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BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC KINH TẾ Tp.HCM …………………………… SOUK SOPHAL URBAN EXPANSION THE EFFECT OF ECONOMIC GROWTH ON URBANIZATION IN VIETNAM LUẬN VĂN THẠC SĨ KINH TẾ TP Hồ Chí Minh-Năm 2013 BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC KINH TẾ Tp.HCM …………………………… SOUK SOPHAL URBAN EXPANSION THE EFFECT OF ECONOMIC GROWTH ON URBANIZATION IN VIETNAM Chuyên ngành: Kinh tế phát triển Mã số: 60310105 LUẬN VĂN THẠC SĨ KINH TẾ NGƯỜI HƯỚNG DẪN KHOA HỌC: Dr Nguyễn Lưu Bảo Đoan TP Hồ Chí Minh-Năm 2013 ACKNOWLEDGEMENTS Firstly, I would like to take this opportunity to thanks my Advisor Dr Nguyễn Lưu Bảo Đoan for his guidance during the process of researching and writing this thesis He was supportive of helping me to successfully complete this thesis It would not have been possibly written without his help I am very fortunate to have him as my master’s thesis supervisor I would also like to express my profound thanks to Dr.Pham Khanh Nam for his help in collecting Vietnam data Special thanks to Dr.Nguyen Huu Dung, Deputy Dean at the University of Economics HoChiMinh City I would like to thanks my family and my good friends for always encouraging me to think and supporting me spiritually throughout my life Finally, I would like to dedicate this work to my lost relatives and I hope that this work makes them proud HoChiMinh City, December 15, 2013 SOUK SOPHAL i Abstract Urbanization is a major change taking place globally, especially in Southeast Asia which is one of the world’s fast growing regions in terms of population and urban growth The total population in Southeast Asia accounts for 14.64 per cents of Asia’s population Meanwhile, urbanization is also increasingly taking place in many cities in Southeast Asia Phnom Penh is the capital of Cambodia with an estimated population of 2.3 million by 2013, with the area of 678.46 square kilometers Recently, the development in the economy has impacts on the growth of Phnom Penh Capital The demand for more living spaces has increased so it lead to unplanned urbanization and industrialization in the outer periphery of Phnom Penh Capital, which, has created pressure on the change in land use pattern Therefore, it is important to study impacts of different factors on urban expansion However, the absence of data for Phnom Penh does not make a regression analysis possible Thus, the study employs available data of cities and provinces in Vietnam, a country which has a similar economic structure and level of development In this paper, the overall goals are to examine the change in population, GDP, agricultural investment and other that lead to the urban spatial growth and, the expansion of urbanized areas Based on the Monocentric model and panel analysis, the result shows that population, agricultural investment, industrialization and GDP are major pushing factors in the processing of urban expansion The analysis demonstrates the overwhelming importance of economic growth in the determination of urban land use This study examines the effect of economic growth on urbanization in Vietnam Based on this information, a case study analysis of Cambodia and Phnom Penh is also conducted Keywords: economic growth, monocentric model, urban expansion, land use ii Table of Contents ACKNOWLEDGEMENTS i ABSTRACT ii LIST OF ABBREVIATION LIST OF TABLES LIST OF FIGURES Chapter : Introduction…………………………………………………………… 1.1 Research problem……………………………………………………… 1.2 Research Objective………………………………………………………2 1.3 Research Question……………………………………………………….3 1.4 Scope and Methodology of Research……………………………………3 1.5 Research Structure ………………………………………………………3 Chapter 2: Urbanization in Vietnam……………………………………………… 2.1 The overview of the study area………………………………………… 2.2 Urbanization in Vietnam………………………………………………….7 Chapter 3: Literature Review…………………………………………………… 12 3.1 Theoretical Literature Review of Monocentric…………………………12 3.2 The Monocentric model……………………………………………… 13 3.3 Empirical Study… …………………………………………………….16 3.4 Analytic Framework……………………………………………………19 Chapter 4: Data and Methodology……………………………………………… 21 4.1 Data Source…………………………………………………………… 21 4.2 Data Description……………………………………………………… 22 4.3 Research Method ……………………………………………… 23 4.4 Analysis Method…………….