Akito Matsumoto (IMF)

1. Comments on “International Risk Sharing in the Long Run and in the Short Run” by Marianne Baxter Akito Matsumoto (IMF)

2. Interesting Paper • Consumption growth rate correlations behave differently at different intervals (e.g. quarterly growth rates versus 4 year growth rates) • Though this is an interesting observation on its own, growth rate correlations are not good measures of the degree of risk sharing. • Nonetheless, I agree with the basic message of the paper: it is important to look at different horizons when risk sharing is not perfect.

3. First: correlation is not a good measure of risk sharing.

4. Example 1

5. Another Example

6. So... • The only thing the correlation can tell us about risk sharing is the rejection of the null of perfect risk sharing. • Once the perfect risk sharing hypothesis is rejected at any k (perfect risk sharing implies that it should holds for all k), then one should consider how to measure the degree of risk sharing under imperfect risk sharing. • It is not quite right to draw conclusions regarding the degree (extent) of risk sharing from correlations.

7. The same applies to regression coefficients in most cases. • One can reject the null. But there seems to be no good theory to draw an economic inference except in some cases. • Asdrubali et.al. (1996): Smoothing of output shocks. • Crucini (1999) : Closeness to the two underlying models. • In time series: Flood, Marion, and Matsumoto (2010)

8. But stillanimportant contribution! • Reality may not be as nasty (average growth rates and variances of consumption and marginal utility may be similar at least among OECD countries.) • Even if the correlation is not a good measure of risk sharing, it is a measure of co-movement. Provides an interesting stylized fact. • Basic message is still valid! The horizon matters once risk sharing is not perfect. It is important to look at the data under the assumption of imperfect risk sharing.

9. When risk sharing is not perfect • Average consumption growth rates can be different • Standard deviation of consumption growth rates can be different • Correlation of consumption growth rates may not be unity (It could be unity even under imperfect risk sharing!) • The correlations at different horizons can be different (This paper)

10. Key Contribution • Correlation of consumption growth rates is high in the medium to long run. • Typically, correlations are higher among European pairs. The conclusions raise several questions: • What’s the source of correlation? • long-run consumption (and probably output) growth rate across countries are converging? • What’s the mechanism of convergence? • Probably through technological transfer (FDI?) • Currency Union?

11. Suggestions • Focus on comovement rather than risk sharing as correlation is a measure of co-movement, not a measure of the degree of risk sharing. • Once the focus is on co-movement, the natural questions arise. What about comovement of output (figure 7), investment and so on. • The paper should at least acknowledge the issue with the possible differences in average growth rates and standard deviations. • Different time horizons versus different BP filters. (related to Pakko, restat 1998) • Non-time-separable utility: may be a different paper. It is important in its own right.

12. Minor Comment on r CI :d-method to Pearson’s Correlation? • Why not to use Fisher’s Z transformation of correlation before applying d-method? • z=arctanh(r) z is approximately normally distributed. • Correlation CI is restricted to be in (-1,1)

13. Conclusions • An interesting paper: focusing on the extent of risk sharing when risk sharing is imperfect. • Approach: still based on the assumptions of perfect risk sharing so hard to interpret the results. • Nonetheless, the findings on co-movement are interesting. • The paper should either be supplemented with the theory that underpins the findings or reoriented towards broader stylized facts on co-movements.