Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

ECONOMETRIC FLEXIBILITY IN MICROSIMULATION: 

AN AGE-CENTERED REGRESSION APPROACH 

John Sabelhaus (E-mail: john.sabelhaus@cbo.gov) 

Lina Walker (E-mail: lina.walker@cbo.gov) 

Congressional Budget Office 

Washington, D.C. 

January 2007 

2007-02 

Working papers in this series are preliminary and are circulated to stimulate discussion 

and critical comment. These papers are not subject to CBO’s formal review and editing 

processes. The analysis and conclusions expressed in them are those of the authors and 

should not be interpreted as those of the Congressional Budget Office. References in 

publications should be cleared with the authors. Papers in this series can be obtained at 

http://www.cbo.gov/publications/. 
Abstract 

 

This paper describes a strategy for estimating predictive equations that has been shown to work well 

in microsimulation modeling. The technique, referred to here as “age-centered regression,” is 

particularly useful when the available data set for estimating a model equation is limited and the 

marginal effect of one or more explanatory variables might be expected to vary systematically by 

age. The examples used here to describe how age-centering works are taken from the labor supply 

equations in the Congressional Budget Office Long-Term (CBOLT) dynamic microsimulation 

model. By switching from a traditional single-equation approach to age-centered regression, we 

show that marginal effects of independent variables can vary significantly across age groups. The 

comparison also reveals that improvements in mean predictions by age can be achieved with little if 

any loss in statistical precision of coefficient estimates. 
1

I. Introduction

A fundamental goal of microsimulation modeling is to replicate empirically observed 

heterogeneity in person-, household-, or firm-level outcomes. If individuals with certain 

characteristics are more likely to have certain outcomes, a good model will have transition 

equations that generate those correlations in simulations. Sample size limitations in the data sets 

used to estimate model equations can make achieving this goal a challenge, however, as they 

make it difficult to statistically sort out all of the covariance needed to replicate the desired 

heterogeneity. This paper discusses an estimation strategy, referred to as “age-centered 

regression,” that has proved useful for mitigating the types of problems in microsimulation that 

are typically associated with small sample sizes. 

There are several conditions under which age-centered regression might be useful in 

microsimulation modeling. First, the behavioral processes being estimated vary systematically 

with age; these processes include marital status transitions, fertility, mortality, and labor market 

outcomes. Second, these processes are such that the effect of any given explanatory variable 

could also vary by age; for example, higher educational attainment might lower the probability 

of marriage for very young singles, but increase the probability of marriage for middle-aged 

singles. Third, the data set available for estimating the model equation is limited, so that 

estimating separate equations for each age is infeasible and therefore some sort of grouping is 

required. 

A typical approach in microsimulation when these conditions arise is to estimate separate 

equations for two or more age groups. For instance, in the marital transition equation, one might 

estimate separate marriage probability equations for young, middle-aged, and perhaps older 
2

individuals, so the model would have three marriage equations. Age centering takes this 

grouping approach a step further. The idea is to estimate a separate equation for each unique (or 

“reference”) age, but include every observation in the sample whose age is within a preset range 

(or “bandwidth”) around the reference age being estimated. Thus, if the sample being analyzed 

is 25-year-olds and the bandwidth is 4 years, the estimation phase would use all observations in 

the data set with ages 21 through 29. The equation for 26-year-olds would use every observation 

with ages 22 to 30, and so on. The end result is that the model will have separate equations for 

each reference age, but the sample used to estimate the equation for any given age overlaps with 

the data used to estimate nearby ages.

There are two benefits when using age-centered regressions, in terms of econometric 

flexibility. First, there is flexibility in the shape of the functional form with respect to age 

itself—one does not have to rely on polynomial terms or linear splines to specify how the 

process in question varies with age. Second, the effect of any given independent variable in the 

equation is no longer constrained to be equal for all age groups (or even a subset of age groups, 

as when one splits the sample). If the data suggest that the magnitude or even sign of an 

explanatory variable systematically varies with age, the differential relationship will show up in 

the estimates. 

