更改

'''Difference in differences''' ('''DID'''<ref>{{cite journal |last=Abadie |first=A. |year=2005 |title=Semiparametric difference-in-differences estimators |journal=[[Review of Economic Studies]] |volume=72 |issue=1 |pages=1–19 |doi=10.1111/0034-6527.00321 |citeseerx=10.1.1.470.1475 }}</ref> or '''DD'''<ref name=Bertrand>{{cite journal |last1=Bertrand |first1=M. |last2=Duflo |first2=E. |author-link2=Esther Duflo |last3=Mullainathan |first3=S. |year=2004 |title=How Much Should We Trust Differences-in-Differences Estimates? |journal=[[Quarterly Journal of Economics]] |volume=119 |issue=1 |pages=249–275 |doi=10.1162/003355304772839588 |s2cid=470667 |url=http://www.nber.org/papers/w8841.pdf }}</ref>) is a [[statistics|statistical technique]] used in [[econometrics]]  and [[quantitative research]] in the social sciences that attempts to mimic an [[experiment|experimental research design]] using [[observational study|observational study data]], by studying the differential effect of a treatment on a 'treatment group' versus a '[[control group]]' in a [[natural experiment]].<ref>{{cite book |last1=Angrist |first1=J. D. |last2=Pischke |first2=J. S. |year=2008 |title=Mostly Harmless Econometrics: An Empiricist's Companion |publisher=Princeton University Press |isbn=978-0-691-12034-8 |pages=227–243 |url=https://books.google.com/books?id=ztXL21Xd8v8C&pg=PA227 }}</ref> 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., [[regression to the mean|mean regression]], [[Reverse causality bias|reverse causality]] and [[omitted variable bias]]).

'''Difference in differences''' ('''DID'''<ref>{{cite journal |last=Abadie |first=A. |year=2005 |title=Semiparametric difference-in-differences estimators |journal=[[Review of Economic Studies]] |volume=72 |issue=1 |pages=1–19 |doi=10.1111/0034-6527.00321 |citeseerx=10.1.1.470.1475 }}</ref> or '''DD'''<ref name=Bertrand>{{cite journal |last1=Bertrand |first1=M. |last2=Duflo |first2=E. |author-link2=Esther Duflo |last3=Mullainathan |first3=S. |year=2004 |title=How Much Should We Trust Differences-in-Differences Estimates? |journal=[[Quarterly Journal of Economics]] |volume=119 |issue=1 |pages=249–275 |doi=10.1162/003355304772839588 |s2cid=470667 |url=http://www.nber.org/papers/w8841.pdf }}</ref>) is a [[statistics|statistical technique]] used in [[econometrics]]  and [[quantitative research]] in the social sciences that attempts to mimic an [[experiment|experimental research design]] using [[observational study|observational study data]], by studying the differential effect of a treatment on a 'treatment group' versus a '[[control group]]' in a [[natural experiment]].<ref>{{cite book |last1=Angrist |first1=J. D. |last2=Pischke |first2=J. S. |year=2008 |title=Mostly Harmless Econometrics: An Empiricist's Companion |publisher=Princeton University Press |isbn=978-0-691-12034-8 |pages=227–243 |url=https://books.google.com/books?id=ztXL21Xd8v8C&pg=PA227 }}</ref> 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., [[regression to the mean|mean regression]], [[Reverse causality bias|reverse causality]] and [[omitted variable bias]]).

