When to trigger
- Main results are already robust, but only one dimension was cut ("East/Central/West" or "SOE / non-SOE")
- Reviewers request additional heterogeneity analysis
- Multiple dimensions were cut but there is no theoretical guidance
Priority of splitting dimensions
Ordered by expected interest of 《经济研究》 readers:
- Institutional environment / degree of marketization — Wang Xiaolu's 《中国分省份市场化指数》 (China's Provincial Marketization Index), regional rule-of-law indices
- Firm ownership / corporate governance — SOE / private / foreign, board independence
- Industry attributes — high-tech / traditional, upstream / downstream, regulated or not
- Time window — early vs. late policy period / economic cycle
- Individual characteristics(if applicable) — age, education, skill level
Cut at least 3 dimensions, with at least 2 subsample comparisons per dimension.
Three principles for dimension selection
- Theoretically guided: the splitting dimension must be able to explain "why the effect differs along this dimension"
- Sufficient sample size: each subsample N ≥ 100 is the bottom line
- Test of significance of coefficient differences: a Chow test or interaction term must be reported
Heterogeneity writing template
本文进一步检验[维度]异质性。
理论上，[原因]……
实证上，本文将样本按[维度]分为[组 1] 和 [组 2]，分别估计主回归（结果见表 X 第 (1)(2) 列）。
结果显示，[组 1] 的处理效应为 X，而 [组 2] 为 Y，系数差异在 [显著水平] 上显著。
这一发现与本文的[机制]一致。
The journal's presentation conventions: subsample tables vs. interaction terms
Both presentation approaches are common in the main text of 《经济研究》. Selection criteria:
- Subsample regressions (placed side by side in the same table): suitable when the splitting variable is a discrete institutional attribute (ownership, industry regulation, regional marketization grouping). The convention is one table for one dimension, with columns (1)(2) as the two subsamples, and a note below the table giving the grouping standard and the source of the grouping variable (e.g., marketization index grouped by the sample-period median), andreport the empirical p-value of the between-group coefficient difference in a separate row(Fisher permutation test / bootstrap method), rather than leaving readers to eyeball the asterisks in the two columns.
- Interaction term regression: suitable when the splitting variable is continuous (financing constraint index, degree of digitalization), avoiding artificial dichotomization and loss of information. The interaction coefficient is "the heterogeneity itself"; the main-text interpretation should be written as "the effect of X strengthens by β units for each one-standard-deviation increase in Z," rather than merely saying "the interaction term is significant."
Two tastes specific to this journal:
- Heterogeneity subsection headings should state the economic meaning, not the variable name— use "The moderating role of financing constraints" rather than "Grouped by SA index"; the first sentence of the subsection should give the theoretical expectation first, then the results.
- Dimensions that are not significant should also be addressed: if a dimension that theoretically should show a difference does not, honestly report and explain it in one or two sentences in the main text (measurement noise / channel offset by policy), which wins more reviewer trust than quietly deleting it.
Mini comparison (before / after rewriting)
❌ Before rewriting: "Grouped regressions show that the coefficient for the SOE group is 0.021 and for the private-firm group is 0.058, indicating ownership heterogeneity."
✅ After rewriting: "The treatment effect for the private-enterprise group (0.058) is about 2.8 times that for the state-owned enterprise group (0.021), and the empirical p-value for the between-group difference is 0.03. This is consistent with the expectation of Hypothesis 2: private enterprises face tighter external financing constraints, so the improvement in cash flow brought by the policy has higher marginal value for them; the difference along the ownership dimension therefore constitutes indirect evidence for the financing-constraint mechanism."
The rewrite accomplishes three things at once: reporting the difference test, providing a theoretical explanation, and tying back to the mechanism.
Relationship with mechanism analysis
Heterogeneity ≈ reverse verification of the mechanism:
- The mechanism tells us "why there is an effect"
- Heterogeneity tells us "under what conditions the effect is stronger / weaker"
An ideal empirical paper should have:Mechanism (strong M → strong effect) and Heterogeneity (samples with strong M → strong effect) corroborating each other.
Must-check list
- At least 3 heterogeneity dimensions
- Each dimension has theoretical guidance
- Report of significance tests for coefficient differences
- Sufficient sample size for each subsample
- Heterogeneity conclusions are consistent with the mechanism (or inconsistencies are reasonably explained)
Anti-patterns
- Attaching interaction terms to control variables and calling it "heterogeneity"
- Still interpreting results after splitting when one group has N=30
- Splitting into 8 dimensions to pad the paper, but none is significant
- Heterogeneity conclusions conflict with the mechanism but are not explained
Heterogeneity as indirect evidence for the mechanism (important)
Following the approach of Jiang Ting (2022),theory-driven heterogeneity is more credible mechanism evidence than mediation decomposition: if the mechanism is M, then in subsamples where the "M channel is smoother / more constrained," the main effect should be stronger / weaker. When designing heterogeneity, deliberately make at least one dimensioncorrespond to some mechanism, so that mechanism and heterogeneity corroborate each other (see details in er-mechanism）。
Companion materials and examples
- Complete sample essay:
resources/worked-examples/06-heterogeneity.md(three-dimensional heterogeneity + indirect mechanism evidence) - Benchmark against a model: Zhang Xun et al. (2019, Economic Research Journal, Issue 8) use group heterogeneity to support the digital finance channel, see
resources/exemplars/
Output format
【异质性维度】X 个
【系数差异检验】是 / 否
【与机制一致性】是 / 否（哪一维度对应哪条机制）
【最小子样本量】X
【下一步】er-tables-figures