Time
Economists are finding increasing areas of application for their trade. One area of recent growth is in the economics of the environment, assisting policy makers in understanding the consequences of environmental preservation and degradation. Practitioners of environmental economics are often called upon to apply two important extensions to the basic economic analysis we have studied so far in this book. These extensions are time and uncertainty.
By time, we mean simply that most economic decisions, actions or results do not occur at a single instance. Instead, they are spread over many periods, perhaps weeks, years or even decades. Thus, economists somehow must compare the values of different factors at various times. Environmental economists, for example, looking at an oil spill, need to assess the damage from environmental degradation not just at the time of the spill, but over the entire period of cleanup and the recovery time during which the oil spill affects economic activity. A technique called present value analysis allows such comparisons by taking future values and reducing them to current dollars.
Uncertainty is another addition to the basic model. Few things in life are certain, and economists need to incorporate probabilistic outcomes, when two or more results are possible from a decision or, more common, a decision must be made which holds under two or more possible states of the world. In environmental economics there is often uncertainty about the amount of damage an oil spill might cause, the cost of cleanup, or even if a spill will occur. Off shore oil fields, for example, bring benefits of expanded oil reserves. But that must be balanced by possible oil spills which would (only if they occur) bring environmental damage. Thus, in a simple analysis there are two states under which the net benefits of off shore drilling must be compared - without a spill or when one occurs. The most the economist can know is the probability of a spill, which will be positive even if the best precautions are taken. Economists customarily approach uncertainty (that events are possible but not certain) with a technique called expected value, which accounts for the fact that there is less than certainty of events occurring, and adjusts the values accordingly.
Example 1: Economics in the Courtroom: The Industry of Forensic Economics
Forensic economists are used by attorneys for assessing damages and losses in torts, breach of contract, and other civil and criminal cases of the law. This emerging industry offers a unique perspective on incorporating time and uncertainty in economic analysis.
Forensic economists work on a wide variety of issues, but perhaps the two most common are employment related torts and those involving wrongful death and personal injury. Death and injury can be viewed as different severities of the same basic issue - temporary or permanent loss of body and enjoyment. Employment related torts usually involve wrongful discharge or discrimination in the work place. Both the employment area and the injury/death issues require that the economic analyst consider both time and uncertainty.
Suppose we have a case involving personal injury, where a factory worker is forced to give up his livelihood because of an automobile accident that was the fault of another party. He sues for many things; medical bills, pain and suffering, lost enjoyment of life, and also lost wages and benefits.
Wages and benefits are not paid out in a single instance, but instead are earned over the individual's working life. In most cases, however, courts and insurance companies have pushed for single, lump sum payments of damages, bringing to closure all litigation between the parties. So the forensic economists must take this stream of benefits and find the lump sum payment that offers the equivalent present value to the plaintiff. This requires a compilation of values at different times into a present value by adjusting dollars earned in the future to their worth as if they were earned in the present.
Moreover, few if any of the losses are certain. Assessing lost value requires an application of decision making under uncertainty. Wages should account for expected periods of unemployment and expected work life. Future medical bills are based on likely values rather than certain costs. In the case of lost enjoyment of life, called hedonics in the literature of forensic economics, the actual valuation often depends on applications of expected value. By taking an average of how much individuals will pay to avoid death, adjusted by the probability of death, the economist calculates the statistical value of life.
Statistical estimates of the value of life work because we pay to avoid the probability of death, not death itself. Faced with certain death, most of us would pay all we could - exhausting our budgets and savings. Luckily, however, we usually face only the possibility of death, which we pay to reduce by buying such things as smoke detectors, air bags, and healthy diets. By adjusting what a group of people pay to avoid possible death by the amount of death they avoid, the lower probability of death that comes from spending, economists can estimate how much a group would pay to avoid a certain death (presumably not their own), and call that the hedonic value of life. For example, if a collection of buyers of smoke detectors pay, as a group, $1 million dollars expecting to save one life by having the smoke detectors, then the statistical value of life is $1 million.
Present Value Analysis
Suppose an eccentric rich aunt offers you the following choice: she will give you $1000 today, $1200 three years from now or $1300 four years from now. Your problem is to decide which you would rather have. You must compare whether fewer dollars now is worth more to you than more dollars in the future. Implicitly (at least) you will be doing an exercise in present value analysis. Present value analysis is a mathematical approach which uses a technique called discounting to take values obtained at different periods of time to a single period, called the present value, allowing them to be compared.
