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计量经济学试题（Econometrics questions）A glossary (a total of 20 points, 4 points for each item)1 Econometrics2 least square method3 dummy variables4 instrumental variable methodIdentification of 5 simultaneous equationsTwo short answer questions (30 points, 6 points for each item)1 the classical assumption that the least square method should be satisfied2 steps to solve problems in EconometricsThe reason for the existence of 3 sequence correlation Steps of economic structure test in 4 regression analysis Characteristics of 5 stochastic perturbationsThree calculation analysis (30 points)1., according to the following information, study the income and consumption of farmers in Hebei province.Requirements: (1) to establish regression model (list and calculation formula, test only for economic significance and goodness of fit test);(2) if the per capita net income of farmers in Hebei in 2008 is 3200 yuan, 2008 of the per capita living expenses of farmers in Hebei should be predicted.Particular yearItem 1994199519961997 1998199920002001 20022003Per capita net income of farmers (100 yuan) 111721232424252627 29Living expenses (100 yuan) 811141413131414151Four discussion questions (20 points)1 briefly describe the meaning, sources and consequences of heteroscedasticity, and write the test steps combined with the G-Q test method.Econometrics entry final exam questions B answerFirst, noun interpretation1 econometrics is the integration of mathematics, statistics and economic theory, combined with the theory and practice of economic behavior and phenomenon.2 least square method: the least square method for minimizing the sum of residuals of all observations is the least square method.3 dummy variables: there are some temporary factors in the study of economic life. Such as war, natural disasters, man-made disasters, these factors do not occur frequently in the economy, but with the same characteristics, these economists do not occur frequently, and temporary effect called virtual variables.4 instrumental variable method: instrumental variable method takes the predetermined variable as instrumental variable instead of the endogenous variable in structural equation as explanatory variable, in order to reduce the correlation between random item and explanatory variable.Identification of 5 simultaneous equations: a single equation that constitutes a simultaneous equation has only a statistical form in its simultaneous equations, and this equation is known to be identifiable, otherwise it is called non recognizable. If every equation in the simultaneous equation can be identified, this simultaneous equation is called identity, otherwise it is called non recognizable.Two, simple answer1 the classical assumption that the least square method should be satisfiedAnswer: (1) the mean of random items is zero;(2) random sequence non correlation and heteroscedasticity;(3) explanatory variables are non random, and if random, they are not related to random items;(4) there is no multicollinearity between explanatory variables.2 the steps of applying econometrics to solve economic problemsAnswer: 1) building models;2) estimation parameters;3) verification theory;4) use modelThe reason for the existence of 3 sequence correlationSequence correlation: that is, the random term U is related to other previous terms. It is called sequence correlation or autocorrelation.The cause of existence:First of all, with the continuous problem in economic life and time, namely the repetition time repeated, therefore, the explanatory variables associated with.Secondly, the error of model selection is established, which makes the explanatory variables relevant.Finally, when the model is established, the random term has autocorrelation, and the sequence has autocorrelation.The method of economic structure test in 4 regression analysisChow puts forward the following test method:Firstly, two samples were merged to form the sample of the number of observation value +, and the model (4.25) was regressed, and the regression equation was obtained:(4.28)The sum of squares of residuals is obtained, and the degree of