………………………………………… 24 Chapter 5: Result and Discussion…………………………………………………26 5.1 Descriptive Analysis……………………………………………………26 5.2 Empirical Result….…………………………………………………… 33 Chapter 6: A Case Study about Cambodia and Phnom Penh …………………… 37 6.1 Overview of urbanization in Cambodia……………………………… 37 6.2 Overview of urbanization in Phnom Penh………………………………40 Chapter 7: Discussion 7.1 Explaination of differences between theory and my analysis… 46 7.2 Limitations of this analysis…………………………………… 46 Chapter 8: Conclusion……………………………… 48 REFERENCES APPENDIX LIST OF ABBREVIATION CBD Central Business District FEM Fixed Effect Model GDP Gross Domestic Product GSO General Statistics Office IND Industrialization SVS Service Sector REM Random Effect Model LIST OF TABLES Table 3.3.1 The proxies and list studies of independent variables………………….17 Table 5.1.1 Descriptive Statistics………………………………………………… 25 Table 5.1.2 Correlation test…………………………………………………………26 Table 5.1.3 Multicolinearity test……………………………………………………27 Table 5.1.4 Normality test………………………………………………………….27 Table 5.2.1 Estimation result……………………………………………………….31 Table 5.2.1.1 Heteroskedasticity test…………………………………………………33 LIST OF FIGURES Figure 2.1.1 Expansion of city boundaries between 1999 and 2009 … Figure 2.1.2 Urbanization rate 1960-2010…………………………………………8 Figure 3.1 PLUREL concept of peri-urban areas and rural- region…………… 12 Figure 3.2 Dimension of regional urban form …………………………………13 Figure 5.1.5 Graph of changes in urbanized land across the country………… ….28 Figure 5.1.6 Graph of explanation for changes of province &cities …………… 30 Figure 6.1 Phnom Penh map by districts………………………………………… 39 Figures 6.2 Planning of city development………………….……………………….41 CHAPTER 1: INTRODUCTION 1.1 Research problem One of the most remarkable changes over the centuries is urbanization, or the shift from rural areas to large cities Urbanization has had important consequences in many aspects of social, political, and economic life (Kleniewski & Thomas, 2011) Kleniewski, N., & Thomas, A R (2011) The world remained largely rural until the industrialization of the nineteenth century Urbanization is a major change taking place globally, especially in Southeast Asia Between the 1870s and World War II, a few dominant Southeast Asian urban centers such as Yangoon (Myanmar), Malaya (Singapore), Bangkok (Thailand), Saigon (Vietnam) and Manila (Philippines) were ports of Western and the gateways that connected the frontier southeast Asia to the global economy (Gregg Huff, 2012) The study of urbanization is very necessary for developing countries because these countries are in the process of facing with rapid urbanization Urbanization is the process which leads to a higher proportion of total population of an area living in cities and towns and generally occurs with modernization and industrialization Moreover, modernization and industrialization pull people to cities at the same time that they push people from rural home And when more and more people leave villages and farms to live in cities, it is the results of urban growth According to experiences of most part of the world, urbanization is part of the development process Rapid urbanization is closely linked to economic development that is contributed with the rising demand of land in manufacturing and service sector in urban and the decline of agricultural land in rural Urbanization occurs as countries shift from rural agricultural activities into urban industrial activities Successful urbanization requires the expansion of the industrial and service sector (Parker, 1996) Similarly, urban expansion mainly depends upon the urban requirement, facilities available and industrialization The development of cities plays a very important role in economic development in developing countries The major dynamic driving forces of cities in developing countries are economic and social http://2012books.lardbucket.org/books/a-primer-on-social-problems/s17-01-a-brief-history-ofurbanizatio.html  Centralization of urban infrastructure development and finance, given limited staff and financial resources of the newly established municipalities  Improvement of urban management capacity and good urban governance Therefore, it