Identification of Dynamic Latent Factor Models: The Implications of Re-Normalization in a Model of Child Development / Francesco Agostinelli, Matthew Wiswall.

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Agostinelli, Francesco

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TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w22441.Publication details: Cambridge, Mass. National Bureau of Economic Research 2016.Description: 1 online resource: illustrations (black and white)Subject(s):

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Abstract: A recent and growing area of research applies latent factor models to study the development of children's skills. Some normalization is required in these models because the latent variables have no natural units and no known location or scale. We show that the standard practice of "re-normalizing" the latent variables each period is over-identifying and restrictive when used simultaneously with common skill production technologies that already have a known location and scale (KLS). The KLS class of functions include the Constant Elasticity of Substitution (CES) production technologies several papers use in their estimation. We show that these KLS production functions are already restricted in the sense that their location and scale is known (does not need to be identified and estimated) and therefore further restrictions on location and scale by re-normalizing the model each period is unnecessary and over-identifying. The most common type of re-normalization restriction imposes that latent skills are mean log-stationary, which restricts the class of CES technologies to be of the log-linear (Cobb-Douglas) sub-class, and does not allow for more general forms of complementarities. Even when a mean log-stationary model is correctly assumed, re-normalization can further bias the estimates of the skill production function. We support our analytic results through a series of Monte Carlo exercises. We show that in typical cases, estimators based on "re-normalizations" are biased, and simple alternative estimators, which do not impose these restrictions, can recover the underlying primitive parameters of the production technology.

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Item type	Home library	Collection	Call number	Status	Date due	Barcode	Item holds
Working Paper	Biblioteca Digital	Colección NBER	nber w22441 (Browse shelf(Opens below))	Not For Loan

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July 2016.

A recent and growing area of research applies latent factor models to study the development of children's skills. Some normalization is required in these models because the latent variables have no natural units and no known location or scale. We show that the standard practice of "re-normalizing" the latent variables each period is over-identifying and restrictive when used simultaneously with common skill production technologies that already have a known location and scale (KLS). The KLS class of functions include the Constant Elasticity of Substitution (CES) production technologies several papers use in their estimation. We show that these KLS production functions are already restricted in the sense that their location and scale is known (does not need to be identified and estimated) and therefore further restrictions on location and scale by re-normalizing the model each period is unnecessary and over-identifying. The most common type of re-normalization restriction imposes that latent skills are mean log-stationary, which restricts the class of CES technologies to be of the log-linear (Cobb-Douglas) sub-class, and does not allow for more general forms of complementarities. Even when a mean log-stationary model is correctly assumed, re-normalization can further bias the estimates of the skill production function. We support our analytic results through a series of Monte Carlo exercises. We show that in typical cases, estimators based on "re-normalizations" are biased, and simple alternative estimators, which do not impose these restrictions, can recover the underlying primitive parameters of the production technology.