双重差分法（DID 或 DD）是一种用于计量经济学和社会科学定量研究的统计技术，它试图利用观察性研究数据来模拟实验研究设计，通过研究自然实验中的“治疗组”和“对照组”之间的差异性效果。它通过比较治疗组和对照组的结果变量在一段时间的平均变化，计算出治疗（即解释变量或自变量）对结果（即反应变量或因变量）的影响。虽然该方法旨在减轻外部因素和选择偏差的影响，但取决于治疗组的选择方式，该方法仍可能受到某些偏差的影响（例如，均值回归、反向因果关系和遗漏变量偏差）。

双重差分法（DID 或 DD）是一种用于计量经济学和社会科学定量研究的统计技术，它试图利用观察性研究数据来模拟实验研究设计，通过研究自然实验中的“治疗组”和“对照组”之间的差异性效果。它通过比较治疗组和对照组的结果变量在一段时间的平均变化，计算出治疗（即解释变量或<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 自变量Independent variable</font></nowiki><nowiki>'''</nowiki>）对结果（即反应变量或因变量）的影响。虽然该方法旨在减轻外部因素和选择偏差的影响，但取决于治疗组的选择方式，该方法仍可能受到某些偏差的影响（例如，均值回归、反向因果关系和遗漏变量偏差）。

In contrast to a [[time series|time-series estimate]] of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses [[panel data]] to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.

In contrast to a [[time series|time-series estimate]] of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses [[panel data]] to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.

与受试者治疗效果的时间序列估计（分析随时间变化的差异）或治疗效果的横截面估计（衡量治疗组和对照组之间的差异）不同，双重差分法使用面板数据来衡量治疗组和对照组的结果变量随时间变化的差异。

与受试者治疗效果的时间序列估计（分析随时间变化的差异）或治疗效果的横截面估计（衡量治疗组和对照组之间的差异）不同，双重差分法使用面板数据来衡量治疗组和对照组的结果变量随时间变化的差异。

= = 正式定义 = =  

= = 正式定义 = =  

Consider the model

Consider the model

考虑以下模型

考虑以下模型

: <math>y_{it} ~=~ \gamma_{s(i)} + \lambda_t + \delta I(\dots) + \varepsilon_{it}</math>

: <math>y_{it} ~=~ \gamma_{s(i)} + \lambda_t + \delta I(\dots) + \varepsilon_{it}</math>

: y_{it} ~=~ \gamma_{s(i)} + \lambda_t + \delta I(\dots) + \varepsilon_{it}

: y_{it} ~=~ \gamma_{s(i)} + \lambda_t + \delta I(\dots) + \varepsilon_{it}

 

:  

: y _ { it } ~ = ~ gamma _ { s (i)} + lambda _ t + delta i (dots) + varepsilon _ { it }

 

where <math>y_{it}</math> is the dependent variable for [[Sampling (statistics)|individual]] <math>i</math> and time <math>t</math>, <math>s(i)</math> is the group to which <math>i</math> belongs (i.e. the treatment or the control group), and <math> I(\dots) </math> is short-hand for the [[Dummy variable (statistics)|dummy variable]] equal to 1 when the event described in <math> (\dots) </math> is true, and 0 otherwise. In the plot of time versus <math>Y</math> by group, <math>\gamma_s</math> is the vertical intercept for the graph for <math>s</math>, and <math>\lambda_t</math> is the time trend shared by both groups according to the parallel trend assumption (see [[#Assumptions|Assumptions]] below). <math>\delta</math> is the treatment effect, and <math>\varepsilon_{it}</math> is the [[Errors and residuals in statistics|residual term]].

where <math>y_{it}</math> is the dependent variable for [[Sampling (statistics)|individual]] <math>i</math> and time <math>t</math>, <math>s(i)</math> is the group to which <math>i</math> belongs (i.e. the treatment or the control group), and <math> I(\dots) </math> is short-hand for the [[Dummy variable (statistics)|dummy variable]] equal to 1 when the event described in <math> (\dots) </math> is true, and 0 otherwise. In the plot of time versus <math>Y</math> by group, <math>\gamma_s</math> is the vertical intercept for the graph for <math>s</math>, and <math>\lambda_t</math> is the time trend shared by both groups according to the parallel trend assumption (see [[#Assumptions|Assumptions]] below). <math>\delta</math> is the treatment effect, and <math>\varepsilon_{it}</math> is the [[Errors and residuals in statistics|residual term]].

