Difference in Difference Models
【精品】消费者行为学基本概念
消费者行为学核心概念的中英文对照表P5消费者行为学consumerbehavior研究个体或群体为满足需要与欲望而挑选、购买、使用或处置产品、服务、观念或经验所涉及的过程。
P5角色理论roletheory许多消费者行为类似于戏剧情节。
由于要扮演许多角色，人们有时候会根据自己当时所处的特定“剧情”改变消费决策。
P7重度使用者(频繁使用者)heavyusersP9关系营销relationshipmarketing在品牌与消费者间建立起维持终身的关系.P11全球营销/消费文化globalconsumerculture在这种文化中世界各地的消费者出于对品牌消费品、电影明星、名人及休闲活动的热爱而联结起来。
P49差别阈限differentialthreshold指感觉系统察觉两种刺激之间的差别或者变化的能力。
P49最小可觉察差别justnoticeabledifference能够察觉到的两种刺激之间的最小差别。
P49韦伯定律Weber'sLawK=△i/I（K为常数【不同感觉常数不同】；△i为产生最小可察觉差别所要求的刺激强度的最小变化量；I为引起变化的刺激强度)P50阈下知觉subliminalperception刺激在消费者的感知水平之下。
P52知觉警惕perceptualvigilance消费者更可能意识到与他们目前需要有关的刺激物。
P52知觉防御perceptualdefense人们看他们所要看的，而不看他们所不想看的。
P57知觉地图perceptualmap画出产品或品牌在消费者心目中“处于”何种位置的形象方式。
P72经典性条件反射classicalconditioning（伊凡·巴普洛夫狗铃声干肉粉分泌唾液)指将一种能够诱发某种反应的刺激与另一种原本不能单独诱发这种反应的刺激想配对,随着时间的推移，因为与能够诱发反应的第一种刺激相联结，第二种刺激会引起类似的反应。
（重点研究包括饥饿、口渴、性唤起以及其他基本内驱力的视觉和嗅觉线索。
diffusion模型解读
diffusion模型解读## Diffusion Models Explained.Diffusion models are a type of generative model that has gained popularity in recent years for their ability to generate high-quality images, text, and other data from scratch. They work by gradually "denoising" a random input, adding details and structure until a coherent output is produced.Diffusion models are based on the idea of diffusion, a process that spreads out a substance over time. In the context of generative modeling, diffusion is used to spread out the noise in a random input, making it gradually more uniform. By reversing the diffusion process, the model can then learn to generate data that is increasingly structured and detailed.The training process for a diffusion model involves two main steps:1. Forward diffusion: In this step, a random input is gradually "denoised" by adding noise to it over multiple iterations. This process makes the input increasingly uniform and unstructured.2. Reverse diffusion: In this step, the model learns to reverse the diffusion process, generating data that is increasingly structured and detailed. The model is trained on a dataset of real data, and it learns to generate data that matches the distribution of the real data.Diffusion models have several advantages over other generative models. First, they can generate high-quality data that is visually appealing and realistic. Second, they are relatively easy to train, and they can be used to generate a wide variety of data types. Third, they are computationally efficient, and they can be used to generate large amounts of data quickly.However, diffusion models also have some limitations. First, they can be slow to generate data, especially forlarge datasets. Second, they can be difficult to control, and it can be difficult to generate data with specific properties.Despite these limitations, diffusion models are a promising new approach to generative modeling. They havethe potential to revolutionize the way we generate data,and they could be used to create new applications in a wide range of fields.## 中文回答：扩散模型通俗解释。
DID双重差分回归 PPT课件
17
What is nice about the model
• Suppose interventions are not random but systematic
– Occur in states with higher or lower average Y – Occur in time periods with different Y’s
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Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
12
Basic Econometric Model
• Data varies by
– state (i) – time (t) – Outcome is Yit
• Year effects
– Capture differences over time that are common to all groups
19
Questions to ask?
• What parameter is identified by the quasiexperiment? Is this an economically meaningful parameter?
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment
双重差分模型幻灯片+-+difference+in+differences+models
Y Yc1 Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2 Yt1
control Yt2 treatment t1 t2 Treatment Effect
time
11
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups • If the intervention occurs in an area with a different trend, will under/over state the treatment effect • In this example, suppose intervention occurs in area with faster falling Y
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• ui is a state effect • vt is a complete set of year (time) effects • Analysis of covariance model • Yit = β0 + β3 TitAit + ui + λt + εit
18
What is nice about the model
3
Y True effect = Yt2-Yt1 Estimated effect = Yb-Ya Yt1 Ya Yb Yt2
t1
ti
t2
time
4
• Intervention occurs at time period t1 • True effect of law
双重差分模型幻灯片
unsure how much of the change is due to secular changes
2
Y
Yt1 Ya Yb Yt2
True effect = Yt2-Yt1 Estimated effect = Yb-Ya
6
Difference in Difference
Before Change
Group 1 Yt1 (Treat)
Group 2 Yc1 (Control)
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
• Key concept: can control for the fact that the intervention is more likely in some types of states
5
Three different presentations
• Tabular • Graphical • Regression equation
• Application of two-way fixed effects model
1
Problem set up
• Cross-sectional and time serintervention • Have pre-post data for group receiving
t1
ti
t2
time
3
• Intervention occurs at time period t1 • True effect of law
abaqus python 集合布尔运算
abaqus python 集合布尔运算Abaqus是一种常用的有限元分析软件，在该软件中，用户可以使用Python进行脚本编写，以便实现更高效、更灵活的模拟分析。
在Python脚本中，我们可以利用集合布尔运算操作实现更多的功能，本文将对这一方面进行详细介绍。
1. 集合概述在Python语言中，集合是一种无序、可变的数据类型，其中每个元素唯一且不可重复。
集合可以通过花括号{}或set()函数来创建。
在Abaqus中，集合通常是由节点和单元构成的，集合中的节点或单元也可以通过节点或单元编号、坐标或其它属性来确定。
2. 集合布尔运算集合布尔运算有并集（union）、交集（intersection）、差集（difference）和对称差集（symmetric difference）四种，这些运算都可以用于集合之间的操作。
并集（union）：将两个集合中的所有元素合并在一起形成一个新集合。
交集（intersection）：找到两个集合中共有的元素，形成一个新集合。
