APPLIED ECONOMIC MODELLING Theory (Chapter 3) Instructor: Joaquim - PowerPoint PPT Presentation

APPLIED ECONOMIC MODELLING Theory (Chapter 3) Instructor: Joaquim J. S. Ramalho E-mail: jjsro@iscte-iul.pt Personal Website: http://home.iscte-iul.pt/~jjsro Office: D5.10 Course Website: http://home.iscte-iul.pt/~jjsro/appliedeconomicmodelling.htm Fénix: https://fenix.iscte-iul.pt/disciplinas/03178-3/2017-2018/2- semestre

3.1. Hedonic Regression Models Definition Hedonic regression: ▪ Regression model that relates values (prices, wages,...) to characteristics (of assets, individuals,...) ▪ It produces estimates of the contributory value (implicit price) of each characteristic to the overall value of the item being researched ▪ It allows the decomposition of a difference in a statistic between two groups, or its change over time, into various explanatory factors Main applications: ▪ Construction of quality-adjusted price indexes for infrequently traded heterogeneous assets (houses, artworks, collectables,...) ▪ Production of measures of discrimination or other differences across groups (wage inequality between males and females,...) ▪ Measurement of quality / productivity changes over time or across groups Our focus: construction of quality-adjusted house price indexes 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 2

3.1. Hedonic Regression Models House price indexes Construction of house price indexes: ▪ Issues: – Each house is a unique combination of many characteristics (houses are heterogeneous) – House prices are rarely observed ▪ Consequences: – House price indexes cannot be constructed simply by comparing the average prices of houses sold in each time period: » Unadjusted price indexes reflect not only pure price movements but also quality differences – House heterogeneity has to be taken into account in order to separate the influences of quality changes from pure price movements: » Need for a quality-adjusted price index in order to measure correctly house price inflation 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 3

3.1. Hedonic Regression Models House price indexes Steps: 1. Choose a price index (arithmetic, geometric) 2. Choose an hedonic function (linear, log-linear) 3. For each time period, regress house prices on house characteristics 4. Apply a method to remove the effects of quality changes and capture pure price movements 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 4

3.1. Hedonic Regression Models House price indexes Notation: ▪ p it : price of house i at period t ▪ t = 0 (base period) or t = s (current period) ▪ N t observations at period t ▪ x it : vector of characteristics of house i at period t ▪ I A : Arithmetic unadjusted price index ▪ I Aq : Arithmetic quality index ▪ I Ap : Arithmetic quality-adjusted price index ▪ I G : Geometric unadjusted price index ▪ I Gq : Geometric quality index ▪ I Gp : Geometric quality-adjusted price index 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 5

3.1. Hedonic Regression Models Step 1: Choose a Price Index Unadjusted price indexes (observed): ▪ Arithmetic: 1 𝑂 𝑡 𝑞 𝑗𝑡 𝑂 𝑡 σ 𝑗=1 𝐵 = 𝐽 𝑡 1 𝑂 0 𝑞 𝑗0 𝑂 0 σ 𝑗=1 ▪ Geometric: 1 exp 1 𝑂 𝑡 ln 𝑞 𝑗𝑡 𝑂 𝑡 𝑞 𝑗𝑡 𝑂 𝑡 σ 𝑗=1 𝑂 𝑡 ς 𝑗=1 𝐻 = 𝐽 𝑡 = 1 1 𝑂 0 ln 𝑞 𝑗0 𝑂 0 σ 𝑗=1 exp 𝑂 0 𝑞 𝑗𝑡 𝑂 0 ς 𝑗=1 Decomposition (cannot be observed): 𝐵 𝑟 𝐽 𝑡 𝐵 𝑞 𝐵 = 𝐽 𝑡 ▪ Arithmetic: 𝐽 𝑡 𝐻 𝑟 𝐽 𝑡 𝐻 𝑞 𝐻 = 𝐽 𝑡 ▪ Geometric: 𝐽 𝑡 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 6

3.1. Hedonic Regression Models Step 2: Choose an Hedonic Function Regression models: ▪ Linear models, for arithmetic indexes: 𝑞 𝑗𝑢 = 𝑦 𝑗𝑢 𝛾 𝑢 + 𝑣 𝑢 ▪ Log-linear models, for geometric indexes: ln 𝑞 𝑗𝑢 = 𝑦 𝑗𝑢 𝛾 𝑢 + 𝑣 𝑢 𝛾 𝑢 : ▪ Gives an estimate of the implicit price of each house characteristic at period t ▪ Multiplied by 𝑦 𝑗𝑢 , measures the contribution of each house charateristic to the house price 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 7

Ƹ Ƹ 3.1. Hedonic Regression Models Step 3: Regress House Prices on House Characteristics Estimation: ▪ For each time period it is estimated a different regression model ▪ Price estimates: 𝑞 𝑗𝑢 = 𝑦 𝑗𝑢 መ – Linear model, for arithmetic indexes: Ƹ 𝛾 𝑢 – Log-linear model, for geometric indexes: ෣ ln 𝑞 𝑗𝑢 = 𝑦 𝑗𝑢 መ 𝛾 𝑢 ▪ Unadjusted price index estimates: – Arithmetic: 1 𝑂 𝑡 𝑂 𝑡 σ 𝑗=1 𝑞 𝑗𝑡 𝐵 = መ 𝐽 𝑡 1 𝑂 0 𝑂 0 σ 𝑗=1 𝑞 𝑗0 – Geometric: 1 𝑂 𝑡 ෣ 𝑂 𝑡 σ 𝑗=1 exp ln 𝑞 𝑗𝑡 𝐻 = መ 𝐽 𝑡 1 𝑂 0 ෣ 𝑂 0 σ 𝑗=1 exp ln 𝑞 𝑗0 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 8

