Production and consumption externalities of human capital: an empirical study for Italy

Abstract

The estimation of the effect of local human capital on wages only might not identify properly human capital spillovers. Appropriate identification requires considering the joint effect of local human capital on both wages and rents. Empirically, we study the effects of local human capital on household-level rents and individual-level wages for a sample of Italian local labour markets. Our results show a positive and robust effect of local human capital on rents, supporting the idea that human capital generates positive externalities at the local level. Our results also suggest that consumption and production externalities have a similar impact on wages.

Appendix

1.1 Derivation of the model solution

The maximum problem for an individual i who lives and works in area c can be written as:

$${\mathop {\max }\limits_{{\left\{ {Y_{{ic}} ,L_{{ic}} } \right\}}} }\,{\ell } = A_{U} {\left( {H_{c} } \right)} \cdot L^{{1 - \mu }}_{{ic}} \cdot Y^{\mu }_{{ic}} + \lambda \cdot {\left[ {h_{i} \cdot w_{c} - r_{c} \cdot L_{{ic}} - p_{c} \cdot Y_{{ic}} } \right]}$$

(A1)

where p _c =1. The first-order conditions are given by:

$$\frac{{\partial {\ell }}}{{\partial Y_{{ic}} }} = \mu \cdot A_{U} {\left( {H_{c} } \right)}L^{{1 - \mu }}_{{ic}} \cdot Y^{{\mu - 1}}_{{ic}} - 1 = 0$$

(A2)

$$\frac{{\partial {\ell }}}{{\partial L_{{ic}} }} = {\left( {1 - \mu } \right)} \cdot A_{U} {\left( {H_{c} } \right)} \cdot L^{{ - \mu }}_{{ic}} \cdot Y^{\mu }_{{ic}} - r_{c} = 0$$

(A3)

Rearranging Eqs. A2 and A3 and dividing side by side, one obtains:

$${\left( {\frac{{1 - \mu }}{\mu }} \right)} \cdot \frac{{Y_{{ic}} }}{{L_{{ic}} }} = r_{c} $$

(A4)

From Eq. A4, one can find an expression for L _ic to be substituted into the worker’s budget constraint. This yields the optimal value of Y _ic as a function of worker’s income:

$$Y_{{ic}} = \mu \cdot {\left( {h_{i} w_{c} } \right)}$$

(A5)

Again, one can exploit the budget constraint together with Eq. A5 to get the optimal value of L _ic :

$$L_{{ic}} = \frac{{{\left( {1 - \mu } \right)}}}{{r_{c} }} \cdot {\left( {h_{i} w_{c} } \right)}$$

(A6)

By substituting Eqs. A5 and A6 into the utility function (1), one obtains worker i’s indirect utility function:

$$V_{{ic}} = {\left( {1 - \mu } \right)}^{{1 - \mu }} \mu ^{\mu } A_{U} {\left( {H_{c} } \right)}\frac{{h_{i} w_{c} }} {{r^{{1 - \mu }}_{c} }}$$

(A7)

Dividing Eq. A7 by h _i and defining v _ic ≡V _ic /h _i , one obtains Eq. 2 in the text, which is the utility obtained per unit of efficiency by worker i. “Free mobility” of workers will imply that each worker must receive the same utility per unit of individual education across all areas. Thus, condition (3) in the text holds true.

Each firm j maximizes profits by choosing the inputs {L _jc , h _j N _jc }, land and efficiency units of labour, respectively. Here, h _j can be interpreted as the average level of efficiency possessed by the N _jc workers in the firm. (More formally, the labour input as measured in efficiency units is given by ${\sum\limits_{s = 1}^{N_{{jc}} } {h_{s} } }$. Since workers of different ability are perfect substitutes in this model, this expression can be rewritten as h _j N _jc not only when all workers in firm j have the same level of efficiency, but also when h _j is the average value of efficiency of the workers in the firm.)