The examples used here to illustrate the age-centering approach are taken from the labor 

force modules in the U.S. Congressional Budget Office Long-Term dynamic microsimulation, 

also known as CBOLT.1 The equations we consider sequentially predict labor force 

 

1 See Congressional Budget Office (2006). The age-centering technique is also applied to marital transitions in 

CBO’s model; see O’Harra and Sabelhaus (2002) and Harris and O’Harra (2001). For a general overview of the 

CBOLT model see O’Harra, Sabelhaus, and Simpson (2004). The model has been applied in several academic 

papers, such as Harris, Sabelhaus, and Simpson (2005), Harris and Sabelhaus (2005), Harris and Simpson (2005), 
3

participation, full-time versus part-time employment, and hours worked for part-time employed 

persons. All of the equations are univariate or multinomial logit specifications with standard 

controls: the explanatory variables include age, marital status, educational attainment, in-school 

status, number of children under 6 years of age (for women), receipt of social insurance benefits, 

and cohort/time effects. The equations are all estimated using about thirty years of data from the 

March Current Population Survey (CPS), which is a large, annual, nationally representative 

cross-section. 

For each of the three labor market equations, we compare the results using a standard 

(linear in age) specification with age-centered results. We show that estimated coefficients in 

the age-centered equations do vary systematically by age, and those differences in coefficients 

imply very different marginal effects by age. One example is the extent to which lagged labor 

force participation is correlated with current labor force participation; the effect varies 

systematically over the life cycle and the age-centered equation is better able to capture that 

pattern than the more standard equation. A second example is the effect of marital status on 

expected part-time hours (conditional on working part-time). The extent to which being married 

affects part-time hours worked also varies significantly across age groups. 

A further benefit of using the age-centered approach in microsimulation modeling is that, 

by its nature, age-centered regressions are better at capturing any differences in mean predicted 

outcomes by age. In general, microsimulation modelers rely on the fact that the single equation 

approach will work if the underlying outcomes by age are smooth and if one uses an appropriate 

polynomial in age. Using the predictions from the labor force module, we show that deviating 

 and Sabelhaus and Topoleski (forthcoming). There are also several published CBO reports and studies using 
4

from those conditions can lead to biased predictions by age in some cases. 

II. The Mechanics of Age-Centered Regression 

 Age-centered regression is useful for estimating microsimulation model equations in 

cases where the underlying process varies systematically by age and one is trying to achieve 

maximum flexibility in the estimated econometric relationships. In microsimulation modeling, 

researchers typically split the sample by age when estimating equations, although it is well 

understood that the effect of certain independent variables differs across age groups. Agecentered regression takes this logic a step further by estimating different equations for each 

unique “reference” age. Estimating the equation for each age, however, limits the regression 

sample and reduces the statistical precision of the estimation. In order to overcome the smallsample-size problem, age-centered regression borrows a principle from kernel density analysis 

and includes all observations that are within a certain “bandwidth” of the reference age group in 

question. The technique allows statistical precision to be maintained at the same time that 

improved flexibility in estimated coefficients by age is achieved. 

 For any given bandwidth, the actual estimation strategy for an age-centered regression is 

straightforward. Assume the equation being estimated is for a reference group that is 25 years 

old and the bandwidth is set to five years. The equation estimation will include every 

observation in the data set with ages 20 through 30. However, the observations are not weighted 

equally. As in kernel density estimation, declining weights are applied to observations that are 

farther from the reference age group. A simple triangular weighting pattern is used, so if the 

 CBOLT, available on the CBO website under “Publications by Study Area, Social Security and Pensions.” 
5

reference group is 25-year-olds with a 5-year bandwidth, then 25-year-olds have weights of one, 

persons who are one year plus or minus 25 (24- and 26-year-olds) have weights of 0.8, persons 

who are two years plus or minus 25 (23- and 27-year-olds) have weights of 0.6, persons three 

years plus or minus 25 (22- and 28-year-olds) have weights of 0.4, persons four years plus or 

minus 25 (21- and 29-year-olds) have weights of 0.2, and persons five years plus or minus 25 

(20- and 30-year-olds) have weights of 0.0. 

 The decision about how wide a bandwidth to use when estimating an age-centered 

regression will depend on the tradeoff between desired flexibility and statistical precision. If the 

bandwidth is set low (with bandwidth one, the only observations included are in the reference 

group itself) the estimation process has the most possible flexibility. There is no smoothing of 

the estimated effect of independent variables across ages; therefore, if people of different ages 

are really very different in terms of mean outcomes or the effects of some independent variable, 

those differences will come through in the estimation. The tradeoff is the loss of statistical 

precision when the bandwidth is set too low; there may be too few observations exactly at or 

near some ages and one cannot estimate the coefficients of interest with any reliability. 

