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# How would you explain the movements in personal savings ratios in the UK since 1970?

Savings ratio(SR) is the average propensity to save, SR = Personal Disposable Income(PDI)/Savings(S). SR has fluctuated widely since 70-s being between 14% and 4%. But as PDI = Consumption(C) + S we can analyse the movements and theory based on C and PDI. Furthermore taxes can be seen as exogenous, so PDI can be approximated to Y. Latter on when I reach my conclusion I will return to APS. When specific numeric values are used they have been optimised for APS to include years 1950-90, and although the factors influencing APS have remained mainly the same these figures are approximate and a better fit could be obtained if date is optimised for 1970-96, because some things (like housing) have changed in importance. On the other hand period from 1970-s onward have only captured one and a half serious business cycles, so the data before 1970 is beneficial in determining the correlation. Savings ratio looked like:

It is seen from this graph that savings ratio moved broadly upwards until 1980, then fell sharply until 1989 and then rose again. Although there is one emprical model that can be used to estimate this, it includes multiple regression and we are inable to calculate that. But luckily there are factors that affect the savings ratio heavily in certain periods. Doing simple regression on these we can estimate if they were important or not and how has the importance of different factors changed.

Keynes' theory explains the rise in savings' ratio up to 1984. Aftter that it does not work so I will not use later data for regression. The theory was that C=A+MPCxY, where A is a constant called autonomous consumption and MPC is the marginal propensity to consume. So this equation implies that savings is a type of super good that can be substituted for consumption. By diagram:

E is expenditure in here and I investment. C - consumption.

As seen the movement in savings ratio can occur because of a change in income that will cause movement along the C curve and thus cause relatively more savings. Or it can be because of a shift in the C curve, caused by, as Keynes suggested, capital gains etc. Keynes model is also thought to work in the short-run, and here comes the major difference between the Keynes and the Rational expectations(RE) view.

During the 1970's income rose. That means wealth did too and thus people should have saved more.As income was rising quite quickly and unexpectdely, people did not make an automatic adjustment to their lifetime income hypotheses. Thus their transitory income rose (current income-expected lifetime income). Friedman theory says this should have increased savings. In order to prove that I must regress change in income and savings ratio. Infact the r2=0.66, which implies fairly high correlation. Note however that Keynes theory does not predict the fluctuations in the savings ratio accurately. It only describes the general trend.

CORRELATION

In order to determine the cyclical movement in the savings ratio I must make first of all a minor adjustment. The correlation between actual APS and predicted one is better when C is put in logarithmic form - i.e. C=AYb where b is the elasticity of consumption, denoting c=log(C) and y=log(Y) we get c=k+by, where k is again a constant. Putting values in:

C=3.65+0.89Y

c=0.19+0.95y

CORRELATION

This function can explain the general trends in savings ratio up to 1980-s better than the original Keynes one. But it still cannot predict the cycles. Some writers have said it is wrong to count savings as a good, that the savings are used to even out fluctuations in income. This view is called the life cycle hypothesis by Modigliani (or with similar outcome permanent income hypothesis by Friedman). Graphically:

 Dissaving       Saving

Permanent income depends on the expectations of the previous incomes. For example if people base their expectations of next income on say 3 previous time periods(it could be any number of time periods) then:

yp=(yt+y(t-1)+y(t-2))/3

ct=0.27+0.94yp

This equation looks very much like the equation above, elasticity being only 0.01 smaller. But there is a very important difference here - the short term(one year) elasticity is only 0.31. That means when the income were to rise by 10% then the consumption would go up approx. 3.1% on the three subsequent years not all on the first year. That gives rise to a substantial savings in the first two years. This equation can estimate the consumption more accurately.

### REGRESSION

But people will not value the previous information evenly - information a while ago is less important. So it is right to include geometrical weights to expectations:

ypt=(1-w)yt+w(1-w)y(t-1) +w2(1-w)y(t-2) ...

1>w>0

ct=kyt+et   e is the error, so is k

summing the GP ct=k(1-w)ypt+wct-1

That means current consumption is based on the previous consumption and the expected income this year. Putting in numbers:

ct=0.26ypt+0.73ct-1+0.05

Income is predicted by rational consumers with all the information they have - i.e. the information that they know in t-1 period and new uncorrelated information that becomes available in t. Under permanent life time hypothesis they will try to even out the cycles in consumption. So in equation

ct=kct-1+et

the et term is the error and with mean 0 and uncorrelated with any of the variables in the equation. This is Euler's equation and suggests that consumption could not be predicted. When k=1 the situation is called a random walk as the ct can either go up or down. However the evidence suggests that k>1 because income rises over the time and people expect it to rise.

