├── .gitignore ├── README.md ├── io ├── io1 │ ├── 8853_LectureNotes.pdf │ ├── 8853_LectureNotes.tex │ ├── chapters │ │ ├── auctions.tex │ │ ├── blp.tex │ │ ├── conduct.tex │ │ ├── demandavail.tex │ │ ├── dynamic.tex │ │ ├── entry.tex │ │ ├── introdemand.tex │ │ ├── logits.tex │ │ ├── momineq.tex │ │ ├── papers.tex │ │ ├── retail.tex │ │ └── vertical.tex │ └── figures │ │ ├── entry-br90-ineq.jpg │ │ └── entry-br90-multeq.jpg └── io2 │ ├── 8854_LectureNotes.pdf │ ├── 8854_LectureNotes.tex │ └── chapters │ ├── commonown.tex │ ├── dynamics.tex │ ├── endogprod.tex │ ├── insurance.tex │ ├── learning.tex │ ├── momineq.tex │ ├── nlp.tex │ ├── pricedisc.tex │ ├── production.tex │ ├── search.tex │ └── switchcosts.tex ├── macro ├── 7750_M01 │ ├── 7750_LectureNotes.aux │ ├── 7750_LectureNotes.log │ ├── 7750_LectureNotes.pdf │ ├── 7750_LectureNotes.synctex.gz │ ├── 7750_LectureNotes.tex │ ├── 7750_LectureNotes.toc │ └── images │ │ ├── Ramseyinitc.JPG │ │ ├── Ramseyphase.JPG │ │ ├── Ramseysavingshock.JPG │ │ ├── Solowbreakeven.JPG │ │ ├── Solowphase.JPG │ │ ├── akphase.JPG │ │ ├── cdynamics.JPG │ │ ├── desktop.ini │ │ ├── kdynamics.JPG │ │ └── solowsshock.JPG └── 7751_M02 │ ├── 7751_LectureNotes.aux │ ├── 7751_LectureNotes.log │ ├── 7751_LectureNotes.pdf │ ├── 7751_LectureNotes.synctex.gz │ ├── 7751_LectureNotes.tex │ ├── 7751_LectureNotes.toc │ └── images │ ├── PIH.PNG │ ├── RBC1-graph.PNG │ ├── RBC1-gshock.PNG │ ├── RBC1-zshock.PNG │ ├── RBC2-gshock.png │ ├── RBC2-zshock.png │ ├── RBC3-gshock0.PNG │ ├── RBC3-gshock1.PNG │ ├── RBC3-gshock2.PNG │ ├── RBC3-zshock1.PNG │ ├── RBC3-zshock2.PNG │ ├── graphDNKK.JPG │ ├── moneyshock3DNK.JPG │ ├── moneyshock3DNKi.JPG │ ├── moneyshockDNKKg.JPG │ ├── noPIH.PNG │ ├── techshock3DNK1.JPG │ ├── techshock3DNK1i.JPG │ ├── techshock3DNK2.JPG │ └── techshock3DNK2i.JPG ├── metrics ├── 7772_INTRO │ ├── 7772_LectureNotes.aux │ ├── 7772_LectureNotes.log │ ├── 7772_LectureNotes.pdf │ ├── 7772_LectureNotes.synctex.gz │ ├── 7772_LectureNotes.tex │ ├── 7772_LectureNotes.toc │ ├── Chapters │ │ ├── c01_estimatorproperties.tex │ │ ├── c02_asympestimatorproperties.tex │ │ ├── c03_classicalregression.tex │ │ ├── c04_specificationissues.tex │ │ ├── c05_mlestimation.tex │ │ ├── c06_inferencehyptests.tex │ │ ├── c07_generalizedls.tex │ │ ├── c08_dynamicmodels.tex │ │ ├── c09_ivreg2sls.tex │ │ ├── c10_gmm.tex │ │ ├── c11_nonparamreg.tex │ │ ├── c12_policyeval.tex │ │ ├── c12_regdiscontinuity.tex │ │ └── c13_regdiscontinuity.tex │ └── Images │ │ └── DefCorrelogram.png └── 8822_CSPDE │ ├── 8822_LectureNotes.aux │ ├── 8822_LectureNotes.log │ ├── 8822_LectureNotes.pdf │ ├── 8822_LectureNotes.synctex.gz │ ├── 8822_LectureNotes.tex │ ├── 8822_LectureNotes.toc │ └── images │ ├── b2.PNG │ ├── bag1.PNG │ ├── bag3.PNG │ ├── bag4.PNG │ ├── distcompare.PNG │ ├── lassograph.PNG │ ├── localtreatmentclass.PNG │ ├── quantilereg.PNG │ ├── ridgegraph.PNG │ └── tbmethod.PNG └── micro ├── 7740_ConsGE ├── 7740_LectureNotes.aux ├── 7740_LectureNotes.log ├── 7740_LectureNotes.pdf ├── 7740_LectureNotes.synctex.gz ├── 7740_LectureNotes.tex ├── 7740_LectureNotes.toc └── IMAGES │ ├── edge01.JPG │ ├── edge02.JPG │ ├── edge03.JPG │ ├── edge04.JPG │ ├── edge05.JPG │ ├── edge06.JPG │ └── prodset.JPG ├── 7741_GameTh ├── 7741_GT_LectureNotes.aux ├── 7741_GT_LectureNotes.log ├── 7741_GT_LectureNotes.pdf ├── 7741_GT_LectureNotes.synctex.gz ├── 7741_GT_LectureNotes.tex ├── 7741_GT_LectureNotes.toc └── IMAGES │ ├── LIORgame.JPG │ ├── advselecprofit.JPG │ ├── advselecsep.JPG │ └── advselecutil.JPG └── 7741_SocialChoice ├── 7741_LectureNotes.aux ├── 7741_LectureNotes.dvi ├── 7741_LectureNotes.log ├── 7741_LectureNotes.out.ps ├── 7741_LectureNotes.pdf ├── 7741_LectureNotes.synctex.gz ├── 7741_LectureNotes.tex ├── 7741_LectureNotes.toc └── images ├── advsel.JPG ├── advsel2.JPG ├── budgline.JPG ├── certline.JPG ├── certline.aux ├── fosd.JPG ├── fullins.JPG ├── hirisk.JPG ├── lorisk.JPG ├── machinaallais.JPG ├── machinaallais2.JPG ├── machinaallais3.JPG ├── machinatri.JPG ├── mrsrisk.JPG ├── rdprob.JPG ├── rdprobfi.JPG ├── sosd.JPG └── sppref.JPG /.gitignore: -------------------------------------------------------------------------------- 1 | *.out 2 | *.synctex.gz 3 | *.aux 4 | *.log 5 | *.bbl 6 | *.blg 7 | *.nav 8 | *.toc 9 | *.snm 10 | *.opt 11 | /io/io2/articles/ 12 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Lecture Notes 2 | 3 | 4 | This repository consists of the majority of my lecture notes taken during my Ph.D. in Economics at Boston College. They are divided in four folders: micro, macro, metrics and io. 5 | 6 | 1. Econometrics 7 | - ECON7772: Introduction to Econometrics (taught by Pr. Arthur Lewbel in Spring 2018) 8 | - ECON8822: Cross-section and Panel Data Econometrics (taught by Pr. Stefan Hoderlein in Fall 2018) 9 | - ECON8825: Topics in Econometric Theory (not available yet) 10 | - ECON: Empirical Methods in Applied Microeconomics (not available yet) 11 | 12 | 2. Microeconomic Theory 13 | - ECON7740: Consumer Choice, Firm Choice and General Equilibrium (taught by Prs. Marvin Kraus and Hideo Konishi in Fall 2017) 14 | - ECON7741a: Social Choice and Expected Utility Theory (tauhgt by Pr. Uzi Segal in Spring 2018) 15 | - ECON7741b: Game Theory (taught by Pr. Utku Unver in Spring 2018) 16 | 17 | 3. Macroeconomic Theory 18 | - ECON7750: Macroeconomic Theory I (Long-run) (taught by Pr. Fabio Schiantarelli in Fall 2017) 19 | - ECON7751: Macroeconomic Theory II (Real Business Cycles) (taught by Pr. Susanto Basu in Spring 2018) 20 | 21 | 4. Industrial Organization 22 | - ECON8853: Industrial Organization I (not available yet) 23 | - ECON8854: Industrial Organization II (not availableyet) 24 | 25 | 26 | ## Improving these notes 27 | 28 | These notes are a work in progress, therefor, any suggestion on how to improve these notes in any way (content or more) are welcome. I feel that Git is ideal to share these potential suggestions, so please feel free to create issues or submit pull requests/update. 29 | 30 | ## Disclaimer 31 | 32 | These notes are based on Lectures given by various professors of Boston College, as well as textbooks used in the classes. However, they did not participate in the writing or compiling of these notes, thus, all errors and opinions are my own. 33 | 34 | Contact: sarkisp@bc.edu 35 | 36 | -------------------------------------------------------------------------------- /io/io1/8853_LectureNotes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/io/io1/8853_LectureNotes.pdf -------------------------------------------------------------------------------- /io/io1/8853_LectureNotes.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{report} 2 | \usepackage[utf8]{inputenc} 3 | \usepackage[english]{babel} 4 | \usepackage{microtype} 5 | \usepackage{libertine} 6 | \usepackage{amsmath,amsthm} 7 | \usepackage[varg]{newtxmath} 8 | \usepackage{setspace,graphicx,epstopdf} 9 | \usepackage{marginnote,datetime,url,enumitem,subfigure,rotating} 10 | \usepackage{multirow} 11 | \usepackage{xfrac} 12 | \usepackage[openlevel=3]{bookmark} 13 | \usepackage[tikz]{bclogo} 14 | \usepackage{enumitem} 15 | 16 | \setcounter{tocdepth}{1} 17 | 18 | \def\D{\mathrm{d}} 19 | 20 | \setlength{\parindent}{0ex} 21 | \setlist[itemize]{topsep=-6pt, itemsep=-1pt} 22 | \setlist[enumerate]{topsep=-6pt, itemsep=-1pt} 23 | 24 | \newcommand{\smalltodo}[2][] {\todo[caption={#2}, size=\scriptsize,% 25 | fancyline, #1]{\begin{spacing}{.5}#2\end{spacing}}} 26 | \newcommand{\rhs}[2][]{\smalltodo[color=green!30,#1]{{\bf PS:} #2}} 27 | 28 | \newcommand{\E}[1]{\operatorname{E}\left[#1\right]} 29 | \newcommand{\Et}[1]{\operatorname{E}_t\left[#1\right]} 30 | \newcommand{\V}[1]{\operatorname{Var}\left[#1\right]} 31 | \newcommand{\cov}[1]{\operatorname{Cov}\left(#1\right)} 32 | \newcommand{\covt}[1]{\operatorname{Cov}_t\left(#1\right)} 33 | \newcommand{\avg}[2]{\frac{#1}{#2} \sum_{i=#1}^{#2}} 34 | \def\D{\mathrm{d}} 35 | \newcommand{\prob}[1]{\operatorname{Pr}\left[#1\right]} 36 | 37 | 38 | \begin{document} 39 | 40 | \date{} 41 | \title{\textbf{\huge{ECON8853 - Industrial Organization I}}\\ \textit{Lecture Notes from Julie H. Mortimer's lectures}} 42 | \author{Paul Anthony Sarkis\\ Boston College} 43 | 44 | \maketitle 45 | 46 | \tableofcontents 47 | 48 | \setlength{\parskip}{1em} 49 | 50 | \chapter{Overview of Demand Systems and Vertical Model} 51 | \input{chapters/introdemand} 52 | 53 | \chapter{Logit, Nested Logit and Multinomial Probit} 54 | \input{chapters/logits} 55 | 56 | \chapter{Mixed Logit (BLP)} 57 | \input{chapters/blp} 58 | 59 | \chapter{Product Availability} 60 | \input{chapters/demandavail} 61 | 62 | \chapter{Entry Models} 63 | \input{chapters/entry} 64 | 65 | \chapter{Moment Inequalities} 66 | \input{chapters/momineq} 67 | 68 | \chapter{Single-agent Discrete Dynamic Programming} 69 | \input{chapters/dynamic} 70 | 71 | \chapter{Retailing and Inventories} 72 | \input{chapters/retail} 73 | 74 | \chapter{Conduct and Antitrust} 75 | \input{chapters/conduct} 76 | 77 | \chapter{Auctions} 78 | \input{chapters/auctions} 79 | 80 | \chapter{Vertical Contracts} 81 | \input{chapters/vertical} 82 | 83 | \chapter{Additional papers} 84 | \input{chapters/papers} 85 | 86 | 87 | \end{document} -------------------------------------------------------------------------------- /io/io1/chapters/auctions.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | Auctions are an important part of economic research because of their features and applications: they rely on a simple game, with well-specified rules (= less assumptions needed), they can be observed directly, they are used in a lot of settings and are very diverse. All these elements make auctions markets particularly interesting for IO research. 4 | 5 | First, we need to define four types of auctions based on the type of bidding and the payment rules: \begin{enumerate} 6 | \item First-price sealed-bid auctions: No agent sees the opponents' bids. Highest bidder wins and pays their bid. Losers get nothing. 7 | \item Second-price sealed-bid auctions: No agent sees the opponents' bids. Highest bidder wins and pays second highest bid. Losers get nothing. 8 | \item English auction: Price goes up until only one player is willing to pay the price. Effectively pays the second highest valuation (in eqm). 9 | \item Dutch auction: Price goes down until one player is willing to pay the price. Effectively pays the highest valuation (in eqm). 10 | \end{enumerate} 11 | 12 | Dutch auctions are not very common and most of the empirical work is centered on the three other types (depending on the situation). Theoretically, we consider FPSB and Dutch auctions to be equivalent (same equilibrium strategies). The same holds between SPSB and English auctions. 13 | 14 | Not covered in this chapter are multi-unit and combinatorial auctions, which both usually ask for a lot more computation power for empirical work. 15 | 16 | In the empirical IO literature, the goals of studying auction markets are to (1) describe and elicit, among others, how agents bid, their valuations for the goods, the difference with the models, or the presence of collusion; but also (2) to identify optimal rules given the setting. Researchers typically use two approaches to do this:\begin{itemize} 17 | \item Reduced-form: to test assumptions or theoretical predictions, make inferences about behavior or the bidding environment. 18 | \item Structural: assuming theory holds, to estimate the primitives of the model (distribution of private values, affiliation, etc.) 19 | \end{itemize} 20 | 21 | \section{Private Value Auctions} 22 | 23 | 24 | 25 | \section{Common Value Auctions} 26 | 27 | 28 | 29 | \section{Estimation of Auction Models} 30 | 31 | 32 | 33 | \section{Asker (2010)} 34 | 35 | \subsection{Summary} 36 | 37 | \subsubsection{Background} 38 | 39 | Collusion in an English auction can yield lower winning bids (thus lower auction revenues). To see that, consider three bidders with values 10, 8, and 5 in an English auction, such that in a competitive outcome, the price would be 8. If bidders 1 and 2 collude, they can bring the price to 5. Note that it needs not to happen as when bidders 1 and 3 collude, the price is still 8. The research questions are thus: how do bidding rings work in practice? and how do they affect market outcomes? 40 | 41 | To study this: look at bidding ring in the stamps auction market! Eleven dealers are part of a ``ring'' (subset of all bidders). They are organized in two periods: knockout stage and target auction. The first is to determine who from the ring will get the object if the ring wins, and the price at which they stop (with payments), while the second is the actual auction. 42 | 43 | \subsubsection{Model} 44 | 45 | Structural approach: design of a IPV-style model, with two types of bidders (because weaker bidders in data) and focus only on auctions with two bidders in the knockout phase! 46 | 47 | \subsubsection{Data} 48 | 49 | Complete record of ring's activity. Observation unit is an auction, observed variables are bidders in the knockout, amount bid, side payments, price of target auction etc. 50 | 51 | \subsubsection{Assumptions} 52 | 53 | 54 | 55 | \subsubsection{Results} 56 | 57 | Bidding rings can introduce inefficiencies in auctions, but in that case, effect is small. Asymmetry of bidders is a big weakness of maintaining rings. Other bidders (outside the ring) are also affected by the ring. -------------------------------------------------------------------------------- /io/io1/chapters/blp.tex: -------------------------------------------------------------------------------- 1 | For now we have seen three types of discrete-choice models and their applications to demand estimation for differentiated products: the simple logit model, the nested logit model and the multinomial probit model. The first two models, although quite useful and fairly simple to estimate were limited in three dimensions: they do not allow for random taste variation (\ref{sssec:tastevar}), they have restricted substitution patterns (\ref{sssec:logitiia}), they do not allow for correlation over time. Mixed logit models (which contains BLP) are highly flexible models that can deal with the previously mentioned issues. 2 | 3 | Mixed logit models are a class of models that encompasses all types of models where the market shares are computed as integrals over simple logit functional form. We'll see in detail later what that means but intuitively, you should think of the model as everyone having her/his own logit model of demand, and aggregate demand would be computed by integrating over consumer attributes. In particular, IO economists are most interested in the BLP (for \cite{blp_95}) model and extensions of it like \cite{dfs_12}. 4 | 5 | We'll first cover the basics of mixed logit and random coefficients, before talking in depth about estimation techniques as found in BLP and DFS. 6 | 7 | \section{Base Model} 8 | 9 | Generally, we write utility derived from consumption of a good $j$ by consumer $i$ as the function $U(X_j, p_j, \xi_j, \nu_i, \theta)$, which is a function of product $j$ observable characteristics ($X_j$ of dimension $L-1$), price ($p_j$), unobservable characteristics ($\xi_j$) and consumer characteristics (observable $z_i$ and unobservables $\nu_i$), all entering the utility function through a vector of parameters $\theta$. As a simpler case, define utility as a linear function of those parameters such that: $$u_{ij} = \sum_{l=1}^L x_{jl}\beta_{il} + \xi_j + \varepsilon_{ij} $$ $$ \text{where } \beta_{il} = \bar\beta_l + \beta_l^o z_i + \beta_l^u \nu_i $$ There are five elements in this utility function:\begin{itemize} 10 | \item Observed ($x_j\lambda$) and unobserved ($\xi_j$) product quality. 11 | \item Observed ($x_{j}\beta^o z_i$) and unobserved ($x_{j}\beta^u \nu_i$) consumer-product interactions. 12 | \item A type-I EV iid error term ($\varepsilon_{ij}$). 13 | \end{itemize} 14 | The main difference with the typical discrete-choice models described in the previous chapter is that a ``contribution'' of $\lambda$ to product $j$'s $l$-th characteristic is given by $(\bar\beta_l + \beta_l^o z_i + \beta_l^u \nu_i)\cdot\lambda$, meaning that it varies across consumers. These consumer-product interactions are the main feature of mixed logit models, as they allow for more complex (and thus realistic) substitution patterns between products. For example, if we consider demand for cars, this model will allow consumers who have a preference for size to attach higher utility to all large cars, inducing larger substitution effects between goods that share the same characteristics. 15 | 16 | For simplicity, we usually rewrite the utility function as the sum of a product-specific mean and a consumer-specific mean deviation: $$u_{ij} = \underbrace{\sum_{l=1}^L x_{jl}\lambda_l + \xi_j}_{\delta_j\text{: product mean utility}} + \underbrace{\sum_{l=1}^L x_{jl}\beta_l^o z_i + \sum_{l=1}^L x_{jl}\beta_l^u \nu_i + \varepsilon_{ij}}_{\mu_{ij}\text{: mean deviation}} $$ 17 | 18 | This general form of the mixed logit model includes both observed and unobserved consumer characteristics. In general however, market data does not come with exact description of consumer characteristics for each interaction. At best, we might have aggregate consumer data (about a geographical region, a point in time, ...) but most often we cannot observe any characteristic. When we do observe consumer characteristics, we can use them in $z_i$ to estimate the model. A particularly influential paper using this type of data is the MicroBLP paper. When such data is unobserved, we work with just the $\nu_i$ part of the model, as in the original BLP paper. 