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Community Size and Electoral Preferences: Evidence From Post-Second World War Baden-Württemberg
- Luciana Fiorini, Michael Jetter, Christopher F. Parmeter, Christopher Parsons
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- Journal:
- British Journal of Political Science , First View
- Published online by Cambridge University Press:
- 15 December 2023, pp. 1-22
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We examine whether electoral preferences depend on a community's population size by studying post-Second World War Baden-Württemberg in Southwest Germany. Our identification strategy exploits the fact that the French administration zone prohibited German expellees from entering, contrary to the contiguous American zone. Population size positively predicts voting for the Social Democrats (the party advocating substantial government involvement in practically all domains) and negatively for the Christian Democrats (the small-government party advocating free-market policies). Results are neither driven by pre-existing voting patterns, religious compositions, and location- and time-specific unobservables, nor other measurable cultural, demographic, economic, or political characteristics. Alternative explanations pertaining to expellee voting behaviour or a backlash of natives against expellees appear unlikely – population size prevails as a predominant voting predictor.
Accounting for Skewed or One-Sided Measurement Error in the Dependent Variable
- Daniel L. Millimet, Christopher F. Parmeter
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- Journal:
- Political Analysis / Volume 30 / Issue 1 / January 2022
- Published online by Cambridge University Press:
- 14 January 2021, pp. 66-88
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While classical measurement error in the dependent variable in a linear regression framework results only in a loss of precision, nonclassical measurement error can lead to estimates, which are biased and inference which lacks power. Here, we consider a particular type of nonclassical measurement error: skewed errors. Unfortunately, skewed measurement error is likely to be a relatively common feature of many outcomes of interest in political science research. This study highlights the bias that can result even from relatively “small” amounts of skewed measurement error, particularly, if the measurement error is heteroskedastic. We also assess potential solutions to this problem, focusing on the stochastic frontier model and Nonlinear Least Squares. Simulations and three replications highlight the importance of thinking carefully about skewed measurement error as well as appropriate solutions.
7 - Smoothing discrete variables
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 187-204
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Summary
In this chapter, we discuss the intuition underlying the smoothing of discrete variables in the context of a probability density. In virtually all applied economic milieus, many variables will be discrete (also termed categorical), which is to say the variables take on a countable number of outcomes. For example, when we include a regional indicator in a growth regression, this variable takes on anywhere from four to eight distinct values depending upon how finely we wish to partition the globe. Alternatively, a variable categorizing membership into the OECD would present itself as a classic dummy variable, taking only two values. In these instances, smoothing with traditional kernels – such as the s-class of kernels described in Chapter 2 – is inappropriate. Here we outline kernels that are appropriate for smoothing discrete variables. We discuss the interpretation of these smoothing parameters. However, we must delineate between two types of discrete variables: unordered (such as a region indicator) and ordered (say, year).
The elegance of the inclusion of categorical variables to the empirical analysis is that while the interpretation and handling of the variables requires some care beyond what we covered with continuous variables, the mechanics of the estimators do not vary greatly, requiring nothing more than some additional notation and a generalization of the product kernel. The beauty of discrete variables is that (with respect to data requirements) their addition to the model does not lead to severe consequences as was the case with the addition of continuous variables. As with all nonparametric estimation, bandwidth selection is of primary importance and the presence of categorical variables does nothing to change this perception.
We end the chapter incorporating region and time into our investigation of cross-country output. We investigate the distribution of cross-country output looking both over time (ordered discrete) and across regions (unordered discrete). This allows us to document how smoothing these variables aids our understanding of the global distribution of cross-country output without resorting to the common frequency approach, which simply splits the data by each individual category.
2 - Univariate density estimation
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 15-58
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Summary
In this chapter, we discuss univariate density estimation. We are well aware that most interesting applications are with respect to multivariate data, but we must first discuss univariate density estimation so that we can generalize the univariate methods to the multivariate setting. That being said, there are many interesting applications of univariate densities in economics as well as in other fields. The most common application of univariate density estimation in the context of economic growth is the examination of output-per-worker distributions, most commonly attributed to Quah (1993a,b).
We start by considering nonparametric density estimation in the crudest possible way: a histogram. In fact, histograms are nonparametric in nature and can show information that may be hidden (e.g., multimodality) when assuming a pre-specified parametric density (say Gaussian). However, it is well known that the shape of the histogram is determined by the pre-specified binwidth, and hence we spend a large amount of time discussing this “smoothing” parameter. Another problem with this type of approach is that the density is discontinuous, and hence we cannot view gradients and other interesting pieces of information. Although the estimator is simplistic, the discussion of this type of density estimation leads quite naturally to our preferred choice of a smooth, continuous estimator: the kernel density estimator.