Ƹ Ƹ 3.1. Hedonic Regression Models Step 4: Decompose the Estimated Price Index Arithmetic indexes: 1 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 𝑂 𝑡 σ 𝑗=1 𝑞 𝑗𝑡 𝑂 𝑡 σ 𝑗=1 𝛾 𝑡 𝐵 = መ 𝐽 𝑡 = 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 0 𝑂 0 σ 𝑗=1 𝑞 𝑗0 𝑂 0 σ 𝑗=1 𝛾 0 ▪ Laspeyres-type indexes: 1 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 𝑡 σ 𝑗=1 𝑂 0 σ 𝑗=1 𝛾 𝑡 𝛾 𝑡 𝐵 𝑟 መ 𝐵 𝑞 𝐵 = መ = መ 𝐽 𝑡 𝐽 𝑡 𝐽 𝑡 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 0 σ 𝑗=1 𝛾 𝑡 𝑂 0 σ 𝑗=1 𝛾 0 ▪ Paasche-type indexes: 1 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 σ 𝑗=1 𝑂 𝑡 σ 𝑗=1 𝛾 0 𝛾 𝑡 𝐵 𝑟 መ 𝐵 𝑞 𝐵 = መ = መ 𝐽 𝑡 𝐽 𝑡 𝐽 𝑡 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 0 σ 𝑗=1 𝑂 𝑡 σ 𝑗=1 𝛾 0 𝛾 0 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 9

3.1. Hedonic Regression Models Step 4: Decompose the Estimated Price Index Geometric indexes: 1 exp 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 ෣ 𝑂 𝑡 σ 𝑗=1 𝑂 𝑡 σ 𝑗=1 exp ln 𝑞 𝑗𝑡 𝛾 𝑡 𝐻 = መ 𝐽 𝑡 = 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 0 ෣ 𝑂 0 σ 𝑗=1 𝑂 0 σ 𝑗=1 exp ln 𝑞 𝑗0 exp 𝛾 0 ▪ Laspeyres-type indexes: exp 1 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 𝑡 σ 𝑗=1 𝑂 0 σ 𝑗=1 𝛾 𝑡 exp 𝛾 𝑡 𝐵 𝑟 መ 𝐵 𝑞 𝐵 = መ = መ 𝐽 𝑡 𝐽 𝑡 𝐽 𝑡 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 0 σ 𝑗=1 𝑂 0 σ 𝑗=1 exp 𝛾 𝑡 exp 𝛾 0 ▪ Paasche-type indexes: exp 1 exp 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 𝑡 σ 𝑗=1 𝑂 𝑡 σ 𝑗=1 𝛾 0 𝛾 𝑡 𝐵 𝑟 መ 𝐵 𝑞 𝐵 = መ = መ 𝐽 𝑡 𝐽 𝑡 𝐽 𝑡 1 exp 1 𝑂 0 𝑦 𝑗0 መ 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 0 σ 𝑗=1 𝑂 𝑡 σ 𝑗=1 exp 𝛾 0 𝛾 0 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 10

3.1. Hedonic Regression Models Decomposition across groups A similar analysis may be performed across groups Example (arithmetic, Laspeyres index): ▪ Suppose that one wants to measure wage discrimination between males ( t = 0) and females ( t = s) ▪ Wage differences may be due to individual characteristics ( x it ) or how those characteristics are valued by employers for each gender ( መ 𝛾 𝑢 ) ▪ Two hedonic functions are estimated, one for males and another for females ▪ Index decomposition is performed in the same way as before: 1 1 𝑂 𝑡 𝑦 𝑗𝑡 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 𝑡 σ 𝑗=1 𝑂 0 σ 𝑗=1 𝛾 𝑡 𝛾 𝑡 𝐵 𝑟 መ 𝐵 𝑞 𝐵 = መ = መ 𝐽 𝑡 𝐽 𝑡 𝐽 𝑡 1 1 𝑂 0 𝑦 𝑗0 መ 𝑂 0 𝑦 𝑗0 መ 𝑂 0 σ 𝑗=1 𝑂 0 σ 𝑗=1 𝛾 𝑡 𝛾 0 𝐵 𝑞 measures the wage gap due to gender discrimination ▪ መ 𝐽 𝑡 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 11

3.2. Program Evaluation Definitions Program evaluation: ▪ Field of study that concerns estimating the effect of a program, policy or some other intervention (“ treatment ”) ▪ Examples: – What is the effect on employment of low-skilled workers of an increase in the minimum wage? – What is the effect on earnings of going through a job training program? In these evaluations, the sample must comprise two groups, with individuals being randomly assigned to each group: ▪ Treatment group: individuals receiving the experimental treatment ▪ Control group: individuals not receiving the experimental treatment 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 12