Inaccuracy of Loglinearization in Welfare Calculations: Complete vs. Incomplete Market Economies

Most general equilibrium models calculate welfare gains from international risk sharing based on a loglinear approximation. They have reported welfare gains ranging from zero to one percent of permanent consumption. Some simulation results -- Tesar (1995), van Wincoop (1997), and Kim (1997) -- even reported negative gains from risk sharing. Despite these controversial results, the accuracy of the loglinear approximation in calculating welfare has not been thoroughly examined. This paper investigates the accuracy of the loglinear approximation in welfare calculations by comparing certainty-equivalent consumption levels under complete-market and bond-only economies. We compare the welfare gains determined by two solution methods: exact solution and log-linear approximation. We replicate the results in Tesar (1995) on welfare-gain calculations by solving the nonlinear equation system under certainty equivalence using the TROLL program. Under certain parameter values, we show that the loglinear approximation generates higher welfare in the bond-only economy than the complete-market economy, while the nonlinear solution produces a correct welfare ordering. Even though loglinearization generates accurate results in calculating the first and second moments, it generates significantly incorrect results in calculating welfare. This robust result suggests that all the welfare calculations based on the loglinear approximation should be abandoned.