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In the colonial period of American history, the British Crown reviewed, and sometimes nullified, acts of colonial assemblies for “repugnancy to the laws of England.” In this way, Crown review established external, legal constraints on American legislatures. I present a formal model to argue that Crown legislative review counteracted political pressure on imperial governors from colonial assemblies, to approve laws contrary to the empire’s interests. Optimal review in the model combines both legal and substantive considerations. This gives governors the strongest incentive to avoid royal reprisal by vetoing laws the Crown considered undesirable. Thus, review of legislation for consistency with higher law helped the Crown to grapple with agency problems in imperial governance, and ultimately achieve more (but still incomplete) centralized control over policy. I discuss the legacy of imperial legislative review for early American thinking about constitutional review of legislation by courts.
We generalize standard delegation models to consider policymaking when both information and authority are dispersed among multiple actors. In our theory, the principal may delegate partial authority to a privately informed agent while also reserving some authority for the principal’s use after observing the agent’s decision. Counterintuitively, the equilibrium amount of authority delegated to the agent is increasing in the preference divergence between the principal and agent. We also show that the amount of authority delegated depends upon whether the agent can observe the principal’s own private information (a condition we refer to as “top-down transparency”): this form of transparency increases the authority that must be delegated to the agent to obtain truthful policymaking. Accordingly, such transparency can result in less-informed policymaking. Nonetheless, the principal will sometimes but not always voluntarily choose such transparency.
Separation of powers existed in the British Empire of North America long before the U.S. Constitution of 1789, yet little is known about the strategic foundations of this institutional choice. In this article, I argue that separation of powers helps an imperial crown mitigate an agency problem with its colonial governor. Governors may extract more rents from colonial settlers than the imperial crown prefers. This lowers the Crown’s rents and inhibits economic development by settlers. Separation of powers within colonies allows settlers to restrain the governor’s rent extraction. If returns to settler investment are moderately high, this restraint is necessary for colonial economic development and ultimately benefits the Crown. Historical evidence from the American colonies and the first British Empire is consistent with the model. This article highlights the role of agency problems as a distinct factor in New World institutional development, and in a sovereign’s incentives to create liberal institutions.
We develop a model of “notice and comment” rulemaking, focussing on strategic issues facing agencies and interest groups in light of judicial review in this process. Specifically, we analyse the incentives for agencies and groups to produce and reveal information during rulemaking. We show that judicial review can produce informed policymaking, but that participatory rulemaking can bias agency policymaking in favour of groups with access to the rule-making process. In addition, the model allows an analysis of doctrines of judicial review of agency policymaking. The model reveals that “politicised” judicial review can be beneficial because of its effects on agency incentives for information acquisition in policymaking. Accordingly, socially optimal judicial review may be “legally irrational” and, contrary to standard doctrines of judicial review in the United States, judicial deference to rules with thin records can be optimal.
This text is written for a first course on statistics and quantitative methods for Ph.D. students in social science and allied fields. Anyone undertaking to write such a book must sooner or later confront the question of whether the world really needs another introductory statistics textbook. In my surveys of the market for my own classes on this subject in two social science Ph.D. programs, I clearly decided that it does.
Students in social science Ph.D. programs outside of economics have widely divergent levels of previous exposure to statistical methods, as well as comfort with mathematical expression of concepts. The typical Ph.D. program does not have the luxury of multiple “tracks” to suit different backgrounds, so one course must accommodate all of them. That course must be accessible to students with divergent levels of preparation but must also prepare them technically for future quantitative methods coursework ahead of them.
More important, I have found that students of whatever background will plunge relatively enthusiastically into methods training once they understand why it is essential for the purely substantive elements of their research. Simply put, many students, particularly those without much prior exposure to statistics, do not understand what it is or how it can help them as social scientists. Without this understanding they lack the buy-in necessary to make the technical rigors of the course seem worthwhile.
Recognizing a distinction between events that did occur and events that did not occur but might have is the point of the previous chapter. Given this distinction, we are generally uncertain, before a process unfolds, about what its outcome will be. We would like to relate the observable to the more fundamental data-generating process (DGP) behind it. But if the DGP is stochastic, we will always be uncertain about its defining features, and we need a language to express that uncertainty. Turning this around, given some stochastic DGP, we are generally uncertain about what might result from it. We need to be able to express this uncertainty explicitly and carefully.
To do so, we need some tools from the theory of probability. Probability theory is a conceptual apparatus in mathematics for expressing and evaluating uncertainty. As such, it is an important foundational component of statistical inference. But it is different from statistics. In probability theory, we start with a DGP with basic properties that we know (or assume, or pretend to know) and work out the consequences for the events that might be observed (e.g., their probabilities, how those probabilities are related to the DGP).
In (classical) statistical theory, by contrast, we start with a set of events we have observed and attempt to infer something about the properties of the stochastic DGP that generated them. In other words, probability contemplates what data will be observed from a given stochastic process.
Written specifically for graduate students and practitioners beginning social science research, Statistical Modeling and Inference for Social Science covers the essential statistical tools, models and theories that make up the social scientist's toolkit. Assuming no prior knowledge of statistics, this textbook introduces students to probability theory, statistical inference and statistical modeling, and emphasizes the connection between statistical procedures and social science theory. Sean Gailmard develops core statistical theory as a set of tools to model and assess relationships between variables - the primary aim of social scientists - and demonstrates the ways in which social scientists express and test substantive theoretical arguments in various models. Chapter exercises guide students in applying concepts to data, extending their grasp of core theoretical concepts. Students will also gain the ability to create, read and critique statistical applications in their fields of interest.
In hypothesis testing, we make conjectures about the data-generating process (DGP) and assess the weight of evidence that the sample offers in support of them. The conjectures about the DGP that are subject to testing should have some theoretically interesting foundation, but they are made before any evaluation or analysis of the observed sample data. Hypothesis testing does not address where the conjectures come from; they are taken as given, supplied by theory, and are tested against data.
Statistical estimation, by contrast, does not take as given conjectures to be evaluated. Instead it uses the observed data to make conjectures about the unobserved DGP that are in some sense good or reasonable. There are two general types of estimation, interval estimation and point estimation. These types of estimation are treated in this chapter.
Interval estimates specify a range of values that are all “reasonable” guesses about an unknown parameter of a DGP. Typically the interval estimate contains the parameter of a DGP in a user-specified probability of random samples. Interval estimates are useful because they combine a sense of the “best guess” of a parameter's value and some uncertainty about that best guess into one statement. Another name for an interval estimate in classical statistics is a confidence interval. Although a hypothesis test asks whether a particular conjecture about the DGP is reasonable in light of the data, a confidence interval can be thought of as a range of reasonable conjectures about the DGP.
Moving from a mass of data to an informative description of patterns within that data is a basic point of quantitative techniques social science, an area of quantitative analysis called descriptive statistics. It is not the fanciest math, nor does it comprise the most subtle concepts, but it requires serious attention in any quantitative work. Descriptive statistics is an important part of constructing an argument using data and includes making apparent the tendencies, patterns, and relationships in that data. Equally important is that descriptive statistics helps a researcher get a feel for the behavior of the variables in a dataset and for conjectures about relationships that are worth further analysis, both statistically and theoretically.
Before meaningful analysis can proceed, it is necessary to understand how we observe and measure the concepts of interest in any research. Thus this chapter begins with a brief overview of empirical measurement of variables. It then discusses common graphical and statistical summaries and descriptions of aggregate data, first for one variable at a time (univariate distributions) and then for relationships (bivariate or multivariate distributions). It also covers some important theoretical properties of these descriptive tools.
Some basic concepts are important. To fix ideas, imagine a dataset with a set of observations of one or more characteristics of some collection of units. For instance, on the “democratic peace” (see Chapter 1), the units might be pairs of nation-states.
