random Behaviour,' Report 7925/E, Econometric Institute, Erasmus University Rotterdam, 1979.

W. Sellekaerts, 'Optimal and Actual Policies for Price Stability and High Employment and the Canadian Price-Unemployment Cycle,' Weltwirtschaftliches Archiv, 93(1975), pp. 699-712.

A.K. Sen, Collective Choice and Social Welfare, Oliver & Boyd, Edinburgh-London, 1970.

W. Shafer and H. Sonnenschein, 'Market Demand and Excess Demand Functions,' Chapter 15 of K.J. Arrow and M.D. Intrilligator (eds.), Handbook of Mathematical Economics, vol. II, North-Holland Publishing Company, Amsterdam, 1982.

Shou ·Shan Pu, 'A Note on Macroeconomics,' Econometrica, 14(1946), pp. 299-302.

R.W. Sheppard, Theory of Cost and Production Functions, Princeton University Press, Princeton, 1970.

REFERENCES

R. Shone, Microeconomics, a Modern Treatment, Macmillan & Co Ltd, London, 197~.

R.M. Solow, 'Technical Change and the Aggregate Production Function,' Review of Economics and Statistics, 39(1957), pp. 312-320.

R. M. Solow, I Capi tal ,Labor and Income in Manufacturing, I Conference in Income and Wealth, the Behaviour of Income Shares, Princeton University Press, Princeton, 1964, pp. 101-128.

317

W.H. Somermeyert 'Interregional Income Differences in the Netherlands, I

Statistical Studies, Netherlands Central Bureau of Statistics, No. 12, 1961.

W.H. Somermeyer, Inkomensongelijkheid (Dutch, with Summary in English: Ine~uality of Incomes), Statistische en Econometrische Onderzoekingen, Netherlands Central Bureau of Statistics, No. 3, 1965.

W.H. Somermeyer, 'Delimination of the Class of Budget-Constrained Utility Maximizing Partially Linear Consumer Expenditure Functions, an Alternative Approach, I Zeitschrift flier Nationaloekonomie, 34(1974), pp. 309-326.

W.H. Somermeyer and R. Bannink, A Consumption-Savings Model and its Applications, North-Holland Publishing Company, &~sterdam,

1972.

W.H. Somermeyer and J. van Daal, 'An Alternative Derivation and a Generalisation of Nataf's Theorem,' Zeitschrift fuer Nationaloekonomie, 38(1978), pp. Nationaloekonomie, 384-401.

W.H. Somermeyer and A. Langhout, 'Shapes of Engel Curves and Demand Curves: Implications of the Expenditure Allocation Model, Applied to Dutch Data,' European Economic Review, 3(1972), pp. 351-386.

M. Sono, 'The Effect of Price Changes on the Demand and Supply of Separable Goods,' International Economic Review, 2(1961), pp. 239-271. R. Stone, 'Linear Expenditure Systems and Demand Analysis, an Application to the Pattern of British Demand,' Economic Journal, 114(1954), pp. 511-527.

R.H. Strotz, 'The Empirical Implications of a Utility Tree,' Econometrica, 25(1957), pp. 269-280.

R.H. Strotz, 'The Utility Tree - a Correction and a Further Appraisal,' Econometrtca, 27(1959), pp. 482-488.

P.A.V.B. Swamy, Statistical Inference in Random Coefficient Models, Springer, Berlin-Heidelberg-New York, 1971.

H. Theil, Linear Aggregation of Economic Relations, North-Holland

318 REFERENCES

Publishing Company, Amsterdam, 1954.

H. Theil, 'Econometric Models of Welfare Maximization,' Weltwirtschaftliches Archiv, 72(1954), pp. 60-83.

H. Theil, 'Alternative Approaches to the Aggregation Problem,' in E. Nagel, P. Suppes and A. Tarski(Ed.), Logic, Methodology and Philosophy of SCience, 1962.

H. Theil, 'On the Symmetry Approach to the Committee Decision Problem,' Managment Science, 9(1963), pp. 380-393.

H. Theil, Optimal Decision Rules for Government and Industry, North-Holland Publishing Company, Amsterdam, 1964.

H. Theil, Principles of Econometrics, North-Holland Publishing Company, Amsterdam, 1971.

H. Theil, Theory and Measurement of Consumer Demand, 1 and 2, North-Holland Publishing Company, Amsterdam, 1975-1976.

H. Theil and A.S. Goldberger, 'On Pure and Mixed Statistical Estimation in Economics,' International Economic Review, 2(1961), pp. 65-78.