Although we focus solely on kernel methods in this book, this does not imply that they are necessarily the best methods for any particular problem or data set. However, these methods are arguably the most popular in the literature, and as such they are the most developed. Here we will discuss how to construct such estimators as well as examine their theoretical properties. For example, we typically give the bias, variance, and mean square error of each estimator. Although this can be found in several existing books, we pay special attention to the choice of kernel function, the role and selection of the smoothing (bandwidth) parameter, and the sample size. Given that we have a specific focus on the application of these methods, we attempt to clarify what is necessary for theoretical purposes and what is necessary for application.
Frontmatter
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp i-iv
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4 - Inference about the density
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 83-112
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Summary
Estimation of univariate and multivariate densities and examining their plots is of direct interest to practitioners. However, as is the case with a photograph, a thousand people viewing an estimated density may have a thousand different opinions on its shape. Therefore, it is imperative to conduct formal statistical tests for various phenomena of interest. In this chapter, we consider common and useful tests for both estimated univariate and multivariate densities.
Given that a correctly specified parametric model is efficient, it is important to test the nonparametric model versus a parametric alternative. For instance, if the density is normally distributed, it would be advantageous to exploit this fact when conducting an empirical analysis. For some economic problems, theory may provide information on the underlying distribution and hence this test could be used to validate theory with empirical data. Alternatively, this test can be used to test the assumptions other practitioners have used in the past. A test of interest for multivariate data is a test for joint normality. It is known that if two variables, say y and x, are jointly normal, then the conditional mean of y given x is linear. In other words, E (y|x = xβ. Hence, we can use this test to determine whether or not OLS would be an appropriate estimator in a regression framework.
In addition to the test for a correctly specified parametric distribution, we consider tests for equality between two unknown densities. This is common in the growth and development literature, where testing for equality of income densities of two different regions (Western and Central Europe), groups (WTO and non-WTO), or time periods is insightful. Another useful test in practice is that of symmetry around a particular point, most commonly zero. For example, in the nominal wage rigidity literature, symmetry of the wage-change distribution is key (e.g., Christofides and Stengos, 2001).
A test which requires multivariate data is the test for independence.
Dedication
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp v-vi
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9 - Semiparametric methods
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 227-266
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Summary
Nonparametric methods are often criticized because of their need for large amounts of data. The study of economic growth is a prime example of where nonparametric methods are being stretched to their limits (Henderson, Papageorgiou, and Parmeter, 2012, 2013). Here a wide variety of covariates exist and at best the available sample size is moderate. Thus, issues regarding the accuracy and insightfulness of the results from nonparametric estimation/inference are in question. In the presence of dimensionality issues, we often resort to semiparametric methods, which place additional structure on the model.
While a variety of semiparametric methods exist, perhaps the most famous is the partially linear model (PLM), popularized in econometrics by Robinson (1988). In this model, some of the variables enter the conditional mean nonparametrically, while others enter in linearly. It is assumed that the groups of variables are separable from one another and estimation of each part can be obtained as a combination of OLS and the estimators from Chapter 5. The estimator for the nonparametric component generally converges at the standard nonparametric rate, albeit faster because we have fewer regressors, while the parametric estimator converges at the standard rate. It is this result that is the most appealing empirically regarding the PLM.
Both the statistical and econometric literature is rich in treatises on semiparametric estimation and inference. Our goal here is to provide a simple overview of many of the most common methods, paying careful attention to empirical implementation issues. We start with the aforementioned PLM and then discuss single-index models. The latter of these methods is often used for discrete-choice models, where you may be uncomfortable assuming a distribution for the errors, such as Gaussian (for probit), but are comfortable with the single-index framework. Afterwards we discuss semipara-metric smooth coefficient models (SPSCMs). Here the functional form is assumed to be linear in a given set of covariates while the coefficients are allowed to depend on another set of covariates in an unknown way. These methods are becoming increasingly popular in many applied economic milieus.