19 | 20 | \section{Berry, Levinsohn and Pakes, 1995} 21 | 22 | The Berry, Levinsohn and Pakes (1995) paper made a very important contribution to the discrete-choice demand literature by designing a procedure to estimate random-coefficient logit models. Their approach comprises the usual GMM estimator as an outer loop and a nested fixed-point algorithm in the inner loop to circumvent computational issues. Note that the nested fixed-point (NFP) terminology refers only to the computational algorithm used to compute the estimator; BLP refers to the estimator. Other approaches exist, some exploring other procedures within the inner loop, like Bajari, Fox, Kim and Ryan (2011), others relying on a different philosophy altogether (for example, the MPEC approach introduced by Su and Judd (2012) and Dubé, Fox and Su (2012)). Nevertheless, BLP stands as one of the most common and known demand models in IO, as well as in other fields. 23 | 24 | \subsection{Getting to the shares equation} 25 | 26 | Recall the utility function from the previous section (without $z_i$ by assumption): $$ U_{ij} = \delta_j + \sum_{l=1}^L x_{jl}\beta_l^u \nu_i + \varepsilon_{ij} $$ Using the fact the error term is a type-I EV as in the simple logit, we can integrate it and get logit shares, but only conditional on $\nu_i$! Formally, we get: $$ P_{ij}|\nu_i = \frac{\exp(\delta_j + x_{j}\beta \nu_i )}{\sum_k \exp(\delta_k + x_{k}\beta \nu_i )} $$ $$ \Rightarrow s_{j} = \int \frac{\exp(\delta_j + x_{j}\beta \nu_i )}{\sum_k \exp(\delta_k + x_{k}\beta \nu_i )} f(\nu_i)\D \nu_i $$ However, this integral cannot be reduced to a simple unidimensional integral but rather is a $L$-dimensional integral and thus is very hard to compute for large $L$, even using modern computers. The BLP paper's main addition to the literature consists in solving this computational issue using an ``aggregation by simulation'' designed in Pakes (1986). 27 | 28 | \subsection{BLP estimation algorithm} 29 | 30 | Consider the situation where data is available only on the aggregate product-level, and no consumer data is observable. We will work out the estimation of demand following four steps:\begin{enumerate} 31 | \item Conditional on a value for $\theta$, estimate the implied market shares by simulation. 32 | \item Solve for the vector pf product unobservables $\xi$ as a function of both implied and observed market shares. 33 | \item Estimate $\theta$ by GMM on implied moment conditions. 34 | \item Update $\theta$ with the new results and repeat until convergence. 35 | \end{enumerate} 36 | 37 | As in the estimation procedures of logit and nested logit models, the key to estimate $\theta$ is to use the interaction of the unobservable product characteristic $\xi$ and adequate instruments. However, there are two main differences: (1) the product-specific constant $\xi$ is not a linear function of market shares and characteristics anymore and (2) the implied market shares to be used in computing $\xi$ are multi-dimensional integrals. The second point is the reason why we need to estimate market shares by simulation, for a given $\theta$; the first point will require a more complex solving process based on a contraction mapping. 38 | 39 | 40 | \subsubsection{Step 1: Estimating market shares by simulation} 41 | 42 | Recall that we computed the market shares as a function of product characteristics: $$s_j(\delta, \beta) = \int \frac{\exp(\delta_j + X_j\nu_i\beta^u)}{1 + \sum_k \exp(\delta_k + X_k\nu_i\beta^u) } f(\nu) \D\nu $$ 43 | The issue with this integral is that it cannot be solved analytically ($\nu_i$ is usually a multivariate normal distribution, which makes the market share a multi-dimensional integral); we can approximate it by taking the sample average over a set of $ns$ draws in a simulation. This yields: $$\hat s_j^{ns}(\delta, \beta) = \frac{1}{ns} \sum_{i} \frac{\exp(\delta_j + X_j\nu_i\beta^u)}{1 + \sum_k \exp(\delta_k + X_k\nu_i\beta^u) } $$ 44 | As we can see, even using simulations we can only estimate market shares using values for $\delta$ and $\beta$, but these parameters are precisely the ones we are trying to estimate. Because of this, we will have to ``nest'' this estimation procedure into a bigger loop that will find the best values $\delta$ and $\beta$ (using convergence properties). This convergence result requires to keep the set of simulated $\nu_i$ for the whole exercise: the process of drawing these simulated individuals must not be nested inside any loop. If the distribution of these $\nu_i$ (not observations, but at least the pdf) is observed, then we can draw from the said distribution, but usually, we assume $\nu_i$ to come from a multivariate normal distribution (across multiple consumer unobserved characteristics). 45 | 46 | Moreover, it is important to note that the use of a finite number of draws in the simulation will create a new source of errors within our estimation routine. Enough simulation draws should help tampering this issue, although finding the good number of draws is not an exact science, but more like a tradeoff between computation speed and errors. Overall, numerical evaluation of integrals is a particular topic that is deep enough to think about it carefully. For deeper explanations on selecting the right way to simulate, solve nonlinear equations in the case of random-coefficients logit, refer to Knittel and Metaxoglou (2013). 47 | 48 | \subsubsection{Step 2: NFP inversion} 49 | 50 | We now need to recover the product unobservable term $\xi_j$. In the same way as we did in the simple logit models, we already have the link between $\delta$ and $\xi$, but $\delta$ is "buried" in a nonlinear fashion into the the market shares: we need to invert the market shares to get delta, thus $\xi$, as a function of the shares (rather than the opposite). Doing that requires a special trick that is at the very core of\cite{blp_95} contribution. 51 | 52 | Their trick is to use the fact that the following system: $$\delta_j^k(\beta) = \delta_j^{k-1}(\beta) + \ln(s_j) - \ln(\hat s_j^{ns}(\delta^{k-1}, \beta)) $$ is a contraction mapping. To see it, understand that $s_j$ is the observed market share, the exponent $k$ represents the iteration process. In other words, by iterating over this function, the $\delta$ values will converge to the true value, $\delta^*(\beta, s, \hat s)$, where $s, \hat s$ are respectively the vectors of observed and estimated shares conditional on $\beta$. Finally, we can write: $$\xi(\beta, s, \hat s) = \delta^*(\beta, s, \hat s) - X_j\bar\beta $$ and use this form to construct the moments. 53 | 54 | \subsubsection{Step 3: Constructing the moments} 55 | 56 | Now that we have recovered $\xi$ as a function of $\beta$, we can construct the moment conditions for demand estimation. To do this, we can go the OLS route if no component of $x$ is endogenous but most probably we will go the IV route, using $w$ as the instrument matrix. The moment condition would therefore be: $$ \E{\xi_j(\beta) w_j} = 0 $$ As always in GMM, we want to select $\beta$ such that the average analog to the moment equation is the closest possible to 0. 57 | 58 | \subsubsection{Step 4: Outer loop optimization} 59 | 60 | The first three steps were performed for a given $\beta$, thus we now need to find the best $\beta$, using a nonlinear search over $\beta$. 61 | 62 | \subsection{Identification} 63 | 64 | In order to fully identify the model, we need four elements:\begin{enumerate} 65 | \item Choice set variation: 66 | \item Product characteristics variation: 67 | \item Consumer characteristics variation: 68 | \item Functional form: 69 | \end{enumerate} 70 | 71 | \subsection{Adding a supply side} 72 | 73 | Supply-side estimation in BLP is similar to what was done in simpler logit models. Refer to section \ref{sec:supplyside} for more information. 74 | 75 | \section{Dubé, Fox and Su, 2012} 76 | 77 | Dubé, Fox and Su (2012) introduce a new computational algorithm (DFS) for implementing the BLP estimator. The intuition behind the paper is to ``recast'' the GMM objective function of BLP into a mathematical program with equilibrium constraints (MPEC). Compared to the NFP method described earlier, the MPEC approaches generates the exact same estimator but differs in the fact that it does not use any nested inner loop and that can use first-order or second-order derivatives to improve convergence. 78 | 79 | \subsection{MPEC: A constrained optimization} 80 | 81 | Let $W$ be the GMM weighting matrix. DFS suggests a constrained optimization formulation as: $$\hat\theta, \hat\xi = \arg \min_{\theta, \xi} g(\xi)' W g(\xi) $$ $$ \text{ s.t. } s(\xi;\theta) = S $$ where the moment condition term is $g(\xi) = 1/T \cdot \sum_{t=1}^T \sum_{j=1}^J \xi_{j,t} w_{j,t}$; $s(\xi;\theta)$ is the vector function of implied market shares (aggregated by simulation as in the previous approach) and $S$ is the vector of observed market shares. From this optimization problem, it is clear that the nested loop has disappeared to accommodate a nonlinear search over both the utility function parameters and product-specific constants $\xi$. 82 | 83 | \subsubsection{Advantages over NFP} 84 | 85 | There are two main advantages of using MPEC instead of the traditional NFP procedure:\begin{enumerate} 86 | \item Without inner loop, there are no errors that propagate to the outer loop, thus reducing errors in the overall estimates. 87 | \item MPEC does not require its constraint to hold for each iteration, as long as they hold at the end, thus improving speed of convergence. 88 | \end{enumerate} -------------------------------------------------------------------------------- /io/io1/chapters/conduct.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | Antitrust laws are designed with the goal to control how firms attain and maintain their market position, in order to improve consumer welfare, or welfare in a broader sense. 4 | 5 | Around the end of the 19th century, people were growing frustrated at the excessive control of monopolies and cartels over markets. This led to the passage of key legislation and the creation of regulatory agencies. Today, the main institutional actors in antitrust are the Department of Justice (DOJ) and the Federal Trade Comission (FTC). 6 | 7 | The creation of these agencies show the implicit belief that society cannot rely on private firms to control the market, nor on consumers to organize and fight against market power. But it remains that the goals of antitrust institutions are unclear: are they figthing for consumer welfare? for economic efficiency? What would happen if some consumers win and some lose? 8 | 9 | \section{Mergers} 10 | 11 | Mergers are the simplest antitrust situation to analyze because there exists a pre and post outcome. 12 | 13 | \subsection{Some cases} 14 | 15 | 16 | 17 | \subsection{Merger guidelines} 18 | 19 | The Merger Guidelines are a document issued by the DOJ and the FTC (for the first time in 1982, most recently in 2010) with the purpose of clarifying situations where antitrust agencies might impede merger. 20 | 21 | These ``rules'' seek to prevent firms from merging if it would lead to unilateral exercise of market power or to coordinated interactions. They describe tools for merger analysis in two main sections: screening and analysis. 22 | 23 | The role of screening is to raise flags in markets where mergers would lead to significantly concentrated markets, where unfair markups could be sustained. Merger analysis is then completed by simulating over the market under merger and not, to compare both outcomes in terms of welfare, prices, markups, etc. 24 | 25 | \subsection{Screening} 26 | 27 | Screening can be done using one of two tools: 28 | 29 | \subsubsection{Using HHI} 30 | 31 | The Herfindahl-Hirschman Index, or HHI, is defined as the sum of squared market shares in a market. While previously designed on its own, it can be derived analytically using the Cournot model of competition. 32 | 33 | Using it for merger analysis is done by looking at the current HHI in combination with the potential post-merger HHI and their difference. Small changes would then not be challenged compared to bugger changes, but given a change in HHI, more concentrated markets will get challenged more often. 34 | 35 | The problem with using the HHI is market definition. In fact, using market shares implies that competitors are clearly defined, whereas in reality, it is not often the case. Moreover, market definition will have a huge impact on the numbers, and thus on what the guidelines have to say about the merger. 36 | 37 | \subsubsection{Using UPP} 38 | 39 | Using the intuition that a merger might induce a price change, the Upward Pricing Pressure is a theoretical measure of the incentives of raising prices after a potential merger between two firms. By definition it does not require any market definition because it looks at only the two merging firms. However, it assumes away the price responses of potential competitors, uses the pre-merger prices for one of the goods. 40 | 41 | All in all, it is not a perfect measure but can be used as a quick screening process for unilateral mergers. 42 | 43 | \subsection{Market definition} 44 | 45 | A market is defined as group of products and a geographic area such that a hypothetical profit-maximizing firm (hypothetical monopolist), not subject to price regulation, likely would impose a small but significant and nontransitory increase in price (SSNIP), assuming that the terms of sale of all other products is held constant. A relevant market is no larger (in terms of products and geography) than is needed to satisfy this criteria. 46 | 47 | The intuition behind this definition is to use the fact that if a monopolist (one with the most market power) would not increase prices by a significant amount, then no one would. 48 | 49 | Usually, this threshold is set at 5\% although it varies across industries and situations. 50 | 51 | Then, we need to define market participants which obviously would include the firms that own the products in the marker, but also other firms such as potential entrants (that could enter if only one firm was in the market). 52 | 53 | \subsection{Merger Analysis} 54 | 55 | As mentioned earlier, the three steps to studying a merger is:\begin{enumerate} 56 | \item Define a market. 57 | \item Screen using HHI or UPP. 58 | \item Simulate the merger (fully or partially). 59 | \end{enumerate} 60 | 61 | The last step is the only we have not looked at yet. 62 | 63 | \subsubsection{Merger Simulation} 64 | 65 | There are two ways of simulating a merger:\begin{itemize} 66 | \item Partial Merger Simulation: where market outcomes are simulated for the merging products only, holding everything else fixed, then the effects are compared to synergies or cost savings. 67 | \item Full Merger Simulation: where market outcomes are simulated using a structural model describing the behavior of all firms in the market. 68 | \end{itemize} 69 | 70 | \subsubsection{Potential issues} 71 | 72 | Merger analysis typically will not allow for some elements that will bias the analysis in questions. Among others, we find product repositioning, committed entry, possible entry, efficiency gains, exit, etc. 73 | 74 | \section{Conlon and Mortimer (2018)} 75 | 76 | -------------------------------------------------------------------------------- /io/io1/chapters/momineq.tex: -------------------------------------------------------------------------------- 1 | This chapter provides a more rigorous introduction to estimation of models through the use of inequality restrictions, henceforth called moment inequalities. We have seen them in the previous chapter on entry, but they can be applied more generally to any type of games that would yield cumbersome computations using traditional methods, or for estimation when data are imperfect. 2 | 3 | \section{Framework} 4 | 5 | \subsection{The agent's decision problem} 6 | 7 | Consider a situation with $n$ decision makers indexed by $i$, having access to their own information set $I_i$ when decisions are made and $D_i$ the set of available decisions. The strategy played by agent $i$ is a mapping $s_i:I \to D$ (from information to action), such that it generates the observed decisions $d_i$ (which could be a vector). 8 | 9 | The profit function of agent $i$ is determined by his decision ($d_i$), the other agents' decisions ($d_{-i}$) and other environment variables $y_i$. At the time of the decision, the agent has expectations over what happens in the game ($\pi(\cdot)$, $s_i$, $I_i$ and $Y_i$); they are denoted by $\mathcal{E}\left[\cdot\right]$, which is not the same operator as the typical expectation operator. 10 | 11 | \subsubsection{Best-response condition (Nash)} 12 | 13 | If $d_i$ is the observed decision of player $i$, we assume: $$ \sup_{d\in\D_i} \mathcal{E}\left[ \pi(d, d_{-i}, y_i) | I_i \right] \leq \mathcal{E}\left[ \pi(d_i, d_{-i}, y_i) | I_i \right] \text{ for all } i = 1, ..., n $$ 14 | 15 | Quite obviously, we can see this assumption as an assumption for ``rationality'', meaning that at the time of the decision, the agent chose the best option. In single agent problems, this comes directly from optimization behavior, while in games, it is only a necessary condition for a Bayes-Nash equilibrium to be played, but it does not rule out multiple equilibria, or restrict the selection between equilibria. 16 | 17 | \subsubsection{Counterfactual condition} 18 | 19 | In order for the agents to ensure optimal behavior, they need to evaluate the alternative decisions in their counterfactual environment. Thus we need to define what happens to $d_{-i}$ and $y_i$ following the decision of agent $i$. Note that in single-agent problems and simultaneous games, the counterfactual is assumed away using a conditional independence assumption. 20 | 21 | In other cases, we assume that $y_i = y(z_i, d, d_{-i})$ and that the distribution of $(d_i, z_i)$ conditional on $I_i$ and $d$ do not depend on $d$. In words, this assumption means that environment variables $y_i$ depend only on variables $z_i$ and decisions by the agents (which are all exogenous conditional on $I_i$ and $d$). 