The problem of firm j in area c is then:

$${\mathop {\max }\limits_{{\left\{ {L_{{jc}} ,h_{j} N_{{jc}} } \right\}}} }\Pi _{{jc}} = A_{Y} {\left( {H_{c} } \right)}L^{{1 - \alpha }}_{{jc}} {\left( {h_{j} N_{{jc}} } \right)}^{\alpha } - r_{c} L_{{jc}} - w_{c} {\left( {h_{j} N_{{jc}} } \right)}$$

(A8)

The first-order conditions for problem (A8) are thus given by:

$$\frac{{\partial \Pi _{{jc}} }} {{\partial {\left( {h_{j} N_{{jc}} } \right)}}} = \alpha A_{Y} {\left( {H_{c} } \right)}L^{{1 - \alpha }}_{{jc}} {\left( {h_{j} N_{{jc}} } \right)}^{{\alpha - 1}} - w_{c} = 0$$

(A9)

$$\frac{{\partial \Pi _{{jc}} }} {{\partial L_{{jc}} }} = {\left( {1 - \alpha } \right)}A_{Y} {\left( {H_{c} } \right)}L^{{ - \alpha }}_{{jc}} {\left( {h_{j} N_{{jc}} } \right)}^{\alpha } - r_{c} = 0$$

(A10)

From Eqs. A9 and A10, together with Eq. 4 in the text, one obtains that:

$${\left( {1 - \alpha } \right)}Y_{{jc}} = r_{c} L_{{jc}} $$

(A11)

and

$$\alpha Y_{{jc}} = w_{c} {\left( {h_{j} N_{{jc}} } \right)}$$

(A12)

One can exploit Eqs. A11 and A12 to obtain expressions for {L _jc , h _j N _jc }, which can be substituted into the production function (4) in the text. Thus, one obtains the “free-entry” condition (5). (By using Eqs. A11 and A12 to substitute {L _jc , h _j N _jc } away from the profit expression, one can verify that profit is zero in equilibrium.)

Finally, the “free-entry” condition (5) can be coupled together with the “free-mobility” condition (expressed in labour efficiency units), given by:

$$v = \eta A_{U} {\left( {H_{c} } \right)}\frac{{w_{c} }} {{r^{{1 - \mu }}_{c} }}$$

(A13)

where $\eta = {\left( {1 - \mu } \right)}^{{1 - \mu }} \cdot \mu ^{\mu }$.

By taking the logs of expressions (5) and (A13), one obtains two log-linear equations in (log w _c , log r _c ), i.e.

$$0 = \log \,\xi + \log \,A_{Y} {\left( {H_{c} } \right)} - {\left( {1 - \alpha } \right)}\log \,r_{c} - \alpha \log \,w_{c} $$

(A14)

$$\log \,v = \log \,\eta + \log \,A_{U} {\left( {H_{c} } \right)} - {\left( {1 - \mu } \right)}\log \,r_{c} + \log \,w_{c} $$

(A15)

By finding log w _c from Eq. A14 and substituting it into Eq. A15, one obtains Eq. 6 in the text. Then, expression (6) can be exploited to get rid of log r _c in Eq. A14 to obtain expression (7).