J. Tinbergen, Economic Polocy: Principles and Design, North-Holland Publishing Company, Amsterdam, 1956.

G. Tintner and A. Sondermann, 'Statistical Aspects of Economic Aggregation,' in R. Henn and O. Moeschlin(Ed.), Mathematical Economics and Game Theory, Essays in Honour of Dskar Morgenstern, Springer, Berlin etc., 1977.

A.C.F. Vorst and J. van Daal, 'On Generalized Linear Demand Systems (The Case of the "Continuous" Consumer Without Money Illusion),' Paper presented at the World Meeting of the Econometric society, Aix en Provence, September 1980.

L. Walras, Elements of Pure Economics, (Translated from French by W. Jaffe), R.D. Irwin Inc., Homewood, Illinois, 1954.

J.J. Walschots, 'Errors of Aggregation: Some Simulations,' Unpublished, Econometric Institute, Erasmus University, Rotterdam, 1976.

R.E. Welsh and E. Kuh, 'The Variances of Regression Coefficients Estimates Using Aggregate Data,' Econometrica, 44(1975), pp. 353-364.

H. Wold and L. Jureen, Demand Analysis, Wiley, New York, 1953.

P. de Wolff, 'Income Elasticity of Demand, a Micro-Economic and a Macro-Economic Interpretation,' Economic Journal, 51(1941), pp. 140-145.

A. Zellner, 'On the Aggregation Problem, a New P.pproach to a Troublesome Problem, I in Estimation and Risk Programming, Essays in Honour of Gerhsrd Tintner, Springer, Berlin-Heidelberg, 1969.

AUTHOR INDEX

Ackoff, R. Akkina, K.R. Allen, K.G.D. Anderson, R.W.

272

Ando, A. 269

207 4,195

222

Armstrong, W. 89,150 Arnaiz, G. 275,276 Arrow, K.J. 8,88,89,94,98,105

106,113,117,150,151,233,280 Bannink, R. 11,245,246,249

250,252,255,258,259,260 Barbera, S. 150 Bard, Y. 242 Barnett, W.A. 151 Barten, A.P. 242,274 Bikker, J.R. 162 Black, D. 117 Blackorby, C. 211 Blau, J.H. 111 Blokland, J. 242 de Boer, P.M.C. 87,256 van den Boogaard, P.J.M.

275,276,278,279,281 Boo~, J.C.G. 194,195 Branson, W.H. 227,228 den Broeder, G. 182 Brown, M. 83 Buddenberg, F.H. Bu rkil 1 , H. 151 Bu rki 11 , J.C. 151 Carlevaro, L. 222 Chang, W.W. 83

182

274

Chossudovsky, M.J. 285,286 287,288,289,298

Churchman, W.C. 272 Condorcet, Marquis de 99 Cramer, J.S. 51,161,162,183

199 Dasgupta, A. K. Deaton, A.S. Debreu, G. De Meyer, F. Denizot, F.B. van den Doel, Driehuis, W. van Driel, J. Eckstein, W. van Eijk, C.J. Eisenberg, B. Fair, R.C. Fishburn, P. C. Fisher, F.M. Fisher, W.D.

92,93 8,11,14,236

151 104 46,303

J. 100 182,269 49,54

225 274,285

130 227

111,150,151 34,83 12

319

Friedlaender, A.F. 273 Frisch, R. 285.286 Fromm, G. 225 Garman, M. 104 Geary, R.C. 116 van der Geest, L.P.J. 285 Gibbard, A. 150 Goldberger, A. S. 294 Gorman, W.M. 41,43,44,82,115

217,218 Green, H.A.J. XII,XIII,7,26

28,40,59,91,122,150,195,212 218

Guilbaud, G.Th. 100,298 Gupta, K.L. 195 Harkema, R. 49,51,273 Hartog, J. 240 Hicks, J. 5,150,212,225 Houthakker, H.S. 5,155,168

169,170,225 Howe,H. 125,147 Huyser, A.P. 49 Ijiri, Y. 46,47,211 Johansen, L. 170,272,285,298 Jorgenson, D.W. 126 Kamien, M. 104 Kapteyn, A. 150 Keller, W.J. 163,218,239,242

263 Keynes, J.M. 66,87 Kirman, P. 112 Klahr, D. 105 Klein, L.R. 9,34,38,49,62 Klevorick, A.K. 227,228 Kloek, T. 155,178,180,182,184 Kooiman, P. 155,178,180,182 Kuh, E. 198,204,207 Kuipers, S.K. 182 Langhout, A. 222 Lau, L.J. 119,122,126 Leontief, W. 28,29,74,168,211 Levhari, D. 170 Levy-Garboua, V. 46,303 Lluch, C. 261 Louter, A.S. 119,244,255,269 Malinvaud, E. 12,14,22,179 Modigliani, F. 269 Muellbauer, J. 8,11,14,119

