Labor Force Participation and Labor Supply

"The presence of young children is always expected to increase the reservation wage, lowering the probability of participation. This may be because child care costs would be incurred if the mother participated in the labor market or because of the mother's increased productivity in home production." Rachel Connelly

Individual labor supply is determined by a series of choices including labor force participation, the decision to work or not. In this assignment you will address several of the primary issues relating to limited dependent variable models and estimation of labor supply responses. The data for this set of exercises is available for downloading as LFPDATA in MS Excel workbook format. Although based on data from the Current Population Survey, it should only be used for instructional purposes due to various revisions and additions made for the purposes of this exercise. The data represent a cross-section of working and non-working married women. Variable definitions are provided.

ü initial data exploration

Begin with the entire sample and note the total number of observations. Sort the full sample into participants and nonparticipants and identify how many observations are in each subsample. Take a look at descriptive statistics (mean and standard deviation) for all other variables (working hours, wage, education, experience, children under six, husband's earnings, etc.).  Describe any notable differences between the two subsamples.

A number of the variables are truncated, that is, they are not available for nonparticipants. The most essential of these, for labor supply estimation, is the wage. Define a new series P_LWAGE that contains actual LWAGE for participants and predicted values for nonparticipants. You will need to run a regression model for LWAGE on the participant subsample and construct predicted values for the other subsample based on the estimated coefficients. Take a look at descriptive statistics of P_LWAGE across the two subsamples and provide an interpretation of any notable differences.

ü labor force participation: three alternatives

Evaluate the determinants of labor force participation using probit analysis on the full sample. In this exercise you will use three alternative specifications: (1) a reduced form specification, (2) a standard structural equation and (3) a model of labor force participation including child care costs. It would be helpful to view results from these three alternatives side-by-side in the same table (for example, see Connelly Table 3). You may want to review "Estimating Binary Models in EViews" before you begin.

Develop your alternative specifications based on the following general model. Individuals face wage offers W = f(X). Participation occurs when the wage offer exceeds the reservation wage of the individual Wr = g(Z). Thus, we would model labor force participation as a function of wage offers and reservation wage determinants LFP = h( W(X), Z ). Consider carefully which variables belong in X, which variables belong in Z, and which should appear in both sets. The "reduced form" model can be expressed in terms of X and Z. The "structural model" includes W and Z but excludes elements of X. The "participation cost" model is simply the structural model with child care costs included.

Present coefficient estimates and standard errors for your alternative specifications. Evaluate the goodness of fit of your estimated equations using McFadden's R-Square (provided with the estimation output) and Count R-Square (accessible in View – Expectation Prediction Table).

How do your findings compare to those reported in Connelly? What proportion of your sample consists of labor force participants and how would this proportion change with 50% and 100% subsidies for child care? Hint: Do not reestimate the model based on altered child care costs. Use parameter estimates based on actual child care cost and simulate (or predict) participation outcomes with subsidized child care costs. View the representation of your model with estimated coefficients to see the functional form required to generate your alternative predicted values.

ü partial effects for interpretation

The estimated coefficients and standard errors can be used to discuss statistical significance of the explanatory variables. However, you must derive the partial effects to discuss the marginal impact on LFP probability. In EViews, use Forecast, Index, @dnorm to implement the conversion (see help topic "Procedures for Binary Equations"). You can generate the partial effects one parameter at a time; however, notice that you have different values for every observation. Due to the nonlinear nature of the probit function the partial effetcs are conditional on the levels of all explanatory variables. You should present mean values for each of the partial effects and provide a clear interpretation. You may want to present additional information on the distribution of partial effects for the child care cost variable (for example, across quintiles of child care costs or quintiles of another explanatory variable).

ü related references

Wooldridge, "Limited Dependent Variable Models and Sample Selection Corrections," in Introductory Econometrics: A Modern Approach, second edition, Thompson-Southwestern, 2003. Berndt. "Whither and How Much Women Work for Pay," in The Practice of Econometrics: Classic and Contemporary, 1991. Connelly, “The Effect of Child Care Costs on Married Women’s Labor Force Participation,” Review of Economics and Statistics, February 1992. Ehrenberg and Smith, "Child Care, Commuting and the Fixed Costs of Work," in Modern Labor Economics: Theory and Public Policy, sixth edition, Addison-Wesley, 1997.

update 11/9/06