APPLIED ECONOMIC MODELLING Theory (Chapter 1) Instructor: Joaquim - PowerPoint PPT Presentation

APPLIED ECONOMIC MODELLING Theory (Chapter 1) 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

Course Description This course provides an introduction to the modern econometric techniques used in applied economic studies: ▪ The interaction between theoretical economic models and empirical econometric analysis is emphasized ▪ Students will be trained in formulating and testing economic models using real data Pre-requisites (recommended): ▪ Microeconomics, Macroeconomics, Econometrics 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 2

Grading Continuous assessment: ▪ Test (50% of the grade) ▪ Problem Set (50% of the grade) ▪ Approval requires: – Weighted mean of at least 10 – Minimum grade at the test of 7 – Minimum attendance: 80% of classes or Final examination (100% of the grade): 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 3

Contents 1. Microeconomic Models 1.1. Linear Regression Models for Cross-Sectional and Panel Data 1.2. Demand Analysis 1.3. Production and Cost Functions 1.4. Efficiency and Stochastic Frontier Models 2. Macroeconomic Models 2.1. Linear Regression Models for Time Series Data 2.2. The Demand for Money 2.3. The Philips Curve 3. Econometric Models for Policy Analysis 3.1. Hedonic Regression Models 3.2. Differences-in-Differences Estimator Software: Stata 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 4

Textbooks Recommended: ▪ Intriligator, M., Bodkin, R. and Hsiao, C. (1995), Econometric Models, Techniques and Applications , 2nd Ed., Prentice Hall. ▪ Patterson, K. (2000), An Introduction to Applied Econometrics: A Time Series Approach , Palgrave. ▪ Verbeek, M. (2017), A Guide to Modern Econometrics , 5th Ed., Wiley. Others: ▪ Berndt, E.R. (1991), The Practice of Econometrics – Classic and Comtemporary , Addison-Wesley. ▪ Coelli , T.J., D.S.P. Rao, C.J. O’Donnell, G.E. Battese (2005), An Introduction to Efficiency and Productivity Analysis , 2nd Ed., Springer. ▪ Deaton, A., J. Muellbauer (1980), Economics and Consumer Behavior , Cambridge University Press. ▪ Wooldridge, J.M. (2015), Introductory Econometrics: a Modern Approach , 6ª Ed., South-Western Publishers. 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 5

1.1. Linear Regression Models for Cross-Sectional and Panel Data Cross-Sectional Data Model Specification: 𝑍 𝑗 = 𝛾 0 + 𝛾 1 𝑌 𝑗1 + ⋯ + 𝛾 𝑙 𝑌 𝑗𝑙 + 𝑣 𝑗 𝑗 = 1, ⋯ , 𝑂 𝑍 = 𝑌𝛾 + 𝑣 𝐹 𝑍|𝑌 = 𝑌𝛾 Assumptions: 𝑣 : error term 1. Random sampling 𝛾 : parameters 2. 𝐹 𝑣|𝑌 = 0 𝑙 : n. explanatory variables 3. No perfect colinearity 𝑞 : n. parameters : 𝑊𝑏𝑠 𝑣|𝑌 = 𝜏 2 4. Homoskedasticity 𝑂 : n. observations : 𝑣~𝑂𝑝𝑠𝑛𝑏𝑚 0, 𝜏 2 5. Normality 𝜏 2 : error variance 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 6

Cross-Sectional Data Estimation Estimation method - Ordinary Least Squares (OLS): 𝑂 2 , 𝑗 = መ 𝛾 0 + መ 𝛾 1 𝑌 𝑗1 + ⋯ + መ 𝑗 − ෠ ෠ min ෍ 𝑣 𝑗 ො 𝑣 𝑗 = 𝑍 ො 𝑍 𝑗 , 𝑍 𝛾 𝑙 𝑌 𝑗𝑙 𝑗=1 𝑣 : residual ො መ 𝛾 = 𝑌 ′ 𝑌 −1 𝑌 ′ 𝑧 ෠ 𝑍 : fitted value of 𝑍 Estimator properties: መ 𝛾 : estimate for 𝛾 Finite samples: ▪ Assumptions 1-3: Unbiasedness Stata regress Y 𝑌 1 ⋯ 𝑌 𝑙 ▪ Assumptions 1-4: Unbiasedness and efficiency ▪ Assumptions 1-5: Unbiasedness, efficiency and normality Asymptotically: ▪ Assumptions 1-3: Consistency ▪ Assumptions 1-4: Consistency, efficiency and normality 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 7