130,132,178,235,236,269 Muysken, J. 170,175 Nanson, E.J. 99 Nataf, A. 6,26,27,30,34,37,38

40,43,44,48,49,114,115.127

320 AUTHOR INDEX

163,232,234 Niemi, R. 105 Nijkamp, P. 273 Nijman, T.E. 272,293,294,296 Ninomiya, H. 62 Patinkin, D. 227,228 Pearce, D.W. 92,93 Pearce, I. F. 8,119,1 30,131

148,236 87

5,225 Peston, M.H. Phlips, L. Plott, C.R. Pokropp, F. Pollak, R.A. Primont, D.

104 20,41,43,44,62

125,147 211

Pu, S.S. 33 Rietveld, P. 285 Riker, W.H. 100 Ringwald, K. 303 Ritzen, J. 298 Russel, R.R. 211 Samuelson, P.A. 116 Sandee, J. 274,285 Sato, K. 155,170,172,174,175 Satterthwaite, M. 150 Schim van der Loeff, S. 49,51

273 Sellekaerts, W. 287,298 Sen, A.K. 104,105,150

Shafer, W. 130 Shephard, R.W. 87 Solow, R.M. 4 Somermeijer, W.H. 11,49,115

161,222,245,246,249,250,252 255,258,259,260,269,273

Sondermann, D. 112,303 Sonnenschein, H. 130 Sono, M. 212 Stoker, T.M. 126 Stone, R. 116 Taylor, L.D. 5,225 Theil, H. 5,6,10,64,87,165

184,188,189,193,195,210,211 236,272,275,276,277,278,280 294

Tinbergen, J. 272 Tintner, G. 303

240 289,290,291 269

125,147 262,270

105

Veenbergen, J.G. Vermaat, A.J. Vorst, A.C.F. Wales, T.J. Walschots, J.J. Weisberg, H. Welsh, R.E. de Wit, G.M. de Wolff, P. Zellner, A.

207 194,195 117,183

184

SUBJECT INDEX

aggregate income aggregation bias

231

3,227,353 1 O,184ff ,227

aggregation error 5,10,51 163ff,255,266,303

aggregation gain 10,197ff aggregation of prices 212 aggregation over goods 10

211 ff analogy 4,5,9,l19,162ff approximate aggregation 34

119,151 Arrow's conditions

233,271ff 94ff,l17

atomistic macro function 22 33,40,84

auxiliary equations 64,189 capacity distribution 170ff C.E.S. relations 25,170,218

263 Cobb-Douglas relations 24,169 collective choice 11,94ff

271ff committee decision 276,278 composite goods 10,212 Condorcet's paradox 99,280 consistent aggregation 6,7,19

20ff,119ff,154,269,301 consumer theory 11,114ff,232ff consumption function 3,227ff

257,259 convergence approach 116,167 cost-benefit analysis 93 cost function 124,126,237 De Borda rule 100ff,282,283

290 decisive 106ff demand (analysis) 8,89,113ff

225,232ff,244ff dictator 98,109 disequilibrium 177 entropy measure 122 homothcticity 71,114,130,216 income distribution 120ff,130

148,161,234,239,270 inconsistencies (of aggregation)

7,89,104,151,163ff,300 interdependency 8 leisure 262ff Leitmotiv 14 Leontief production function

43,168ff linear aggregation 10,184ff

321

linear relations 24,34,73,74 11 6 , 11 8, 1 35, 1 58, 1 59, 1 68,325 242,272,304,305

majority voting 89,98,280,281 mean, geometric 3,49,50ff,232 mean, harmonic 3,49,50ff,232 mean, unweighted 33,49 money illusion 226ff,269 Nataf's theorem see Nataf One Supporter rule 102 optimal aggregation 12,302ff Pareto principle 96,111,277

290,297 perception threshold (perfect) competition

225

90,150 83,171

planning cycle 245ff,262,269 Possibility Theorem (Arrow) 8

88,105ff,150,232,280 preferences 88,94ff,233,271ff preference function 273ff

293ff production frontier production function

155,168ff quadratic Engel curves

147,237ff

64ff,76 7,65ff

125

quasi-separable representativity

149,174,235

28ff

savings 245,250 separable functions

120,214,217,302 similarity 72,114 single-peakedness Slutsky coefficients

139ff,244 taboo 103

9, 11 9 , 1 29ff

7,23ff

117 ,151 118,131

utility 8,88ff,117,124,126 150,151,165,213,217,229 233,247,262,287

variance 3,118,131,161,167 206,236,265