L3 - Consumption
Introduction to Consumption Theory
This lecture provides an overview of the most important concepts and theories regarding how and why people spend money (consume):
John Maynard Keynes: Focused on the direct relationship between current income and consumption.
Irving Fisher: Explored how people make choices about spending and saving across different time periods (intertemporal choice).
Franco Modigliani: Developed the Life-Cycle Hypothesis, suggesting people plan consumption over their entire lives.
Milton Friedman: Proposed the Permanent Income Hypothesis, emphasizing that people base consumption on their long-term, 'permanent' income.
Robert Hall: Introduced the Random-Walk Hypothesis, building on previous ideas with the concept of rational expectations.
Borrowing constraints: Examines how limits on borrowing can affect consumption decisions.
Precautionary savings: Explores why people save extra money for unexpected future events.
The Life-Cycle Hypothesis (LCH)
Developed by Franco Modigliani in the 1950s.
The LCH suggests that consumption depends on lifetime income rather than just current income. This means individuals don't just look at their paycheck today, but consider all the money they expect to earn and have access to throughout their entire life. The goal is to achieve a smooth consumption pattern, meaning they try to avoid big ups and downs in their spending, preferring to spend a relatively constant amount each year.
Key insights into LCH include:
Basic Model:
Variables:
W = initial wealth (money or assets you have at the start).
Y = annual income until retirement (assumed to be constant for simplicity).
R = number of years until retirement (how many more years you expect to work).
T = total lifetime in years (how long you expect to live).
Assumptions:
Zero real interest rate (for simplicity): This means money today is worth the same as money in the future, with no gain or loss from interest, simplifying calculations.
Consumption-smoothing is optimal: The idea that people prefer a stable level of consumption over their lifetime.
Lifetime Resources Equation:
Total lifetime resources are the sum of your initial wealth and all the income you expect to earn before retiring:
\text{Lifetime Resources} = W + (Y \times R)W: Your starting financial assets.
Y \times R: The total income you will earn from now until retirement. If you earn Y per year for R years, your total future income is Y multiplied by R.
Consumption Smoothing Model:
To achieve smooth consumption, the consumer divides their total lifetime resources equally over their total lifetime:
C = \frac{(W + RY)}{T}C: This is your annual consumption, which is kept constant over your lifetime.
The equation shows that your annual consumption (C) is determined by your total lifetime resources (W + RY) divided by the total number of years you expect to live (T).
Alternatively, this can be expressed as: C = aW + bY
This form of the equation shows how consumption (C) responds to changes in wealth (W) and income (Y).
a = \frac{1}{T}: This is the marginal propensity to consume (MPC) out of wealth. It tells us how much consumption increases for every extra dollar of wealth. Since you spread wealth over your entire life, an extra dollar of wealth leads to 1/T extra dollars of consumption each year.
b = \frac{R}{T}: This is the marginal propensity to consume (MPC) out of income. It tells us how much consumption increases for every extra dollar of annual income. An extra dollar of income earned for R years means R additional dollars in total resources, which are then spread over your T years of life.
Consumption Puzzle Solving:
The average propensity to consume (APC), which is the fraction of income spent on consumption (C/Y), is indicated by the LCH consumption function as:
\frac{C}{Y} = a\left(\frac{W}{Y}\right) + bWhy higher-income households have a lower APC: Wealth (W) tends to vary less from household to household compared to income (Y). This means for households with much higher incomes, the ratio of wealth to income (W/Y) will be smaller. Consequently, their average propensity to consume (C/Y) will be lower because a smaller proportion of their total resources (which include wealth) makes up their income. They save a larger fraction of their current high income.
Why aggregate APC is stable over time: Over long periods, both the total wealth and total income of an economy tend to grow at a similar rate. Since W and Y grow synchronously, the ratio W/Y remains relatively stable, ensuring that the aggregate (economy-wide) APC also stays stable, as observed in historical data.