1.2 Description of the variables

Variable	Description	Source
Rents	Log of the annual rent. For each household, the interviewee can be either the property owner or the tenant. In the first case, the SHIW collects the rent the owner charges (or, if the dwelling is not rented or it is the family residence, the best estimate for the rent that could be charged). In the second case, the tenant reports the actual rent paid	SHIW
Wages	Log of hourly wages. Hourly wages are calculated by dividing the annual earnings (from any activity as employee, including fringe benefits, net of taxes and social security contributions) by the total amount of hours worked in a year (average hours worked per week×months worked×4.3333). The sample is trimmed at the 1st and 99th and percentile of the distribution of earnings	SHIW
Local human capital	Average years of schooling (1991) in the LLM where the dwelling is located or the individual resides	ISTAT
Surface area	Area in m2	SHIW
Age of the house	Calculated as the difference between the year of the survey and the year the house was built, which is a datum available from the SHIW	SHIW
Bathrooms	Indicator variable equal to 1 if two or more bathrooms are available in the dwelling	SHIW
Heating system	Indicator variable equal to 1 if a heating system is available in the dwelling	SHIW
Imputed rents	Indicator variable equal to 1 if the rent recorded is imputed by the interviewee	SHIW
House’s location	Series of dummies for the location of the dwelling (isolated area, countryside; town outskirts; between outskirts and town centre; town centre; other; hamlet)	SHIW
LLM population	Log of the LLM population	ISTAT
South	Indicator variable equal to one for the following Italian regions: Abruzzi, Molise, Campania, Puglia, Basilicata, Calabria, Sicilia, and Sardegna	SHIW
Individual human capital	Number of years of study required to achieve the highest qualification earned by the individual. We derived the length of education by assigning: 2 years to no qualification; 5 years to elementary school; 8 years to middle school; 11 years to professional secondary school diploma; 13 years to high school; 16 years to a diploma or other short course university degree; 18 years to a bachelor’s degree; and 20 years to a postgraduate qualification	SHIW
Experience	Calculated as the difference between worker’s age at the survey date and the age at first job held, which is a datum available from the SHIW	SHIW
Subjective house rating	Series of dummies for the subjective (the survey asks “How do you rate this dwelling?”) rating of the dwelling (luxury; highly desirable; mid-range; modest; low income; very low income; rural; other)	SHIW
Subjective location rating	Series of dummies for the subjective (the survey asks “How would you rate the location where the dwelling is located?”) rating of the dwelling’s location (highly desirable; run-down; neither highly desirable nor run-down)	SHIW
Job qualification	Series of dummies for the employment work status (blue-collar worker or similar; office worker or school teacher; junior manager, clerk; manager, senior official)	SHIW
Industries	Series of dummies for the sector of activity of the firm in which the individual works (agriculture; manufacturing; building and construction; wholesale and retail trade, lodging and catering services; transport and communications; services of credit and insurance institutions; real estate and renting services, other professional, business activities; general government and other private and public services)	SHIW
Firm size	Series of dummies for the size of the firm in which the individual works (up to 4; from 5 to 19; from 20 to 49; from 50 to 99; from 100 to 499; 500 or more; not applicable, public-sector employee)	SHIW
Per capita GDP	Per capita net disposable income in the province in thousand lira	ISTAT
LLM unemployment rate	LLM 1993 unemployment rate	ISTAT
LLM physical capital	Ratio between stock of capital (valued at the replacement price) and value added in each LLM	Cannari–Signorini
LLM infrastructures	Ratio between kilometers of roads and LLM’s surface in km2	Cannari–Signorini
LLM population	Log of the LLM population	ISTAT
LLM plant intensity	Ratio between the number of plants and the LLM’s surface in km2	Cannari–Signorini
LLM share of population under 35	Ratio of inhabitants less than 35 over the entire population of the LLM	ISTAT
Theatre	Theatre shows over the population residing in the province	ISTAT DEMOS
Cinema	Cinema halls over the population residing in the province	ISTAT DEMOS
Crime	First-degree murders, robberies and blackmail divided by the population residing in the province	ISTAT DEMOS
Nurseries	Public nurseries for children aged 0–5 over the corresponding age group for the population residing in the province	ISTAT DEMOS
Doctors	Doctors in public hospitals over the population residing in the province	ISTAT DEMOS
Hospital beds	Beds in public hospitals over the population residing in the province	ISTAT DEMOS
1981 share of population 0–5	Share of the LLM population between the age of 0 and 5 in 1981	ISTAT
1981 share of population 5–10	Share of the LLM population between the age of 5 and 10 in 1981	ISTAT