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Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

This chapter uses a dynamic structural model of household choices on savings, consumption, fertility, and education spending to perform policy experiments examining the impact of tax-free education savings accounts on parental contributions toward education and the resulting increase in the education attainment of children. The model is estimated via maximum simulated likelihood using data from the National Longitudinal Survey of Young Women. Unlike many similarly estimated dynamic choice models, the estimation procedure incorporates a continuous variable probability distribution function. The results indicate that the accounts increase the amount of parental support, the percent contributing and education attainment. The policy impact compares favorably to the impact of other policies such as universal grants and general tax credits, for which the model gives results in line with those from other investigations.

The expansion of marketing data is encouraging the growing use of deep learning (DL) in marketing. I summarize the intuition behind deep learning and explain the mechanisms of six popular algorithms: three discriminative (convolutional neural network (CNN), recurrent neural network (RNN), and Transformer), two generative (variational autoencoder (VAE) and generative adversarial networks (GAN)), and one RL (DQN). I discuss what marketing problems DL is useful for and what fueled its growth in recent years. I emphasize the power and flexibility of DL for modeling unstructured data when formal theories and knowledge are absent. I also describe future research directions.

The nature of immigration to the United States has varied tremendously over the course of the last 100 years. While the rate of immigrants in comparison to the total population was as high as 14% in the early 1900s, it steadily declined due to regulations passed at the beginning of the First World War reaching its lowest point in 1970 at less than 5% (Bernard, 1998). Yet, ever since the early 1970s, in response to the Immigration and Nationality Act Amendments that replaced national-origin quotas with a single annual worldwide ceiling for all other immigrants while eliminating any numerical limitations for immediate relatives of U.S. citizens, the number of immigrants has been continuously on the rise. In 1996, about 1 of every 10 residents in the United States was foreign born. This is exemplified by the fact that more than one fourth of the present foreign-born population of the United States arrived after 1990 (U.S. Department of Homeland Security, 2004).

This paper investigates the usefulness of switching Gaussian state space models as a tool for implementing dynamic model selection (DMS) or averaging (DMA) in time-varying parameter regression models. DMS methods allow for model switching, where a different model can be chosen at each point in time. Thus, they allow for the explanatory variables in the time-varying parameter regression model to change over time. DMA will carry out model averaging in a time-varying manner. We compare our exact method for implementing DMA/DMS to a popular existing procedure which relies on the use of forgetting factor approximations. In an application, we use DMS to select different predictors in an inflation forecasting application. We find strong evidence of model switching. We also compare different ways of implementing DMA/DMS and find forgetting factor approaches and approaches based on the switching Gaussian state space model to lead to similar results.

“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.