22 | 23 | Using this, we define the ``differential profit'' as: $$\Delta\pi(d, d', d_{-i}, z_i) = \pi(d, d_{-i}, y(z_i, d, d_{-i})) - \pi(d', d_{-i}, y(z_i, d', d_{-i})) $$ as the difference in profits between two decisions. 24 | 25 | Finally, we rewrite the first condition as: $$ \mathcal{E}\left[ \Delta\pi(d_i, d, d_{-i}, z_i) | I_i \right] \geq 0 \text{ for all } i = 1, ..., n $$ 26 | 27 | This might seem like the inequality to use in estimation, however, recall that the expectation is only the agent's so we need to recover empirical analogues of these in order to use them. 28 | 29 | \subsection{Observables and disturbances} 30 | 31 | We assume that the econometrician has a parametric function, denoted $r(\cdot)$, that approximates $\pi(\cdot)$ given arguments $d_i$, $d_{-i}$, observable variables of $z_i$, denoted $z_i^o$ and unknown parameters $\theta$ to estimate. 32 | 33 | Using that function, we can approximate the differential profit with $\Delta r(d, d', d_{-i}, z_i^o, \theta)$. From there, define two types of errors: \begin{align*} 34 | \nu_{2, i, d, d'} & = \mathcal{E}\left[ \Delta\pi(d, d', d_{-i}, z_i) | I_i \right] - \mathcal{E}\left[ \Delta r(d, d', d_{-i}, z_i^o, \theta) | I_i \right] \\ \nu_{1, i, d, d'} & = \nu_{1, i, d, d'}^\pi - \nu_{1, i, d, d'}^r \\ \nu_{1, i, d, d'}^\pi & = \Delta\pi(d_i, d, d_{-i}, z_i) - \mathcal{E}\left[ \Delta\pi(d_i, d, d_{-i}, z_i) | I_i \right] \\ \nu_{1, i, d, d'}^r & = \Delta r(d, d', d_{-i}, z_i^o, \theta) - \mathcal{E}\left[\Delta r(d, d', d_{-i}, z_i^o, \theta)|I_i\right] 35 | \end{align*} 36 | that we refer to in general as $\nu_{2,i}$ and $\nu_{1,i}$ (composed of $\nu_{1,i}^\pi$ and $\nu_{1,i}^r$). Note that the first error, while not observed by the econometrician, is a part of the information set $I_i$ of the agent (he ``knows'' $\nu_{2,i}$). The second error is not observed by either the agent nor the econometrician. 37 | 38 | \subsection{Moment inequalities} 39 | 40 | 41 | 42 | \section{Applications} 43 | 44 | 45 | 46 | %\subsection{Discrete games} 47 | % 48 | %Let $\pi(\cdot)$ be the profit function (continuation value) earned in the second period, $d_i$ and $d_{-i}$ be agent $i$'s and its competitors' discrete decisions respectively, $y_i$ be the set of variables that affect the agent's profits, $D_i$ be the choice set (of decisions) and $I_i$ the information set. Further, denote as $\mathcal{E}\left[ \cdot | I_i \right] $ the agent's expectation (note that we do not use the usual expectation term because we want to differentiate from the ``econometric'' expectation we usually use). 49 | % 50 | %In order to estimate this discrete game, we need two conditions to hold: 51 | % 52 | %\subsubsection{Nash condition} 53 | % 54 | %The Nash condition states that: $$ \sup_{d\in\D_i, d\neq d_i} \mathcal{E}\left[ \pi(d, d_{-i}, y_i, \theta) | I_i \right] \leq \mathcal{E}\left[ \pi(d_i, d_{-i}, y_i, \theta) | I_i \right] \text{ for all } i = 1, ..., n $$ In words, this condition ensures that the observed decision $d_i$ was at least among the best (in expectations) compared to alternatives, given the information set available. 55 | % 56 | %Note that this condition does not restrict the choice set to be discrete (and thus could apply to more settings than entry). Moreover, while this condition imply some kind of rationality, it does not imply anything about uniqueness of the solution (i.e. the observed decision might be one of multiple equilibria). 57 | % 58 | %\subsubsection{Counterfactual condition} 59 | % 60 | %The counterfactual condition allows us to recover what would have happened in the case of other decisions: $$ d_{-i} = d(d_i, z_i) \text{ and } y_i = y(z_i, d) $$ where $z_i$ is exogenous of $d_i$. This condition implies that conditional on the information set, beliefs about the competitors' actions depend only on the agent's decision and exogenous variables (that do not change with the decision). 61 | % 62 | %In the case of simultaneous games, notice that $d(\cdot)$ is just the observed action $d_{-i}$ for any $d_i$. 63 | % 64 | %\subsubsection{Implications} 65 | % 66 | %Let $d' \in D_i$ be any alternative choice and let $$ \Delta\pi(d_i, d', d_{-i}, z_i) \equiv \pi(d_i, d_{-i}, z_i) - \pi(d', d_{-i}, z_i) $$ then, using the Nash and the counterfactual conditions, we have that: $$\mathcal{E}\left[ \Delta\pi(d_i, d', d_{-i}, y_i) | I_i \right] \geq 0 \text{ for all } d' \in D_i $$ While this implication seems straightforward considering the two conditions presented earlier, it will serve as a basis for the estimation algorithm. However, for that relation to be useful, we need to specify two more elements: (1) the relation between agents' expectations ($\mathcal{E}$) and observed sample moments ($\text{E}$) and (2) the functional form of $\pi$ in relation to the variables $z_i, d_i$ and $d_{-i}$ and how they can be described by observed variables. 67 | % 68 | %\subsection{Entry model with structural error} 69 | 70 | 71 | -------------------------------------------------------------------------------- /io/io1/chapters/papers.tex: -------------------------------------------------------------------------------- 1 | \section{Lee (2013)} 2 | 3 | \begin{itemize} 4 | \item \textbf{Research questions:} What are the effects of vertical integration and exclusive dealing on industry (1) structure and (2) welfare? 5 | \item \textbf{Goals of the paper:} test a model (competitive effects of networks) + measure an effect (effects on structure and welfare). 6 | \item \textbf{Importance of the paper:} New knowledge on network industries (which are more and more common). 7 | \item \textbf{Theoretical foundations:} (1) Two-level demand system (for consoles and software) and (2) developer choice for consoles. \begin{itemize} 8 | \item Strengths: 9 | \item Shortcomings: No competition between consoles, no console-level strategies. 10 | \end{itemize} 11 | \item \textbf{Empirical strategy:} (1) use dynamic demand and (2) use moment inequalities for developing process.\begin{itemize} 12 | \item Strengths: 13 | \item Shortcomings: 14 | \end{itemize} 15 | \item \textbf{Data:} (1) Software sales (genre, release date, exclusivity contract, price, shares, etc.) (2) Hardware sales (shares, prices) and (3) market-level (demographics + survey for heterogeneity). 16 | \begin{itemize} 17 | \item Exogenous: 18 | \item Endogenous: 19 | \end{itemize} 20 | \item \textbf{Results:} Exclusive arrangements have (1) helped entrants, (2) hurt incumbent and (3) increased differentiation. 21 | \end{itemize} 22 | 23 | \section{Ho (2009)} 24 | 25 | \subsection{Discussion} 26 | 27 | \begin{itemize} 28 | \item \textbf{Research questions:} (1) How do insurer-provider networks arise? (2) What are the effects of ``star'' hospitals, capacity-constrained hospitals and merged hospitals on the bargaining process? 29 | \item \textbf{Goals of the paper:} test a model (contracting between insurers and providers) + measure an effect (hospital demand or size on bargaining) and maybe slightly interested in policy implications. 30 | \item \textbf{Importance of the paper:} Implications on policy since health providing is so important. 31 | \item \textbf{Theoretical foundations:} (1) Two-level BLP demand system (for insurers and providers) and (2) bargaining game between insurers and providers. \begin{itemize} 32 | \item Strengths: 33 | \item Shortcomings: 34 | \end{itemize} 35 | \item \textbf{Empirical strategy:} (1) use BLP moments and (2) use moment inequalities for bargaining process (profits from observed network must be higher than reversing decision on one hospital).\begin{itemize} 36 | \item Strengths: 37 | \item Shortcomings: 38 | \end{itemize} 39 | \item \textbf{Data:} (1) Hospital-level (size, teaching?, for-profit?, staff size, services, etc.) (2) Plan-level (shares, premia, network size, services included, people included, type of plan, etc.) and (3) market-level (demographics). 40 | \begin{itemize} 41 | \item Exogenous: 42 | \item Endogenous: contracts, prices, shares. 43 | \end{itemize} 44 | \item \textbf{Results:} Consumer demand, hospital costs, ``star'' status, capacity constraints and system hospitals are the main features to determine bargaining power of hospitals. 45 | \end{itemize} -------------------------------------------------------------------------------- /io/io1/chapters/retail.tex: -------------------------------------------------------------------------------- 1 | \section{Aguirregabiria (1999)} 2 | 3 | \subsubsection{Background} 4 | 5 | There is substantial evidence of price dispersion and staggering (prices are not flexible), most commonly explained by menu costs (changing prices is costly) and not perfect correlation in demand (different demand shocks across firms). Confirmed by theory of (S, s) rule (= target price and adjustment bands with adjustment only outside the bands). But what to make of evidence that retail firms might not use (S, s) rules, or that prices go down sometimes (with inflation, prices should always go up)? Most explanations rely on ``consumer-side'' phenomenons, not on inventories (supply-side)! 6 | 7 | Maybe a model of (S, s) rule with inventories would explain some variation! 8 | 9 | \subsubsection{Model} 10 | 11 | Firms maximize profits as a function of expected sales, order costs, inventory costs and menu costs (all three are lump-sum!) = (S, s) rule is still optimal! 12 | 13 | Without menu costs, inventories are perfectly negatively correlated with markups: giving evidence of price markdowns when inventory is high (right after an order) but no price staggering. 14 | 15 | With menu costs, you get price staggering as well as markdowns. 16 | 17 | \subsubsection{Data} 18 | 19 | Monthly information on prices, sales, orders and inventories for every item = balanced panel data. Price data is monthly averages (for regular price and sales price). 20 | 21 | \subsubsection{Assumptions} 22 | 23 | \begin{itemize} 24 | \item Monopolistic competition in product market, price-taker in wholesale market 25 | \item Typical Rust + utility assumptions: additive separability, independence of errors, first-order Markov processes, logit errors, etc. 26 | \item Hotz-Miller approach where estimate policy functions then include in moments. 27 | \end{itemize} 28 | 29 | \subsubsection{Empirical evidence} 30 | 31 | Naive analysis and reduced form regressions show infrequent price changes, prevalence of sales promotions, infrequent orders, negative correlations between inventories and prices. 32 | 33 | Using a Hotz-Miller approach, authors find the same results: data is consistent with high lump-sum cost of ordering and menu costs. 34 | 35 | \subsubsection{Counterfactuals} 36 | 37 | Removing these lump sum costs actually leads to more variability = they explain a lot of price staggering and price reductions! Demand might explain the rest. 38 | 39 | \section{Hendel and Nevo (2002)} 40 | 41 | \subsubsection{Background} 42 | 43 | When goods are storable, price variation might create bias in demand estimation. In fact, if prices decrease (during sales for example), then consumers might stockpile: creates large demand increase in the short run which, measured in long-run (when prices have gone back up) will inflate own-price elasticities. Cross-price elasticities be ambiguous. Because these elasticities are so important in industry analysis, you have to get them right! 44 | 45 | This is the analog analysis to the Aguirregabiria (1999) paper where he studies price variation and inventories (= the supply side). 46 | 47 | \subsubsection{Data} 48 | 49 | Scanner data on store-level and household-level consumption in the detergent market. Hendel and Nevo observe price, quantities, some measure of advertising, sales, inventories (both at the store and household levels). 50 | 51 | Reduced form analysis shows that duration between purchases has a positive effect on quantity purchased (= household do hold inventories); storage costs are negatively correlated with buying on sale (= not being able to store leads to less storage?); households buy more on sale, even when they do hold inventories already (= stockpiling). 52 | 53 | \subsubsection{Model} 54 | 55 | Do not model quantity purchases but only sizes! Dynamic discrete choice model with utility of purchase and inventory costs. 56 | 57 | \subsubsection{Assumptions} 58 | 59 | \begin{itemize} 60 | \item Typical Rust + utility assumptions: additive separability, independence of errors, first-order Markov processes, logit errors, etc. 61 | \item Purchase of different brands yield different utilities but consumption of different brands yields the same utility. 62 | \item Recover initial inventory by simulation and likelihood mapping with sequence of purchases. 63 | \item To reduce dimensionality: for each ``size'' estimate a static demand model to recover logit inclusive value of each size, and use this in standard approach (with prices and ads only for those sizes). 64 | \end{itemize} 65 | 66 | -------------------------------------------------------------------------------- /io/io1/chapters/vertical.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | Manufacturers rarely supply final consumers directly but are usually vertically separated by one or more intermediaries. In this particular type of setting, we often refer to the manufacturer as the upstream firm, and the intermediary as the downstream firm. This relationship is the same as in a typical market, considering the downstream firm as the customer and the upstream firm as the producer, thus leading to the same topics as usual: endogenous pricing, price discrimination, etc. 4 | 5 | The main addition to the usual models is that now the downstream firm is not the end consumer, but rather an agent that will serve the end consumers, thus doing its own share of pricing, advertising, etc. Because these activities will affect the consumers, the upstream firm has incentives to control the downstream firms in some way, we call this ``vertical control''. There are several types of vertical restraints used by firm:\begin{itemize} 6 | \item Exclusive territories: a single retailer is assigned to a ``territory'' (geographical or not) and has monopoly rights over the area. 7 | \item Exclusive dealings: a retailer that chooses the upstream firm cannot sell nor carry any of the competitors' goods. 8 | \item Full-line forcing: a dealer is committed to sell the whole product line of the upstream manufacturer. 9 | \item Resale Price Maintenance (RPM): a dealer commits to retail prices (or a range) that will hold for the product. Equivalently, quantity forcing or rationing will commit the retailer on the quantity side. 10 | \item Contractual arrangements: more flexible agreement between upstream and downstream firms to transfer the product. Profit and revenue sharing are the most common. 11 | \end{itemize} 12 | 13 | \section{Theoretical insights} 14 | 15 | \subsection{Basic Framework} 16 | 17 | Start with a simple model with a homogeneous good with demand given by $p = a - Q$. Moreover, both the upstream and downstream firms are monopolists. The downstream firm has a distribution cost equal to $d$ (the price it pays for the upstream good), while the upstream firm has a marginal cost equal to $c$. 18 | 19 | \subsection{Externalities} 20 | 21 | Because the downstream firm has a monopoly over retailing, its optimal strategy is to charge the monopoly price for the product. The manufacturer also has a monopoly over the production of the good, thus will charge a monopoly price to the retailer! 22 | 23 | From this example we can draw multiple results: \begin{itemize} 24 | \item The upstream firm earns higher profits than the retailer. 25 | \item The upstream firm would earn even more by selling directly to the market. 26 | \item Total industry profits are lower than vertically integrated profits. 27 | \end{itemize} 28 | These results come from the presence of two markups! This is what we call double marginalization. Going around this issue can be done by including additional terms in the contracts (RPM, quantity forcing, etc.). 29 | 30 | \subsection{Downstream Moral Hazard} 31 | 32 | 33 | 34 | \subsection{Interbrand Competition and Legal Issues} 35 | 36 | 37 | 38 | \newpage 39 | 40 | \section{Papers} 41 | 42 | \subsection{Mortimer (2008)} 43 | 44 | \subsubsection{Background} 45 | 46 | This paper studies the efficiency improvements linked to vertical contracts in the video rental industry. It follows the contractual innovation of revenue-sharing which became widespread after 1998. The revenue sharing contracts are designed as an upfront fee per tape, then a royalty based on rentals. This comes in contrast to the previous main contract called ``linear-pricing'' where the retailer would just buy the tape upfront and hold it in inventory at whatever price they chose. 47 | 48 | \subsubsection{Model} 49 | 50 | Straightforward model of vertical market with contracting. The main resulting equations are used as moment equations in the estimation (by GMM). 51 | 52 | \subsubsection{Data} 53 | 54 | Main observation unit is the store-title-week level, where observed variables include number of transactions (rentals), etc. At more aggregated levels, store-title pairs include average rental price, type of contract, etc. Title data include the type of movie, the box-office, rating etc. and finally the store data include demographics about the area. 55 | 56 | \subsubsection{Assumptions} 57 | 58 | \begin{itemize} 59 | \item No coordination between stores, even within a chain. 60 | \item No competition between films and film distributors (= monopolistic suppliers). 61 | \end{itemize} 62 | 63 | \subsubsection{Results} 64 | 65 | Revenue-sharing contracts had positive effects on welfare across the board (consumer surplus, profits, etc.). Other vertical contracts are having a positive effect on profits while decreasing consumer surplus. 