Implications of LCH:
Saving behavior varies systematically throughout a person’s lifetime: People save during their working years (especially middle age) to fund consumption during retirement (when income is low or zero). They dissave (spend savings) in retirement.
Short-run Policy Implications:
The Monetary Mechanism: LCH highlights the importance of incorporating wealth into consumption functions for economic modeling, not just income. Changes in asset prices (affecting wealth) can thus influence consumption.
Effects of transitory income tax changes: If a tax change is temporary (transitory), it has a smaller impact on lifetime resources, and therefore a smaller impact on current consumption, compared to a permanent tax change.
Criticism:
The LCH has been criticized for not fully accounting for:
Uncertainty: People face uncertain futures (e.g., unexpected medical costs, longer lifespans), which can lead them to save more than the LCH predicts (precautionary savings).
Bequest motives: Some individuals save not just for their own consumption but also to leave an inheritance for their heirs.
Variables (reiterating for clarity, as used generally in consumption theory discussions):
Y = annual income
A = wealth (often used interchangeably with W)
N = years worked or working life
L = years lived or life expectancy
C = consumption
The Permanent Income Hypothesis (PIH)
Proposed by Milton Friedman in 1957.
Central ideas include:
Consumers don't just react to their current income; they use saving and borrowing to smooth consumption against transitory income changes. This means if income temporarily goes up (e.g., a bonus), they might save most of it rather than spending it all immediately, aiming to keep their consumption stable. Conversely, if income temporarily drops, they might borrow or use savings to maintain their consumption level.
Consumption Function in PIH:
C = aY_P
C: Annual consumption.
Y_P: Permanent income, which is the average or long-term income an individual expects to receive over their lifetime. It's their sustainable income level.
a: This is a constant fraction (between 0 and 1) representing the portion of permanent income that consumers choose to spend annually. It's their marginal propensity to consume out of permanent income.
APC through PIH:
The PIH implies an average propensity to consume (APC) of:
APC = \frac{C}{Y} = \frac{aY_P}{Y}Y here represents current income, which can include both permanent and transitory components.
Why high-income households exhibit a lower APC: If a household has unexpectedly high current income (Y) due to a large transitory income component (YT), their current income (Y) will be much higher than their permanent income (YP). Since consumption (C) is based on the lower permanent income (Y_P), the ratio C/Y will be smaller, leading to a lower APC. They save the temporary excess income.
Over the long term, variations in income arise primarily from changes in permanent income, not just temporary fluctuations. This means that on average, Y will be close to YP. When Y is approximately equal to YP, the APC = aY_P/Y approximates a, yielding a stable APC over long periods.
Definition of Income:
Friedman distinguishes between current income and its components:
Y = YP + YTY: Total current measured income.
Y_P = Permanent income: The part of income that individuals expect to persist into the future. It's the stable, long-term component of income.
Y_T = Transitory income: The temporary, unexpected deviations from permanent income. This could be a bonus, a one-time windfall, or a temporary job loss.
Comparison between LCH and PIH
Both hypotheses fundamentally agree that individuals attempt to achieve smooth consumption despite fluctuations in their income. They both move beyond simple Keynesian current-income consumption.
LCH: Explains systematic variations in income over a person's life (low when young/old, high during working years) and how consumption remains stable by saving/dissaving in response to this predictable pattern.
PIH: Explains how consumption fluctuates less than income due to random, transitory income changes. People use saving/borrowing buffers to smooth over these unpredictable short-term income shocks.
Both hypotheses were significant breakthroughs because they effectively address the consumption puzzle: explaining why the average propensity to consume (APC) is stable over the long run but tends to be lower for higher-income households in cross-sectional data.
Application of Consumption Theories
Example scenario: Consider a 50-year-old anticipating 25 more work years before 15 years of retirement, with an assumed interest rate of 0%.
How a windfall affects consumption: How would this individual adjust their consumption if they won £1,000,000 versus if they received £10,000 each year until the end of their life?
Keynesian approach: Might suggest a large immediate increase in consumption if the £1,000,000 is spent quickly. If it's £10,000 annually, consumption rises by £10,000 annually.
LCH/PIH approach: Both would suggest that the £1,000,000 lump sum would be spread out over the remaining years of life (T). The increase in annual consumption would be £1,000,000 / T. Similarly, the £10,000 per year would be considered a relatively permanent addition to income, leading to an increase in consumption closer to £10,000 annually, potentially adjusted for the MPC out of income (b).
The timing and permanence of the income stream are crucial here. A one-time windfall (like £1,000,000) is a large transitory income, which PIH suggests should be saved and spread out. A regular, lasting income stream (like £10,000 each year for life) is more like an increase in permanent income, leading to a larger, more sustained increase in consumption.
Policy Implications from such case studies are explicitly derived and compared with the simpler Keynesian approach, which often focuses solely on current income and a constant MPC.
The Random-Walk Hypothesis
Introduced by Robert Hall in 1978.
This hypothesis builds on Fisher’s intertemporal choice model (people plan spending over time) and Friedman’s PIH model (consumption depends on permanent income).
It includes the crucial assumption of rational expectations, meaning consumers use all available and relevant information (including future expectations and economic theories) to forecast their future income as accurately as possible. They are forward-looking and smart.
Random Walk Consumption Model:
If the PIH holds true and consumers have rational expectations, then changes in consumption should appear random and unpredictable.
Anticipated changes in income/wealth: Any income or wealth changes that consumers expect to happen (e.g., a known salary raise next year, a scheduled pension increase) are already incorporated into their expected permanent income today. Therefore, when these anticipated changes actually occur, there should be no new change in consumption because consumers have already adjusted their spending plans. Their consumption path is already optimized based on this future knowledge.
Only unanticipated changes that affect permanent income will alter consumption behavior. For example, a sudden job loss or an unexpected inheritance would lead to an immediate, unpredictable change in consumption because it alters their perception of permanent income after they had already made their plans.
Testing the Consumption Hypotheses
Investigative questions include:
Expected reactions to anticipated income changes: The theories (especially Hall's) predict no significant response in consumption to income changes that were already foreseen, due to consumption smoothing and rational expectations.
Reactions to unanticipated shocks:
Marginal Propensity to Consume (MPC) from transitory shocks is minimal: If a temporary (unanticipated) bonus is received, consumers should save most of it to smooth consumption, leading to a very small increase in current consumption.
MPC from permanent shocks tends towards 1: If an unexpected income change is perceived as permanent (e.g., a permanent raise or job loss), consumers will adjust their permanent income significantly. This will lead to a much larger change in consumption, potentially close to 100% of the perceived permanent change, as they re-optimize their lifetime spending.
Noteworthy literature includes:
Jappelli and Pistaferri (2010) - Provides a comprehensive review of the empirical literature (studies using real-world data) testing these consumption theories.
Anticipated Changes in Income
While theory suggests no reaction to anticipated income changes, empirical research indicates that households often do react to anticipated income changes.
Findings by numerous studies highlight significant behavioral shifts responding to anticipated income increases (e.g., people may start spending more before a known future raise).
Conversely, responses to anticipated income declines tend to be more limited (e.g., people don't cut consumption as sharply before a known retirement income drop).
This discrepancy often stems from the role of borrowing constraints. Without the ability to borrow against future anticipated income (especially if it's an increase), people might delay consumption until the income actually arrives. Similarly, if facing an anticipated decline, borrowing constraints might prevent them from smoothing as much as they'd like, forcing a larger, earlier cut in consumption.
Unanticipated Changes in Income
Studies affirm the higher consumption response to permanent shocks than to transitory ones, consistent with both PIH and LCH.
However, evidence also suggests consumers might not fully adjust consumption based on permanent income changes as much as the pure theories predict. This could be due to continued uncertainty or other factors.
