Tradable and nontradable directed technical change

ABSTRACT

We wish to reconcile the major trends in wages and the terms of trade using a directed technical change approach in which: (i) tradable and nontradable goods can be substitutes or complements; and (ii) scale effects can be present or can be partially or totally removed. With a lower skilled labour ratio and a higher relative wage in the tradable sector, the price (real exchange rate or terms of trade) mechanism is crucial in determining sectoral productivity differences and thus wage inequality. Along the balanced growth path, the real exchange rate can be negatively related with the relative productivities in horizontal innovation (the Balassa-Samuelson effect) and with the relative labour level, depending on scale effects. The wage premium increases due to an increase in the relative labour level in the nontradable sector under substitutability with scale effects or under complementarity without scale effects. A calibrated version of the model indicates that the model closely replicates the data for Germany. Moreover, while the Balassa-Samuelson effect is quantified, an increase in the relative supply of labour in the tradable sector decreases both terms of trade and inequality.

KEYWORDS:

• Directed technological change
• substitutability
• scale effects
• relative prices
• wage premium
• economic growth

JEL CLASSIFICATION:

• O30
• O41
• F10
• F43
• J31

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ We regard the independence between the labour employed in the nontradable sector and in the tradable sector as mainly instrumental to the isolation of ‘pure’ directed technical change effects.

² As Zeugner (2013, p. 5, fn: 5) points out ‘The AMECO database conventionally classifies the NACE setors A_E, G_I (agriculture and fishing, mining and utilities, manufacturing, trade, hotels, communications) as tradable, while sectors F, J_P (construction, finance and business services, market services, other service activities) are considered as nontradable.’ Table 1 depicts this classification.

³ We consider the set for tradable and nontradable sector, following the AMECO approach (Zeugner 2013) – see Table 1. The Laborsta database is available online at (accessed for the first time in December 2013) http://laborsta.ilo.org/data_topic_E.html and evaluates workers from level 1 (the most skilled level) to level 9 (the most unskilled level): level 1 ‘legislators, senior officials and managers’, level 2 ‘professionals’, level 3 ‘technicians and associate professionals’, level 4 ‘clerks’, level 5 ‘service workers and shop and market sales workers’, level 6 ‘skilled agricultural and fishery workers’, level 7 ‘craft and related trade workers’, level 8 ‘plant and machine operators and assemblers’, and level 9 ‘elementary occupations’ . We have considered levels 1, 2 and 3 as skilled levels, and levels 4, 5, 6, 7, 8 and 9 as unskilled levels.

⁴ We have also collected data for other countries and the conclusion remains: the nontradable sector is more skilled than the tradable sector.

⁵ Afonso (2019) uses a closed related set-up to study the role of IPRs on prices, wages and growth in a two country directed technical change model, under different trade regimes.

⁶ When $\epsilon =0$ there is no substitution between $Y_T$ and $Y_D$, and the production function is Leontieff. When $\epsilon =1$ the production function is Cobb-Douglas. When $\epsilon =+\mathrm{\infty }$, $Y_T$ and $Y_D$ are perfect substitutes, and the production function is linear. As we shall see later, this parameter plays a central role in our analysis. There is a spirited discussion in the literature on the estimated value, looking at the elasticity of substitution between domestic and foreign goods. Some examples, using the US data, include Blonigen and Wilson (1999) – average value of 0.81 –, Feenstra et al. (2014) – with elasticities ranging from approximately 0.88 to 4 –, Acemoglu and Ventura (2002) – average value of 2.60 –, Gallaway et al. (2003) – average value for macro elasticities of 1.55 –, Broda and Weinstein (2006) and Epifani and Gancia (2009) – have estimated $\epsilon$, respectively, in the intervals 2.7–3.6 and 2.2–2.6. Moreover, for the European Monetary Union, Rabanal and Tuesta (2013) present values that range between 0.13 and 1.

⁷ To simplify notations we suppress the time argument $t$ and will do so throughout as long as this causes no confusion.

⁸ It is a measure of the real exchange rate between intermediate final goods sectors since it evaluates how one unit of the $T$-sector exchanges for a unit of the $D$-sector. Since international trade is always assumed to be balanced and, under international trade, $P_T$ should be common in all countries, whereas $P_D$ generally differs across countries, the ratio $\frac{P_D}{P_T}$ is indeed ‘the real exchange rate’.