Discounting exploits the fact that dollars obtained earlier can always be saved, usually earning some interest or dividends, to be spent in the future. Thus, current dollars, or dollars earned earlier, are worth more than dollars earned later. And the difference in value depends on the interest that could be earned.
Take as an example saving for college. Suppose you know that one year from now you will have to pay a tuition bill of $1000. The question is how much you must save today to have the $1000 then. If you can earn 10 percent (simple) real interest, you will need to save $1000/1.10, or $909.09 today, because 909.09x1.1=1000. Figuring out how much to save today is an exercise in discounting. It brings the future value, $1000, to its equivalent value in current dollars, $909.09.
Discounting to present value is easily extended over multiple years by compounding, that is, recognizing that over multiple periods it is possible to earn interest on interest. College, for example, usually takes four years. If you are saving now for the second year of college, two years from now, and the cost will still be $1000, you need to bring that number back two years. At 10 percent simple interest, it requires that you save $1000/(1.10)2 or $826.45 now. Notice, the first year you earn $82.64, so there is $909.09 to earn interest the second year. That earns $90.91, giving $1000 for college in two years.
Besides helping determine the amount to save now for future needs, present value analysis allows an individual to compare amounts received at different times. Take the rich aunt example, and suppose the interest rate is 10 percent. Twelve hundred dollars three years from now is equivalent to her giving you $1200/1.13 or $901.58 now and you putting it in the bank for three years. Analogously, the $1300 four years from now is equivalent to getting about $888 now. Presumably you would rather have the $1000 now. Even if you plan on using it three years hence, by saving it for three years at 10 percent interest you would have $1000x1.13 or $1331.
An important thing about present value is that it depends on the interest rate. If instead of 10 percent, the interest rate were only 5 percent, $1200 three years from now is equivalent to getting $1036.61 now. Equivalently, $1000 now is worth only $1092.73 three years hence. As the interest rate falls, the present value of future amounts grows, and equivalently, the future value of present amounts gets smaller.
If capital markets were perfect individuals would always be able to borrow against future values just as they are almost always able to save for the future with current assets. When it is possible, individuals would always take the highest present value option, once accounting for any of the costs of borrowing or saving. But capital markets are not perfect. Banks usually will not lend against promises of future gifts from aunts (although they do lend against future pay from employers), and tax incentives often favor income at different times. Thus, individuals often must compare their own (as opposed to the market) valuation of different options. This depends on the individual's rate of time preference.
The rate of time preference is the rate at which the individual, not the market, would transfer value between time periods. It may differ significantly from the market rate, and thus the individual's valuation may differ from the present value.
Again, let us look at your aunt's offer. Suppose the market interest rate is 5 percent, so $1200 three years hence has a present value of $1036. If your needs for money is more immediate, say for current college costs, your rate of time preference may be more that 5 percent - maybe 10 percent. Then you value the $1200 in three years at only a little over $900, and so would prefer $1000 now.
The rate of time preference
This brings us to an interesting comparison of equivalent present values at different times. Individuals will choose a sooner payout if their rate of time preference exceeds the real (adjusted for inflation) market rate of interest, and a later payout if the opposite is true.
Compare the following payouts, all which have a present value of $1000 at a real market rate of interest of 5 percent:
Years in the future Amount
0 $1000.00
1 $1050.00
2 $1102.50
3 $1157.63
Now compare the (approximate) present values depending on the
rate of time preference:
Present Valuation According to Time Preference
Years in Rate of time preference
future (amount) 5 % 3 % 7 %
0 ($1000) $1000 $1000 $1000
1 ($1050) $1000 $1019 $981
2 ($1102) $1000 $1039 $963
3 ($1158) $1000 $1059 $945
Clearly, if the rate of time preference exceeds the (5 percent) interest rate, individuals prefer early payments to later payments. Thus, an individual with a 7 percent rate of time preference prefers the $1000 now to any choice, but the $1050 next year over $1102 two years hence, and so forth. But someone with a low rate of time preference would prefer receiving an equivalent present value as far in the future as possible - $1158 in three years instead of $1000 now or $1050 one year from now.
Comparisons of present value and the rate of time preference has important implications for savings behavior. As the rate of time preference gets larger, it means people more strongly prefer current consumption over future consumption. To get them to save, more value must be offered in the future. Thus, in general if the rate of time preference exceeds the interest rate people spend more now, and save less for the future. But if the opposite holds, so the (real) rate of interest is larger than the rate of time preference, people save more because they can get more value in the future.
