Difference-of-differences approach

The dashed line P ₁ -Q shows how the values ​​should have developed if the two groups were exposed to the same influencing factors ( control group ). However, the line P ₁ -P ₂ shows the actual measured development. The difference between the prognosis and the actual development (QP ₂ ) shows the effect size .

The difference-in-difference approach , short DvD approach ( English Difference-in-Differences approach , short DID , or Double difference , short DD ) is in the Ökonometrie common approach to a causal determine effect and to describe the strength of .

The underlying research design works with a treatment group and a control group . It corresponds roughly to a longitudinal study , i.e. data from the same study units must be available for at least two points in time (cf. panel data , cohort study ) before and after an influence, e.g. B. an information campaign or policy measure. However, since with many econometric questions a random assignment ( randomization ) of the test participants to a treatment or control group is not possible, an already defined group of people (e.g. a district or a city) is treated as the treatment group and another group than the control group (e.g. neighboring district). Due to the lack of randomization, the research design differs from a psychological experiment and is more like a quasi-experiment .

An early application of the method can be found in Feldstein (1995). However, the basic idea of ​​the DVD approach is probably as old as that of the instrument variable . There is a reference by Kennan (1995) to a report from 1915 that uses a kind of DVD approach to investigate the effects of minimum wages. A similar technique for discovering causal effects is regression discontinuity analysis .

approach

The approach is based in principle on regression analysis , the assumptions of which are also assumed for DvD. In addition, there is the trend assumption that both observation groups would have behaved or developed in the same way without a corresponding intervention or program. There are various options for testing the assumption of parallel trends. If data are available from early periods before the intervention, a placebo DvD effect can be investigated (no effect should be seen). Another variant provides for the use of a further control group (the effect should still be evident).

There is a group C ( control group ) and a group T ( treatment group ) as well as a dummy variable that indicates belonging to the second group; also a dummy variable that marks the second point in time. Then the relationship between the groups over time can be described by the following equation: ${\displaystyle D_{T}}$ ${\displaystyle D_{2}}$

${\displaystyle y=(\beta _{0}+\delta _{0}D_{2})+\beta _{1}D_{T}+\delta _{1}D_{2}\cdot D_{T}+\varepsilon }$,

where y is the dependent variable . The interesting effect of a measure (e.g. a policy measure) can be found as the interaction of the dummy variables ( difference-of-differences estimator ):

${\displaystyle {\hat {\delta }}_{1}=({\overline {y}}_{2,T}-{\overline {y}}_{2,C})-({\overline {y}}_{1,T}-{\overline {y}}_{1,C})}$,

The dash describes the arithmetic mean of a variable and the first index stands for the point in time, the second for group membership. The parameter then describes the average estimated causal effect. ${\displaystyle {\hat {\delta }}}$

Application examples

Thought example

In a city A there are 5,675 and in city B 3,113 unemployed . The government of B is running a project for the professional development of the unemployed. At the end of the project, city B had 3,201 unemployed - unemployment rose due to a recession despite the project. The increase in B is 88 people (corresponds to 2.83%). Assuming that the number of unemployed in city A would have developed in the same time, if a similar training project had been undertaken there, 5,675 × 102.83 / 100 = 5,836 unemployed would have to live there. In fact, however, there are now 5,851 unemployed people in city A at the second point in time (increase 3.1%).

The difference in the number of unemployed in each city (before-and-after comparison for both cities separately) leads to the difference in the differences (difference between the two before-and-after comparisons). This allows a statement to be made about the effectiveness of the further training measure. The conclusion would be that 3.1% - 2.83% = 0.27% of the unemployed would have found a job through the training measure.

Operation Barga

Operation Barga was a land reform in West Bengal, an Indian state (started in 1978). The neighboring state of Bangladesh has a lot in common in terms of population, culture, climate and other aspects. Before Operation Barga, productivity growth in the agricultural sector was about the same in both regions. Mainly rice was produced. The rice harvest in both countries was measured over a period from around 1970 to 1990 ( panel data ). To show that the policy measure of this land reform had a demonstrable effect on rice yields, a difference-of-differences estimation can be performed.

The change in yields (before and after Operation Barga) in the districts of West Bengal is compared with the corresponding changes in the control districts in Bangladesh.

