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Learning Microeconometrics with R [Hardback]

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  • Formāts: Hardback, 398 pages, height x width: 234x156 mm, weight: 689 g, 40 Tables, black and white; 72 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC The R Series
  • Izdošanas datums: 30-Dec-2020
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367255383
  • ISBN-13: 9780367255381
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  • Formāts: Hardback, 398 pages, height x width: 234x156 mm, weight: 689 g, 40 Tables, black and white; 72 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC The R Series
  • Izdošanas datums: 30-Dec-2020
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367255383
  • ISBN-13: 9780367255381
"This book provides an introduction to the field of microeconometrics through the use of R. The focus is on applying current learning from the field to real world problems. It uses R to both teach the concepts of the field and show the reader how the techniques can be used. It is aimed at the general reader with the equivalent of a bachelor's degree in economics, statistics or some more technical field. It covers the standard tools of microeconometrics, OLS, instrumental variables, Heckman selection and difference in difference. In addition, it introduces bounds, factor models, mixture models and empirical Bayesian analysis"--

This book provides an introduction to the field of microeconometrics through the use of R. The focus is on applying current learning from the field to real world problems. It uses R to both teach the concepts of the field and show the reader how the techniques can be used. It is aimed at the general reader with the equivalent of a bachelor’s degree in economics, statistics or some more technical field. It covers the standard tools of microeconometrics, OLS, instrumental variables, Heckman selection and difference in difference. In addition, it introduces bounds, factor models, mixture models and empirical Bayesian analysis.

Key Features:

  • Focuses on the assumptions underlying the algorithms rather than their statistical properties.
  • Presents cutting-edge analysis of factor models and finite mixture models.
  • Uses a hands-on approach to examine the assumptions made by the models and when the models fail to estimate accurately.
  • Utilizes interesting real-world data sets that can be used to analyze important microeconomic problems.
  • Introduces R programming concepts throughout the book.
  • Includes appendices that discuss some of the standard statistical concepts and R programming used in the book.

Recenzijas

'The book offers a great set of statistical and econometric methods useful not only in microeconometrics but in many other fields where the statistical modeling is needed. At the same time, it is a great source of the R programming, particularly, in data simulation and solving complex problems. The whole volume is saturated with R scripts, examples of the language application to numerous aims, and each chapter suggests multiple links to the internet websites related to the topics under consideration. Bibliography of more than eighty sources is also supplied. The book presents an incredibly useful source of information on the modern statistical techniques and their implementations to solving various real-life problems, that makes it very helpful to students and researchers in their projects.'

- Stan Lipovetsky, Technometrics, Vol. 63, Issue 3, August 2021 "...Very friendly and accessible in tone; informal in presentation. This book starts explaining code writing from the beginning. It is intended for graduate students interested and studying or researching in applied economics/econometrics. It provides all data sources with their corresponding links ... Two noticeable features in this book are practicality in applying econometrics and R codes for estimation and simulation of many examples in the book ... This book is very suitable as a textbook in applied economics/econometrics and adaptable for class teaching and a valuable resource for graduates." -Morteza-Alabaf Sabaghi, Journal of the Royal Statistical Society, Series A

