Glossary

8.2 Parallel trends assumption

5 min read•august 20, 2024

The assumption is crucial for estimation, a method used to measure causal effects in observational studies. It states that without treatment, the average outcomes for treatment and control groups would follow parallel paths over time.

This assumption allows researchers to attribute differences in outcomes between groups to the treatment itself. Violating this assumption can lead to biased estimates and incorrect conclusions about causal effects, making it essential to carefully assess and address potential violations.

  • Fundamental assumption in difference-in-differences (DiD) estimation, a popular method for estimating causal effects in observational studies
  • Requires that in the absence of treatment, the average outcomes for the treatment and control groups would have followed parallel paths over time
  • Implies that any differences in outcomes between the two groups after treatment can be attributed to the causal effect of the treatment itself

Importance in difference-in-differences estimation

  • Crucial for the validity of DiD estimates as it allows for the isolation of the causal effect of interest
  • Enables the to serve as a valid counterfactual for the , representing what would have happened to the treatment group in the absence of treatment
  • Violation of this assumption can lead to biased estimates and incorrect conclusions about the causal effect of the treatment

Treatment vs control groups

Top images from around the web for Treatment vs control groups

  • Randomised Trials View original

    Is this image relevant?

  • Randomised Trials View original

    Is this image relevant?

1 of 2

Top images from around the web for Treatment vs control groups

  • Randomised Trials View original

    Is this image relevant?

  • Randomised Trials View original

    Is this image relevant?

1 of 2
  • Requires that the treatment and control groups are similar in terms of their pre-treatment characteristics and trends
  • Groups should be affected by the same external factors and shocks over time
  • Differences between the groups should be stable and not vary systematically with the treatment
  • Assumption is more plausible when the treatment and control groups exhibit similar trends in the outcome variable prior to the treatment
  • Parallel suggest that the groups would have continued to follow similar paths in the absence of treatment
  • Divergence in pre-treatment trends raises concerns about the validity of the assumption

Absence of time-varying confounding

  • Requires that there are no unobserved factors that affect the outcome variable differently for the treatment and control groups over time
  • Time-varying confounders can cause the groups to diverge even in the absence of treatment, violating the parallel trends assumption
  • Presence of such confounders can lead to biased estimates of the treatment effect
  • Plotting the outcome variable for the treatment and control groups over time can provide a visual assessment of the parallel trends assumption
  • Similar pre-treatment trends suggest that the assumption is plausible, while diverging trends raise concerns
  • Visual inspection should be supplemented with statistical tests for more rigorous evaluation

Placebo tests

  • Involve artificially assigning the treatment to a different time period or group where no effect is expected
  • If the parallel trends assumption holds, should yield estimates close to zero
  • Significant placebo effects suggest that the assumption may be violated and the DiD estimates may be biased

Covariate balance tests

  • Check whether the treatment and control groups are balanced in terms of observable characteristics before and after the treatment
  • Significant differences in covariates over time can indicate the presence of time-varying confounding and violation of the parallel trends assumption
  • tests help assess the comparability of the groups and the plausibility of the assumption

Biased causal effect estimates

  • Violation of the parallel trends assumption can lead to biased estimates of the treatment effect
  • If the treatment and control groups would have followed different paths even in the absence of treatment, the DiD estimate will capture not only the true treatment effect but also the difference in underlying trends
  • Bias can be positive or negative, depending on the direction of the violation

Misinterpretation of results

  • Biased estimates can lead to incorrect conclusions about the effectiveness of the treatment
  • Policymakers and researchers may attribute changes in outcomes to the treatment when they are actually driven by other factors
  • can have serious consequences for policy decisions and future research directions

Strategies for addressing violations

Including covariates

  • Adding relevant covariates to the DiD model can help control for observable time-varying confounders
  • Covariates should be selected based on theoretical considerations and data availability
  • can reduce bias and improve the plausibility of the parallel trends assumption

Synthetic control methods

  • Involve constructing a synthetic control group as a weighted combination of untreated units that closely resembles the treatment group in terms of pre-treatment characteristics and trends
  • can help address violations of the parallel trends assumption by creating a more suitable comparison group
  • Requires a sufficient number of untreated units and careful selection of weighting variables

Triple difference estimators

  • Extend the DiD approach by adding a third difference, such as a comparison group that is unaffected by the treatment
  • can help control for time-varying confounders that affect both the treatment and control groups
  • Requires the identification of a suitable third comparison group and additional assumptions about the nature of the confounding

Unobserved time-varying confounders

  • Parallel trends assumption can be violated by the presence of unobserved factors that affect the treatment and control groups differently over time
  • Such confounders are often difficult to measure or control for in observational studies
  • can lead to biased estimates even if the parallel trends assumption appears to hold based on observable characteristics

Anticipation effects

  • Occur when individuals or entities change their behavior in anticipation of the treatment, even before it is implemented
  • can cause the treatment and control groups to diverge prior to the actual treatment, violating the parallel trends assumption
  • Ignoring anticipation effects can lead to biased estimates of the treatment effect