Chapter 2 dealt with the summary and analysis of data that is actually observed. It is possible that a researcher or analyst has no interest in the variables or concepts being analyzed beyond the particular set of observations available to him or her. If a university wants to know whether its admissions decisions last year were less favorable to members of underrepresented groups than to others, taking as given other aspects of each application file (grade point average, entrance exam scores, etc.), it need only analyze last year's admissions data. A linear regression, purely descriptive of this data, would shed light on the question.
However, the remainder of this book covers elements of probability theory and statistical inference and modeling, which itself rests heavily on probability theory. Before launching into that treatment, it is necessary to consider why (or conditions under which) we need it.
When a theory relating two or more variables is part of the consideration, it is unusual that a researcher's interest in the variables ends with the data that happens to have been observed. Such a theory deals with the process or behaviors that give rise to the data that was observed, not just that data itself. That data helps to inform whether the theory has any drawing power in reality, but that data is not the sum total of possible observations of the social process in question.
As datasets can be usefully summarized to compress much information into small pieces (Chapter 2), probability distributions can be as well. We review some of these summaries in this chapter. These summaries of probability distributions revolve around various kinds of expectations of the behavior of a random variable. These expectations are important because they typically relate to the specific aspects of stochastic data-generating processes (DGPs), called parameters, that social scientists connect to substantive theory and attempt to uncover in empirical work. In one sense, the material in this chapter helps to explain why that is. In addition, this chapter also provides some basic familiarity with these important formal constructs that we use repeatedly in subsequent material.
One of the most important points of this chapter is to define the regression function, or expected value of Y as a function of X, as it exists in a DGP specified as a joint distribution function. We then proceed to establish some important properties about this DGP regression that help to motivate and justify the widespread interest in this function in empirical social science. Later chapters spend a great deal of time developing common models for this regression (and techniques to make inferences about the DGP regression from regression models fit to sample data), so it is important to get a handle on why anyone should care about it.
In Chapter 6, we saw a variety of examples of data-generating processes (DGPs) that are common in statistical models, which consist of a DGP for the data and a link from its parameters to explanatory factors. Although the parametric family of the DGP may be assumed, the specific parameters of the DGP that gave rise to data we have available are generally not known. The whole point of empirical analysis is to use observable data to learn something about those parameters. A theory may assert that the conditional mean of Y increases as X increases, for instance, but in empirical analysis, we wish to determine how credible this assertion actually is. That is the point of statistical inference, which is the subject of the rest of this book.
To understand how we can use data to inform ourselves about parameters of DGPs when they are unknown, it is useful to see what happens when we pretend these parameters are known. If we have data drawn from a known DGP with known parameters, we can see how summaries and statistics computed from that observed data are related to those parameters. That is the subject of the present chapter. Here we study how summaries and statistics computed exclusively from observable data are related to the DGP, given a collection of observations from the DGP.
Statistical inference and modeling are different topics. One involves expressing the properties of DGPs in terms of parameters and parameters as functions of other variables. The other involves making inferences from observable data back to DGPs, whether those inferences are structured by a model or not.
Statistical inference is necessary to learn about a social process broader than the mere data in front of a researcher any time the process that generates that data or makes it observable has a stochastic element. Statistical modeling is not a necessary implication of any particular metaphysical view about DGPs. But it is helpful to social scientists attempting to learn about stochastic ones. First, statistical models allow for crisp expressions of the link between the positive theory that is often of ultimate interest in social science and data-generating processes (DGPs). Second, statistical models narrow the range of possible DGPs that might have generated the data considerably. This does a great deal of work in structuring the estimation and inference problems that researchers face. In a sense, a model represents a sort of “prior belief” about the workings of the social process under analysis. The analysis precedes from and is informed by that prior belief. And in another sense, models represent “free” information: generating equally certain, equally strong conclusions without a model as are possible with the aid of a model requires a massive increase in available data.