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Micro Data For Macro Models

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  1. Micro Data For Macro Models Topic 2: Lifecycle Consumption

  2. Part A:Overview of Lifecycle Expenditures

  3. Why Do We Care About Lifecycle Expenditure? Why is it important? Learn about household preferences broadly C.E.S. vs. log vs. other / Habits? / Status? - Estimate preference parameters intertemporal elasticity of substitution/ risk aversion/ discount rate - Learn about income process permanent vs. transitory shocks / expected vs. unexpected - Learn about financial markets/constraints liquidity constraints / risk sharing arrangements - Learn about policy responses spending after tax rebates, fiscal multipliers, etc.

  4. Why Do We Care (continued)? The big picture with consumption: - Use estimated parameters to calibrate models - Understand business cycle volatility - Conduct policy experiments (social security reform, health care reform, tax reform, etc.) - Estimate responsiveness to fiscal or monetary policy - Broadly understand household behavior

  5. How We Will Proceed The outline of the next part of the lecture: - Understand lifecycle consumption movements o Illustrative of how one fact can spawn multiple theories. o Show how a little more data can refine the theories o Illustrate the empirical importance of the Beckerian consumption model (i.e, incorporating home production and leisure).

  6. Fact 1: Lifecycle Expenditures Plot: Adjusted for cohort and family size fixed effects

  7. Define Non-Durable Consumption (70% of outlays) • Use a measure of non-durable consumption + housing services • Non-durable consumption includes: Food (food away + food at home) Entertainment Services Alcohol and Tobacco Utilities Non-Durable Transportation Charitable Giving Clothing and Personal Care Net Gambling Receipts Domestic Services Airfare • Housing services are computed as: Actual Rent (for renters) Imputed Rent (for home owners) – Impute rent two ways • Exclude: Education (2%) , Health (6%), Non Housing Durables (16%), and Other (5%) <<where % is out of total household expenditures>>

  8. Empirical Strategy: Lifecycle Profile of Expenditure • Estimate: (1) where is real expenditure on category k by household i in year t. Note: All expenditures deflated by corresponding product-level NIPA deflators. Cohortit= year-of-birth (5 year range – i.e., 1926-1930) Dt= Vector of normalized year dummies (See Hall (1968)) Family Composition Controls: Household size dummies, Number of Children Dummies Marital status dummies , Detailed Age of Children Dummies

  9. Fact 2: Hump Shaped Profile – By Education From Attanasio and Weber (2009)

  10. Fact 3: Retirement Consumption Dynamics From Bernheim, Skinner and Weinberg (AER 2001)

  11. The Puzzle? (Friedman, Modigliani, Hall, etc.) {Nt, Vt} are permanent and transitory mean zero shocks to income with underlying variances equal to σ2N and σ2V

  12. Preferences

  13. Euler Equation

  14. What Are Potential Taste Shifters Over Life Cycle Family Size o Makes some difference o Hump shaped pattern still persists o See Facts 1 and 3 (above) – these were estimated taking out detailed family size controls. 2. Other Taste Shifters (that change over the lifecycle – for a given individual)?

  15. Fact 4: Deaton and Paxson (1994) “Intertemporal Choice and Inequality” (JPE) Hypotheses: PIH implies that for any cohort of people born at the same time, inequality in both consumption and income should grow with age. How much consumption inequality grows informs researchers about: o Lifecycle shocks to permanent income o Insurance mechanisms available to households. Data: U.S., Great Britain, and Taiwan

  16. Deaton and Paxson Methodology (U.S. Application) Variance of Residual Variation Compute variance of εkitat each age and cohort Regress variance of εkiton age and cohort dummies Plot age coefficients (deviation from 25 year olds) Note: This is my application of the Deaton/Paxson Methodology (very similar in spirit to theirs).

  17. Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services

  18. Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services Cross Sectional Variance of Total Nondurables for 25 Year Olds = 0.16

  19. Fact 4: Deaton-Paxson Cross Sectional Dispersion: With and With Out Housing Services Cross Sectional Variance of Total Nondurables for 25 Year Olds = 0.16

  20. Questions: 1. What Else Drives the Hump Shaped Expenditure Profile? 2. Why Does Expenditures (on food) Fall Sharply At Retirement? 3. Why Does Cross Sectional Consumption Inequality Increase Over the Lifecycle?

