The Life-Cycle Hypothesis and its Role in Household Saving

Today’s Growth and Development Class was about the role of savings and the resource gap. One of the readings for the lecture is Chapter 10 Investment and Savings in Perkins, Radelet, Lindauer and Block (2013). This is why I want to dedicate today’s post to one of the concepts of the chapter, namely the life-cycle model of household saving (pp. 376-379). It was formalized by Economist and Nobel-Prize laureate Franco Modigliani (1954, 1963).

The life-cycle model attempts to explain how savings and consumption tend to vary over a person’s lifespan. In particular, young adults are expected to save less or even dis-save (borrow) due to lower incomes and the costs of starting a family and raising children. Later in life people can save more because (1) incomes rise in working life and (2) expenditures on children fall in family life. At this stage most people start to accumulate their retirement savings. Finally, after retirement people are expected to dis-save again living of their accumulated wealth (Perkins et al., 2013). Overall, the manifestation of such a life-cycle model also depends on factors like the state of pensions, or public and private retirement plans in a country which determine whether there is a need to accumulate money for retirement or whether there is a tax-financed pension system.

This is the microeconomic part of the life-cycle model which can explain in-country differences in saving rates. However, there is also a macroeconomic part to it, meaning that one would expect cross-country differences in saving rates due to different demographic structures of societies in international comparison. According to Perkins et al. (2013) this stems from a demographic transition all societies pass through. It has the following three distinct phases:

  • Phase 1: High birth and death rates and therefore low population growth
  • Phase 2: Decreasing death rates coupled with constant high birth rates from phase 1 and therefore an increasing population growth rate
  • Phase 3: Decreasing birth rates with steady low death rates reached in phase 2 and therefore dropping population growth rates

These three phases have a significant influence on a country’s age dependency ratio, i.e. the share of the population below the working age (children) and above the working age (retired) to the working-age population. The World Bank’s formal definition is “the ratio of dependents – people younger than 15 or older than 64 – to the working-age people – those ages 15-64”. Their figures are reported as “the proportion of dependents per 100 working-age population” (2016).

This age dependency ratio indicates in which phase a country is currently in. For example, poor countries in stage 2 of the demographic transition face high population growth and have a high number of young dependents (children) in relation to the working-age population. As workers need to care for many young dependents they are expected to save little or even dis-save. Once these countries transition into stage 3, the make-up of the population shifts from many young dependents to many adult workers. Hence the age dependency ratio is expected to fall which allows workers to save and the country to move from a lower income to a middle income per capita.

This link between a drop in the age dependency ratio and a rise in saving rates is what the life-cycle hypothesis predicts and what can actually be observed in some middle-income countries today. Due to dropping birth rates and a larger working-age population these middle-income countries tend to have high gross domestic saving rates. However, this is not the end of the demographic change. In the long run these countries are expected to have an ageing population. At some point there is an increasing number of retirees due to generations of low birth rates coupled with increasing life expectancy. This is what currently happens in East Asia and Pacific (for example in Korea, Japan, Thailand, China) which is ageing faster than any other region (world Bank, 2015). At this point of the demographic transition, the age dependency ratio is expected to pick up again and this is also one of the main reasons why rich countries tend to save less. Many of them have entered that stage of demographic transition, where a large share of the population are adult dependents (retirees) in relation to the working-age population. These rich countries tend to have (1) longer life expectancies together with (2) a large number of retirees drawing on accumulated savings. Overall, the life-cycle model therefore suggests lower saving rates both for low income and high income countries compared to middle-income countries.

One can test for the hypothesis of a relationship between the level of savings in a society and the demographic transition by plotting gross domestic savings (as percentage of GDP) against the age dependency ratio (as percentage of working-age population), as shown in the diagram below. For 2014 there are 155 observations on gross domestic savings and 194 observations for the age dependency ratio available from the World Development Indicators database. The average gross domestic saving rate across countries in 2014 was around 18.8 percent of GDP with a standard deviation of 18.7. The average age dependency ratio was at 59.0 percent with a standard deviation of 18.1. This means that, on average, for every 10 workers there were 5.9 people not of working age (either being young or old dependents). Gross domestic saving ranged from -50.5 percent (Liberia=LBR) to 76.3 percent (Equatorial Guinea=GNQ) of GDP. The United Arab Emirates (ARE) had the lowest age dependency ratio of only 17.5 percent, meaning that for every 10 workers there were less than 2 dependents. On the other hand, Niger (NER) had the highest age dependency ratio of 112.7 percent, meaning that for every 10 workers there were more than 11 dependents in 2014, which is expected to constrain the country’s saving capacity.

graph1.png
(Source: World Bank, 2016a; 2016b)

When regressing gross domestic saving on the age dependency ratio one can obtain the slope coefficient and the intercept for the line of best fit which is shown in the diagram. The regression results are included in the table below. It can be seen that a 10 percent increase in the age dependency ratio is associated with a 4 percent decrease in gross domestic saving. One should note though that (1) this does not infer causation and that (2) the R-squared of 15 percent reveals that there are large unexplained deviations from the trend line. Only 15 percent of the variability in gross domestic savings around the mean of 18.8 percent can be explained by the model.

