Pre-Treatment Trend Plots as Diagnostics

Why Plot Pre-Treatment Trends?

Difference-in-differences (DiD) relies on a counterfactual claim: after treatment begins, the treated group’s outcome in the absence of treatment would have changed like the comparison group’s outcome. A plot of earlier outcomes cannot show that unobserved post-treatment counterfactual directly. It can, however, reveal whether the groups’ observed pre-treatment trajectories look sufficiently similar to make the parallel-trends assumption plausible.

The key visual comparison is not whether the groups start at the same outcome level. They may have different baseline levels and still have parallel trends. Instead, examine how their means change across pre-treatment periods and whether the gap between them remains roughly stable. The plot is a diagnostic: patterns that depart from parallel movement raise questions, while apparently parallel lines do not prove the assumption.

Define the Quantities to Plot

A basic trend plot puts time on the horizontal axis and the outcome mean on the vertical axis, with a separate connected line for each group. Include all available pre-treatment periods and mark the treatment date so the boundary between diagnostic periods and post-treatment periods is clear. A second, often useful display plots \(D_t\) over time. If the two group means move in parallel, their gap should be approximately stable.

For equally spaced periods, parallel movement means that corresponding changes are similar:

Equivalently, the gap changes little from one pre-treatment period to the next:

These are descriptions of observed pre-treatment means. The identifying assumption concerns the groups’ mean outcomes under no treatment, including after treatment begins. Pre-treatment observations are therefore informative about the assumption, but they do not reveal whether it will hold in the post-treatment period.

Worked Examples

How to Read the Plot Carefully

A useful diagnostic examines both the group-mean plot and the gap plot. The first shows the direction and shape of each trajectory; the second makes changes in the treated-minus-comparison difference easier to see. In an idealized parallel pattern, the lines may be separated vertically but move together, while the gap plot is roughly horizontal. In contrast, sustained divergence, convergence, or visibly different curvature can signal that the groups were already changing differently.

For periods that are not equally spaced, compare changes per unit of elapsed time rather than raw differences alone. If period \(t-1\) is \(h_t\) time units before period \(t\), the corresponding mean rate of change is:

For example, an increase of 4 units over one month is not the same rate as an increase of 4 units over a year. Label the time axis clearly and make the spacing of plotted points reflect elapsed time when intervals differ.

The outcome scale also matters. Construct the plot using the outcome definition and scale chosen for the DiD analysis. A pattern that looks parallel in outcome levels need not look parallel after a transformation, and vice versa. Interpret the plotted changes in the units of that chosen scale rather than switching scales while comparing groups.

If the plotted values are sample means, they are estimates and may fluctuate because of sampling variability. Showing uncertainty intervals can help readers see that the means are not known exactly, but such intervals do not convert a visual check into proof of parallel trends. In particular, visual overlap or non-overlap of separate intervals is not a stand-alone test of equality of trends. A plot should communicate the data clearly, not invite stronger conclusions than its design supports.

A Short Justification: Why a Stable Gap Represents Similar Changes

The gap formulation follows directly from the definitions. Subtract the gap in the earlier period from the gap in the later period:

Therefore, if the group means have equal changes in an interval, the gap does not change in that interval. Conversely, if the gap is stable, the group means have equal changes over that interval. This algebra explains why plotting the gap is a compact way to inspect relative movement, while plotting both means retains information about their individual trajectories.

Practical Construction and Common Pitfalls

• Mistake: Treating different starting levels as a trend violation. A student sees the treated group above the comparison group throughout the pre-period and concludes that parallel trends fails. Correction: level differences alone are not the issue; compare changes or inspect whether the gap changes over time.
• Mistake: Treating similar-looking lines as proof. A plot may show similar pre-treatment movement, but it cannot establish how untreated outcomes would have evolved after treatment began. Correction: describe the plot as diagnostic evidence and state the assumption separately.
• Mistake: Calling any bend a violation. Both groups can share a bend or temporary dip and still have similar changes. Correction: compare their movements over the same intervals, not whether each line is straight.
• Mistake: Reading too much into a few noisy periods. A single unusual mean can make a gap appear to jump. Correction: show all relevant pre-periods, report the means and gaps, and consider the uncertainty and context rather than selecting only favorable intervals.

Pre-treatment trend plots matter because they make a central identifying assumption more transparent and can expose patterns that deserve investigation before interpreting a DiD estimate. They are neither a substitute for the assumption nor a guarantee that it holds. Their strongest use is disciplined: describe what the observed trajectories show, identify departures that could matter, and keep the causal conclusion proportional to the evidence.