Multiple‐Output Child Health Production Functions: The Impact of Time‐Varying and Time‐Invariant Inputs

Many production activities generate undesirable outputs in conjunction with the desirable outputs. In this paper we present the first estimates of a multiple‐input, multiple‐output directional distance function that relates good and bad inputs from home, school, and environment to good and bad outputs, measured as children's cognitive and behavioral development. This household directional distance function is estimated using a balanced panel of 369 families from the National Longitudinal Survey of Youth‐Child Sample for 1996 to 2000 using the generalized method of moments within estimator and instrumental variables. We recover consistent partial effects for the time‐invariant variables in a second‐stage regression and estimate their corrected asymptotic standard errors. We then compute and examine productivity differences among households defined as the increase (decrease) in good (bad) outputs that families could attain with constant inputs if they were operating on the technological frontier. Our estimates suggest the presence of significant inefficiency among sample families that diminishes over time.