66 | 67 | \newpage 68 | \subsection{Conlon and Mortimer (2017)} 69 | 70 | \subsubsection{Background} 71 | 72 | This paper studies the effects of vertical rebates on efficiency (greater retail effort) and foreclosure (of competing products). Using field experiment, consumer choice and retailer behavior. Vending machine industry: AUD (all-units discount) gives discount per-unit, quantity target and facing requirement. 73 | 74 | \subsubsection{Model} 75 | 76 | Consumer choice model: random-coefficients logit. 77 | 78 | Retailer behavior (portfolio and effort): dynamic model of restocking à la Rust (1987). 79 | 80 | \subsubsection{Data} 81 | 82 | Dataset from field experiment: observation unit is machine-visit, observed variables are quantity vended, price, other facings, etc. 83 | 84 | Data from Mars: AUD contractual terms. 85 | 86 | \subsubsection{Assumptions} 87 | 88 | \begin{itemize} 89 | \item Instruments: no price coefficient because no variation. 90 | \end{itemize} 91 | 92 | \subsubsection{Results} 93 | 94 | Vertical rebates do increase effort levels for the retailer. 95 | 96 | \newpage 97 | \subsection{Ho, Ho and Mortimer (2012)} 98 | 99 | \subsubsection{Background} 100 | 101 | This paper studies the effects of bundling as a vertical contract between manufacturers and retailers (= full-line forcing) on welfare. In the video rental industry, the content is very important so need of both supply and demand models (always renewed, etc.). 102 | 103 | \subsubsection{Model} 104 | 105 | Sort of dynamic nested-logit model (static with decay) with focus on changing choice sets: typical nested-logit with a decay term (months since release fixed effect). 106 | 107 | Portfolio choice for the retailer: using moment inequalities, under the assumption that on average portfolio choice is optimal. 108 | 109 | Profit model for counterfactuals. 110 | 111 | \subsubsection{Data} 112 | 113 | Dataset from Rentrak. Observation unit is transaction (store-title), observed variables are distributor, genre, box-office categories, type of release, etc. and type of vertical contract. Additional information on demographics. 114 | 115 | \subsubsection{Assumptions} 116 | 117 | \begin{itemize} 118 | \item Data and computation limitation: no stockouts, month-level aggregation, nests based on box-office categories (not genre?), monopolies (because don't observe competition). 119 | \item Instruments: average inventory in other stores of same size (for inventory); average number of movies in group and average within group share in other stores of same size (for within group share); no instrument for price (results were the same). 120 | \item Supply side: stores have perfect foresight of demand 121 | \end{itemize} 122 | 123 | \subsubsection{Results} 124 | 125 | 126 | 127 | \newpage 128 | \subsection{Crawford et al. (2017)} 129 | 130 | \subsubsection{Background} 131 | 132 | This paper studies the welfare effects of vertical integration (a type of vertical contract), in terms of reduced double marginalization (positive) and foreclosure (negative). In the multichannel TV market: acquisitions of regional sports networks by multichannel video programming distributors. 133 | 134 | \subsubsection{Model} 135 | 136 | Viewership: Static time-allocation problem yields value function. 137 | 138 | Subscription: Typical logit model including viewership based utility parameters. 139 | 140 | Distributor pricing: Static profit maximization given fees, over bundle choice and price. 141 | 142 | Affiliate fee bargaining: Nash-in-Nash bargaining. 143 | 144 | \subsubsection{Data} 145 | 146 | Downstream data: prices, quantities and characteristics for both cable TV and satellite providers. 147 | 148 | Viewership data: individual viewership data and aggregate data. 149 | 150 | Channel fees and ad revenues: fees (per subscriber) paid to distribute channel; average ad revenue per subscriber. 151 | 152 | \subsubsection{Assumptions} 153 | 154 | 155 | 156 | \subsubsection{Results} 157 | 158 | -------------------------------------------------------------------------------- /io/io1/figures/entry-br90-ineq.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/io/io1/figures/entry-br90-ineq.jpg -------------------------------------------------------------------------------- /io/io1/figures/entry-br90-multeq.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/io/io1/figures/entry-br90-multeq.jpg -------------------------------------------------------------------------------- /io/io2/8854_LectureNotes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/io/io2/8854_LectureNotes.pdf -------------------------------------------------------------------------------- /io/io2/8854_LectureNotes.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{report} 2 | \usepackage[utf8]{inputenc} 3 | \usepackage[english]{babel} 4 | \usepackage{microtype} 5 | \usepackage{libertine} 6 | \usepackage{amsmath,amsthm} 7 | \usepackage[varg]{newtxmath} 8 | \usepackage{setspace,graphicx,epstopdf} 9 | \usepackage{marginnote,datetime,url,enumitem,subfigure,rotating} 10 | \usepackage{multirow} 11 | \usepackage{xfrac} 12 | \usepackage[openlevel=3]{bookmark} 13 | \usepackage[tikz]{bclogo} 14 | \usepackage{enumitem} 15 | 16 | \setcounter{tocdepth}{1} 17 | 18 | \def\D{\mathrm{d}} 19 | 20 | \setlength{\parindent}{0ex} 21 | 22 | \setlist[itemize]{topsep=-6pt, itemsep=-1pt} 23 | \setlist[enumerate]{topsep=-6pt, itemsep=-1pt} 24 | 25 | \newcommand{\smalltodo}[2][] {\todo[caption={#2}, size=\scriptsize,% 26 | fancyline, #1]{\begin{spacing}{.5}#2\end{spacing}}} 27 | \newcommand{\rhs}[2][]{\smalltodo[color=green!30,#1]{{\bf PS:} #2}} 28 | 29 | \newcommand{\E}[1]{\operatorname{E}\left[#1\right]} 30 | \newcommand{\Et}[1]{\operatorname{E}_t\left[#1\right]} 31 | \newcommand{\V}[1]{\operatorname{Var}\left[#1\right]} 32 | \newcommand{\cov}[1]{\operatorname{Cov}\left(#1\right)} 33 | \newcommand{\covt}[1]{\operatorname{Cov}_t\left(#1\right)} 34 | \newcommand{\avg}[2]{\frac{#1}{#2} \sum_{i=#1}^{#2}} 35 | \def\D{\mathrm{d}} 36 | \newcommand{\prob}[1]{\operatorname{Pr}\left[#1\right]} 37 | 38 | 39 | \begin{document} 40 | 41 | \date{} 42 | \title{\textbf{\huge{ECON8854 - Industrial Organization II}}\\ \textit{Lecture Notes from Charlie Murry and Michael Grubb's lectures}} 43 | \author{Paul Anthony Sarkis\\ Boston College} 44 | 45 | \maketitle 46 | 47 | \tableofcontents 48 | 49 | \setlength{\parskip}{1em}%Espacement des par 50 | 51 | 52 | \chapter{Production Function Estimation} 53 | \input{chapters/production} 54 | 55 | \chapter{Endogenous Products} 56 | \input{chapters/endogprod} 57 | 58 | \chapter{Common Ownership} 59 | \input{chapters/commonown} 60 | 61 | \chapter{Dynamics} 62 | \input{chapters/dynamics} 63 | 64 | \chapter{Nonlinear Pricing} 65 | \input{chapters/nlp} 66 | 67 | \chapter{Price Discrimination} 68 | \input{chapters/pricedisc} 69 | 70 | \chapter{Search} 71 | \input{chapters/search} 72 | 73 | \chapter{Switching Costs} 74 | \input{chapters/switchcosts} 75 | 76 | \chapter{Learning} 77 | \input{chapters/learning} 78 | 79 | \chapter{Insurance} 80 | \input{chapters/insurance} 81 | 82 | \end{document} -------------------------------------------------------------------------------- /io/io2/chapters/commonown.tex: -------------------------------------------------------------------------------- 1 | \section{Backus, Conlon and Sinkinson (2019)} 2 | 3 | \subsection{Discussion} 4 | 5 | \begin{itemize} 6 | \item \textbf{Research question:} Does common ownership (overlapping sets of investors) provide incentives that distort competitive behavior? 7 | \item \textbf{Goals of the paper:} test model and measure an effect (common ownership on markups?). 8 | \item \textbf{Importance of the paper:} Growing body of literature in interested in finding a link since enormous rise in common ownership. 9 | \item \textbf{Theoretical foundations:} Basic IO/Game Theory framework with profit maximizing competing firms, owned by profit maximizing investors. \begin{itemize} 10 | \item Strengths: yields a simple (observable) way to measure common ownership incentives 11 | \item Shortcomings: simplistic; does not treat endogeneity; no dynamics 12 | \end{itemize} 13 | \item \textbf{Empirical strategy:} use a reduced-form model to show changes in ``modified'' concentration (to include profit sharing) across time.\begin{itemize} 14 | \item Strengths: 15 | \item Shortcomings: no correlation between variables, just presentation over time, no instruments. 16 | \end{itemize} 17 | \item \textbf{Data:} 13-f filings dataset (investor's share in all companies, both control and profit) 18 | \begin{itemize} 19 | \item Exogenous: 20 | \item Endogenous: changes in these shares (not controlled for) 21 | \end{itemize} 22 | \item \textbf{Results:} Common ownership incentives have increased, even before BlackRock, Vanguard, etc. Common ownership is positively correlated with retail shares (non 13-f shares). 23 | \end{itemize} -------------------------------------------------------------------------------- /io/io2/chapters/dynamics.tex: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/io/io2/chapters/dynamics.tex -------------------------------------------------------------------------------- /io/io2/chapters/endogprod.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | While it was often assumed away in the first semester of IO, we know that firms consider market interactions when choosing entry of products, product positioning, product-line length, etc., thus making these variables endogenous! 4 | 5 | Mankiw and Whinston (1986) is among the first paper to consider this issue after Tirole 1980's revolution. The paper shows two main results: (1) entry in a market is endogenous and (2) imperfect competition affects the ``wedge'' between social optimum and private optimum. 6 | 7 | \section{Berry and Waldfogel (1999 and 2001)} 8 | 9 | \subsection{Discussion} 10 | 11 | \begin{itemize} 12 | \item \textbf{Research question:} What are the effects of mergers on product variety? 13 | \item \textbf{Goals of the paper:} test model and measure an effect (concentration, in particular mergers, on product variety). 14 | \item \textbf{Importance of the paper:} Strand of literature on endogeneity of market structure (products), important because regulation can have effects on this. 15 | \item \textbf{Theoretical foundations:} NOT USED IN EMPIRICAL STRATEGY! Hotelling-style models show ambiguous effects of concentration on product variety. \begin{itemize} 16 | \item Strengths: yields two testable implications. 17 | \item Shortcomings: not used as supply-side in empirical strategy. 18 | \end{itemize} 19 | \item \textbf{Empirical strategy:} use a reduced-form model to correlate changes in concentration with changes in variety using (1) institutional shock and (2) market ``size'' as instruments (number of stations, population).\begin{itemize} 20 | \item Strengths: 21 | \item Shortcomings: no demand ``adjustment'' to the market due to lacking structural model (tastes?); no welfare study either. 22 | \end{itemize} 23 | \item \textbf{Data:} Market-station-level observations (audience, owner, programming format, size); listening data (AQH) 24 | \begin{itemize} 25 | \item Exogenous: population and listening? 26 | \item Endogenous: changes in concentration, changes in formats (variety) 27 | \end{itemize} 28 | \item \textbf{Results:} Increased concentration reduced station entry without reducing variety (more variety per station). 29 | \end{itemize} 30 | 31 | \section{Eizenberg (2014)} 32 | 33 | 34 | 35 | \section{Wollmann (2018)} 36 | 37 | -------------------------------------------------------------------------------- /io/io2/chapters/insurance.tex: -------------------------------------------------------------------------------- 1 | \section{Cohen and Einav (2007)} 2 | 3 | \subsection{Summary} 4 | 5 | \subsubsection{Background} 6 | 7 | There is little empirical research on the link between risk aversion and individual characteristics (how different agents might have different aversion to risk). But it is possible to recover these by looking at market outcomes in which participants had to make a choice between risky outcomes. 8 | 9 | \subsubsection{Data} 10 | 11 | Auto insurance company in Israel, data for 100k new customers, only focus on the first choice (to remove discussion about switching and search costs). Observation unit is thus transaction-level with all customer info that insurance provider got + menu of choice (four policies and premia), but also the length of contract and the actual use of the contract (claims and amounts claimed). 12 | 13 | \subsubsection{Model} 14 | 15 | Using Expected Utility Theory to derive utility function (vNM style). Two main factors to the choice: risk aversion and claim risk (tradeoff is given by an equation recoverable from the data). Estimation by ML. 16 | 17 | \subsubsection{Assumptions} 18 | 19 | Claims are drawn from a Poisson distribution estimated on consumer characteristics. No moral hazard. 20 | 21 | \subsubsection{Results} 22 | 23 | Risk averse is heterogenous (dependent on observables). Claim risk is heterogenous. 24 | 25 | \subsection{Discussion} 26 | 27 | \begin{itemize} 28 | \item \textbf{Research questions:} (1) How risk-averse are individuals? (2) How do risk preferences vary across individuals (observed and unobserved)? 29 | \item \textbf{Goals of the paper:} develop a method (introduce structural estimation of demand for risk) and measure an effect (adverse selection) 30 | \item \textbf{Importance of the paper:} Adverse selection and heterogeneity of preferences towards risk are very important, 1st paper to measure empirically how important they are. 31 | \item \textbf{Theoretical foundations:} Expected utility theory. \begin{itemize} 32 | \item Strengths: 33 | \item Shortcomings: does it really work? (Uzi's class in micro theory). Where is moral hazard? 34 | \end{itemize} 35 | \item \textbf{Empirical strategy:} use a structural model to recover unobserved variables (risk using outcome data and risk preferences using contract choice data). \begin{itemize} 36 | \item Strengths: 37 | \item Shortcomings: 38 | \end{itemize} 39 | \item \textbf{Data:} From an insurance firm, contract-level data (driver characteristics, contract choice set, chosen contract, claims) 40 | \begin{itemize} 41 | \item Exogenous: claims (no moral hazard), price, customers. 42 | \item Endogenous: contract choice. 43 | \end{itemize} 44 | \item \textbf{Results:} Median driver is risk-neutral, mean driver is risk-averse. Risk aversion is correlated to risk (= adverse selection). More heterogeneity in risk aversion than in risk. 45 | \end{itemize} 46 | 47 | \section{Einav, Finkelstein and Cullen (2010)} 48 | 49 | \subsection{Summary} 50 | 51 | \subsubsection{Background} 52 | 53 | Welfare loss in insurance market is not to be proved anymore, but it is still difficult to quantify (because of hidden information mostly). With fewer assumptions, yet enough structure, this paper provides a methodology to evaluate welfare in insurance market. 54 | 55 | \subsubsection{Model} 56 | 57 | Given two choices of policies, normalize price and quantities to represent the difference between the two contracts. Then, crossing between demand and MC is the efficient, while crossing with AC is equilibrium. The difference is the deadweight loss. 58 | 59 | \subsubsection{Data} 60 | 61 | Employer-provided health insurance at Alcoa. -------------------------------------------------------------------------------- /io/io2/chapters/learning.tex: -------------------------------------------------------------------------------- 1 | \section{Literature Review} 2 | 3 | 4 | 5 | \section{Covert (2015)} 6 | 7 | \subsection{Summary} 8 | 9 | The research question in this paper is: ``Do firms learn (in production)?'' 10 | 11 | Using data on hydraulic fracturing in the Bakken Shale and a model of input choice under technology uncertainty, Covert shows that firms only learned partially, leaving out 40\% of profits in the process. 12 | 13 | \subsubsection{Background} 14 | 15 | New industry after advances on how to extract shale gas. Almost 1000\% growth in 8 years. 16 | 17 | Fracking is pumping a mix of sand, water and chemicals in the ground = choice to make on the ``recipe'' that affects production and costs! But no one knew at the time how to do it = opportunities for learning. 18 | 19 | Firms have their own data (private for 6 months) and then get access to other data (after six months). 20 | 21 | \subsubsection{Evidence for learning} 22 | 23 | Covert looks for three types of learning: (1) is experience (age of firms) correlated with productivity (oil per well drilled)? Which is estimated using a Benkard type of model. (2) is the choice of inputs more profitable over time? which is estimated using ex ante and ex post profits comparison. 24 | 25 | \subsubsection{Results} 26 | 27 | One of the first empirical analyses of learning behavior in production. Find that firms increased the profit capturing rate from 20\% to 60\%. No experimenting to learn as firms go to more certain input choices. Firms overweight their data compared to other firms' data. 28 | 29 | \subsection{Model} 30 | 31 | \subsubsection{Production function} 32 | 33 | The output is log-log specified as a function of:\begin{itemize} 34 | \item $t$: the number of days of operation of the well. 35 | \item $D$: the number of days of production. 36 | \item $H$: length of the well. 37 | \item $Z$: other topologic controls 38 | \item $\epsilon$: well-specific shock 39 | \item $\nu$: idiosyncratic shock 40 | \end{itemize} 41 | 42 | \subsubsection{Profits} 43 | 44 | Firm's profits depend on the usual stuff: share, market size, price, and cost of inputs. 45 | 46 | \subsubsection{Preferences} 47 | 48 | Firms get utility from the mean profit and standard deviation of profits given an input. 