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Difference In Differences
Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias). In contrast to a time-series estimate of the treatment effect on subjects (wh ...
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Review Of Economic Studies
''The Review of Economic Studies'' (also known as ''REStud'') is a quarterly peer-reviewed academic journal covering economics. The journal is widely considered one of the top 5 journals in economics. It is managed by the editorial board currently chaired by Ruben Enikolopov. The current joint managing editors are Thomas Chaney at University of Southern California, Xavier D’Haultfoeuille at Center for Research in Economics and Statistics, Andrea Galeotti at London Business School, Bard Harstad at Stanford Graduate School of Business, Nir Jaimovich at University of California, San Diego, Katrine Loken at Norwegian School of Economics, Elias Papaioannou at London Business School, Vincent Sterk at University College London, and Noam Yuchtman at University of Oxford. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 6.345. History The journal was founded in 1933 by a group of economists based in Britain and the United States. The original editori ...
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Panel Data
In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time. Time series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter). A literature search often involves time series, cross-sectional, or panel data. A study that uses panel data is called a longitudinal study or panel study. Example In the multiple response permutation procedure (MRPP) example above, two datasets with a panel structure are shown and the objective is to test whether there's a significant difference between people in the sample data. Individual characteristics (income, age, sex) are collected for different persons and different years. In the first dataset, two persons (1, 2) are observed every year for three ...
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Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a random variable at different points in time. The analysis of autocorrelation is a mathematical tool for identifying repeating patterns or hidden periodicities within a signal obscured by noise. Autocorrelation is widely used in signal processing, time domain and time series analysis to understand the behavior of data over time. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Various time series models incorporate autocorrelation, such as unit root processes, trend-stationary processes, autoregressive processes, and moving average processes. Autocorrelation of stochastic processes In statistics, the autocorrelation of a real ...
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Average Treatment Effect
The average treatment effect (ATE) is a measure used to compare treatments (or interventions) in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control. In a randomized trial (i.e., an experimental study), the average treatment effect can be estimated from a sample using a comparison in mean outcomes for treated and untreated units. However, the ATE is generally understood as a causal parameter (i.e., an estimate or property of a population) that a researcher desires to know, defined without reference to the study design or estimation procedure. Both observational studies and experimental study designs with random assignment may enable one to estimate an ATE in a variety of ways. The average treatment effect is under some conditions directly related to the partial dependence plot. General definition Originating from e ...
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Observational Studies
In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints. One common observational study is about the possible effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator. This is in contrast with experiments, such as randomized controlled trials, where each subject is randomly assigned to a treated group or a control group. Observational studies, for lacking an assignment mechanism, naturally present difficulties for inferential analysis. Motivation The independent variable may be beyond the control of the investigator for a variety of reasons: * A randomized experiment would violate ethical standards. Suppose one wanted to investigate the abortion – breast canc ...
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Matching (statistics)
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is to reduce bias for the estimated treatment effect in an observational-data study, by finding, for every treated unit, one (or more) non-treated unit(s) with similar observable characteristics against which the covariates are balanced out (similar to the K-nearest neighbors algorithm). By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding. Propensity score matching, an early matching technique, was developed as part of the Rubin causal model, but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods. A si ...
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Formal Definition
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to: Dress code and events * Formal wear, attire for formal events * Semi-formal attire, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or symbolic logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics *Formal cause, Aristotle's intrinsic, determining cause *Formal power series, a generalization of power series without requiring convergence, used in combinatorics *Formal calculation, a calculation which is systematic, but without a rig ...
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Parallel Trend Assumption
Parallel may refer to: Mathematics * Parallel (geometry), two lines in the Euclidean plane which never intersect * Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Science and engineering * Parallel (latitude), an imaginary east–west line circling a globe * Parallel of declination, used in astronomy * Parallel, a geometric term of location meaning "in the same direction" * Parallel electrical circuits Computing * Parallel (software), a UNIX utility for running programs in parallel Language * Parallelism (grammar), a balance of two or more similar words, phrases, or clauses * Parallelism (rhetoric) Entertainment * ''Parallel'' (manga) * ''Parallel'' (2018 film), a Canadian science fiction thriller film * ''Parallel'' (2024 film) an American science fiction thriller film * ''Parallel'' (video), a compilation of music videos by R.E.M. * ''Parallel'' (The Black Dog album), 1995 * ''Parallel'' (Fou ...
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Without Loss Of Generality
''Without loss of generality'' (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as ''without any loss of generality'' or ''with no loss of generality'') is a frequently used expression in mathematics. The term is used to indicate the assumption that what follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are sufficiently similar to the one presented that proving them follows by essentially the same logic. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases. In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. For example, if some property ''P''(''x'',''y'') of real numbers is known to be symmetric in ''x'' and ''y'', namely that ''P''(''x'',''y'') is equivalent to ''P''(''y'',''x''), then in proving that ''P''(''x'',''y'') holds for every ...
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Ordinary Least Squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ... model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Some sources consider OLS to be linear regression. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression ...
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Errors And Residuals In Statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the '' estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors a ...
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Assumptions
Assumption, in Christianity, refers to the Assumption of Mary, a belief in the taking up of the Virgin Mary into heaven. Assumption may also refer to: Places * Assumption, Alberta, Canada * Assumption, Illinois, United States ** Assumption Township, Christian County, Illinois * Assumption Island, Seychelles ** Assumption Island Airport * Assumption, Minnesota, United States * Assumption, Nebraska, United States * Assumption, Ohio, United States * Assumption Parish, Louisiana, United States Arts, entertainment, and media * "Assumption" (short story), a 1929 story by Samuel Beckett * Assumption of Moses, a Jewish apocryphal pseudepigraphical work of uncertain date and authorship * "Assumptions" (''Doctors''), a 2003 television episode * Assumption (film), a 2017 short film by Anthony Leone * "Assumptions" (''Law & Order: Special Victims Unit''), a 2019 television episode * "Assumptions" (song), 2021 song by Sam Gellaitry Churches * Assumption Chapel, Minnesota, United State ...
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