Present value for a stream of values over time
Often we are faced with a problem of comparing payoffs and costs that occur over a period of time, rather than all at once. For example, when firms face investment decisions, the cost of capital often is incurred at once, while the payoff, profit, comes over time. Thus, to decide if the investment is worthwhile requires that the stream of profit be discounted. Happily, this is just a simple process of adding up the present value of each particular component.
As an example, suppose a firm is considering investing $10,000. It has two possible options. The first is to buy a machine that increases the firm's capacity, and brings $2500 in additional revenue each year for 5 years, after which the machine is useless. A second option is to buy an alternative machine which lasts 5 years also, but brings in only $1500 each year. After 5 years, this machine can be sold for scrap for $5500.
A present value analysis allows us to compare these two alternatives. It is facilitated by the equal period of each investment. The more complicated case of comparing investments over different period lengths is reserved for the next section.
Assume the discount rate is 5 percent. The present value of the first investment is
(2500/1.05)+(2500/1.052)+(2500/1.053)
+(2500/1.054)+(2500/1.055) = 10824.
The present value of the second investment is
(1500/1.05)+(1500/1.052)+(1500/1.053)
+(1500/1.054)+(1500/1.055)+(5500/1.055) = 10804.
Although over five years the first possible investment returns only $12500 compared to the $13000 the second investment returns over the same period, the first investment has a higher present value. The difference is that for the second investment much of the benefit is back-loaded in the residual value of the machine, meaning that it is discounted further.
An interesting question is how a change in the discount rate changes the ordering of these present values. This is left as exercise 4.
Example 2: Is Social Security Worth It?
Social Security (FICA) is increasingly viewed by workers as an investment for retirement of questionable worth. Most workers are now reported as not expecting to get back what they put into the system, despite assurances by government officials that the system will be kept sound, and just about every worker takes more out in benefits during retirement than what was paid in during the working life of the individual. But these reports usually ignore two things - employer contributions and present value analysis.
Let us look at an example. Take a new but high wage worker of age 30 (she was a student for a long time) planning on working until age 67, who will then retire and collect benefits for 15 years (180 months). Adjusting for inflation, the rules tax wages up to $48,000 per year (1987 dollars) at a rate of 6.2 percent. Suppose this worker makes the $48,000 (in 1987 dollars) per year. In non-discounted dollars she would pay $2976 per year in Social Security taxes, so over 37 years she would contribute $110,112 which her employer would match. Under Social Security rules, this worker would get $1770 per month (again in 1987 dollars) when she retires - $318,600 over 15 years. This is larger than her contributions, or even her contributions plus her employer's contributions on her behalf. It looks like Social Security is a pretty good deal.
But (there is always a but when economics is involved) we have ignored the fact that the benefits are paid well into the future, while the contributions are paid much earlier. Thus, we have a need for present value analysis.
The math is a little tricky, but the $21240 she would collect during her first year of retirement is 38 years from now, so in present value dollars is worth $21240/1.0338 or only $6908 at a 3 percent real rate of interest. Similarly, the second year of retirement income (39 years henceforth) is worth only $6707 now. Discounting the last year of benefits (52 years from now) gives a present value of only $4567. Overall, the present value of her Social Security benefits is the sum of the present value of the benefit earned each year.
Contributions are made much earlier. The first year she will pay in $2976. Simple discounting at 3 percent makes that worth $2889 now. The present value of the second year contributions (again $2976) is down to $2805. Adding up the present value of all the contributions gives the total cost to the worker.
The following table shows the present values of the employees contributions and the Social Security benefit at three rates of discount.
Rate of Present value Present value
discount contributions benefits
3 percent $65,970 $84,939
4 percent $56,968 $55,330
5 percent $49,733 $36,252
As the rate of discount grows larger, the net present value (benefits minus contributions) of the Social Security program turns from positive to negative. Even at the low real rate of discount (3 percent) however, the real difference is much lower (about $19,000) than the $218,000 ($318,600-$100,112) difference in non-discounted dollars.
When employer contributions are counted (remember we saw in chapter 6 that Social Security taxes probably lower wages) Social Security is a poor deal even at the 3 percent rate of discount. Then the present value of all contributions is almost $132,000 and so the net present value of the social security benefit is negative.