Cross-Sectional Data Partial / Marginal Effects Effects from unitary changes in a given explanatory variable: ∆𝑌 𝑘 = 1 ⇒ ∆𝑍 = 𝛾 𝑘 Needs adaptation for: ▪ Transformed dependent variables ▪ Transformed quantitative explanatory variables ▪ Qualitative explanatory variables Aims: ▪ Testing whether the effect is null or significantly different from zero → it is equivalent to test whether a parameter or a set of a parameters or a linear combination of parameters are significantly different from zero ▪ If significant, analyzing the sign of the effect (positive, negative) ▪ If significant, calculating and analyzing the magnitude of the effect 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 8

Cross-Sectional Data Inference Variance of the parameter estimators: Needed for performing hypothesis tests Alternative estimators: ▪ Standard – assumes homoskedasticity 𝜏 2 𝑌 ′ 𝑌 −1 𝑊𝑏𝑠 መ 𝛾 = ො ▪ Robust – valid under both homoskedasticity and heteroskedasticity 𝑊𝑏𝑠 መ 𝛾 = 𝑌 ′ 𝑌 −1 𝑌′෡ Ω𝑌 𝑌 ′ 𝑌 −1 , where ෡ 2 Ω = 𝑒𝑗𝑏𝑕 ො 𝑣 𝑗 ▪ Cluster-robust – specific for panel data −1 σ 𝑗=1 −1 , where 𝐘 𝑗 and ෝ 𝑊𝑏𝑠 መ 𝑂 ′ 𝐘 𝑗 𝑂 ′ ෝ ′ 𝐘 𝑗 σ 𝑗=1 𝑂 ′ 𝐘 𝑗 𝛾 = σ 𝑗=1 𝐘 𝑗 𝐘 𝑗 𝐯 𝑗 ෝ 𝐯 𝑗 𝐘 𝑗 𝐯 𝑗 are based on the 𝑈 observations available for individual 𝑗 Stata regress Y 𝑌 1 … 𝑌 𝑙 regress Y 𝑌 1 … 𝑌 𝑙 , vce(robust) regress Y 𝑌 1 … 𝑌 𝑙 , vce(cluster clustvar ) 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 9

Cross-Sectional Data Inference Test for the individual significance of a parameter – t test: 𝐼 0 : 𝛾 𝑘 = 0 𝐼 1 : 𝛾 𝑘 ≠ 0 or 𝐼 1 : 𝛾 𝑘 > 0 or 𝐼 1 : 𝛾 𝑘 < 0 መ 𝛾 𝑘 𝑢 = ~𝑢 𝑂−𝑞 𝜏 ෡ ො 𝛾 𝑘 Stata regress Y 𝑌 1 … 𝑌 𝑙 regress Y 𝑌 1 … 𝑌 𝑙 , vce(robust) regress Y 𝑌 1 … 𝑌 𝑙 , vce(cluster clustvar ) 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 10