Introduction xvii
I Experiments
1(100)
1 Ordinary Least Squares
3(22)
1.1 Introduction
3(1)
1.2 Estimating the Causal Effect
3(4)
1.2.1 Graphing the Causal Effect
3(1)
1.2.2 A Linear Causal Model
4(1)
1.2.3 Simulation of the Causal Effect
4(1)
1.2.4 Averaging to Estimate the Causal Effect
5(2)
1.2.5 Assumptions of the OLS Model
7(1)
1.3 Matrix Algebra of the OLS Model
7(6)
1.3.1 Standard Algebra of the OLS Model
8(1)
1.3.2 Algebraic OLS Estimator in R
9(1)
1.3.3 Using Matrices
9(1)
1.3.4 Multiplying Matrices in R
10(1)
1.3.5 Matrix Estimator of OLS
11(1)
1.3.6 Matrix Estimator of OLS in R
12(1)
1.4 Least Squares Method for OLS
13(3)
1.4.1 Moment Estimation
13(1)
1.4.2 Algebra of Least Squares
14(1)
1.4.3 Estimating Least Squares in R
14(1)
1.4.4 The lm() Function
15(1)
1.5 Measuring Uncertainty
16(4)
1.5.1 Data Simulations
16(2)
1.5.2 Introduction to the Bootstrap
18(1)
1.5.3 Bootstrap in R
18(1)
1.5.4 Standard Errors
19(1)
1.6 Returns to Schooling
20(3)
1.6.1 A Linear Model of Returns to Schooling
20(1)
1.6.2 NLSM Data
20(1)
1.6.3 Plotting Returns to Schooling
21(1)
1.6.4 Estimating Returns to Schooling
22(1)
1.7 Discussion and Further Reading
23(2)
2 Multiple Regression
25(26)
2.1 Introduction
25(1)
2.2 Long and Short Regression
25(6)
2.2.1 Using Short Regression
25(1)
2.2.2 Independent Explanatory Variables
26(1)
2.2.3 Dependent Explanatory Variables
27(1)
2.2.4 Simulation with Multiple Explanatory Variables
27(3)
2.2.5 Matrix Algebra of Short Regression
30(1)
2.3 Collinearity and Multicollinearity
31(2)
2.3.1 Matrix Algebra of Multicollinearity
32(1)
2.3.2 Understanding Multicollinearity with R
32(1)
2.4 Returns to Schooling
33(3)
2.4.1 Multiple Regression of Returns to Schooling
33(1)
2.4.2 NLSM Data
34(1)
2.4.3 OLS Estimates of Returns to Schooling
34(2)
2.5 Causal Pathways
36(7)
2.5.1 Dual Path Model
36(2)
2.5.2 Simulation of Dual Path Model
38(1)
2.5.3 Dual Path Estimator Versus Long Regression
39(3)
2.5.4 Matrix Algebra of the Dual Path Estimator
42(1)
2.5.5 Dual Path Estimator in R
43(1)
2.6 Are Bankers Racist or Greedy?
43(6)
2.6.1 Boston HMDA Data
44(1)
2.6.2 Causal Pathways of Discrimination
44(1)
2.6.3 Estimating the Direct Effect
45(1)
2.6.4 Adding in More Variables
46(1)
2.6.5 Bootstrap Dual Path Estimator in R
47(1)
2.6.6 Policy Implications of Dual Path Estimates
48(1)
2.7 Discussion and Further Reading
49(2)
3 Instrumental Variables
51(24)
3.1 Introduction
51(1)
3.2 A Confounded Model
52(2)
3.2.1 Confounded Model DAG
52(1)
3.2.2 Confounded Linear Model
53(1)
3.2.3 Simulation of Confounded Data
54(1)
3.3 IV Estimator
54(7)
3.3.1 Graph Algebra of IV Estimator
55(1)
3.3.2 Properties of IV Estimator
56(1)
3.3.3 IV Estimator with Standard Algebra
56(1)
3.3.4 Simulation of an IV Estimator
56(1)
3.3.5 IV Estimator with Matrix Algebra
57(1)
3.3.6 Two-Stage Least Squares
58(1)
3.3.7 IV Estimator in R
59(1)
3.3.8 Bootstrap IV Estimator for R
59(2)
3.4 Returns to Schooling
61(5)
3.4.1 Distance to College as an Instrument
62(1)
3.4.2 NLSM Data
62(1)
3.4.3 Simple IV Estimates of Returns to Schooling
63(1)
3.4.4 Matrix Algebra IV Estimates of Returns to Schooling
64(1)
3.4.5 Concerns with Distance to College
65(1)
3.5 Instrument Validity
66(3)
3.5.1 Test of Instrument Validity
67(1)
3.5.2 Test of Instrument Validity in R
68(1)
3.6 Better LATE than Nothing
69(4)
3.6.1 Heterogeneous Effects
69(1)
3.6.2 Local Average Treatment Effect
70(2)
3.6.3 LATE Estimator
72(1)
3.6.4 LATE Estimates of Returns to Schooling
72(1)
3.7 Discussion and Further Reading
73(2)
4 Bounds Estimation
75(26)
4.1 Introduction
75(1)
4.2 Potential Outcomes
76(3)
4.2.1 Model of Potential Outcomes
76(1)
4.2.2 Simulation of Impossible Data
76(1)
4.2.3 Distribution of the Treatment Effect
77(2)
4.3 Average Treatment Effect
79(3)
4.3.1 ATE and Its Derivation
79(1)
4.3.2 ATE and Do Operators
80(1)
4.3.3 ATE and Unconfoundedness
81(1)
4.3.4 ATE and Simulated Data
82(1)
4.4 Kolmogorov Bounds
82(2)
4.4.1 Kolmogorov's Conjecture
82(1)
4.4.2 Kolmogorov Bounds in R
83(1)
