Hatemi-J Asymmetric Causality Test
Also known as: Hatemi-J Asymmetric Causality Test, Asymmetric Causality Test, Positive and Negative Causality Test, Asimetrik Nedensellik Testi
The Hatemi-J asymmetric causality test, introduced by Abdulnasser Hatemi-J in 2012, extends the Granger causality framework to allow causal relationships between the positive and negative components of integrated time series to differ. By decomposing each series into cumulative positive and negative partial sums and embedding the Toda-Yamamoto approach within a VAR, the test enables researchers to distinguish whether positive shocks, negative shocks, or both drive causation between economic variables.
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When to use it
Use the Hatemi-J asymmetric causality test when you suspect that positive and negative shocks in one variable have different predictive effects on another, and when the series are integrated of order one or possibly two. The test suits macroeconomic and financial panel or time-series data where boom-bust asymmetries are theoretically motivated—for example, energy prices and output, exchange rates and trade balances, or stock returns and economic activity. Prerequisites include sufficient sample length for reliable bootstrap inference (at least 80–100 observations is advisable) and the absence of structural breaks severe enough to invalidate the VAR. If series are stationary, standard asymmetric Granger causality with OLS suffices; if cointegration is present, an asymmetric error-correction model may be preferred.
Strengths & limitations
- Captures asymmetric causal dynamics that symmetric Granger or Toda-Yamamoto tests cannot detect, preventing misleading null results when positive and negative effects cancel.
- Inherits the Toda-Yamamoto augmentation strategy, avoiding pre-testing for unit roots and cointegration while maintaining valid asymptotic inference.
- Bootstrap critical values improve finite-sample size accuracy compared with chi-squared approximations.
- Applicable to series integrated of different orders (I(0), I(1), I(2)), making it flexible across econometric contexts.
- Requires a reasonably large sample for bootstrap inference to be reliable; small samples inflate size distortion.
- Decomposition into partial sums discards information about the timing and magnitude of sign changes within a period, which may be relevant for high-frequency data.
- The test does not model the dynamic path of the asymmetric response (impulse responses require additional tools such as nonlinear IRFs).
- Selection of VAR lag length p can substantially affect results, and standard information criteria may not optimally balance fit and parsimony in the augmented system.
Frequently asked
How does this test differ from standard Granger causality?
Standard Granger causality estimates a single VAR on the original series, implicitly assuming that positive and negative movements have the same predictive content. The Hatemi-J test decomposes each series into cumulative positive and negative parts and tests causality among all four component combinations, revealing whether causation runs through increases, decreases, or both asymmetrically.
Do I need to test for cointegration before applying this test?
No. Following the Toda-Yamamoto logic, the test adds d_max extra lags to the VAR estimated in levels, which preserves asymptotic chi-squared validity of the Wald statistic regardless of whether the series are cointegrated or not. This eliminates the need for a pre-test and avoids the associated sequential size distortion.
How many bootstrap replications are typically sufficient?
The literature generally recommends at least 1,000 bootstrap replications for reliable p-value estimation in this context, with 2,000–10,000 replications used in published applications to ensure stability of the bootstrap distribution and accurate inference near conventional significance thresholds.
Sources
- Hatemi-J, A. (2012). Asymmetric causality tests with an application. Empirical Economics, 43(1), 447–456. DOI: 10.1007/s00181-011-0484-x ↗
How to cite this page
ScholarGate. (2026, June 2). Hatemi-J Asymmetric Causality Test. ScholarGate. https://scholargate.app/en/econometrics/hatemi-j-asymmetric-causality
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Granger CausalityEconometrics↔ compare
- Hatemi-J Cointegration TestEconometrics↔ compare
- Toda-Yamamoto CausalityEconometrics↔ compare