This page intentionally left blank Real Estate Modelling and Forecasting As real estate forms a significant part of the asset portfolios of most investors and lenders, it is crucial that analysts and institutions employ sound techniques for modelling and forecasting the performance of real estate assets. Assuming no prior knowledge of econometrics, this book introduces and explains a broad range of quantitative techniques that are relevant for the analysis of real estate data. It includes numerous detailed examples, giving readers the confidence they need to estimate and interpret their own models. Throughout, the book emphasises how various statistical techniques may be used for forecasting and shows how forecasts can be evaluated. Written by a highly experienced teacher of econometrics and a senior real estate professional, both of whom are widely known for their research, Real Estate Modelling and Forecasting is the first book to provide a practical introduction to the econometric analysis of real estate for students and practitioners. Chris Brooks is Professor of Finance and Director of Research at the ICMA Centre, University of Reading, United Kingdom, where he also obtained his PhD. He has published over sixty articles in leading academic and practitioner journals, including the Journal of Business,theJournal of Banking and Finance,theJournal of Empirical Finance,theReview of Economics and Statistics and the Economic Journal. He is associate editor of a number of journals, including the International Journal of Forecasting. He has also acted as consultant for various banks and professional bodies in the fields of finance, econometrics and real estate. He is the author of the best-selling textbook Introductory Econometrics for Finance (Cambridge University Press, 2009), now in its second edition. Sotiris Tsolacos is Director of European Research at Property and Portfolio Research, a CoStar Group company. He has previously held positions with Jones Lang LaSalle Research and the University of Reading, where he also obtained his PhD. He has carried out extensive research work on modelling and forecasting real estate markets, with over forty papers published in major international real estate research and applied economics journals. He is also a regular commentator on topical themes in the real estate market, with numerous contributions to practitioner journals. Real Estate Modelling and Forecasting Chris Brooks ICMA Centre, University of Reading Sotiris Tsolacos Property and Portfolio Research CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK First published in print format ISBN-13 978-0-521-87339-0 ISBN-13 978-0-511-67751-9 © Chris Brooks and Sotiris Tsolacos 2010 2010 Information on this title: www.cambrid g e.or g /9780521873390 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Published in the United States of America by Cambridge University Press, New York www.cambridge.org eBook ( NetLibrar y) Hardback Contents List of figures page x List of tables xii List of boxes xiv Preface xv Acknowledgements xix 1 Introduction 1 1.1 Motivation for this book 2 1.2 What is econometrics? 3 1.3 Steps in formulating an econometric model 4 1.4 Model building in real estate 5 1.5 What do we model and forecast in real estate? 6 1.6 Model categorisation for real estate forecasting 8 1.7 Why real estate forecasting? 9 1.8 Econometrics in real estate, finance and economics: similarities and differences 12 1.9 Econometric packages for modelling real estate data 13 1.10 Outline of the remainder of this book 15 Appendix: Econometric software package suppliers 20 2 Mathematical building blocks for real estate analysis 21 2.1 Introduction 21 2.2 Constructing price index numbers 21 2.3 Real versus nominal series and deflating nominal series 29 2.4 Properties of logarithms and the log transform 32 2.5 Returns 33 2.6 Matrices 34 2.7 The eigenvalues of a matrix 38 v vi Contents 3 Statistical tools for real estate analysis 41 3.1 Types of data for quantitative real estate analysis 41 3.2 Descriptive statistics 44 3.3 Probability and characteristics of probability distributions 54 3.4 Hypothesis testing 55 3.5 Pitfalls in the analysis of real estate data 65 4 An overview of regression analysis 72 4.1 Chapter objectives 72 4.2 What is a regression model? 