Cross-Sectional Data Inference Test for the joint significance of a set of parameters – F / Wald tests: Model: 𝑍 = 𝛾 0 + 𝛾 1 𝑌 1 + ⋯ +𝛾 𝑕 𝑌 𝑕 +𝛾 𝑕+1 𝑌 𝑕+1 + ⋯ + 𝛾 𝑙 𝑌 𝑙 + 𝑤 Hypotheses: 𝑆 2 : coefficient of determination of the model under H 1 𝐼 0 : 𝛾 𝑕+1 = ⋯ = 𝛾 𝑙 = 0 2 : coefficient of determination of the model 𝑆 ∗ under H 1 𝐼 1 : No 𝐼 0 𝑟 : n. of parameters being tested Test: መ 𝛾 ∗ : vector of parameters to be tested 𝑆 2 −𝑆 ∗ 2 𝑂−𝑞 𝑟 𝐺 = 𝑟 ~𝐺 → valid only under homoskedasticity 𝑂−𝑞 1−𝑆 2 −1 መ ′ Var መ 2 → general formula 𝑋 = 𝑂 መ 𝛾 ∗ 𝛾 ∗ 𝛾 ∗ ~𝜓 𝑟 Stata regress Y 𝑌 1 ⋯ 𝑌 𝑕 𝑌 𝑕+1 ⋯ 𝑌 𝑙 ,… test 𝑌 𝑕+1 ⋯ 𝑌 𝑙 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 11

Cross-Sectional Data RESET Test RESET test: Intuition: ▪ Any model of the type 𝐹 𝑍|𝑌 = 𝑇 𝑌𝛾 may be approximated by 𝑘+1 γ j 𝑌 መ ∞ = 𝑌𝛾 + σ 𝑘=1 𝐹 𝑍|𝑌 𝛾 Stata (only test version based on three fitted powers) Implementation: regress Y 𝑌 1 … 𝑌 𝑙 ▪ Estimate the original model estat ovtest 2 , 𝑌 መ 3 , 𝑌 መ 4 , … ▪ Generate the variables 𝑌 መ 𝛾 𝛾 𝛾 ▪ Add the generated variables to the original model and estimate the following auxiliary model: 2 + γ 2 𝑌 መ 3 + γ 3 𝑌 መ 4 + ⋯ + 𝑤 𝑍 = 𝛾 0 + 𝛾 1 𝑌 1 + ⋯ + 𝛾 𝑙 𝑌 𝑙 + γ 1 𝑌 መ 𝛾 𝛾 𝛾 ▪ Apply an F / Wald test for the significance of the added variables: 𝐼 0 : γ 1 = γ 2 = γ 3 = ⋯ = 0 (suitable model functional form) 𝐼 1 : No 𝐼 0 (unsuitable model functional form) 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 12

Endogeneity Definition and Consequences Definitions: Exogenous explanatory variables: 𝐹 𝑣|𝑌 = 0 → essential assumption in any regression model Endogenous explanatory variables: 𝐹 𝑣|𝑌 ≠ 0 Consequences: OLS estimators become inconsistent Motivation: Omitted variables Simultaneity 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 13

Endogeneity Omitted Variables Example: True model: 𝑍 = 𝛾 0 + 𝛾 1 𝑌 1 + 𝛾 2 𝑌 2 + 𝑤 Estimated model: 𝑍 = 𝛾 0 + 𝛾 1 𝑌 1 + 𝑣 As 𝑣 = 𝛾 2 𝑌 2 + 𝑤: ▪ If 𝑑𝑝𝑤 𝑌 1 , 𝑌 2 = 0 , then 𝐹 𝑣 𝑌 1 = 0 → 𝑌 1 is exogenous ▪ If 𝑑𝑝𝑤 𝑌 1 , 𝑌 2 ≠ 0 , then 𝐹 𝑣 𝑌 1 ≠ 0 → 𝑌 1 is endogenous 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 14

Endogeneity Simultaneity Example: Model: ቊSupply: 𝑅 = 𝛾 0 + 𝛾 1 𝑄 + 𝑣 Demand: 𝑅 = 𝛽 0 + 𝛽 1 𝑄 + 𝑤 As: ൞𝑄 = 𝛽 0 − 𝛾 0 + 𝑤 − 𝑣 𝛾 1 − 𝛽 1 𝛾 1 − 𝛽 1 𝑅 = ⋯ then 𝑄 is function of 𝑤 and 𝑣 ; hence: ▪ 𝐹 𝑣 𝑄 ≠ 0 in the supply equation → 𝑄 is endogenous ▪ 𝐹 𝑤 𝑄 ≠ 0 in the demand equation → 𝑄 is endogenous 2017/2018 Joaquim J.S. Ramalho Applied Economic Modelling 15