Treatment effects can be estimated without a traditional control group by forecasting counterfactual outcomes—essentially predicting what would have happened to the treated units if they had not received the treatment. This approach relies on constructing a credible model of the untreated scenario, often using data from before the treatment or from comparable units, and then comparing the observed outcomes to these forecasts.
Short answer: Treatment effects without a control group are estimated by creating forecasted counterfactuals—predictions of untreated outcomes based on historical data or modeling—that serve as a baseline to measure the causal impact of the treatment.
Understanding Counterfactuals and Their Role in Causal Inference
At the core of causal inference is the concept of the counterfactual: what would have happened to a subject had they not received the treatment. When a control group is absent, researchers must estimate this counterfactual using predictive models built from available data. This can involve time series forecasting, synthetic control methods, or machine learning algorithms trained on pre-intervention data or similar units not subject to treatment. The key challenge is ensuring that these forecasts are unbiased and capture the true untreated trajectory, so that the difference between observed and counterfactual outcomes reliably reflects the treatment effect.
For example, in economics and policy evaluation, if a new program is introduced in a city without a comparable untreated city, analysts may use the city's own historical trends—adjusted for external factors—to forecast what would have happened without the program. This forecasted counterfactual becomes the benchmark against which the program's impact is measured.
Methodologies for Forecasting Counterfactuals
Several approaches exist to estimate counterfactuals without a control group. One popular technique is the synthetic control method, which constructs a weighted combination of other units to approximate the treated unit’s pre-treatment characteristics and trajectory. However, this requires a donor pool of untreated units. In cases where no such pool exists, researchers rely on forecasting methods that use the treated unit’s own pre-treatment data to extrapolate the untreated outcome.
Time series models—like ARIMA or state-space models—can predict future trends based on historical patterns. Machine learning models, such as random forests or neural networks, can incorporate complex covariates to improve forecast accuracy. The precision of these forecasts depends on the quality and length of pre-treatment data, the stability of the system, and the absence of confounding shocks.
The NBER study on bargaining efficiency indirectly illustrates the importance of modeling unobserved counterfactuals. Although the paper focuses on bargaining outcomes in used-auto auctions, it estimates distributions of valuations and outcomes that reflect what could have happened under different bargaining scenarios. This kind of structural modeling, which bounds possible outcomes under varying assumptions, parallels the concept of forecasting counterfactuals to estimate treatment effects when direct controls are unavailable.
Challenges and Assumptions in Forecasting Counterfactuals
Estimating treatment effects without a control group hinges on strong assumptions. The primary assumption is that the forecasting model accurately captures the untreated outcome trajectory. This requires that no other factors besides the treatment changed during the evaluation period—known as the assumption of no confounders or stable unit treatment value assumption (SUTVA).
Violations of these assumptions can bias estimates. For instance, if an economic shock unrelated to the treatment occurs after the intervention, the forecasted counterfactual may be inaccurate. Researchers often conduct placebo tests or sensitivity analyses to assess the robustness of their forecasts.
Moreover, the uncertainty around the forecasted counterfactuals must be accounted for. Unlike controlled experiments where randomization provides a natural benchmark, forecasting introduces model uncertainty. Confidence intervals around the estimated treatment effect should incorporate this uncertainty to avoid overconfident conclusions.
Applications and Examples
Forecasted counterfactuals are widely used in fields where randomized control trials or untreated comparison groups are infeasible. In economics, policy evaluation often employs these methods to assess the impact of interventions such as tax reforms, minimum wage laws, or public health campaigns.
In the wholesale used-auto auction study from NBER, although not directly about treatment effects, the estimation of buyer and seller valuations under incomplete information shows how researchers use models to infer unobserved counterfactual states. Similarly, in labor economics, researchers might forecast employment levels without a new training program to estimate its effect on job placement.
Another domain is marketing, where companies test a new advertising campaign without a control group by forecasting sales based on historical data and seasonal trends. The difference between actual and forecasted sales during the campaign period estimates the campaign’s effectiveness.
Conclusion: Forecasted counterfactuals offer a powerful alternative for estimating treatment effects when control groups are unavailable. Their success depends on rigorous modeling, rich pre-treatment data, and careful consideration of assumptions and uncertainties. While they cannot fully replicate the robustness of randomized experiments, these methods enable causal inference in complex real-world settings where controls are impractical or impossible.
For further reading on these methods and their applications, resources from nber.org provide empirical examples and theoretical foundations, while econometrics literature often details the underlying assumptions and technical approaches. Although some sources like sciencedirect.com and rand.org were inaccessible or irrelevant here, foundational knowledge from econometrics and applied economics remains essential to understanding treatment effect estimation via forecasted counterfactuals.
Potential sources for deeper exploration include:
nber.org – for empirical research and working papers on treatment effects and forecasting econometrics textbooks and surveys on causal inference methods journals like The Review of Economic Studies for structural modeling examples policy evaluation guides focusing on synthetic control and forecasting techniques machine learning resources for predictive modeling in causal inference contexts These offer a comprehensive framework for researchers and practitioners aiming to estimate treatment effects without a control group, by leveraging forecasted counterfactuals.
