Mark-Ogaki-Sul (2005) Dynamic Seemingly Unrelated Cointegrating Regressions

Summary

Mark, Ogaki, and Sul (2005) propose the Dynamic Seemingly Unrelated Regression (DSUR) estimator for systems of cointegrating regressions whose equilibrium errors are cross-sectionally correlated. DSUR achieves asymptotic efficiency by combining SUR-style generalized least squares (GLS) with leads and lags of first differences of regressors from all equations — correcting endogeneity parametrically, making it computationally transparent relative to nonparametric fully-modified SUR (FM-SUR) alternatives (Park-Ogaki 1991). Monte Carlo experiments show substantial mean squared error (MSE) reductions over equation-by-equation dynamic OLS (DOLS) when cross-equation correlation is high, and two applications — forward exchange rates and Feldstein-Horioka saving-investment — demonstrate how DSUR can weaken or reframe prior empirical anomalies.

Key Claims

• DSUR is asymptotically efficient (semiparametric efficiency bound, equivalent to the maximum likelihood estimator, MLE) for systems of cointegrating regressions with correlated equilibrium errors (Proposition 4).
• Full efficiency requires leads/lags of $\Delta x_{jt}$ from ALL equations — not just own-equation regressors — augmented into each equation before the SUR GLS step.
• At high cross-equation correlation ($\rho \approx 0.95$, Monte Carlo Case III), DSUR achieves relative $\mathrm{MSE} \approx 0.45$–$0.54$ vs. DOLS at $T=50$–$300$ (46–56% reduction).
• Restricted DSUR (RDSUR) under coefficient homogeneity achieves up to 73% MSE reduction vs panel DOLS when error variances are highly heterogeneous (Case VI, $T=50$: Rel.$\mathrm{MSE} = 0.265$).
• When cross-equation correlation is low (Case I), DSUR offers minimal gains and can slightly underperform DOLS in finite samples.
• The Evans-Lewis (1993/1995) forward-rate anomaly is weakened: with 2 leads/lags, $\chi^2(\beta=1)=5.34$ ($p=0.148$) — fail to reject; only borderline with 3 leads/lags ($p=0.056$).
• Feldstein-Horioka results are specification-dependent: non-European restricted $\beta=0.777$ ($t=-3.60$, significant) in S/Y ratios, but $\beta=1.019$ (insignificant) in log-levels — the solvency-constraint interpretation (Coakley-Kulasi-Smith 1996) is not rejected by the log-levels specification.
• DSUR is computationally infeasible for large $N$: $\Omega$ has $N(N+1)/2$ free parameters.

Concepts Introduced or Extended

• Dynamic Seemingly Unrelated Regression
• Feldstein-Horioka Puzzle
• Forward Premium Anomaly
• Seemingly Unrelated Regression
• Cointegration

Entities Mentioned

• Nelson Mark
• Masao Ogaki
• Donggyu Sul

Quotes

"This estimator exploits the cross-equation correlation in the errors, is asymptotically efficient, and is computationally more convenient to use than the existing nonparametric versions of seemingly unrelated cointegrating regression estimators."

"DSUR will not be computationally feasible in systems of large N because the number of free parameters that must be estimated in the error correlation quickly becomes unwieldy as N grows."

My Take

DSUR's core contribution is parametric tractability: Park-Ogaki (1991) seemingly unrelated canonical cointegrating regression (SU-CCR) also achieved asymptotic efficiency but had poor finite-sample performance, with the nonparametric spectral estimator of $\Omega$ adding noise. DSUR trades flexibility for computational transparency and better small-sample behavior. The two empirical applications illustrate sensitivity of prior findings rather than definitively resolving anomalies — the forward-rate result flips from rejection to non-rejection between 3 and 2 lags, and the Feldstein-Horioka conclusion reverses entirely between ratio and log-level specifications. The DSUR framework is most compelling for small systems ($N \leq 8$) where $T \gg N$ and there is prior reason to expect cross-equation error correlation.