  Model 1   
 Gross domestic saving Coef. Std.  Significance
Age dependency ratio -0.3976 0.0771 ***
_cons 41.9959 4.6710 ***
N 152
F(1, 150) 26.61
Prob > F 0.0000
R-squared 0.1507
Adj R-squared 0.145

Hence the life-cycle hypothesis seems to hold for some countries or might be a sign for an indirect link through some other factors but clearly does not hold universally for all countries. For example, the Republic of the Congo (COG) and Liberia (LIB) had similar age dependency ratios but significantly differing gross domestic saving ratios. The Republic of the Congo had an age dependency ratio of around 86 percent and gross domestic saving of 44 percent of GDP. Liberia had a similar age dependency ratio of around 84 percent but gross domestic saving of -50.45 percent of GDP. Both deviate significantly from the trend. The regression model would have predicted a gross domestic saving rate of 7.6 percent for Congo and a gross domestic saving rate of 8.6 percent for Liberia.

Another example are Hong Kong (HKG) and the Republic of Chad (TCD). They had similar gross domestic saving rates but largely differing age dependency ratios in 2014. Chad’s gross domestic saving rate stood at around 25.5 percent and Hong Kong’s gross domestic saving stood at around 24.1 percent of GDP. However, Chad’s age dependency ratio was at almost 102 percent of working-age population while Hong Kong’s age dependency ratio was only around 36 percent. Overall, while Hong Kong is close to the predicted saving rate of 27.7 percent of GDP, Chad has a significantly higher gross domestic saving rate than predicted by the model (1.5 percent of GDP).

One can also test for the hypothesis that the age dependency ratios for the young and the old have a different impact on gross domestic saving by separating age dependency into two variables (model 2). Firstly, the coefficient for the young age dependency ratio is more significant (1 percent level) than the one of the old (5 percent level). Second, a 10 percent increase in the old age dependency ratio is associated with a 5.4 percent decrease in gross domestic saving while a 10 percent increase in the young age dependency ratio is only associated with a 4.2 percent decrease in gross domestic saving. This contrasts with the findings of Perkins et al. (2013) which find a stronger relationship between the young age dependency ratio and the gross domestic saving rate. However, a stronger relationship between the age dependency ratio of the old and the gross domestic saving rate might be explained by the trend that children are increasingly a ‘luxury’ and people today tend to have already accumulated resources when deciding to have children and therefore the negative link between savings and children might weaken. Also, government support systems might decrease the cost of raising children and enable families to save despite raising children through policies like tax breaks or a negative income tax credit. However, the second model does not have a higher adjusted R-squared than the first one, indicating that separating the effects of young and old dependents does not increase the variability in gross domestic saving which can be explained by the model.

Model 2
Gross domestic saving Coef. Std.  Significance
Age dependency ratio old -0.5435 0.2144 **
Age dependency ratio young -0.4193 0.0827 ***
_cons 44.8889 6.1364 ***
N 152
F(2, 149) 13.53
Prob > F 0.0000
R-squared 0.1537
Adj R-squared 0.1423

So while the life-cycle hypothesis explains differences in saving rates (1) within countries at microeconomic level and (2) across countries at macroeconomic level in theory, the hypothesis has only limited applicability in practice. There are clearly other factors (for example institutional development) that cause large deviations from the trend and can explain why some countries save a lot more than others.

Thanks for reading!

Jasse

 


References

Aldo, A., and Modigliani, F. (1963). The Life-Cycle Hypothesis of Saving: Aggregate Implications and Tests. American Economic Review, 53(1), 55-84.

Modigliani F., and Brumberg, R. (1954). Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data. In K. Kurihara (ed.)., Post Keynesian Economics. New Brunswick, N.J.: Rutgers University Press.

Perkins, D.H., Radelet, S., Lindauer, D.L., and Block, S.A. (2013). Economics of Development (7th ed.). New York, N.Y.: W.W. Norton & Company.

World Bank (2015). Rapid Aging in East Asia and Pacific Will Shrink Workforce and Increase Public Spending. Retrieved from: http://www.worldbank.org/en/region/eap/brief/rapid-aging-in-east-asia-and-pacific-will-shrink-workforce-increase-public-spending

World Bank (2016a). Age dependency ratio (% of working-age population). Retrieved from: http://data.worldbank.org/indicator/SP.POP.DPND

Word Bank (2016b). Gross domestic savings (% of GDP). Retrieved from: http://data.worldbank.org/indicator/NY.GDS.TOTL.ZS

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s