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Consider an economy with two dates, denoted by t = 1, 2. There are two goods: consumption and capital. There is a continuum of entrepreneurs and a continuum of consumers. All individuals have linear utility and consume only in period 2, so U = E[c2]. There is a fixed supply of capital k, initially owned by the consumers. Consumers are endowed with a large amount of consumption good in each period and they can store this good between dates, such that if they store one unit of the consumption good in t = 1 they get one unit of the good in t = 2. The entrepreneurs have access to a linear technology that produces A units of consumption good in period 2 per unit of capital they own. The consumers have access to a concave technology G( ?k), where ?k denotes the capital owned by consumers in period 2. Assume limk?0G0 (k) = ? and G0 (k) = 0. The entrepreneurs enter period 1 with a given net worth N1 in terms of consumption goods. Assume agents can trade a risk-free bond b2 that pays an interest rate r. a) Argue that the gross rate of return on the risk-free bond is equal to 1 (i.e., the net return, r, is zero). b) Suppose that entrepreneurs face no borrowing constraints. State the optimization problems of an entrepreneur and a consumer. Show that the equilibrium capital price is q1 = A and the entrepreneurs buy k ? , where G0 (k ? k ? ) = A. c) Suppose that the entrepreneurs cannot borrow at all, so q1k2 ? N1. Find the equilibrium price and allocation, show that q1 ? A in equilibrium and that the expected utility of the entrepreneur is A q1 N1 (18) irrespective of whether the constraint q1k2 ? N1 binds or not. Show that q1 is increasing in N1 for N1

Section C Question 5 Production Function Estimation. Suppose that you have a random cross section of firm- level data, with information on output, labor and capital. In logs, (uni, hi, k : i = 1, 2, ..., N} You are interested in estimating the Cobb-Douglas production function: wi = auditakkitwiter 1. Discuss the issues with estimating this PF using OLS. 2. What are the two main reasons (in terms of identification, not availability) why input prices are likely poor candidates for instruments? 3. Now suppose that you have panel data and want to estimate the Olley & Pakes (1996) model. Describe clearly how to implement the two-step approach that they propose. 4. What are the three assumptions/requirements for identification of az? 5. What is the basis of the Ackerberg, Caves, & Fraser (2006) critique of the OP model? 6. What assumptions do they suggest that allow the OP approach to be salvaged? How does the two-step procedure change in this context? Question 6 Dynamic Discrete Choice Models. 1. Discuss the main challenges inherent in empirical estimation of dynamic games. Pick the two or three most important, in your view. Be clear and concise. 2. Define a Markov Perfect Equilibrium. Explain why it is useful in estimation of dynamic games. Practically speaking (and in plain english), what does it imply about the beliefs of firms? 3. The next few questions relate to the Pakes, Ostrovsky, & Berry (2007) model, but touch on some common elements of dynamic estimation more generally. Below is the Bellman 2 equation for incumbent firms in the POB framework. What data are required to estimate the parameters of interest in the POB model? To which static entry/exit model is this most similar? Name the types of firms that this (static) paper examined. VC(n, z;0) = _ [#(m', ?'; 0) + BEsmart, VC(n', =';0)}]] P(n', ='In, z, x = 1) where w(n, 2; 0) is a one-period profit function, n is the number of active firms, z is a vector of exogenous profit shifters, 0 is the parameter vector, e and z are the number of entrants and exitors, respectively, $ is the sell-off (exit) value, and x is an indicator variable equal to one if an incumbent remains.Section C Question 5 Production Function Estimation. Suppose that you have a random cross section of firm- level data, with information on output, labor and capital. In logs, (uni, hi, k : i = 1, 2, ..., N} You are interested in estimating the Cobb-Douglas production function: wi = auditakkitwiter 1. Discuss the issues with estimating this PF using OLS. 2. What are the two main reasons (in terms of identification, not availability) why input prices are likely poor candidates for instruments? 3. Now suppose that you have panel data and want to estimate the Olley & Pakes (1996) model. Describe clearly how to implement the two-step approach that they propose. 4. What are the three assumptions/requirements for identification of az? 5. What is the basis of the Ackerberg, Caves, & Fraser (2006) critique of the OP model? 6. What assumptions do they suggest that allow the OP approach to be salvaged? How does the two-step procedure change in this context? Question 6 Dynamic Discrete Choice Models. 1. Discuss the main challenges inherent in empirical estimation of dynamic games. Pick the two or three most important, in your view. Be clear and concise. 