The role of precautionary savings is highlighted for different income scenarios: People tend to save more of unanticipated income if they perceive greater future uncertainty, rather than spending it all immediately, even if it seems permanent.
The Impacts of Borrowing Constraints
A borrowing constraint is a limit on how much an individual can borrow. It restricts a consumer's ability to shift consumption from the future to the present.
The constraint defines the relationship between current and future consumption. A simplified form is: Ct \leq Yt
This constraint indicates that consumption (Ct) in period t cannot exceed current income (Yt) in period t. In other words, you can't spend more money than you currently have (or can earn) if you can't borrow.
Impacts on consumer optimization: When the borrowing constraint is:
Non-binding: The consumer can borrow and lend freely, allowing them to perfectly smooth consumption over time, as predicted by LCH and PIH. Their consumption is not limited by their current income but by their lifetime resources.
Binding: The consumer is unable to borrow as much as they would like (or at all). This forces their current consumption to be lower than their desired smoothed level. For example, a young person with low current income but high expected future income might want to borrow to consume more today, but a binding constraint prevents this. Their consumption becomes directly tied to their current income, resembling the Keynesian model more closely in the short run.
Applications of Economic Policies and Consumer Behavior
Practical examples demonstrating the effects of economic policies:
A 1.9 trillion stimulus (American Rescue Plan Act of 2021) with immediate direct payments: Analyzing consumption across different borrowing constraints.
Without borrowing constraints (ideal LCH/PIH): The direct payments, if perceived as transitory income, would largely be saved, leading to a small increase in current consumption. If they improve perceived long-term financial security, consumption might rise more.
With binding borrowing constraints: For households facing liquidity constraints (unable to borrow), these direct payments provide immediate cash, allowing them to increase current consumption significantly, as it directly alleviates their inability to spend up to their desired level.
A substantial announcement regarding National Insurance Contributions increase: This would lead to varying consumer responses based on different theories.
If perceived as a permanent reduction in future net income, PIH/LCH would predict a reduction in current consumption as people adjust their permanent income down. The size of the reduction depends on when the change takes effect and its perceived permanence.
A Keynesian view might only see a consumption impact once the contribution actually affects disposable income.
Precautionary Savings
Precautionary savings refers to the saving of current income to guard against future uncertainty, such as unexpected expenses (e.g., medical emergencies, job loss) or an uncertain future income stream.
Investigative works such as Mody et al. (2012) show:
Significant increases in savings with corresponding reductions in consumption, especially during times of economic uncertainty.
At least 40\% of savings attributed to precautionary motives, suggesting it is a very important driver of saving behavior.
Literature reviews reveal mixed conclusions regarding the magnitude of precautionary savings across different contexts. This means its importance can vary depending on economic conditions, cultural factors, and individual circumstances.
The importance of situational factors such as economic crises influencing consumer behavior: During recessions or pandemics, people tend to increase precautionary savings dramatically due to heightened uncertainty about jobs, health, and economic stability.
Conclusion and Summary
Recap of the most significant consumption theories, showing how they build upon each other:
Keynes: Early focus on current income.
Fisher: Introduced intertemporal choice – spending decisions across time.
Modigliani (LCH): Emphasized lifetime income and systematic income variations.
Friedman (PIH): Focused on permanent income and smoothing against transitory shocks.
Hall (Random Walk): Integrated rational expectations, leading to unpredictable consumption changes based only on unanticipated shocks.
And the addition of instant gratification from Laibson (not detailed in this note but an important modern contribution), suggesting self-control problems can influence consumption, leading to deviations from purely rational smoothing models.
Evolving consumption functions now reflect a more complex understanding, taking into account current and expected future income, wealth, interest rates, and self-control mechanisms.
References
Comprehensive list of citations including key papers and studies that substantiate the theories and findings discussed throughout the lecture.
References include works from influential economists and recent empirical studies that inform current understanding