is very important to study the trend of urban expansion and to estimate for the future I believe that the study of urbanization in Phnom Penh is a major contribution to the development of Cambodia and especially is an achievement of master plan Phnom Penh city in 2020 45 CHATER 7: DISCUSSION 7.1 Explanation of the difference between theory and my analysis After my analysis, I observe that the result of my analysis is consistent with Monocentric theory condition except the agricultural rent In my model, agricultural rent is replaced by agricultural investment (Wei.1993, Deng et al 2008) It means that when the agricultural investment increases, more land will be urbanized It is different from the theory of monocentric city which predicts that less land will be urbanized I think this is because speculation of agricultural land takes place in Vietnam; people still buy more agricultural land to urbanize it Here agricultural investment is the investment in agricultural land by construction infrastructures and so on for convert agricultural land into urban land 7.2 Limitation of this analysis Although this thesis reaches several new findings, it also has several limitations in assumptions, methods, dataset and discussions  Limitations of assumptions The study assumes the same definition of urban expansion land This assumption is not really exactly like that in real life In fact, implementation of Monocentric model in urban economics and verify with conditions13 And many of researchers found some points different from the assumption In reality, we cannot identify which part of the city is the center of business district (CBD) In addition, there are more factors that push the urban expansion land  Limitations of method It is very clearly that the empirical researches have used methods to estimate the effect of the economic growth on urban expansion land such as OLS, First –Difference model (fixed effect model) However, based on the nature of dataset and the goals of research, this study uses only one of these methods that is fixed effect method and does not apply other methods 13 See page 15 46 Based on the monocentric model and empirical researches and the nature of dataset, the research just applies the log linear form on some variables except service and industrialization variables  Limitations of dataset First, the study covers 63 selected cities and provinces of Vietnam, because of lack of dataset I decide to drop three provinces including Hoa Binh, Hau Giang,Lai Chau from my analysis Second, the study just considers one kind of measure independent variable urban land use that it is from the sum of housing land and non-agricultural land use and does not covers all the 26 kinds of land use in Vietnam Third, the dataset sample just takes into account 11 years period from 2000 to 2011 and unbalanced panel data The result from my regression is not surely correct because of the missing of data in my analysis Fourth, urban expansion in cities and in provinces happens in different periods of time, which makes my estimation not accurate Fifth, the study does not separate the region of country There are regions in Vietnam By using fixed effect model, the result of this analysis is omitted all dummy variables Therefore, it is impossible to conclude which one of cities and provinces tends to be urbanized  Limitations of discussion Even though, the study has mentioned about the monocentric model, finding and discussion of number of researches in regional and urban economics, it cannot cover really abundant evidences from urban studies and urban expansion studies 47 CHAPTER 8: CONCLUSION Urbanization has an important role to play in developing countries on economic development of any nation such as Vietnam and Cambodia This paper demonstrates the effect of economic growth on urbanization in Vietnam This study focuses on the close relation between urban land expansion and economic growth Following this empirical analysis study, it shows that population GDP, and agricultural investments have positive effects on urban land expansion in Vietnam To investigate the determinant of Vietnam’s urban land expansion, this paper has estimated from the empirical study The dependent variables (sum of residential land