A Comparison of Structural and Non-Structural Econometric Models in the Toronto Office Market. Kimberly Gole

Transcription

1 A Comparison of Structural and Non-Structural Econometric Models in the Toronto Office Market by Kimberly Gole B.S., Mathematics and Statistics and Applied Probability, 2007 University of Alberta Submitted to the Program in Real Estate Development in Conjunction with the Center for Real Estate in Partial Fulfillment of the Requirements for the Degree of Master of Science in Real Estate Development at the Massachusetts Institute of Technology September, Kimberly Gole All rights reserved The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of Author Center for Real Estate July 30, 2014 Certified by William C. Wheaton Professor, Department of Economics Thesis Supervisor Accepted by Albert Saiz Chair, MSRED Committee, Interdepartmental Degree Program in Real Estate Development

2 A Comparison of Structural and Non-Structural Econometric Models in the Toronto Office Market by Kimberly Gole Submitted to the Program in Real Estate Development in Conjunction with the Center for Real Estate on July 30, 2014 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Real Estate Development ABSTRACT This thesis aims to compare five systems of econometric equations to describe the Toronto office market. It compares four structural systems differing in their demand equations and a non-structural system that does not require predefined relationships to exist between variables. Within the structural system of equations the predefined equations require that real rent is estimated solely from vacancy, long-run supply is dependent upon real rent and changes in employment only affect demand. Demand can be estimated either directly by estimating occupied stock and obtaining vacancy through an identity or by estimating vacancy; both occupied stock and vacancy can either be estimated in levels or estimated by an error correction model. Through the analysis of the structural models it is found that real rent shows significant momentum of real rent one year previous. As well the long-run supply curve is rising, while the real rent curve is not rising through the analysis period, as such the long-run supply is estimated in differences as the theoretical relationship between real rent and long run supply in levels cannot be estimated with the correct sign for the Toronto market. The structural demand equations show that error correction terms add value to predictions of demand. The nonstructural model is defined as a vector autoregressive model and allows the variables to freely interact between themselves without the restrictions placed in the structural model. When comparing the structural systems to the non-structural system in the back test, the non-structural system produces superior estimates in the system as a whole. The superior results of the VAR agree with the notion that in complicated dynamic systems by placing restrictions on the interactions of the variables poorer forecasts may result. Thesis Supervisor: William Wheaton Title: Professor of Economics 2

3 Table of Contents 1. Introduction Previous Literature... 8 Research on Structural Econometric Models in Commercial Rent Analysis... 8 Research on Non- Structural Econometric Models in Commercial Rent Analysis Research on Error Correction Models in Commercial Rental Analysis Research on the Comparison of Structural versus Non- Structural Models in Macroeconomics Exploratory Data Analysis Toronto Office Market Overview Variable Descriptions Economic Variables Office Stock Rent and Vacancy Structural Econometric Model Structural Model Framework Stationarity Tests of Variables Cointegration Tests Real Rental Rate Equation Long- Run Supply Equation Demand Equations Summary of Cointegration Test Results Real Rental Rate Equation Econometric Model Long- Run Supply Equation Econometric Model Demand Equations Econometric Model Direct Demand in Levels Econometric Model Direct Demand as an Error Correction Model Econometric Model Indirect Demand in Levels Econometric Model Indirect Demand as an Error Correction Model Non- Structural Econometric Model Econometric Model Comparison of the Structural and Non- Structural Framework Back- Testing of Models Conclusion Bibliography Appendices Data as Provided by CBRE Econometric Advisors Stationarity Tests Statistical Output Business Services Employment Business Services Employment First Difference Real Net Effective Rent Real Net Effective Rent First Difference Vacancy Rate

4 Vacancy Rate First Difference Occupied Stock Occupied Stock First Difference (Net Absorption) Office Stock Office Stock First Difference (Net Completions) Summary of Additional Stationarity Tests Cointegration Tests Statistical Results Rental Rate Equation Cointegration Test Results Additional Cointegration Tests Explored for Rental Rate Equation Supply Equation Cointegration Test Results Additional Cointegration Tests Explored for Supply Equation Direct Demand in Levels Cointegration Test Results Additional Cointegration Tests Explored for Direct Demand in Levels Equation Indirect Demand in Levels Cointegration Test Results Additional Cointegration Tests Explored for Indirect Demand in Levels Equation Direct Demand in Differences (ECM) Cointegration Test Results Additional Cointegration Tests Explored for Direct Demand in Differences (ECM) Equation Indirect Demand in Differences (ECM) Cointegration Test Results Additional Cointegration Tests Explored for Indirect Demand in Differences (ECM) Equation. 64 Structural System Econometric Models Real Rental Rate Equation Additional Models for Real Rental Rate Equation Long- Run Supply Equation Additional Models for Supply Equation Direct Demand in Levels Equation Additional Models for Direct Demand in Levels Equation Direct Demand as an Error Correction Model Equation Additional Models for Direct Demand as an Error Correction Model Equation Indirect Demand in Levels Equation Additional Models for Indirect Demand in Levels Equation Indirect Demand as an Error Correction Model Equation Additional Models for Indirect Demand as an Error Correction Model Equation Non- structural Econometric Models Rental Rate Equation Long- Run Supply Equation Vacancy (Indirect Demand) Equation

5 1. Introduction The ability to predict rental rates of a market into the near future is of crucial importance in commercial real estate. The typical proforma analysis of an investment or development relies fundamentally on the future rental forecast to determine if the investment is one that will be financially feasible. This thesis endeavors to determine which econometric model is a more suitable fit, a structural or a non-structural model. It investigates whether rent is impacted by only vacancy, whether only demand depends upon job growth and whether rent is solely sufficient to generate new supply as required in the structural framework or if the variables exist together with less stringent requirements on their relationships. Within the structural framework this thesis endeavors to determine which econometric model of modeling demand is a more suitable fit in the Toronto office market. It investigates whether demand for the amount of space occupied is better estimated by using variables in levels or by using the changes in variables (differences). It also investigates which methodology of structuring the system of equations to estimate demand produces better results, either by directly estimating demand or indirectly estimating demand. The structure of the econometric models used to forecast the commercial property market has been dependent upon where the subject city is located. In the United States the research has revolved around the economic theory that the change in real rents is linked exclusively to changes of the vacancy rate from the natural vacancy rate. This change in the vacancy rate from the natural vacancy rate is characterized as a move away from the market equilibrium. The divergence of vacancy from its natural level causes rents to also move away from their equilibrium level, which provides a signal to developer. Development then either increases or decreases in response to the vacancy movement and acts to return the market to equilibrium. This additional development potentially changes the amount of occupied stock, which by definition changes the vacancy observed in the market. The structural model requires that the relationships described above are valid and there hasn t been faulty inferences made between the variables. The main theory behind the structural model is that rent is determined through vacancy, and changes in the vacancy rate drives changes in the whole system. In Europe structural models have evolved differently, as these markets have limited vacancy rate data available for analysis. Due to the limited availability of vacancy information reduced form demand-supply equations have been developed. Instead of estimating occupied stock to determine the market vacancy as their American counterparts, European models tend to estimate vacancy. By estimating vacancy the model does not require the stock information that an estimate of occupied stock would require. A possible limitation of this framework is that there is no ability to control the vacancy rate within the range of zero to one. In order to test whether the required variable relationships in the structural system of equations are necessary or if the variables can interact more than allowed in the economic theory, a nonstructural model will be analyzed. The non-structural model will be predicted using a vector autoregressive model. In this model the three variables are specified as linear functions of a set number of their own lags, and the same number of lags of the other two variables. The 5