Functional form misspecification

  • Parallel trends assumption is often tested and assessed using linear models, such as linear regression
  • If the true relationship between the outcome and time is non-linear, the assumption may appear to hold even if it is actually violated
  • Misspecification of the functional form can lead to incorrect conclusions about the validity of the parallel trends assumption and the causal effect of the treatment

Alternatives to difference-in-differences

Regression discontinuity designs

  • Exploit a discontinuity in treatment assignment based on a continuous variable (running variable)
  • Compares outcomes for units just above and below a cutoff value of the running variable
  • Relies on the assumption that units near the cutoff are similar in terms of unobservable characteristics

Instrumental variables

  • Use an exogenous source of variation (instrument) that affects the treatment but not the outcome directly
  • Instrument should be correlated with the treatment and uncorrelated with unobserved confounders
  • Allows for the estimation of causal effects in the presence of unmeasured confounding

Matching methods

  • Involve pairing treated units with similar untreated units based on observable characteristics
  • aim to create a balanced sample that mimics a randomized experiment
  • Common matching techniques include propensity score matching and coarsened exact matching

Key Terms to Review (27)

Anticipation Effects: Anticipation effects refer to changes in behavior or outcomes that occur because individuals or groups expect a future event, such as a policy change or intervention. These effects can influence the validity of causal inferences drawn from observational studies, particularly when considering how subjects react prior to the implementation of an intervention. Understanding anticipation effects is essential for correctly interpreting results and ensuring that the assumptions underlying causal models are met.
Assumption of No Confounding: The assumption of no confounding is the principle that ensures the treatment effect being studied is not influenced by other variables that could affect both the treatment and the outcome. This means that any observed changes in the outcome can be attributed directly to the treatment itself, rather than being skewed by other factors. This assumption is crucial for establishing causal relationships, especially when employing methods like difference-in-differences that rely on parallel trends to support valid conclusions about treatment effects.
Biased causal effect estimates: Biased causal effect estimates refer to inaccurate measurements of the impact of a treatment or intervention on an outcome due to confounding factors or violations of key assumptions. When researchers attempt to determine causal relationships, biases can lead to incorrect conclusions, making it essential to account for factors that could distort the results. Understanding these biases is crucial in establishing valid causal inferences in research.
Causal identification: Causal identification is the process of establishing a cause-and-effect relationship between variables in a study, ensuring that the observed effects can be attributed to specific interventions or exposures rather than confounding factors. This concept is essential in evaluating how interventions impact outcomes and relies on various assumptions and methodologies to substantiate claims of causality, particularly through methods like difference-in-differences and instrumental variables. Understanding causal identification enables researchers to discern genuine effects from spurious correlations.
Control group: A control group is a baseline group in an experiment that does not receive the treatment or intervention being tested, allowing for comparison against the experimental group. It plays a crucial role in isolating the effect of the treatment by minimizing confounding variables and establishing causality between the treatment and the outcome. This concept is essential for accurately estimating the average treatment effect and ensuring the validity of experimental designs.
Counterfactual reasoning: Counterfactual reasoning is a method of thinking about what could have happened if different choices or conditions had been in place, focusing on hypothetical scenarios rather than actual events. This type of reasoning helps in understanding causal relationships by considering alternative outcomes that did not occur, which is essential for evaluating the impact of interventions and understanding causal inference. It allows researchers to conceptualize the 'what if' scenarios that provide insight into the dynamics of cause and effect.
Covariate balance: Covariate balance refers to the state where covariates, or characteristics that could influence the outcome, are distributed equally across treatment and control groups in a study. Achieving covariate balance is crucial for ensuring that any observed effects can be attributed to the treatment rather than differences in those characteristics. It plays a vital role in various study designs and methods, including randomization, propensity score matching, and causal inference assumptions.
Difference-in-differences: Difference-in-differences is a statistical technique used to estimate the causal effect of a treatment or intervention by comparing the changes in outcomes over time between a group that is exposed to the treatment and a group that is not. This method connects to various analytical frameworks, helping to address issues related to confounding and control for external factors that may influence the results.
Donald Rubin: Donald Rubin is a prominent statistician known for his contributions to the field of causal inference, particularly through the development of the potential outcomes framework. His work emphasizes the importance of understanding treatment effects in observational studies and the need for rigorous methods to estimate causal relationships, laying the groundwork for many modern approaches in statistical analysis and research design.
Functional Form Misspecification: Functional form misspecification occurs when the assumed relationship between the independent and dependent variables in a model does not accurately reflect the true relationship. This can lead to biased estimates and incorrect conclusions, particularly when the model fails to capture essential nonlinearities or interactions. It's crucial to understand this concept as it directly impacts the validity of causal inference and the assumptions behind methods like difference-in-differences.
Including Covariates: Including covariates refers to the practice of accounting for additional variables that might influence the outcome in a causal analysis. By incorporating these covariates, researchers can better isolate the effect of the primary independent variable on the dependent variable, helping to control for confounding factors that could skew results.
Instrumental Variables: Instrumental variables are tools used in statistical analysis to estimate causal relationships when controlled experiments are not feasible or when there is potential confounding. They help in addressing endogeneity issues by providing a source of variation that is correlated with the treatment but uncorrelated with the error term, allowing for more reliable causal inference.
