Regression can be defined as a multipurpose and dominant arithmetical technique which is utilized to concurrently form the outcomes of numerous independent variables on one single dependent variable (for example, Cohen & Cohen, 1983; Fox, 1997; Pedhazur, 1997). The instantaneous assessment of independent variables is what makes it feasible or easier to better comprehend, calculate, and clarify a dependent variable; to guess their independent and collective effects; to discard unauthentic effects; to resolve more precisely the course and force of their outcomes; and to manage the likelihood of Type I errors.
Over the years, there have been many analysis made and researches done on the relationship of retirement and the incentives given i.e. pensions and social security provided. Most of these researches have been done in the perspective of a single-equation, reduced-form model, which are most commonly and regularly utilized in behavioral and policy studies. A good example to explain this would be that the Social Security Administration has signed up a deal to use this type of a model in order to foresee the results of an alteration in the existing policy, to be exact, raising the age of entitlement for the initial Social Security retirement profits.
There were, however, quite a few circumstances where the coefficients anticipated in retirement equations for variables demonstrating the imminent incentive from Social Security and pensions to constant work will permit us to calculate the individual's reaction to a modification in the remuneration. For instance, if people were to act in line with a simple life-cycle model and if capital markets are ideal, the likely connection involving retirement effects and procedures of the alterations in assets from Social Security or pensions with constant work will show how these monetary incentives shape retirement outcomes and how transformations in these line ups will control retirement manners. However, there are other circumstances where not all the procedures are constant. For instance, if capital markets are flawed, as a result a certain group of people are going through limited liquidity, the coefficient on a variable calculating the alteration in the upcoming importance of pensions and Social Security cannot be utilized to foretell the consequence of a variation in Social Security policy. The importance of future work is dependent upon the overlooked inclinations. Therefore, the coefficient anticipated in the retirement equation has to vary to balance the variations in the policy.
The studies done on retirement have been very visible about the fact that the reward of pensions and social security do have a strong influence on the decision for continuing work and hence, these two factors or incentives are integrated here. (4) The research on saving is only now starting to include the incentives of pensions and social security, even though the pensions and social security reimbursements have a huge percentage in the finance collected for retirement, still there are many studies that do not include these two incentives and sources of finance while carrying out the studies for saving. (Gustman and others 1999. Besides, it is not only about the pensions and social security being included in the savings analysis, even when they are included as a part of wealth, many essential uncertainties persist.
Gale (1998) believes that in order to accurately calculate the pension offset in an individual's wealth, it is vital that factors like pension, assets, lifetime gains and every stage of the life cycle are properly calculated and adjusted in the equation. In his research and analysis, while using a simple life-cycle model, he comes across major pension offsets utilizing the data collected from the Survey of Consumer Finances. However, this was not the case for Gustman and Steinmeier (1999) who followed the same direction and calculated the pension offsets using the HRS data, and in opposition to Gale's foresight, they found minor pension offset. Using the HRS data has its advantages: the people whose earnings are used as a sample for the analysis are nearing their retirement age so it becomes a lot easier, precise and proficient to calculate their lifetime gains and total lifetime assets; lifetime gains are calculated using both self-reported salary records and salary records attained from the Social Security Administration; the importance of pension is calculated by the utilization of thorough descriptions of pension campaigns acquired from companies. Gustman and Steinmeier (1999) established that if the lifetime gain and retirement income was treated as a constant then the people who get pensions would have more financial assets that those who don't get pensions. So, in the end, they establish that pensions cannot be a substitute for savings of any kind with a tax-favored technique of saving when the concept is being dealt in a wealth equation.
Significant development has been made in terms of measuring the future value agreed by a pension or Social Security which in turn is used to explain retirement or job mobility. It is according to Lazear and Moore (1988) and Stock and Wise (1990a and 1990b) that the "option value" of the pension is referred to the potential value of the pension resulting from nonstop work at the company for a number of years in the future.
A measure of pension back loading is used by Gustman and Steinmeier (1993 and 1995) to estimate the discouragement to mobility from pensions. However, Coile and Gruber (2000 and 2001) have adopted a measure called the peak value. This is the maximum found for all future dates of retirement, and it is used to assess retirement incentives from Social Security.
However, in a reduced-form setting, the challenge is to accurately value current and future reimbursement in terms of benefits, particularly the spikes in the pension increase profile observed at the early and normal retirement dates. This can be done by simply downplaying the relative significance of the spikes in the benefit accrual profile at early and normal retirement ages and adding up the probable future benefit for every year of future employment.
For instance, when benefits are summarized, a clear contribution plan will have a misleading large future value. This is discussed below, by merging together the existing measures for valuing future benefits, based on the evaluation of the expected future value of the pension or Social Security on the premium value as seen in table 1 below:
Accruals and premium values for pensions and Social Security (as a percentage of current earnings)
Source of Standard Percentage with accrual Mean deviation nonzero values
Accruals at the start of the period:
Social Security 6.1-11.4-78.0
Accruals at the end of the period
Social Security 5.6-10.8-80.0
According to Coile and Gruber (2000 and 2001), the difference between "premium value" and "peak value" in that the peak value includes all increases in benefits with continued work and add in time as benefits gathered in defined contribution plans. While on the other hand, the premium value does not.
There are a number of other issues that affect the requirement of retirement and saving equations. These findings are susceptible to how retirement is measured based on self-reported status, hours of work, or combination of both (Gustman, Mitchell, and Steinmeier 1995; Gustman and Steinmeier 2001). Findings will also be subjective by whether the partially retired are counted among retired or not retired (Gustman and Steinmeier 1984). This issue can be further discussed below:
Joint Determination of Retirement and Wealth in a Simple Model
In order to support the discussion of the relationship between retirement and wealth, one can look at the model .in which the consumer maximizes a lifetime utility function:
U = [[integral].sup.T.sub.0] [e.sup.-[rho]t] u[C (t)] dt
Subject to a lifetime budget constraint [[Integral].sup.T.sub.0] C (t) dt = WR
C (t): consumption at time t,
W (constant) wage rate,
R is the retirement age, and T. is the lifetime.
The above model solves for consumption and wealth, giving the optimal retirement date. The result of variation for retirement on saving is replicated by varying the date of retirement. However, a fully complete examination would not just include leisure in the utility function but also allow heterogeneity in the leisure parameter.
This model, illustrates the major points without undue complications.
The Euler-Lagrange condition for this problem is:
U'[C (t)] = [lambda] [e.sup.[rho]t]
where [lambda] is a Lagrangian multiplier that, in this difficulty, is constant over time. Distinguishing this condition with respect to the retirement date R. yields
Since U" < 0, this condition involves that [differential]C/[differential]R and [differential][lambda]/[differential]R are of opposite signs, and furthermore, since [lambda] is constant over time, that the sign of [differential]C/[differential]R is uniform over time.
Differentiating the budget constraint with respect to R. gives [[integral].sup.T.sub.0] [differential]C/[differential]R dt = W > 0
Since [differential]C/[differential]R has a uniform sign over time, that sign must be positive. Assets at any point in time before retirement are simply the difference between the cumulative wages and the cumulative consumption: