Consider the mode of enquiry that involves thinking about thinking. The expansion methodology originates within it, from an analysis of the thought processes presiding upon the construction of any mathematical models of any realities. The focal point of this paper is a discussion of the relations between the expansion methodology, mathematical modeling, and spatial econometrics.
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References
1.
Allen, O. A.1990. Probability, statistics, and queueing theory with computer science applications. New York: Academic Press.
2.
Anselin, L.1988a. Lagrange multiplier test diagnostics for spatial dependence and spatial heterogeneity. Geographical Analysis20: 1-17.
3.
Anselin, L.1988b. Spatial econometrics: Methods and models. Dordrecht: Kluwer Academic.
4.
Anselin, L., ed. 1992a. Space and applied econometrics. Special Issue, Regional Science and Urban Economics22 (3).
5.
Anselin, L.1992b. SpaceStat tutorial: A workbook for using SpaceStat in the analysis of spatial data. Santa Barbara: University of California, National Center for Geographic Information and Analysis.
6.
Anselin, L.1992c. Spatial dependence and spatial heterogeneity: Model specification issues in the spatial expansion paradigm. In Applications of the expansion method, eds. J. P. Jones III and E. Casetti. New York: Routledge.
7.
Anselin, L.
, and R. Florax, eds. 1995a. New directions in spatial econometrics. Berlin: Springer-Verlag.
8.
Anselin, L.
, and R. Florax. 1995b. Small sample properties of tests for spatial dependence in regression models: Some further results. In New directions in spatial econometrics, eds. L. Anselin and R. Florax. Berlin: Springer-Verlag.
9.
Anselin, L.
, and S. Rey. 1991. Properties of tests for spatial dependence in linear regression models. Geographical Analysis23: 112-131.
10.
Burridge, P.1980. On the Cliff-Ord test for spatial autocorrelation. Journal of the Royal Statistical Society B42: 107-108.
11.
Casetti, E.1972. Generating models by the expansion method: Applications to geographic research. Geographical Analysis4: 81-91.
12.
Casetti, E.1986. The dual expansions method: An application to evaluating the effects of population growth on development. IEEE Transactions on Systems, Man, and CyberneticsSMC-16: 29-39.
13.
Casetti, E.1991. The investigation of parameter drift by expanded regressions: Generalities and a `family planning' example. Environment and Planning A23: 1045-1061.
14.
Casetti, E.1993. Spatial analysis: Perspectives and prospects. Urban Geography14: 526-537.
15.
Casetti, E.1995. Spatial mathematical modeling and regional science. Papers in Regional Science74: 3-11.
16.
Casetti, E.
, and R. K. Semple. 1969. Concerning the testing of spatial diffusion hypotheses. Geographical Analysis1: 254-259.
17.
Casetti, E.
, and S. Krakover. 1990. Spatio-temporal dynamic of the U.S. population: Estimates and extrapolations. Socio-Spatial Dynamics1: 139-159.
18.
Chow, G. C.1984. Random and changing coefficients models. In Handbook of econometrics, Vol. 2, eds. Z. Griliches and M. D. Intriligator. New York: Elsevier Science Publishers.
19.
Cressie, N.1991. Statistics for spatial data. New York: Wiley.
20.
Darnell, A. C.
, and J. L. Evans. 1990. The limits of econometrics. Hants: E. Elgar.
21.
De Marchi, N.
, and C. Gilbert, eds. 1989. History and methodology of econometrics. Oxford: Oxford University Press.
22.
Demko, G. J.
, and E. Casetti. 1970. A diffusion model for selected demographic variables: An application to Soviet data. Annals of the Association of the American Geographers60: 533-539.
23.
Fair, R. C.1984. Specification, estimation, and analysis of macroeconometric models. Cambridge: Harvard University Press.
24.
Fan, C. C.1994. The temporal and spatial dynamics of income and population growth in Ohio, 1950-1990. Regional Studies28: 241-258.
25.
Flowerdew, R.1989. Some critical views of modelling in geography. In Remodelling geography, ed. B. Macmillan. Oxford: Blackwell.
26.
Getis, A.
, and B. N. Boots. 1978. Models of spatial processes: An approach to the study of point, line, and area patterns. Cambridge: Cambridge University Press.
27.
Gilbert, C. L.1986. Professor Hendry's econometric methodology. Oxford Bulletin of Economics and Statistics48: 283-307.
28.
Granger, C. W. J.
, ed. 1990. Modeling economic series. Oxford: Oxford University Press.
Haining, R. P.1990. Spatial data analysis in the social and environmental sciences. Cambridge: Cambridge University Press.
31.
Harvey, H.1989. From models to Marx: Notes on the project to `remodel' contemporary geography. In Remodelling geography, ed. B. Macmillan. Oxford: Blackwell.
32.
Isaaks, E.
, and R. Srivastava. 1989. An introduction to applied geostatistics. Oxford: Oxford University Press.
33.