and suppose for simplicity that <math>s=1,2</math> and <math>t=1,2</math>. Note that <math>D_{st}</math> is not random; it just encodes how the groups and the periods are labeled. Then

and suppose for simplicity that <math>s=1,2</math> and <math>t=1,2</math>. Note that <math>D_{st}</math> is not random; it just encodes how the groups and the periods are labeled. Then

为简单起见，假设 s = 1,2， t = 1,2。请注意， d _ { st }不是随机的，它只是编码了组和时期的标记方式。那么

为简单起见，假设 s = 1,2， t = 1,2。请注意， d _ { st }不是随机的，它只是编码了组和时期的标记方式。那么

The [[Ordinary least squares#Assumptions|strict exogeneity assumption]] then implies that

The [[Ordinary least squares#Assumptions|strict exogeneity assumption]] then implies that

严格的<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 外生性假设Strict exogeneity assumption</font></nowiki><nowiki>'''</nowiki>则意味着

严格的<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 外生性假设Strict exogeneity assumption</font></nowiki><nowiki>'''</nowiki>则意味着

which can be interpreted as the treatment effect of the treatment indicated by <math>D_{st}</math>. Below it is shown how this estimator can be read as a coefficient in an ordinary least squares regression. The model described in this section is over-parametrized; to remedy that, one of the coefficients for the dummy variables can be set to 0, for example, we may set <math>\gamma_1 = 0</math>.

which can be interpreted as the treatment effect of the treatment indicated by <math>D_{st}</math>. Below it is shown how this estimator can be read as a coefficient in an ordinary least squares regression. The model described in this section is over-parametrized; to remedy that, one of the coefficients for the dummy variables can be set to 0, for example, we may set <math>\gamma_1 = 0</math>.

这可以解释为 D _ { st }所示的治疗效果。下面展示了如何将这个估计值解读为普通最小二乘回归中的系数。本节描述的模型是过度参数化的; 为了弥补这一点，可以将哑变量的一个系数设置为0，例如，我们可以设置 gamma _ 1 = 0。

这可以解释为 D _ { st }所示的治疗效果。下面展示了如何将这个估计值解读为普通最小二乘回归中的系数。本节描述的模型是过度参数化的; 为了弥补这一点，可以将哑变量的一个系数设置为0，例如，我们可以设置 gamma _ 1 = 0。

As illustrated to the right, the treatment effect is the difference between the observed value of ''y'' and what the value of ''y'' would have been with parallel trends, had there been no treatment. The Achilles' heel of DID is when something other than the treatment changes in one group but not the other at the same time as the treatment, implying a violation of the parallel trend assumption.

As illustrated to the right, the treatment effect is the difference between the observed value of ''y'' and what the value of ''y'' would have been with parallel trends, had there been no treatment. The Achilles' heel of DID is when something other than the treatment changes in one group but not the other at the same time as the treatment, implying a violation of the parallel trend assumption.

如右图所示，治疗效果是观察到的 y 值与未治疗的情况下y 值的平行趋势之间的差异。DID的致命缺点是当一组中治疗以外的某些因素发生了变化，而另一组在治疗的同时没有变化，这意味着违反了平行趋势假设。

如右图所示，治疗效果是观察到的 y 值与未治疗的情况下y 值的平行趋势之间的差异。DID的致命缺点是当一组中治疗以外的某些因素发生了变化，而另一组在治疗的同时没有变化，这意味着违反了平行趋势假设。

To guarantee the accuracy of the DID estimate, the composition of individuals of the two groups is assumed to remain unchanged over time. When using a DID model, various issues that may compromise the results, such as [[autocorrelation]]<ref>{{cite journal |first1=Marianne |last1=Bertrand |first2=Esther |last2=Duflo | first3=Sendhil | last3=Mullainathan |year=2004 |title=How Much Should We Trust Differences-In-Differences Estimates? |journal=[[Quarterly Journal of Economics]] |volume=119 |issue=1 |pages=249–275 |doi=10.1162/003355304772839588|s2cid=470667 |url=http://www.nber.org/papers/w8841.pdf }}</ref> and [[Ashenfelter dip]]s, must be considered and dealt with.

