L2 - Consumption Pt. 2

Question 1

Who came up with the life-cycle hypothesis?

Answer 1

Franco Modigliani (1950s)

Question 2

How is the life-cycle hypotheisis linked to Fishers model of intertemporal choice?

Answer 2

• Fisher’s model says that consumption depends on lifetime income, and people try to achieve a smooth consumption pattern (Euler equation).
• The LCH says that income varies systematically over the phases of the consumer’s “life cycle,” and saving allows the consumer to achieve smooth consumption.

Question 3

What is the basic model of the life-cycle hypothesis?

Answer 3

The basic model:

W = initial wealth

Y = annual income until retirement (assumed constant) –> varies systematically –> income falls to zero at retirement so to smooth consumption you need to save to have money when you retire.

R = number of years until retirement

T = lifetime in years

Question 4

What are the assumptions of the life-cycle hypothesis?

Answer 4

• zero real interest rate (for simplicity)
• consumption-smoothing is optimal

Question 5

How do you calculate your lifetime resources in life-cycle hypothesis model?

Answer 5

Lifetime resources = W + RY

• To achieve smooth consumption, consumer divides her resources equally over time: C = (W + RY )/T , or C = aW+bY –>

where:

• a = (1/T ) is the marginal propensity to consume out of wealth
• b = (R/T ) is the marginal propensity to consume out of income

Question 6

How does the Life-Cycle Hypothesis solve the consumption?

Answer 6

The APC implied by the life-cycle consumption function is

• C/Y = a(W/Y ) + b
• so consumption is based on wealth and income not just income, and in the short term wealth and income do not vary protionately.
• Across households, wealth does not vary as much as income, so high income households should have a lower APC than low income households.
• Over time, aggregate wealth and income grow together, causing APC to remain stable.

Question 7

How is the Consumption fuction for the Life-cycle hypothesis different to Keynes model?

Answer 7

• different from Keynes model as he assumed autonomous consumption was fixed but our intercept here can change with wealth
• Keynes focused on current income whereas the LCH focuses on income and wealth over lifetime.

Question 8

What does the Life-cycle Hypothesis look like on a graph?

Answer 8

Y- annual income;

A – wealth;

N – number of years one works;

L – number of years one lives;

C – consumption

Question 9

What are the short-run policy implications of the Life-cycle hypothesis model?

Answer 9

1. The Monetary Mechanism – wealth in the consumption function
2. Transitory (temporary) change in) Income Taxes –> if you have a fixed income, and there is a change in income tax, the government need to consider how this will affect how much you consume and save between periods 0 to N ( retirement age)

Question 10

What are some criticism of Life-cycle model?

Answer 10

Criticism – saving behavior of the elderly:

1. Uncertainty –> the model says that as soon as people hit retirement age they automatically switched to disaving, however in reality they did not consume savings at such a rapid rate due to uncertainty about the future due to medical bills or how long they would acutally live.
2. Bequest motive –> the elderly didnt want to consume all their savings to pass onto their children - if they didnt have children they had a greater motive to save for uncertainty because if they ran out of money with family they have some to rely on but if not they would have to handle that themselves

Question 11

Who came up with the Permanent Income Hypothesis?

Answer 11

Due to Milton Friedman (1957)

Question 12

What is the basic Model of the Permanent Income Hypothesis?

Answer 12

•Y = Y^P + Y^T

Where:

Y = current income

Y^P = permanent income average income, which people expect to persist into the future

Y^T = transitory income temporary deviations from average income –> win lottery all a bet –> doesnt happen every year

• Consumers use saving & borrowing to smooth consumption in response to transitory changes in income

Question 13

What is the Consumption Function Permanent Income Hypothesis?

Answer 13

•The PIH consumption function:

C = aY^P

where a is the fraction of permanent income that people consume per year.

• Friedman argued that income was the determinant of consumption like Keynes, but said he look at the wrong type of income
• Friedman look at permant income (average income over the lifetime) not just current income

Question 14

How does the Permanent Income Hypothesis solve the consumption puzzle?