⁹ That is, since in reality workers perform very different tasks in $D$-sector and $T$-sector, we will treat these two types of labour as distinct, and assume, also in accordance with reality, that schooling (on-te-job-training) skills are employed relatively more intensively in the $D$-sector ($T$-sector). In a certain sense we can say that this argument is in line with Grossman and Shapiro (1982), Grossman and Helpman (1991, chs. 5 and 6), Mincer (1993), Van Zon and Antonietti (2004), and Hassler and Rodriguez-Mora (2000).

¹⁰ Since the (labour complementary) intermediate goods depreciate fully after use, the optimizations for the $j$-sector, $j=T,D$, are static.

¹¹ The result about wage setting follows from basic microeconomic principles on the assumption that the labour market is competitive.

¹² In accordance with this Berka and Devereux (2010, 2013) should be recalled. These authors show that for European Union countries, differentials in prices are generated exclusively by differences in nontradable goods.

¹³ The international technology linkages are channelled through, for example, communication patterns and have been frequently adopted in the growth literature that looks into cross-country data (e.g. Borensztein, Gregorio, and Lee 1998; Dinopoulos and Thompson 2000; Caselli and Coleman 2006; Vandenbussche et al., 2006; Fadinger and Mayr 2014).

¹⁴ In the standard directed technical change literature (e.g. Acemoglu 1998; 2002, 2008), the scale has no impact on R&D technology; i.e. scale effects are not removed, $\delta =0$, and the chain of effects is dominated by the market-size channel, by which technologies that use the more abundant labour type are favoured; thus, this literature has been interpreting the rise in the skill premium as a result of the market-size effect. In our case, however, the level of scale effects removal lends much more flexibility to the technological-knowledge bias.

¹⁵ In general terms, concerning the production of final goods there is complementarity between inputs – labour and intermediate goods – and substitutability between technologies – $D$ and $T$.

¹⁶ Comparing (34) to (24) results that, in line with the LeChatelier principle, the response of relative wages $\frac{w_D}{w_T}$ to changes in relative supply $\frac{L_D}{L_T}$ is now more elastic since the respective demand curves become more elastic after the adjustment of the ‘other factors’, which here correspond to the number of intermediate goods $N_D$ and $N_T$; thus, bearing in mind the exponents of $\frac{L_D}{L_T}$ it results that $\alpha \left(\epsilon -1\right)\left(1-\delta \right)-1>-\frac{1}{\alpha \left(\epsilon -1\right)-1}$ in all four cases (i), (ii), (iii), and (iv).

¹⁷ Data available (accessed in February 2016) at: www.ilo.org.

¹⁸ Data available at (accessed February 2016) http://ec.europa.eu/eurostat/statistics-explained/index.php/R_$\mathrm{\%}$ 26_D_expenditure, Table 3.

¹⁹ We wish to note that variations in $\frac{L_D}{L_T}$ may represent mobility of labour between the two sectors in the economy.

²⁰ Recall that due to Equation (36)(36) $\frac{{\sigma }_D}{{\sigma }_T}=\frac{\frac{{\dot{N}}_D}{{\dot{N}}_T}}{\frac{Z_D}{Z_T}{\left(\frac{L_D}{L_T}\right)}^{-\delta }}.$(36) , the ratio of productivities change with the labour supply ratio. This is incorporated in this exercise.

²¹ In the steady state, the lifetime utility function is evaluated at $\frac{\frac{C_0^{1-\theta }-1}{1-\theta }+\frac{g}{\rho }}{\rho -(1-\theta )g}$ and this expression can be used to calculate welfare effects. We normalized $C_0=1.$ The implied welfare effects are non-negligible when compared to those calculated, e.g. by Sequeira (2008) or Gómez and Sequeira (2013a) to evaluate the effect of fiscal policies.

Additional information

Funding

This research has been financed by the European Regional Development Fund through COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) and by Portuguese public funds through FCT (Fundação para a Ciência e a Tecnologia) in the framework of the project has financial support from FCT and FEDER/COMPETE.