In this paper, we extend Powell et al.’s (1989) results to a situation where the index contains functionally dependent covariates. This allows one to obtain semiparametric, root-N consistent, estimates of index parameters when the index includes polynomial or interaction terms.

Recent work estimating production functions has often used methodologies proposed in two literatures: (1) “proxy variable” estimation techniques (Olley, S. and Pakes, A., 1996, Econometrica , 64, pp. 1263–1295), and (2) “dynamic panel” estimation techniques. I illustrate how timing and information set assumptions are key to both, and how these assumptions can be strengthened (or weakened) almost continuously. I examinehow, in some common production datasets, strengthening or weakening these assumptions affects the precision of estimates—comparing these impacts to those achieved by imposing alternative assumptions sometimes utilized in these literatures. This illustrates efficiency tradeoffs between different possible assumptions, at least in the production function context.

We revisit identification based on timing and information set assumptions in structural models, which have been used in the context of production functions, demand equations, and hedonic pricing models (e.g. Olley and Pakes, 1996, Blundell and Bond, 2000). First, we demonstrate a general under-identification problem using these assumptions in a simple version of the Blundell–Bond dynamic panel model. In particular, the basic moment conditions can yield multiple discrete solutions: one at the persistence parameter in the main equation and another at the persistence parameter governing the regressor. We then propose a possible solution in the simple setting by enforcing an assumed sign restriction and discuss more general practical advice for empirical researchers using these methods.

In this comment I illustrate that in the model of (Lee et al. (2019). Oxford Bulletin of Economics and Statistics. Vol. 81, pp. 80-97), firm profit maximizing implies that Assumption 2 and Equation 14 may be contradictory. More specifically, there is generally a contradiction when investment is used as the control variable, but there is generally not a contradiction when a static input like material input is used as the control variable (both types of control variables are discussed in Lee et al.). While the Lee et al. model and techniques are an interesting way to incorporate fixed effects into Olley and Pakes-style production function estimators, this observation suggests that their application should be restricted to cases where static inputs are used as control variables.

This paper examines some of the recent literature on the estimation of production functions. We focus on techniques suggested in two recent papers, Olley and Pakes (1996) and Levinsohn and Petrin (2003). While there are some solid and intuitive identification ideas in these papers, we argue that the techniques can suffer from functional dependence problems. We suggest an alternative approach that is based on the ideas in these papers, but does not suffer from the functional dependence problems and produces consistent estimates under alternative data generating processes for which the original procedures do not.

This policy study uses U.S. Census microdata to evaluate how subsidies for universal telephone service vary in their impact across low-income racial groups, gender, age, and home ownership. Our demand specification includes both the subsidized monthly price (Lifeline program) and the subsidized initial connection price (Linkup program) for local telephone service. Our quasi-maximum likelihood estimation controls for location differences and instruments for price endogeneity. The microdata allow us to estimate the effects of demographics on both elasticities of telephone penetration and the level of telephone penetration. Based on our preferred estimates, the subsidy programs increased aggregate penetration by 6.1% for households below the poverty line. Our results suggest that automatic enrollment programs are important and that Linkup is more cost-effective than Lifeline, which calls into question a recent FCC (2012) decision to reduce Linkup subsidies in favor of Lifeline. Our study can inform the evaluation of similar universal service policies for Internet access.

The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the already-well-known parametric literature. This means that for computational purposes, an empirical researcher can ignore the semiparametric nature of the problem and do all calculations as if it were a parametric situation. We hope that this simplicity will promote the use of semiparametric procedures.

We introduce two simple new variants of the jackknife instrumental variables (JIVE) estimator for overidentified linear models and show that they are superior to the existing JIVE estimator, significantly improving on its small-sample-bias properties. We also compare our new estimators to existing Nagar (1959) type estimators. We show that, in models with heteroskedasticity, our estimators have superior properties to both the Nagar estimator and the related B2SLS estimator suggested in Donald and Newey (2001). These theoretical results are verified in a set of Monte Carlo experiments and then applied to estimating the returns to schooling using actual data.

The signatories to this document are economists who have studied telecommunications, auctions, and competition policy. While we may disagree about the stimulus package, we believe that it is important to implement mechanisms that make stimulus spending as efficient as possible. To that end, we have come together to encourage the National Telecommunications Information Agency (NTIA) and Rural Utilities Service (RUS) to adopt auction mechanisms to allocate broadband stimulus grants.

DRAFT - Please do not cite without permission Abstract: We use a comprehensive data set on local telephone service prices and telephone penetration rates for low-income households to evaluate the effect of Lifeline and Linkup programs. Consistent with previous studies, we find that the elasticity of demand for telephone service is relatively low. However, by using nonlinear two-stage least squares, we find that elasticities are somewhat higher than previously estimated. In addition, we find that low-income households have very high discount rates for initial hookup charges. We run a policy experiment and find that penetration without the low-income programs would be about 5% lower among low-income households. Because of the high discount factor among low-income households, the Linkup program is a more cost effective means to subsidize low-income households.