Answer 14

The PIH can solve the consumption puzzle:

• The PIH implies
  APC = C/Y = aY^P/Y
• Friedman argued in the short term you are more likely to have changes in your transitory income
• To the extent that high income households have on average a higher transitory income than low income households, the APC will be lower in high income households.
• As high income households have the luxury to save their transitory income compared to those of low income households, so the APC is falling as we are saving more of that increase rather than consuming it - proportion of consumption is falling due tot the savings.
• Over the long run, income variation is due mainly if not solely to variation in permanent income (pay rise or job change), which implies a stable APC.

Question 15

How can we use a two period model two demostrate the permanent and transitory change in income?

Answer 15

• What can our simple two period model say about the temporary and permanent changes in income?
• Recall that C_t=f(Y_t, Y_t+1, r_t)
• Show what will be the impact of a small change in each of the variable:
• ΔC_t=(∂C_t/∂Y_t) ΔY_t+(∂C/∂Y_t+1) ΔY_t+1 +(∂C/∂r_t) Δr_t
• Assume ΔY_t= ΔY_t+1 and Δr_t=0 –> (no change in relative prices only want to look at wealth effect) then:

A temporary change:

ΔC_t/ΔY_t=(∂C_t/∂Y_t) –> increase is based on current income and not persistent so need to save

A permanent change:

ΔC_t/ΔY_t=(∂C_t/∂Y_t) +(∂C/∂Y_t+1) –> this increase is persistent so dont need to save as much and consumption can be greatly effected if permant income changes

Implication –> consumption responds more to a permanent change in income

Question 16

Who came up with the random walk hypothesis?

Answer 16

• Due to Robert Hall (1978)

Question 17

How is the Random-Walk Hypothesis linked to Fisher’s model of intertemporal choice and the Permenant Income Hypothesis?

Answer 17

• based on Fisher’s model & PIH, in which forward-looking consumers base consumption on expected future income
• Hall adds the assumption of rational expectations, that people use all available information to forecast future variables like income.
• If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should be unpredictable.
• A change in income or wealth that was anticipated thas already been factored into expected permanent income, so it will not change consumption
• Only unanticipated changes (change in personal income tax) in income or wealth that alter expected permanent income will change consumption in the current period ready for the change in the future.
• anticipated just means implement e.g. as you are getting a new job, your income will rise so consumption in this month will increase, however when you already have the job you income has changed from the salary you earn so consumption will stay the same.

Question 18

What does the evidence say about the LCH, PIH and RWH when there is an anticipation of income increasing?

Answer 18

• For Anticipated change in income there would be no change in consumption as that has already been factored in.
• Wicox (1989) –> looked at the announcement in increase in social security benefits, people did not adjust their consumption before they had received the increase –> Data does not support the model
• Shapiro and Slemrod (1995,2003,2009) –> when the US government announced a reduction in tax withholding, if they announced that their is an expectation that tax fares would spend before because their expecting their disposable income to increase - this did not happen many people did not spend until it was implemented –> Data does not support the model
• On substance, there is by now considerable evidence that consumption appears to respond to anticipated income increases, over and above what is implied by standard models of consumption smoothing

Question 19

What does the evidence say about the LCH, PIH and RWH when there is an anticipation of income decreasing?

Answer 19

Banks, Blundell and Tanner (1998) - data does not support the model

• used repeated cross-sectional data drawn from the U.K. Family Expenditure Survey and find a remarkable drop in consumption after retirement
• One possibility, of course, is that the life-cycle theory is not valid, and that consumers are myopic or lack selfcontrol. That is, they fail to anticipate that retirement brings about a steep decline in income.–> forced to adjust their consumption downward - Jappelli and Pistaferri (2010)
• Most of the fall in consumption at retirement may be due to the decline of work-related expenses (such as transportation, canteen meals, etc.), rather than a decline of all consumption categories - Jappelli and Pistaferri (2010)
• If consumption and leisure are substitutes in utility, the sudden increase in leisure time from the period before retirement (l) to the period after retirement (L) requires a corresponding sharp adjustment in consumption - Jappelli and Pistaferri (2010)?
• retirement is an actual shock Haider and Stephens (2007) emphasize that for most workers the timing of retirement is uncertain, and that it is sometimes forced upon the individuals by events such as prolonged unemployment or disabilities.
• increase in home production as more leisure time people may opt to grow their own vegetables than by them Hurd and Rohwedder (2006)
• Indeed, consumption appears much less responsive to anticipated income declines (for instance, after retirement)

Question 20

What does the evidence say about LCH, PIH and RWH when there is an unanticipated change in income?

