Consumption smoothing

Consumption smoothing is an economic concept stating that people want to optimize their standard of living over their lifetime. In other words, "people seek to smooth spending over their lifetimes in order to obtain the greatest satisfaction from their limited resources, and the problem to be solved is how high this standard of living can be". An optimal consumption rate should be relatively similar at each stage of a person's life rather than fluctuate wildly.

The principle of consumption smoothing follows directly from the law of diminishing returns: individuals are well advised to reallocate dollars from time periods in which they are consuming a great deal (and in which incremental dollars therefore add relatively little to wellbeing), to periods in which they are consuming relatively little (and in which incremental dollars are therefore particularly valuable). To economists, consumption smoothing is the central purpose of saving.

To maintain their standard of living (purchasing power) after retirement, investors need to build up financial assets by saving a portion of their employment income during their work years. How much saving is actually needed to achieve this is a difficult question.

Traditional approaches to retirement planning start either with a fixed savings rate goal (e.g., "save 10% of your income"), or an income replacement goal (e.g., "replace 70% of your pre-retirement salary"). These approaches are likely to result in either a sudden drop or an abrupt increase of purchasing power at retirement, because they can lead the investor to save either not enough, or too much. A more rational approach is to start with the explicit aim to smooth consumption over one’s remaining lifetime, calculate this optimal consumption amount, and adjust other parameters accordingly.

This article explores the consumption smoothing approach to financial planning, first starting with a very simplified example. This example illustrates one of the main features of the economists' "optimal" recommendations, i.e. a quickly increasing (as opposed to fixed) savings rate. Whether this is realistic or not is discussed, given behavioral considerations. Then the articles mentions the uncertainty of many variables in the real world (variable salaries, unknown retirement date, ...), and additional complexities (taxes, ...) that make consumption smoothing calculations very difficult. Such difficulties can, in theory, be solved with "dynamic programming".

Deterministic example

To illustrate the concept of consumption smoothing, here is an example presented in chapter 4 of Chapurat et al. (2012). The example is "deterministic" is that there is no uncertainty involved.

A 25 year old person is about to start working, plans to retire at age 65, and plans to die broke at exactly 90. There is $3000 in a savings account, and no debt. The initial salary, payable at year end, will be $50,500, and will grow at a real (after-inflation) rate of 1%. All valuation rates are 3% real (return on investment, discount rate for human capital, etc.). Yearly consumption is to remain constant in real terms.

The following table shows the results of the calculations, in today’s dollars, with human capital and financial capital given at the beginning of each year:

Age	Gross human capital	Financial capital	Salary	Consumption	Savings	Savings rate
25	$1 372 536	$3 000	$50 500	$48 334	$2 156	4.3%
26	$1 363 212	$5 246	$51 005	$48 334	$2 661	5.2%
35	$1 240 356	$54 036	$55 783	$48 334	$7 439	13.3%
45	$999 502	$185 839	$61 620	$48 334	$13 275	21.5%
55	$605 986	$432 799	$68 066	$48 334	$19 722	29.0%
64	$72 275	$791 969	$74 443	$48 334	$26 099	35.1%
65	$0	$841 827	$0	$48 334	-$48 344	n.a.
75	$0	$577 132	$0	$48 334	-$48 344	n.a.
85	$0	$221 403	$0	$48 334	-$48 344	n.a.
89	$0	$46 936	$0	$48 334	-$48 344	n.a.

The following graphs illustrate the variations in human capital, financial capital, salary, consumption, and yearly savings.

The details of how such calculations are performed are given in Chapurat et al. (2012).. It is possible to adjust consumption so that it has an upward trend (for patient investors) or downward trend (for impatient investors). One can also change the discount rate, etc.

Rising savings rate

A key point from the above example is that the savings rate increases rather steeply over time during the working years, in line with benchmark academic advice, because the salary increases in real terms.

Consumption smoothing might even require borrowing ("dissaving") when young. While borrowing when young (beyond a mortgage) or using variable savings rates might be economically optimal, it ignores "the usefulness of establishing saving consistently as a discipline", as early as possible. In other words, people have limited willpower, and saving more and more (in percentage terms) every year might be difficult.

This example also assumes than consumption does not increase at all over time in real terms, which might be difficult to achieve in practice (many people increase their standard of living, at least partly, along with salary increases, during their working lives).

On the other hand, constant savings rates -- which are a feature of many popular books, etc. -- are unlikely to smooth consumption.

A plausible compromise between behavioral considerations and the economists' prescriptions might be something like:

• a very slowly rising standard of living (real consumption level) from perhaps age 25 to 50, and flat afterwards (ignoring the effects of household size)
• a moderately rising savings rate

Uncertainty and complexity

There is no uncertainty in the simplified illustrative model presented above: everything is known in advance. There are no income shocks, no surprises, the retirement date and lifespan is known, investment returns are constant and known in advance, etc.

The real-life complexities of taxes, government pensions and benefits (OAS, CPP/QPP), RRSP limits, variable household size over time (e.g., kids are born, grow up and eventually leave the house), and so on, are also ignored.

Dynamic programming

Given the many relevant variables, the economists' solution to consumption smoothing is called "dynamic programming". This term was created by Richard Bellman, an applied mathematician, in 1949. The 'programming' part of the name is more akin to 'planning' than to computer programming, and 'dynamic' indicates that the planning "includes multiple stages across varying time periods and decision-making junctures".

The financial planning software/tools used by most practitioners do not rely on dynamic programming and are not explicitly attempting to smooth consumption over the life cycle. Instead they target specific savings target, replacement rates, and the like. Proponents of dynamic programming argue that these conventional approaches can lead to large "mistakes", i.e. either saving too much or not enough.

Planning software based on dynamic programming is available in the US, but possibly not in Canada.

Further reading

• Kenton, Will (August 31, 2021). "Consumption Smoothing Definition, Affect on Living Standards". Investopedia.

External links

• Bogleheads wiki, Life-cycle finance. Consumption smoothing is at the core of life-cycle finance.