6 exogenous variable will be business services employment. The strength of this framework is that it does not assume any of the variables require relationships but is able to look at each one as a function of a lagged value of itself and the other variables. The following charts summarize the relationships between the variables for the direct demand model, indirect demand model and the non-structural model. In the charts the E represents that the variable is used in the estimation, the I represents that the variable is part of an identity. Direct Demand Is a Function of: Variable Completions Real Rent Vacancy Occupied Stock Stock Completions E Real Rent E Vacancy I I Occupied E Stock Stock I I Employment E Indirect Demand Is a Function of: Variable Completions Real Rent Vacancy Occupied Stock Employment Stock Completions E Real Rent E Vacancy E E E Occupied I I Stock Stock I I Vector Autoregressive Model (VAR) Is a Function of: Variable Completions Real Rent Vacancy Occupied Stock Employment (lagged) (lagged) (lagged) Stock Completions E E E E Real Rent E E E Vacancy E E E E Occupied E E Stock Stock I I A relatively new development in commercial forecasting is the use of error correction models (ECM). These models are dynamic models that allow long-term effects to be separated from short-term effects, and are especially useful in determining whether commercial real estate 6

7 demand is a product of short-term effects or long-run deviations from equilibrium. This type of model requires that the equation it is applied to show cointegration. The error correction framework will be applied to the direct and indirect demand equations in differences. This will allow investigation into whether short-term effects add significant value in predicting demand. By comparing four systems of structural econometric models and the non-structural econometric for the Toronto office market this thesis aims to determine which method of forecasting provides more accurate results. It aims to determine if the error correction model in differences adds any value to the prediction above that which the typical long-run model in levels does. It also aims to determine if better results are achieved by estimating the demand directly by estimating occupied stock or indirectly by estimating vacancy. Along with variable identities, three equations will be specified to describe the relationships within the structural framework of the variables in the Toronto market. One model with all of the independent variables will be specified as a vector autoregressive model for the non-structural system. Once both model forms are created, the models predictive power will be tested using a portion of the data, from the first quarter of 2008 to the fourth quarter of As this portion of the data includes both the global recession of and the recovery it should provide an accurate indication of predictive power. This thesis will be presented in the following format with the chapters outlined below: Chapter 1 introduces the topic and provides a description of the econometric models being considered. Chapter 2 describes the historical development of commercial forecasting. The previous literature spans several locations and includes research on the development of structural models, reduced form demand-supply models, and error correction models. Chapter 3 provides a description on the Toronto office market and includes exploratory analysis of the data used in the thesis. Chapter 4 creates the four systems structural econometric equations. It begins by exploring the stationarity of the variables and cointegration between variables. It then explores the real rental rate equation, the long-run supply equation and the four demand equations: direct demand in levels, direct demand as an error correction model, indirect demand in levels, and indirect demand as an error correction model. Chapter 5 focuses on the non-structural econometric system. It creates the real rental rate equation, the long-run supply equation and the demand equation without the necessity of theoretical relationships between the variables. Chapter 6 compares the systems of equations to one another and the actual observed values through back testing between the first quarter of 2008 to the fourth quarter of Chapter 7 provides the conclusion and summarizes the relevant findings. 7

8 2. Previous Literature Research on Structural Econometric Models in Commercial Rent Analysis The model of rental adjustment has its origins in labor economics. This model was first applied to rents and vacancy rates in the rental housing market by Blank and Winnick (1953). This research was the first to determine that there is an inverse relationship between rents and vacancy. Following this study several iterations of this idea have been researched. Early support of the model structure of relating rents to vacancy rates was provided by Smith (1969) who researched a model of housing starts as a function of the price of houses, the vacancy rate, the construction and land costs and the cost and availability of mortgage credit. The research was conducted on quarterly data from of Canadian housing markets. Smith (1974) presented support for the traditional view that vacancy rates are very important in describing housing rents as rents vary inversely with the vacancy rate. Using annual data from for five Canadian cities, Halifax, Montreal, Toronto, Winnipeg and Vancouver, he regresses the vacancy, lagged vacancy, property tax change, and lagged property tax change to determine the change in rents. It was found that the vacancy rate and the rate of change in property taxes do significantly affect the change in rents. Along with corroborating the original structure presented by Blank and Winnick (1953), the study also was able to calculate the natural vacancy rate for the five cities. Following similar lines to the Smith (1974) study, Eurbank and Sirmans (1979) study the structural model using operating expenses and vacancy rates using data from on four United States cities and four different apartment types. The study found that the operating expenses were more important in predicting changes in rent levels than the vacancy rate. Using data from 17 United States cities Rosen and Smith (1983) confirm that the rental price changes are significantly affected by excess supply or demand in the marketplace. They find that both the vacancy rate and operating expenses are significant in predicting the percentage increase in rents. Rosen (1984) added an additional variable to the previously completed research. He connected the stock of office space in addition to the vacancy and rent variables previously used. Using these variables and data from San Francisco from , he created three equations to determine the changes in rental rates. The first equation estimated the stock of office space as a function of employment, rent and price. The regression analysis of this equation showed that there was a strong positive relationship between occupied stock and FIRE employment. It also showed a negative relationship between real rents and occupied stock. The second equation estimated the rent as a function of the change in rents, the natural vacancy, the actual vacancy and the change in the overall price level. The regression analysis of this equation confirmed that changes in rent are inversely related to changes in vacancy, and that changes in rent are directly related to changes in the cost of living. The third equation explained occupied office stock as a function of the stock in the previous period and the new office stock completions. Through the regression analysis he found that this equation was not important in determining the supply, only lagged vacancy was significant. 8

9 Further expanding the research on structural econometric models to analyze the office market, Wheaton (1987) undertakes research to determine if there is a national real estate cycle. The national office market is analyzed using five time series: construction, completions, office employment, absorption, and vacancy rate. Three behavioral equations are specified to describe the market process. The first, the absorption equation, is specified as a function of the level of office employment, current real rents, expectations of future space needs, rate of employment growth, and amount of demand realized each year. The second equation describes supply as a function of the cost of construction, the cost to finance construction, current rent, current vacancy, future expectations upon project completion and rate of employment growth. The final equation describes the rent adjustment process using current rent and vacancy, the previous period s realized rent and the natural vacancy level. In addition, three identities are specified: net absorption which is the difference between the occupied stock this period and last period, the occupied stock which is the total office stock multiplied by the percentage of occupancy (1- vacancy rate), and the total office stock which is made up of the previous period s office stock plus the completions in the previous period. Using this system of six equations he is able to forecast the real estate cycle ahead and finds in the immediate future the oversupply will not clear as fast as it has in previous cycles. Schilling, et al. (1987) applied the structural econometric model to 17 United States cities to determine if the unoccupied space has an impact on what landlords are able to charge for rent in the local office market. Using the pooled approach on the office data, they find that the operating expenses are significant in explaining changes in rent in only four of the cities, while vacancy rate is significant in eleven of the cities. The study finds unrealistic values for the natural vacancy rates in the cities. Gabriel and Nothaft (1987) apply the structural model to rental housing in 16 United States cities using data from They confirm that the vacancy rate is important in explaining the rental rate adjustment process in rental housing. The research on the relationship between vacancy and rental rates is further studied by Wheaton and Torto (1988) with the examination of the relationship between excess vacancy and changes in rent. Excess vacancy is defined as the difference between the natural vacancy rate and the actual vacancy rate. The research finds that the natural vacancy is increasing over time. It also finds that the relationship between excess vacancy and real rents is statistically significant and quantitatively meaningful. Silver and Goode (1990) determined rents for retail properties in Britain derived as a reduced form equation from supply, demand and equilibrium equations. They find that demand for retail space is determined to be a function of rents charged, current expenditures in retail outlets, and an asset demand (investor demand) component. Wheaton et al. (1997) estimate three structural equations for the London office market using data from The three structural equations for office space demand, new supply and rental movements are accompanied by two identities to determine the stock and vacancy. They find the increase in construction can be explained with the traditional model but only as long as the 9