The approach in kernel density estimation is to explicitly test for optimal bandwidth, but 

the decision on bandwidth ultimately depends on how much weight one puts ex ante on 

flexibility versus statistical precision. In the examples here (and other equations in the CBOLT 

dynamic microsimulation model) the bandwidth is set to five years, which balances the goals of 

flexibility and precision in these types of equations. The five-year bandwidth is large enough 

that the coefficients are precisely estimated, with significance levels on most coefficients that are 

comparable to those from the standard single equations using the entire data set. At the same 
6

time, the five-year bandwidths are small enough that one can observe any systematic differences 

in estimates across the age distribution. Capturing these differences will improve the capacity of 

the microsimulation model to reflect the heterogeneity in the underlying data. 

 There are a few mechanical observations about using age-centered regression worth 

noting. First, in the estimates discussed in this paper (see Section III.) all of the age-centered 

equations include an age term as well as an intercept. Note that if the bandwidth is set to one, 

the intercept and age will be perfectly correlated. However, when the bandwidth is greater than 

one, the age term can be estimated and captures any systematic age differences (within the 

bandwidth range) not captured by other independent variables. It is probably easiest to think of 

this coefficient as the derivative by age of the process being estimated, evaluated at that 

particular reference age. In model simulations, when predicting outcomes for a given 

observation, the age term is effectively combined with the constant term for each reference age 

group.

2

 

A second mechanical observation concerns how one actually estimates and uses agecentered regressions. At first glance it might seem that age centering is somewhat more 

cumbersome, because it replaces one equation for the entire population with separate equations 

for each age group. However, in practice the actual estimation and implementation are both 

straightforward. The equations here are all estimated using a simple looping feature in a 

standard software package, so the actual code for estimating, evaluating, and outputting multiple 

 

2

 It is worth noting that this also can lead to a lot of apparent imprecision in the estimated constant and age terms, 

because if the slope of the process being estimated is relatively flat over a particular age range, there is too little 

variation by age to separately identify a constant and age coefficient. Indeed, in some processes, one observes a 

pattern of estimated age and constant term coefficients that appear volatile, but the linear combination of the two 

actually input to the microsimulation model is much more stable. 
7

equations is only slightly more cumbersome than estimating a single equation.3 In the actual 

CBOLT model code, switching from a single equation to age-centered equations simply involves 

adding an extra dimension (age) in the coefficient arrays used in the simulation. In sum, the 

benefits of adopting age centering exceed any computational burdens the technique introduces. 

III. Age Centering in the CBOLT Labor Force Equations

 The overarching goal of CBOLT is the same as many other dynamic microsimulation 

models: to simulate demographic, labor market, and government tax/transfer outcomes for a 

representative sample of the population forward through time. Although age centering is used in 

several CBOLT equations, for reasons of brevity the analysis in this paper is focused on the 

labor force participation and hours worked equations in the CBOLT labor force module. The 

approach used here to demonstrate age centering is to compare and contrast age-centered results 

with a more standard single-equation approach for each of the three equations in the CBOLT 

labor market module. 

CBOLT Labor Force Equations 

In CBOLT, annual hours worked for each individual are estimated using a sequence of 

three equations. For each individual, the model solves for (1) labor force participation, (2) fulltime versus part-time work for those in the labor force, and (3) part-time hours worked for those 

who work part-time. The first two equations are univariate logits, and the resulting probability is 

compared to a random number draw to determine the actual model outcome. The third equation 

 

3

 The Stata code used to estimate all of the equations in the next section is available from the authors upon request. 
8

is a multinomial logit with seven possible outcomes (or “bins”) for annual part-time hours 

outcomes.4 As with the first two equations, a random number draw is used to place individuals 

into each of the seven annual part-time bins. 

Each of the three equations in the labor force module is estimated separately for men and 

women. The explanatory variables used in the CBOLT labor force equations include age, 

marital status, educational attainment, in-school status, number of children under 6 years of age 

(for women), receipt of social insurance benefits, and cohort/time effects. The labor force 

participation equation also includes a lagged independent variable in order to capture the 

observed persistence in the data.5

 

The three CBOLT labor force equations are estimated using pooled Current Population 

Survey (CPS) data. The March CPS collects information on about 60,000 households each year. 

