Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; semi-nonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in semi-nonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and non-negativity. This chapter describes estimation of semi-nonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve M-estimates, pointwise normality of series estimates of regression functions, root-n asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.

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help and advice and to Sergio Urzúa for providing help and advice with software codes. Quheng Deng contributed invaluable research assistance. a

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We introduce a novel semi-parametric estimator of American option prices in discrete time. The specification is based on a parameterized stochastic discount factor and is nonparametric w.r.t. the historical dynamics of the Markovian state variables. The historical transition density estima-tor minimizes a distance built on the Kullback-Leibler divergence from a kernel transition density, subject to the no-arbitrage restrictions for a non-defaultable bond, the underlying asset and some American option prices. We use dynamic programming to make explicit the nonlinear restrictions on the Euclidean and functional parameters coming from option data. We study asymptotic and finite sample properties of the estimators.

Abstract As demand in an industry shrinks, pressure for the reduction of capacity arises. Against this background, a key issue is whether plants which, from an efficiency perspective, should reduce output or close down in fact do so. Focusing on the Japanese cement industry, this paper empirically examines whether less efficient plants reduce capacity, and analyzes the presence and extent of production misallocation resulting from capacity divestment. We find that less efficient firms are not more likely to reduce capacity than more efficient firms; however, less efficient plants within a multi-plant firm are more likely to reduce capacity than more efficient plants. In addition, conducting an experimental exercise, we find that this divestment pattern has lead to a substantial drop in industry-wide allocative efficiency. The experimental exercise further reveals that it is the misallocation of production across firms that accounts for the largest part of the drop in allocative efficiency. This result suggests that the presence of multi-plant firms can help to alleviate inefficiencies arising in a period of industry decline. JEL Classification: L13, L41, L61 Keywords: declining industry, capacity divestment, production reallocation, cement producing plants * This is a revised version of chapter 4 of Masato Nishiwaki's PhD thesis. We would like to thank Tetsu Murao, Hiroyuki Odagiri, and Fabiano Schivardi for helpful comments. We also thank the editor, John Asker, and two anonymous referees for constructive comments and suggestions. Masato Nishiwaki benefited from financial support from the Ministry of Education, Culture, Sports, Science and Technology, Japan, through the Global COE program "Research Unit for Statistical and Empirical Analysis in Social Sciences." All errors, of course, remain our responsibility. † National Graduate Institute for Policy Studies (GRIPS), 7-22-1, Roppongi, Minato-ku, Tokyo, Japan. Email:mstnishi@gmail.com. 1 I Introduction In declining industries, as demand shrinks, pressure for the reduction of capacity arises. Firms in such industries are forced to reduce production capacity in order to remain profitable or, in the extreme case, to exit altogether. An important issue from the viewpoint of economic efficiency and public policy in this context is whether in these industries, it is the "losers" that are "picked," that is, whether it is less efficient plants that reduce their production capacity or exit altogether To assess the outcome, it is usually compared with the situation that would prevail if there were a social planner, or if a market were perfectly competitive. A social planner would choose plants based on their efficiency to reduce output as demand shrinks. That is, the capacity of less efficient plants would be reduced in the earlier stages of the demand decline and more efficient plants would continue to maintain their production capacity. The same pattern of contraction of industry capacity would be observed in a perfectly competitive market in which "losers" (less efficient plants) are selected through the market mechanism. In an imperfectly competitive market, however, the outcome may differ from that achieved by a social planner or in a competitive market, because the size of a plant or firm may be a key determinant of the decision to reduce capacity. Nalebuff (1985, 1990) in their simple model for example show that, in an oligopoly, small plants can have a strategic advantage over, and maintain production capacity longer than, larger plants. An important implication of the theoretical result is that capacity reduction decisions are not necessarily governed by plants' efficiency. In other words, there is the possibility that more efficient plants cut their capacity more than their smaller rivals. However, the result that plant size may act as an important determinant of the pattern of industry contraction applies only to the simplest of situations and not necessarily to more complex ones. As Whinston (1988) has shown, introducing a 2 multi-plant into the setting, for example, can dramatically complicate the capacity withdrawal decision problem, so that it is difficult to obtain a clear prediction for capacity reduction behavior. That is, even in a relatively simple multi-plant setting in which there is one firm with two plants and one single-plant firm, it is not possible to make any generalizations of Ghemawat and Nalebuff's simple rule that are based on plant (or firm) size, since the smaller firm will not necessarily maintain its level of production capacity and the smallest plant does not necessarily survive. In this paper, with this theoretical ambiguity in mind, we examine capacity reduction behavior in an oligopolistic market in the real world. More concretely, we examine empirically the impact of plant and firm characteristics on capacity divestment decisions and measure the magnitude of the inefficiency of production reallocation as a result of such divestment. Our empirical analysis addresses the following two questions. The first concerns whether any inefficiency in the capacity divestment pattern can be observed in the sense that more efficient plants (or firms) reduce their capacity more than less efficient plants (or firms). The second question concerns how the resulting production allocation differs from the optimal production allocation of a social planner. To answer these questions, we take a detailed look at capacity divestment behavior during the decline of a specific industry, namely the Japanese cement industry. The Japanese cement industry provides a good case study to examine the capacity divestment problem in an imperfectly competitive market. The demand for cement mainly depends on private and public investment in construction, which has been declining since the burst of Japan's bubble economy in the early 1990s. Along with this decline in demand, cement firms have been forced to reduce the capacity of their plants. Another important feature of the cement industry in addition to the decline in demand is that the number of firms operating in Japan is relatively small, so that the strategic interaction among cement firms plays an important role. A further important 3 feature of the cement industry is the presence of multi-plant firms, which means that we can also investigate the impact of the characteristics of other plants within the same multi-plant firm on capacity reduction decisions for a particular plant. The results of our empirical analysis to examine the first question can be summarized as follows. We find that the effects of differences in firm size and efficiency are not statistically significant and not substantial in size. On the other hand, differences in plant efficiency and in plant size do have an influence on the divestment probability. What these results suggest is that when firms are under pressure to divest, and they have several plants under their control, they pick less efficient plants in their choice set to reduce capacity. To this extent, multi-plant firms contribute to the efficient industry contraction. However, our results also suggest that less efficient firms do not necessarily reduce production capacity more than efficient firms. Such inefficient divestment pattern will lead to a loss in welfare. In order to address the second question, we quantify the extent of production misallocation caused by the divestments in the industry. We conduct an experimental analysis to compare the observed production allocation and the optimal allocation of a social planner. Our experiment shows that allocative efficiency, which is defined as the ratio of the optimal allocative efficiency to the actual efficiency, dropped by up to 18-percentage points in the 13 years period we examine. Further, we find that the largest part of this efficiency drop can be explained by the misallocation of production across firms. This paper has the following four important features. First, this is one of only a handful of studies on industry contraction. Since the early works by The remainder of the paper is organized as follows. Section II reviews previous theoretical and empirical studies on divestment behavior in declining industries. Section III then provides a brief overview of the cement industry in Japan and the cement production process, while Section IV provides a description of the data used in this study. Next, Section V presents the empirical procedure employed. To obtain plant-specific efficiency, which we cannot observe, we estimate it through the production function. Using the estimate of plant level efficiency, we then examine the impacts of plant and firm characteristics on divestment behavior. The empirical results are presented in Section VI, before Section VII examines the efficiency of the actual reallocation of production when compared with the optimal production allocation of a social planner. 5 Section VIII concludes. II Previous Studies In this section, we provide a brief review of previous theoretical and empirical studies on declining industries. The best known model of declining industries is provided by 1 They show that, under these assumptions, the order of exit is determined by plant size: the larger one exits first. The reason is that the smaller plant has a strategic advantage since it can be a profitable monopolist over a longer period of declining demand. The model is easily extended to a situation with more than two plants and the efficiency level of plants differs to some extent. 2 Multiple equilibria can arise at the first date when duopoly profit goes to less than zero. In one equilibrium the larger plant exits earlier, but in the other equilibrium the smaller plant exits first. However, the larger plant equilibrium is not trembling hand perfect. If the smaller plant missed its exit date and failed to leave immediately, the larger plant's plan is no longer optimal. 3 They also consider the effect of plant-specific efficiency, when this is not identical, on the exit order and show that the condition under which the more efficient plant can outlast the less efficient one. However, to outlast the smaller rival, the larger plant needs a huge cost advantage against the smaller rival. 6 exceed that achieved in the monopoly of the larger plant. 4 In contrast to a perfectly competitive market, there is the possibility of a welfare loss due to declining demand. Extensions of the G&N (1985) model go in two directions. First, The result is similar to that of the above exit model. They show that the larger plant reduces capacity first and continues to do so until it shrinks to the size of its smaller rival. Alternatively, the simple size-driven rule can be applied to a continuous divestment problem in an oligopoly. The intuition underlying this result is that the larger plant has lower marginal revenue and hence a greater incentive to cut capacity. To the best of our knowledge, there are only a few empirical studies testing the theoretical predictions or examining the divestment behavior in declining industries. One of these is the study by 5 This model is also easily extended to a situation with more than two plants. Finally, in a more recent study,

JEL No. J24 A growing proportion of the U.S. workforce will have been raised in disadvantaged environments that are associated with relatively high proportions of individuals with diminished cognitive and social skills. A cross-disciplinary examination of research in economics, developmental psychology, and neurobiology reveals a striking convergence on a set of common principles that account for the potent effects of early environment on the capacity for human skill development. Central to these principles are the findings that early experiences have a uniquely powerful influence on the development of cognitive and social skills, as well as on brain architecture and neurochemistry; that both skill development and brain maturation are hierarchical processes in which higher level functions depend on, and build on, lower level functions; and that the capacity for change in the foundations of human skill development and neural circuitry is highest earlier in life and decreases over time. These findings lead to the conclusion that the most efficient strategy for strengthening the future workforce, both economically and neurobiologically, and for improving its quality of life is

journal homepage: www.elsevier.com/locate/jeconom Optimal convergence rates, Bahadur representation, and asymptotic normality

This paper considers the problem of making inferences about the effects of a program on multiple outcomes when the assignment of treatment status is imperfectly randomized. By imperfect randomization we mean that treatment status is reassigned after an initial randomization on the basis of characteristics that may be observed or unobserved by the analyst. We develop a partial identification approach to this problem that makes use of information limiting the extent to which randomization is imperfect to show that it is still possible to make nontrivial inferences about the effects of the program in such settings. We consider a family of null hypotheses in which each null hypothesis specifies that the program has no effect on one of several outcomes of interest. Under weak assumptions, we