10 previous boom is taken into consideration. The movements in demand and rent are explained by the office employment growth. Finally, they find that rents react to changes in the vacancy rates and to leasing activity. Research on Non- Structural Econometric Models in Commercial Rent Analysis Dobson and Goddard (1992) relate prices, rents and exogenous economic variables in industrial, retail and office properties in a British time series from They recognize that commercial property is a factor of production as well as an asset with stored value. The models developed take into account this feature of commercial property as well as distinctions between different types of property users and different types of property owners. The research concludes that prices and rents are sensitive to employment rates, interest rates and residential property values. Using a reduced form demand-supply model D Arcy, et al. (1997) study 22 European cities with data from to explore the impact of national economic conditions, market size, measures of office growth and changes in the city economy to explain fluctuations in office rents. They find that national GDP and short-term interest rates are important predictors of office rent, while market size and city economic growth have an insignificant impact on office rent. D Arcy, et al. (1999) expands on their research with the addition of available supply side data in the Dublin office market. Dublin presented a substantial challenge as it is a small market and with that large swings in supply can occur in any year due to new completions. Rent is specified as a function of service sector employment, GDP, and stock of office floor space. They find that real GDP lagged one period, and changes in office space lagged three periods are significant determinants of rental rates. Thompson and Tsolacos (1999) use the reduced form demand-supply model to analyze the industrial market in the United Kingdom. They specify real rent as a function of lagged changes in GDP, industrial vacancy rates and lagged values of rental rate changes. They find that real rent changes are related positively to real GDP and inversely affected by absorption rates. Taking a global approach De Wit and van Dijk (2003) research the determinants of office returns for 46 major markets in Asia, Europe and the United States. They find that GDP, inflation, unemployment, vacancy rate and available office stock all have an impact on real estate returns. Research on Error Correction Models in Commercial Rental Analysis Research starting in the early 2000 s has explored error correction models (ECM) as a way to estimate long-run equilibrium relationships and short-term dynamic corrections of commercial real estate. Error correction models do not require the variables to be stationary, however it does require that they be cointegrated. 10

11 Hendershott, et al. (2002a) use London data to estimate both the long-run relationship and the short-run adjustment equation. The error correction model they specify has been widely used in the literature that has followed. They conclude that the ECM model has many advantages over the vacancy gap model. The coefficients in the ECM have useful economic interpretations, the price and income elasticities of demand. As well it does not require estimates of real interest rates and risk, and it can be used in studies where vacancy data is unavailable. Following the research described above Hendershott, et al. (2002b) continues with analysis using the error correction model framework by examining London retail and office properties. The Hendershott, et al. (2002b) study concludes that economic drivers may vary, there is no evidence of differences in the operation of property markets outside of London and they find that elasticities for retail and office properties are similar. The final models presented support the use of an error correction model framework. De Francesco (2008) uses the error correction model framework to analyze the Sydney and Melbourne office markets. Within the framework vacancy and the work-space ratio are allowed to be endogenously determined. The research looks at the rental adjustment mechanism and the demand-employment relationship. In addition whether office market determinants have a permanent or transitional effect is studied. With the rental adjustment model he finds that in Sydney the vacancy rate and the real interest rate are long-term determinants, while in Melbourne only vacancy is a long-term determinant. In the demand-employment relationship he finds that a variety of macroeconomic factors have a transitory influence while real rent and real interest are long-term demand drivers only in Sydney. Using 15 United State s metropolitan statistical areas, Brounen and Jennen (2009a) adapt the Hendershott, et al model above to test the asymmetry in rent response to positive changes in office employment. They find that rents adjust positively with a rise in office employment and lagged rent rate changes. They also find that office rents react stronger to changes in employment when the vacancy rate has deviated from the natural level. Brounen and Jennen (2009b) use the Hendershott, et al. model specified above to determine whether the long run relationships between premier and second tier cities are similar in ten European markets. This is to test whether local and national markets move in sync; if they do not move in sync then a local model based on national economics would be inaccurate. They find that national and local changes in economic variables to a large extent move in tandem. The results do not provide evidence that the economic variables defined at the local or national level produce better estimates. Again using the Hendershott, et al model above, Ibanez (2013) investigates how rental rates evolve over time across four different property types, office, industrial, flex and retail. The study focuses on the speed at which rents move back to equilibrium and it s found that the office market is the slowest to return to equilibrium levels. 11

12 Research on the Comparison of Structural versus Non- Structural Models in Macroeconomics Sims (1980) advocates an alternative class of model, one which there is the opportunity to drop standard economic assumptions while retaining the ability to test meaningful hypothesis. He suggests that the vector autoregressive model could be the alternate class of model as it can still capture the rich inter-relationship between variables in the time series analysis. He comes to the conclusion that it is unlikely that macroeconomic models have been over identified. Sims (1989) theorizes that an ideal model is made up of three important features. The model contains an interpretation of the behavioral interactions for all of the included parameters. It also connects to the data in detail and takes into account the inherent uncertainty of behavioral hypothesis. He recommends experimenting with simple behavioral models before moving into a vector autoregressive model as a safeguard to ensure that interpretations of the vector autoregressive model are theatrically valid. In the research he uses interest rates, money stock, output and price level to show how useful interpreting evidence from a vector autoregressive model can be. Clements and Mizon (1991) analyze structural and non-structural models by using a vector autoregressive model to assess the merits of the structural model. They present the two models in a complementary (as opposed to competing) format and suggest using the vector autoregressive model to suggest an efficient model development strategy. 3. Exploratory Data Analysis Toronto Office Market Overview Toronto is the capital city of the province of Ontario, and is Canada s largest city. According to the 2011 Canadian census, the population of the greater Toronto area is approximately 5.5 million and the population within the city of Toronto is approximately 2.6 million1. Toronto is the largest Canadian office market with over 150 million total square feet of office stock as of the fourth quarter of The key industries occupying office space in Toronto include business and professional services, financial services, design services, fashion and apparel services, film and television services, music services, life sciences and tourism. Toronto is the financial center of Canada and is the location of the Toronto Stock Exchange. As well the financial district is centered on Bay Street, the Canadian equivalent to Wall Street. The big five Canadian banks, the Bank of Montreal, Canadian Imperial Bank of Commerce, Toronto- Dominion Bank, Royal Bank of Canada, and the Bank of Nova Scotia all have their headquarters in Toronto. Many large Canadian corporations have their headquarters in Toronto; eighteen of Canada s fifty most profitable companies have their headquarters in Toronto. Global headquarters in Toronto include Brookfield Asset Management, Fairmont Hotels and Resorts, Manulife Financial, Nortel, 1 Census information can be accessed through: 2 As per data provided by CBRE 12

