Individual labour income, stock prices and whom it may concern

ABSTRACT

In this paper, a panel model which describes the relationship between individual labour income and stock prices in Germany is estimated. The specification allows the individuals to cluster concerning the model parameters that describe first the individual labour income dynamics and second the relationship between the individual labour income and financial markets. Methodically, a Bayesian model-based non-Gaussian panel data approach, proposed by Juarez and Steel (2010a), is used. A group of individuals with a high cluster assignment probability is found. The characteristics of this group, whose individuals share the same autoregressive dynamics and a common, relatively high dependence on financial markets, are investigated further. It can be shown that this group has a statistically significantly different partition of the major occupational groups. This leads to implications for various branches of the literature, such as the pricing of human capital contracts, the hedging of individual income risk, portfolio optimization or asset pricing.

KEYWORDS:

• Hedgeability of wages
• pricing human capital contracts
• financial properties of labour income
• occupational income risk

JEL CLASSIFICATION:

• G11
• G12
• J17
• J30

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ For an overview, see Palacios (2004).

² See Cochrane (2000) for an introduction on Good-deal asset price bounds and Huggett and Kaplan (2011) for its application in the context of individual human capital, Bernardo and Ledoit (2000) and Voelzke (2015) for further developments.

³ Cp. Davis and Willen (2000).

⁴ Cp. Mehra and Prescott (1985).

⁵ See Constantinidies, Donaldson, and Mehra (1998) for an alternative explanation.

⁶ For a description of the G-SOEP, see Wagner, Frick, and Schupp (2007). In particular, I use the individual labour income and for the main occupational grouping, the first digit of the ISCO-88 Occupation Code.

⁷ That is, individuals were dismissed if their average yearly income was below 10,000 euros, or their maximal income was larger than two times their average income or the variance of their income was in the upper 5% quantile. Gaps of one year in income were interpolated and did not result in the dismissal of the individual.

⁸ I model individual labour income as a discrete stochastic process on a suitable filtered probability space . Furthermore, I assume that the evolution of stock prices can be described by an appropriate time-continuous semi-martingale. Here ‘appropriate’ means that a corresponding predictable representation property is fulfilled.

⁹ For a proof and a comment on the link between the predictable representation property and complete markets in the modelling of financial markets, see Jeanblanc, Yor, and Chesney (2009, 58).

¹⁰ The only notational difference is that the original is defined as the actual reciprocal.

¹¹ The cluster index is given by .

¹² Juárez and Steel (2010a) use a skewed version, which is renounced here, after first estimations did not exhibit any skewness.

¹³ The unspecified parameters were set to , and . Note for the interpretation that S_t and y_t are upfront divided by 10 000 for better readability.

¹⁴ Cp. Plummer et al. (2003) concerning JAGS.

¹⁵ With a ‘large probability’ I denote in the following probabilities larger than 100%–5%K to account for the number of clusters.

¹⁶ The group of clustering individuals can be identified by a moderate autoregressive coefficient of (for the different K) in contrast to close to one coefficient for the other clusters. Using that and a large cluster probability to this particular cluster as an identification, the member variation of this group between different K is low. In particular have over 60% of all individuals that have a large assignment probability for the specific cluster for as well large assignment probabilities for the corresponding cluster for .

¹⁷ The estimate for for the identified group is .

¹⁸ Cp. Table 2.