差集（difference）：找到第一个集合中不在第二个集合中的元素，形成一个新集合。
对称差集（symmetric difference）：找到两个集合中不共有的元素，形成一个新集合。
其中，集合之间的交集运算非常常见，尤其是在Abaqus中。
3. Abaqus中的集合布尔运算在Abaqus中，集合布尔运算可以直接应用于节点集和单元集，以实现更高级的分析预处理，如：3.1. 创建节点集通过以下Python脚本创建节点集nodeset1和nodeset2：nodeset1 = mdb.models["Model-1"].parts["Part-1"].nodes.getByBoundingBox(x1=0.0, y1=0.0, z1=0.0, x2=100.0, y2=100.0, z2=100.0) nodeset2 =mdb.models["Model-1"].parts["Part-1"].nodes.getByBoundingBox(x1=50.0, y1=50.0,z1=50.0, x2=150.0, y2=150.0, z2=150.0)其中nodeset1和nodeset2根据节点坐标的范围来定义。
variational diffusion models详解
variational diffusion models详解Variational Diffusion Models (VDMs) are a class of generative models that are used for modeling images and videos. VDMs are based on the concept of diffusion processes and leverage variational inference techniques to learn the underlying probability distribution of the data.Here is a detailed explanation of variational diffusion models:1. Diffusion Processes:Diffusion processes model the evolution of probability distributions over time. It starts with an initial distribution and gradually transforms it into the desired target distribution through a series of diffusion steps. Each diffusion step introduces a small amount of noise into the current distribution, pushing it closer to the target distribution. Diffusion processes are commonly used in physics and other fields to describe the spread of particles or heat.2. Generative Modeling:VDMs use diffusion processes for generative modeling of images and videos. Instead of directly modeling the target distribution, VDMs learn a series of diffusion steps that transform a simple initial distribution, suchas a Gaussian distribution, into the target distribution. By iteratively applying these diffusion steps, VDMs generate samples from the target distribution.3. Variational Inference:VDMs employ variational inference techniques to learn the diffusion steps. Variational inference is a framework for approximating complex probability distributions by optimizing a lower bound on the log-likelihood of the data. In VDMs, the diffusion steps are represented by a neural network, known as the diffusion model or encoder. The encoder takes an input sample and performs a series of transformations to generate a latent representation.4. Reverse Diffusion:During training, VDMs use a reverse diffusion process to estimate the likelihood of the data. This involves starting from a sample drawn from the target distribution and iteratively applying reverse diffusion steps to recover the initial distribution. The goal is to maximize the likelihood of the data under the reverse diffusion process, which indirectly maximizes the likelihood under the forward diffusion process.5. Applications:VDMs have found applications in various areas, including image and video generation, denoising, inpainting, and super-resolution. By learning the underlying probability distribution of the data, VDMs can generate high-quality samples and perform tasks like image interpolation and manipulation.In summary, variational diffusion models combine diffusion processes and variational inference to learn the underlying probability distribution of images or videos. By iteratively applying diffusion steps, VDMs generate samples from the target distribution and can be used for various generative modeling tasks.If you have any further questions, feel free to ask!。
DID双重差分回归课件
(return to this in the regression equation)
• Cross section and time fixed effects
• Use time series of untreated group to establish what would have occurred in the absence of the intervention
• Key concept: can control for the fact that the intervention is more likely in some types of states
• If the intervention occurs in an area with a different trend, will under/over state the treatment effect
• In this example, suppose intervention occurs in area with faster falling Y
Difference in Difference Models
DID双重差分回归
1
What is DID
• How can we estimate the effects of higher education reform in China?
• Yang and Chen (2009)
双重差分模型difference in differences models
• Use time series of untreated group to establish what would have occurred in the absence of the intervention • Key concept: can control for the fact that the intervention is more likely in some types of states
• Only two periods • Intervention will occur in a group of observations (e.g. states, firms, etc.)
14
• Three key variables
– Tit =1 if obs i belongs in the state that will eventually be treated – Ait =1 in the periods when treatment occurs – TitAit -- interaction term, treatment states after the intervention
Difference in Difference Models
Bill Evans Spring 2008
1
Difference in difference models
• Maybe the most popular identification strategy in applied work today • Attempts to mimic random assignment with treatment and “comparison” sample • Application of two-way fixed effects model
DID方法
1
What is DID
• How can we estimate the effects of higher education reform in China? • Yang and Chen (2009)
2
Problem set up
• Use time series of untreated group to establish what would have occurred in the absence of the intervention • Key concept: can control for the fact that the intervention is more likely in some types of states
20
• Year effects
– Capture differences over time that are common to all groups
19
Questions to ask?
• What parameter is identified by the quasiexperiment? Is this an economically meaningful parameter? • What assumptions must be true in order for the model to provide and unbiased estimate of β3? • Do the authors provide any evidence supporting these assumptions?
• Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
Finite_Difference_Methods
Fig. 1 Common two-dimensional gridpatterns Finite Difference Methods“Research is to see what everybody else has seen, and think what nobody has thought.” – Albert Szent-GyorgyiI. IntroductionAnalytical methods may fail if:1. The PDE is not linear and can’t be linearized without seriously affecting the result.2. The solution region is complex.3. The boundary conditions are of mixed types.4. The boundary conditions are time-dependent.5. The medium is inhomogeneous or anisotropic.The finite difference method (FDM) was first developed by A. Thom * in the 1920s under the title “the method of square” to solve nonlinear hydrodynamic equations. *A. Thom an C. J. Apelt, Field Computations in Engineering and Physics . London: D. Van Nostrand, 1961.The finite difference techniques are based upon the approximations that permit replacing differential equations by finite difference equations . These finite difference approximations are algebraic in form, and the solutions are related to grid points.Thus, a finite difference solution basically involves three steps:1. Dividing the solution into grids of nodes.2. Approximating the given differential equation by finite difference equivalence that relates the solutions to grid points.3. Solving the difference equations subject to the prescribed boundary conditions and/or initial conditions.II. Finite Difference SchemeDifferential equations Æ estimating derivatives numerically Æ finite difference equationsGiven a function f(x) shown in Fig. 2, we can approximate its derivative, slope or tangent at P by the slope of the arcs PB , PA , or AB , for obtaining the forward-difference, backward-difference, and central-difference formulas respectively.Fig. 2 Estimates for the derivative of f(x) at P by using forward, backward,and central differences.central-difference formulaThe approach used for obtaining above finite difference equations is Taylor’s series:4'''3''2')()()(!31)()(!21)()()(x O x f x x f x x xf x f x x f o o o o o ∆+∆+∆+∆+=∆+, (1)and4'''3''2')()()(!31)()(!21)()()(x O x f x x f x x xf x f x x f o o o o o ∆+∆−∆+∆−=∆−, (2)where O(∆x)4is the error introduced by truncating the series.To subtract (1) by (2), we can obtain3')()(2)()(x O x xf x x f x x f o o o ∆+∆=∆−−∆+, which could be re-written as2')(2)()()(x O x x x f x x f x f o o o ∆+∆∆−−∆+≅, i.e. the central-difference formula. Notethat the O(∆x)2means the truncation error is the order of (∆x)2 for the central-difference.The forward-difference and backward-difference formulas could be obtained by re-arranging (1) and (2) respectively, and we have)()()()('x O xx f x x f x f o o o ∆+∆−∆+≅, for forward difference,and)()()()('x O xx x f x f x f o o o ∆+∆∆−−≅, for backward difference. We can find thetruncation errors of these two formulas are of order ∆x . Upon adding (1) and (2),4''2)()()()(2)()(x O x f x x f x x f x x f o o o o ∆+∆+=∆−−∆+,terms in Taylor series expansion.To apply the difference method to find the solution of a function Φ(x,t), we divide the solution region in x -t plane into equal retangles or meshes of sides ∆x and ∆t . The derivatives of Φ at the (i ,j )th node are shown in the table, wherex = i •∆x t = j •∆t .Fig. 3 Finite difference mesh for twoindependent variable x and t . Fig. 4 Computational molecule forparabolic PDE: (a) for 0 < r < 1/2 (b) r =1/2. Finite Differencing of Parabolic PDE’sConsider a simple example of a parabolic (or diffusion) partial differential equation with one spatial independent variable22xt k∂Φ∂=∂Φ∂, (3) where k is a constant. The equivalent finite deference approximation is2)(),1(),(2),1(),()1,(x j i j i j i t j i j i k ∆+Φ+Φ−−Φ=∆Φ−+Φ. (4) where x =i ∆x , i =1,2,3,…,n, t =j ∆t , j =1,2,…. In (4), we use the forward difference formula for the derivative with respective to t and central difference formula for the with respect to x . If we let2)(x k tr ∆∆=, (5) Eq. (4) could be written as),1(),()21(),1()1,(j i r j i r j i r j i −Φ+Φ−++Φ=+Φ. (6)This explicit formula can be used to compute Φ(x ,t +∆t ) explicitly in terms of Φ(x ,t ).Thus the values of Φ along the first time row (see Fig.3), t =∆t , can be calculated in terms of the boundary and initial conditions, then the values of Φ along the second row, t =2∆t , are calculated in terms of the first time row, and so on.A graphic way of describing the difference equation (6) is through the computational molecule of fig. 4, where the square is used to represent the grid point where Φ is presumed known and a circle where Φ is unknown.Fig. 5 Error as a function of the mesh size.Stability Analysis of the explicit algorithmReducing the mesh size could increase accuracy, but the mesh size could not be infinitesimal.Decreasing the truncation error by using a finer mesh may result in increasing the round-off error due to the increased number of arithmetic operations. A point is reached where minimum total error occurs for any particular algorithm using any given word length. This is illustrated in Fig. 5.The concern about accuracy leads us to a question whether the finite difference solution can grow unbounded, or a property termed the instability of the difference scheme. A numerical algorithm is said to be stable if a small error at any stage produces a smaller cumulative error. Otherwise, it is unstable .To determine a whether a finite difference scheme is stable, we define an error, εn , which occurs at time step n , assuming there is one independent variable. We define the amplification of this error at time step n +1 asεn +1=g εn , (7) where g is the amplification factor . In more complicated situation, we have more independent variables, and (7) becomes[ε]n +1=[G ][ε]n , (8) where [G ] is amplification matrix .For the stability of the finite difference scheme, it is required that Eq. (7) satisfy|εn +1| ≤ |εn |, (9) or|g | ≤ 1.