13 the Hudson s Bay Company, Bell Media and Rogers Corporation. Canadian operation corporate headquarters located in Toronto include McDonald s Canada, Coca-Cola Company, Sirius Canada, and Marriott International. In addition to being the center of the Canadian financial industry, Toronto is also the center of the Canadian media industry. Focus in the fashion, film and music industry has given aided in business services occupying a significant portion of the Toronto marketplace. Variable Descriptions The dataset is provided by the CBRE Econometric Advisors Canadian Office, and contains quarterly observations for the Toronto office market. The dataset contains nine variables as described below: 1. Year Observation year and quarter 2. FIRE Emp. (Jobs x 1000) Finance, insurance, and real estate services employment sector 3. Business Svc. Emp. (Jobs x 1000) Business services employment sector 4. Office Stock (SF x 1000) Total office space square footage 5. Completions (SF x 1000) Office space completions during the observation year and quarter 6. Net Absorption (SF x 100) Office space absorbed by market during the observation year and quarter 7. Vacancy Rate (%) Vacancy rate 8. Net Effective Rent ($) Nominal rental rate 9. Net Effective Rent (2013 $) Real rental rate expressed in 2013 values The variables used in the final analysis are: Year, Business Svc. Emp., Office Stock, Vacancy Rate, Net Effective Rent (2013 $). Using these variables the following additional variables have been computed: 1. Occupied Stock = (1-Vacancy Rate) * Office Stock 2. Occupied Stock First Difference (Computed Net Absorption) = Occupied Stock t Occupied Stock t-1 3. Office Stock First Difference (Net Completions) = Office Stock t Office Stock t-1 4. Real Net Effective Rent First Difference = Real Net Effective Rent t Real Net Effective Rent t-1 5. Year-Over-Year Completions = Office Stock t-4 Office Stock t 6. Year-Over-Year Employment Growth = Business Services Employment t-4 Business Services Employment t 7. Year-Over-Year Absorption = Occupied Stock t-4 Occupied Stock t 8. Year-Over-Year Rent Growth = Real Net Effective Rent t-4 Real Net Effective Rent t Note that while completions are available in the dataset, a net completions has been computed using the first difference of occupied stock. Due to redevelopment happening in the office space market, net completions takes into account the fact that some buildings may have been demolished and new buildings built in their place. The completions variable available in the dataset is gross completions and does not take into account this reduction in stock due to demolition. A summary of the descriptive statistics of the variables used in the analysis is provided below: 13

14 Descriptive Statistics Variable Mean Median Std. Dev. Min Max FIRE Emp Bus Svc Emp Office Stock 117, ,284 28, , ,440 Real Net Effective Rent Vacancy Rate Occupied Stock 102, , , , ,086.5 Occupied Stock First Difference (Computed Net Absorption) , , Office Stock First Difference (Computed Net Completions) ,515 Real Net Effective Rent First Difference Year-Over-Year Completions Year-Over-Year Employment Growth Year-Over-Year Absorption Year-Over-Year Rent Growth Economic Variables The dataset presents two economic indicator variables, FIRE employment and business services employment. From the above descriptive statistics we can see that while business services employment starts lower than FIRE employment it ends significantly higher. The following graph illustrates the patterns in the economic variables from quarter one of 1980 to quarter four of

15 Both series show an increasing trend until the late 1980 s and then a stagnant period in the early 1990s during the recession. The FIRE employment stays stagnant for a considerably longer period after the recession than business services employment. The business services series shows a much stronger increase throughout the late 1990s until present than does the FIRE employment series. Business service employment also shows a stronger recover from the global recession. 15

16 Office Stock The office stock series shows a large increase in stock from 1980 to the early 1990 s. The gain in stock exhibited during this period is more than the total increase in stock from the end of the building boom until present. Incorporating the knowledge of the recession, the conclusion that the decrease in building output occurs a few years after the recession is consistent with developers taking building signals from the current economic state. However, given that office buildings are a product with a long-term build schedule, the additional stock coming onto the market is consistent with buildings that were started previous to the recession. 16

17 Rent and Vacancy The real net effective rent peaks at a value of $39.01 in the fourth quarter of Following this peak, the rent falls to a low of $4.42 in the fourth quarter of From this point the rent does not recover to it s previous high; the highest real net effective rent achieved after the low is $23.61 in the first quarter of This type of real rental rate pattern is similar to that of cities with significant ability access to new supply. This is more typical of cities that have weak constraints on supply, either geographical or political, than Toronto, which is typically considered land constrained. This is pattern of real rental rates is also characterized by rents that show less sensitivity to vacancy rates. 17

18 The two main peaks, the rental high in 1989 and the rental rate low in 1993, correspond to the same two peaks in the vacancy rate. As vacancy and rents typically have an inverse relationship to one another the rental high corresponds to a low in the vacancy rate, and the rental low corresponds to a high in the vacancy rate. The two series exhibit this inverse relationship until the early 2000s. After this point they both appear to level out and the relationship doesn t look to be as strong. 4. Structural Econometric Model Structural Model Framework The economic theory of the structural econometric model is defined by the following relationships when demand is estimated directly: 1. Rent is determined exclusively through vacancy: Rent = F(Vacancy) 2. Long-run supply curve is determined by the real rental rate: Supply = F(Rent) 3. Demand (occupied stock) is determined through the employment variable as an economic indicator and the rental rate Occupied Stock = F(Employment, Rent) 4. The vacancy rate is determined as: 18

19 Vacancy = 1 (Occupied Stock/Stock) When demand is estimated indirectly the structural econometric model is estimated through the following system of equations: 1. Rent is determined exclusively through vacancy: Rent = F(Vacancy) 2. Long-run supply curve is determined by the real rental rate: Supply = F(Rent) 3. Demand is determined through estimating vacancy as a function of the employment variable as an economic indicator, the rental rate, and the total office stock Vacancy = F(Employment, Rent, Stock) In addition, to complete the structural model framework two further identities are required: 1. Occupied Stock t = Total Stock t-1 + Absorption t-1 2. Total Stock t = Total Stock t-1 + Construction t-1 The following variables required for the structural model have been computed in the dataset as: Occupied Stock t = (1 - Vacancy Rate t ) * Office Stock t Net Absorption t = Occupied Stock t Occupied Stock t-1 Completions t = Office Stock t Office Stock t-1 When appropriate the structural model is constructed using the variables in levels (using only the actual variables and the lagged versions of themselves). However, the equations can also be specified in differences and in the ECM framework, the equations will be specified in differences. In order to specify any of the equations in levels the variables must be stationary, if they are not an ordinary least squares regression is not appropriate. If the variables do not show stationarity and the series are cointegrated, then an error correction model can be used to estimate the relationships. Stationarity Tests of Variables To decide if the structural equations can be specified, as preferred by the economic theory, in levels the variables are tested to determine if they are stationary. The stationarity test results will provide a starting point to creating the general framework for the econometric equations. Dickey and Fuller (1979) developed the procedure to test whether a variable has a unit root. The original test was further developed to allow lags into the autoregressive process by Said and Dickey (1984). The augmented Dickey-Fuller test has the null hypothesis that the series has a unit root; the alternative hypothesis is that a stationary process generates the series. The augmented Dickey-Fuller test fits a model of the form: Δx t = α + βx t-1 + ζ 1 Δx t-1 + ζ 2 Δx t ζ n Δx t-n + ε t where n is the number of lags specified for the test. The augmented Dickey-Fuller tests whether β=0, which is equivalent to x t having a unit root. To test for stationarity of the variables, the augmented Dickey-Fuller test is used for each of the variables. As the test is very sensitive to the number of lags used, the optimal number of lags will be selected for each variable using the Akaike s Information Criterion (AIC), and the augmented Dickey-Fuller test explored for this optimal number of lags. The summary chart below shows the results of the tests for stationarity: 19

20 Stationarity Results Dickey-Fuller and Augmented Dickey-Fuller Test Results Variable Optimum Lag (AIC) Test Statistic (optimum lag) MacKinnon p-value (optimum lag) Business Service Employment Business Service Employment First Difference Net Effective Rent (Real) Net Effective Rent (Real) First Difference Vacancy Vacancy First Difference Occupied Stock Occupied Stock First Difference (Net Absorption) Office Stock Office Stock First Difference (Net Completions) The time series for the economic variable, business services employment, is not stationary series. However, when the first difference the series is stationary at a 1% significance level3. Real net effective rent and the vacancy rate are stationary at the 10% level for their optimum number of lags. The occupied stock series is stationary without any lags and the first difference of the occupied stock series, net absorption, is stationary at the 1% level for without lags and the optimum number of lags. The total office stock series and its first difference, net completions, are stationary without any lags. The variables stationary in levels are real net effective rent and vacancy. All of the variables are stationary in differences, including the employment variable. Note that while total employment, FIRE employment and their respective first differences are not used in the final analysis, they were explored as options for the economic indicator variable when selecting the optimum variable set. As such they have been included in the stationarity analysis and the results of these tests are summarized in the Appendix. A direct regression with non-stationary series would be problematic, as such going forward the stationarity results as summarized above will be important in defining the econometric equations. Cointegration Tests Two series are cointegrated if they tend to move together through time, sharing a stochastic drift. The error correction model framework approach requires that the variables exhibit cointegration. Engle and Granger (1987) suggest a two-step process to determine cointegration. Using an ordinary least squares (OLS) a regression equation is first determined between the two variables. The augmented Dickey-Fuller test is used to test the stationarity of the residuals from this regression. The augmented Dickey-Fuller test has the null hypothesis that the residuals are nonstationary. As such a statistically significant result produces the conclusion that the residuals 3 For the Augmented Dickey-Fuller tests the following critical values from MacKinnon (1996) are used: 1% -3.49, 5% -2.89, 10% -2.58, 20%