73 4.3 Regression versus correlation 74 4.4 Simple regression 74 4.5 Some further terminology 79 4.6 Linearity and possible forms for the regression function 85 4.7 The assumptions underlying the classical linear regression model 86 4.8 Properties of the OLS estimator 87 4.9 Precision and standard errors 88 4.10 Statistical inference and the classical linear regression model 93 Appendix: Mathematical derivations of CLRM results for the bivariate case 104 4A.1 Derivation of the OLS coefficient estimator 104 4A.2 Derivation of the OLS standard error estimators for the intercept and slope 105 5 Further issues in regression analysis 108 5.1 Generalising the simple model to multiple linear regression 108 5.2 The constant term 109 5.3 How are the parameters (the elements of the β vector) calculated in the generalised case? 111 5.4 A special type of hypothesis test: the t-ratio 113 5.5 Goodness of fit statistics 115 5.6 Tests of non-nested hypotheses 119 5.7 Data mining and the true size of the test 123 5.8 Testing multiple hypotheses: the F -test 124 5.9 Omission of an important variable 129 5.10 Inclusion of an irrelevant variable 130 Appendix: Mathematical derivations of CLRM results for the multiple regression case 133 5A.1 Derivation of the OLS coefficient estimator 133 5A.2 Derivation of the OLS standard error estimator 134 Contents vii 6 Diagnostic testing 135 6.1 Introduction 135 6.2 Violations of the assumptions of the classical linear regression model 136 6.3 Statistical distributions for diagnostic tests 136 6.4 Assumption 1: E(u t ) = 0 137 6.5 Assumption 2: var(u t ) = σ 2 < ∞ 138 6.6 Assumption 3: cov(u i ,u j ) = 0 for i=j 144 6.7 Causes of residual autocorrelation 152 6.8 Assumption 4: the x t are non-stochastic (cov (u t ,x t ) = 0) 166 6.9 Assumption 5: the disturbances are normally distributed 167 6.10 Multicollinearity 171 6.11 Adopting the wrong functional form 175 6.12 Parameter stability tests 178 6.13 A strategy for constructing econometric models 186 Appendix: Iterative procedures for dealing with autocorrelation 191 7 Applications of regression analysis 194 7.1 Frankfurt office rents: constructing a multiple regression model 194 7.2 Time series regression models from the literature 210 7.3 International office yields: a cross-sectional analysis 214 7.4 A cross-sectional regression model from the literature 222 8 Time series models 225 8.1 Introduction 225 8.2 Some notation and concepts 226 8.3 Moving average processes 230 8.4 Autoregressive processes 231 8.5 The partial autocorrelation function 234 8.6 ARMA processes 235 8.7 Building ARMA models: the Box–Jenkins approach 241 8.8 Exponential smoothing 244 8.9 An ARMA model for cap rates 246 8.10 Seasonality in real estate data 251 8.11 Studies using ARMA models in real estate 257 Appendix: Some derivations of properties of ARMA models 261 8A.1 Deriving the autocorrelation function for an MA process 261 8A.2 Deriving the properties of AR models 263 9 Forecast evaluation 268 9.1 Forecast tests 269 viii Contents 9.2 Application of forecast evaluation criteria to a simple regression model 274 9.3 Forecast accuracy studies in real estate 290 10 Multi-equation structural models 303 10.1 Simultaneous-equation models 304 10.2 Simultaneous equations bias 306 10.3 How can simultaneous-equation models be estimated? 307 10.4 Can the original coefficients be retrieved from the πs? 308 10.5 A definition of exogeneity 310 10.6 Estimation procedures for simultaneous equations systems 313 10.7 Case study: projections in the industrial property market using a simultaneous equations system 316 10.8 A special case: recursive models 322 10.9 Case study: an application of a recursive model to the City of London office market 322 10.10 Example: a recursive system for the Tokyo office market 325 11 Vector autoregressive models 337 11.1 Introduction 337 11.2 Advantages of VAR modelling 339 11.3 Problems with VARs 340 11.4 Choosing the optimal lag length for a VAR 340 11.5 Does the VAR include contemporaneous terms? 342 11.6 A VAR model for real estate investment trusts 344 11.7 Block significance and causality tests 347 11.8 VARs with exogenous variables 352 11.9 Impulse responses and variance decompositions 352 11.10 A VAR for the interaction between real estate returns and the macroeconomy 357 11.11 Using VARs for forecasting 362 12 Cointegration in real estate markets 369 12.1 Stationarity and unit root testing 369 12.2 Cointegration 382 12.3 Equilibrium correction or error correction models 385 12.4 Testing for cointegration in regression: a residuals-based approach 387 12.5 Methods of parameter estimation in cointegrated systems 388 12.6 Applying the Engle–Granger procedure: the Sydney office market 390 [...]