Minimum wage in New Jersey

Studying the effect of a minimum wage on unemployment is an important question in labor economics . In April 1992, the New Jersey minimum wage was raised from $ 4.25 to $ 5.05. David Card and Alan B. Krueger collected data from fast food restaurants in February and November 1992 (i.e. before and after the reform) and similar data in Pennsylvania, a neighboring state. The minimum wage there remained at $ 4.25 during this period.

In this case, the authors could not find any evidence that the increase in the minimum wage would have led to less employment.

extension

There are also models that work with a three-fold difference. The corresponding generalization is called the differences-of-differences-of-differences-approach, or triple-differences-approach ( English difference in differences in differences , short DDD or short triple difference , short TD ). A corresponding example would assume, in addition to the times and group membership (e.g. life in a region and a neighboring region), another variable of the study objects, such as a personal characteristic of the participants (e.g. according to their qualifications).

Theoretically, the method can be expanded as required. The additional benefit is questionable, however. In the case of one treatment group and two control groups, a DvD estimator that is zero would only reduce the test power and increase the standard error . If it were not zero, questions would arise about the internal validity of the original DvD estimator.

An example work that uses both the DDD approach and instrument variable estimation can be found in Tsoutsoura, 2010. This work examines the effect of inheritance tax on company succession and investment decisions.

See also

• Linear panel data models
• Average treatment effect

literature

• Alberto Abadie: Semiparametric difference-in-differences estimators. In: The Review of Economic Studies. 72.1, 2005, pp. 1-19, doi: 10.1111 / 0034-6527.00321 .
• Franziska Kugler, Guido Schwerdt, Ludger Wößmann: Econometric methods for evaluating causal effects of economic policy. In: Perspectives of Economic Policy. 15 (2), 2014, pp. 105-132, doi: 10.1515 / pwp-2014-0013 .
• Vern Henderson, Jacques-François Thisse (Ed.): Handbook of regional and urban economics: cities and geography . Vol. 4. Elsevier, 2004, ISBN 0-444-50967-4 , pp. 30-37.

Individual evidence

1. ↑ Hannes Schellhorn: Income Tax Efficiency Effects on Tax Avoidance . Springer-Verlag, 2005, ISBN 3-8244-0793-0 , doi: 10.1007 / 978-3-322-81169-1 , p. 5.
2. ↑ Joshua D. Angrist, Jörn-Steffen Pischke: Mostly harmless econometrics: An empiricist's companion . Princeton university press, 2008, ISBN 978-1-282-60809-2 , p. 170.
3. ↑ Dominic J. Brewer, Lawrence O. Picus (Ed.): Encyclopedia of Education Economics and Finance . SAGE Publications, 2014, ISBN 978-1-4833-4659-5 , pp. 206ff.
4. ↑ Jeffrey Wooldridge: Introductory econometrics: A modern approach . Nelson Education, 2013, ISBN 978-1-111-53104-1 , p. 410ff.
5. ↑ Abhijit V. Banerjee, Paul J. Gertler, Maitreesh Ghatak: Empowerment and efficiency: tenancy reform in West Bengal. In: Journal of Political Economy. 110.2, 2002, pp. 239-280, doi: 10.1086 / 338744 JSTOR 338744 .
6. ↑ Joshua D. Angrist, Jörn-Steffen Pischke: Mostly harmless econometrics: An empiricist's companion. Princeton university press, 2009, ISBN 978-0-691-12035-5 , p. 169.
7. ^ D. Card, AB Krueger: Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. In: The American Economic Review. 84 (4), 1994, pp. 772-793. doi: 10.3386 / w4509 JSTOR 2118030
8. ↑ Myoung-Jae Lee: Micro-econometrics for policy, program, and treatment effects. Oxford University Press, Oxford 2005, ISBN 0-19-926768-5 , pp. 111ff.
9. ↑ George M. Constantinides, Milton Harris, René M. Stulz (Eds.): Handbook of the Economics of Finance. Vol. 1A: Corporate finance . Elsevier, 2003, ISBN 0-444-51362-0 , p. 530.
10. ↑ Margarita Tsoutsoura: The effect of succession taxes on family firm investment: Evidence from a natural experiment. In: The Journal of Finance. 70.2, 2015, pp. 649-688, doi: 10.1111 / jofi.12224 .