Granger (1997) On Modelling the Long Run in Applied Economics

Summary

Granger (1997) is a reflective methodological essay on how to model long-run relationships in macroeconomics, covering pre-testing, cointegration methodology, generalisations, and the philosophy of model selection. The paper introduces "extended memory" as a more general definition of persistence than unit roots, warns against the conflation of I(1) with non-stationarity, presents the Gonzalo-Granger (1995) permanent/transitory decomposition via common stochastic trends, and makes the case for model evaluation by forecast competition rather than theoretical debate.

Key Claims

• Extended memory is the appropriate concept of persistence: a process has it if $E(X_{t+h}|I_t)$ does not tend to a constant as $h \to \infty$. Unit roots are the simplest example; failing to reject an I(1) null does not mean the process IS I(1).
• Stochastic unit root (Granger-Swanson 1994): $X_t = \alpha_t X_{t-1} + \varepsilon_t$ with $E(\alpha_t)=1$, $\alpha_t$ stationary and exogenous to $X$. Not rejected by standard Dickey-Fuller (DF) tests; variance grows exponentially (not linearly as T) — fundamentally different behavior from a pure I(1) process.
• I(2) skepticism: if $\Delta^2 X_t = \varepsilon_t$, a WWI shock has greater current impact than a WWII shock — "If something does not feel right it probably is not right." I(2) classifications are usually better explained as I(1) plus a broken linear trend.
• Gonzalo-Granger (1995) common trends: In a cointegrated system with $m$ I(1) variables and rank $r$, there are $m-r$ common stochastic trends $W_t = \alpha_\perp' x_t$ (where $\alpha' \alpha_\perp = 0$). The identifying criterion is that equilibrium errors $z_t = \beta' x_t$ do not Granger-cause $W_t$ at very low frequencies. The pair $(z_t, W_t)$ is the multivariate analogue of Beveridge-Nelson permanent/transitory decomposition.
• Johansen cautions: choice of lag length affects rank estimates; super-consistency concerns asymptotics that may not dominate in typical sample sizes; models with many lags are far from parsimonious; individual coefficients should not be interpreted when cointegrations are not identified in the classical sense.
• Non-linear error correction models (ECMs): threshold terms $|z_t|$ or $z_t^+ = \max(z_t, 0)$ can improve fit and occasionally forecasts; ECM-based common-trend estimates are robust even when series are merely persistent rather than strictly I(1). Temporal and cross-sectional aggregation dampens nonlinearity in quarterly macro but not in financial series (interest rates, exchange rates).
• Model competition philosophy: the only way to adjudicate between modelling approaches is forecast-based competition; theoretical debate alone cannot settle the question. Granger explicitly rejects formal Bayesian prior specification for himself but endorses its value for those with sufficient self-confidence.

Concepts Introduced or Extended

• Cointegration — Gonzalo-Granger common trends; I(2) skepticism; Johansen cautions; extended memory taxonomy
• Spurious Regression — stochastic unit root as a model not rejected by I(1) tests; extended memory taxonomy

Entities Mentioned

• Clive Granger

Quotes

"If something does not feel right it probably is not right."

"I personally lack sufficient self-confidence to be a formal Bayesian, stating a specific prior, but am happy that not everyone has this personal characteristic."

"The only way to decide which consumers really prefer is to make all three fruit available and see which is purchased. The equivalence with models is to make several available and see which is selected and used in practice."

My Take

A characteristically lucid and unpretentious essay. The Gonzalo-Granger (1995) common-trends result is the main technical contribution referenced here — it provides the multivariate permanent/transitory decomposition that was missing from the original Engle-Granger (1987) framework. The stochastic unit root warning is important but underappreciated: the I(1) test literature treats the I(1)/I(0) binary as exhaustive when it is not. The I(2) skepticism argument (impulse response monotonicity problem) is elegant and convincing. The model competition philosophy anticipates later literature on forecast evaluation and is consistent with Granger's empirical, non-dogmatic style throughout his career. The explicit anti-Bayesian remark is notable given that Bayesian vector autoregression (VAR) methods (Litterman, Sims-Zha) were already standard at the time — Granger preferred frequentist tools throughout his career.