Answer 20

AGREED WITH THE THEORY

Wolpin (1982) and Paxton (1993) used changes in rainfall in India and Thailand would affect consumption, respectively. –> transitory changes in income

• In agricultural economies, weather shocks affect income directly through the production function and deviations from normal weather conditions are truly unanticipated events
• permanent income shocks had a higher consumption reaction than transitory. –> agrees with PIH
• Blundell, Pistaferri, Preston (2008) –> in the US that consumers did not revise their consumption fully in response to permanent shocks
• in the long term consumption was increasing as much as income, in a lot of cases consumption increased by a small proportion than an increase in income (income and consumption grew at different rates)

Question 21

What is a potential problem the Fisher’s model of intertemporal choice faces?

Answer 21

• In Fisher’s theory, the timing of income is less important because the consumer can borrow and lend across periods.
• Example: If a consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period.
• However, if consumer faces borrowing constraints (“liquidity constraints”), then she may not be able to increase current consumption and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking

Question 22

What does a binding and non-binding borrowing constraint look like on a graph?

Answer 22

• not binding –> doesnt affect you as you didnt want to borrow ( in this case you are a saver as C₀ < Y₀)

Question 23

What happens to a borrowing constraint when their is a an increase in income?

Answer 23

• If its not binding your, budget constraint will shift outwards to an new indifference curve –> still as a saver so consumer less than your endowment point allows
• If it binding and you still want to borrow, you seen a shift outwards of your budget curve, but as you still want to consume at point D and can’t, the best you can do is consume all available income at E
• This increases current consumption, but not future consumption, as consumers behave like a keynesian individual and consume based on current income as they cannot adjust consumption for the future due to budget constraints
• Therefore, theory may not match data as people cant just borrow and save when they want to?

Question 24

What are the literature say about Rule-of Thumb Households?

Answer 24

• Showed that some people behaved as Keynes predicted some like the PIH and RWH predicted
• Campbel and Mankiw (1989, NBER):
• They show that in the data there is response to expected income which is in contrast with PIH and life cycle theory –> combined with RWH consumption only changes when there is unexpected changes in income,
• They also show that periods in which consumption is high relative to income are followed by a rapid growth in income – behaviour in line with PIH
• They suggest 50% of RoT hhlds and 50% of forward looking households

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Question 25

What are Rule-of Thumb Households?

Answer 25

also know as hand to mouth households

• households who satisfy only one’s immediate needs because of lack of money for future plans and investments.

Question 26

In the research, what are the two main reasons why the evidence deviates from the theories?

Answer 26

• Budget Constraints
• Precautionary Saving

Question 27

What was found in the paper about Precautionary Savings?

(Mody et al. (2012), IMF WP)

Answer 27

• for individual they saw a reduction in private consumption growth but an increase in the savings rate
• increasing uncertainty so the only response is to save as they don’t know what will happen in the future.

Question 28

What are the implications for consumption due to uncertainty?

Answer 28

• The key insight to understanding the effects of uncertainty is that in general the function of the expected value is not equal to the expected value of a function. –> because of uncertainty we are looking at expected utiltiy not the utility based on current and future consumption
• A little bit of tedious mathematics, but implications are very important!
• Example:
• C^g_t​+1=4; C^b_t+1=2; p=0.5;

E(C_t+1)=p*C^g_t+1+(1-p)*C^b_t+1=0.5*2+0.5*4=3;

• Assume log utility i.e. U_t=log(C_t); U’{C_t}= MU_Ct=1/C_t
• Marginal utility of expected consumption =>U’(E(C_t+1))=1/3=0.33;
• Expected marginal utility =>E(U’(C_t+1)) = 0.375

E(U’(C_t+1))=0.5*1/2+0.5*1/4=3/8=0.375

•Implications: E(U’(C_t+1))>U’(E(C_t+1))

• if uncertainty is in the model, there is a greater affect on utility, if the state is good there is a good pay off to save, but if there is a bad state there would be a greater reduction in utility due to uncertainty in the future.