Investment over time
In the previous section we used an example of two possible investment to explore the discounted present value of a stream of payments. Present discounted value plays an integral part in choosing investments that pay off over time. However, the analysis of investment decisions must account for other opportunities for which the capital can be used, most specifically, lending the money to others at the market rate of interest, usually by putting it in a bank, Treasury bill, or other such instrument. One criterion for the "best" investment is if it provides the highest possible rate of return to capital. We need a method of measuring the rates of return of a diversity of investment so they can be compared.
One such measure is called the marginal rate of return or internal rate of return to an investment. It is equivalent to the discount rate which equates the present value of the cost of the investment to the present value of the revenue stream generated by the investment. It is particularly useful when both costs and revenues occur over time.
The internal rate of return is the discount rate r* such that
S(Ci/(1+r*)i) = S(Ri/(1+r*)i)
where Ci indicates the cost of the investment each period, Ri is the revenue generated by the investment each period, and the summation (over i) is for the entire length for which the investment has costs or revenues. Under this formulation, if the discount rate equals the internal rate of return, the net present value of the investment is zero. The present value of the returns would just equal the present value of the cost stream.
Only rarely will the internal rate of return equal the actual discount rate. More usually, its use derives from the fact that it allows the comparison of investments that have different lengths of costs and/or revenues, as well as offering a comparison to the returns of more mundane investment possibilities like savings accounts.
Consider the $10000 investment that returned 2500 for five years. We found that the present value assuming a discount factor of 5 percent exceeded the cost. One way to compare it to other investments, is by the internal rate of return. Using the formula, the internal rate of return, r, solves the equation
$10000 = (2500/1+r)+(2500/(1+r)2)+(2500/(1+r)3)
+(2500/(1+r)4)+(2500/(1+r)5).
Although not possible to solve analytically, an iterative method shows that r equals about 0.0793. Thus, it is a better investment than a savings account that pays 7 percent, but not as good as one that pays 9 percent.
Firms use the internal rate of return to decide how much investment is worthwhile. Most investment by firms does not come from ready cash. Instead, firms borrow money from banks or by selling bonds to investors at some market determined interest rate. Even if a firm invests its own cash, the opportunity cost of such investment is the market rate of interest. Generally, the firm chooses the investment with the highest internal rate of return first, the second highest next, and so on. To maximize profit the firm should invest in all projects with expected internal rates of return which exceed the interest rate at which money can be borrowed. It demands (borrows) funds until the internal rate of return is just equal to the cost of borrowing the money.
Figure 15.1 shows why this is a reasonable strategy. The horizontal axis measures the dollars used for investment, while the vertical axis measures the interest rate - the cost of funds - and the internal rate of return - the value derived from using the funds in the investment. The internal rate of return curve slopes downward because the firm does the investments which pay the most first, and according to such ranking, later investment dollars yield a lower internal rate of return. The graph shows that for all investments that can be done with D1 dollars, the internal rate exceeds the interest rate, so there is a net profit even if the funds for the investment are borrowed. For later investments, those that push the total amount invested beyond D1, the cost of the funds exceeds the benefits derived, thus the firm would lose money on such investments.
The figure assumes the firm is a competitor in the funds market. Thus, it can borrow all it wants at the market rate of interest, hence the supply curve of investment dollars to the firm is horizontal. It should be clear that the internal rate of return curve is equivalent to the firm's demand curve for investment dollars. As the interest rate rises fewer investments yield an internal rate of return sufficient to cover the cost of funds, and so the demand for investment dollars decreases. Lower interest rates increase the demand for funds.
Lower interest rates spur economic growth for just this reason. As market interest rates fall, firms see that more and more projects have positive values. Investment grows, increasing the demand for physical capital, labor and other inputs. Meanwhile, consumers can borrow money at lower rates, inducing greater consumption. The lower interest rate instigates a cycle of increased investment and increased demand, and thus economic growth.
Example 3: The Interest Rate Sensitivity of Stock and Bond Prices
One of the more confusing aspects of financial markets is the affect of interest rate changes on the prices of bonds and stocks. Stocks are equities, which means the owner of a share of stock is in effect a partial owner of the corporation which issued the stock. Thus, the value of the stock is tied directly to (the expectations of) how well the firm will do in terms of profit. Bonds, on the other hand, are notes which indicate that the firm has borrowed some money from investors. They carry no sense of ownership of the firm, only an obligation of the firm to pay back the principal of the loan at some future time, and any coupon (interest) that comes due before hand.