To guarantee the accuracy of the DID estimate, the composition of individuals of the two groups is assumed to remain unchanged over time. When using a DID model, various issues that may compromise the results, such as [[autocorrelation]]<ref>{{cite journal |first1=Marianne |last1=Bertrand |first2=Esther |last2=Duflo | first3=Sendhil | last3=Mullainathan |year=2004 |title=How Much Should We Trust Differences-In-Differences Estimates? |journal=[[Quarterly Journal of Economics]] |volume=119 |issue=1 |pages=249–275 |doi=10.1162/003355304772839588|s2cid=470667 |url=http://www.nber.org/papers/w8841.pdf }}</ref> and [[Ashenfelter dip]]s, must be considered and dealt with.

为了保证DID估计的准确性，假定两组个体的组成在一段时间内保持不变。在使用 DID 模型时，必须考虑和处理可能影响结果的各种问题，如自相关和 Ashenfelter 倾斜。

为了保证DID估计的准确性，假定两组个体的组成在一段时间内保持不变。在使用 DID 模型时，必须考虑和处理可能影响结果的各种问题，如自相关和 Ashenfelter 倾斜。

where <math>\widehat{E}(\dots \mid \dots )</math> stands for conditional averages computed on the sample, for example, <math>T=1</math> is the indicator for the after period, <math>S=0</math> is an indicator for the control group. Note that <math>\hat{\beta}_1</math> is an estimate of the counterfactual rather than the impact of the control group. The control group is often used as a proxy for the [[counterfactual]] (see, [[Synthetic control method]] for a deeper understanding of this point). Thereby, <math>\hat{\beta}_1</math> can be interpreted as the impact of both the control group and the intervention's (treatment's) counterfactual. Similarly, <math>\hat{\beta}_2</math>, due to the parallel trend assumption, is also the same differential between the treatment and control group in <math> T=1 </math>. The above descriptions should not be construed to imply the (average) effect of only  the control group, for <math>\hat{\beta}_1</math>, or only the difference of the treatment and control groups in the pre-period, for <math>\hat{\beta}_2</math>. As in [[David Card|Card]] and [[Alan Krueger|Krueger]], below, a first (time) difference of the outcome variable <math>(\Delta Y_i = Y_{i,1} - Y_{i,0})</math> eliminates the need for time-trend (i.e., <math>\hat{\beta}_1</math>) to form an unbiased estimate of <math>\hat{\beta}_3</math>, implying that <math>\hat{\beta}_1</math> is not actually conditional on the treatment or control group.<ref>{{cite journal |first1=David |last1=Card |first2=Alan B. |last2=Krueger |year=1994 |title=Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania |journal=[[American Economic Review]] |volume=84 |issue=4 |pages=772–793 |jstor=2118030 }}</ref> Consistently, a difference among the treatment and control groups would eliminate the need for treatment differentials (i.e., <math>\hat{\beta}_2</math>) to form an unbiased estimate of <math>\hat{\beta}_3</math>. This nuance is important to understand when the user believes (weak) violations of parallel pre-trend exist or in the case of violations of the appropriate counterfactual approximation assumptions given the existence of non-common shocks or confounding events.  To see the relation between this notation and the previous section, consider as above only one observation per time period for each group, then