 The data sets are cross-sectional and contain a wide variety of economic and demographic 

information on the individual, family, and household. The data used to estimate the equations in 

the labor force module are for calendar years 1975 through 2003. In the equations discussed 

here, the sample is restricted to individuals ages 25 through 61, which includes nearly 1 million 

observations over the 29 year period.6 

The CBOLT approach to estimating annual hours worked may seem overly 

complicated—one could use a single equation that directly predicts annual hours worked—but 

 

4

 The bins for the multinomial logit are for annual part-time hours of 125, 375, 625, 875, 1,125, 1,375, and 1,625. 

Everyone who works full-time (determined by the second equation in the module) has annual hours worked of 2,080. 5

 The other two equations—full-time versus part-time work, and part-time hours conditional on working part-time—

exhibit the same longitudinal persistence as labor force participation, but the CPS data used to estimate the equations 

do not have the requisite lagged information. CBOLT introduces that persistence into the simulation ex post using a 

technique described in Congressional Budget Office (2006). 

6

 CBOLT uses different equations and/or bandwidth limits for people under age 25 and over 61. For the young, the 

effects of schooling dominate labor force decisions. For people over 61 the effects of social insurance dominate 
9

there are good reasons to separate the process into the three steps. Because each process has 

different dynamics and marginal impacts from changing independent variables, separately 

identifying each equation improves the simulations of actual population heterogeneity. Also, 

separating the module into these three logical steps makes it easier to build in other features of 

labor market outcomes. For example, unemployment incidence and spell lengths differ for partand full-time workers. The CBOLT approach also makes it feasible to introduce behavioral 

responses into the model. In particular, retirement in CBOLT is modeled as a decision to start 

collecting Social Security, which does not necessarily end labor market activity—it just changes 

the intensity.7

Estimated Coefficients in Single-Equation and Age-Centered Regressions 

In order to draw out how age-centered regression differs from traditional single-equation 

estimates we compare versions of each labor force equation, estimated using the same data set 

for the same time period. Table 1 shows six sets of single-equation estimates, three each for men 

and women. For each sex group, the first column shows estimated coefficients for the labor 

force participation equation, the second column for the full-time work equation, and the third 

column for part-time hours worked.8

 

The signs of the coefficients in Table 1 make sense, and most of the parameters of 

interest are significant at the 1 percent level. In general, more education is associated with 

 

labor force decisions, because the eligibility age for Social Security is 62 in the United States. 7

This is not the only way to achieve desired heterogeneity in labor market outcomes. For other examples, see the 

description of the labor force modules for the Urban Institute’s DYNASIM model in Favreault and Smith (2004) or 

for the Social Security Administration’s Modeling Income in the Near Term (MINT) model in Toder et al. (2002). 8

 The estimated thresholds or “cut” parameters are not shown for the part-time multinomial logits. Those are 

available from the authors upon request. 
10

higher labor supply for both men and women, while marriage is associated with higher labor 

supply for men but lower labor supply for women. Receipt of Social Security income has a 

strong negative effect on labor supply for both men and women. The most dominant effect in the 

labor force participation equation is from lagged labor force participation, which we focus on 

below when computing marginal effects. This coefficient shows that persistence in labor supply 

within the population is a first-order effect that should be accounted for, clearly dominating the 

magnitude of the other zero-one dummy variables. 

The CBOLT age-centered versions are shown for two reference ages (age 30 and 55) in 

Table 2a (for men) and Table 2b (for women).9

 The first observation about Tables 2a and 2b is 

that the estimated coefficients often vary significantly between the two age samples. For 

example, the coefficient on lagged labor force participation for 55-year-olds is about 30 percent 

higher than the coefficient for 30-year-olds, and that holds for both men and women. What that 

suggests is that persistence in labor supply is much stronger at age 55 than it is at age 30, 

everything else constant. 