(10) For the case in (8), the determinant of [G ] must vanish, i.e. Det[G ] = 0. (11)One useful method and simple method of finding a stability criterion for a finite difference scheme is to construct a Fourier analysis of the difference equation and thereby derive the amplification factor. The technique is known as von Neumann’s method. The stability condition is called the von Neumann condition. (ref. To J. W. Thomas, Numerical PartialDifferential Equations – Finite Difference Methods, Springer-Verlag New York, 1995)Considering the explicit scheme of Eq. (6):)()21(111n i n i n i n i r r −++Φ+Φ+Φ−=Φ, (12) where r =∆t /k (∆x )2. We have changed our notation so that we can use 1−=j in the Fourier series. Suppose the solution is∑∆=Φx i j n n i e t A κ)(, 0 ≤ ∆x ≤ 1, (13)where κ is the wave number. Since the differential equation is linear, we need consider only one Fourier mode, i.e.x i j n n i e t A ∆=Φκ)(. (14)Substituting (14) into (12) givesx i j n x j x j x i j n x i j n e A e e r e A r e A ∆∆−∆∆∆+++−=κκκκκ)()21(1 (15) or]cos 221[1x r r A A n n κ+−=+. (16)Hence the amplification factor is2sin 41cos 22121xr x r r A A g n n κκ−=∆+−==+. (17)In order to satisfy (10)12sin 412≤−xr κ. (18)Since this condition must hold for every wave number κ, we take the maximum value of the sine function so that1 − 4r ≥ −1 and r ≥ 0 orr ≥ ½ and r ≥ 0.Of course, r = 0 implies ∆t = 0, which is impractical. Thus we have 0 < r ≤ 1/2.In order to ensure a stable solution or reduce errors, care must be exercised in selecting the value of r in (5) and (6). If we choose r=1/2, then (12) becomes)(21111n i n i n i −++Φ+Φ=Φ, (19)as shown in Fig. 4(b).Fig. 5 Computational molecule for Crank-Nicholson method: (a) for finite r and (b) r = 1. Alternative Schemes for parabolic PDE’sAlthough the formula is simple to implement, its computation is slow. An implicit formula, proposed by Crank and Nicholson in 1974, is valid for all finite values of r .We replace 22x ∂Φ∂ in Eq. (3) by the average of the central difference formulas on the j thand (j+1)thtime rows such that])()1,1()1,(2)1,1( )(),1(),(2),1([21),()1,(22x j i j i j i x j i j i j i tj i j i k∆++Φ++Φ−+−Φ+∆+Φ+Φ−−Φ=∆Φ−+Φ, (20) which can be re-written as),1(),()1(2),1( )1,1()1,()1(2)1,1(j i r j i r j i r j i r j i r j i r +Φ+Φ−+−Φ=++Φ−+Φ+++−Φ−. (21)Where r is defined in (5). The left hand side of (21) consists of three unknown values of Φ. This is illustrated in the computational molecule of Fig. 5(a). Thus if there are n nodes along each time row, then for j =0, applying (21) tonodes i =1,2,…,n results in n simultaneous equations with n unknown values of Φ andknown initial and boundary values of Φ. Similarly, for j =1, we obtain n simultaneous equations for n unknown values of Φ in terms of the known values at j =0, and so on. The combination of accuracy and unconditional stability allows the use of a much larger time step with Crank-Nicholson method than is possible with the explicit formula. Although the method is valid for all finite values of r , a convenient choice of r =1 reduces (21) to),1(),1()1,1()1,(4)1,1(j i j i j i j i j i +Φ+−Φ=++Φ−+Φ++−Φ−, (22)with the computational molecule of Fig. 5(b).<HW> Use the von Neumann approach to determine the stability condition of Eq. (21).[Example ]Solve the diffusion equationtx ∂Φ∂=∂Φ∂22 0 ≤ x ≤ 1subject to the boundary conditionsΦ(0,t ) = 0, Φ(1,t ) = 0, t > 0 and initial conditionΦ(x ,0) = 100.SolutionThis problem may be regarded as a mathematical model of the temperature distribution in a rod of length L=1m with its end in contacts with ice blocks (or held at0℃) and the rod initially at 100℃. With the physical interpretation, out problem is finding the internal temperature Φ as a function of position and time. We will solve this problem using both explicit and implicit methods.(a)Analytical solution)exp()sin(1400),(220t n x n nt x k πππ−=Φ∑∞=, n =2k +1t ∆x 0.00 0.10 0.20 0.30 0.40 0.50 ------------------------------------------------- 0.0000 50.00 100.00 100.00 100.00 100.00 100.00 0.0050 0.00 68.27 95.45 99.73 99.99 100.00 0.0100 0.00 52.05 84.27 96.61 99.53 99.92 0.0150 0.00 43.63 75.18 91.67 97.85 99.22 0.0200 0.00 38.29 68.26 86.59 95.18 97.52 0.0250 0.00 34.52 62.86 81.85 91.91 94.93 0.0300 0.00 31.67 58.47 77.51 88.32 91.75 0.0350 0.00 29.39 54.78 73.50 84.61 88.24 0.0400 0.00 27.50 51.58 69.78 80.88 84.58 0.0450 0.00 25.87 48.74 66.31 77.21 80.88 0.0500 0.00 24.42 46.16 63.04 73.63 77.23 0.0550 0.00 23.12 43.79 59.96 70.18 73.67 0.0600 0.00 21.93 41.59 57.04 66.86 70.22 0.0650 0.00 20.82 39.53 54.27 63.68 66.90 0.0700 0.00 19.79 37.59 51.65 60.63 63.72 0.0750 0.00 18.81 35.75 49.15 57.73 60.68 0.0800 0.00 17.89 34.01 46.78 54.96 57.78 0.0850 0.00 17.02 32.37 44.52 52.32 55.00 0.0900 0.00 16.20 30.80 42.38 49.81 52.36 0.0950 0.00 15.41 29.31 40.34 47.41 49.85 0.1000 0.00 14.67 27.90 38.39 45.13 47.45(b) Explicit MethodFor simplicity, let us choose ∆x =0.1, r =1/2 so that005.0)(2=∆=∆kx r tsince k =1. We need the solution for only 0 ≤ x ≤ 0.5 due to the fact that the problem is symmetric with respect to x =0.5. Notice that the value of Φ(0,0) and Φ(1,0) are taken as the average of 0 and 100.t ∆x 0.00 0.10 0.20 0.30 0.40 0.50 ------------------------------------------------- 0.0000 50.00 100.00 100.00 100.00 100.00 100.00 0.0050 0.00 75.00 100.00 100.00 100.00 100.00 0.0100 0.00 50.00 87.50 100.00 100.00 100.00 0.0150 0.00 43.75 75.00 93.75 100.00 100.00 0.0200 0.00 37.50 68.75 87.50 96.88 100.00 0.0250 0.00 34.38 62.50 82.81 93.75 96.88 0.0300 0.00 31.25 58.59 78.12 89.84 93.75 0.0350 0.00 29.30 54.69 74.22 85.94 89.84 0.0400 0.00 27.34 51.76 70.31 82.03 85.94 0.0450 0.00 25.88 48.83 66.89 78.12 82.03 0.0500 0.00 24.41 46.39 63.48 74.46 78.12 0.0550 0.00 23.19 43.95 60.42 70.80 74.46 0.0600 0.00 21.97 41.81 57.37 67.44 70.80 0.0650 0.00 20.90 39.67 54.63 64.09 67.44 0.0700 0.00 19.84 37.77 51.88 61.04 64.09 0.0750 0.00 18.88 35.86 49.40 57.98 61.04 0.0800 0.00 17.93 34.14 46.92 55.22 57.98 0.0850 0.00 17.07 32.42 44.68 52.45 55.22 0.0900 0.00 16.21 30.88 42.44 49.95 52.45 0.0950 0.00 15.44 29.33 40.41 47.45 49.95 0.1000 0.00 14.66 27.92 38.39 45.18 47.45(c) Implicit MethodLet us choose ∆x =0.1, r =1 so that ∆t =0.01.t ∆x 0.00 0.10 0.20 0.30 0.40 0.50 ------------------------------------------------- 0.0000 50.00 100.00 100.00 100.00 100.00 100.00 0.0100 0.00 59.81 89.23 97.10 99.17 99.59 0.0200 0.00 40.18 71.50 88.92 95.77 97.47 0.0300 0.00 32.96 60.34 79.30 89.59 92.68 0.0400 0.00 28.33 52.97 71.30 82.31 85.95 0.0500 0.00 25.06 47.28 64.41 75.09 78.70 0.0600 0.00 22.46 42.56 58.30 68.27 71.68 0.0700 0.00 20.25 38.46 52.82 61.98 65.13 0.0800 0.00 18.32 34.82 47.87 56.23 59.11 0.0900 0.00 16.59 31.54 43.40 51.00 53.61 0.1000 0.00 15.03 28.59 39.34 46.24 48.62The temperature profiles at ∆t =0.1xt e m p e r a t u r eFinite Differencing of Hyperbolic PDE’sConsider a simple example of a hyperbolic partial differential (or wave) equation with one spatial independent variable 22222tx u ∂Φ∂=∂Φ∂, (23) where u is the speed of the wave. The equivalent finite deference approximation is2)()1,(),(2)1,()(),1(),(2),1(t j i j i j i x j i j i j i u ∆−Φ+Φ−+Φ=∆+Φ+Φ−−Φ. (24) where x =i ∆x , i =1,2,3,…,n, t =j ∆t , j =1,2,…. In (24), we use the central difference formula for the derivatives with respective to t as well as with respect to x . If we let2⎟⎠⎞⎜⎝⎛∆∆=x t u r , (25) Eq. (24) could be written as)1,()],1(),1([),()1(2)1,(−Φ−−Φ++Φ+Φ−=+Φj i j i j i r j i r j i . (26) If we choose r = 1, Eq. (26) becomes)1,(),1(),1()1,(−Φ−−Φ++Φ=+Φj i j i j i j i . (27)(26)(28) (29)(30) (31) (30)(31)(32)[Example]Solution(33)(26)(34)(34)(35)(34)(35)II(33)Table IFigure IReferences1. "Numerical Techniques in Electromagnetics," by Matthew and Sadiku, CRC Press,Inc. (1992)2. “Applied Numerical Analysis,” by C. F. Gerald and P. O. Wheatley, AddisionWesley Longman, Inc. (1997)3. “High Performance Computing,” by Kelvin Dowd and C. R. Severance, O’Reillyand Associates, Inc. (1998)。