### REGRESSION

Furthermore et seems to be correlated with itself and thus the random walk model could be enhanced. This last equation was used a lot a while ago and called adaptive expectations. But the consumers will have a permanent bias when income changes regularly. RE dealt with that including more variables, that I introduce later, to consumption function. Also it has been suggested the consumers have a target long-term income. In short term there are shocks affecting consumers, so they will try to balance the current consumption to meet his long-term target. This is called the error correction method and it says that the correlation is between the change in ct and y­t not in the absolute values.

ct=a+bypt+gst-1+f­t

In here s is the savings ratio in the period before (i.e. people learn from their previous experience of e­­). denotes inflation, that is also thought to be one of the major causes of change in APS. It reduces the real value of debt. So originally it was thought by Keynesians that higher levels of inflation reduced savings and forced people to consume more as the value of savings fell. But after 1970 the idea about inflation changed changed. Consumers are largely net creditors. So inflation is like a tax on their savings to the government who is a net debtor. This tax is not included in the PDI. Although in long-term the effect could 0 due to lower taxes arising from reduced national debt, in the short term savings will rise. Also there is usually a lag between receiving income and spending it, with high inflation this will decrease consumption. People also hold some money as a proportion of their wealth for rainy days. With inflation its real value falls so people have to make it up by saving more. Businesses are also included in the consumption. Their stock (which is savings)appreciates, so they save more. Inflation also favours young, who borrow to buy their house. Unfortunately this is a multiple regression equation. So I have to take these hypothesis as given.

House prices are another major item affecting APS. This was especially true after 1984, when Keynes model did not work anymore. The evidence is more of an empirical sort here. Economists tried to find explanation for the rise in APS in late 80s and the housing boom seemed like a good initial guess. One can have a theoretical reasoning that says when house prices went up people could either sell their houses and use the money to spend quite a lot or they could borrow more on existing housing with the liberal credit policy.  House is a part of wealth and people's wealth increased. This is generally attributed as being a source of more consumption as people's expectations were not set for higher wealth and they find they can allow themselves a lot more without affecting their life cycle hypothesis. We can test the wealth hypotheses by regression. Increase in wealth is denoted by W/Y, so we get

APS=16.19-164W/Y, R2=0.29, coeficient of correlation is approx=3, which is bigger than 2, so the correlation is significant here. When looking at the change in house prices closer we can observe that the rise in house prices also attributed for the reduction in APS in 72-3 as well as in 80s and its fall made the savings to rise again in 1990s.

Credit liberalisation and the reduction in the uncertainty of income (i.e. the income growth stayed more stable) were also playing their part. We cannot test the credit liberalisation, but we can test how much the income changed in absolute terms when compared to previous year. The hypotheses goes that when the income fluctuates widely then savings should be higher as there is larger uncertainty.

### GRAPH

So high levels of savings in 1990s were due to larger uncertainty arising possibly from the  recession.

Interest rates were originally thought to have no effect on savings ratio. Interest rates are also strange because theoretical reasoning for them affecting the savings can be put either way and in practice there was very little correlation before 1989. Although there was some lagged correlation (as seen from the graph) and much more correlation in 1990-s - high interest was causing savings.

### GRAPH and CORRELATION

So the finial equation with values in it includes a provision for the change in house prices(RHP) and uncertainty():

ct=a+bypt+gst-1+f­t+hRHP+k

ct=-0.009+0.73ypt+0.19st-1-0.09­t+0.018RHP-0.51

This equation allows the prediction of the savings ratio to quite a large extent. In calculating the prediction we must take the contribution of each individual item relatively. That means, for example, that when the average inflation (*)over a period of time was 5% and this year we have 6% then the actual contribution is 1% and we should use that for our figures. So *=5% in that example. I cannot put any simpler than an example. If the inflation was 10% at a time period and the average infaltion was 5% for previous 100 years, then we expect the consumption ratio to fall by 0.45% not by 0.9% (look at the equation above which says ct=-0.09 times inflation).

However we have not included the split between consumer durables and other current goods in here. Economists have said these are so different and the motives for buying them are different as well, so there should not be just one c. However, no study has yet proved any significant relationship increase when consumer goods are splitt. There should be internal substitution occurring between investment and consumption when interest rates rise, but no study has yet shown that this holds true. There is also the credit availability in crises hypothesis, that predicts that the consumption can move down but cannot move up for families with liquidity problems as they cannot get credit freely. Again not much empirical evidence has been found.

Now as y appeared in the equation all the factors that influence y influence also c. That means that unemployment affects the savings ratio and so do world influences and trade cycles. Also demographic changes will change people's lifetime hypothesis - when they will expect to live longer and be longer pensioners then they will save more. But these effects are very long-term ones and thus cannot be very relevant to this 25year period. Similarly institutional and social changes influence savings. For example the appearance of well established pension funds caused savings to rise in the 70s. That can explain why savings are high now. Different groups of people have also different transitionary incomes (deviations from the lifetime income) so they are expected to save more. One example with high transitory income are farmers, so when their proportion rises in the population, then the savings will increase too.

Richer people, especially those in top 20% , also save more as bequests. Rising income inequality from 1979 onwards could attribute partially to the rise in savings ratio. This means savings is a luxury.