The estimated coefficients for the 30- and 55-year-old reference age samples diverge 

from the single-equation estimates to varying degrees across independent variables and 

equations, but the presumption that using age centering can reveal differences in estimated 

effects by age is clearly borne out in Tables 2a and 2b. It is worth noting that single-equation 

parameter estimates (in Table 1) generally fall in the range spanned by the age-centered 

estimates in Tables 2a and 2b, which is expected given the way the data are used to estimate the 

equations. Finally, there also appears to be no significant loss of statistical precision when 

 

9

 The entire list of coefficients for reference ages 16 through 70 can be found in Congressional Budget Office 
11

shifting to age centering in these equations. Almost every variable that is significant in Table 1 

remains so in Tables 2a and 2b. 

Differences in Marginal Effects by Age

 Differences in estimated coefficients across age groups are one way to show how age 

centering can affect predicted outcomes, but a better way to see the implications for model 

simulations is to compute marginal effects. The marginal effect of a given independent variable 

is computed by applying the estimated equation coefficients within-sample. The value of the 

independent variable being investigated is varied and the difference in the corresponding 

predicted outcomes is the marginal effect. 

 The first set of marginal effects computed for the CBOLT labor force equations applies 

to the lagged dependent variable in the labor force participation equations. For each person in 

the full sample the probability of working is computed using the estimated coefficients, with all 

independent variables set to actual values except lagged labor force participation. In the first set 

of calculations, the value of lagged labor force participation is set to zero (no work in the 

previous period) for every observation and the mean predicted labor force participation 

probability by age is computed. In the second set of calculations, the value of lagged labor force 

participation is set to one for every observation, and again the mean participation probability by 

age is computed. Because lagged labor force participation has a positive effect on current-year 

participation, the second set of mean probabilities is higher at every age. The marginal effect of 

lagged labor force participation is the gap between these two sets of mean probabilities. 

 (2006). 
12

 Figure 1 shows four sets of marginal effects for lagged labor force participation. There is 

one set each for men and women and for the two equations (single-equation and age-centered). 

For both men and women, the marginal effects in the single-equation estimates show much less 

variation by age than in the age-centered regressions. This makes sense because the singleequation estimate provides the weighted-average marginal effect of lagged labor force 

participation across the age distribution. Indeed, the only variation by age in marginal effects is 

associated with underlying variation in the other independent variables in the data set; there is 

only one coefficient on lagged labor force participation that applies to every age group, so the 

range of marginal effects is limited. 

 The variation in marginal effects by age is much more pronounced in the age-centered 

regressions, which is consistent with observations about the estimated coefficients by age made 

in the previous section. The coefficient on lagged labor force participation rises systematically 

by age in the age-centered regressions for both men and women, and this rise is reflected in 

significant increases in marginal effects as age increases. The fact that both age-centered 

marginal effects lines cross their respective single-equation lines is also consistent with the 

observations made about the coefficients in Tables 1 and 2a, 2b. 

 These observed differences in estimated marginal effects could be of first-order 

importance in the microsimulation. The lagged labor force participation coefficient is a key to 

establishing longitudinal persistence in labor force participation within the micro sample, and in 

a single-equation model that persistence will be biased up for the young and biased down for 

workers nearing retirement. One often-used technique in microsimulation—calibration factors 

by age—could be used to match predicted outcomes by age, but unless one addresses the 
13

underlying cause of the bias calibration will not fix the problems with the equation. 

 A second comparison of estimated marginal effects using single-equation estimates and 

age-centered regression leads to the same basic conclusion. Figure 2 shows the marginal effect 

of being married on part-time hours worked (conditional on working part-time). In this case, the 

marginal effect of being married for both men and women is fairly similar between the agecentered and single-equation estimates, with the notable exception of the youngest and oldest age 

ranges, where the bias is noticeable. 

Differences in Mean Predicted Outcomes by Age

 In addition to eliminating bias by age in estimated marginal effects, age centering can 

also improve the mean predicted outcomes by age in the microsimulation. The examples used 

here to draw out this point are somewhat contrived, because we estimate the single-equation 

versions using only a linear age term. In many applications, microsimulation modelers will 

examine patterns by age for the types of processes we are considering and estimate higher-order 

age polynomials. 

Figure 3 shows the mean probability of working by age for men and women, evaluated 

within-sample using the single-equation and age-centered regression approaches. Both 

equations clearly capture the concave shape in labor force participation between ages 25 and 61. 