49 | 50 | \subsubsection{Gaussian Process Regressions} 51 | 52 | 53 | 54 | \subsection{Comments} 55 | 56 | \subsubsection{Results} 57 | 58 | Firms underutilize sand and water but: are costs measured correctly? If costs are convex, then findings corroborate optimal choice? Overestimate return to production? 59 | 60 | \subsubsection{Public policy} 61 | 62 | Delayed disclosure of information lowers barriers to entry while leaving rents on the table. 63 | 64 | \subsubsection{Experimenting} 65 | 66 | Nice framework but conclusion too hasty? Experimenting is too linked with risk, what if even when experimenting firms would choose safe levels of inputs? Or sub-optimal experimenting? 67 | 68 | \subsubsection{Other questions} 69 | 70 | Risk aversion or myopia? 71 | 72 | Prior beliefs are correctly specified? 73 | 74 | \subsection{Discussion} 75 | 76 | \begin{itemize} 77 | \item \textbf{Research questions:} How do firms learn to use new technologies? 78 | \item \textbf{Goals of the paper:} test models (learning models) and measure an effect (information on production) 79 | \item \textbf{Importance of the paper:} 1st empirical study of learning behavior. 80 | \item \textbf{Theoretical foundations:} Learning the production function (different than learning-by-doing) \begin{itemize} 81 | \item Strengths: 82 | \item Shortcomings: 83 | \end{itemize} 84 | \item \textbf{Empirical strategy:} use Gaussian Process Regression (Bayesian technique) to identify learning process of production distribution. Identifies experimenting by looking at ``taste'' for variance. \begin{itemize} 85 | \item Strengths: perfect fit for learning setting of functions rather than points. 86 | \item Shortcomings: taste for variance is not exactly the same as experimenting. 87 | \end{itemize} 88 | \item \textbf{Data:} well-period level (location, length, sand-water combination, firm identity, production, age) + location characteristics (geological variables) + environment variables (oil prices, etc.) + information available at each period in time. 89 | \begin{itemize} 90 | \item Exogenous: 91 | \item Endogenous: sand-water combination, output. 92 | \end{itemize} 93 | \item \textbf{Results:} Firms learn (form 20\% to 60\% of max profits captured); firms underutilize sand and water; firms overweight their own data; firms do not experiment. 94 | \end{itemize} -------------------------------------------------------------------------------- /io/io2/chapters/momineq.tex: -------------------------------------------------------------------------------- 1 | This chapter provides a more rigorous introduction to estimation of models through the use of inequality restrictions, henceforth called moment inequalities. We have seen them in the previous chapter on entry, but they can be applied more generally to any type of games that would yield cumbersome computations using traditional methods, or for estimation when data are imperfect. 2 | 3 | \section{Framework} 4 | 5 | \subsection{The agent's decision problem} 6 | 7 | Consider a situation with $n$ decision makers indexed by $i$, having access to their own information set $I_i$ when decisions are made and $D_i$ the set of available decisions. The strategy played by agent $i$ is a mapping $s_i:I \to D$ (from information to action), such that it generates the observed decisions $d_i$ (which could be a vector). 8 | 9 | The profit function of agent $i$ is determined by his decision ($d_i$), the other agents' decisions ($d_{-i}$) and other environment variables $y_i$. At the time of the decision, the agent has expectations over what happens in the game ($\pi(\cdot)$, $s_i$, $I_i$ and $Y_i$); they are denoted by $\mathcal{E}\left[\cdot\right]$, which is not the same operator as the typical expectation operator. 10 | 11 | \subsubsection{Best-response condition (Nash)} 12 | 13 | If $d_i$ is the observed decision of player $i$, we assume: $$ \sup_{d\in\D_i} \mathcal{E}\left[ \pi(d, d_{-i}, y_i) | I_i \right] \leq \mathcal{E}\left[ \pi(d_i, d_{-i}, y_i) | I_i \right] \text{ for all } i = 1, ..., n $$ 14 | 15 | Quite obviously, we can see this assumption as an assumption for ``rationality'', meaning that at the time of the decision, the agent chose the best option. In single agent problems, this comes directly from optimization behavior, while in games, it is only a necessary condition for a Bayes-Nash equilibrium to be played, but it does not rule out multiple equilibria, or restrict the selection between equilibria. 16 | 17 | \subsubsection{Counterfactual condition} 18 | 19 | In order for the agents to ensure optimal behavior, they need to evaluate the alternative decisions in their counterfactual environment. Thus we need to define what happens to $d_{-i}$ and $y_i$ following the decision of agent $i$. Note that in single-agent problems and simultaneous games, the counterfactual is assumed away using a conditional independence assumption. 20 | 21 | In other cases, we assume that $y_i = y(z_i, d, d_{-i})$ and that the distribution of $(d_i, z_i)$ conditional on $I_i$ and $d$ do not depend on $d$. In words, this assumption means that environment variables $y_i$ depend only on variables $z_i$ and decisions by the agents (which are all exogenous conditional on $I_i$ and $d$). 22 | 23 | Using this, we define the ``differential profit'' as: $$\Delta\pi(d, d', d_{-i}, z_i) = \pi(d, d_{-i}, y(z_i, d, d_{-i})) - \pi(d', d_{-i}, y(z_i, d', d_{-i})) $$ as the difference in profits between two decisions. 24 | 25 | Finally, we rewrite the first condition as: $$ \mathcal{E}\left[ \Delta\pi(d_i, d, d_{-i}, z_i) | I_i \right] \geq 0 \text{ for all } i = 1, ..., n $$ 26 | 27 | This might seem like the inequality to use in estimation, however, recall that the expectation is only the agent's so we need to recover empirical analogues of these in order to use them. 28 | 29 | \subsection{Observables and disturbances} 30 | 31 | We assume that the econometrician has a parametric function, denoted $r(\cdot)$, that approximates $\pi(\cdot)$ given arguments $d_i$, $d_{-i}$, observable variables of $z_i$, denoted $z_i^o$ and unknown parameters $\theta$ to estimate. 32 | 33 | Using that function, we can approximate the differential profit with $\Delta r(d, d', d_{-i}, z_i^o, \theta)$. From there, define two types of errors: \begin{align*} 34 | \nu_{2, i, d, d'} & = \mathcal{E}\left[ \Delta\pi(d, d', d_{-i}, z_i) | I_i \right] - \mathcal{E}\left[ \Delta r(d, d', d_{-i}, z_i^o, \theta) | I_i \right] \\ \nu_{1, i, d, d'} & = \nu_{1, i, d, d'}^\pi - \nu_{1, i, d, d'}^r \\ \nu_{1, i, d, d'}^\pi & = \Delta\pi(d_i, d, d_{-i}, z_i) - \mathcal{E}\left[ \Delta\pi(d_i, d, d_{-i}, z_i) | I_i \right] \\ \nu_{1, i, d, d'}^r & = \Delta r(d, d', d_{-i}, z_i^o, \theta) - \mathcal{E}\left[\Delta r(d, d', d_{-i}, z_i^o, \theta)|I_i\right] 35 | \end{align*} 36 | that we refer to in general as $\nu_{2,i}$ and $\nu_{1,i}$ (composed of $\nu_{1,i}^\pi$ and $\nu_{1,i}^r$). Note that the first error, while not observed by the econometrician, is a part of the information set $I_i$ of the agent (he ``knows'' $\nu_{2,i}$). The second error is neither observed by the agent nor by the econometrician. 37 | 38 | Intuitively, $\nu_{2,i}$ represents the expected error the econometrician makes by using $\Delta r$ as a value for $\Delta \pi$. Because the agent ``knows'' this value, the decision he makes might depend on $\nu_{2,i}$, which would cause a selection problem (since $ \mathcal{E}\left[\nu_{2,i}\right]\neq 0$). In contrast, errors in $\nu_{1,i}$ are do not affect expected profits, thus cannot determine $d_i$. They are called expectational errors because they come from unexpected shocks. 39 | 40 | \subsection{Moment inequalities} 41 | 42 | 43 | 44 | %\subsection{Discrete games} 45 | % 46 | %Let $\pi(\cdot)$ be the profit function (continuation value) earned in the second period, $d_i$ and $d_{-i}$ be agent $i$'s and its competitors' discrete decisions respectively, $y_i$ be the set of variables that affect the agent's profits, $D_i$ be the choice set (of decisions) and $I_i$ the information set. Further, denote as $\mathcal{E}\left[ \cdot | I_i \right] $ the agent's expectation (note that we do not use the usual expectation term because we want to differentiate from the ``econometric'' expectation we usually use). 47 | % 48 | %In order to estimate this discrete game, we need two conditions to hold: 49 | % 50 | %\subsubsection{Nash condition} 51 | % 52 | %The Nash condition states that: $$ \sup_{d\in\D_i, d\neq d_i} \mathcal{E}\left[ \pi(d, d_{-i}, y_i, \theta) | I_i \right] \leq \mathcal{E}\left[ \pi(d_i, d_{-i}, y_i, \theta) | I_i \right] \text{ for all } i = 1, ..., n $$ In words, this condition ensures that the observed decision $d_i$ was at least among the best (in expectations) compared to alternatives, given the information set available. 53 | % 54 | %Note that this condition does not restrict the choice set to be discrete (and thus could apply to more settings than entry). Moreover, while this condition imply some kind of rationality, it does not imply anything about uniqueness of the solution (i.e. the observed decision might be one of multiple equilibria). 55 | % 56 | %\subsubsection{Counterfactual condition} 57 | % 58 | %The counterfactual condition allows us to recover what would have happened in the case of other decisions: $$ d_{-i} = d(d_i, z_i) \text{ and } y_i = y(z_i, d) $$ where $z_i$ is exogenous of $d_i$. This condition implies that conditional on the information set, beliefs about the competitors' actions depend only on the agent's decision and exogenous variables (that do not change with the decision). 59 | % 60 | %In the case of simultaneous games, notice that $d(\cdot)$ is just the observed action $d_{-i}$ for any $d_i$. 61 | % 62 | %\subsubsection{Implications} 63 | % 64 | %Let $d' \in D_i$ be any alternative choice and let $$ \Delta\pi(d_i, d', d_{-i}, z_i) \equiv \pi(d_i, d_{-i}, z_i) - \pi(d', d_{-i}, z_i) $$ then, using the Nash and the counterfactual conditions, we have that: $$\mathcal{E}\left[ \Delta\pi(d_i, d', d_{-i}, y_i) | I_i \right] \geq 0 \text{ for all } d' \in D_i $$ While this implication seems straightforward considering the two conditions presented earlier, it will serve as a basis for the estimation algorithm. However, for that relation to be useful, we need to specify two more elements: (1) the relation between agents' expectations ($\mathcal{E}$) and observed sample moments ($\text{E}$) and (2) the functional form of $\pi$ in relation to the variables $z_i, d_i$ and $d_{-i}$ and how they can be described by observed variables. 65 | % 66 | %\subsection{Entry model with structural error} 67 | 68 | 69 | -------------------------------------------------------------------------------- /io/io2/chapters/nlp.tex: -------------------------------------------------------------------------------- 1 | \section{Two types} 2 | 3 | This section covers the model of nonlinear pricing where a monopolist offers a menu of two quantity/quality-price pairs to consumers of two types ($H$, with high value for the good and $L$ with low value). 4 | 5 | Without loss of generality, we consider contracts such that each type chooses a contract and has no incentives to deviate. The monopolist chooses a quantity/quality and a price for each contracts, such that its profits are maximized. We get a problem with three elements: (1) an optimization problem, (2) a set of participation constraint (making sure each type buys the contract) and (3) an incentive constraint (making sure no type deviates). 6 | 7 | The results of this model tells us that the optimal contracts are designed in such a way that the quantity/quality of the highest type is not distorted, while for the lowest type, they will receive a lower quantity/quality than their first best! 8 | 9 | \section{Continuous types} 10 | 11 | The continuous types model has the same structure as the one presented in the previous section, however, now types lie on a continuum from lowest to highest. As before, the model is separated in the three same parts and display a similar distrortion where consumers of the highest types get their first best contract, while the lowest types get lower quantity/quality. 12 | 13 | \section{Crawford and Shum (2007)} 14 | 15 | \subsection{Summary} 16 | 17 | The research question of this paper is: ``To what extent is quality degradation prevalent in cable TV markets? And what are the effects of regulation on this issue?'' 18 | 19 | They add quality to the decision of the monopolist (add a dimension). Because of imperfect competition, we might think that quality will also be distorted (as prices are), which would create welfare losses. This is the framework of Mussa-Rosen, which is applied to the setting of cable TV. 20 | 21 | \subsubsection{Mussa-Rosen} 22 | 23 | There are three types of consumers (one to allow some consumers to not care about cable TV), and two contracts. The model displays distortion for the lowest types and no distortion at the top. They further go to show that this result holds even if consumer types are continuous if qualities are discrete. 24 | 25 | Regulation is set up as a constraint on the optimization problem such that quality cannot go lower than a certain point. This turns out to only restrict the lowest quantity, while the top quantity stays undistorted. 26 | 27 | \subsubsection{Cable TV industry} 28 | 29 | Contracts are based on bundles of networks. Basic service is the one that everyone has, then you can buy extended service or premium (maps well to theory presented before, but premium is ignored because horizontal differentiation). 30 | 31 | Bundle quality is measured in two ways: number of networks in said bundle (assuming same underlying quality) or through the implied values from consumer distribution (a first-stage problem from Mussa-Rosen). 32 | 33 | \subsubsection{Empirical model} 34 | 35 | 36 | 37 | \subsubsection{Results} 38 | 39 | Quality distortion is present. Regulation mitigates the problem. 40 | 41 | \subsection{Discussion} 42 | 43 | \begin{itemize} 44 | \item \textbf{Research questions:} (1) how much do cable TV distributors ``degrade'' quality? (2) how do local regulations affect quality distortion? 45 | \item \textbf{Goals of the paper:} measure an effect (incentives to distort quality) and answer a policy question (quality regulation) 46 | \item \textbf{Importance of the paper:} 1st empirical framework oriented towards measure of quality degradation. 47 | \item \textbf{Theoretical foundations:} mainly Mussa and Rosen (1978), which is a model of monopoly facing discrete types of consumers, choosing prices and quantity/quality \begin{itemize} 48 | \item Strengths: monopoly setting fits well with institutional details. 49 | \item Shortcomings: (1) lack of horizontal preferences (2) truncation of ``real'' high types (3) some bundles do not fit model. 50 | \end{itemize} 51 | \item \textbf{Empirical strategy:} use a structural model to (1) infer quality (unobservables) and (2) study counterfactuals.\begin{itemize} 52 | \item Strengths: 53 | \item Shortcomings: (1) lack of horizontal preferences (2) truncation of ``real'' high types (3) functional form assumptions drive the results and (4) reduced-form could be used more. 54 | \end{itemize} 55 | \item \textbf{Data:} Cable system-market level (prices, shares, content, market size, demographics) 56 | \begin{itemize} 57 | \item Exogenous: market size, demographics. 58 | \item Endogenous: prices, shares, content (quality). 59 | \end{itemize} 60 | \item \textbf{Results:} Degradation exists, gets better with stricter regulation. 61 | \end{itemize} 62 | 63 | -------------------------------------------------------------------------------- /io/io2/chapters/pricedisc.tex: -------------------------------------------------------------------------------- 1 | \section{Dana (1999)} 2 | 3 | \subsection{Model} 4 | 5 | \begin{itemize} 6 | \item Consumers on a continuum of types with unit demand. 7 | \item Firm has marginal production and capacity cost. 8 | \item Firm chooses price before learning demand. 9 | \item Proportional rationing imply all types have access and buy to the good proportionately. 10 | \end{itemize} 11 | 12 | \subsection{Residual Demand} 13 | 14 | \begin{itemize} 15 | \item Residual demand is very important: 16 | \begin{itemize} 17 | \item Start with any price, say $\tilde p$: some people buy, some don't, say $\tilde q$ have bought. 18 | \item Residual demand at another price, say $p$ is not simply base demand - $\tilde q$, because some of those who bought at $\tilde p$ would not have bought at $p$ = use proportional rationing to determine residual demand 19 | \end{itemize} 20 | \end{itemize} 21 | 22 | \subsection{Perfect Competition} 23 | 24 | \begin{itemize} 25 | \item Competitive market = profit is 0 (but probability!) 26 | \item Price dispersion: from $\underline{p}$ to $\bar p$ 27 | \end{itemize} 28 | 29 | \subsection{Monopoly} 30 | 31 | \begin{itemize} 32 | \item Market power imply markup: prices support is narrower! 33 | \end{itemize} 34 | 35 | \subsection{Price Dispersion and Market Structure} 36 | 37 | \begin{itemize} 38 | \item Two results: 39 | \begin{itemize} 40 | \item Support of prices widens with competition. 41 | \item Variance of prices increases with competition (given linear demand). 42 | \end{itemize} 43 | \item In summary: price dispersion increases with PTR (which increases with competition). 44 | \end{itemize} 45 | 46 | \section{Leslie (2004)} 47 | 48 | \subsection{Background} 49 | 50 | The paper answers the question of welfare effects of price discrimination (consumer = ambiguous; firms = positive). Broadway play where second and third degree price discrimination. Second degree happens because of different seats are offered at different prices based on quality (nonlinear pricing as in Dana (1999)). Third degree is targeted coupons. Finally, discount sales for day-of-performance tickets is damaged goods. Same marginal cost for all seats but capacity costs (again, as in the Dana paper). 