Welcome To The Menagerie IV

The next paper in the Bryant/McKibbin saga is Incorporating Demographic Change in Multi-Country Macroeconomic Models: Some Preliminary Results (2003). As in the 1998 paper they suggest:

Demographic shifts may profoundly influence the world economy, directly in the countries experiencing the demographic change and indirectly through changes in global trade, capital markets, and exchange rates. Though that point is now widely acknowledged, it is much less widely understood that existing analytical tools are inadequate for assessing the generalequilibrium and cross-border consequences of demographic change.

Unsurprisingly, they propose to remedy that:The research reported in this paper takes preliminary steps to improve the required analytical tools.

They inform us that they build on earlier theoretical work by Blanchard, P. Weil, Faruqee, Laxton, and Symansky, who use a revised life cycle approach to consumption and saving behaviour. (Actually, the MIT opencourseware, just coincidentally, has some notes on the OLG model, they are a bit technical, but here they are).


The Blanchard model could be called 'forever young'.

Bryant and Mckibbin allow changes in birth and mortality rates to be combined with an approximation of age-earning profiles in orderto allow demographic shifts to influence human wealth, consumption, and asset accumulation. They do this using two simplified empirical models: (i) a two region abridgement of the IMF’s MULTIMOD model and (ii) a two-region abridgement of the McKibbin MSG3 multi-country model. As they indicate "the stylized shock on which we initially focus is an unanticipated and transitory demographic bulge, analogous to the "baby boom" experienced by some industrial nations several decades ago."

So this is a very partial and specific shock. What this model effectively looks at it an 'ageing' scenario, where one very large cohort distorts the age pyramid as it moves upwards.They use a two economy (home and away) model to test for this shock both on an equally distributed and on a lop-sided (restricted to one country) basis.

They report that their research "strongly confirms the hypothesis that differences across countries in the timing and intensity of demographic shifts can have significant effects on exchange rates and cross-border trade and capital flows".

Parts of the paper reads - even word for word - as very similar to the 1998 one.

This part, which I didn't go into in any detail before is important:

The tradeoff facing researchers about the two routes is primarily a matter of time horizon. Multi-cohort OLG approaches that explicitly keep track of different cohorts, their saving decisions, and their wealth stocks can be more rigorous theoretically. Other things being equal, a multi-cohort OLG approach thus may appear more attractive. But other things are not equal. Multi-cohort OLG models are more difficult and demanding than models that use analytical shortcuts to get demographic effects into the consumption-saving specifications in macroeconomic models. The OLG
models, moreover, are likely to take much longer to advance to the stage where the models can deliver interesting empirical conclusions. The requirements of a multi-cohort specification are of course especially demanding in a model with numerous separate national economies and national currencies.

Another disadvantage of the multi-cohort OLG specification is that it might, if calibrated only to partial-equilibrium relationships derived from micro-level evidence, deliver misleading inferences about aggregative macroeconomic relationships. As Hamid Faruqee emphasized to us in a comment made after the international workshops that launched this project, it is both the virtue and the vice of a micro-level specification for individual agents that variables such as goods prices and interest rates are taken as exogenously given. Goods prices and interest rates self-evidently cannot be modeled as exogenous at an aggregative, economy-wide level. It is thus unclear whether a disaggregated OLG model, based on partial-equilibrium relationships estimated from micro-level data, will yield correct inferences and predictions for general-equilibrium, macroeconomic behavior (in the sense of being able to replicate the moments of actual macroeconomic data).


Forever Young

Blanchard showed that a simplifying assumption can expedite aggregation and modeling and thereby allow a researcher to avoid the adoption of a more complex and analytically difficult multicohort OLG approach. Blanchard’s key assumption was that each individual, throughout life and regardless of age, faces a constant probability of death, p. The expected life of an individual is thus 1/p . With this assumption, researchers can choose a value for p anywhere between zero and a large number. If p is put at the limiting case of zero,individuals live forever and the model yields the infinite-horizon results familiar from still simpler models; values of p in the range .03 to .01 yield model "life expectancies" in the range of 33 to 100 years.

The constant-probability-of-death assumption can be combined with an assumption, based on Yaari (1965), that the economy contains life insurance companies permitting agents to costlessly make annuities contracts contingent on their deaths.18 The two assumptions together permit the derivation of an aggregate consumption function without keeping explicit track of the consumption and wealth of multiple cohorts. Aggregate consumption turns out to be a relatively simple linear function of human and non-human (financial) wealth, with the marginal propensity to consume dependent on the age-invariant probability of death and individuals’ rate of time preference.

The authors inform us that in order to facilitate a clearer comparison of models and alternative treatments of economic behavior they constructed stylized and simplified versions of two existing macroeconomic models. The first a stylized, two-region
abridgement of the IMF staff’s MULTIMOD model as modified by Bryant and Long Zhang, and secondly a stylized, two-country abridgement of the McKibbin and Wilcoxen G-Cubed models.


As I have been indicating the study looks at the impact of a 'baby bulge' generation passing through one or both economies, and its impact on consumption and saving. Since exactly this process is taking place in the US at this moment, the following is not without some significance:

The cyclical movements in per capita human wealth and consumption during the years 10 to 30 and the associated cyclical behavior of other domestic macroeconomic variables are partly due to the fact that the new members of the population resulting from the (adult) baby bulge are at first relatively low savers. Speaking loosely, these younger adults are ascending the left side of the hump of their age-earning profiles (Figures 1 and 2). As the bulge cohorts reach their years of peak earnings and high savings, another inflection point is reached. Per capita human wealth and consumption in the fourth decade of the shock begin a long decline relative to baseline. Eventually, as the baby boomers become elderly, their labor income and human wealth decline and they begin to consume out of their financial wealth. Per capita consumption in the long run returns to the baseline level of the initial steady state.

Obviously there will be an impact on US consumption and saving as this generation pass through the earnings peak.

Finally, and as with so many of these dense technical papers, perhaps the most interesting part comes with the diagrammatic figures which start on page 59 as viewed with the adobe acrobat reader.