Both stocks and bonds trade in secondary markets, selling for prices determined in part by the market rate of interest. Stock prices generally reflect the present value of the future stream of payments while bond prices are generally the present value of the maturity amount of the bond figured at the market rate of interest.
Bond prices are easily seen to respond inversely to interest rates. According to the present value formula, the price of a bond (Pb) which carries a maturity value of M some t periods in the future follows
Pb=M/(1+k)t
where k is the (risk adjusted) market rate of interest. We already know that as k falls Pb should increase. A one year bond with a $100 maturity value has a present value of $90.09 at 10 percent interest, but is worth $95.23 now if interest rates are 5 percent.
Stocks seemingly behave in the same way. One theory for the formulation of a stock's price is the dividend discount model, where the stock price (Ps) depends on the dividend paid by the firm (D), and the interest rate (k - adjusted for riskiness), according to the formula
Ps = SD/(1+k)i
where the summation is over the life of firm for which the dividend will be paid. In its simplest formulation D is assumed constant and for most stocks the life of the firm is assumed to be infinite.
Lower interest rates increase the prices of a stocks as well as bonds. Suppose that D=10. At an interest rate k=.1 (10 percent), next year's dividend has a present value of 10/1.1 or 9.09. But if k falls to .05, the present value of next year's dividend is 9.52. And this change is compounded over the entire future history of the stock. For every period, the present value of the dividend is larger when interest rates are lower. If the stock has an infinite life, the price of the stock at 10 percent is $110, but at 5 percent the price is $210.
Right away we see that stock prices are generally more sensitive to interest rates than bonds, primarily because of the terminal value of bonds. But there are further reasons. A change in interest rate is likely to affect future dividends that accompany stock ownership. We saw in the text (figure 15.1) that firms invest more (and presumably earn higher profits) when interest rates are low. Higher dividends mean greater present value, and thus a higher stock price, for any given interest rate. To the extent that dividend growth is inversely related to the interest rate, stocks suffer a double penalty from increases in the interest rate, and a double benefit when interest rates drop, as compared to bonds. Thus, stock prices are usually more volatile than bond prices.
Indifference Curve Analysis of Consumption Over Time
Back in chapter 5 (box 8) we used consumption over time in the context of the indifference curve model of utility maximization to explain the effect of the Reagan tax reforms on savings incentive. In this section we review these concepts, and extend them some with the tools developed earlier in this chapter.
The simple utility maximizing model is generalized to account for consumption over time by assuming the individual lives only two periods, "Now" and "Later." She earns a total after tax income of M=MN+ML, called her endowment, where the subscript indicates which period the income is from. But she can borrow or save money in capital markets, so her consumption can be transferred between periods. If the market interest rate is r, funds can be transferred from Now to Later by saving, and if all of MN is saved, then Later she would have (1+r)MN+ML. Alternatively, she can borrow against future income (ML) for consumption Now. If all of her future income is borrowed ML=(1+r)B, where B is the amount borrowed, and the amount available for current consumption is MN+B (notice that B=ML/(1+r)).
If this consumer wishes to transfer less than all of her income from one period to the other, the same general concept holds. Suppose less than all of her future income is borrowed so (1+r)B<ML. She will have MS+B for consumption Now, but only ML-(1+r)B left for consumption Later. Saving from Now to Later works the opposite way. Suppose S is saved from Now. Later she would have ML+(1+r)S, but she has only MN-S for consumption Now. More generally, we can set up her budget constraint by the formula
(eq 15.1) [MN/PN]+[ML/PL]={[MN-S+B]/PN}+{[ML+(1+r)S-(1+r)B]}/PL
where PN is the price per unit of consumption Now and PL is the price per unit of consumption Later. We make use of the fact that she can always use the income from each period for consumption that period (the left hand side), or she can save or borrow to move consumption power across periods (the right hand side). The left hand side is simply the consumption value of income from each period, called the endowment point.
The possible consumption points are illustrated by the intertemporal budget constraint shown in figure 15.2. The endpoints are easily determined by setting S=MN (for all consumption Later) or B=ML/(1+r) for all consumption now. Connecting these two points gives the budget constraint. As always, the slope of the budget constraint equals the negative of the rise over the run, or [((1+r)MN+ML)]/PL ) [MN+(ML/(1+r))]/PN, which reduces to !(1+r)PN/PL. Point E is her endowment point.