  21. Explanations for Questions (1) and/or (2) Liquidity Constraints and Impatience - Gourinchas and Parker (2002) Myopia - Keynes (and others) Time Inconsistent Preferences (with liquidity constraints) - Angeletos et al (2001) Habits and Impatience Non-Separable Preferences Between Consumption and Leisure - Heckman (1974) Home Production/Work Related Expenses - Aguiar and Hurst (2005, 2008)

  22. Part B:Gourinchas and Parker (2002)

  23. Gourinchas and Parker (2002) “Consumption Over the Lifecycle” (Econometrica) You should read this paper. Estimates lifecycle consumption profiles in the presence of realistic labor income uncertainty (via calibration). Use CEX data on consumption (synthetic cohorts). Estimates the riskiness of income profiles (from the Panel Study of Income Dynamics) and feeds those into the model. Use the model and the observed pattern of lifecycle profiles of expenditure to estimate preference parameters (risk aversion and the discount rate).

  24. Gourinchas and Parker Structure Impose some liquidity constraints on model: Wt > some exogenous level

  25. Goal of Gourinchas-Parker: Estimate Utility Parameters Intertemporal elasticity of substitution (I.E.S.) (1/ρ) Risk Aversion (ρ) Time Discount Factor (β = 1/(1+ δ)) Note: Risk aversion = (1/I.E.S.) with CES preferences

  26. Why is the I.E.S. (1/ρ) important? The intertemporal elasticity of substitution determines how levels of consumption respond over time to changes in the price of consumption over time (which is the real interest rate – or more broadly – the real return on assets). This parameter is important for many macro applications. Economics: Raising interest rates lowers consumption today (substitution effect) Raising interest rates raises consumption today (income effect – if net saver) Consumption tomorrow unambiguously rises

  27. C High interest rate Graphical Illustration – No Substitution Effect ΔC2 = X ΔC1 = X Low interest rate 1 2 period With only an income effect – consumption growth rate will not respond to interest rate changes. Estimate of (1/ρ) = 0.

  28. C High interest rate Graphical Illustration – With Substitution Effect ΔC2 > X Low interest rate ΔC1 < X 1 2 period As the substitution effect gets stronger, the growth rate of consumption increases more as interest rates increase. Estimate of (1/ρ) > 0.

  29. One Way to Estimate I.E.S.

  30. Issues With Estimating I.E.S. Use of data source (micro or aggregate) Forecast of future interest rates? Correlation of forecast of interest rate with error term (things that make interest rates go up could be news about permanent income – which affect consumption). Hall (1988) “Intertemporal Substitution in Consumption” (JPE; 1/ρ = 0) Attanasio and Weber (1993) “Consumption Growth, the Interest Rate and Aggregation” (ReStud; 1/ρ = 0.60-0.75). Vissing-Jorgensen (2002) “Limited Asset Market Participation and the Elasticity of Intertemporal Substitution” (JPE; 1/ρ = 0.3 (stockholders) and 1/ρ = 0.8 (bondholder).

  31. Gournichas-Parker Methodology: Calibration Choose preference parameters that match the lifecycle profiles of consumption given the mean and variance of income process. Use synthetic individuals (based on education and occupation) Using PSID Computed “G” from the data (mean growth rate of income over the lifecycle). Estimated the variances from the data. Using CEX Compute lifecycle profiles of consumption Compute lifecycle profile of wealth/income (at beginning of life)

  32. Intuition No Uncertainty: No “Buffer Stock Behavior” (uncertainty coupled with liquidity constraints) Consumption growth determined by Rβ (where β = 1/(1+δ)) With Income Uncertainty Buffer stock behavior takes place (household reduce consumption and increase saving to insure against future income shocks). Consumption will track income if households are sufficiently “impatient” Sufficiently Impatient with Uncertainty: RβE[(GN)-ρ] < 1

  33. Results Estimates (Base Specification): δ = 4.2% - 4.7% (higher than chosen r = 3.6%) ρ = 0.5 – 1.4 (1/ρ = 0.6 – 2.0) Interpretation Early in the lifecycle, households act as “buffer stock households”. As income growth is “high”, consumption tracks income (do not want to accumulate too much debt to smooth consumption because of income risk) In the later part of the lifecycle, consumption falls because households are sufficiently impatient such that δ > r.

  34. Gourinchas-Parker Conclusions Optimizing model of household behavior with income risk can match the lifecycle profile of household consumption Liquidity constraints can explain early life patterns. Impatience explains the late lifecycle patterns. Households face significant labor earnings risk (holding assets early in lifecycle even though they are impatient). Take Away: Households are sufficiently impatient Households face non-trivial income risk (even in middle age).