21 are stationary and the series are cointegrated. This process will be used to determine cointegrating relationships for the rental equation, the supply equation, and the four demand equations in the structural framework. As with the stationary tests the results are sensitive to the number of lags used, as such the AIC has been used to select the optimum number of lags. The cointegration tests that were explored for the econometric equations are summarized below4. Real Rental Rate Equation Starting the cointegration tests with the relationship between rent and vacancy, it is determined that real net effective rent is not cointegrated with vacancy nor with vacancy lagged four, eight or twelve periods for the optimum number of lags. A summary table of the statistical results is provided below: Cointegration with Real Net Effective Rent Variable R 2 Regression Optimum Lag (AIC) ADF Test Statistic (Optimum Lag) MacKinnon p- value (Optimum Lag) Vacancy Vacancy- 4 period lag Vacancy- 8 period lag Vacancy- 12 period lag The relationship between vacancy and the real net effective rental rate is not cointegrated at any statistical level, even when lagged vacancy has been introduced. As such, the equation where the rental rate level is determined solely by the vacancy rate cannot be specified as an error correction model. The relationship between vacancy and the first difference of the real net effective rental rate (change in rent) was also explored. The quarterly change in rent shows cointegration with the vacancy series at 1% when the AIC optimum one lag is included5. Long- Run Supply Equation Moving into the supply equation and starting with single variable cointegration tests with total office stock it is determined that none of the employment relationships exhibit cointegration even at a very generous 20% level. As the econometric equation specified for supply equation can be multivariate, testing various combinations of independent variables with dependent variable total office stock have been included. Using the results from the AIC determination of the optimum lag in the residuals, the only combinations that do not show cointegration are the two combinations with the rental and vacancy rate lagged one and four periods and the combination with only business services employment and real net effective rent. From these results it is determined that the best 4 For the sake of brevity, only the full statistical outputs for the final econometric equations are included in the Appendix. As well summary charts for the cointegration tests for variable combinations that ultimately were not selected for the econometric models are also available in the Appendix. 5 For the Augmented Dickey-Fuller tests the following critical values from MacKinnon (1996) are used: 1% -3.49, 5% -2.89, 10% -2.58, 20%

22 combination of cointegrating relationships with total office stock is with business services, real net effective rent lagged one period and the vacancy rate lagged one period. The supply equation can also be specified as a change in stock instead of using total office stock as the dependent variable. As such the cointegrating relationships with the first difference of office stock (net completions) will also be explored. The following chart shows the results of the cointegration between net completions and real net effective rent, the variables used in specifying the supply equation. Cointegration with Total Office Stock First Difference (Net Completions) Variable R 2 Regression Optimum Lag (AIC) ADF Test Statistic (Optimum Lag) MacKinnon p- value (Optimum Lag) Real Net Effective Rent Net completions show cointegration with business services employment and total employment in addition to real net effective rent at the 10% level6. Similar to total office stock, the supply equation can be specified as a multivariate regression with net completions as the dependent variable. All of the tested combinations of independent variables show cointegration with net completions at the 10% for the augmented Dickey-Fuller test with the optimum number of lags as selected using AIC. Net completions show very significant cointegration with all the combinations of independent variables at the optimum lag length. The only set of variables that is less significant, business services employment and vacancy rate, are still significant at the 10% level. Based on the cointegration relationships of the independent variables with office stock both in levels and in differences, it is likely that the final choice of variables for the supply equation in the structural model will be cointegrated. If the final model shows cointegration an error correction model can be specified for this equation. Demand Equations The demand variable can be specified either directly or indirectly and either in levels or in differences; as such four separate combinations of cointegration relationships will be explored. The first is for the direct specification of demand in levels and will test potential cointegrating relationships with occupied stock. The following chart shows the results of the cointegration between occupied stock and the multivariate selection real net effective rent and business services employment, the variables used when specifying the demand equation in levels. Occupied stock doesn t exhibit cointegration with any of the multivariate combinations of series explored, nor does it exhibit cointegration individual with real net effective rent, business services employment, FIRE employment or total employment. 6 For the Augmented Dickey-Fuller tests the following critical values from MacKinnon (1996) are used: 1% -3.49, 5% -2.89, 10% -2.58, 20%

23 Multivariate Cointegration with Occupied Stock Variable R 2 Regression Optimum Lag (AIC) Real Net Effective Rent, Business Services Employment ADF Test Statistic (Optimum Lag) MacKinnon p- value (Optimum Lag) The demand equation can also be indirectly specified in levels by using vacancy as the dependent variable, and the changes in office stock and business services as explanatory variables. All of the multivariate combinations tested show cointegration with vacancy, as do the employment variables; the following table summarizes the results of the cointegration tests for the combination of variables used in specifying the indirect demand equation in levels: Multivariate Cointegration with Vacancy Variable R 2 Regression Optimum Lag (AIC) Business Services Employment, Office Stock, and Real Net Effective Rent ADF Test Statistic (Optimum Lag) MacKinnon p- value (Optimum Lag) Demand can also be specified both directly and indirectly using differences. These models will specified with net absorption and the change in vacancy as the dependent variables. Starting with the relationships with net absorption, all of the variables and variable combinations show significant cointegration with the net absorption series. The following table summarizes the results of the cointegration tests for the combination of variables used in specifying the direct demand equation in differences: Multivariate Cointegration with Occupied Stock First Difference (Net Absorption) Variable R 2 Regression Optimum Lag (AIC) ADF Test Statistic (Optimum Lag) Real Net Effective Rent, Business Services Employment MacKinnon p- value (Optimum Lag) The final specification of demand for the structural systems will be using the change in vacancy. This is the indirect demand equation specified in differences. Similar to the net absorption series, all of the variables and variable combinations explored show cointegration with the change in vacancy series. The following table summarizes the results of the cointegration tests for the combination of variables used in specifying the indirect demand equation in differences: Multivariate Cointegration with Vacancy First Difference Variable R 2 Regression Optimum Lag (AIC) ADF Test Statistic (Optimum Lag) Real Net Effective Rent, Business Services Employment, and Office Stock MacKinnon p- value (Optimum Lag)