3 - Multivariate density estimation
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 59-82
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Summary
In traditional applied econometric settings, we typically have access to several variables. For example, in our growth example presented in Chapter 2, not only would a typical analysis have access to output per worker, but also physical and human capital stocks, measures of corruption, natural resource levels, institutional quality, and perhaps many other variables. In this sense, univariate density exploration is limited. For example, suppose you view a univariate density estimate and find bimodality to be a plausible feature. Is this bimodality inherent to the variable of interest, or is there some connection with a secondary variable? Jones, Marron, and Sheather (1996) find exactly this pattern in their research. They have a visually bimodal univariate density (202 observations) of lean body mass. Subsequent analysis shows that the bimodal nature of this density is linked to the gender of the individual. By splitting the data into 100 men and 102 women, each individual density is strongly unimodal. Thus, generically, the lean body mass measurements data was not bimodal, it was combining two different subpopulations into what was believed to be a homogeneous population.
To aptly characterize these types of issues, multivariate nonparametric methods need to be deployed. The natural extension of the univariate kernel density estimator developed in Chapter 2 is the multivariate kernel density estimator. This estimator looks and operates similarly to the univariate estimator and so the intuition built in Chapter 2 will prove useful here. However, there are some conceptual issues. How do we conceive of a kernel function in multiple dimensions? Should we have a bandwidth for each dimension or a single bandwidth which smooths all variables equally? What happens to the statistical properties of our estimator if we incorporate more variables into our density?
In this chapter, we outline both joint and conditional density estimation. We discuss asymptotic properties as well as bandwidth selection and the presence of irrelevant variables.
6 - Testing in regression
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 159-186
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Summary
In regression, estimation is only one component of an empirical analysis. It is incumbent upon the researcher to conduct inference regarding various features underlying the unknown data generating process. The story is no different for nonparametric methods. Many of the tests discussed in this chapter will be analogous to tests performed with parametric estimators. The tests here are similar to those in Chapter 4 and we suggest that you familiarize yourself with the fundamentals discussed in that section before proceeding further if you have not done so already.
As with inference in the density setting, the use of nonparametric testing facilities offers the opportunity to deploy consistent tests. Our main discussion here will be on goodness-of-fit and nonparametric conditional-moment tests. While there are numerous testing approaches, conditional-moment tests serve the same purpose here as the ISE-based tests in Chapter 4. Conditional-moment tests have a rich history in applied econometrics and they are sufficiently general to offer tests for an array of important hypotheses within the regression framework.
Our discussion sets out with perhaps the most common nonparametric regression testing problem, that of correct functional form specification. Recall that a correctly specified parametric regression model will always produce more efficient estimates of the unknown model parameters than a nonparametric model will. Thus, testing the functional form of an empirical model is important for applied econometric research. Another popular inferential concern in the regression context is that of variable significance (either individual or joint). This type of inference can also be supported with the conditional-moment tests discussed here. Finally, we show how a test for heteroskedasticity of the error term can also be cast as a conditional-moment test. Testing for heteroskedasticity is important because knowledge of the presence of it may be used to construct more efficient nonparametric estimators.
Implementation of these tests faces similar hurdles that our ISE tests in Chapter 4 encountered, namely, issues related to appropriate selection of the bandwidths to be used when constructing the test statistic, as well as the choice between using the limiting distribution versus a bootstrap approximation.
Bibliography
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 343-358
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5 - Regression
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 113-158
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Summary
Regression is the backbone of applied econometric research. Although regression is widespread, the vast majority of economic research assumes that regressors enter the conditional mean linearly and that each regressor is separable without any theoretical justification. Here were discuss how to estimate regression functions where we are unsure of the underlying functional form.
The nonparametric regression estimators that we will describe in this chapter will construct an estimate of the unknown function in much the same way that we constructed the unknown density: by using a local sample for each point. Whereas parametric estimators are considered global estimators (using all data points), non-parametric kernel regression estimators are local estimators, using a local sample of nearby data points to fit a specific parametric model (typically a constant or a line) and then “smooth” each of these local fits to construct the global function estimator. This allows you to focus on the local peculiarities inherent in your data set while estimating the unknown function without judicious choice of parametric functional form.
We first motivate regression through explanation of the conditional mean via its connection to conditional and joint densities. Then, similar to our discussion of the construction of kernel densities, we also consider a simplistic (nonparametric) estimator of the conditional mean. We choose a method that uses indicator functions to evaluate the conditional mean at various points. Specifically, we calculate the average value of the dependent variable at specific values of the covariates. This method is crude, but does not require us to specify the functional form a priori. As we also saw with density estimation, we will use our crude estimator to gain intuition and motivate kernel estimators.
Within kernel regression, there are several existing estimators which seek to estimate the unknown smooth function of interest. Here we will primarily discuss three of the most popular methods. The oldest, local-constant least-squares (LCLS), has seen less use in recent years, but is still being used, despite its shortcomings.