Johnston, J.1963. Econometric methods. New York: McGraw-Hill.
34.
Johnston, J.1984. Econometric methods. 3d ed.New York: McGraw-Hill.
35.
Jones, J. P., III
. 1992. Paradigmatic dimensions of the expansion method. In Applications of the expansion method, eds. J. P. Jones III and E. Casetti. New York: Routledge.
36.
Jones, J. P., III
, and R. Q. Hanham. 1995. Contingency, realism, and the expansion method. Geographical Analysis27: 185-207.
37.
Jones, K.
, and N. Bullen. 1994. Contextual models of urban house prices: A comparison of fixed- and random-coefficient models developed by expansion. Economic Geography70: 252-272.
38.
Judge, G. G.
, W. E. Griffiths, R. Carter Hill, H. Lutkepohl, and T. C. Lee. 1985. The theory and practice of econometrics. New York: Wiley.
39.
Kmenta, J.1986. Elements of econometrics. 2d ed.New York: Macmillan.
40.
Kristensen, G.
, and Z. Tkocs. 1994. The determinants of distance to shopping centers in an urban model context. Journal of Regional Science34: 425-443.
41.
Krueger, L.
, L. J. Daston, and M. Heidelberger, eds. 1987. The probabilistic revolution. 2 vols. Cambridge: MIT Press.
42.
Lucas, R. E., Jr.1976. Econometrics policy evaluations: A critique. In The Phillips curve and labor markets. eds. K. Brunner and A. H. Meltzer. Amsterdam: North-Holland.
43.
Maddala, G. S.1977. Econometrics. New York: McGraw-Hill.
44.
Morgan, M. S.1990. The history of econometric ideas. Cambridge: Cambridge University Press.
45.
Nicholls, D. F.
, and A. R. Pagan. 1985. Varying coefficient regression. In Handbook of statistics, Vol. 5, eds. E. J. Hannan, P. R. Krishnaiah, and M. M. Rao. New York: Elsevier Science Publishers.
46.
Odland, J.
, E. Casetti, and L. J. King. 1973. Testing hypotheses of polarized growth within a central place hierarchy. Economic Geography49: 74-79.
47.
Paelinck, J. H. P.
, and L. H. Klaassen. 1979. Spatial econometrics. Farnborough: Saxon House.
48.
Pagan, A. R.1987. Three econometric methodologies: A critical appraisal. Journal of Economic Surveys1: 3-24.
49.
Pandit, K.
, and S. Bagchi-Sen. 1993. The spatial dynamics of U.S. fertility, 1970-1990. Growth and Change24: 229-246.
50.
Parzen, E.1962. Stochastic processes. San Francisco: Holden-Day.
51.
Qin, D.1993. The formation of econometrics: A historical perspective. Oxford: Oxford University Press.
52.
Raj, B.
, and A. Ullah. 1981. Econometrics, a varying coefficients approach. New York: St. Martin Press.
53.
Ross, S. M.1983. Stochastic processes. New York: Wiley.
54.
Sayer, A.1984. Method in social science: A realist approach. London: Hutchinson.
55.
Sims, C. A.1980. Macroeconomics and reality. Econometrica48: 1-48.
56.
Swamy, P. A. V. B.
, R. K. Conway, and M. R. LeBlanc. 1988a. The stochastic coefficients approach to econometric modeling, Part I: A critique of fixed coefficients models. Journal of Agricultural Economics Research40,2: 2-10.
57.
Swamy, P. A. V. B.,R. K. Conway
, and M. R. LeBlanc. 1988b. The stochastic coefficients approach to econometric modeling, Part II: Description and motivation. Journal of Agricultural Economics Research40, 3: 21-30.
58.
Swamy, P. A. V. B.
, R. K. Conway, and M. R. LeBlanc. 1989. The stochastic coefficients approach to econometric modeling, Part III: Estimation, stability testing, and prediction. Journal of Agricultural Economics Research41, 1: 4-20.
59.
Swamy, P. A. V. B.
, R. K. Conway, and P. von zur Muehlen. 1985. The foundations of econometrics—Are there any?Econometric Reviews4: 1-61.
60.
Taylor, H. M.
, and S. Karlin. 1984. An introduction to stochastic modeling. Orlando: Academic Press.
61.
Thrall, G. I.
, and J. G. Tsitanidis. 1983. A model of the change, attributable to government health insurance plans, in location patterns of physicians, with supporting evidence from Ontario, Canada. Environment and Planning C1: 45-55.
62.
Todd, R. M.1984. Improving economic forecasting with Bayesian vector autoregression. Federal Reserve Bank of Minneapolis Quarterly Review8, 4: 18-29.
63.
Uyanga, J.1977. Testing formal polarization of growth in spatial context. Nigerian Geographical Journal20: 145-151.
64.
Zhang, J.,
and G. Kristensen. 1995. A gravity model with variable coefficients: The EEC trade with third countries. Geographical Analysis27: 307-320.