PUBLIC FINANCE AND TAX POLICY Lecture 10

Taxation and Savings The decision about how much of one’s income to Save Spend This decision is also affected by taxation policies Just like effect of taxation on labour supply and leisure

Traditional Theory: Consumption behavior? Under this theory the role of saving is to smooth consumption across periods of time. There are different income periods in an individual’s life More income period Working lives Less income period Retirement Consumption behavior? Although they can consume more in the first period they will not

Intertemporal choice model: The choice that individuals make about how to allocate their consumption over time Savings: The difference between a person’s income and his or her current consumption

A simplified model: Suppose that Jack lives for two periods. Period 1: Working life He earns income Y Consumption= Cw Income – savings (S) The savings are put in the bank and earn a rate of interest r Period 2: Retirement No income Consumption= CR Savings plus the interest earned S * (1+r) Jack needs to choose optimal level of consumption in both periods

Intertemporal choice model Before taxation on savings, if Jack saves nothing: He can consume Y If he saves his total income, he can consume: Y*(1+r) The slope of the budget constraint line: -(1+r) The opportunity cost of first period consumption: The interest not earned on savings for second period consumption plus the foregone second period consumption Saving in the first period: S=Y-Cw1 Consumption in the second period: S*(1+r)=(Y-Cw1)*(1+r) Consumption while retired CR Y*(1+r) Slope= -(1+r) A Consumption while working Cw Cw1 Y

The government taxes interest income Reduction in after tax return to savings from r to r*(1-t) The government takes a portion of (r*t) New budget constraint New slope= -(1+r*(1-t)) The opportunity cost has fallen Each dollar of saving yields less consumption in the second period Consumption while retired CR Y*(1+r) Slope= -(1+r) Y* (1+r*(1-t)) CR1 CR2 Consumption while working Cw Cw1 Y

Substitution and Income effects of Taxes on Savings The lower after tax interest rate (lower price of Cw) Increase the consumption in period 1 through the substitution effect Reduction in savings What about Income effect after introducing tax? Jack is now poorer at all levels of savings because the amount of interest he keeps from each dollar of savings has fallen If Jack has a certain amount of consumption for retirement in period 2 ( such as a certain standard of living in his retirement) then when the after tax interest rate falls he must save more and reduce Cw in period one to achieve that target.

Interpret the coefficient on after-tax wages. Suppose that you estimate the following female labor supply relationship: Labor supplyi = –320 + 85(after-tax wage)i + 320(college graduate)i –120(married)i , where labor supply is measured in annual hours worked and wages are expressed in hourly wages. Interpret the coefficient on after-tax wages. What does this coefficient imply about the effect of increasing wages from $6 to $10 per hour on labor supply? The coefficient on after-tax wages is positive, indicating that a higher after-tax wage increases labor supply. The magnitude of the effect is 85: for each dollar increase in after tax wage, all else equal, a female will work 85 more hours per year. For a $4 increase (from $6 to $10), that translates to 4 × 85 = 340 hours.

How might this coefficient estimate be biased? Explain. This estimate holds marital status and having a college degree constant. Given those controls, the coefficient of interest is +85, indicating that women who earn a higher wage work more hours. A number of other explanatory variables would have to be included to avoid bias. There is no control for family size or presence of children, and it may be the case that mothers are more likely to work part-time and to accept a lower hourly wage in exchange for work hour flexibility. It is also possible that the women who are earning the highest wages and working the longest hours are somehow different from other women, not just in presence of children but in chosen careers, in attitudes about working, or in ambition. Thus, there are a number of competing explanations for the observed correlation between wages and hours that this cross-sectional estimate cannot distinguish.

You graduate from college and take a job at a consulting firm with a wage of $25 per hour. Your job is extremely flexible: you can choose to work any number of hours from 0 to 2,000 per year. Suppose there is an income tax of the following form: Income up to $10,000: no tax Income from $10,000–$30,000: 20% tax rate Income from $30,000 up: 30% tax rate Draw a graph in hours worked/consumption space, showing your opportunity set with and without the tax system.

Say you choose to work 1,500 hours per year Say you choose to work 1,500 hours per year. What is your marginal tax rate? What is your average tax rate? Do these rates differ? Why or why not? Working 1,500 hours per year would yield an income of 1,500 ≈ $25 = $37,500 and would put you in the highest tax bracket, with a marginal tax rate of 30%. To calculate the average tax rate, divide total taxes paid by income: the first $10,000 of income is untaxed; the next $20,000 of income is taxed at the rate of 20%, or $4,000; the remaining $7,500 is taxed at the rate of 30%, or $2,250. Total taxes are $6,250. The average tax rate is 6,250/37,500 ≈ 16.66%. The marginal tax rate is higher than the average tax rate because the progressive structure of this tax system taxes the last dollar earned at the highest rate; the average tax rate includes the lower marginal rates paid on the first $30,000 of income.