 The age-centered predictions will, by virtue of maximum likelihood principles, more closely 

track the actual patterns of labor force participation by age, so we can characterize the deviation 

of the single-equation from the age-centered line as bias. Although the deviation is not too 

extreme, it is systematically biased upwards for women. For men, the single-equation estimate is 
14

biased up for young workers and biased down for older workers, in generally the same direction 

of bias as the marginal effects of lagged labor force participation noted above. Adding higherorder age terms to the equation may help the single-equation track better, but it is unlikely to 

eliminate the bias. 

Figure 4 shows the mean of part-time hours conditional on working part-time, and for 

these outcomes the bias is even stronger. The effect of imposing a linear coefficient on age 

comes through clearly for men, as the functional form induces a predicted relationship with age 

that is linear. As with labor force participation, the higher-order age-terms could improve 

predicted outcomes but the predictions will only asymptotically approach the age-centered 

values as higher-order terms are added. 

IV. Conclusions 

 The technique described here as “age-centered regression” analysis is a useful way to 

extract information from a limited data set when estimating equations for dynamic 

microsimulation models. The situation in which age centering can help is very common: when 

the behavioral process in question varies systematically by age and the effect of one or more 

independent variables might also differ across age groups. The basic idea is to estimate separate 

equations for each age sample, but to include observations that are close to the reference age 

being estimated. Using the extra information from nearby observations makes it possible to 

statistically identify how marginal effects and predicted mean outcomes differ across the age 

distribution under consideration. 

 The examples used here to illustrate age centering are fairly simple labor supply 
15

equations—the sequence of participation, full- versus part-time, and part-time hours given parttime employment—used in the Congressional Budget Office Long-Term (CBOLT) dynamic 

microsimulation. We show that moving from a single-equation to an age-centered approach 

involves little loss of statistical precision but has a significant impact on estimated marginal 

effects and mean predicted outcomes by age. 
16

V. References 

Congressional Budget Office, Projecting Labor Force Participation and Earnings in CBO’s 

Long-Term Microsimulation Model. Background Paper, Congressional Budget Office, 

Washington, DC (October 2006). 

Favreault, Melissa M., and Karen E. Smith, “A Primer on the Dynamic Simulation of Income 

Model (DYNASIM3).” Discussion paper, Retirement Project, The Urban Institute, Washington, 

DC (December 2004). 

Harris, Amy Rehder, and Josh O’Harra, “The Impact of Marriage and Labor Force Participation 

Trends on the Social Security Benefits of Women.” Proceedings of the National Tax 

Association (November 2001). 

Harris, Amy Rehder, John Sabelhaus, and Michael Simpson, “Uncertainty About OAI Worker 

Benefits Under Individual Accounts.” Contemporary Economic Policy, 23:1, 1-16 (January 

2005). 

Harris, Amy Rehder, and John Sabelhaus, “How Does Differential Mortality Affect Social 

Security Progressivity and Finances?” Technical Paper 2005-5, Congressional Budget Office, 

Washington, DC (May 2005). 

Harris, Amy Rehder and Michael Simpson, “Winners and Losers Under Various Approaches to 

Slowing Social Security Benefit Growth,” National Tax Journal, Vol. LVIII, No. 3, pp 523-544 

(September 2005). 

O’Harra, Josh, John Sabelhaus, and Michael Simpson, “Overview of the Congressional Budget 

Office Long-Term (CBOLT) Policy Simulation Model.” Technical Paper 2004-1, Congressional 

Budget Office, Washington DC (January 2004). 

O’Harra, Josh, and John Sabelhaus, “Projecting Longitudinal Marriage Patterns for Long-Term 

Policy Analysis” Technical Paper 2002-2, Congressional Budget Office, Washington, DC 

(October 2002). 

Sabelhaus, John, and Julie Topoleski, “Uncertain Policy for an Uncertain World: The Case of 

Social Security” Journal of Policy Analysis and Management (forthcoming, 2007). 

Smith, Karen E., David B. Cashin, and Melissa M. Favreault, “Modeling Income in the Near 

Term 4.” The Urban Institute, Washington DC (April 2005). 

