Lu (2001) Vector Autoregression (VAR) — An Approach to Dynamic Analysis of Geographic Processes

Summary

Pedagogical introduction of vector autoregression (VAR) methodology to geographers, published in Geografiska Annaler 83 B(2): 67–78. Argues VAR's feature of treating all variables as endogenous suits geographic research where strong structural restrictions are rarely justified by theory. Estimates a 4-variable VAR(5) for US population dynamics 1910–1990 (total population, birth rate, immigration, per capita GNP) and interprets impulse response function (IRF) and variance decomposition results. Briefly surveys Bayesian VAR (BVAR), spatial BVAR, and cointegration as recent extensions relevant to geography.

Key Claims

• A VAR model for US population 1910–1990 (log-transformed, lag 5 selected by Sims' likelihood-ratio (LR) test) shows: (a) total population depends on its own history, birth rate, and immigration, but not per capita GNP; (b) birth rate is statistically determined outside the system in F-tests, but IRF shows a short-term positive response to immigration shocks that reverses after year 7; (c) immigration is explained by all four variables; (d) per capita GNP depends on its own history and population/birth rate, not immigration.
• Variance decomposition: immigration explains 21.7% of population forecast variance 1 year ahead; birth rate dominates the long run (49.7% at 9 years, 59.8% at 12 years).
• BVAR with smoothness priors (Minnesota/Litterman) outperforms unrestricted VARs; spatial BVAR (LeSage-Krivelyova 1999) extends this to regional multi-unit systems using contiguity weights.
• Proposed geographically weighted VAR (GWVAR) for spatial non-stationarity — local rather than global parameter estimation, analogous to geographically weighted regression (GWR) — cited as unpublished (LeSage 1999).
• Identification of IRF ordering: per capita GNP → immigration → birth rate → population, chosen on economic grounds; sensitivity check confirms moving-average representation (MAR) responses are robust to reordering.

Concepts Introduced or Extended

• Vector Autoregression
• Variance Decomposition
• Impulse Response Function
• Granger Causality
• Spatial VAR
• Minnesota Prior

Entities Mentioned

• Max Lu

Quotes

"VAR has some very attractive features and may also provide a valuable tool for analysing dynamics among geographic processes."

My Take

A clearly written survey aimed at geographers; adds no new econometric content but provides a concrete population-dynamics application. The finding that birth rate appears determined outside the VAR system (independent of immigration in F-tests) yet shows a positive IRF response to immigration shocks illustrates the well-known tension between joint significance tests and dynamic IRF analysis in small systems. The GWVAR proposal is interesting but remained unpublished as of 2001. For the wiki, the main value is as an example of applied VAR — IRF and variance decomposition for a 4-variable non-economic system — and a pointer to spatial VAR extensions already covered by LeSage-Krivelyova (1999).