where <math>\widehat{E}(\dots \mid \dots )</math> stands for conditional averages computed on the sample, for example, <math>T=1</math> is the indicator for the after period, <math>S=0</math> is an indicator for the control group. Note that <math>\hat{\beta}_1</math> is an estimate of the counterfactual rather than the impact of the control group. The control group is often used as a proxy for the [[counterfactual]] (see, [[Synthetic control method]] for a deeper understanding of this point). Thereby, <math>\hat{\beta}_1</math> can be interpreted as the impact of both the control group and the intervention's (treatment's) counterfactual. Similarly, <math>\hat{\beta}_2</math>, due to the parallel trend assumption, is also the same differential between the treatment and control group in <math> T=1 </math>. The above descriptions should not be construed to imply the (average) effect of only  the control group, for <math>\hat{\beta}_1</math>, or only the difference of the treatment and control groups in the pre-period, for <math>\hat{\beta}_2</math>. As in [[David Card|Card]] and [[Alan Krueger|Krueger]], below, a first (time) difference of the outcome variable <math>(\Delta Y_i = Y_{i,1} - Y_{i,0})</math> eliminates the need for time-trend (i.e., <math>\hat{\beta}_1</math>) to form an unbiased estimate of <math>\hat{\beta}_3</math>, implying that <math>\hat{\beta}_1</math> is not actually conditional on the treatment or control group.<ref>{{cite journal |first1=David |last1=Card |first2=Alan B. |last2=Krueger |year=1994 |title=Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania |journal=[[American Economic Review]] |volume=84 |issue=4 |pages=772–793 |jstor=2118030 }}</ref> Consistently, a difference among the treatment and control groups would eliminate the need for treatment differentials (i.e., <math>\hat{\beta}_2</math>) to form an unbiased estimate of <math>\hat{\beta}_3</math>. This nuance is important to understand when the user believes (weak) violations of parallel pre-trend exist or in the case of violations of the appropriate counterfactual approximation assumptions given the existence of non-common shocks or confounding events.  To see the relation between this notation and the previous section, consider as above only one observation per time period for each group, then

其中 widehat { e }(\dots \mid \dots)代表在样本上计算的条件平均值，例如，T = 1是后时期的指标，S = 0是对照组的指标。请注意，hat { beta }1是对反事实的估计，而不是对照组的影响。对照经常被用作<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 反事实+Counterfactual</font></nowiki><nowiki>'''</nowiki>的替代(见<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 合成控制方法+Syntheic control method</font></nowiki><nowiki>'''</nowiki>，以便更深入地理解这一点)。因此，hat { beta } _ 1可以被解释为对照组和干预(治疗)的反事实的影响。同样，由于平行趋势假设，T= 1时，治疗组和对照组之间也存在相同的差异，即\hat{\beta}_2。上述描述不应该被解释为仅是对照组对\hat{\beta}_1的(平均)效应，或者仅仅是治疗组和对照组在前期的差异，hat { beta } _ 2。正如 Card 和 Krueger 所说，结果变量的一阶差分(Delta y _ i = y _ { i，1}-y _ { i，0})消除了对时间趋势（即 hat { beta } _ 1）形成无偏估计的需要（hat { beta } _ 3），这意味着 hat { beta } _ 1实际上并不取决于治疗组或对照组。一致地，治疗组和对照组之间的差异将消除治疗差异(即，hat { beta } _ 2)的需要，进而形成对 hat { beta } _ 3的无偏估计。这种细微差别对于了解用户何时认为（微弱）违反平行预趋势或在存在非共同冲击或混杂事件的情况下违反适当的反事实近似假设是非常重要的。为了看清该符号与前面章节之间的关系，如上所述，考虑小组每个时间段只有一个观察值，那么