10 - Instrumental variables
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 267-292
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Summary
Many situations in applied econometric work require knowledge of a structural or causal relationship in order to guide policy recommendations. Aside from possessing valid instrumental variables to correctly capture endogeneity, uncovering the structural relationship of interest usually requires specifying a utility or cost function or the distribution of preferences in order to derive a reduced form model that can be estimated. Unfortunately, this route is unappealing, as it is uncommon to know the underlying distribution or specification of the model primitives necessary for deriving the corresponding reduced form. Moreover, economic theory rarely provides tight correspondence between the model primitives and their functional forms. However, turning directly to a nonparametric approach has not been a common choice among empiricists, as the methods necessary to provide consistent estimates in the face of endogeneity have only recently been developed and may present complications for implementation (see Newey, Powell, and Vella, 1999; Pinske, 2000; Newey and Powell, 2003; Horowitz and Hall, 2005; Su and Ullah, 2008; and Darolles, Fan, Florens, and Renault, 2011; Martins-Filho and Yao, 2012; Ozabaci, Henderson, and Su, 2014).
A key difficulty with the implementation of instrumental variable nonparametric methods is that, in their most general form, they require inversion of an integral equation, and this inversion does not represent a continuous mapping: the so-called ill-posed inverse problem. Thus, the typical analog estimation routines (replacing population expectations with sample ones) that we have seen in previous chapters are unlikely to work here. That is, replacing an unknown (smooth) mean with a sample analog will not guarantee consistent estimation of the object of interest in this setting. One approach to avoiding the ill-posed inverse problem is to use a control function approach. From an applied standpoint, the control function approach produces estimators that are easier to implement in practice.
In this chapter, we outline the inherent difficulty induced by endogeneity in a non-parametric framework. We then discuss why a control function approach is suitable for dealing with endogeneity.
Contents
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp vii-xii
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12 - Constrained estimation and inference
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 321-342
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Summary
While the nonparametric regression methods we have discussed are flexible, a side effect of this flexibility is that the estimated function may not satisfy certain prior information (exact or assumed), such as monotonicity or positivity. A generic example of this is estimating a conditional mean model where the left-hand-side variable lies between zero and one. It is well known that a local-linear estimator is not guaranteed to produce a smooth function that always lies between these bounds. Thus, it is useful to discuss a set of tools that can be used to ensure that nonparametric estimates satisfy specific smoothness constraints.
An additional benefit of imposing constraints in a nonparametric framework is that it may provide nonparametric identification (see Matzkin, 1994). Also, Mammen, Marron, Turlach, and Wand (2001) show that when we impose constraints on derivatives higher than the first order, the rate of convergence is faster than it would be had the constraints not been imposed.
A rich and diverse literature on constrained estimation has emerged and a multitude of potential estimators have been proposed for various constrained problems. We do not attempt to survey all existing constrained estimation methods. Rather, we refer the interested reader to Henderson and Parmeter (2009) for a detailed survey. Instead, we focus our discussion on three flexible and widely used methods: rearrangement, data sharpening, and constraint-weighted bootstrapping. Each of these methods has its costs and benefits, but all three are sufficiently flexible to warrant further investigation.
Perhaps the most general of the methods, constraint-weighted bootstrapping can be used to impose a wide range of smoothness constraints, from positivity and monotonicity, to constant returns to scale and additive separability. Further, this method is sufficiently flexible that it can be implemented with any of the local-polynomial estimators described in Chapter 5. We detail the implementation of this estimator and conduct inference for general hypotheses regarding the smoothness of the unknown conditional mean.
Applied Nonparametric Econometrics
- Daniel J. Henderson, Christopher F. Parmeter
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- Published online:
- 05 February 2015
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- 12 January 2015
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The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.
8 - Regression with discrete covariates
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 205-226
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Summary
In this chapter, we outline how to construct nonparametric estimators for a regression model in the presence of discrete regressors. Estimating a regression model when either all of the covariates are discrete or there is mixed data is relatively straightforward, given our earlier discussion in Chapter 5. The key is that we must use kernels appropriate for smoothing discrete data, as discussed in Chapter 7. As with density estimation we will need to modify the kernel weights. Aside from this modification from the continuous-only setting, the intuition and construction of the estimators follow. We feel that you will have little trouble following the arguments in this chapter (assuming you understand the previous chapters). We leave our treatment of estimation with a discrete left-hand-side variable for the presentation of semiparametric methods (Chapter 9).
