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Methodology

Research articles · Dec 31, 2009

Econometric flexibility in microsimulation: An age-centred regression approach

John Sabelhaus, Lina Walker

Department of Economics, University of Maryland, Washington, DC, United States; Investment Company Institute, Washington, DC, United States; Public Policy Institute, AARP, Washington, DC, United States

Volume 2(2) Autumn 2009

Cite as: J. Sabelhaus, L. Walker; 2009; Econometric flexibility in microsimulation: An age-centred regression approach; International Journal of Microsimulation; 2(2); 1–14. doi: 10.34196/ijm.00013

Abstract

This paper describes a strategy for estimating predictive equations that has been shown to work well in microsimulation modelling. The technique, referred to here as “age-centred 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-centring works are taken from the labour supply equations in the Congressional Budget Office Long-Term (CBOLT) dynamic microsimulation model. By switching from a traditional single-equation approach to age-centred 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.

This article contains 4 figures and 3 tables.

Figures

Figure 1. Marginal effect of lagged LFP on labour force participation comparing single-equation and age-centred regressions men and women, ages 25–61.
Figure 2. Marginal effect of being married on part-time hours worked comparing single-equation and age-centred regressions men and women, ages 25–61.
Figure 3. Mean predicted labour force participation comparing single-equation and age-centred regressions men and women, ages 25–61.
Figure 4. Mean expected part-time hours comparing single-equation and age-centred regressions men and women, ages 25–61.

Tables

Table 1. Regression results using single equation with linear age term, men and women.
  Men Women
Covariate Pr(LFP = 1) Pr(FT = 1) PT Hours Pr(LFP = 1) Pr(FT = 1) PT Hours
Lagged Labour Force Participation 4.082     4.361    
(0.012)**     (0.008)**    
Married 0.166 0.822 0.236 −0.525 −0.708 −0.371
(0.012)** (0.009)** (0.015)** (0.009)** (0.006)** (0.010)**
Age of Person −0.021 −0.002 −0.011 −0.004 0.012 0.013
(0.001)** (0.001)** (0.001)** (0.001)** (0.000)** (0.001)**
Receiving Social Security Income −2.081 −2.243 −1.218 −1.085 −1.110 −0.606
(0.026)** (0.035)** (0.042)** (0.020)** (0.022)** (0.025)**
High School Education 0.111 0.552 0.111 0.398 0.299 0.101
(0.015)** (0.012)** (0.019)** (0.011)** (0.009)** (0.012)**
Some College Education −0.049 0.491 −0.074 0.482 0.325 0.093
(0.017)** (0.013)** (0.022)** (0.013)** (0.010)** (0.014)**
College Education 0.241 0.646 −0.116 0.637 0.490 0.071
(0.016)** (0.013)** (0.021)** (0.013)** (0.010)** (0.014)**
Number of Children Under 6 Years       −0.481 −0.516 −0.299
      (0.008)** (0.006)** (0.007)**
Birth Year: 1920–1929 0.208 0.129 0.074 0.175 0.078 0.055
(0.042)** (0.041)** (0.066) (0.032)** (0.033)* (0.045)
Birth Year: 1930–1939 0.376 0.202 0.073 0.422 0.157 0.185
(0.041)** (0.041)** (0.064) (0.032)** (0.033)** (0.044)**
Birth Year: 1940–1949 0.392 0.331 0.178 0.64 0.347 0.337
(0.042)** (0.042)** (0.065)** (0.032)** (0.033)** (0.044)**
Birth Year: 1950–1959 0.341 0.293 0.151 0.831 0.543 0.547
(0.043)** (0.042)** (0.068)* (0.034)** (0.033)** (0.045)**
Birth Year: 1960–1969 0.147 0.266 0.068 0.863 0.700 0.660
(0.046)** (0.044)** (0.070) (0.035)** (0.034)** (0.046)**
Birth Year: 1970–1979 −0.001 0.115 0.002 0.744 0.732 0.711
(0.052) (0.047)* (0.074) (0.040)** (0.036)** (0.049)**
Constant −0.443 1.125   −2.169 0.152  
(0.063)** (0.056)**   (0.048)** (0.041)**  
Observations 1,034,541 9,44,231 86,049 1,113,085 7,82,972 2,54,685

Notes: (i) Models denoted by Pr(LFP = 1) – labour force participation; Pr(FT = 1) –full-time or part-time work; PT Hours –part-time hours for those working part-time. (ii) Robust standard errors italicised and in parentheses.

significant at 5%.

significant at 1%.

Table 2a. Regression results using age centring, men ages 30 and 55.
  Men, Age 30 Men, Age 55
Covariate Pr(LFP = 1) Pr(FT = 1) PT Hours Pr(LFP = 1) Pr(FT = 1) PT Hours
Lagged Labour Force Participation 3.451     4.594    
(0.022)**     (0.025)**    
Married −0.043 0.793 0.226 0.335 0.562 0.091
(0.018)* (0.014)** (0.024)** (0.028)** (0.022)** (0.036)*
Age of Person 0.046 0.064 0.028 −0.123 −0.089 −0.062
(0.004)** (0.003)** (0.005)** (0.005)** (0.004)** (0.006)**
Receiving Social Security Income −1.687 −1.905 −1.211 −2.293 −2.555 −1.248
(0.052)** (0.075)** (0.090)** (0.050)** (0.067)** (0.068)**
High School Education −0.088 0.617 0.230 0.152 0.360 0.012
(0.026)** (0.021)** (0.034)** (0.030)** (0.024)** (0.039)
Some College Education −0.364 0.475 −0.060 0.123 0.371 −0.078
(0.028)** (0.022)** (0.036)** (0.037)** (0.029)** (0.047)
College Education −0.043 0.536 −0.248 0.464 0.580 0.047
(0.028) (0.022)** (0.035) (0.035) (0.027)** (0.046)
Birth Year: 1920–1929       −0.065 −0.180 −0.169
      (0.081) (0.067)** (0.103)
Birth Year: 1930–1939       −0.133 −0.382 −0.291
      (0.082) (0.067)** (0.104)**
Birth Year: 1940–1949       −0.277 −0.388 −0.295
      (0.082)** (0.068)** (0.105)**
Birth Year: 1950–1959 0.011 −0.124 −0.008 −0.365 −0.289 −0.232
(0.030) (0.025)** (0.041) (0.098)** (0.080)** (0.126)
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 3,08,015 2,90,385 29,024 1,88,934 1,60,656 16,547

Notes: (i) Models denoted by Pr(LFP = 1) – labour force participation; Pr(FT = 1) –full-time or part-time work; PT Hours –part-time hours for those working part-time. (ii) Robust standard errors italicised and in parentheses.

significant at 5%.

significant at 1%.

Table 2b. Regression results using age centring, women ages 30 and 55.
  Women, Age 30 Women, Age 55
Covariate Pr(LFP = 1) Pr(FT = 1) PT Hours Pr(LFP = 1) Pr(FT = 1) PT Hours
Lagged Labour Force Participation 3.717     5.028    
(0.013)**     (0.020)**    
Married −0.534 −0.547 −0.306 −0.535 −0.780 −0.413
(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 −0.017
(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 −0.718
(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 −0.201
(0.008)** (0.007)** (0.009)** (0.084) (0.060)** (0.085)*
Birth Year: 1920–1929       −0.054 −0.094 −0.034
      (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 40,052

Notes: (i) Models denoted by Pr(LFP = 1) – labour force participation; Pr(FT = 1) –full-time or part-time work; PT Hours –part-time hours for those working part-time. (ii) Robust standard errors italicised and in parentheses.

significant at 5%.

significant at 1%.