DRD DISCUSSION PAPER Report No o DRD 232 LABOR t1ARKETS AND THE CHOICE OF TECHNOLOGY IN AN OPEN DEVELOPING ECONOMY by Joshua Aizenman January 1987 Development Research Department Economics and Research Staff World Bank The t\forld Bank does not accept responsibility for the views expressed herein whieh are those of the autt1or(s) and should not be attributed to the World Bank or to its affiliated organizationso The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Banko The designations employed, tile pr~.~st.::ntation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any \)pinion ~-vhatsoevt~r on the part of the World Bank or its affiliates concerning the leg~l status of any country, territory, city, area~ or of its authorities, t)r .~oneerning the delimitations of its boundaries, or national affiliation. LABOR MARY~TS AND THE CHOICE OF TECHNOLOGY IN AN OPEN DEVELOPING ECONOMY by Joshua Aizenman Table of contents Page 1. Introduction and summary • 2 2. The Model •• 7 2.1 The Production Side • 7 2.2 Preferences • • • • • 9 The Choice of Technology - The Flexible Wage Case. 10 3.1 Welfare Comparison- Labor • • • • • • • 10 3.2 Welfare Comparison - Entrepreneurs. • • • ••• 13 3.3 The Choice of Technology and Potential Conflicts. 14 4. The Choice of Technology - The Minimum Wage Case 17 5. Concluding Remarks • 21 Footnotes • • 22 References 24 - 1 - Labor Markets and tne cnotce of Technology in an Open Qevetopjng Economu ABSTRACT This paper ntghllgnts economic factors determining the cnolce of technology and openness In an intertemporal context ln the presence of institutional constraints In the JaDor market. It considers the case In which a ·more aggressive· development strategy Involves an Investment in a mooern technol~y. Trtis teChnology raises the degree to which real wages and productivity depend on external factors while at tne same time it atso raises the expected value of rea~ Income. In the absence of such investment. production takes place In a traditional sector, using a t~-nnotogy that limits exposure to external shocks. The analysis evaluates the dependence of the choice of technology on the volatility of the shocks affecting the economy, the expected pry (2) w = exp(S). - 8 - If investment I Is undertaken In per ioo one, the economy will produce In period two using the foJ tow lng process: where M stands for an imported input. A is the efficiency coeff lclent, and x" stands for tne output ODtalnea us lng the new technology. we assume that Installing the second technology Involves an Irreversible change In the capital stock, Implying that following the Investment the economy cannot apply the old production process. To capture the not ion that openness can expose the economy to external shOCks we assume that the external prIce of the Imported Input (P m) is subject to shOCks, denoted by e. our choice to mOdel external dependence In the form of Imported Input Is arbitrary In the sense that all the results can be derived for the case where external shocks manifest themselves in shocks to the terms of trade and the choice of tecnnotogy Is also a choice Detween sectors with a different exposure to external shocks. The choice of the technology embodied In (1) and (3) Is motivated by the presumption that the new technology involves higher capital Intensity. For simplicity of exposition we take the extreme case where the traditional technology does not use capital. Consider the case where the price of M Is given by The use of labor and the Imported Input Is at a tevel that minimizes the production costs, yielding the following first order conditions: ... 9 - (S) $Xn = m exp (e) (6) ocX0 = LW Applying (3) and (5)-(6) we obtain that (B) w = exp(p - £')L (oc+ $-!)/( l- $) The introduction of the new tectmotogy lmplhes that the productivity of tabor Is determined by a measure related to the efficiency of the new technology and the price of the imported Input (p and £' In (8)). The value of £' corresponds to the drop In labor prOductivity due to the supply shock Induced by the rise In the cost of the imported input. The value of p corresponds to the gain In productivity due to the adopt ion of the new technology. 2.2. Er:eferences 13 The economy is composed of risk averse workers and risk neutral entrepreneurs. The second-period utility of a representative worker Is given by: (9) H = -k exp(-eu) where U = (2-L)C where c stands for the consumption and we normalize leisure endowment to 2. The attitude towards risk Is measured by e -- a higher e Implies a l'llgher aversion to risk. - 10- The problem facing the entrepreneur In per lod one Is to determine If the switCh to the new tecnnotoou Is desirable. sucn a swltcn necessitates an Investment 1 In periOd one, and we assume the entrepreneur faces an opportuotty cost of capital given by r. In the next sect tons we evaluate the condlt Ions under whlcn the entrepreneur wiII undertake the Investment, and the conditIons under which the adopt ion of th~ new technology wiII ra lse the expected ut lllty of the workers. 