24 Both the direct demand and the indirect equations show a stronger cointegrating relationship with business services employment than they do with total employment. Based on the cointegration relationships of the independent variables when demand is specified both directly and indirectly, it is likely that the final choice of variables for the demand equation in the structural model will be cointegrated. If the final models for demand show cointegration an error correction model can be specified for the equation. Summary of Cointegration Test Results For the rental rate equation the series does not show cointegration with the vacancy rate series. As such an error correction model cannot be specified for this relationship. However, since the series are individually stationary a regular ordinary least squares regression can be used to estimate their relationship. The supply equation explored using net completions shows cointegrating relationships with the majority of the combinations of independent variables. Once the final equation has been determined it is likely that an error correction model will be able to be specified, however, a final check on the cointegration of the specified series will be tested to ensure the error correction framework is appropriate. The only demand equation that does not show a cointegration relationship is that with occupied stock (direct demand in levels). The remaining three options for demand to complete the system of equations in the structural framework show cointegrating relationships. Both of the equations specified in differences show strong cointegration, which will be particularly important, as these equations will be specified as error correction models. Real Rental Rate Equation The structural model assumes that changes in rent are determined exclusively through deviations in the vacancy rate from the natural vacancy rate. As office properties tend to have long-term leases, rents will tend to be slow to adjust to changes in the vacancy rates. While the strength of the inverse relationship between the change in real rental rates and the vacancy rate in the Toronto dataset depletes in the early 2000s the series does show the typical relationship: low (high) vacancy rates correspond to high (low) real rental rates. Vacancy is the state through which space passes through while waiting to be leased. It can be quite cumbersome for a tenant to find appropriate space for their needs as vacant space can come in very different sizes and spatial arrangements. Once an appropriate space has been found owners and tenants can begin bargaining over the lease agreements, including the rental rate. Owners set a minimum reserve price for the space at which they are indifferent between renting the space to the tenant and leaving it vacant. The longer the anticipated lease up time the lower the reservation price will be. Tenants similarly set a maximum reserve price for the space, the price at which they are indifferent between leasing the space and continuing to search for a different vacant space. When there is ample available vacant space and few tenants in the market, it is easier for the tenant to find space and the maximum reserve price will be lower. The final agreed upon price should lie between the owner s reservation price and the tenant s reservation price, Wheaton, et al. (1997). Both the owner s and the tenant s reservation price move inversely with vacancy, Wheaton (1990). 24

25 The modern theory of search and bargaining specifies that a given level of vacancy, either above or below the natural rate, does not cause rents to rise or fall continuously, Wheaton and Torto (1993). This deviation from the natural vacancy rate leads to a stable level of rent reflective of the rental rate that would be an acceptable outcome of bargaining. Reflecting that rents do not fall or rise continuously for a given level of vacancy, the relationship between the real rental rate and vacancy will be specified generally as: Real Rent t = a + b*vacancy Rate t + c* Real Rent t-n Econometric Model From the stationarity tests results, we know that both rent and vacancy are stationary series. As well from the cointegration it was determined that the two series are not cointegrated. An error correction model cannot be specified for this equation, however, since both series are stationary an ordinary least squares regression analysis can be specified for the relationship between the two variables. As such, the econometric model for the real rent at time t will be specified as (where n 0): Real Rent t = a b*vacancy Rate t-n + c*real Rent t-n Models that were investigated but subsequently discarded are summarized in the Appendix. The real rent equation as specified using yearly lags using the Toronto data yields7: Real Rent t = *Vacancy Rate t *Real Rent t-4 (6.85) (-6.77) (26.38) Adjusted R 2 = ; N = 132; F(2,129) = The coefficients on the vacancy rate and the lagged real rent are in the correct direction. The model suggests that rent would have a stable value of approximately $20 using a vacancy of 12% (the average vacancy rate between for Toronto). As shown through the vacancy rate coefficient, vacancy has an inverse relationship with the rental rate. This result is consistent with conclusions drawn from previous research on the relationship between the vacancy rate and rent. The coefficient on the lagged real rent of 0.85 is consistent with the rental rate being sticky and having a slow speed of adjustment to changes in the vacancy rate. The market would move towards an equilibrium rent at 15% per year. This slow rate of adjustment is expected, as office leases are generally long-term. As well, the slow rate of adjustment reflects the fact that real rent and vacancy are poorly correlated and not cointegrated. The model with only vacancy as the independent variable has an R 2 of only , and without the series being cointegrated this relationship cannot be improved upon without additional variables being specified to the model. 7 Full statistical output for regression is in the Appendix 25

26 The above graph depicts the dynamic forecast based on the model with the coefficients as specified above. The lagged rent variable is endogenous while the remaining variables are treated as exogenous to the equation for the purposes of this graph. The predicted rental values show the same general pattern as the actual rental rates, which are expected with the high R 2 of the model and the lagged rent variable being present in the model. However, the dynamic forecast provides much more extreme swings in movement than the actual rental rates experienced. The predictions exhibit overcorrections, most notably becoming negative in the mid-1990s and a large increase after Long- Run Supply Equation The long-run supply is measured as the net completions added to the previous periods total office stock. New office space is developed when the value of developing the space exceeds the cost to develop it. The value of an office space asset is directly correlated to the rent that it can generate. The net effective rental income is used to measure the value typically along with a capitalization rate. It follows from the asset value calculation that the amount of completions should be related to the real net effective rent. The graph below compares the movement of the real rental rate over time and the net completions delivered to the market. The peak in net completions occurs shortly after the peak in the rental rate, which would be due to the long-term construction in delivering new office space into the market. The decision to develop space occurs long before the space is actually delivered 26

27 to the market suggesting that the completions delivered to the market are dependent on a lagged rental rate. The supply equation is specified as a change in supply because the real rental rate does not show an increasing trend. Supply has an increasing trend throughout the dataset even though the real rental rate is not increasing. As such it will not be possible to have a correctly signed equation, which according to economic theory would be increase in supply is due to an increase in real rent, using supply and real rent. Reflecting that the decision to deliver office stock based on the prevailing market rental rate occurs before the completions are delivered to the market, the relationship for the long-run office supply will be specified generally as: Net Completions t = a + b* Real Rent t-n Econometric Model From the stationarity tests results, we know that both net completions and vacancy are stationary series. As both series are stationary an ordinary least squares regression analysis can be specified for the relationship between the two variables. As such, the econometric model for the net completions at time t will be specified as (where n 0): Net Completions t = a + b* Real Rent t-n 27

28 Models that were investigated but subsequently discarded are summarized in the Appendix. The year-over-year net completions equation as specified using yearly lags using the Toronto data yields8: Net Completions YoY = *Real Rent t-4 (-5.95) (16.41) Adjusted R 2 = ; N = 132; F(1,130) = The coefficient on the lagged rental value is positive, as expected. Rent increases act as a signal to developers to increase development resulting in more net completions in one-year time. With the last observed rent, $15.56, in the dataset (the fourth quarter of 2013) we can anticipate that there will be approximately 1.85 million square feet of office space added to the market by the end of As well the equation suggests that real rent would have to fall to $7.92 in real dollars in order for development to completely cease. The above graph shows the predicted values for the yearly changes in supply and the actual yearly changes in supply. The predicted values follow a much smoother course for reasons including a smoothing effect. Actual supply tends to be delivered in large amounts when large buildings are completed and the predicted values do not reflect the times when an atypical 8 Full statistical output for regression is in the Appendix 28

29 amount of supply is delivered due to a large development s completion. The predicted values also unrealistically have negative values. This is a short-coming of the predicted values as in reality, when real rent decreases space is not demolished to return the system to equilibrium, rather developments not yet completed are completed and new developments are not started until market conditions improve. Demand Equations Previous research indicates that the primary office demand driver is employment in select economic sectors, DiPasquale and Wheaton (1995). These economic sectors are the main users of office space and growth in their workforces translates into a need for more office space. Studies of the economic sectors in the United States submit that greater than 75% of the space in larger buildings is occupied by the FIRE or the business service sector of the economy, Wheaton (1987). Given that the demand depends on the number of space users it follows that it would also be related to the stock of space. The availability of space and the total supply of space also impact the demand of space. If every office worker in Toronto were to use the exact same amount of space a comparison between the change in occupied stock and employment change should follow the same path, increases in office workers should lead to a proportionate increase in space to the number of workers added. The graph below shows the relationship between the amount of occupied stock and the amount of business services employment throughout the data series. When the absorption and change in office workers diverge the amount of office space per worker is changing. 29