We now have an easy way to see how changes in income, prices or interest rates affect the budget constraint. Keep in mind that the budget constraint must go through the endowment point. Changes in ML or MN are equivalent to increases in income. An increase in ML to ML' would cause a parallel shift upward to E' (see figure 15.3), while an increase in MN to MN" would cause a parallel shift outward to E".
Price changes and interest rate changes pivot the budget constraint, although the line is always forced through the endowment point. So if PN or r goes up the line gets steeper, as shown in figure 15.4. Here we have PN'>PN or r'>r, or both. Equivalently, an increase in PL or a decrease in r pivots the line flatter.
Any change in price or the interest rate has both income and substitution effects. We want to focus on a change of the interest rate. Holding prices constant, as r goes up current consumption becomes more expensive relative to future consumption. Savings earns more interest,and borrowing costs more. This is a shift to the steeper budget constraint in figure 15.4.
The net effect of this change is unclear because of the income and a substitution effects. We can show that the substitution effect is always such that current consumption decreases, but the income effect depends on the shape of the indifference curve.
Look at figure 15.5. Suppose an individual has an endowment point of E, and at interest rate r she consumes at point 1. She borrows from the future for current consumption. When interest rates rise to r' her consumption shifts to point 3. She still borrows, but less. This shift can be separated into two parts. The substitution effect is from point 1 to point 2. The budget constraint becomes steeper, but utility is held at U (the dotted line). When utility is maintained, the person pictured would definitely borrow less, that is consume less Now, at higher interest rates, just what we would expect as current consumption gets more expensive. The shift from 2 to 3 shows the income effect. It is a parallel because the shift is equivalent to a change in the endowment point, at the original prices but at the new interest rate.
How the income effect changes consumption is an indication of the marginal rate of time preference. If point 3 shows current consumption increasing over point 2, the marginal rate of time preference sees consumption Now as an inferior good - lower endowment causes an increase, but if point 3 shows less consumption Now, current consumption is a normal good. Classification of the rate of time preference in consumption is based on the relative shifts in consumption each period from an endowment change.
In figure 15.5 we show the marginal rate of time preference favoring future consumption. This is better understood by working backwards. Suppose this shift is from 3 to 2, an endowment increase (the lighter line to the darker line). Later consumption increases while current consumption actually decreases, so the marginal rate of time preference is towards future consumption.
Example 4: Savings and the Deductible IRA
Ever since income tax deductions for individual retirement accounts ceased for most tax payers there has been considerable debate about the effect on the savings rate. Since the U.S. is perceived to have a low rate of savings, this becomes an important policy question. An analysis of consumption over time provides some insights into this issue.
The IRA deduction allowed individuals to avoid taxes on up to $2000 per year if the money is set aside for retirement. We split the time periods into working and retirement. All income (M) is earned during the working period, and some is saved for retirement.
Without any deduction all income, whether used for current consumption or retirement is taxed at a rate t (0<t<1), leaving (1-t)M for the budget (the thin line in figure 15.box4.1). At an interest rate r, the slope of the budget line is !(1+r) where for simplicity we assume the price in each period is equal to 1. But if the first $2000 of savings for retirement avoids taxes, part of the budget line gets steeper, equivalent to future consumption getting cheaper. For the first $2000 diverted to retirement consumption by saving the budget line has a slope !(1+r)/(1-t). Thus, the budget constraint follows the heavy line when IRAs are deductible.
Notice for most of the line the shift is equivalent to an increase in income, although for small savers, who put aside less than $2000 for retirement, it is a price drop. Thus, except for the small saver, there is no substitution effect. The overall effect on saving depends on preferences. As long as the new utility optimizing point is above point a savings will increase. The extent to which it increases, however, depends on the marginal rate of time preference. Individuals whose preferences (at the margin) lean more towards future consumption will increase retirement savings a lot, but those with preferences leaning more towards current consumption will have little increase in retirement savings, and thus future consumption.
The debate rages on which effect is most prevalent. Money magazine, in periodic surveys, finds most of its readers support the fully deductible IRA. But those are mostly higher income individuals who already save a lot. Thus, it may be that they would substitute IRA savings for other savings, and the economy would see little increase in the savings rate. As is usual in economics, the effectiveness of the deductible IRA as a policy to increase the savings rate is an empirical question.