Question 29

How can we model uncertainty when considering future income?

Answer 29

•We have been looking maximise utility based off current and future consumption, but if we have an uncertainty future how will that affect overall consumption

• Assume that the future income is state dependent; for simplicity, we will assume that there are possible only two states:
• good state - income Y^g_t+1; probability p
• bad state - income Y^b_t+1; probability of occurring (1-p)
• Then expected future income is given by:

E(Y_t+1)=p*Y^g_t+1+(1-p) Y^b_t+1

•Household maximizes expected utility; implication – expectation operator is introduced to the Euler equation

Question 30

What does the consumption model when considering uncertainty look like on a graph?

Answer 30

• With Marginal utlity of future consumption on the y-axis and future consumption on the x-axis
• if in a good state, future consumption will be higher and marginal utility of an increase in future consumption is lower
• is in a bad state future consumption will be lower and marginal utility of an increase in future consumption is higher –> we react more when bad things happen than good things so if something bad happen there will be a bigger swing in consumption than in a good state.
• average is expected consumption in the middle of the two states.
• to find out expected marginal utility of future consumption –> connect the points on the utility curve of the two state with a straight line, then draw up from the expect future consumption up to this line and across to find it out
• therefore when we have factored in uncertainty marginal utility is high as we are unsure about the future

Question 31

What happens to the consumption model with uncertainty when uncertainty is increasing?

Answer 31

• if uncertainty is increasing, if in a good state, consumption in the future is even higher as an investment pays off well, however if the risk doesnt go well future consumption in a bad state is even lower than usual
• When taking the average of the new points, we see that expected marginal utility will rise
• this is why there is precautionary savings because when the future is uncertain, people save more as they know that their marginal utility will be affected in a good or a bad way - so you need to save in case it goes bad

Question 32

What is the empircal evidence say about the affect on uncertainty on future consumption?

Answer 32

• Mody et al (2012) show that there was a significant increase in savings and drop in consumption - and that at least 40% of savings was due to the precautionary motives.
• There is a very good literature review by Lugilde et al (2019). The conclusion is that in general there is precautionary savings motive in the data, however, the extent of this differ.
• Guiso, Jappelli and Terlizzese (1992, JME) indicate that precautionary savings accounts for 2 percent of households net worth.
• For example, Carrol and Samwick (1998) indicate that roughly 40-45% of savings is due to the precautionary savings;
• “In sum, although most of the reviewed works find evidence of precautionary motive for saving there is not a consensus on the magnitude of this effect, and some works conclude that this motive is nearly irrelevant.” Lugilde, Bande and Riveiro (2019, Journal of Economic Surveys, p. 507)

•

Question 33

What is the psychology of Instant Gratification?

Answer 33

• Theories from Fisher to Hall assume that consumers are rational and act to maximize lifetime utility.
• Recent studies by David Laibson and others consider the psychology of consumers.
• Consumers consider themselves to be imperfect decision-makers.
• e.g., in one survey, 76% said they were not saving enough for retirement.
• Laibson: The “pull of instant gratification” explains why people don’t save as much as a perfectly rational lifetime utility maximizer would save.
• People are impatient in the short term, but in the long term people are willing to wait, as the difference between 1 sweet today and 2 tomorrow seems large in comparison to 1 sweet in 100 days compared to 2 sweets in 101 days.
• However on day 100 they would become impatient again and want instant gratification
• Laibsons argued overall consumers are rational and their preferences change over time, thus we need to start including psychology into economic models.

Question 34

What is the Monetary Transmission Mechanism?

Answer 34

The monetary transmission mechanism is the process by which asset prices and general economic conditions are affected as a result of monetary policy decisions.