30 DiPasquale and Wheaton (1995) attribute the difference in changes in office space and changes in employment to two explanations. The first is that as the makeup of the workforce changes so too does the space the changing workforce will occupy. Their example to illustrate this theory is that clerical services will use less office space than management services will, and if technology is eliminating clerical jobs then it would be expected that the space per worker would rise over time. The second explanation for the differing changes in office spaces and changes in employment are predicated on the fact that office space is a factor of production. Similar to other factors of production, the amount of space used per worker should vary with the cost of providing that space. As such, when office space costs rise it is expected that employers will reduce the amount of space per employee to reduce their costs, and conversely, when office space costs fall employers will provide more office space per employee. At this point in the structural system of equations demand can be specified in one of two ways, directly or indirectly. When estimated directly occupied stock is estimated and then vacancy is created as an identity based off of this estimation. When estimated indirectly vacancy is estimated directly and the occupied stock estimation is not necessary. Due to the lack of supply information in many European countries estimating demand indirectly is preferred. In the US the preferred estimation of demand is directly with the creation of vacancy through an identity. The direct demand equation will reflect the impacts that changes in employment, rent and the stock of space have on the amount of space occupied in the marketplace. The dependent variable 30

31 will be occupied stock and once estimated, vacancy will be derived using the estimation. This equation can be specified in both levels and differences. When estimated in levels, the actual occupied stock is estimated; when estimated in differences, the net absorption is estimated and occupied stock can then be calculated. The following equations show the general format for the direct demand equation in levels and then in differences: Direct Demand Equation Levels Occupied Stock t = a + b*employment t + c*real Net Effective Rent t-n Direct Demand Equation Differences (Error Correction Model) Net Absoprtion t = a + b*employment t + c*real Net Effective Rent t-n + d*occupied Stock t-n + e*change in Employment t + f*change in Real Rent t The indirect demand equation will reflect the impact that the above discussion of the impact of office space drivers has on the demand for office space. Vacancy will be used as the dependent variable in the equation as when vacancy rises it suggests that demand has lessened for the product. Reflecting that rental rates are solely dependent upon vacancy rates in the structural framework, lagged vacancy will be included to capture the change in demand for office space as a factor of production due to changes in cost. Changes in office space and employment are also included to reflect the change in demand due to increases in the stock of space and changes in the number of users of space. Similarly to the direct demand equations, the indirect demand equations will be estimated both in levels (dependent variable is vacancy) and differences (dependent variable is change in vacancy). The general form of the equations will be: Indirect Demand Equation Levels Vacancy t = a + b*real Net Effective Rent t-n + c*employment t + d*office Stock t Indirect Demand Equation Differences (Error Correction Model) Change in Vacancy t = a + b*real Net Effective Rent t-n + c*employment t + d*office Stock t + e*vacancy t-n + f*change in Employment t + g*change in Real Rent t + h*change in Supply t Econometric Model Direct Demand in Levels The cointegration test results showed that occupied stock series is not cointegrated with business services employment and the real net effective rent. Using the ordinary least squares analysis the following model has been estimated for the long-run direct demand equation (where n 0): Occupied Stock t = a + b*business Services Employment t + c*real Net Effective Rent t-n Models that were explored but were not used for the direct demand equation in levels are summarized in the Appendix. The occupied stock equation as specified using yearly lags using the Toronto data yields9: 9 Full statistical output for regression is in the Appendix 31

32 Occupied Stock t = *Business Services Employment t (19.06) (37.82) *Real Net Effective Rent t-4 (-5.92) Adjusted R 2 = ; N = 132; F(2,129) = The coefficient on the lagged rental value is negative, as expected. Rent increases in the marketplace cause space users to decrease the amount of space they wish to occupy in order to reduce costs. The coefficient on current business services employment is positive, as expected. An increase in the number of office users causes an increase in demand, as additional space is needed for these additional workers. As shown in the above graph the occupied stock as predicted by the direct demand equation treating both business services and the lagged rent as exogenous variables shows more fluctuations than the actual occupied stock series. This is partly due to the immediate ability of the predicted series to react to changes in employment and changes in the real rent. The predicted series starts higher than the actual series as it does not have any anchor of the amount of stock in the marketplace. The first prediction point is 71M square feet of occupied space while the market had only 61M square feet available. Using the direct demand equation a portion of the building boom in the 1980s can be attributed to the market not having enough supply to support the market demand. 32

33 Econometric Model Direct Demand as an Error Correction Model The cointegration test results showed that the net absorption series is cointegrated with business services employment and the real rental rate. As such an error correction model can be specified for the relationship. Using a one-step error correction model the following model has been estimated for the direct demand equation (where n 0): Net Absorption t = a + b*business Services Employment t + c*real Net Effective Rent t-n + d*occupied Stock t-n + e*change in Employment t + f*change in Real Rent t Models that were explored but were not used for the direct demand equation in levels are summarized in the Appendix. The net absorption equation as specified using yearly lags using the Toronto data yields10: Net Absorption YoY = *Business Services Employment t + (1.33) (-1.40) *Real Net Effective Rent t *Occupied Stock t-4 (1.29) (0.54) *Change in Employment YoY *Change in Real (3.40) (2.07) Rent YoY Adjusted R 2 = ; N = 132; F(5,126) = 8.34 The coefficients in the equation have the expected sign. As this is an error correction model the change in real rent and change in employment variables represent the short-term effects in the market while the variables in levels and lagged levels represent the long-term effects in the market. As the error correction terms are the only variables that are significant in the model, they suggest that net absorption is affected only by immediate changes in the market, the long-term effect variables are not having a significant effect on net absorption. 10 Full statistical output for regression is in the Appendix 33

34 The above graph is the predicted values from the equation with all variables being considered as exogenous variables with the exception of lagged occupied stock, which is endogenous to the equation. As the significant variables in the equation are the short-term effects, it is expected that the predicted values will show changes form period to period. The equation doesn t capture the periods of negative absorption that occur in the actual values. As well it does not reflect the larger values of absorption that can occur when a tenant of a large space footprint either vacates or moves into a space. While there is period-to-period variability in the predictions the equation reduces the range of variability that is shown in the actual values. Econometric Model Indirect Demand in Levels Using the ordinary least squares analysis the following model has been estimated for the longrun indirect demand equation (where n 0): Vacancy t = a + b*business Services Employment t + c*real Net Effective Rent t-n + d*stock t Models that were explored but were not used for the direct demand equation in levels are summarized in the Appendix. The vacancy equation as specified using yearly lags using the Toronto data yields11: 11 Full statistical output for regression is in the Appendix 34

35 Vacancy t = *Business Services Employment t *Real (-0.47) (-22.99) (2.43) Net Effective Rent t *Stock t (19.26) Adjusted R 2 = ; N = 132; F(3,128) = The indirect demand equation in levels shows quite good predictive power with an adjusted R 2 of The coefficients on the variables are of the expected sign. An increase in employment decreases the vacancy rate as there are more workers requiring space. Increasing the rent will increase the vacancy rate as more expensive rents cause users to want to occupy less space to keep costs down. As well an increase in space should also increase the vacancy rate as there is more space total space in the market. The above graph is the predicted values of the indirect demand equation in levels with all variables considered exogenous. The predicted values follow the general pattern of the actual vacancy rate quite closely, which is expected giving the high predictive power of the equation. The predicted vacancy isn t as smooth as the actual vacancy rate as the equation has a quicker ability to capture changes in the market while the actual vacancy rate exhibits a smoother series. The equation captures the peaks and troughs that occurred in the market. 35