DID双重差分回归教学文案
• Note that underlying ‘levels’ of outcomes are not important (return to this in the regression equation)
• If the intervention occurs in an area with a different trend, will under/over state the treatment effect
• In this example, suppose intervention occurs in area with faster falling Y
14
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
Before After
Change Change
Difference
Group 1 β0+ β1 (Treat)11
Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
12
Basic Econometric Model
• Data varies by
– state (i) – time (t) – Outcome is Yit
• Only two periods • Intervention will occur in a group of
双向固定效应和双重差分ppt课件
Near universal agreement in results
10% increase in price reduces demand by 4% Change in smoking evenly split between
Reductions in number of smokers Reductions in cigs/day among remaining smokers
Rates differ by type of alcohol, alcohol content Nearly all cigarettes taxed the same
4
Current excise tax rates
Cigarettes
Low: SC($0.07), MO ($0.17), VA($0.30) High: RI ($3.46), NY ($2.75); NJ($2.70) Average of $1.32 across states Average in tobacco producing states: $0.40 Average in non-tobacco states, $1.44 Average price per pack is $5.12
permanent differences between groups vt – time fixed effects. Impacts common to
all groups but vary by year εit -- idiosyncratic error
3
Excises taxes on poor health
10
Taxes now an integral part of antismoking campaigns
teen role models英语作文
teen role models英语作文全文共10篇示例，供读者参考篇1Hey guys, today I want to talk to you about teen role models! Role models are people who we look up to and want to be like. They inspire us to be our best selves and show us that anything is possible if we work hard.One awesome teen role model is Malala Yousafzai. She is a Pakistani activist for female education and the youngest Nobel Prize laureate. Malala was just a teenager when she was shot by the Taliban for speaking out about the importance of education for girls. Instead of giving up, Malala continued to fight for what she believed in and now she is a global advocate for girls' education.Another cool teen role model is Greta Thunberg. She is a Swedish environmental activist who started the#FridaysForFuture movement, where students skip school to protest for climate action. Greta has spoken at the United Nations and inspired millions of young people around the world to take action against climate change.There are also teen role models in sports, like Simone Biles, who is an amazing gymnast and has won multiple Olympic gold medals. She shows us that with hard work and dedication, we can achieve our dreams.It's important to have role models to look up to, because they can motivate us to be the best version of ourselves. They show us that age is just a number and that we can make a difference in the world, no matter how young we are.So, who are your teen role models? What inspires you about them? Let me know in the comments below! Thanks for reading and remember, you can be a role model too!篇2Teen role models are like super cool heroes in real life! They are the ones who inspire us to be our best selves and show us that anything is possible if we work hard and follow our dreams. In this article, I want to talk about some of my favorite teen role models and why they are so awesome.First up, we have Greta Thunberg. She's only 16 years old, but she's already making a big impact on the world. Greta is a climate change activist who has been speaking out about the need to protect our planet and take action to stop globalwarming. She's not afraid to stand up to world leaders and demand change, and her passion and determination are truly inspiring.Next, we have Malala Yousafzai. She's also 16 years old, and she's a champion for girls' education around the world. Malala was shot by the Taliban when she was just a teenager, but she didn't let that stop her from fighting for what she believes in. She's won the Nobel Peace Prize and continues to be a powerful voice for girls' rights.And then there's Ryan Hickman, who is 11 years old and runs his own recycling business. He started collecting recyclables when he was just a toddler, and now he's turned his passion for the environment into a successful business. Ryan shows us that it's never too early to start making a difference in the world.These teen role models remind us that age is just a number, and that we all have the power to make a positive impact on the world. They inspire us to be brave, to speak up for what we believe in, and to never give up on our dreams. Let's all strive to be like them and make the world a better place for everyone!篇3Hey guys! Today I want to talk about teen role models. Teen role models are awesome people who inspire us and show us how to be our best selves. They can be celebrities, athletes, activists, or just regular teens who are doing great things in their communities.One of my favorite teen role models is Greta Thunberg. She's a climate change activist who has been speaking out about the importance of taking care of our planet. She's not afraid to stand up for what she believes in, even when people try to bring her down. Greta is showing us that no matter how young you are, you can make a big difference in the world.Another cool teen role model is Malala Yousafzai. She's a Pakistani activist who fights for girls' education and rights. Malala was even shot by the Taliban for speaking out, but she didn't let that stop her. She's won a Nobel Peace Prize and continues to inspire people all over the world.Closer to home, there are plenty of teen role models in our own communities. They might be classmates who excel in school, teammates who work hard in sports, or friends who volunteer to help others. These teens show us that we can make a positive impact right where we are.Being a teen role model doesn't mean you have to be famous or do something huge. It can be as simple as being kind, standing up for what's right, and being a good friend. We can all be role models in our own way.So let's look up to these amazing teens and learn from them. Let's be the best versions of ourselves and make a difference in the world, just like they do. Let's follow their lead and be awesome teen role models too!Thanks for listening, guys! Let's go out there and be the change we want to see in the world. Go teen role models!