4.5 Do "Nudges" Increase Savings?
84(3)
4.5.1 Field Experiment Data
85(1)
4.5.2 Bounds on the Distribution of Balance Changes
86(1)
4.5.3 Intent To Treat Discussion
87(1)
4.6 Manski Bounds
87(7)
4.6.1 Confounded Model
87(1)
4.6.2 Simulation of Manski Bounds
88(1)
4.6.3 Bounding the Average Treatment Effect
88(1)
4.6.4 Natural Bounds of the Average Treatment Effect
89(1)
4.6.5 Natural Bounds with Simulated Data
90(1)
4.6.6 Are Natural Bounds Useless?
90(1)
4.6.7 Bounds with Exogenous Variation
91(1)
4.6.8 Exogenous Variation in Simulated Data
92(1)
4.6.9 Bounds with Monotonicity
92(1)
4.6.10 Bounds with Monotonicity in Simulated Data
93(1)
4.7 More Guns, Less Crime?
94(4)
4.7.1 Crime Data
94(1)
4.7.2 ATE of RTC Laws under Unconfoundedness
95(1)
4.7.3 Natural Bounds on ATE of RTC Laws
95(2)
4.7.4 Bounds on ATE of RTC Laws with Exogenous Variation
97(1)
4.7.5 Bounds on ATE of RTC Laws with Monotonicity
98(1)
4.8 Discussion and Further Reading
98(3)
II Structural Estimation
101(130)
5 Estimating Demand
103(32)
5.1 Introduction
103(1)
5.2 Revealed Preference
104(2)
5.2.1 Modeling Demand
104(1)
5.2.2 Simulating Demand
105(1)
5.2.3 Revealing Demand
106(1)
5.3 Discrete Choice
106(4)
5.3.1 Simple Discrete Choice Model
107(1)
5.3.2 Simulating Discrete Choice
108(1)
5.3.3 Modeling Discrete Choice
108(2)
5.4 Maximum Likelihood
110(7)
5.4.1 Binomial Likelihood
110(2)
5.4.2 Binomial Likelihood in R
112(1)
5.4.3 OLS with Maximum Likelihood
112(2)
5.4.4 Maximum Likelihood OLS in R
114(1)
5.4.5 Probit
115(1)
5.4.6 Probit in R
116(1)
5.4.7 Generalized Linear Model
116(1)
5.5 McFadden's Random Utility Model
117(4)
5.5.1 Model of Demand
117(1)
5.5.2 Probit and Logit Estimators
118(1)
5.5.3 Simulation with Probit and Logit Estimators
119(2)
5.6 Multinomial Choice
121(6)
5.6.1 Multinomial Choice Model
121(1)
5.6.2 Multinomial Probit
122(2)
5.6.3 Multinomial Probit in R
124(1)
5.6.4 Multinomial Logit
125(1)
5.6.5 Multinomial Logit in R
125(1)
5.6.6 Simulating Multinomial Choice
126(1)
5.7 Demand for Rail
127(5)
5.7.1 National Household Travel Survey
128(1)
5.7.2 Demand for Cars
129(2)
5.7.3 Estimating Demand for Rail
131(1)
5.7.4 Predicting Demand for Rail
131(1)
5.8 Discussion and Further Reading
132(3)
6 Estimating Selection Models
135(28)
6.1 Introduction
135(1)
6.2 Modeling Censored Data
136(5)
6.2.1 A Model of Censored Data
136(1)
6.2.2 Simulation of Censored Data
136(2)
6.2.3 Latent Value Model
138(2)
6.2.4 Tobit Estimator
140(1)
6.2.5 Tobit Estimator in R
140(1)
6.3 Censoring Due to Minimum Wages
141(3)
6.3.1 National Longitudinal Survey of Youth 1997
142(1)
6.3.2 Tobit Estimates
143(1)
6.4 Modeling Selected Data
144(6)
6.4.1 A Selection Model
145(1)
6.4.2 Simulation of a Selection Model
145(1)