36 Econometric Model Indirect Demand as an Error Correction Model The cointegration test results showed that the first difference in vacancy series is cointegrated with business services employment, the real rental rate and office stock. As such an error correction model can be specified for the relationship. Using a one-step error correction model the following model has been estimated for the indirect demand equation (where n 0): Change in Vacancy t = a + b*business Services Employment t + c*real Net Effective Rent t-n + d*stock t + e*vacancy t-n + f*change in Employment t + g*change in Real Rent t + h*change in Stock t Models that were explored but were not used for the direct demand equation in levels are summarized in the Appendix. The yearly change in vacancy equation as specified using yearly lags using the Toronto data yields12: Change in Vacancy YoY = *Business Services Employment t + (1.15) (-3.36) *Real Net Effective Rent t *Stock t - (1.16) (3.02) *Vacancy t *Change in Employment YoY (-5.56) (-0.89) *Change in Real Rent YoY *Change in (-5.39) (0.39) Stock YoY Adjusted R 2 = ; N = 132; F(7,124) = The coefficients of the variables all have the expected sign. As the yearly change in vacancy is specified as an error correction model the significant coefficients can be separated into long-term and short-term effects. Current business services employment, current total office stock, and lagged vacancy have a long-term effect on the change in vacancy. The only error correction term that is significant is the yearly change in real rent, and as such it is the only short-term effect that is significant in the model. 12 Full statistical output for regression is in the Appendix 36

37 The above graph shows the predicted vacancy year-over-year changes using all of the variables in the equations as exogenous variables, except the lagged vacancy term, which is considered endogenous. The graph shows the predicted values following the same general pattern as the actual yearly vacancy changes. The predicted values are both smoother and less varied in total range than the actual observed yearly vacancy changes. 5. Non- Structural Econometric Model The non-structural econometric model allows the dependent variables from the structural model to depend not only upon the theoretical predefined economic relationships, but also on each of the other variables. The strength of the non-structural model is that it does not require any of the predefined relationships to exist and instead allows the data to determine the interactions between the variables. The non-structural model will be specified as a vector autoregressive (VAR) model. The three dependent variables rent, net completions and vacancy are specified as linear functions of a set of their own lags and the lags of the other two variables. As well the economic indicator variable, change in business services employment, will be included in each of the models. The VAR is capable of explaining the interactions occurring between the variables without imposing relationships from prior economic theory. 37

38 Econometric Model As with the structural model, the VAR will use variables that are stationary. As such business services employment and stock will be specified in differences. The real rental rate and the vacancy rate were stationary series so will be specified in levels. The general formats of the equations produced in the non-structural model are as follows: Rent t = a + b*rent t-n + c*vacancy t-n + d*net Completions t-n + e*business Service Employment Growth t Net Completions t = a + b*rent t-n + c*vacancy t-n + d*net Completions t-n + e*business Service Employment Growth t Vacancy t = a + b*rent t-n + c*vacancy t-n + d*net Completions t-n + e*business Service Employment Growth t In order to make an apple-to-apple comparison between the structural systems of equations and the VAR, the VAR is specified using yearly lags and changes in the variables to be consistent with the structural specification. The following set of three equations using yearly lags have been determined for the VAR model using the Toronto office market data: Rent t = *Rent t *vacancy t *net (3.97) (15.30) (-5.59) (-1.25) Completions YoY *Business Service Employment Growth YoY (2.97) Net Completions t = *Rent t *Vacancy t-4 + (-5.65) (9.92) (3.15) *Net Completions YoY *Business Service (2.05) (2.78) Employment Growth YoY Vacancy t = *Rent t *Vacancy t E-06*Net (1.16) (0.48) (20.27) (4.76) Completions YoY *Business Service Employment Growth YoY (-2.65) As the purpose of the VAR is to estimate the system as a whole the individual coefficients in each equation and their signs will not be discussed. However it is of note that the rental equation has significant coefficients outside of the vacancy rate and the lagged rental rate, which were the only two allowed variables in the structural econometric system of equations. As well net completions also shows significant variables over and above the predetermined relationship with the rental rate. 38

39 39

40 The above three graphs show the predicted values of the three equations making up the VAR model. The graphs are generated using only the change in employment as an exogenous variable, the remaining variables are endogenous to the system. The rental rate equation shows a significant amount of small fluctuations throughout the year. It follows the general pattern of the smoother actual real rent series until the early 2000s. At this point the actual real rent series starts to level out but the predicted values continue to increase until the end of the data period. The net completions equation is generally above the actual net completions equation, predicting more completions than were actually observed. The predicted series follows the patterns of the actual data fairly closely and shows very similar peaks and troughs. The predicted vacancy values create a much smoother series than the actual observed values. As well the predicted vacancy values show a much smaller range of values than the actual observed values. The prediction completely misses both the rise and the fall in vacancy in the early 2000s and produces a smooth period at a low vacancy. As well the predicted vacancy values are lower than the actual observed values for the majority of the data series and reach lows that are not observed anywhere in the actual vacancy series. 40

41 6. Comparison of the Structural and Non- Structural Framework To compare the five systems of equations and determine which one provides the best fit for the Toronto market, back testing will be used. In order to make comparisons on the same variables, the real rental rate, year-over-year net completions and vacancy will be used. In the systems where vacancy is not directly estimated it will be calculated using the appropriate identities. The three variables that are commonly estimated through the five systems will be used to predict movements in the market from the first quarter in 2008 to the fourth quarter in This period of time includes both the global recession of and the subsequent recovery. As such it should provide an accurate indication of the predicting power of the five systems. For the back testing all variables are considered endogenous to the system of equations with the exception of business services employment, the economic indicator, and the only true exogenous variable. Back- Testing of Models The above graph of the observed real net effective rent and the predicted real rental values have all five variations show rent increasing after None of the models capture the leveling out that actually occurred in the market. The following graph shows only the period between the first quarter of 2008 and the fourth quarter of 2013 to show the five predicted real rent series in more detail. 41

42 The predictions of demand in levels (estimated both directly and indirectly) and the VAR all show a slightly increasing trend through the date range. Both of the models specified as error correction models show an increase followed by a decrease. The direct error correction model shows the larger decrease out of the two for the date range. The lack in variation between the systems, particularly the structural systems, is due to the large amount of momentum in the lagged rental values. As such, the vacancy rates generated by the structural systems have a lesser impact than they do in the VAR system causing the structural systems to have very similar rental predictions. 42

43 The completions year-over-year predictions show an increasing pattern throughout the back test period with the exception of the year-over-year completion as predicted by the error correction model capturing direct demand. The indirect demand specified as an error correction model system provides estimates that are very smooth in contrast to the uneven actual year-over-year completions series. 43

44 The above graph shows the same completions predictions as the previous; it is showing a restricted date rage to clearly show the details of the five predicted series. The structural system of equations using the direct demand specified as an error correction model provides year-overyear completions estimates that are quite similar to the actual completions series. The short-term effects captured in the demand by this model allow the estimates to come quite close to the actual series. The structural system using indirect demand specified as an error correction model provides a very smooth increasing series that produces considerably more stock throughout the back testing data than the other series and considerably more than the actual completions observed in the market. The remaining three models, the VAR and the two structural systems specified with demand in levels, show very similar predictions for completions, predicting a fairly flat slightly increasing amount of stock each year. 44

45 All of the equations show a very uneven series as compared to the much smoother series of the actual vacancy rate. This is partly due to the equations having a faster reaction to market conditions than the slower reaction of the market due to the long-term nature of office leases. 45

46 The vacancy graph with only the back test date range shows considerably more variation than the real rental rate graph between the different systems of equations. This is due to the rental equation for the structural models having considerable momentum in the lagged rental coefficient. As these rental predictions are so close to one another, the variation in the vacancy predictions shows the difference in predictions due to the differences between the systems. All of the systems show troughs in their predicted values where the actual observed series shows a peak. While the systems of equations that have demand predicted in levels show high predictive capability in their adjusted R 2 s, they do not perform nearly as well in the back testing. This suggests that the short-term effects introduced through the error correction models have value in the prediction power of the structural system of equations. 7. Conclusion In general, the year-over-year changes and the yearly lags provide better results than their quarterly counterparts across all the systems of equations. This leads to the deduction that there is either something in the way the data is surveyed or in the operation of the market that makes yearly data a better representation than quarterly. 46