篇4Hey guys, today I want to talk about teen role models. Teen role models are so cool because they show us how to be awesome and do great things. They inspire us to be our best selves and make the world a better place.One of my favorite teen role models is Greta Thunberg. She is only 16 years old but she is already making a huge impact on the world. She cares a lot about the environment and is fighting to stop climate change. Greta is brave and speaks up for what she believes in, even when people try to bring her down. Sheshows us that no matter how old you are, you can make a difference.Another awesome teen role model is Malala Yousafzai. She is from Pakistan and when she was just a teenager, she was shot by the Taliban for speaking out about girls' education. But that didn't stop her. Malala kept fighting for what she believed in and won the Nobel Peace Prize when she was only 17. She is such a strong and inspiring girl who shows us that we should never give up on our dreams.There are so many other amazing teen role models out there, like Emma Gonzalez who is fighting for gun control, and Zendaya who is breaking boundaries in the entertainment industry. These teens show us that we can achieve anything we set our minds to, no matter how old we are.So let's look up to these awesome teen role models and follow their example. Let's be kind, brave, and stand up for what we believe in. Let's make the world a better place, just like they are doing. Let's show everyone that teens can change the world! Thanks for listening, guys. Bye!篇5Teen role models are people who inspire us to be our best selves and make a positive impact on the world around us. They show us that with hard work, dedication, and a positive attitude, we can achieve our goals and make a difference in the lives of others.One of my favorite teen role models is Malala Yousafzai. She is a Pakistani activist for female education and the youngest Nobel Prize laureate. Despite facing threats to her own life, Malala has continued to fight for the rights of girls to receive an education. Her bravery and determination are truly inspiring, and she reminds us that we should never give up on our dreams, no matter how difficult the circumstances may be.Another teen role model that I look up to is Greta Thunberg. She is a Swedish environmental activist who has gained international recognition for her efforts to raise awareness about climate change. Greta has shown us that young people have a powerful voice and can make a difference in the fight against environmental destruction. Her passion and commitment to creating a greener future for all of us are truly admirable.In addition to Malala and Greta, there are many other teen role models who are making a difference in their communities and beyond. From artists and musicians to athletes and scientists,there are countless young people who are using their talents and passions to inspire others and bring about positive change.As teenagers, we have the power to shape the future and make a difference in the world. By looking up to teen role models like Malala and Greta, we can learn valuable lessons about perseverance, compassion, and the importance of standing up for what we believe in. Let's follow in their footsteps and strive to be the best versions of ourselves, making a positive impact on the world around us.篇6Hey guys, today I want to talk about teen role models! Teen role models are super cool people who we look up to and want to be like when we grow up. They can be famous people, like singers or athletes, or even just older kids at our school.One of my favorite teen role models is Malala Yousafzai. She's a teenage girl from Pakistan who stood up for girls' rights to education, even after being shot by the Taliban. Malala is so brave and determined, and she's shown me that anyone, no matter how young, can make a difference in the world.Another awesome teen role model is Greta Thunberg. She's a teenage climate activist from Sweden who has inspired kids allover the world to join the fight against climate change. Greta is proof that you're never too young to speak up about important issues and try to make a change.Closer to home, I look up to the older kids at my school who are kind, inclusive, and hardworking. They show me that being a good student and a good friend is important, and that it's cool to be yourself and follow your passions.So, let's all try to be like our teen role models – brave, determined, and kind. Let's stand up for what we believe in and work hard to make the world a better place. Remember, you're never too young to be a role model to someone else!篇7Title: My Teen Role ModelsHey guys, today I want to talk about teen role models! Role models are people we look up to and admire because they inspire us to be better and do great things. I have a few teen role models that I really look up to and want to share with you.First up, we have Malala Yousafzai. She is a super brave teenager who stood up for girls' education in Pakistan, even after she was shot by the Taliban. I think she is amazing because shenever gave up on her beliefs and fought for what she thought was right. She even won the Nobel Peace Prize! Malala shows us that we should never be afraid to speak up for what we believe in.Next, there's Greta Thunberg. She is a young environmental activist who has been speaking out about climate change and urging world leaders to take action. Greta is so passionate about protecting our planet, and she has inspired so many people to join the fight against climate change. She is living proof that young people can make a big difference in the world.Another one of my teen role models is Zendaya. She is a talented actress and singer who uses her platform to speak out about important issues like racial inequality and mental health. Zendaya is not only a great role model for her acting skills, but also for her advocacy work. She shows us that it's important to use our voice to stand up for what is right.Last but not least, I admire LeBron James. He is a professional basketball player who is not only amazing on the court, but also off the court. LeBron has done a lot of charity work and has started his own school for underprivileged kids. He is a great example of using your success to help others and make a positive impact in your community.In conclusion, teen role models are important because they show us that age is just a number and that we can make a difference no matter how young we are. I hope you guys have some teen role models that inspire you too! Let's all work together to make the world a better place. Thanks for listening!