  35. Part C: The Beckerian Model of Consumption

  36. Ghez and Becker (1975); Aguiar, Hurst and Karabarbounis (2011) subject to: (assume C.E.S., CRS) Let μ, λ, θ, andκbe the respective multipliers on the time budget constraint, the money budget constraint, the positive hours constraint and the positive assets constraint. Assume U(.) is additively separable across time and across goods. ψ= is vector of wages, commodity prices (p), taxes and transfers

  37. First Order Conditions If θ= 0 (L > 0), price of time (in permanent income units) (μ/λ = w) More generally (given L often = 0), μ/λ = ω

  38. First Order Conditions Intra-period tradeoff between time and goods: (1) Marginal rate of transformation between time and goods in production of n is equated to the relative price of time.

  39. First Order Conditions A few assumptions: o Fi is constant elasticity of substitution o pi’s are constant over time Some algebra (2) (3) Note: To get (3), sub (2) into (1)

  40. Static First Order Condition The static F.O.C. pins down expenditure relative to time inputs. If we know σ and the change in the opportunity cost of time, we should be able to pin down the relative movement in expenditures relative to time. %ΔXi -%ΔHi=σi %Δω Notice, this equation does not require us to make any assumptions about borrowing or lending, perfect foresight, etc.

  41. More Intuition (Assume separability in cn’s) Differentiate FOC for xn with respect to ω holding λ constant. Get: This is just Ghez and Becker (1975) Need to compare the intra-elasticity of substitution between time and goods (σ) to the elasticity of substitution in utility across consumption goods (γ). Note: Complicates mapping of expenditures into permanent income in general and the estimation of Engel curves in particular.

  42. Different Than Standard Predictions Differentiate FOC for xn with respect to ω holding λ constant. Get: Spending should fall the most (with declines in the marginal value of wealth) for goods that have high elasticities of substitution (high income elasticities).

  43. Implications • For given resources (λ): • As the price of time increases, consumers substitute market goods for time (Xiincreases) – depends on σi • As the price of time increases, consumers substitute to goods (periods) in which consumption is “cheaper” (Xi falls) – depends on γi • What goods have high/low σ: - High σ: goods for which home production is an available margin of substitution (e.g., food) - Low σ: goods for which time and spending are complements (e.g., entertainment goods) • What goods have high/low γ: - High γ: goods which have a high income elasticity (luxuries) - Low γ: goods which have a low income elasticity (necessities)

  44. Predictions: Lifecycle Movements Gourinchas and Parker model (and most other models) o Luxuries (entertainment) should decline more late in life relative to necessities (food) o No importance of changing opportunity cost of time over lifecycle Beckerian Model o Goods for which home production is important can move over the lifecycle in ways that are different than goods for which expenditure and time are complements. o If opportunity cost of time declines after middle age, food may decline more than entertainment later in life.

  45. Part D: Tests for Beckerian Model of Consumption

  46. Test 1: Aguiar and Hurst “Consumption vs. Expenditure” (JPE 2005)

  47. Question What causes the decline in spending for households at the time of retirement? Bernheim, Skinner, and Weinberg (AER 2001) “What Accounts for the Variation in Retirement Wealth Among U.S. Households” o People do not plan for retirement (myopic) Banks, Blundell, and Tanner (AER 1998) “Is There a Retirement Savings Puzzle” o People get bad news (on average) at retirement (shock to λ) Hundreds of other papers documenting similar patterns for different countries. Do not think about the cost of time changing with retirement.

  48. Fact 3: Retirement Consumption Dynamics From Bernheim, Skinner and Weinberg (AER 2001)

  49. Our Approach: Measuring Consumption Directly Main Data Set: Continuing Survey of Food Intake of Individuals (CSFII) Conducted by Department of Agriculture Cross Sectional / Household Level Survey Two recent waves: Wave 1 (1989 -1991) ; Wave 2 (1994-1996) Nationally Representative Multi Day Interview All individuals within the household are interviewed (C at individual level) Tracks final food intake (not intermediate goods --- think about a cake) Detailed food expenditure, demographic, earnings, employment, and health measures Large sample sizes: 6,700 households in CSFII-91 8,100 households in CSFII-96 Focus on intake NOT expenditure!

  50. Actual Consumption Data (CSFII) The key to the data: 24 hour food intake diaries (asked for all days in the survey) Diaries are detailed: Amount of food item consumed (detailed 8 digit food codes) Brand of food item (often unusable by researchers) Cooking method Condiments added Dept of Agriculture converts the total day’s food intake into several nutritional measures (calories, protein, saturated fat, total fat, vitamin C, riboflavin, etc.). The conversion is made using all food diary data (i.e., brand, whether cooked with butter).