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Reduced Form
In statistics, and particularly in econometrics, the reduced form of a system of equations is the result of solving the system for the endogenous variables. This gives the latter as functions of the exogenous variables, if any. In econometrics, the equations of a structural form model are estimated in their theoretically given form, while an alternative approach to estimation is to first solve the theoretical equations for the endogenous variables to obtain reduced form equations, and then to estimate the reduced form equations. Let ''Y'' be the vector of the variables to be explained (endogeneous variables) by a statistical model and ''X'' be the vector of explanatory (exogeneous) variables. In addition let \varepsilon be a vector of error terms. Then the general expression of a structural form is f(Y, X, \varepsilon) = 0 , where ''f'' is a function, possibly from vectors to vectors in the case of a multiple-equation model. The reduced form of this model is given by Y = g(X, \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonsingular
In linear algebra, an -by- square matrix is called invertible (also nonsingular or nondegenerate), if there exists an -by- square matrix such that :\mathbf = \mathbf = \mathbf_n \ where denotes the -by- identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix is uniquely determined by , and is called the (multiplicative) ''inverse'' of , denoted by . Matrix inversion is the process of finding the matrix that satisfies the prior equation for a given invertible matrix . A square matrix that is ''not'' invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is zero. Singular matrices are rare in the sense that if a square matrix's entries are randomly selected from any finite region on the number line or complex plane, the probability that the matrix is singular is 0, that is, it will "almost never" be singular. Non-square matrices (-by- matrices for which ) do not h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jarrow–Turnbull Model
The Jarrow–Turnbull model is a widely used "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow and Stuart Turnbull. Under the model, which returns the corporate's probability of default, bankruptcy is modeled as a statistical process. The model extends the reduced-form model of Merton (1976) to a random interest rates framework. Reduced-form models are an approach to credit risk modeling that contrasts sharply with "structural credit models", the best known of which is the Merton model of 1974. Reduced-form models focus on modeling the probability of default as a statistical process, whereas structural-models inhere a microeconomic model of the firm's capital structure, deriving the (single-period) probability of default from the random variation in the (unobservable) value of the firm's assets.Robert C. Merton “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” ''Journal of Finance'' 29, 1974, pp. 449–470 Large fina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield Spread
Yield may refer to: Measures of output/function Computer science * Yield (multithreading) is an action that occurs in a computer program during multithreading * See generator (computer programming) Physics/chemistry * Yield (chemistry), the amount of product obtained in a chemical reaction ** The arrow symbol in a chemical equation * Yield (engineering), yield strength of a material as defined in engineering and material science * Fission product yield * Nuclear weapon yield Earth science * Crop yield, measurement of the amount of a crop harvested, or animal products such as wool, meat or milk produced, per unit area of land ** Yield (wine), the amount of grapes or wine that is produced per unit surface of vineyard * Ecological yield, the harvestable population growth of an ecosystem, most commonly measured in forestry and fishery * Specific yield, a measure of aquifer capacity * Yield (hydrology), the volume of water escaping from a spring Production/manufacturing * Yield (c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simultaneous Equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: * System of linear equations, * System of nonlinear equations, * System of bilinear equations, * System of polynomial equations, * System of differential equations, or a * System of difference equations See also * Simultaneous equations model, a statistical model in the form of simultaneous linear equations * Elementary algebra Elementary algebra encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables (quantities without fixed values). This use of variables entail ..., for elementary methods {{set index article Equations Broad-concept articles de:Gleichung#Gleichungssysteme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Of Linear Equations
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the three variables . A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple :(x,y,z)=(1,-2,-2), since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually. In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simultaneous Equations Model
Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just independent variables. This means some of the explanatory variables are jointly determined with the dependent variable, which in economics usually is the consequence of some underlying equilibrium mechanism. Take the typical supply and demand model: whilst typically one would determine the quantity supplied and demanded to be a function of the price set by the market, it is also possible for the reverse to be true, where producers observe the quantity that consumers demand ''and then'' set the price. Simultaneity poses challenges for the estimation of the statistical parameters of interest, because the Gauss–Markov assumption of strict exogeneity of the regressors is violated. And while it would be natural to estimate all simultaneous equations at once, this often leads to a computationally costly non-linear optimization p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter Identification Problem
In economics and econometrics, the parameter identification problem arises when the value of one or more parameters in an economic model cannot be determined from observable variables. It is closely related to non-identifiability in statistics and econometrics, which occurs when a statistical model has more than one set of parameters that generate the same distribution of observations, meaning that multiple parameterizations are observationally equivalent. For example, this problem can occur in the estimation of multiple-equation econometric models where the equations have variables in common. In simultaneous equations models Standard example, with two equations Consider a linear model for the supply and demand of some specific good. The quantity demanded varies negatively with the price: a higher price decreases the quantity demanded. The quantity supplied varies directly with the price: a higher price increases the quantity supplied. Assume that, say for several years, we ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1 p. 1–34Abstract ( 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Econometri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Column Vector
In linear algebra, a column vector with m elements is an m \times 1 matrix consisting of a single column of m entries, for example, \boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end. Similarly, a row vector is a 1 \times n matrix for some n, consisting of a single row of n entries, \boldsymbol a = \begin a_1 & a_2 & \dots & a_n \end. (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: \begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end and \begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end. The set of all row vectors with ''n'' entries in a given field (such as the real numbers) forms an ''n''-dimensional vector space; similarly, the set of all column vectors with ''m'' entries forms an ''m''-dimensional vector space. The space of row vectors with ''n'' entries can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supply And Demand
In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a particular Good (economics), good, or other traded item such as Labour supply, labor or Market liquidity, liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted. The concept of supply and demand forms the theoretical basis of modern economics. In macroeconomics, as well, the AD–AS model, aggregate demand-aggregate supply model has been used to depict how the quantity of real GDP, total output and the aggregate price level may be determined in equilibrium. Graphical representations Supply schedule A supply schedule, depicted graphically as a supply cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