freedom is + -k-1,Here K is the number of variables explained.Secondly, the use of two small sample given above, respectively (4.25) of the regression analysis, the regression equation respectively (4.26) and (4.27), calculated the sum of squared residuals, respectively, the degree of freedom for -k-1 and -k-1 respectively.Then, according to the sum of squares of residuals, the following statistic is constructed:~ F (k+1, + -2k-2) (4.29)Using statistical (4.29) test (4.26), (4.27) the significant similarities and differences, that is, test hypothesis: (j=0, 1,2,... K).Given the significant level (such as =0.05, =0.01), the F distribution table with the first degree of freedom as k+1 and the second degree of freedom as the + -2k-2 is obtained, and the critical value is obtained.If rejected, that (4.26), (4.27) there is a significant difference, the economic relations of the two or two samples reflect different, we say that the changes in the economic structure; on the contrary, we believe that the economic structure is relatively stable.Some properties of the 5 random perturbation term:1. the complex represented by many factors on the explanatory variable Y;2., the influence direction of Y should be different, there are positive and negative;3. as a secondary factor, the total average impact on Y may be zero;The effect of 4. on Y is non trending and stochastic.Three computational analysis1., according to the following information, study the income and consumption of farmers in Hebei province.Particular yearItem 1994199519961997 1998199920002001 20022003Per capita net income of farmers (100 yuan) 111721232424252627 29Living expenses (100 yuan) 811141413131414151According to economic theory, there is a correlation between farmers' living expenditure and their net income. The basic source of farmers' consumption expenditure lies in their net income, so the increase of per capita net income of farmers is the reason for the increase of their living expenses. In addition, farmers' living expenses are also affected by savings, psychological preferences and other factors, so the model is regression model.If Ct is the farmer's consumption expenditure, and Y is the net income per capita of farmers, the following regression model can be establishedCt=c+aYtDependent Variable: CTMethod: Least SquaresDate: 12/15/97 Time: 16:44Sample: 19942003Included observations: 10Variable Coefficient Std. Error t-Statistic Prob.YT 0.406238 0.046500 8.736250 0C 3.978409 1.080867 3.680755 0.0062R-squared 0.905126 Mean dependent var 13.20000Adjusted R-squared 0.893266 S.D. dependent var 2.250926 S.E. of regression 0.735380 Akaike info criterion 2.399998 Sum squared resid 4.326269 Schwarz criterion 2.460515Log likelihood -9.999988 F-statistic 76.32207Durbin-Watson stat 1.329130 Prob (F-statistic) 0.000023 The regression equation was Ct=3.9784+0.4062Yt(3.6801) (8.7363)Because T (a) =8.7363>T0.025 (8) =2.306F=76.3221>F0.05 (1,8) =5.32So the regression equation and its coefficients are significantR2=0.9051, which shows that the regression equation and the sample observation value have good goodness of fitFour topics1. answers:Meaning: for the random perturbation of the UI regression model, if the other assumption, the second assumption is not established, that is to say in the variance of random UI different observation value is not equal to a constant, Var (UI) = constant (i=1, 2,... (n), or Var (U) Var (U) (I J), then we call the random perturbation term UI has heteroscedasticity.Source: 1. model omitted economic variables, the measurement error of 2.The consequence of heteroscedasticity: the 1. parameter estimator is still linear unbiased, but not valid. 