and non agricultural land) of empirical study and taken all data such as GDP, population, agricultural investment (sum of all budget investment project every year) ,industrialization (GDP1_share) and service sector (GDP2_share) for all provinces expect Hoa Binh, Hau Giang ,Lai Chau because of the missing data The empirical estimates use annual data from 2000 to 2011 By using result from the fixed effect method, this paper demonstrates the powerful role that population has played in Vietnam’s economy including urban expansion in each cities and provinces It shows that people move from rural to urban area increasingly In developing countries, population is growing faster in urban areas Moreover, regardless of empirical approach I also found that the role of the other factors such as GDP and agricultural investment are relatively small in Vietnam It means that GDP and agricultural investment have fewer effects on urban expansion If my result is correct, this suggests that if Vietnam continues to expansion urban land, Vietnam have to increase the rate of GDP growth, more agricultural investment because they are major factors that push the urban land expansion In 2025, Vietnam expects to become a middle income country and 50 per cent urbanized In a case study of Phnom Penh Capital, I believe that the result of analysis in Phnom Penh will be similar to Vietnam Because of Vietnam and Cambodia are in the process of facing rapid urbanization and both countries have a similar level of economics Following this empirical study of Vietnam, I think that Cambodia will get profit from urbanization but not much because my country still have a lot poor urban and low income people In the future, Phnom Penh will develop if we can increase the growth 48 of GDP every year and government should increase the investment in agriculture: because economic growth contributes in the processing of Urbanization in Phnom Penh It will give more and more profit for all people in Phnom Penh and also people living in Cambodia Meanwhile, Setting up the satellite cities, skyscraper and residential in Phnom Penh will push the GDP growth, population growth and urban expansion land Moreover, new urban areas will give Cambodian people a better way of living in the future In the near future, I think that Phnom Penh will become a small metropolitan in Asia 49 REFERENCES Alonso,W.(1964) Location and Land Use Cambridge, MA: Harvard University Press Anas, A & Kim, I 1996, 'General Equilibrium Models of Polycentric Urban Land Use with Endogenous Congestion and Job Agglomeration', Journal of Urban Economics, vol 40, no 2, pp 232-256 Anton Parlow(2010), Panel Data Analysis in Stata Bertaud, A 2003, The Spatial Organization of Cities: Deliberate Outcome or Unforeseen Consequence? World Development Report 2003: Dynamic Development in a Sustainable World,World Bank Bruecker, and D.A Fansler(1983), The economics of urban Sprawl: Theory and Evidence on the spatial sizes of cities The Review of economics and statistics 63, 479-482 Bruecker and David A Fansler (1983), The Economics of Urban Sprawl: Theory and Evidence on the Spatial Sizes of Cities, Notes Burchfield M., Overman H.G, Puga D and Turner M.A (2006) Cause of sprawl : a portrait from space, Quarterly Journal of Economics, 121 (2),pp.587-633 Bryant CR, Russwurm LH, McLellan AG (1982) The city’s countryside: land and its management in the rural–urban fringe Longman, New York Champion A (1999) Urbanization and counter-urbanization In: Pacione M (ed) Applied geography.Principle and practice Routledge, London, pp 347–357 Chen,Solon (2004), Infrastructure after Rapid Urbanization: Phnom Penh, Cambodia Chhay Rithisen and Eric Huybrechts (2007), Master Plan of Phnom Penh by 2020 D.T.McGrath (2005), More evidence on the spatial scale of cities Journal of Urban Economics 58,1-10 Daniel Gat (2005), Mono-Centric Urban Model including the switch from Mono to Poly-Centric, Annual Meeting of the Israeli Regional Science Association at Haifa University Deng X., Huang J., Rozell,S and Uchida E (2008) Growth population and industrialization and urban land expansion of China, Journal of Urban Economics, 63(1),pp 96-115 Ding C (2007), Urban Spatial Planning: Theory, Method and Pratice, Higher Education