其中 widehat { e }(\dots \mid \dots)代表在样本上计算的条件平均值，例如，T = 1是后时期的指标，S = 0是对照组的指标。请注意，hat { beta }1是对反事实的估计，而不是对照组的影响。对照经常被用作<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 反事实+Counterfactual</font></nowiki><nowiki>'''</nowiki>的替代(见<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 合成控制方法+Syntheic control method</font></nowiki><nowiki>'''</nowiki>，以便更深入地理解这一点)。因此，hat { beta } _ 1可以被解释为对照组和干预(治疗)的反事实的影响。同样，由于平行趋势假设，T= 1时，治疗组和对照组之间也存在相同的差异，即\hat{\beta}_2。上述描述不应该被解释为仅是对照组对\hat{\beta}_1的(平均)效应，或者仅仅是治疗组和对照组在前期的差异，hat { beta } _ 2。正如 Card 和 Krueger 所说，结果变量的一阶差分(Delta y _ i = y _ { i，1}-y _ { i，0})消除了对时间趋势（即 hat { beta } _ 1）形成无偏估计的需要（hat { beta } _ 3），这意味着 hat { beta } _ 1实际上并不取决于治疗组或对照组。一致地，治疗组和对照组之间的差异将消除治疗差异(即，hat { beta } _ 2)的需要，进而形成对 hat { beta } _ 3的无偏估计。这种细微差别对于了解用户何时认为（微弱）违反平行预趋势或在存在非共同冲击或混杂事件的情况下违反适当的反事实近似假设是非常重要的。为了看清该符号与前面章节之间的关系，如上所述，考虑小组每个时间段只有一个观察值，那么

But this is the expression for the treatment effect that was given in the [[#Formal Definition|formal definition]] and in the above table.

But this is the expression for the treatment effect that was given in the [[#Formal Definition|formal definition]] and in the above table.

但这是正式定义和上表中给出的治疗效果的表达式。

但这是正式定义和上表中给出的治疗效果的表达式。

Consider one of the most famous DID studies, the [[David Card|Card]] and [[Alan Krueger|Krueger]] article on [[minimum wage]] in [[New Jersey]], published in 1994.<ref>{{cite journal |first1=David |last1=Card |first2=Alan B. |last2=Krueger |year=1994 |title=Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania |journal=[[American Economic Review]] |volume=84 |issue=4 |pages=772–793 |jstor=2118030 }}</ref> Card and Krueger compared [[Unemployment|employment]] in the [[fast food]] sector in New Jersey and in [[Pennsylvania]], in February 1992 and in November 1992, after New Jersey's minimum wage rose from $4.25 to $5.05 in April 1992. Observing a change in employment in New Jersey only, before and after the treatment, would fail to control for [[Omitted-variable bias|omitted variables]] such as weather and macroeconomic conditions of the region. By including Pennsylvania as a control in a difference-in-differences model, any bias caused by variables common to New Jersey and Pennsylvania is implicitly controlled for, even when these variables are unobserved. Assuming that New Jersey and Pennsylvania have parallel trends over time, Pennsylvania's change in employment can be interpreted as the change New Jersey would have experienced, had they not increased the minimum wage, and vice versa. The evidence suggested that the increased minimum wage did not induce a decrease in employment in New Jersey, contrary to what some economic theory would suggest. The table below shows Card & Krueger's estimates of the treatment effect on employment, measured as [[Full-time equivalent|FTEs (or full-time equivalents)]]. Card and Krueger estimate that the $0.80 minimum wage increase in New Jersey led to a 2.75 FTE increase in employment.

Consider one of the most famous DID studies, the [[David Card|Card]] and [[Alan Krueger|Krueger]] article on [[minimum wage]] in [[New Jersey]], published in 1994.<ref>{{cite journal |first1=David |last1=Card |first2=Alan B. |last2=Krueger |year=1994 |title=Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania |journal=[[American Economic Review]] |volume=84 |issue=4 |pages=772–793 |jstor=2118030 }}</ref> Card and Krueger compared [[Unemployment|employment]] in the [[fast food]] sector in New Jersey and in [[Pennsylvania]], in February 1992 and in November 1992, after New Jersey's minimum wage rose from $4.25 to $5.05 in April 1992. Observing a change in employment in New Jersey only, before and after the treatment, would fail to control for [[Omitted-variable bias|omitted variables]] such as weather and macroeconomic conditions of the region. By including Pennsylvania as a control in a difference-in-differences model, any bias caused by variables common to New Jersey and Pennsylvania is implicitly controlled for, even when these variables are unobserved. Assuming that New Jersey and Pennsylvania have parallel trends over time, Pennsylvania's change in employment can be interpreted as the change New Jersey would have experienced, had they not increased the minimum wage, and vice versa. The evidence suggested that the increased minimum wage did not induce a decrease in employment in New Jersey, contrary to what some economic theory would suggest. The table below shows Card & Krueger's estimates of the treatment effect on employment, measured as [[Full-time equivalent|FTEs (or full-time equivalents)]]. Card and Krueger estimate that the $0.80 minimum wage increase in New Jersey led to a 2.75 FTE increase in employment.