2. Define a Markov Perfect Equilibrium. Explain why it is useful in estimation of dynamic games. Practically speaking (and in plain english), what does it imply about the beliefs of firms? 3. The next few questions relate to the Pakes, Ostrovsky, & Berry (2007) model, but touch on some common elements of dynamic estimation more generally. Below is the Bellman 2 equation for incumbent firms in the POB framework. What data are required to estimate the parameters of interest in the POB model? To which static entry/exit model is this most similar? Name the types of firms that this (static) paper examined. VC(n, z;0) = _ [#(m', ?'; 0) + BEsmart, VC(n', =';0)}]] P(n', ='In, z, x = 1) where w(n, 2; 0) is a one-period profit function, n is the number of active firms, z is a vector of exogenous profit shifters, 0 is the parameter vector, e and z are the number of entrants and exitors, respectively, $ is the sell-off (exit) value, and x is an indicator variable equal to one if an incumbent remains.(e) How might you expand on the simple empirical model in (d)? Relate your suggestion to paper(s) we covered in class. (f) How might you "correct" your standard errors in (e) (or even (d))? (g) To strengthen their paper, the authors make the following argument: What we do know is that stations do not buy gasoline every day. According to Beta (the organization for independent gasoline retailers), many stations are supplied with new stock three times a week (Van Gelder 2008). Naturally, there are important differences between stations. This means that each day on average 43% (3/7) of the gasoline stations get new stock. We also know the dates at which the suggested prices change and also that these dates are independent of the delivery moments of new gasoline to stations. As a consequence, if the cost of a liter of gasoline depends on the suggested price and if gasoline stations simply adjust their retail price to the cost level, we expect that only 43% of all gasoline stations will change their price when the suggested price changes (and the suggested price is not equal to the suggested price on the previous day that the gasoline stations bought new stock). We can therefore check how many gasoline stations change their retail prices on days that the suggested price changes to discriminate between the two alternative hypotheses. The non-tacit collusion hypothesis says that (slightly changed to hide potential answers to previous questions) at most 43% of the stations should change their price. The coordinated effect hypothesis says that this percentage is (much) higher: it does not say that it should be 100% as this would be implied only if the suggested prices fully coordinate retail prices (which we know is not the case) and there are no menu costs or other costs of price adjustments. Evaluate this empirical test.2. This question deals with Guerre, Perrigne, and Vuong, "Optimal Nonparametric Estimation of First-Price Auctions" (Econometrica, 2000), Haile and Tamer, "Inference with an Incomplete Model of English Auctions" (JPE, 2003) and Haile, Hong, and Shum, "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions" (2005). Common Assumptions to both (a) and (b): There are / potential bidders. Assume / is exogenous and known. Bidders are symmetric and risk-neutral. Independent Private Values. Each bidder draws her private value v, from a common distribution F(v), which has a support [0, co). (a) Consider a single-object, first-price sealed-bid auction. Assume there is no reserve price for simplicity. Carefully derive symmetric Bayesian Nash equilibrium bidding strategies, A(v.). (Consider increasing and differentiable strategies only.) (b) Consider a single-object, Milgrom-Weber "button" auction. The seller's value for the object is vo and she wants to maximize her revenue from the auction by setting a reserve price r. Write down the seller's maximization problem and derive a condition for the optimal reserve price ,* from the F.O.C. of the max problem. (c) Describe, as fully as you can, the nonparametric identification result and the two-step nonparametric estimation strategy of GPV (2000). (d) State the two axioms (or behavioral assumptions) of Haile and Tamer (2003) and construct, as fully as you can, the nonparametric (partial) identification result of Haile and Tamer (2003). Discuss the advantages and disadvantages of this incomplete approach. (e) Discuss, in general, the advantages and disadvantages of using structural models when conducting empirical research in auctions. (f) Prove the following theorem from Haile, Hong, and Shum (2005), which is the basis of their nonparametric test of common values. Theorem Under standard assumptions of symmetry, affiliation, nondegeneracy and an additional assumption of exogenous participation, v(x, x, ") is invariant to " for all x in a PV model, but strictly decreasing in n for all x in a CV model, where v(x, x', ") = E[V,| X, = x,max X, = x']