Toder, Eric, and others, “Modeling Income in the Near Term: Revised Projections of Retirement 

Income Through 2020 for the 1931-1960 Birth Cohorts.” The Urban Institute, 

Washington DC (June 2002). 
Pr(LFP=1) Pr(FT=1) PT Hours Pr(LFP=1) Pr(FT=1) PT H

Lagged Labor Force Participation 4.082 4.361

(0.012)** (0.008)**

Married 0.166 0.822 0.236 -0.525 -0.708 -0.3

(0.012)** (0.009)** (0.015)** (0.009)** (0.006)** (0.01

Age of Person -0.021 -0.002 -0.011 -0.004 0.012 0.0

(0.001)** (0.001)** (0.001)** (0.001)** (0.000)** (0.00

Receiving Social Security Income -2.081 -2.243 -1.218 -1.085 -1.110 -0.6

(0.026)** (0.035)** (0.042)** (0.020)** (0.022)** (0.02

High School Education 0.111 0.552 0.111 0.398 0.299 0.1

(0.015)** (0.012)** (0.019)** (0.011)** (0.009)** (0.01

Some College Education -0.049 0.491 -0.074 0.482 0.325 0.0

(0.017)** (0.013)** (0.022)** (0.013)** (0.010)** (0.01

College Education 0.241 0.646 -0.116 0.637 0.490 0.0

(0.016)** (0.013)** (0.021)** (0.013)** (0.010)** (0.01

Number of Children Under 6 Years -0.481 -0.516 -0.2

(0.008)** (0.006)** (0.00

Birth Year: 1920-1929 0.208 0.129 0.074 0.175 0.078 0.0

(0.042)** (0.041)** (0.066) (0.032)** (0.033)* (0.0

Birth Year: 1930-1939 0.376 0.202 0.073 0.422 0.157 0.1

(0.041)** (0.041)** (0.064) (0.032)** (0.033)** (0.04

Birth Year: 1940-1949 0.392 0.331 0.178 0.64 0.347 0.3

(0.042)** (0.042)** (0.065)** (0.032)** (0.033)** (0.04

Birth Year: 1950-1959 0.341 0.293 0.151 0.831 0.543 0.5

(0.043)** (0.042)** (0.068)* (0.034)** (0.033)** (0.04

Birth Year: 1960-1969 0.147 0.266 0.068 0.863 0.700 0.6

(0.046)** (0.044)** (0.070) (0.035)** (0.034)** (0.04

Birth Year: 1970-1979 -0.001 0.115 0.002 0.744 0.732 0.7

(0.052) (0.047)* (0.074) (0.040)** (0.036)** (0.04

Constant -0.443 1.125 -2.169 0.152

(0.063)** (0.056)** (0.048)** (0.041)**

Observations 1,034,541 944,231 86,049 1,113,085 782,972 254,Robust standard errors in parentheses* significant at 5%; ** significant at 1%

Table 1: Regression Results Using Single Equation with Linear Age Term, Men and Women

Men Women
Pr(LFP=1) Pr(FT=1) PT Hours Pr(LFP=1) Pr(FT=1) PT 

Lagged Labor Force Participation 3.451 4.594

(0.022)** (0.025)**

Married -0.043 0.793 0.226 0.335 0.562 0

(0.018)* (0.014)** (0.024)** (0.028)** (0.022)** (0

Age of Person 0.046 0.064 0.028 -0.123 -0.089 -0

(0.004)** (0.003)** (0.005)** (0.005)** (0.004)** (0.

Receiving Social Security Income -1.687 -1.905 -1.211 -2.293 -2.555 -1

(0.052)** (0.075)** (0.090)** (0.050)** (0.067)** (0.

High School Education -0.088 0.617 0.230 0.152 0.360 0

(0.026)** (0.021)** (0.034)** (0.030)** (0.024)** (0

Some College Education -0.364 0.475 -0.060 0.123 0.371 -0

(0.028)** (0.022)** (0.036)** (0.037)** (0.029)** (0

College Education -0.043 0.536 -0.248 0.464 0.580 0

(0.028) (0.022)** (0.035) (0.035) (0.027)** (0

Birth Year: 1920-1929 -0.065 -0.180 -0

(0.081) (0.067)** (0

Birth Year: 1930-1939 -0.133 -0.382 -0

(0.082) (0.067)** (0.

Birth Year: 1940-1949 -0.277 -0.388 -0

(0.082)** (0.068)** (0.