Josh Angrist: Josh Angrist is an influential economist known for his work in causal inference, particularly in the development of methods for estimating causal relationships in social science. His research has significantly impacted the way researchers approach the analysis of observational data, emphasizing the importance of understanding and addressing confounding variables and assumptions necessary for causal interpretation.
Matching Methods: Matching methods are statistical techniques used in causal inference to create comparable groups from observational data by aligning individuals based on similar characteristics. These methods aim to mimic randomization, reducing bias and confounding by ensuring that the treatment and control groups are statistically similar across observed covariates. This approach helps satisfy assumptions necessary for valid causal conclusions.
Misinterpretation of results: Misinterpretation of results occurs when the conclusions drawn from data analysis do not accurately reflect the true relationships or effects present in the data. This often happens due to incorrect assumptions, biases, or failure to account for confounding variables, leading to flawed inferences about cause and effect relationships.
Natural Experiments: Natural experiments are observational studies that leverage naturally occurring events or circumstances to identify causal relationships between variables. These experiments take advantage of situations where random assignment is not possible but where an external factor influences the exposure or treatment of subjects, allowing researchers to draw conclusions about causal effects. This concept is closely tied to various statistical methodologies, which aim to identify valid instruments and assumptions needed for causal inference.
Parallel trends: Parallel trends refer to the assumption that in the absence of treatment, the average outcomes for both treatment and control groups would have followed the same trajectory over time. This concept is crucial in causal inference as it underlies the validity of difference-in-differences (DiD) estimation. If the parallel trends assumption holds, any differences in outcomes post-treatment can be attributed to the treatment effect rather than pre-existing trends between the groups.
Placebo tests: Placebo tests are a method used to assess the validity of causal inferences by introducing a 'dummy' treatment or intervention to see if the results hold true in a context where no real effect is expected. This approach helps in confirming whether the observed treatment effects are genuine or if they might be due to confounding factors. By applying placebo tests, researchers can validate their findings and ensure the robustness of their conclusions in various analytical frameworks.
Policy evaluation: Policy evaluation is the systematic assessment of the design, implementation, and outcomes of a policy to determine its effectiveness and inform future decision-making. This process often involves comparing actual outcomes against intended objectives, which helps in understanding the impact of the policy on different populations and contexts. Effective policy evaluation is essential for refining policies and ensuring resources are allocated efficiently.
Pre-treatment trends: Pre-treatment trends refer to the patterns or behaviors observed in data prior to a treatment or intervention being applied. Understanding these trends is crucial because they help establish the baseline conditions and ensure that any observed effects after treatment can be attributed to the intervention rather than pre-existing differences.
Regression Discontinuity: Regression discontinuity is a quasi-experimental design used to identify causal effects by exploiting a cut-off point or threshold in an assignment variable. This method allows researchers to compare outcomes just above and below the cut-off, providing insights into treatment effects while controlling for other confounding variables. The approach is closely tied to various concepts such as regression analysis, validity testing, and external validity in different contexts like education and marketing.
Selection Bias: Selection bias occurs when the individuals included in a study are not representative of the larger population, which can lead to incorrect conclusions about the relationships being studied. This bias can arise from various sampling methods and influences how results are interpreted across different analytical frameworks, potentially affecting validity and generalizability.
Simultaneity bias: Simultaneity bias occurs when two or more variables affect each other simultaneously, making it difficult to determine the direction of causation. This issue arises in observational studies where the independent and dependent variables influence each other, leading to misleading results. Understanding simultaneity bias is crucial because it challenges the validity of causal claims drawn from data that does not adequately account for these interdependencies.
Synthetic Control Methods: Synthetic control methods are statistical techniques used to estimate the causal effect of an intervention or treatment by constructing a synthetic control group that mimics the characteristics of the treatment group before the intervention. This method is particularly useful when a randomized control trial is not feasible and allows researchers to draw causal inferences from observational data by using a weighted combination of untreated units to create a counterfactual.
Treatment group: A treatment group is a set of subjects in an experiment that receives the intervention or treatment being tested. This group is crucial for comparing the effects of the treatment against a control group, which does not receive the treatment. By analyzing outcomes from the treatment group, researchers can determine the effectiveness and impact of the intervention, allowing them to estimate causal relationships.
Triple Difference Estimators: Triple difference estimators, often referred to as the 'difference-in-differences-in-differences' method, are an advanced econometric technique used to estimate treatment effects by comparing changes across multiple groups and time periods. This method builds upon the standard difference-in-differences approach by adding an additional level of comparison, helping to address potential confounding factors and biases. The core idea is to control for unobserved variables that might differ across groups or over time, thereby enhancing the robustness of causal inferences drawn from observational data.
Unobserved time-varying confounders: Unobserved time-varying confounders are variables that affect both the treatment and the outcome over time, but are not measured or included in the analysis. These confounders can lead to biased estimates of treatment effects because their influence fluctuates, potentially leading to incorrect conclusions about causal relationships. They are particularly problematic in observational studies where the assumption of parallel trends may be violated.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide