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Truncated Normal Hurdle Model
In econometrics, the truncated normal hurdle model is a variant of the Tobit model and was first proposed by Cragg in 1971. In a standard Tobit model, represented as y=(x\beta+u) 1 0.html" ;"title="\beta+u>0">\beta+u>0/math>, where u, x\sim N(0,\sigma^2)This model construction implicitly imposes two first order assumptions: # Since: \partial P 0.html" ;"title=">0">>0\partial x_j=\varphi (x\beta/\sigma) \beta_j/\sigma and \partial \operatorname E 0.html" ;"title="\mid x,y >0">\mid x,y >0\partial x_j=\beta_j\, the partial effect of x_j on the probability P 0.html" ;"title=">0">>0/math> and the conditional expectation: \operatorname E 0.html" ;"title="\mid x,y >0">\mid x,y >0/math> has the same sign: # The relative effects of x_h and x_j on P 0.html" ;"title=">0">>0/math> and \operatorname E 0.html" ;"title="\mid x,y>0">\mid x,y>0/math> are identical, i.e.: : \frac=\frac = \frac, However, these two implicit assumptions are too strong and inconsistent with many contexts in econom ...
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Econometrics
Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 [pp. 8–22]. Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1[pp. 1–34].Abstract (The New Palgrave Dictionary of Economics, 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic Phenomenon, 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 toda ...
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Tobit Model
In statistics, a tobit model is any of a class of regression models in which the observed range of the dependent variable is censored in some way. The term was coined by Arthur Goldberger in reference to James Tobin, who developed the model in 1958 to mitigate the problem of zero-inflated data for observations of household expenditure on durable goods. Because Tobin's method can be easily extended to handle truncated and other non-randomly selected samples, some authors adopt a broader definition of the tobit model that includes these cases. Tobin's idea was to modify the likelihood function so that it reflects the unequal sampling probability for each observation depending on whether the latent dependent variable fell above or below the determined threshold. For a sample that, as in Tobin's original case, was censored from below at zero, the sampling probability for each non-limit observation is simply the height of the appropriate density function. For any limit observation, it ...
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Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ...
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Investment
Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing is to generate a return from the invested asset. The return may consist of a gain (profit) or a loss realized from the sale of a property or an investment, unrealized capital appreciation (or depreciation), or investment income such as dividends, interest, or rental income, or a combination of capital gain and income. The return may also include currency gains or losses due to changes in the foreign currency exchange rates. Investors generally expect higher returns from riskier investments. When a low-risk investment is made, the return is also generally low. Similarly, high risk comes with a chance of high losses. Investors, particularly novices, are often advised to diversify their portfolio. Diversification has the statistical effec ...
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Cost
In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this case, money is the input that is gone in order to acquire the thing. This acquisition cost may be the sum of the cost of production as incurred by the original producer, and further costs of transaction as incurred by the acquirer over and above the price paid to the producer. Usually, the price also includes a mark-up for profit over the cost of production. More generalized in the field of economics, cost is a metric that is totaling up as a result of a process or as a differential for the result of a decision. Hence cost is the metric used in the standard modeling paradigm applied to economic processes. Costs (pl.) are often further described based on their t ...
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Price
A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the commercial exchange, the payment for this product will likely be called its "price". However, if the product is "service", there will be other possible names for this product's name. For example, the graph on the bottom will show some situations A good's price is influenced by production costs, supply of the desired item, and demand for the product. A price may be determined by a monopolist or may be imposed on the firm by market conditions. Price can be quoted to currency, quantities of goods or vouchers. * In modern economies, prices are generally expressed in units of some form of currency. (More specifically, for raw materials they are expressed as currency per unit weight, e.g. euros per kilogram or Rands per KG.) * Although prices ...
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Revenue
In accounting, revenue is the total amount of income generated by the sale of goods and services related to the primary operations of the business. Commercial revenue may also be referred to as sales or as turnover. Some companies receive revenue from interest, royalties, or other fees A fee is the price one pays as remuneration for rights or services. Fees usually allow for overhead (business), overhead, wages, costs, and Profit (accounting), markup. Traditionally, professionals in the United Kingdom (and previously the Repu .... This definition is based on International Accounting Standard, IAS 18. "Revenue" may refer to income in general, or it may refer to the amount, in a monetary unit, earned during a period of time, as in "Last year, Company X had revenue of $42 million". Profit (accounting), Profits or net income generally imply total revenue minus total expenses in a given period. In accountancy, accounting, in the balance statement, revenue is a subsection of the ...
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Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed to ...
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Probit Model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from ''probability'' + ''unit''. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. Conceptual framework Suppose a response variable ''Y'' is ''binary'', that is it can have only two possible outcomes ...
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Hurdle Model
A hurdle model is a class of statistical models where a random variable is modelled using two parts, the first which is the probability of attaining value 0, and the second part models the probability of the non-zero values. The use of hurdle models are often motivated by an excess of zeroes in the data, that is not sufficiently accounted for in more standard statistical models. In a hurdle model, a random variable ''x'' is modelled as : \Pr (x = 0) = \theta : \Pr (x \ne 0) = p_(x) where p_(x) is a truncated probability distribution function, truncated at 0. Hurdle models were introduced by John G. Cragg in 1971, where the non-zero values of ''x'' were modelled using a normal model, and a probit model was used to model the zeros. The probit part of the model was said to model the presence of "hurdles" that must be overcome for the values of x to attain non-zero values, hence the designation ''hurdle model''. Hurdle models were later developed for count data, with Poisson, geo ...
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Regression Models
Regression or regressions may refer to: Science * Marine regression, coastal advance due to falling sea level, the opposite of marine transgression * Regression (medicine), a characteristic of diseases to express lighter symptoms or less extent (mainly for tumors), without disappearing totally * Regression (psychology), a defensive reaction to some unaccepted impulses * Nodal regression, the movement of the nodes of an object in orbit, in the opposite direction to the motion of the object Statistics * Regression analysis, a statistical technique for estimating the relationships among variables. There are several types of regression: ** Linear regression ** Simple linear regression ** Logistic regression ** Nonlinear regression ** Nonparametric regression ** Robust regression ** Stepwise regression * Regression toward the mean, a common statistical phenomenon Computing * Software regression, the appearance of a bug which was absent in a previous revision ** Regression testing, a s ...
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