Press, Beijing Dong Lin, Andrew Allan, Jianqiang Cui and Ralph McLaughlin, The Effect of Polycentric Development on Commuting Patterns in Metropolitan Areas Fujita, M, Krugman, PR & Venables, AJ 2001, The Spatial Economy: Cities, Regions and International Trade, MIT Press, Cambridge, MA Gabriel M Ahlfeldt and Nicolai Wendland (2010), How polycentric is a monocentric city? The role of agglomeration economies Garreau J (1991) Edge city: life on the new frontier Doubleday, New York Gallent N, Andersson J, Bianconi M (2006) Planning on the edge: the context for planning at the rural–urban fringe Routledge, Abingdon Gregg Huff (2012) Gateway cities and Urbanization in Southeast Asia before World War II, Discussion papers in Economic and Social History Hun Myoung Park (2011), Practical guides to Panel Data Modeling: A Step by Step Analysis Using Stata Ingram, GK 1997, Patterns of Metropolitan Development: What Have We Learned? World Bank Operations Evaluation Development (OED) Joe Ravetz, Christian Fertner,(2013) and Thomas Sick Nielsen, The Dynamics of Peri-Urbanization (Chapter 2) Kurt Paulsen (2012), Yet even more evidence on the spatial size of cities: Urban spatial expansion in the US, 1980-2000, Regional Science and Urban Economic 42, pp 561-568 Leontidou L, Couch C (2007) Urban sprawl and hybrid city-scapes in Europe: comparisons, theory construction and conclusions In: Couch C, Leontidou L, Petschel-Held G (eds) Urban sprawl in Europe: landscapes, land-use change and policy Blackwell, Oxford Loibl W, Toetzer T (2003) Modelling growth and densification processes in sub-urban regions –simulation of landscape transition with spatial agents Environ Modell Softw 18(2003):553–563 McMillen (2006) Testing for monocentric city In R Arnott and Daniel P McMillen (Eds.), A Companion to Urban Economics (pp 128-140) Malden, MA: Blackwell Publishing Mills, Edwin S (1967) An Aggregative Model of Resource Allocation in a Metropolitan Area, American Economic Review: Papers and Proceedings, 57, 197-210 Mills (1972) Studies in the Structure of the Urban Economy,Baltimore, MD: The Johns Hopkins Press Muth, Richard F (1969) Cities and Housing Chicago: The University of Chicago Press Parker, H.W.(1996) Tunneling urbanization and sustainable development : the infrastructure connection, Tunneling and Underground Space Technology, 11(2), pp.133-134 Robert W Wassmer (2006), The Influence of Local Urban Containment Policies and Statewide Growth Management on the Size of United States Urban Areas, Journal of Regional Science, Vol 46, No 1, pp 25-65 Seto, K.C and Kaufmann C.(1993) Modeling the drivers of urban land use change in the Pearl River Delta, China: integrating remote sensing with socioeconomic data, Land Economics, 79,pp.106-121 Spivey, C., 2008 The Mills–Muth model of urban spatial structure: surviving the test of time? Urban Studies 45 (2), 295–312 Srer Khmer (2007), Phnom Penh Urban Case Study Report (Final Draft), Submitted to: FAO Headquarter, Rome, Italy Stata Web Book, Regression with Stata, Chapter 2- Regression Diagnostics Xiangzheng Deng, Jikun Huang, Scott Rozelle and Emi Uchida (2010), Economic Growth and the Expansion of Urban Land in China, Urban Studies, 47(4),pp 813-843 Xiangzheng Deng, Jikun Huang, Scott Rozelle and Emi Uchida (2006), Growth Population and Industrialization and Urban Land Expansion of China, Wei Y.(1993) Urban land use transformation and determinants of urban land use size in China, GeoJournal, 30(4),pp 435-440 Wheaton, W (1974) , A Comparative Static Analysis of Urban Spatial Structure, Journal of Economic Theory 43, 258-272 World Bank Vietnam No (2012), Vietnam Urban Briefs World Bank (2011)*, Vietnam Urbanization Review, Technical Assistance report World Bank (2011) Vietnam needs to seize its urbanization opportunities to become a middle income country, APPENDIX sum y x1 x2 x3 x4 x5 Variable | Obs Mean Std Dev Min Max -+ -y| 375 10.87592 5035581 9.646658 12.24496 x1 | 519 15.95815 1.545846 13.21458 22.75198 x2 | 516 7.066919 5554301 x3 | 395 11.1684 1.725551 6.162599 17.84311 x4 | 519 3515081 37122 5.7 8.9 000202 4.795003 -+ -x5 | 519 3543324 2843821 000396 5.21313 xtreg y x1 x2 x3 x4 x5, i(province) fe Fixed-effects (within) regression Number of obs Group variable: province = 266 Number of groups = R-sq: within = 0.5153 60 Obs per group: = between = 0.5334 avg = overall = 0.5513 4.4 max = F(5,201) corr(u_i, Xb) = -0.6765 = Prob > F 42.73 = 0.0000 -y| Coef Std Err t P>|t| [95% Conf Interval] -+ -x1 | 1632232 036357 4.49 0.000 0915331 2349133 x2 | 8574721 1396683 6.14 0.000 5820691 1.132875 x3 | 063796 0097878 6.52 0.000 0444961 x4 | 0615622 0483756 1.27 0.205 -.0338265 1569509 x5 | 0658113 0991927 0.66 0.508 -.1297805 2614032 _cons | 1.53974 9798134 1.57 0.118 0830959 -.3922924 3.471771 -+ -sigma_u | 4286614 sigma_e | 14851996 rho | 89282198 (fraction of variance due to u_i) -F test that all u_i=0: F(59, 201) = 16.10 Prob > F = 0.0000 *(7 variables, 519 observations pasted into data editor) xtset province year panel variable: province (unbalanced) time variable: year, 2000 to 2011, but with gaps delta: unit xtreg y x1 x2 x4 x5, fe Fixed-effects (within) regression Number of obs Group variable: province = Number of groups = R-sq: within = 0.5113 Obs per group: = between = 0.4156 avg = overall = 0.3861 6.3 max = F(4,311) corr(u_i, Xb) = -0.8287 = Prob > F 81.35 = 0.0000 -y| Coef Std Err t P>|t| [95% Conf Interval] 375 60 -+ -x1 | 3385248 0256204 13.21 0.000 2881135 388936 x2 | 8738338 1227672 7.12 0.000 6322744 1.115393 x4 | 1186559 052575 2.26 0.025 0152083 2221035 x5 | 0695096 0663919 1.05 0.296 -.0611245 _cons | -.7467651 8402433 -0.89 0.375 2001437 -2.400045 9065153 -+ -sigma_u | 62801953 sigma_e | 17841309 rho | 92532083 (fraction of variance due to u_i) -F test that all u_i=0: F(59, 311) = 20.11 Prob > F = 0.0000 reg y x1 x2 x3 x4 x5 Source | SS df MS Number of obs = -+ -Model | 34.8694524 F( 5, 260) = 71.43 6.97389048 Prob > F Residual | 25.3850241 260 097634708 -+ 266 = 0.0000 R-squared = 0.5787 Adj R-squared = 0.5706 Total | 60.2544765 265 227375383 Root MSE = 31247 -y| Coef Std Err t P>|t| [95% Conf Interval] -+ -x1 | 0422334 0169139 2.50 0.013 0089277 075539 x2 | 5487525 0405802 13.52 0.000 4688448 6286602 x3 | 0699291 0119211 5.87 0.000 046455 0934033 x4 | 052678 0678276 0.78 0.438 -.0808835 1862394 x5 | -.1801898 1294608 -1.39 0.165 _cons | 5.693477 2980829 19.10 0.000 -.4351149 5.106513 0747353 6.280441 The F statistic= 71.43, with a p value of 0.0000 we can reject the null of homoskedasticity This may be because our assumed form for the error variance is incorrect, or the model is mis-specified Fixed Effect Model (FEM) R-sq: within = 0.5153 Obs per group: = between = 0.5334 avg = overall = 0.5513 4.4 max = F(5,201) corr(u_i, Xb) = -0.6765 Std Err = In this case Prob>F =0.0000 F t P>|t| = 0.0000 y Coef [95% Conf Interval] x1 1632232 036357 4.49 0.000 0915331 2349133 x2 8574721 1396683 6.14 0.000 5820691 1.132875 x3 063796 0097878 6.52 0.000 0444961 0830959 x4 0615622 0483756 1.27 0.205 -.0338265 1569509 x5 0658113 0991927 0.66 0.508 -.1297805 2614032 _cons 1.53974 9798134 1.57 0.118 -.3922924 3.471771 sigma_u 4286614 sigma_e 14851996 rho 89282198 (fraction of variance due to u_i) F test that all u_i=0: F(59, 201) = 16.10 Prob > F = 0.0000 Random Effect Model (REM) R-sq: within = 0.4878 between = 0.5715 overall = 0.5725 Obs per group: = avg = max = 4.4 Wald chi2(5) corr(u_i, X) = (assumed) = 254.87 Prob > chi2 Std Err z 0.0000 y Coef x1 0733248 0227069 3.23 0.001 02882 x2 5715573 0674246 8.48 0.000 4394075 7037071 x3 0773032 0088116 8.77 0.000 0600328 0945736 1.51 0.131 -.0215872 x4 0725657 x5 -.0445144 0930171 _cons 0480381 4.890654 481144 sigma_u 27213457 sigma_e 14851996 rho P>|z| = [95% Conf Interval] 1178295 1667186 -0.48 0.632 -.2268247 1377958 10.16 0.000 3.947629 5.833679 7705032 (fraction of variance due to u_i) Hausman test (FEM vs REM) (b) (B) fixed (b-B) random sqrt(diag(V_b-V_B)) Difference S.E x1 1632232 0733248 0898984 0283941 x2 8574721 5715573 2859148 1223158 x3 063796 0773032 -.0135072 0042611 x4 0615622 0725657 -.0110035 0057044 x5 0658113 -.0445144 1103258 0344529 b = consistent under Ho and Ha; obtained from xtreg B = inconsistent under Ha, efficient under Ho; obtained from xtreg Test: Ho: difference in coefficients not systematic chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 18.58 Prob>chi2 = 0.0023 (V_b-V_B is not positive definite) Here Prob>chi2= 0.0023

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