2. test failure based on t distribution and F distribution. The variance of 3. estimator increases, and the prediction accuracy decreases.Inspection: Inspection (Goldfeld - Quart Goldfield - Quandt G - Q test) test in 1965 by S.M.Goldfeld and R.E.Quandt proposed. This test method is applicable to large samples, usually require the capacity of n should be 30 or the number of observations is to estimate the parameters of more than 2 times(i.e., sample size is much larger than the N model included explanatory variables two times large numbers above). To test heteroscedasticity should meet the following conditions: first, using the method of random perturbation UI obey the normal distribution, and the variance of UI increased with a certain explanatory variables; second, random perturbation UI no serial correlation, namely E (uiuj) =0 (I J). The test method is mainly F test.The test hypothesis H0: UI is equal variance, and the alternative assumption is that H1: UI is heteroscedastic, and the specific steps of G - Q test are as follows:1. will explain the observed value of the variable Xi in absolute ascending order, be interpreted correspond to the variables of Xi Yi.2. the Xi are arranged in C values by deleting the centre of the remaining N-C observations is divided into two sub samples of the same capacity, the capacity of each sub sample respectively, a sub sample which is the larger part of the corresponding observation value, the other is a relatively small part of the observed value. It should be noted that the determination of the C value is not arbitrary, and it is determined by experiments by Goldfeld and Quandt. For the sample size when n is greater than 30, the number of C for the entire sample number 1/4 by deleting observations (e.g., sample size is 48, c=, n=12, removal of the observation value is 12, then the two sub sample volume respectively =18).3. the least squares method is used to calculate the regressionequation of the two sub samples, and then the corresponding residual sum of squares is calculated respectively. The sum of squares of residuals is the sum of the residuals of the sub samples with larger sample value, and their degree of freedom is -k, where k is the number of explanatory variables in the econometric model.4. establish statistics:F= can prove that F=RSS2/RSS1 ~ F (), that is, it follows the F distribution of degrees of freedom respectively. Obviously, if the two sub sample variance is equal, the value of F is close to 1, show that UI has equal variance; if the variance is not equal, according to the pre condition of RSS2 is greater than RSS1, F-measure should be greater than 1, then UI has heteroscedasticity, so we can use the F test to verify whether UI has heteroscedasticity of. That is, for the given significance level, the F distribution table is obtained corresponding critical value, if F>, reject H0, accept H1, that is, UI has heteroscedasticity; if F<, then accept H0, UI has equal variance.。
70年代后计量经济学发展简史在上世纪70年代以前，计量经济学研究经历了从简单到复杂、从单一方程到联立方程的进化过程。
进入70年代，西方国家致力于更大规模的宏观计量经济模型研究。
为了理解、预测和控制经济运行过程，计量经济学从着眼于研究适合国内的计量经济模型发展到着眼于国际的大型计量经济模型，以便研究国际经济波动的影响和国际经济发展战略可能引起的各种后果，为制定和评价长期的经济政策服务。
70年代是联立方程模型发展最辉煌的时期。
最著名的联立方程模型是“连接计划”（Link Project），截至1987年，该模型已包括78个国家2万个方程。
这一时期最有代表性的计量经济学家是L.Klein教授，他于1980年获诺贝尔经济学奖。
但是，后来人们发现有的时候联立方程模型的预测能力并不像想象的那样强，模型结构也不稳定。
于是，人们开始寻找它的原因：首先，人们想到的是计量经济学的基本假设，其核心假定是“经济时间序列是平稳的”(注：平稳序列的典型特征是，它的一阶矩和二阶矩都是常数，不随时间而变)。
70年代以前的建模技术都是以“经济时间序列平稳”这一假定为前提的。
然而，70年代后各国的经济结构有了很大变化（石油危机、汇率波动、滞涨等），经济变量出现了非平稳特征。
其次，人们还发现了计量经济模型的“伪回归”问题。
由于经济时间序列的非平稳性和“伪回归”问题直接影响经济计量模型参数估计的准确性，人们开始对计量经济学方法论的缺陷提出质疑。
方法论（Methodology）是指处理问题和从事活动的方式，它构成了我们完成一项任务的一般途径，提供了组织、计划、设计和实施研究的基本原则。
几件主要的事情，促成了协整（协积）分析方法论的形成和发展完善：1974年，Granger-Newbold首先提出“虚假回归”问题。
Granger指出，经济变量间存在可测的因果关系的必要条件应包括，模型参数对于输入变量所含干扰信号具有抗变性。
1967年，Box-Jenkins出版《时间序列分析、预测与控制》一书。
simultaneous three-equation model1. 引言1.1 概述在经济学和社会科学研究中，同时考虑多个相关方程的模型被广泛应用。
这些模型被称为"simultaneous three-equation models"，因为它们包含三个相互关联的方程。
这些方程通常代表着不同的经济变量之间的关系，通过分析这些关系可以更好地理解经济系统的运作机制。
1.2 文章结构本文将对simultaneous three-equation model进行详细的探讨和分析。
首先，我们将介绍该模型的理论背景，包括概述、模型假设以及应用领域。
接下来，我们将阐述模型的建立过程和参数估计方法，并介绍模型选择准则和诊断检验。
然后，我们将展示实证分析结果，并对其进行解释和讨论。
最后，我们将总结主要研究发现并展望存在的问题与改进研究方向。
1.3 目的本文旨在提供一个全面而深入的介绍simultaneous three-equation model，并通过实证分析来展示其在经济学研究中的应用价值。
我们希望通过对该模型的探讨和分析，能够增加读者对经济系统运作机制的理解，并为相关领域的研究和政策制定提供有益的参考。
同时，我们也将指出该模型存在的问题，并展望未来改进研究的方向。
2. 理论背景2.1 三方程模型概述在经济学和社会科学领域，三方程模型是一种常用的统计分析方法。
该模型通过建立三个联立方程来描述多个变量之间的关系和相互作用。
这些方程通常代表着不同变量之间的因果关系，可以揭示出导致某一现象或结果的因素。
三方程模型通常包括三个主要成分：自变量、因变量和错误项。
自变量是研究者选定的与因变量有关的解释变量，它们对因变量产生直接或间接影响。
因变量是研究者希望解释或预测的目标变量。
错误项则代表了未被观察到或遗漏的其他影响因素，即未能被自变量完全解释并捕捉到的部分。
2.2 模型假设为了建立一个有效的三方程模型，需要满足一些基本假设。