51 | 52 | \subsection{Data} 53 | 54 | Unit of observation is a seat (price, quality, discount, etc). Aggregate discount into two categories (coupons or booth). Aggregate advertising is observed. Competing plays attendance is observed. Finally, consumer variables in the NYC region are observed. 55 | 56 | \subsection{Model} 57 | 58 | Product space approach. 59 | 60 | \subsection{Assumptions} 61 | 62 | 63 | 64 | \subsection{Results} 65 | 66 | Main result is that price discrimination improves welfare! But all types of PD are suboptimally designed. 67 | 68 | \subsection{Discussion} 69 | 70 | \begin{itemize} 71 | \item \textbf{Research questions:} What are the welfare consequences of price discrimination for Seven Guitars on Broadway? 72 | \item \textbf{Goals of the paper:} measure an effect (price discrimination) and maybe slightly interested in policy implications. 73 | \item \textbf{Importance of the paper:} empirical framework oriented towards measure of welfare effects of price discrimination. 74 | \item \textbf{Theoretical foundations:} price discrimination models with 3rd degree (market segmentation) and 2nd degree (self-selection/nonlinear pricing) price discrimination \begin{itemize} 75 | \item Strengths: (1) fits market details; (2) adds outside option to theoretical model (= oligopoly?); (3) no selling out means increasing welfare through sales is possible (Tirole on welfare). 76 | \item Shortcomings: (1) Dana (1999) with demand uncertainty is missing (perfect framework); (2) no dynamics in consumer demand (perishable good); (3) relies on functional form assumptions. 77 | \end{itemize} 78 | \item \textbf{Empirical strategy:} use a structural model to study counterfactuals (measure welfare).\begin{itemize} 79 | \item Strengths: No censoring in data (did not sell out so much) 80 | \item Shortcomings: 81 | \end{itemize} 82 | \item \textbf{Data:} (1) Show-level (tickets sold, prices, ads, quality, etc.) (2) Market-level (other shows' sales, customer incomes, demographics, etc.) 83 | \begin{itemize} 84 | \item Exogenous: ads, quality, other shows' sales, consumer variables 85 | \item Endogenous: prices, sales 86 | \end{itemize} 87 | \item \textbf{Results:} Price discrimination has a positive effect on welfare (in general), mostly through profits. All PD schemes are ``suboptimally'' designed. 88 | \end{itemize} -------------------------------------------------------------------------------- /io/io2/chapters/production.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | The firm-level production function can be written as: $$Y_{it} = L_{it}^{\beta_l} K_{it}^{\beta_k} U_{it} $$ where $Y$ is output, $L$ is labor, $K$ is capital and $U$ is the TFP (usually unobserved by the researcher). The goal is to estimate the output elasticities $\beta$! 4 | 5 | But estimation is not straightforward, some issues arise from the very nature of production. First of all, the production process is dynamic since it uses capital, which can grow or depreciate endogenously (it is a decision based on production). Thus, state variables will be very important (R\&D, entry/exit, etc.). Then, we have a problem of simultaneity: variables that are unobserved to the econometrician might be determined by other equations. To see that, consider taking the logs of the production function, decomposing the unobserved TFP into a structural error $\omega$ and a random error $\varepsilon$: $$ y_{it} = \beta_l l_{it} + \beta_k k_{it} + \omega_{it} + \varepsilon_{it} $$ It might be that $l_{it}$ or $k_{it}$ are chosen with knowledge of $\omega_{it}$, even though it is typically safe to assume that $k_{it}$ is chosen at $t-1$ and is thus free from endogeneity. Finally, we have issues of selction bias since using panel data will give extra weight to successful firms that ``survive'' throughout the dataset. However, it might be the case that the firms that do not survive have low productivity draws on average: selection bias! 6 | 7 | \section{Olley and Pakes (1996)} 8 | 9 | \subsection{Intuition} 10 | 11 | This paper suggests a way to go around the simultaneity issue (as well as selection bias) by providing a ``proxy'' for the structural term in the TFP. This proxy is current investment (denoted $i_{it}$). Intuitively, the argument relies on the fact that while investment is directly correlated with productivity shocks, it will not affect labor or capital until the next period! 12 | 13 | This method works only under a set of assumptions:\begin{enumerate} 14 | \item Information: the firm's information set includes only current and past realizations of $\omega$ and $\varepsilon$ is exogenous ($\E{\varepsilon_t|I_t} = 0$). 15 | \item First-order Markov processes: the TFP shock follows a first-order Markov process such that $\prob{\omega_{i,t+1}|I_{it}} = \prob{\omega_{i,t+1}|\omega_{it}}$. 16 | \item Timing of investment: firms accumulate capital according to the law $k_{it} = \kappa(k_{i,t-1}, i_{i,t-1})$. Labor is not dynamic. 17 | \item Scalar unobservable: firms' investment decisions are functions of current capital stock and productivity shock ($i_{it} = f_t(k_{it}, \omega_{it})$). 18 | \item Strict monotonicity: $f_t(\cdot)$ is strictly increasing in $\omega_{it}$. 19 | \end{enumerate} 20 | 21 | In particular, assumptions 2 and 5 are crucial to allow for ``inverting'' investment into TFP, meaning that we can write $\omega_{it}$ as a function of $k_{it}$ and $i_{it}$: $$\omega_{it} = h(k_{it}, i_{it}) $$ 22 | Then, by plugging it back into the production function we get: $$ y_{it} = \beta_l l_{it} + \beta_k k_{it} + h(k_{it}, i_{it})+ \varepsilon_{it} $$ and since $h$ is unknown, we cannot differentiate between the use of $k$ within $h$ and outside of $h$, thus we effectively use: $$y_{it} = \beta_l l_{it} + \Phi(k_{it}, i_{it})+ \varepsilon_{it} $$ where $\Phi$ is unknown (to be estimated). 23 | 24 | \subsection{Estimation} 25 | 26 | The econometric procedure relies on two stages: in the first stage, the goal is to recover $\beta_l$ and $\Phi$, the former is already identified but the latter is not an object of interest per se, thus we only need to be most flexible possible. Then, in the second step, we recover $\beta_k$ by using our first-stage estimates. 27 | 28 | \subsubsection{First stage} 29 | 30 | The first-stage regression is defined as: $$y_{it} = \beta_l l_{it} + \Phi(k_{it}, i_{it})+ \varepsilon_{it} $$ where the goal is to estimate $\beta_l$ and $\Phi$ as flexibly as possible. To do this, there are two main ways: (1) by ``parameterizing'' $\Phi(\cdot)$ as a polynomial of $k$ and $i$ or (2) using a semi-parametric approach as in Robinson (1988) where $\beta_l$ is estimated parametrically and $\Phi$ nonparametrically. 31 | 32 | \subsubsection{Second stage} 33 | 34 | We can decompose $\omega$ into its expected value plus an innovation term $\xi_{it}$: $$\omega_{it} = \E{\omega_{it}|I_{i,t-1}} + \xi_{it} = \E{\omega_{it}|\omega_{i,t-1}} + \xi_{it} = g(\omega_{i,t-1}) + \xi_{it} $$ With $\hat\Phi(k_{it}, i_{it})$ and $\hat\beta_l$ in hand, we can rewrite $\omega_{i,t-1}$ as a function of estimated parameters and thus, given a guess for $\beta_k$ and a parametric form for $g(\cdot)$, we have: $$ \xi_{it}(\beta_k) = \phi_{it} - \beta_k k_{it} - g(\phi_{it-1} - \beta_k k_{it}) $$ which first conditional moment can be used to recover $\beta_k$. Usually, the moment condition used is $\E{\xi k} = 0$. 35 | 36 | \subsection{Results} 37 | 38 | 39 | 40 | \section{Levinsohn and Petrin (2003)} 41 | 42 | \subsection{Intuition} 43 | 44 | The key insight behind Levinsohn and Petrin is to use materials instead of investment as a proxy for the TFP. In fact, it seems fair to assume that the current choice of intermediate inputs is correlated with the current productivity shock. Moreover, the authors argue that investment was not a good proxy to begin with because (1) too many zeroes in the data and (2) investment is lumpy and thus might not react to productivity shocks right away. In contrast, intermediate inputs such as materials will be more flexible and have more variation. 45 | 46 | To include materials in the regression, it helps to think of it as we did with capital in OP. First, the production function is now: $$y_{it} = \beta_l l_{it} + \beta_k k_{it} + \beta_{m} m_{it} + \omega_{it} + \varepsilon_{it} $$ Then, under similar assumptions as in OP, we can ``invert'' the materials function to get $\omega_{it} = h(k_{it}, m_{it}$. Finally, as in OP, we are now able to identify the production function as: $$y_{it} = \beta_l l_{it} + \Phi(k_{it}, m_{it}) + \varepsilon_{it} $$ 47 | 48 | \subsection{Estimation} 49 | 50 | The estimation procedure follows the procedure in OP, with the addition of a moment condition in the last step. In fact, since we now care about $\beta_k$ and $\beta_,$, we need an extra moment. Note that we cannot use a similar moment as with capital since current materials are correlated with the productivity shock $\xi$, thus we need to find an ``instrument'' in the past realization of materials ($m_{it-1}$). 51 | 52 | \section{Ackerberg, Caves and Frazer (2015)} 53 | 54 | \subsection{Intuition} 55 | 56 | Ackerberg, Caves and Frazer (2015) raise an important issue within the two previous approaches. In fact, considering how the production function is parametrized, once conditioned on $k$, $\omega$ and $m$ (in LP), the amount of $l$ is completely determined! Essentially, whenever $l$ can be written as a function of only $k$, $m$ and $t$, then $\beta_l$ will not be identified. 57 | 58 | To go around this issue, ACF suggests to alter how we think about the timing assumptions. In particular, they assume $l$ is set at time $t$ and $k$ at $t-1$ as usual, but $m$ is now set in between at $t-b$ where $b\in (0, 1)$. This implies that at the time when $k$ and $m$ are chosen, there is still a random element that is not known to the firm and will affect production. Moreover, ACF considers the value added production function instead of the gross production. This implies that $m$ can be used to invert productivity but will not end up in the final moment condition. 59 | 60 | \subsection{Estimation} 61 | 62 | Again, the estimation procedure is very similar to the two previous approaches, with the difference that value added production is preferred to gross, and the additional moment condition is now $\E{\xi_{it}l_{it-1}}$ in order to recover $\beta_l$. 63 | 64 | \section{De Loecker and Warzynski (2012)} 65 | 66 | \subsection{From production function to markup} 67 | 68 | The main idea behind De Loecker and Warzynski (2012) is to use production function estimation to derive markups and look into markup dynamics in the last years. 69 | 70 | To do this, they use the fact that, assuming cost minimization, the markup can be written as the ratio of output elasticity to revenue share. It follows a sort of extended LP model to estimate output elasticities, using a translog production function (instead of Cobb-Douglas) and extra covariates for input demand function. 71 | 72 | They find that on average, markups are about 20 to 30\%. 73 | 74 | \subsection{Criticisms} 75 | 76 | This paper received a wide array criticisms, ranging from theoretical to methodological comments. 77 | 78 | First of all, the functional form assumptions made in the paper are seen by many as not being flexible enough to capture the production process of all firms. 79 | 80 | Second, the derivation of markups is done solely on the supply-side, using price-taking assumptions, without ever specifying the type of competition in the markets. 81 | 82 | An extension by De Loecker, Eckhout and Unger show that markups rise from 21\% to 64\% since the 1980s (using the typical method)... They address some of the criticisms described above by controlling for market concentration in their estimation and using cost of goods sold as a variable input for example. From their results, we can see that methodology will have a great effect on the dynamic results. 83 | 84 | Traina (2018) and Raval (2019) explore the choice of input variables and its consequences on the results. -------------------------------------------------------------------------------- /io/io2/chapters/search.tex: -------------------------------------------------------------------------------- 1 | \section{Introduction} 2 | 3 | Search is an alternative explanation to observing different market shares, enormous marketing budgets, etc. than simple product differentiation. 4 | 5 | Search is defined as looking for another price ``quote'' for a homogenous product. Firms simultaneously choose prices, then consumers search among a number of prices to find the best one and purchase. 6 | 7 | If search is sequential, then consumers would search until finding a price less than or equal to a reservation price $r$ such that the expected benefit of finding $r$ is equal to the search cost. 8 | 9 | Diamond (1971) shows that this model is very interesting in that it leads to different results than typical Bertrand competition when $s>0$, the search cost is greater than 0. However, it does not converge to a Bertrand model as $s\to 0$. 10 | 11 | \section{Other models} 12 | 13 | \subsection{Diamond (1971)} 14 | 15 | \begin{itemize} 16 | \item Main result: unique NE is monopoly prices and no search! 17 | \begin{itemize} 18 | \item Independent of the number of firm and search cost (provided $s>0$). 19 | \item Depends on inability to advertise price cuts. 20 | \end{itemize} 21 | \end{itemize} 22 | 23 | \subsection{Stahl (1996)} 24 | 25 | \begin{itemize} 26 | \item Add a portion ($\mu$) of consumers as shopping-lovers $\Rightarrow$ price dispersion! 27 | \begin{itemize} 28 | \item No pure-strategy NE! 29 | \item But very challenging to compute... 30 | \end{itemize} 31 | \end{itemize} 32 | 33 | \subsection{Simpler model} 34 | 35 | \begin{itemize} 36 | \item Simplification of Stahl by adding: inelastic demand + fixed search costs. 37 | \begin{itemize} 38 | \item The upper bound of prices ensures that only shoppers search. 39 | \item The lower bound of prices is marginal cost + a markup that depends negatively on the proportion of shoppers and positively the size of the search cost. 40 | \end{itemize} 41 | \end{itemize} 42 | 43 | \section{Salz (2017)} 44 | 45 | \subsection{Summary} 46 | 47 | \subsubsection{Background} 48 | 49 | Search costs in decentralized markets are important and incentivize the role for intermediaries to enter the market. But how do they influence market outcomes? Empirical study of the NYC trade waste industry. Companies generate waste and have to comply by law to finding a waste management service. Brokers might help with this process by awarding contracts on a competitive bidding process. Given that search costs are about 11-35\% of expenses, what is the effect of brokers on the rents in that market? 50 | 51 | \subsubsection{Data} 52 | 53 | Observation unit is a contract between company and waste management (from regulatory institution). Variables observed include zip code, negotiated price, quantity of waste and whether or not it was brokered. Some markets are very concentrated while others are very competitive. 54 | 55 | There is a lot of price dispersion (even with the same observables), implying search intermediation is useful. 56 | 57 | \subsubsection{Model} 58 | 59 | Sequential game between customers and carters, where brokers are non-strategic. Customers observe search costs, carters observe their search cost (this is private information). The game plays as follows:\begin{enumerate} 60 | \item Customers learn his search cost and carters learn their costs. 61 | \item Customers decide between delegating search or performing a number of search (not sequential). 62 | \item Carters submit prices to either broker (given a first-price auction) or to customers directly. 63 | \end{enumerate} 64 | 65 | \subsubsection{Assumptions} 66 | 67 | \begin{itemize} 68 | \item Simultaneous search rather than sequential. 69 | \item No broker competition. 70 | \item Contract length is fixed to two years: underestimation of search costs. 71 | \item Number of bidders is fixed to observed winners: underestimate number of bidders $\Rightarrow$ search costs are underestimated. 72 | \item Carters are grouped into types. 73 | \end{itemize} 74 | 75 | \subsubsection{Results} 76 | 77 | Intermediaries create benefits to both customers who use brokers and those who do not. 78 | 79 | \subsection{Discussion} 80 | 81 | \begin{itemize} 82 | \item \textbf{Research questions:} (1) How do intermediaries affect buyers and sellers of trash management services? (2) What is the welfare effect? 83 | \item \textbf{Goals of the paper:} develop a method (introduce empirical study of search market with intermediaries) and measure an effect (presence of intermediaries) 84 | \item \textbf{Importance of the paper:} 1st empirical framework to study search including (1) intermediaries and (2) heterogeneous costs. 85 | \item \textbf{Methodology:} Using FPA data (on brokers), able to separate production costs from search costs! (thus get heterogeneous costs). 86 | \item \textbf{Theoretical foundations:} simultaneous search model (fixed number of searches) to identify search costs and first-price auction in brokers market to identify carter costs. \begin{itemize} 87 | \item Strengths: fits well with the data 88 | \item Shortcomings: no long justification on these choices; no broker competition; no switching dynamics. 89 | \end{itemize} 90 | \item \textbf{Empirical strategy:} use a structural model to (1) instrument for the presence of brokers (no reduced form possible) and (2) measure welfare (by measuring costs).