6.4.3 Heckman Model
146(2)
6.4.4 Heckman Estimator
148(1)
6.4.5 Heckman Estimator in R
149(1)
6.5 Analyzing the Gender Wage Gap
150(5)
6.5.1 NLSY97 Data
150(2)
6.5.2 Choosing to Work
152(1)
6.5.3 Heckman Estimates of Gender Gap
152(3)
6.6 Back to School Returns
155(7)
6.6.1 NLSM Data
155(2)
6.6.2 College vs. No College
157(1)
6.6.3 Choosing College
158(1)
6.6.4 Heckman Estimates of Returns to Schooling
158(3)
6.6.5 Effect of College
161(1)
6.7 Discussion and Further Reading
162(1)
7 Demand Estimation with IV
163(20)
7.1 Introduction
163(1)
7.2 Modeling Competition
164(4)
7.2.1 Competition is a Game
164(1)
7.2.2 Hotelling's Line
165(2)
7.2.3 Nash Equilibrium
167(1)
7.3 Estimating Demand in Hotelling's Model
168(3)
7.3.1 Simulation of Hotelling Model
168(1)
7.3.2 Prices are Endogenous
168(1)
7.3.3 Cost Shifters
169(2)
7.3.4 Demand Shifters
171(1)
7.4 Berry Model of Demand
171(4)
7.4.1 Choosing Prices
172(1)
7.4.2 A Problem with Cost Shifters
172(1)
7.4.3 Empirical Model of Demand
173(1)
7.4.4 Inverting Demand
173(1)
7.4.5 Demand Shifters to Estimate Supply
174(1)
7.4.6 Demand Estimation from Supply Estimates
175(1)
7.5 Introduction of Apple Cinnamon Cheerios
175(6)
7.5.1 Dominick's Data for Cereal
176(1)
7.5.2 Instrument for Price of Cereal
177(1)
7.5.3 Demand for Apple Cinnamon Cheerios
178(3)
7.5.4 Value of Apple Cinnamon Cheerios
181(1)
7.6 Discussion and Further Reading
181(2)
8 Estimating Games
183(24)
8.1 Introduction
183(1)
8.2 Mixed Strategy Nash Equilibrium
183(8)
8.2.1 Coaches' Decision Problem
184(1)
8.2.2 Zero-Sum Game
185(1)
8.2.3 Nash Equilibrium
186(1)
8.2.4 Third and Fourth Down Game
187(1)
8.2.5 Equilibrium Strategies
188(1)
8.2.6 Equilibrium Strategies in R
189(1)
8.2.7 Simulation of Third and Fourth Down Game
189(2)
8.3 Generalized Method of Moments
191(6)
8.3.1 Moments of OLS
191(1)
8.3.2 Simulated Moments OLS
192(2)
8.3.3 GMM OLS Estimator
194(1)
8.3.4 GMM OLS Estimator in R
195(1)
8.3.5 GMM of Returns to Schooling
196(1)
8.4 Estimating the Third Down Game
197(2)
8.4.1 Moment Conditions
198(1)
8.4.2 Third Down GMM Estimator in R
198(1)
8.5 Are NFL Coaches Rational?
199(6)
8.5.1 NFL Data
200(1)
8.5.2 Estimating Third Down Game in R
201(2)
8.5.3 Predicting the Fourth Down Game
203(2)
8.5.4 Testing Rationality of NFL Coaches
205(1)
8.6 Discussion and Further Reading
205(2)
9 Estimating Auction Models
207(24)
9.1 Introduction
207(1)
9.2 Sealed Bid Auctions
208(5)
9.2.1 Sealed Bid Model
209(1)
9.2.2 Sealed Bid Simulation
210(1)
9.2.3 Sealed Bid Estimator
211(1)
9.2.4 Sealed Bid Estimator in R
212(1)
9.3 English Auctions
213(5)
9.3.1 Order Statistics
214(1)
9.3.2 Identifying the Value Distribution
215(1)
9.3.3 English Auction Estimator
216(1)
9.3.4 English Auction Estimator in R
216(2)