篇8Being a teenager is not easy. We often feel lost, confused, and unsure about ourselves. That's why it's important to have role models to look up to and learn from. Role models are people who inspire us, who show us the way, and who set a good example for us to follow. In this article, I want to talk about some amazing teen role models who have made a difference in the world.One of my favorite teen role models is Malala Yousafzai. She is a Pakistani activist for girls' education who became the youngest Nobel Prize laureate at the age of 17. Malala was shot in the head by a Taliban gunman in 2012 for her advocacy of girls' education, but she survived and continued to speak out for the rights of all children to receive an education. Malala's courage and determination in the face of adversity inspire me to stand up for what I believe in and to never give up on my dreams.Another teen role model that I admire is Greta Thunberg. She is a Swedish environmental activist who gained international recognition for her efforts to combat climate change. Greta started the "Fridays for Future" movement, where students around the world strike from school to demand action on climate change. Greta's passion for protecting the planet and her ability to speak truth to power motivate me to take action and make a difference in my community.I also look up to Zendaya, a talented actress and singer who uses her platform to advocate for social justice and representation in the entertainment industry. Zendaya's authenticity, compassion, and commitment to diversity inspire me to be true to myself and to stand up for what is right.Finally, I want to mention Emma Gonzalez, a survivor of the Marjory Stoneman Douglas High School shooting in Parkland, Florida, who co-founded the gun-control advocacy group "Never Again MSD." Emma's advocacy for gun control laws and her resilience in the face of tragedy show me that young people have the power to make a difference and create change in the world.In conclusion, teen role models like Malala Yousafzai, Greta Thunberg, Zendaya, and Emma Gonzalez inspire me to be a better person, to stand up for what I believe in, and to make apositive impact on the world. I am grateful for their example and I hope to follow in their footsteps as I navigate the challenges of being a teenager in today's world.篇9Hey guys, today I want to talk about teen role models! Role models are people who inspire us and show us how to be our best selves. They can be famous people, like actors or athletes, or they can be people we know personally, like teachers or family members.One teen role model that I look up to is Malala Yousafzai. She is a Pakistani activist who fights for girls' education. Even though she faced dangers and obstacles, she never gave up on her beliefs. Malala shows us that no matter how young we are, we can make a difference in the world.Another teen role model is Greta Thunberg. She is a Swedish activist who speaks out about climate change. Greta started a global movement called Fridays for Future, where students around the world strike from school to demand action on climate change. Greta reminds us that we can all be advocates for causes we care about.Closer to home, my older sister is also a role model for me. She works hard in school and always helps me with my homework. She is kind and caring to everyone she meets, and she shows me how to be a good friend and sister.So, guys, let's remember that we can all be role models for others. Whether it's standing up for what we believe in, working hard in school, or being kind to others, we can all make a positive impact on the world around us. Let's be the best versions of ourselves and inspire others to do the same!篇10Teen role models are super cool and important for us to look up to. They can inspire us to be our best selves and show us that anything is possible if we work hard and believe in ourselves. I want to talk about some awesome teen role models who are making a big impact in the world.First up is Malala Yousafzai. She's only a teenager, but she's already achieved so much. Malala is a champion for girls' education and human rights. She stood up to the Taliban in Pakistan and fought for her right to go to school. She even won the Nobel Peace Prize for her bravery! Malala's story reminds usthat we should never give up on our dreams, no matter what challenges we face.Next, we have Greta Thunberg. This Swedish teen is a passionate climate activist and has inspired millions of people around the world to take action against climate change. Greta started a movement called Fridays for Future, where students skip school to protest for climate action. She has met with world leaders and spoken at the United Nations to demand action on climate change. Greta's determination and courage show us that we can all make a difference, no matter our age.And how can we forget about Zendaya? She's not just a talented actress and singer, but also a role model for teens everywhere. Zendaya uses her platform to speak out about important issues like diversity and body positivity. She's not afraid to be herself and encourages others to do the same. Zendaya shows us that it's okay to be different, and that we should embrace who we are.These teen role models are just a few examples of the amazing young people making a difference in the world. They inspire us to be brave, kind, and fearless in pursuing our passions. Let's all strive to be the best versions of ourselves and make apositive impact on the world, just like these teen role models do every day.。
双向固定效应和双重差分
Generated from a theoretical model of consumer choice
Thought by economists to be fairly universal in application
Simple research design
Prices typically changed due to state/federal tax hikes
States with changes are ‘treatment’ States without changes are control
vt – time fixed effects. Impacts common to all groups but vary by year
εit -- idiosyncratic error
.