After discussing estimation, we focus on derivative estimation. Estimating derivatives for the continuous regressors (when discrete regressors are present) proceeds exactly as in the continuous-variable-only setting. What requires more care is obtaining the “derivatives” for the discrete variables, but this should be expected. We use the term “derivative” loosely given that it is clear our conditional mean estimator is no longer continuous in the discrete variables. Similar to the case for a discrete regressor in a parametric model, we obtain our partial effect as the difference between the conditional mean evaluated at one value for the discrete regressor minus value of the discrete regressor, holding everything else constant.
As in all nonparametric estimation, bandwidth selection is of primary importance. We discuss how to select the bandwidths for our discrete variables. The methodology is essentially the same as that in Chapter 5. After selecting our bandwidths and running regressions, we subject our models to formal statistical tests. Here we examine tests that are designed specifically for discrete data. We start with a test for correct parametric specification and also examine tests for variable relevance in the presence of discrete regressors.
Index
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 359-367
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11 - Panel data
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 293-320
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Summary
Nonparametric estimation of panel-data models are becoming increasingly popular in the literature. Most of the earlier methods were developed by statisticians and focused on random-effects-type estimators (e.g., Lin and Carroll, 2001). These methods are valid when the individual specific effects are uncorrelated with the regressors. This assumption is generally violated with economic data. More recent work allows for correlation between the individual specific effects and the regressors (e.g., Henderson, Carroll, and Li, 2008; Qian and Wang, 2012). These fixed-effects estimators are more difficult to implement, as is the case with parametric nonlinear panel-data models, as taking a simple first difference or averaging over time and differencing does not lead to a parsimonious model.
In this chapter, we outline several existing fixed and random effects nonparametric estimators. We pay special attention here to the rate of convergence of the estimators as well as how incorporating the variance–covariance structure affects estimation. An unexpected result of the current crop of these estimators is that incorporation of the variance–covariance matrix often leads to no asymptotic improvement. This result often occurs because, as we have explained previously, as the sample size increases, the bandwidth decrease towards zero. Therefore as we have larger samples, we end up using a smaller neighborhood of data around the point, mitigating the ability of the exploitation of the variance–covariance structure to improve estimation efficiency. Recent research has successfully overcome this issue (e.g., Yang, 2013; Yao and Li, 2013).
As with each estimator in our book, we discuss bandwidth selection. Here we discuss cross-validation methods which are unique to panel data. The same holds true for bootstrap methods in order to calculate standard errors and perform tests. We consider tests for poolability, correct functional form specification, and a nonparametric Hausman test.
In most of this chapter we discuss one-way error component models, primarily focusing our discussion on controlling for individual effects. It is possible to also estimate models, controlling for both individual and time effects.
1 - Introduction
- Daniel J. Henderson, University of Alabama, Christopher F. Parmeter, University of Miami
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- Book:
- Applied Nonparametric Econometrics
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- 05 February 2015
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- 12 January 2015, pp 1-14
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Summary
Overview
The goal of this book is to help bridge the gap between applied economists and theoretical nonparametric econometricians/statisticians. The majority of empirical research in economics ignores the potential benefits of nonparametric methods and many theoretical nonparametric advances ignore the problems faced by practitioners. We do not believe that applied economists dismiss these methods because they do not like them. We believe that they do not employ them because they do not understand how to use them or lack formal training on kernel smoothing. Many theoretical articles and texts that develop nonparametric methods claim that they are useful to empirical researchers, which they often are, but many times the level of mathematics is too high for a typical economist or the detail with which the practical considerations are explained is not adequate except for those well versed in econometrics. At the same time, many of these articles and textbooks skip (or do not have room to include) the nuances of the methods which are necessary for doing solid empirical research.
Although nonparametric kernel methods have been around for nearly six decades, their use in economics journals did not become popular until the twenty-first century (noting that there were influential papers prior to 2000). In our opinion, two major developments have drastically increased the use of nonparametric methods in economics. The first is obvious: computing power. Without computers that can quickly provide estimates (coupled with efficient code), these methods are largely impractical for applied work. Of course, we cannot discount the importance of complementary statistical packages for nonparametric methods, such as the popular np package (Hayfield and Racine, 2008) in the R language (2012). The combination of higher-powered computers and available software has done much to popularize the methods across academic fields.
For economics, the second reason we believe this prevalence has increased of late is the assortment of new estimators which allow researchers to handle discrete data. We know that economic data is generally a combination of continuous and discrete variables.