Birth Year: 1950-1959 0.011 -0.124 -0.008 -0.365 -0.289 -0

(0.030) (0.025)** (0.041) (0.098)** (0.080)** (0

Birth Year: 1960-1969 -0.025 -0.058 -0.044

(0.030) (0.025)* (0.042)

Birth Year: 1970-1979 -0.001 0.009 -0.035

(0.034) (0.028) (0.047)

Constant -1.578 -0.549 5.136 6.613

(0.117)** (0.094)** (0.302)** (0.239)**

Observations 308,015 290,385 29,024 188,934 160,656 16Robust standard errors in parentheses* significant at 5%; ** significant at 1%

Men, Age 30 Men, Age 55

Table 2a: Regression Results Using Age Centering, Men Ages 30 and 55
Pr(LFP=1) Pr(FT=1) PT Hours Pr(LFP=1) Pr(FT=1) PT Hou

Lagged Labor Force Participation 3.717 5.028

(0.013)** (0.020)**

Married -0.534 -0.547 -0.306 -0.535 -0.780 -0.41

(0.015)** (0.011)** (0.016)** (0.022)** (0.016)** (0.024

Age of Person 0.029 0.001 0.007 -0.061 -0.020 -0.01

(0.003)** (0.002) (0.003)* (0.004)** (0.003)** (0.004

Receiving Social Security Income -0.882 -0.794 -0.515 -1.110 -1.368 -0.71

(0.044)** (0.050)** (0.054)** (0.047)** (0.050)** (0.050

High School Education 0.436 0.398 0.107 0.373 0.272 0.076

(0.019)** (0.018)** (0.023)** (0.024)** (0.019)** (0.026

Some College Education 0.526 0.454 0.132 0.425 0.290 0.047

(0.021)** (0.019)** (0.024)** (0.031)** (0.022)** (0.032

College Education 0.700 0.731 0.166 0.598 0.403 0.066

(0.021)** (0.019)** (0.024)** (0.033)** (0.023)** (0.034

Number of Children Under 6 Years -0.435 -0.584 -0.309 -0.209 -0.201 -0.20

(.008)** (0.007)** (0.009)** (0.084) (0.060)** (0.085

Birth Year: 1920-1929 -0.054 -0.094 -0.03

(0.062) (0.054) (0.074

Birth Year: 1930-1939 0.096 -0.095 0.084

(0.063) (0.054) (0.075

Birth Year: 1940-1949 0.220 0.135 0.220

(0.063)** (0.055)* (0.075

Birth Year: 1950-1959 0.299 0.255 0.293 0.342 0.244 0.351

(0.020)** (0.016)** (0.022)** (0.076)** (0.062)** (0.086

Birth Year: 1960-1969 0.409 0.449 0.455

(0.021)** (0.017)** (0.023)**

Birth Year: 1970-1979 0.393 0.499 0.510

(0.024)** (0.019)** (0.027)**

Constant -2.408 0.530 0.855 2.184

(0.086)** (0.067)** (0.247)** (0.178)**

Observations 330,794 239,891 81,777 205,062 127,326 40,05Robust standard errors in parentheses* significant at 5%; ** significant at 1%

Women, Age 30 Women, Age 55

Table 2b: Regression Results Using Age Centering, Women Ages 30 and 55
Figure 1: Marginal Effect of Lagged LFP on Labor Force Participation

Comparing Single-Equation and Age-Centered Regressions

Men and Women, Ages 25-61

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5

Age

Percent

Women, Single-Equation

Men, Single-Equation

Women, Age-Centered

Men, Age-Centered
Figure 2: Marginal Effect of Being Married on Part-Time Hours Worked

Comparing Single-Equation and Age-Centered Regressions

Men and Women, Ages 25-61

-150-100

-50

0

50

100150

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 

Age

Hours Worked

Women, 

Women, Age-Centered

Men, Age-Centered
Figure 3: Mean Predicted Labor Force Participation

Comparing Single-Equation and Age-Centered Regressions

Men and Women, Ages 25-61

0.40.50.60.70.80.9

1

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5

Age

Percent

Men, Age-Centered

Women, Age-Centered

Men, Single-Equation

Women, Single-Equation
Figure 4: Mean Expected Part-Time Hours 

Comparing Single-Equation and Age-Centered Regressions

 Men and Women, Ages 25-61

900950

10001050110011501200

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 

Age

Hours

Men, Single-Equation

Women, Single-Equation

Men, Age-Centered

Women, Age-Centered