3
Excises taxes on poor health
Alcohol and cigarettes are taxed at the federal, state and local level
Beer, $0.02 a can Liquor, $13.50 per 100 proof gallon (50% alcohol), or,
$2.14/750 ml bottle of 80 proof liquor Total taxes on cigarettes are such that in NYC, you spend
Medical/psychological view – certain goods not subject to these laws
多市场接触和市场竞争强度
市场接触增强，但是航空公司惧怕对手在其他市场的力量，害怕在一个市 场的竞争会带来另外市场的报复，航空公司在并购后会选择结盟，亦即不 会雄心勃勃地竞争，而会选择“相互容忍”，最终形成低频率服务。
为了测量无法被固定效用模型计量的不同特点 ，我们将使用以下的控制变量： a、市场大小：每个终端人均收入和人口的几何 平均数来计量 b、市场集中度：乘客的HHI指数 c、时间变量：控制相应的异质
四、数据处理
• 我们构建模型的重点将会放在具体航空公司— 市场的具体测量上。 • 我们将使用两个机场—市场水平来测量多市场 接触：一个是抓住多市场接触的绝对程度（表示 为AMMC），一个是测量多市场接触在总体营运 中的相对值（我们将用RMMC来表示）。
为什么是服务频率
• 首先我们来明确为什么要选择“服务频率” 作为我们非价格特征的指标 • 先直观地感受理解下，您选择飞机而不是火 车是否是因为它的快捷呢？如果飞机晚点， 或是准点（整整晚点24个小时），您的旅行 费用是不是相对增加了呢？
•
表示和j航空公司在提供直飞服务上 竞争的i航空公司航班的数量
则有：
•
表示i航空公司在其整个市场上提 供的航班数量
则K市场上i航空公司相对多市场接触可以表示 为：
• •
表示特定航班在K市场的数量 表示航空公司i在这个市场出现的次数
则某一个既定市场绝对多市场接触的平均值（ 这个测量也在1994年被Evans和Kessides使 用过）
固定效应模型 fixed effects model
固定效应模型是指实验结果只想比较每一自变项 之特定类目或类别间的差异及其与其他自变项之特定 类目或类别间交互作用效果，而不想依此推论到同一 自变项未包含在内的其他类目或类别的实验设计。
difference in differences模型
difference in differences模型差异差异模型（Difference-in-Differences Model）差异差异模型是一种经济学中常用的研究方法，用于评估政策或干预措施对特定群体或区域的影响。
它通过比较政策或干预前后的差异差异来确定政策的效果，从而消除其他潜在因素的干扰。
在差异差异模型中，研究者通常选择两个群体或区域进行比较。
其中一个群体或区域接受政策或干预措施，而另一个群体或区域不接受。
通过比较这两个群体或区域在政策实施前后的差异，可以推断出政策对研究对象的影响。
为了实施差异差异模型，研究者需要收集政策实施前后两个群体或区域的数据。
这些数据可以包括经济指标、社会指标、行为数据等。
收集到的数据可以通过统计分析方法进行处理和分析，从而得出结论。
差异差异模型的一个重要前提是平行趋势假设。
平行趋势假设要求政策实施前后的两个群体或区域在除了政策影响之外的其他因素上具有相同的趋势。
如果平行趋势假设成立，那么政策实施前后的差异可以被归因于政策效果，否则可能存在其他因素的干扰。
差异差异模型的优点是可以综合考虑个体和时间的效应，减少了其他因素的干扰。
它在实证研究中得到了广泛应用，例如评估政府政策、社会计划和医疗干预的效果等。
然而，差异差异模型也存在一些限制。
首先，它的结果可能受到数据的选择和处理方法的影响。
其次，由于实施差异差异模型需要进行对比群体或区域的选择，可能存在选择偏差。
此外，平行趋势假设的成立也需要有合理的理论基础和足够的数据支持。
综上所述，差异差异模型是一种有力的研究方法，可以评估政策或干预措施的效果。
它的实施步骤包括选择比较群体或区域、收集数据、进行统计分析和得出结论。
然而，研究者在应用差异差异模型时需要注意一些限制和假设的前提。
通过合理运用差异差异模型，可以为政策制定和社会实践提供有益的参考依据。
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Y
Estimated treatment Yc1
Yt1
Yc2
True treatment effect
control
Yt2 treatment t1 t2
True Treatment Effect
time
12
Basic Econometric Model
• Data varies by
– state (i) – time (t) – Outcome is Yit
6
Y Treatment effect= (Yt2-Yt1) – (Yc2-Yc1) Yc1
Yt1
Yc2
Yt2
control treatment t1 t2
time
7
Difference in Difference
Before Change
Group 1 (Treat) Group 2 (Control) Difference Yt1 Yc1
• Use time series of untreated group to establish what would have occurred in the absence of the intervention • Key concept: can control for the fact that the intervention is more likely in some types of states
– If using time series, estimate Yt1 – Yt2difference models
• Basic two-way fixed effects model
– Cross section and time fixed effects
• Only two periods • Intervention will occur in a group of observations (e.g. states, firms, etc.)
13
• Three key variables
– Tit =1 if obs i belongs in the state that will eventually be treated – Ait =1 in the periods when treatment occurs – TitAit -- interaction term, treatment states after the intervention
After Change
Difference
β0+ β1+ β2+ β3 ΔYt = β2 + β3 β0 + β 2 ΔYc = β2 ΔΔY = β3
15
More general model
• Data varies by
– state (i) – time (t) – Outcome is Yit
• Yit = β0 + β3 TitAit + ui + λt + εit
17
What is nice about the model
• Suppose interventions are not random but systematic
– Occur in states with higher or lower average Y – Occur in time periods with different Y’s
• Year effects
– Capture differences over time that are common to all groups
19
Questions to ask?
• What parameter is identified by the quasiexperiment? Is this an economically meaningful parameter? • What assumptions must be true in order for the model to provide and unbiased estimate of β3? • Do the authors provide any evidence supporting these assumptions?
9
Y
Yc1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2 Yt1
control Yt2 treatment t1 t2 Treatment Effect
time
10
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups • If the intervention occurs in an area with a different trend, will under/over state the treatment effect • In this example, suppose intervention occurs in area with faster falling Y
• Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
14
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
Before Change
Group 1 (Treat) Group 2 (Control) Difference β0 + β1 β0
• Many periods • Intervention will occur in a group of states but at a variety of times
16
• ui is a state effect • vt is a complete set of year (time) effects • Analysis of covariance model
• Cross-sectional and time series data • One group is ‘treated’ with intervention • Have pre-post data for group receiving intervention • Can examine time-series changes but, unsure how much of the change is due to secular changes
• This is captured by the inclusion of the state/time effects – allows covariance between
– ui and TitAit – λt and TitAit
18
• Group effects
– Capture differences across groups that are constant over time
Difference in Difference Models
1
What is DID
• How can we estimate the effects of higher education reform in China? • Yang and Chen (2009)
2
Problem set up
3
Y True effect = Yb-Ya Estimated effect =Yt2-Yt1
Yt1
Ya Yb Yt2
t1
ti
t2
time
4
• Intervention occurs at time period t1 • True effect of law
– Ya – Yb
• Only have data at t1 and t2
20
After Change
Yt2 Yc2
Difference ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment • In this example, Y falls by Yc2-Yc1 even without the intervention • Note that underlying ‘levels’ of outcomes are not important (return to this in the regression equation)