9.4 Are Loggers Rational?
218(3)
9.4.1 Timber Data
219(1)
9.4.2 Sealed Bid Auctions
220(1)
9.4.3 English Auctions
221(1)
9.4.4 Comparing Estimates
221(1)
9.5 Are Loggers Colluding?
221(6)
9.5.1 A Test of Collusion
222(1)
9.5.2 "Large" English Auctions
223(1)
9.5.3 Large English Auction Estimator
224(1)
9.5.4 Large English Auction Estimator in R
224(1)
9.5.5 Evidence of Collusion
225(1)
9.5.6 Large Sealed Bid Auction Estimator
226(1)
9.5.7 Large Sealed Bid Auction Estimator in R
227(1)
9.6 Discussion and Further Reading
227(4)
III Repeated Measurement
231(70)
10 Panel Data
233(18)
10.1 Introduction
233(1)
10.2 First Differences
233(3)
10.2.1 First Difference Model
234(1)
10.2.2 Simulated Panel Data
235(1)
10.2.3 OLS Estimation of First Differences
235(1)
10.3 Difference in Difference
236(2)
10.3.1 Difference in Difference Estimator
236(1)
10.3.2 Difference in Difference Estimator in R
237(1)
10.4 Minimum Wage Increase in New Jersey
238(3)
10.4.1 Data from Card and Krueger (1994)
238(1)
10.4.2 Difference in Difference Estimates
239(2)
10.5 Fixed Effects
241(5)
10.5.1 Fixed Effects Estimator
241(1)
10.5.2 Nuisance Parameter
242(1)
10.5.3 Adjusted Fixed Effects Estimator
243(1)
10.5.4 Two Step Fixed Effects Estimator
243(1)
10.5.5 Fixed Effects Estimator in R
244(2)
10.6 Effect of a Federal Minimum Wage Increase
246(4)
10.6.1 NLSY97
247(1)
10.6.2 Fixed Effects Estimators of the Minimum Wage
248(1)
10.6.3 Are Workers Better Off?
249(1)
10.7 Discussion and Further Reading
250(1)
11 Synthetic Controls
251(26)
11.1 Introduction
251(1)
11.2 Beyond "Parallel Trends"
251(5)
11.2.1 A General Fixed Effects Model
252(1)
11.2.2 A Slightly Less General Model
252(1)
11.2.3 Synthetic Synthetic Control Data
252(2)
11.2.4 Constructing Synthetic Controls with OLS
254(1)
11.2.5 OLS Weights in R
254(1)
11.2.6 A "Wide" Data Problem
255(1)
11.3 Abadie Estimator
256(2)
11.3.1 Restricting Weights
257(1)
11.3.2 Synthetic Control Estimator in R
258(1)
11.4 Regularization
258(3)
11.4.1 Turducken Estimation
259(1)
11.4.2 LASSO
259(1)
11.4.3 LASSO in R
260(1)
11.5 Factor Models
261(7)
11.5.1 Matrix Factorization
262(1)
11.5.2 Convex Matrix Factorization
262(2)
11.5.3 Synthetic Controls using Factors
264(1)
11.5.4 Estimating the Weights
264(1)
11.5.5 Convex Factor Model Estimator in R
265(3)
11.6 Returning to Minimum Wage Effects
268(6)
11.6.1 NLSY97 Data
268(1)
11.6.2 Synthetic Control Estimates
269(1)
11.6.3 LASSO Estimates
270(1)
11.6.4 Factor Model Estimates
270(4)
11.7 Discussion and Further Reading
274(3)
12 Mixture Models
277(24)
12.1 Introduction
277(1)
12.2 Two-Type Mixture Models
278(5)
12.2.1 Simulation of Two-Type Mixture
278(1)
12.2.2 Knowing the Component Distributions
279(1)
12.2.3 Observing Multiple Signals
280(3)
12.3 Two Signal Mixture Models
283(5)
12.3.1 Model of Two Signal Data
283(1)
12.3.2 Simulation of Two Signal Data
283(1)
12.3.3 Conditional Independence of Signals
284(1)
12.3.4 Two Signal Estimator
284(1)
12.3.5 Two Signal Estimator Algorithm
285(1)
12.3.6 Mixture Model Estimator in R
286(2)
12.4 Twins Reports and Returns to Schooling
288(6)
12.4.1 Mixture Model of Twin Reports
289(1)
12.4.2 Twin Reports Data
290(1)
12.4.3 Mixture Model Approach to Measurement Error