A comprehensive data set on local telephone service prices is used to evaluate the effect of Lifeline and Linkup programs on the telephone penetration rates of low-income households in the United States. Lifeline and Linkup programs respectively subsidize the monthly subscription and initial installation charges of eligible low-income households. Telephone penetration rates are explained by an estimated nonlinear function of local service characteristics (including subsidized prices) and the demographic composition of low-income populations. Empirical specification is based on an underlying discrete choice model of household demand for telephone service and an exact aggregation across demographic groups. A generalized method of moments estimator corrects for endogeneity and clustered heteroskedastic residuals. Estimated median price elasticity of demand for telephone service is -0.027 for the monthly charge and -0.008 for the connection charge. A policy simulation predicts that low-income telephone penetration rates would be 6.24% lower without Lifeline and Linkup. The analysis also suggests that Linkup is more cost-effective than Lifeline, and that low-income penetration would increase significantly if all states were to automatically enroll eligible households in Lifeline and Linkup programs.

Empirical models of differentiated product demand have typically allowed price to be endogenous, but proceed under the assumption that observed product characteristics are exogenous, i.e. uncorrelated with unobserved components of demand. This paper shows that such an assumption may not be necessary to obtain consistent estimates of price elasticities. We show that whether this is the case depends on properties of the instrument or instruments used for price. Since these properties are testable, this result has interesting implications on an applied researcher’s choice of price instruments. In the case where one cannot find an instrument that satisfies these properties, one can often bound the potential bias in estimated price elasticities due to endogenous product characteristics. Our ideas also lead to interesting thoughts about what sorts of variables would ideally like to have as price instruments. Lastly, we apply these ideas to data on demand for cable television, obtaining estimates of price elasticities that are in fact robust to endogenous product characteristics. ∗Thanks to Jin Hahn for comments and helpful discussion. All errors are our own.

This paper examines some of the recent literature on the empirical identification of production functions. We focus on structural techniques suggested in two recent papers, Olley and Pakes (1996), and Levinsohn and Petrin (2003). While there are some solid and intuitive indentification ideas in these papers, we argue that the techniques, particularly those of Levinsohn and Petrin, suffer from collinearity problems which we believe cast doubt on the methodology. We then suggest alternative methodologies which make use of the ideas in these papers, but do not suffer from these collinearity problems.

We seek to estimate the causes and magnitudes of network externalities for the automated clearinghouse (ACH) electronic payments system, using a panel data set on individual bank usage of ACH. We construct an equilibrium model of consumer and bank adoption of ACH in the presence of a network. The model identifies network externalities from correlations of changes in usage levels for banks within a network, from changes in usage following changes in market concentration or sizes of competitors and from adoption decisions of banks outside the network with small branches in the network, and can separately identify consumer and bank network effects. We structurally estimate the parameters of the model by matching equilibrium behavior to the data, using simulated maximum likelihood and a data set of localized networks, and use a bootstrap to recover confidence intervals. The parameters are estimated with high precision and fit various moments of the data reasonably well. We find that most of the impediment to ACH adoption is due to large consumer fixed costs of adoption. The deadweight loss from the network externality is moderate: the optimal number of ACH transactions is about 16% higher than the equilibrium level.

[PRELIMINARY AND INCOMPLETE] In 2000, eBay introduced its “buy-it-now” feature, allowing sellers to post a buy price at which a bidder can end the auction early. Theory suggests that a buy price can increase the seller’s expected revenue if bidders are risk-averse or impatient. The linkage between riskaversion, impatience, and the buy-it-now feature also suggests that data from these auctions may be informative about risk aversion and time preference parameters, which are typically dicult or impossible to identify in conventional auction data. In this paper, we develop a structural model for bidding in auctions with eBay’s buy-it-now feature, and apply this to data collected from eBay auctions of Pentium laptops. Because the buy-it-now feature disappears after the first active bidder rejects the buy price, it is important to capture the temporal structure of eBay auctions. We model arrival of potential bidders as a Poisson process, and specify how bidders choose to enter the auction based on information available when they arrive. In eBay, bidders are often observed to raise their bids later in the auction, which is dicult to explain using conventional theory for second-price auctions. To allow for bidders to raise their bids without making assumptions on why or how this rebidding occurs, we follow Haile and Tamer (2003) and Canals-Cerda and Pearcy (2004), and use an “incomplete” specification for bidder behavior. We develop a novel estimation technique for our model, based on partial likelihood arguments combined with moment simulation.

Standard discrete choice models such as logit, nested logit, and random coefficients models place very strong restrictions on how unobservable product space increases with the number of products. We argue (and show with Monte Carlo experiments) that these restrictions can lead to biased conclusions regarding price elasticities and welfare consequences from additional products. In addition, these restrictions can identify parameters which are not intuitively identified given the data at hand. We suggest two alternative models that relax these restrictions, both motivated by structural interpretations. Monte-Carlo experiments and an application to data show that these alternative models perform well in practice.

Very, very preliminary draft ∗Dept. of Economics, UCLA, Los Angeles, CA 90095. Thanks to Ariel Pakes and Jin Hahn for helpful discussions. All errors are our own.

This paper empirically analyzes di erent e ects of advertising in a nondurable, experience good market. A dynamic learning model of consumer behavior is presented in which we allow both \informative" e ects of advertising and \prestige" or \image" e ects of advertising. This learning model is estimated using consumer level panel data tracking grocery purchases and advertising exposures over time. Empirical results suggest that in this data, advertising's primary e ect was that of informing consumers. The estimates are used to quantify the value of this information to consumers and evaluate welfare implications of an alternative advertising regulatory regime. JEL Classi cations: D12, M37, D83 ' Economics Dept., Boston University, Boston, MA 02115 (ackerber@bu.edu). This paper is a revised version of the second and third chapters of my doctoral dissertation at Yale University. Many thanks to my advisors: Steve Berry and Ariel Pakes, as well as Lanier Benkard, Russell Cooper, Gautam Gowrisankaran, Sam Kortum, Mike Riordan, John Rust, Roni Shachar, and many seminar participants, including most recently those at the NBER 1997Winter IO meetings, for advice and comments. I thank the Yale School of Management for gratefully providing the data used in this study. Financial support from the Cowles Foundation in the form of the Arvid Anderson Dissertation Fellowship is acknowledged and appreciated. All remaining errors in this paper are my own.

Method of Simulated Moments (MSM) estimators introduced by McFadden (1989) and Pakes and Pollard (1989) are of great use to applied economists because of their ease of use even for estimating extremely complicated economic models. One simply needs to generate simulated data according to the model and choose parameters that make moments of this simulated data as close as possible to moments of the true data. This paper uses importance sampling techniques to address two caveats regarding these MSM estimators. First, if there are discrete parts of one's model, MSM objective functions are typically discontinuous in the parameter vector, making them hard to miminize or mimimize correctly. McFadden (1989) brie°y suggests the use of importance sampling to smooth simulated moments { we elucidate and expand on this technique. Second, often one's economic model is hard to solve. Examples include complicated equilibrium models and dynamic programming problems. We show that importance sampling can reduce the number of times a particular model needs to be solved in an estimation procedure, signi cantly decreasing computational burden. ¤Dept. of Economics, Boston University and NBER. Thanks to Steve Berry for helpful discussions. All errors are my own. Method of Simulated Moments (MSM) estimators (MacFadden (1989), Pakes and Pollard (1989)) have great value to applied economists estimating structural models due to their simple and intuitive nature. Regardless of the degree of complication of the econometric model, one only needs the ability to generate simulated data according to that model. Moments of these simulated data can then be matched to moments of the true data in an estimation procedure. The value of the parameters that sets the moments of the simulated data "closest" to the moments of the actual data is an MSM estimate. Such estimators typically have nice properties such as consistency and asymptotic normality, even for a nite amount of simulation draws. This paper addresses two computational problems that can arise with such estimators. The rst occurs when there is any discreteness in one's econometric model. In this case, the above simulation process typically results in an objective function that is not continuous in the parameter vector. This can be extremely problematic in optimization, particular when one is searching over many parameters. Not only can this make estimation take longer, but likely increases the probability of erroneously nding local extremum or non extremum. The second problem occurs when one's economic model is computationally time consuming to solve. Examples include dynamic programming problems with large state spaces and complicated equilibrium problems. In the above estimation procedure, one usually needs to solve such a model numerous times, typically once for every simulation draw, for every observation, for every parameter vector that is ever evaluated in an optimization procedure. If one has I observations, performs NS simulation draws, and optimization requires R function evaluations, estimation requires solving the model NS ¤ I ¤ R times. This can be unwieldly for complicated problems. This paper suggests using importance sampling to alleviate or remove these problems. Importance sampling is a technique most noted for its ability to reduce levels of simulation error. McFadden (1989) brie°y notes that importance sampling has an alternative use that of smoothing simulated moments, i.e. addressing our rst computational problem. The technique is quite simple for a simple multinomial choice model. This paper expands and develops this technique, noting that it can be applied to much more complex models. The key step in its application is nding the right change of variables to do the importance sampling over. We exhibit this smoothing technique with a number of examples. We next exhibit that importance sampling can be used to alleviate our second problem. What we show is that importance sampling can be used to dramatically reduce the number of times a complicated economic model needs to be solved within an estimation procedure. Instead of naively solving the model NS ¤ I ¤ R times, with importance sampling one only needs to solve the model NS ¤ I times or NS times. Since R can be