\begin{itemize} 91 | \item Strengths: 92 | \item Shortcomings: (1) homogeneous brokers; (2) broker-customer relations are not observed (price is ``inferred'') 93 | \end{itemize} 94 | \item \textbf{Data:} Contract-level observations (ZIP code, price, quantity, date, brokerage, etc.); NO BROKER FEE! 95 | \begin{itemize} 96 | \item Exogenous: ZIP code, market size, demographics, quantity (!), market structure (types and costs of sellers), search costs, broker sets, fees, search sets (up to $M$). 97 | \item Endogenous: number of searches, seller prices, contracts. 98 | \end{itemize} 99 | \item \textbf{Results:} Costs are lower for bigger customers (economies of scale); number of searches does not depend on quantity = returns to search are stable = cost is increasing?; brokers increase welfare. 100 | \end{itemize} -------------------------------------------------------------------------------- /io/io2/chapters/switchcosts.tex: -------------------------------------------------------------------------------- 1 | \section{Effects} 2 | 3 | \subsection{Model 1: Investing and Harvesting} 4 | 5 | \begin{itemize} 6 | \item Firms ``invest'' in consumers by lowering their prices below marginal cost, then ``harvest'' their loyal base by extracting all surplus! 7 | \begin{itemize} 8 | \item Only if switching cost is high enough and perfect competition! 9 | \item Welfare is intact (average price is still marginal cost) 10 | \end{itemize} 11 | \item No switching in equilibrium. 12 | \end{itemize} 13 | 14 | \subsubsection{Model 1a: Add heterogenous values} 15 | 16 | \begin{itemize} 17 | \item Now there is a DWL: consumers with high value of the good lose! 18 | \item No switching in equilibrium. 19 | \end{itemize} 20 | 21 | \subsubsection{Model 1b: Add heterogenous switching costs} 22 | 23 | \begin{itemize} 24 | \item Identical welfare outcomes but more switching (those who have low draws of switching costs). 25 | \end{itemize} 26 | 27 | \subsection{Model 2: Hotelling Duopoly} 28 | 29 | \begin{itemize} 30 | \item Distance between consumer taste and firm is key to compute demand. 31 | \begin{itemize} 32 | \item Consumer has $\theta \in [0, 1]$ in both periods, firms are at $0$ and $1$. 33 | \item Budget is $B$. 34 | \item Transportation cost is $\tau$. 35 | \end{itemize} 36 | \end{itemize} 37 | 38 | \subsubsection{Model 2a: Taste is known and stable} 39 | 40 | \begin{itemize} 41 | \item As if no switching costs (same equilibrium as pure Hotelling). 42 | \item No switching in equilibrium. 43 | \end{itemize} 44 | 45 | \subsubsection{Model 2b: Taste in second period is unknown} 46 | 47 | \begin{itemize} 48 | \item Average price is half of previous model! 49 | \begin{itemize} 50 | \item This is because when the decision is made, products are not differentiated (taste unknown), thus firms need to ``invest'' harder. 51 | \end{itemize} 52 | \end{itemize} 53 | 54 | \subsubsection{Model 2c: Consumer myopia} 55 | 56 | \begin{itemize} 57 | \item Same as model 2b! 58 | \begin{itemize} 59 | \item Same intuition, myopia means that second period does not come into decision, thus attracting consumers is harder. 60 | \end{itemize} 61 | \end{itemize} 62 | 63 | \section{Measurement} 64 | 65 | \subsection{Measuring switching costs or inertia} 66 | 67 | \begin{itemize} 68 | \item Challenge: is it switching costs or persistent heterogenous preferences? 69 | \begin{itemize} 70 | \item Osborne (2011): look at previous period event's effect on current period (price cut increases probability to buy again? = switching costs). 71 | \item Handel (2013): look at difference between old and new consumers (if old buy more than new = inertia) 72 | \end{itemize} 73 | \end{itemize} 74 | 75 | \subsection{Decomposing inertia} 76 | 77 | \begin{itemize} 78 | \item Inertia is: switching costs, habit formation, search costs, learning, inattention, etc. 79 | \begin{itemize} 80 | \item Usually only one form is considered (others assumed away) = bad (Wilson, 2012) 81 | \end{itemize} 82 | \end{itemize} 83 | 84 | \subsection{Comments on Wilson (2012)} 85 | 86 | \begin{itemize} 87 | \item Insight: a 1\$ search cost has more impact than a 1\$ switching cost because: 88 | \begin{itemize} 89 | \item Searching will cause the cost with probability 1, while switching is only incurred if better option available 90 | \item Potential of multiple searches, while only one switch 91 | \item Inversting from firms might help consumers offset cost 92 | \end{itemize} 93 | \item Thus, design a ``quick and easy'' method for estimating search and switch costs: 94 | \end{itemize} 95 | 96 | \section{Honka (2014)} 97 | 98 | \subsection{Summary} 99 | 100 | \subsubsection{Background} 101 | 102 | Insurance markets can be inefficient for many reasons, two of them being search costs and switching costs (market frictions). What is their value in the auto insurance market? And do they affect consumer choice and welfare? are the two questions Honka (2014) answers. Auto insurance market is perfect in the sense that it includes both (very high retention rate). Honka puts both types of costs in her model: new thing in the literature!! 103 | 104 | \subsubsection{Data} 105 | 106 | the observation unit is a transaction, with contract observables (prices, premium, etc.), consumer observables (previous contract, number of quotes, by whom, and demographics, etc.). Consideration set is very important to identify search costs, previous contract to identify switching costs (but no panel data). 107 | 108 | \subsubsection{Model} 109 | 110 | Multinomial logit model with a search + previous insurer consideration set. There a ``first-step'' search model based on expected utility to decide how many searches. 111 | 112 | \subsubsection{Estimation} 113 | 114 | Simulated semi-parametric way of recovering number of searches (analogous to ordered probit?). With consumer beliefs, recover search costs. Finally, switching costs are inside RUM model. 115 | 116 | \subsubsection{Assumptions} 117 | 118 | Main model assumptions are: (1) search and purchase are conditional on coverage (no search across coverages); (2) search is used to discover prices only and (3) search is simultaneous rather than sequential. 119 | 120 | Other assumptions include: static preferences (utility fixed effect is not correlated with previous choice); switching costs are not exactly identified (confounded with heterogenous persistent preferences. 121 | 122 | \subsubsection{Results} 123 | 124 | Search costs are three times higher than switching if made in person, but comparable if made through internet. Search costs are what drives most of the retention. Both have negative effects on welfare. 125 | 126 | \subsection{Discussion} 127 | 128 | \begin{itemize} 129 | \item \textbf{Research questions:} (1) What are search and switching costs in the US auto-insurance market? (2) How do they affect consumer choice? 130 | \item \textbf{Goals of the paper:} develop a method (introduce simultaneous search with large product choice sets + separate search and switching costs) and measure an effect (presence of search and switching costs) 131 | \item \textbf{Importance of the paper:} 1st empirical framework to study search and switching costs together: which is important to measure (1) market inefficiency, (2) welfare and (3) market power. 132 | \item \textbf{Theoretical foundations:} utility model including a individual-specific coefficient for switching costs and a simultaneous search model to identify search costs. \begin{itemize} 133 | \item Strengths: separates switching costs from search costs; justified in the setting; escape from heterogeneous preferences/switching costs trap using survey data. 134 | \item Shortcomings: no long justification on these choices; no broker competition; no switching dynamics. 135 | \end{itemize} 136 | \item \textbf{Empirical strategy:} use a structural model to recover unobserved variables (search and switching costs); reconstruct unobserved contract prices.\begin{itemize} 137 | \item Strengths: 138 | \item Shortcomings: 139 | \end{itemize} 140 | \item \textbf{Data:} From an insurance shopping study, observation unit is the contract, with observed variables are price, policy characteristics, other policies considered (not their price), previous supplier, consumer characteristics, etc. 141 | \begin{itemize} 142 | \item Exogenous: previous supplier (!!), 143 | \item Endogenous: number of searches, policy choice, price. 144 | \end{itemize} 145 | \item \textbf{Results:} Search costs range 35-170\$ while switching costs are 40\$. 146 | \end{itemize} -------------------------------------------------------------------------------- /macro/7750_M01/7750_LectureNotes.log: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- 1 | \select@language {english} 2 | \contentsline {chapter}{\numberline {1}Solow Growth Model}{7}{chapter.1} 3 | \contentsline {section}{\numberline {1.1}Assumptions}{7}{section.1.1} 4 | \contentsline {subsection}{\numberline {1.1.1}Inputs and Outputs}{7}{subsection.1.1.1} 5 | \contentsline {subsection}{\numberline {1.1.2}Production Function}{8}{subsection.1.1.2} 6 | \contentsline {subsection}{\numberline {1.1.3}Evolution of Inputs}{9}{subsection.1.1.3} 7 | \contentsline {section}{\numberline {1.2}Solving the model}{9}{section.1.2} 8 | \contentsline {subsection}{\numberline {1.2.1}Dynamics of $k$}{10}{subsection.1.2.1} 9 | \contentsline {subsection}{\numberline {1.2.2}Balanced growth path}{11}{subsection.1.2.2} 10 | \contentsline {section}{\numberline {1.3}Impact of a change in $s$}{12}{section.1.3} 11 | \contentsline {subsection}{\numberline {1.3.1}Impact on output}{12}{subsection.1.3.1} 12 | \contentsline {subsection}{\numberline {1.3.2}Impact on consumption}{12}{subsection.1.3.2} 13 | \contentsline {section}{\numberline {1.4}Quantitative Implications}{14}{section.1.4} 14 | \contentsline {subsection}{\numberline {1.4.1}Effect on Output in the Long Run}{14}{subsection.1.4.1} 15 | \contentsline {subsection}{\numberline {1.4.2}Speed of Convergence}{15}{subsection.1.4.2} 16 | \contentsline {section}{\numberline {1.5}Empirical applications}{16}{section.1.5} 17 | \contentsline {subsection}{\numberline {1.5.1}Growth Accounting}{16}{subsection.1.5.1} 18 | \contentsline {subsection}{\numberline {1.5.2}Convergence}{17}{subsection.1.5.2} 19 | \contentsline {chapter}{\numberline {2}Ramsey Model with infinitely-lived agents}{18}{chapter.2} 20 | \contentsline {section}{\numberline {2.1}Assumptions}{18}{section.2.1} 21 | \contentsline {subsection}{\numberline {2.1.1}Firms}{18}{subsection.2.1.1} 22 | \contentsline {subsection}{\numberline {2.1.2}Households}{19}{subsection.2.1.2} 23 | \contentsline {section}{\numberline {2.2}Behavior of Households and Firms}{20}{section.2.2} 24 | \contentsline {subsection}{\numberline {2.2.1}Firm's problem}{20}{subsection.2.2.1} 25 | \contentsline {subsection}{\numberline {2.2.2}Household's budget constraint}{21}{subsection.2.2.2} 26 | \contentsline {subsection}{\numberline {2.2.3}Household's problem}{22}{subsection.2.2.3} 27 | \contentsline {subsubsection}{Euler equation for consumption}{22}{section*.2} 28 | \contentsline {subsubsection}{Transversality Condition}{23}{section*.3} 29 | \contentsline {subsubsection}{Consumption function}{23}{section*.4} 30 | \contentsline {section}{\numberline {2.3}Equilibrium}{23}{section.2.3} 31 | \contentsline {subsection}{\numberline {2.3.1}Dynamics of $c$}{24}{subsection.2.3.1} 32 | \contentsline {subsection}{\numberline {2.3.2}Dynamics of $k$}{25}{subsection.2.3.2} 33 | \contentsline {subsection}{\numberline {2.3.3}Phase diagram}{27}{subsection.2.3.3} 34 | \contentsline {subsection}{\numberline {2.3.4}Initial value of $c$}{28}{subsection.2.3.4} 35 | \contentsline {section}{\numberline {2.4}Welfare and the BGP}{29}{section.2.4} 36 | \contentsline {subsection}{\numberline {2.4.1}First Welfare Theorem}{29}{subsection.2.4.1} 37 | \contentsline {subsection}{\numberline {2.4.2}Properties of the BGP}{29}{subsection.2.4.2} 38 | \contentsline {subsection}{\numberline {2.4.3}Social Optimum and Golden-rule}{29}{subsection.2.4.3} 39 | \contentsline {section}{\numberline {2.5}Impact of a change in the discount rate}{29}{section.2.5} 40 | \contentsline {subsection}{\numberline {2.5.1}Unexpected shock}{30}{subsection.2.5.1} 41 | \contentsline {subsection}{\numberline {2.5.2}Expected shock}{31}{subsection.2.5.2} 42 | \contentsline {subsection}{\numberline {2.5.3}Temporary vs. Permanent shocks}{31}{subsection.2.5.3} 43 | \contentsline {section}{\numberline {2.6}Impact of Government purchases}{32}{section.2.6} 44 | \contentsline {subsection}{\numberline {2.6.1}The role of government}{32}{subsection.2.6.1} 45 | \contentsline {subsubsection}{Lump-sum taxes}{32}{section*.5} 46 | \contentsline {subsubsection}{Distortionary taxes}{32}{section*.6} 47 | \contentsline {chapter}{\numberline {3}Overlapping Generations Model}{33}{chapter.3} 48 | \contentsline {section}{\numberline {3.1}Assumptions}{33}{section.3.1} 49 | \contentsline {section}{\numberline {3.2}Household behavior}{34}{section.3.2} 50 | \contentsline {section}{\numberline {3.3}Dynamics of the economy}{36}{section.3.3} 51 | \contentsline {subsection}{\numberline {3.3.1}Equilibrium conditions}{36}{subsection.3.3.1} 52 | \contentsline {subsection}{\numberline {3.3.2}Evolution of the economy}{37}{subsection.3.3.2} 53 | \contentsline {subsubsection}{General case}{37}{section*.7} 54 | \contentsline {subsubsection}{Log-utility and Cobb-Douglas economy}{37}{section*.8} 55 | \contentsline {section}{\numberline {3.4}Fiscal policies}{38}{section.3.4} 56 | \contentsline {subsection}{\numberline {3.4.1}Lump-sum financed government expenditures}{38}{subsection.3.4.1} 57 | \contentsline {subsection}{\numberline {3.4.2}Bond-financed government expenditures}{38}{subsection.3.4.2} 58 | \contentsline {section}{\numberline {3.5}Social security}{39}{section.3.5} 59 | \contentsline {subsection}{\numberline {3.5.1}Fully-funded system}{40}{subsection.3.5.1} 60 | \contentsline {subsection}{\numberline {3.5.2}Pay-as-you-go system}{41}{subsection.3.5.2} 61 | \contentsline {section}{\numberline {3.6}Welfare properties}{43}{section.3.6} 62 | \contentsline {section}{\numberline {3.7}Intergenerational altruism}{43}{section.3.7} 63 | \contentsline {subsection}{\numberline {3.7.1}Simple OLG with Bequests}{43}{subsection.3.7.1} 64 | \contentsline {subsection}{\numberline {3.7.2}OLG with bequests and government expenditures}{44}{subsection.3.7.2} 65 | \contentsline {subsection}{\numberline {3.7.3}OLG with bequests and social security}{44}{subsection.3.7.3} 66 | \contentsline {chapter}{\numberline {4}Introduction to endogenous growth: One-sector models}{45}{chapter.4} 67 | \contentsline {section}{\numberline {4.1}AK model}{45}{section.4.1} 68 | \contentsline {subsection}{\numberline {4.1.1}Household behavior}{46}{subsection.4.1.1} 69 | \contentsline {subsection}{\numberline {4.1.2}Firms behavior}{47}{subsection.4.1.2} 70 | \contentsline {subsection}{\numberline {4.1.3}Equilibrium}{47}{subsection.4.1.3} 71 | \contentsline {subsection}{\numberline {4.1.4}Phase diagram}{48}{subsection.4.1.4} 72 | \contentsline {subsection}{\numberline {4.1.5}Conclusion}{49}{subsection.4.1.5} 73 | \contentsline {section}{\numberline {4.2}One-sector model with two types of capital}{49}{section.4.2} 74 | \contentsline {section}{\numberline {4.3}Learning by doing and Knowledge Spillovers}{50}{section.4.3} 75 | \contentsline {subsection}{\numberline {4.3.1}Model}{50}{subsection.4.3.1} 76 | \contentsline {subsection}{\numberline {4.3.2}Equilibrium}{51}{subsection.4.3.2} 77 | \contentsline {subsection}{\numberline {4.3.3}Pareto nonoptimality}{51}{subsection.4.3.3} 78 | \contentsline {subsection}{\numberline {4.3.4}Scale effects}{52}{subsection.4.3.4} 79 | \contentsline {section}{\numberline {4.4}Public goods model}{53}{section.4.4} 80 | \contentsline {subsection}{\numberline {4.4.1}Basic model}{53}{subsection.4.4.1} 81 | \contentsline {subsubsection}{Distortionary taxes}{54}{section*.9} 82 | \contentsline {subsubsection}{Optimal public spending}{54}{section*.10} 83 | \contentsline {subsection}{\numberline {4.4.2}Congestion model}{55}{subsection.4.4.2} 84 | \contentsline {subsubsection}{Pareto optimality}{56}{section*.11} 85 | \contentsline {section}{\numberline {4.5}Kremer model}{56}{section.4.5} 86 | \contentsline {chapter}{\numberline {5}Two-sectors model}{58}{chapter.5} 87 | \contentsline {section}{\numberline {5.1}One-sector model with physical and human capital}{58}{section.5.1} 88 | \contentsline {subsection}{\numberline {5.1.1}Assumptions}{58}{subsection.5.1.1} 89 | \contentsline {subsection}{\numberline {5.1.2}Equilibrium}{59}{subsection.5.1.2} 90 | \contentsline {section}{\numberline {5.2}Two-sectors model}{60}{section.5.2} 91 | \contentsline {subsection}{\numberline {5.2.1}Basic Model}{60}{subsection.5.2.1} 92 | \contentsline {subsubsection}{Assumptions}{60}{section*.12} 93 | \contentsline {subsubsection}{Equilibrium}{61}{section*.13} 94 | \contentsline {subsection}{\numberline {5.2.2}Uzawa-Lucas Model}{61}{subsection.5.2.2} 95 | \contentsline {section}{\numberline {5.3}Summary}{61}{section.5.3} 96 | \contentsline {chapter}{\numberline {6}Endogeneizing Technological Change}{62}{chapter.6} 97 | \contentsline {section}{\numberline {6.1}Expanding variety of products models}{62}{section.6.1} 98 | \contentsline {subsection}{\numberline {6.1.1}Producers of final output}{63}{subsection.6.1.1} 99 | \contentsline {subsection}{\numberline {6.1.2}Research Firms}{64}{subsection.6.1.2} 100 | \contentsline {subsubsection}{Step 2: Profit if a new product is developed}{64}{section*.14} 101 | \contentsline {subsubsection}{Step 1: Will they make the new product?