... principles of model building in real estate; ● explain the relationships and variables researchers most frequently model and forecast in the real estate market; ● broadly categorise quantitative and qualitative forecasting approaches; ● understand the objectives and usage of modelling and forecasting work; and ● compare the characteristics of real estate data with those of economic and financial data; ● you... real estate and the forecasting process draw upon the general subjects of econometrics and economic forecasting This chapter also touches on issues relating to the construction of general forecasting models with direct implications for real estate practice 1 2 Real Estate Modelling and Forecasting 1.1 Motivation for this book The complexity of the real estate market, its linkages to the economy and. .. market and developments that might make real estate more attractive in relation to other assets They would like to know what 10 Real Estate Modelling and Forecasting future economic and real estate market conditions will mean for investment transactions Developers would like to have estimates for future demand, rents and prices Investors with loan portfolios, including those secured on real estate, demand... We can define real estate econometrics as the application of statistical techniques to problems in the real estate market Econometrics applied to real estate is useful for testing alternative theories of market adjustments, for determining income and returns, for examining the effect on real estate markets of changes in economic conditions, for studying the 4 Real Estate Modelling and Forecasting Figure... real estate is therefore appropriate The present book aims to address this need by focusing on the key econometric methodologies that will facilitate quantitative modelling in the real estate market and help analysts to assess the empirical support for alternative a priori arguments and models In real estate courses at universities, modelling and forecasting analysis is now introduced A number of real. .. models are We focus on the areas that really matter in real estate modelling and forecasting and that have not been addressed due to the lack of such a textbook For example, forecast evaluation and judgemental forecasting are topics with limited treatment in the real estate context The book also highlights more advanced techniques and illustrates how these can be used for forecasting; most existing studies... econometric modelling and forecasting in the real estate field The book tackles key themes in applied quantitative research in real estate and provides the basis for developing forecast models for this market This chapter sets the scene for the book It describes the rationale for this text and highlights the business areas in which real estate modelling is important The econometric study of relationships in real. .. rent or net operating income and yields (4) Total returns This is the sum of income and capital returns 1.6 Model categorisation for real estate forecasting Real estate forecasting is in many respects not that different from economic forecasting, and the techniques used are similar We summarise forecast approaches that can be used in real estate in figure 1.2 The left-hand panel of figure 1.2 summarises... relationships through time and across real estate sectors and locations, with the ultimate goal of forecasting the market Quantitative work in real estate markets is now sizeable and has brought challenges As real estate analysts are exposed to such work, there is an eagerness to understand the principles and to directly apply them in practice to inform decision making A textbook treatment and application of... understand and evaluate empirical work in real estate modelling and forecasting Who should read this book? The book is intended as an easy-to-read guide to using quantitative methods for solving problems in real estate that will be accessible to advanced undergraduate and Masters students, as well as practitioners who require knowledge of the econometric techniques commonly used in the real estate . 352 11 .10 A VAR for the interaction between real estate returns and the macroeconomy 357 11 .11 Using VARs for forecasting 362 12 Cointegration in real estate markets 369 12 .1 Stationarity and. in real estate? 6 1. 6 Model categorisation for real estate forecasting 8 1. 7 Why real estate forecasting? 9 1. 8 Econometrics in real estate, finance and economics: similarities and differences 12 1. 9. market 325 11 Vector autoregressive models 337 11 .1 Introduction 337 11 .2 Advantages of VAR modelling 339 11 .3 Problems with VARs 340 11 .4 Choosing the optimal lag length for a VAR 340 11 .5 Does