关于DID，最著名的研究之一便是 Card 和 Krueger 在1994年发表的关于新泽西州最低工资的文章。Card 和 Krueger 比较了1992年2月和1992年11月新泽西州最低工资从4.25美元上升到5.05美元之后，新泽西州和宾夕法尼亚州快餐部门的就业情况。仅在治疗前后观察新泽西州的就业情况变化，将无法控制一些<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 被忽略变量Omitted variables</font></nowiki><nowiki>'''</nowiki>，例如该地区的天气和宏观经济状况。通过将宾夕法尼亚州作为双重差分模型的对照，任何由新泽西州和宾夕法尼亚州的共同变量所引起的偏差都会被隐含的控制，即使这些变量是不可被观测到的。假设新泽西州和宾夕法尼亚州随着时间的推移有平行的趋势，那么宾夕法尼亚州的就业变化就可以解释为新泽西州在没有提高最低工资的情况下，会产生的变化，反之亦然。证据表明，提高最低工资并没有导致新泽西州就业率的下降，这与一些经济理论的说法恰恰相反。下表显示了 Card 和 Krueger 对就业治疗效果的估计，以 FTEs (或全职人力工时)衡量。Card 和 Krueger 估计，新泽西州0.80美元的最低工资增长导致了2.75个全职雇员的就业增加。

关于DID，最著名的研究之一便是 Card 和 Krueger 在1994年发表的关于新泽西州最低工资的文章。Card 和 Krueger 比较了1992年2月和1992年11月新泽西州最低工资从4.25美元上升到5.05美元之后，新泽西州和宾夕法尼亚州快餐部门的就业情况。仅在治疗前后观察新泽西州的就业情况变化，将无法控制一些<nowiki>'''</nowiki><nowiki><font color="#ff8000"> 被忽略变量Omitted variables</font></nowiki><nowiki>'''</nowiki>，例如该地区的天气和宏观经济状况。通过将宾夕法尼亚州作为双重差分模型的对照，任何由新泽西州和宾夕法尼亚州的共同变量所引起的偏差都会被隐含的控制，即使这些变量是不可被观测到的。假设新泽西州和宾夕法尼亚州随着时间的推移有平行的趋势，那么宾夕法尼亚州的就业变化就可以解释为新泽西州在没有提高最低工资的情况下，会产生的变化，反之亦然。证据表明，提高最低工资并没有导致新泽西州就业率的下降，这与一些经济理论的说法恰恰相反。下表显示了 Card 和 Krueger 对就业治疗效果的估计，以 FTEs (或全职人力工时)衡量。Card 和 Krueger 估计，新泽西州0.80美元的最低工资增长导致了2.75个全职雇员的就业增加。

{| class="wikitable"

{| class="wikitable"

|-

|-

! !! New Jersey !! Pennsylvania !! Difference

! !!新泽西州

|宾夕法尼亚州

|差异

|-

| Change || 0.59 || −2.16 || 2.75

 

|-

|-

| February || 20.44 || 23.33 || −2.89

| February || 20.44 || 23.33 || −2.89

* [[Average treatment effect]]

* [[Average treatment effect]]

* [[Synthetic control method]]

* [[Synthetic control method]]

* 实验设计

* 实验设计

* 平均处理效应

* 平均处理效应

Category:Subtraction

Category:Subtraction

类别: 计量经济学模型类别: 回归分析类别: 实验设计类别: 观察性研究类别: 因果推理类别: 减法

类别: 计量经济学模型 类别: 回归分析 类别: 实验设计 类别: 观察性研究 类别: 因果推断 类别: 减法

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