}{65}{section*.15} 102 | \contentsline {subsubsection}{Free-entry condition}{66}{section*.16} 103 | \contentsline {subsection}{\numberline {6.1.3}Households}{66}{subsection.6.1.3} 104 | \contentsline {subsection}{\numberline {6.1.4}Equilibrium}{66}{subsection.6.1.4} 105 | \contentsline {subsection}{\numberline {6.1.5}Determinants of the growth rate}{67}{subsection.6.1.5} 106 | \contentsline {subsection}{\numberline {6.1.6}Pareto Optimality}{67}{subsection.6.1.6} 107 | \contentsline {section}{\numberline {6.2}Quality Ladder models}{67}{section.6.2} 108 | \contentsline {section}{\numberline {6.3}Models with technology diffusion}{67}{section.6.3} 109 | \contentsline {chapter}{\numberline {7}Explaining cross-country income differences}{68}{chapter.7} 110 | \contentsline {section}{\numberline {7.1}Extended Solow model}{68}{section.7.1} 111 | \contentsline {subsection}{\numberline {7.1.1}Model}{68}{subsection.7.1.1} 112 | \contentsline {subsection}{\numberline {7.1.2}Steady-state}{69}{subsection.7.1.2} 113 | \contentsline {subsubsection}{Physical capital steady-state}{69}{section*.17} 114 | \contentsline {subsubsection}{Human capital steady-state}{70}{section*.18} 115 | \contentsline {subsubsection}{General steady-state}{70}{section*.19} 116 | \contentsline {section}{\numberline {7.2}Empirical evaluation}{70}{section.7.2} 117 | \contentsline {section}{\numberline {7.3}Social infrastructure}{70}{section.7.3} 118 | \contentsline {section}{\numberline {7.4}Beyond social infrastructure}{70}{section.7.4} 119 | \contentsline {chapter}{\numberline {8}Stochastic Dynamic Programming}{71}{chapter.8} 120 | \contentsline {section}{\numberline {8.1}Investment with adjustment costs}{71}{section.8.1} 121 | \contentsline {subsection}{\numberline {8.1.1}Euler equation for $K$}{72}{subsection.8.1.1} 122 | \contentsline {subsection}{\numberline {8.1.2}Q model of investment}{73}{subsection.8.1.2} 123 | \contentsline {section}{\numberline {8.2}Consumption with stochastic returns}{74}{section.8.2} 124 | \contentsline {subsection}{\numberline {8.2.1}Hall (1978)}{76}{subsection.8.2.1} 125 | \contentsline {subsection}{\numberline {8.2.2}Hansen and Singleton (1983)}{76}{subsection.8.2.2} 126 | -------------------------------------------------------------------------------- /macro/7750_M01/images/Ramseyinitc.JPG: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sarkispa/LectureNotes/8c4c94151996df237d5424f626606686f267c989/macro/7750_M01/images/Ramseyinitc.JPG -------------------------------------------------------------------------------- /macro/7750_M01/images/Ramseyphase.JPG: -------------------------------------------------------------------------------- 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/metrics/7772_INTRO/7772_LectureNotes.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{report} %Police 2 | \usepackage[utf8]{inputenc} 3 | \usepackage[english]{babel} 4 | \usepackage{microtype} 5 | \usepackage{libertine} %Palatino 6 | \usepackage[expert]{mathdesign} 7 | \usepackage{amsmath,amsfonts,amsthm, amssymb} 8 | \usepackage{enumitem} 9 | \usepackage[open,openlevel=1]{bookmark} 10 | \usepackage{todonotes} 11 | \usepackage[tikz]{bclogo} 12 | 13 | \setcounter{tocdepth}{1} 14 | 15 | \setlength{\parindent}{0ex} 16 | \setlength{\parskip}{1em}%Espacement des par 17 | 18 | \setlist[itemize]{topsep=-5pt} 19 | \setlist[enumerate]{topsep=0pt} 20 | 21 | \newtheorem{theorem}{Theorem}[chapter] 22 | \newtheorem{definition}{Definition}[chapter] 23 | \newtheorem{remark}{Remark}[chapter] 24 | \newtheorem{proposition}{Proposition}[chapter] 25 | 26 | \newcommand{\E}[1]{\operatorname{E}\left[#1\right]} 27 | \newcommand{\V}[1]{\operatorname{Var}\left[#1\right]} 28 | \newcommand{\cov}[1]{\operatorname{Cov}\left(#1\right)} 29 | \newcommand{\Prob}[1]{\operatorname{Pr}\left[#1\right]} 30 | \newcommand{\Probhat}[1]{\hat{\operatorname{Pr}}\left[#1\right]} 31 | \newcommand{\plim}{\operatorname{plim}} 32 | \newcommand{\pconv}{\overset{\text{p}}{\to}} 33 | \newcommand{\dconv}{\overset{\text{d}}{\to}} 34 | \newcommand{\msconv}{\overset{\text{ms}}{\to}} 35 | \newcommand{\avg}[2]{\frac{#1}{#2} \sum_{i=#1}^{#2}} 36 | \def\D{\mathrm{d}} 37 | 38 | 39 | \begin{document} 40 | 41 | \date{} 42 | \title{\textbf{\huge{ECON7772 - Econometric Methods}}\\ \textit{Lecture Notes from Arthur Lewbel's lectures}} 43 | \author{Paul Anthony Sarkis\\ Boston College} 44 | 45 | \maketitle 46 | 47 | \tableofcontents 48 | 49 | \chapter{Properties of Estimators} 50 | 51 | \input{Chapters/c01_estimatorproperties} 52 | 53 | \chapter{Classical Regression} 54 | 55 | \input{Chapters/c03_classicalregression} 56 | 57 | \chapter{Specification issues} 58 | 59 | \input{Chapters/c04_specificationissues} 60 | 61 | \chapter{Maximum Likelihood Estimation} 62 | 63 | \input{Chapters/c05_mlestimation} 64 | 65 | \chapter{Inference and Hypothesis Testing} 66 | 67 | \input{Chapters/c06_inferencehyptests} 68 | 69 | \chapter{Generalized Least-Squares and non-iid errors} 70 | 71 | \input{Chapters/c07_generalizedls} 72 | 73 | \chapter{Dynamic models and Time Series models} 74 | 75 | \input{Chapters/c08_dynamicmodels} 76 | 77 | \chapter{Instrumental Variables, 2SLS, Endogeneity and Simultaneity} 78 | 79 | \input{Chapters/c09_ivreg2sls} 80 | 81 | \chapter{Non-linear models, GMM and extremum estimators} 82 | 83 | \input{Chapters/c10_gmm} 84 | 85 | \chapter{Non-parametric estimators} 86 | 87 | \input{Chapters/c11_nonparamreg} 88 | 89 | \chapter{Program Evaluation and Treatment Effects} 90 | 91 | \input{Chapters/c12_policyeval} 92 | 93 | \chapter{Regression Discontinuity Design} 94 | 95 | \input{Chapters/c13_regdiscontinuity} 96 | 97 | 98 | \end{document} -------------------------------------------------------------------------------- /metrics/7772_INTRO/Chapters/c04_specificationissues.tex: -------------------------------------------------------------------------------- 1 | \section{Non-randomness of X} 2 | 3 | Starting with the usual model: $$Y = X\beta + e$$ We assume that:\begin{itemize} 4 | \item $(y_i, x_i)$ are independent but not identically distributed. 5 | \item $\E{e_ix_i} = 0$, which, if $X$ contains a constant, implies that $\E{e} = 0$. 6 | \item For all $i,j: i\neq j$, $\E{e_ie_j} = 0$ so that off-diagonal elements of $\Omega$ are zero. 7 | \item $\E{\sigma^2\vert x_i} = \sigma^2(x_i)$ 8 | \end{itemize} 9 | 10 | The assumption that $\E{e_i\vert X} = 0 $ is not made here, implying that $X$ is now a random variable. The implication of this statement can be visible from the new mean of $\hat\beta_{OLS}$:\begin{align*} 11 | \E{\hat\beta} = \E{(X'X)^{-1}X'Y} & = \E{(X'X)^{-1}X'(X\beta + e)} \\ & = \E{(X'X)^{-1}X'X\beta + (X'X)^{-1}X'e} \\ 12 | & = \beta + \E{(X'X)^{-1}X'e} 13 | \end{align*} Using our definition of $Q_n = \frac{X'X}{n}$, we can write: $$ \E{\hat\beta} = \beta + \E{Q_n^{-1}\frac{X'e}{n}} $$ Note that, even if $\E{e_iX_i} = 0$ we cannot cancel out the expectation term since it might be correlated to $Q_n^{-1}$. 14 | 15 | The same issue arises for $\V{\hat\beta}$:\begin{align*} 16 | \V{\hat\beta} = \V{(X'X)^{-1}X'e} & = \E{(X'X)^{-1}X'ee'X(X'X)^{-1}} \\ 17 | & = \E{Q_n^{-1}\frac{(X'e)(X'e)'}{n^2} Q_n^{-1}} 18 | \end{align*} 19 | 20 | We now want to check if $\hat\beta$ is consistent. We have:\begin{align*} 21 | \plim \hat\beta = \plim\beta + \plim\left[Q_n^{-1}\frac{X'e}{n}\right] & = \beta + \plim Q_n^{-1} + \plim \frac{X'e}{n} 22 | \end{align*} If $\V{\frac{X'e}{n}} \to 0$, we have that $\plim \frac{X'e}{n} = \frac{1}{n}\E{X'e} = 0$ by assumption 2. 23 | 24 | Note that the last part allows us to write: $$\sqrt{n}(\hat\beta - \beta) = Q_n^{-1}\sqrt{n}\frac{X'e}{n} \dconv N(0, \V{Q_n^{-1}\sqrt{n}\frac{X'e}{n}})$$ Since $Q_n^{-1}$ is a constant, the problem reduces to finding $\V{\sqrt{n}\frac{X'e}{n}}$:\begin{align*} 25 | \V{\sqrt{n}\frac{X'e}{n}} = \frac{1}{n}\E{(X'e)(e'X)} = 26 | \end{align*} 27 | 28 | 29 | 30 | \section{Non-stationarity of X} 31 | 32 | \section{High correlation in the error term} 33 | 34 | \section{Collinearity} 35 | 36 | \begin{definition}[Strict multicollinearity] 37 | Strict multicollinearity is a consequence of the columns of matrix $X$ being linearly dependent. In particular, there is at least one column (or row) of $X$ which is a linear combination of any other column (row). Algebraically, $$\exists \alpha\neq 0 : X\alpha = 0$$ 38 | \end{definition} 39 | 40 | \begin{proposition}[Singularity of strictly multicollinear matrices] 41 | If the matrix $X$ is strictly collinear, then its quadratic form $X'X$ is singular and $\hat{\beta}_{OLS}$ is not defined. 42 | \end{proposition} 43 | 44 | \begin{definition}[Near multicollinearity] 45 | A matrix $X$ is said to be near multicollinearity (or simply multicollinear) if the matrix $X'X$ is near singular. 46 | \end{definition} 47 | 48 | The issue with near multicollinearity resides in the definition of what is "near" or in other words, what is "collinear enough"? We can work out a few examples to check for this problem. 49 | 50 | \begin{bclogo}[couleur=blue!10, arrondi=0.1, logo=,ombre=false]{ Multicollinearity in examples} 51 | \begin{small} 52 | Let $x$ be the average hourly wage and $z$ the average daily wage. Then, it could be that $x$ and $z$ are strictly multicollinear if everyone in the population worked 8 hours exactly ($z = 8x$). In practice, the number of hours worked per day may vary slightly but the correlation between $x$ and $y$ will be very close to 1, leading to near multicollinearity. 53 | 54 | Let $h$ be the number of hours worked in a week and $w$ be the total weekly wage. We have that $w = xh$ so $x$ and $w$ are not strictly multicollinear. However, in logs, $\ln(w) = \ln(xh) = \ln(x) + \ln(h)$ implying that $\ln(w)$ and $\ln(x)$ are strictly multicollinear. 55 | 56 | Finally, if we use both $x$ and $x^2$ in a regression, we increase chances of finding near multicollinearity. 57 | \end{small} 58 | \end{bclogo} 59 | 60 | 61 | \section{Coefficient interpretation} 62 | 63 | \subsection{Linear vs. log specification} 64 | 65 | Let us compare two different specifications: $$Y = a + bX + e \text{ and } \ln(Y) = \alpha + \beta \ln(X) + \varepsilon $$ 66 | We know that coefficients should be interpreted as the derivative of the regressed term with respect to the regressor. In this case,\begin{itemize} 67 | \item $b = \frac{dY}{dX}$ is the derivative of $Y$ w.r.t. $X$. 68 | \item $\beta = \frac{d\ln(Y)}{d\ln(X)} = \frac{dY}{dX}\frac{X}{Y}$ is the elasticity of $Y$ w.r.t. $X$. 69 | \end{itemize} 70 | However, whether you want to estimate an elasticity or a derivative should not affect what model you should use. One should only care about the true specification of a model, then make the computations necessary to find a certain variable. 71 | 72 | \subsection{Measurement units} 73 | Now, consider two models $$Y = a + bX + e \text{ and } Y = a^* + b^*X^* + e^* $$ where $X$ is measured in thousands of dollars while $X^*$ is directly measured in dollars. We have $X^* = 1000 X$. Notice that we can rewrite the second model as: $$Y = a^* + b^*\cdot(1000 X) + e^* $$Therefore it must be that $a^* = a$, $b = 1000 b^*$ and $e = e^*$. This also implies that each $t$-statistic will be the exact same. Hence, a change of unit in a linear model does not change the fit of the model. 74 | 75 | If the change of units happens on a logarithmic model, then the result above is different. In particular, \begin{align*} 76 | \ln(Y) & = \alpha^* + \beta^*\ln(1000X) + e^* \\ 77 | & = \underbrace{\alpha^* + \beta^*\ln(1000)}_{\text{new constant}} + \beta^*\ln(X) + e^* 78 | \end{align*} Here, the constant term will change (and its $t$-statistic too). 79 | 80 | \subsection{Percent change} 81 | One should always use a log specification for a percent change variable ($\ln(\frac{X_{t}}{X_{t-1}})$) instead of computing the actual period percent change ($\frac{X_t - X_{t-1}}{X_{t-1}}$). 82 | 83 | \subsection{Interaction variables} 84 | 85 | Consider the following model, $$Y_i = \beta_1 + \beta_2 X_i + \beta_3 Z_i + \beta_4 \underbrace{X_iZ_i}_{\textit{interaction term}} + e_i $$ This specification allows for variables to interact with each other so that $\frac{\partial Y}{\partial X} = \beta_2 + \beta_4 Z$ and $\frac{\partial Y}{\partial Z} = \beta_3 + \beta_4 X$. This means that the effect of $X$ (or $Z$) on $Y$ also depends on the value that $Z$ (or $X$) takes. This model is close to the analysis performed in a diff-in-diff model since having this specification almost implies having two models to estimate. 86 | 87 | A similar model would be one including a polynomial function of one variable such as, $$Y_i = \beta_1 + \beta_2 X_i + \beta_3 X_i^2 + \beta_4 X_i^3 + e_i $$ 88 | 89 | Both these models do not violate any assumptions among the Gauss-Markov assumptions. However, one should consider the fact that interacting variables increase the likelihood of multicollinearity in the variables (since there will be a strong correlation between single and interacted variables). 90 | 91 | \begin{bclogo}[couleur=blue!10, arrondi=0.1, logo=,ombre=false]{ Predicting sales revenue at CVS} 92 | \begin{small} 93 | 94 | \end{small} 95 | \end{bclogo} -------------------------------------------------------------------------------- /metrics/7772_INTRO/Chapters/c06_inferencehyptests.tex: -------------------------------------------------------------------------------- 1 | \section{Review} 2 | 3 | In the case of a linear regression model with iid normal errors $e_i \sim N(0,\sigma^2)$, it is possible to compute the exact distribution of OLS coefficients $\hat\beta_{OLS}$ and OLS residuals $\hat e_i$, even in finite samples (recall that this normality assumption is not need for asymptotic properties). 4 | 5 | First, recall that $\hat{\beta} - \beta = (X'X)^{-1}X'e$, which is a linear projection of the error $e$. Hence, we can get:\begin{align*} 6 | \hat\beta - \beta & \sim (X'X)^{-1}X'N(0,\sigma^2 I_n)\\ 7 | & \sim N(0, \sigma^2 (X'X)^{-1}X'X(X'X)^{-1}) \\ & \sim N(0,\sigma^2(X'X)^{-1}) 8 | \end{align*} 9 | 10 | Second, using $\hat e = Me$, we have that $$\hat e \sim N(0, \sigma^2 MM) \sim N(0, \sigma^2 M) $$ 11 | 12 | These two results can also give us the joint distribution of $\hat \beta$ and $\hat e$, in fact:\begin{align*} 13 | \begin{bmatrix} 14 | \hat\beta - \beta \\ 15 | \hat e 16 | \end{bmatrix} 17 | = \begin{bmatrix} 18 | (X'X)^{-1}X'e \\ 19 | Me 20 | \end{bmatrix} 21 | = \begin{bmatrix} 22 | (X'X)^{-1}X' \\ 23 | M 24 | \end{bmatrix} 25 | e 26 | \end{align*} which, again, is a linear projection of $e$, thus we can guess its mean ($\E{Ae} = \E{e} = 0$) for any constant $A$ and variance matrix ($\V{Ae} = A\V{e}A'$). And indeed, using the variance formulas, we find that $\hat\beta - \beta$ and $\hat e$ are uncorrelated (therefore $\hat\beta$ also is uncorrelated to $\hat e$):\begin{align*} 27 | \V{Ae} = A\V{e}A' = \sigma^2 AA' = \sigma^2 \cdot \begin{bmatrix} 28 | (X'X)^{-1} & 0 \\ 29 | 0 & M 30 | \end{bmatrix} 31 | \end{align*} 32 | 33 | Finally, consider the adjusted sample variance estimator $s^2 = (n-k)^{-1} \sum_{i=1}^{n} \hat e$. We can write that: $$ (n-k)s^2 = \hat e'\hat e = (Me)'Me = e'M'Me = e'Me $$ 34 | Then, using the spectral decomposition of $M$, namely $M = H\Lambda H'$ where $H'H=I_n$ and $\Lambda$ is a diagonal matrix with the first $n-k$ terms equal to $1$, the rest to $0$. 35 | 36 | Let $u=H'e\sim N(0,I_n\sigma^2)$ and partition it as $u=(u_1, u_2)$. Then,\begin{align*} 37 | (n-k)s^2 = e'Me = e'H\Lambda H'e & = u'\Lambda u \\ 38 | & = u_1'u_1 \\ 39 | & \sim \sigma^2 \chi_{n-k}^2 40 | \end{align*} 41 | 42 | The main results derived in this section (that will help us in the next) are:\begin{itemize} 43 | \item $\hat{\beta} \sim N(\beta,\sigma^2(X'X)^{-1})$ 44 | \item $\hat e \sim N(0, \sigma^2M)$ 45 | \item $\hat\beta$ and $\hat e$ are independent 46 | \item $\frac{(n-k)s^2}{\sigma^2}\sim \chi_{n-k}^2$ 47 | \item $\hat\beta$ and $s^2$ are independent 48 | \end{itemize} 49 | 50 | \newpage 51 | 52 | \section{Univariate tests} 53 | 54 | In this section, we cover tests and inference that can be applied to a particular estimator, say the coefficient on a single covariate. 55 | 56 | \subsection{T-statistic} 57 | 58 | We can use all results of the last section to derive two data statistics. 59 | 60 | \begin{definition}[Standardized statistic] 61 | Define the standardized statistic as:$$\frac{\hat{\beta}_j - \beta_j}{\sqrt{\sigma^2\left[(X'X)^{-1}\right]_{jj}}} \sim N(0,1) $$ 62 | \end{definition} 63 | 64 | The issue with this last statistic is that $\sigma^2$ is unknown. If we use $s^2$, the adjusted variance estimator, we can design a more useful statistic (that will be used for hypothesis testing). 65 | 66 | \begin{definition}[T-statistic] 67 | Define the T-statistic as: $$ \frac{\hat{\beta}_j - \beta_j}{\sqrt{s^2\left[(X'X)^{-1}\right]_{jj}}} = \frac{\hat{\beta}_j - \beta_j}{s(\hat\beta_j)} \sim t_{n-k} $$ where $s(\hat\beta_j)$ is the square root of the $j\times j$-th element of the adjusted variance matrix, and $t_{n-k}$ represents the Student's $t$-distribution of $(n-k)$ degrees of freedom. 68 | \end{definition} 69 | 70 | Consider a classical linear regression where $e$ is assumed to follow a normal distribution $N(0,\sigma^2)$. Using Student's $t$-statistic, we can design a test to assess whether the estimated coefficient $\hat\beta$ is equal to a specific value $\beta$ (we are interested in $\beta_0$, the true value of the regression). 71 | 72 | \begin{proposition}[Student's $t$-test] 73 | Define the null hypothesis as $H_0 : \hat\beta = \beta$ while the alternative hypothesis will be $H_1:\hat\beta \neq \beta$. 74 | 75 | The statistic used to test $H_0$ against $H_1$ is the absolute value of Student's $t$-statistic: $$\vert T\vert = \left\vert \frac{\hat{\beta}_j - \beta_j}{s(\hat\beta_j)} \right\vert $$ We reject $H_0$ if $\vert T\vert > c$. 76 | \end{proposition} 77 | 78 | We call $c$ the critical value of the test. We have seen that it is defined as the threshold for the test but its value is in fact determined to control the probability of type-I error. For a given value of $c$, the probability of type-I is:\begin{align*} 79 | \Prob{\text{Reject }H_0\vert H_0\text{ is true}} & = \Prob{\vert T\vert >c\vert H_0} \\ 80 | & = \Prob{T>c\vert H_0} + \Prob{T