290(2)
12.4.4 Estimating Returns to Schooling from Twins
292(2)
12.5 Revisiting Minimum Wage Effects
294(5)
12.5.1 Restaurant Employment
294(1)
12.5.2 Mixture Model Estimation of Restaurant Type
295(1)
12.5.3 Heterogeneous Minimum Wage Effect
295(4)
12.6 Discussion and Further Reading
299(2)
IV Appendices
301(2)
A Measuring Uncertainty
303(28)
A.1 Introduction
303(1)
A.2 Classical Statistics
303(11)
A.2.1 A Model of a Sample
304(1)
A.2.2 Simulation of a Sample
304(1)
A.2.3 Many Imaginary Samples
304(2)
A.2.4 Law of Large Numbers
306(1)
A.2.5 Central Limit Theorem
307(1)
A.2.6 Approximation of the Limiting Distribution
308(1)
A.2.7 Simulation of Approximate Distributions
309(1)
A.2.8 Bootstrap
310(2)
A.2.9 Hypothesis Testing
312(2)
A.3 Bayesian Statistics
314(2)
A.3.1 Bayes' Rule
314(1)
A.3.2 Determining the Posterior
314(1)
A.3.3 Determining the Posterior in R
315(1)
A.4 Empirical Bayesian Estimation
316(6)
A.4.1 A Large Number of Samples
316(1)
A.4.2 Solving for the Prior and Posterior
317(1)
A.4.3 Solving for the Prior in R
318(2)
A.4.4 Estimating the Posterior of the Mean
320(2)
A.5 The Sultan of the Small Sample Size
322(4)
A.5.1 Classical or Bayesian?
322(1)
A.5.2 Uniform Prior
323(1)
A.5.3 Estimating the Prior
323(2)
A.5.4 Paciorek's Posterior
325(1)
A.6 Decision Theory
326(3)
A.6.1 Decision Making Under Uncertainty
327(1)
A.6.2 Compound Lotteries
327(1)
A.6.3 What in the World Does Wald Think?
328(1)
A.6.4 Two Types of Uncertainty?
329(1)
A.7 Discussion and Further Reading
329(2)
B Statistical Programming in R
331(24)
B.1 Introduction
331(1)
B.2 Objects in R
331(7)
B.2.1 Vectors
331(2)
B.2.2 Matrices
333(2)
B.2.3 Lists
335(2)
B.2.4 Data Frames
337(1)
B.3 Interacting with Objects
338(6)
B.3.1 Transforming Objects
338(1)
B.3.2 Logical Expressions
339(1)
B.3.3 Retrieving Information from a Position
340(3)
B.3.4 Retrieving the Position from the Information
343(1)
B.4 Statistics
344(3)
B.4.1 Data
345(1)
B.4.2 Missing Values
345(1)
B.4.3 Summary Statistics
346(1)
B.4.4 Regression
347(1)
B.5 Control
347(3)
B.5.1 Loops
347(1)
B.5.2 Looping in R
348(1)
B.5.3 If Else
349(1)
B.6 Optimization
350(3)
B.6.1 Functions
350(2)
B.6.2 optim()
352(1)
B.7 Discussion and Further Reading
353(2)
Note 355(2)
Bibliography 357(6)
Author index 363(2)
Subject index 365
Chris Adams was born and raised in Melbourne Australia and is a lifelong Carlton supporter. Chris received his PhD in economics from the University of Wisconsin - Madison. He has taught at the University of Vermont and in the Johns Hopkins Masters of Applied Economics program. He has 17 years experience working in merger regulation and antitrust for the US Federal Trade Commission. He is currently a Principal Analyst at the US Congressional Budget Office. Chris work and research focus on econometrics, empirical industrial organization, pharmaceutical innovation and auctions. His work has been published in various academic journals including The Econometrics Journal, Health Affairs, Health Economics, Marketing Science and Economics Letters. Chris is a colon cancer survivor and a research patient advocate with ECOG-ACRIN. Most importantly, he is a father to CJ and husband to Deena.