3. The Choice of Iechnotogu - the Flexible wage case We start by considering a benchmark case where the tabor market ts assumed to be flexible. Note that the employment level using both tecnnologles Is L=l. The consumption level of a worker using the old technoiQ9Y Is c = exp(S). Thus, the worker/s expected utility using the old technology Is (denoting byE the expectation operator) (10) E(H) = -kE[exp(-ec)] ; wnere c = exp(S). Applying (8) we ootain that the wage level with the new technology Is exp(p- e'), and the corresponding expected utility using the new technology is Hn: 0 ( 11) E( H ) = -kE[ exp( -ec 0)] ; wnere c0 = exp(p - e') 3.1 Welfare comparison- Lat>oc We turn now to an evatuat ion of the welfare impllcat Ions of the new tecnnology. This Is done by calculating the expected utility of a representative worker, Obtained oy applying a second-order Taylor approximation of H0 around e· = e and of H - 11 - aroond 8 = e. This procedure results In approximations whose accuracy is determined oy the var lances of e' and of 8. Henceforth we assume these var lances to be small enough to merit the appllcabi11ty of the resultant approximations. USing (11) we get that where w Is the real wage ( a) obtained for E.' 0 =0 (w0 = exp(p)). Applying the expectation operator to (12) we conclude that Direct calculation reveals that Applying a second-order Taylor approximation of H around s = 0 we obtain (following steps simi \ar to ( 12)-( 1'1)) ( ts) E(H) ~ - k exp{-e } [ 1 + .5V(s)e(e - 1) 1. Ttte new technology will be adopted if E(H0) > E(H). To gain further insight Into the factors that determine the choice of technology we assume that the variances of e and 8 are small ~ and that the value of w0 Is close to one. Subject to these assumptions, we can conclude that w!th flexible labor markets the adoption of the new technology Is advantageous If - 12- ( 16) p > .s(e - l)[V(e') - v(s)l· Equation 16 has a simple lnterpretatlc:, In terms of ·mean-variance· analysis. The left-hand term is a measure of tne expected rise In income due to the adoption of the new teChnology. The right hand-sloe Is a suDjective measure of the rise In volatility that Is assoclate 1) a rise in the volatility of foreign shocks must be accompanied by a corresponding rise In the prOductivity gain of the new technology In order to keep labor Indifferent between the two technologies. Notice that for tow degrees of risk aversion A A Is 1 2 downward-sloping. This corresponds to the case where volatility is a ·virtue· [In terms of (lq),(l5) a rise In the volatility of productivity shOCks raises expected welfare for a <1). This result stems from the convexity of profits and the 1), as Is assumed In Figure One. The area above A 1A2 defines the region where t~uor expects to benefit from the new technology. A rise In domestic volatility (V ) shifts 8 - 12a - p 0 VE. v, s. jso 8 c3 c1 ~S I 2 I FIGURE 1 - 13- A 1A2 downwards, Increasing that area. This corresponds to the fact that higher domestic volatility makes investmefit in openness more attractive. A rise in the degree of risk aversion rotates A1A 2 counter clOCkwise around point K, thereby reducing the advantage of the new technology If forel~n exceeds domestic volatility. 3.2 Welfare comparIson - Entrepreneurs The decision to undertake Investment In the new technology Is determined oy risk-neutral entrepreneurs. The residual income corresponds to the capital share In costs. Applying (11) we find that the entrepreneur's Income Is (I 7) [( 1-o:- $)/ od exp(p-e'). The entrepreneur w111 invest In the new technology If the expected income exceeds the cost of capital. or If (18) E{ ((1-oc-$)/od exp(p-e')} > (l+r)l where r is the opportunity cost of capital. Applying a second-order Taylor ap"'~ oximation to (18) around s· = a we obtain that the condition for undertaking the investment can t>e approx i mateo by (18') In((l+r)l] < p+ tn [(1-oc-$)/o<) + .5 V(e'). Line c1c2 (Figure one) plots combinations of (V(e} p) where the entrepreneur Is - 14- Indifferent regarding the new tecnnot()(Jy. The area above c 1c 2 def lnes ti"~e region where tne entrepreneur expects to Denef It from ttte new tecnnot~y. It Is noteworthy tnat c1c2 is downward sloping. This reflects the convexity of profits with respect to the product lvlty snocts, which In turn Implies that higher volat lllty raises expected Income. 3.3 The Choice of Technolog•J and Potent Iat Conf] lets we now combine ttte Information sum mar Ized In curves A 1A2 and c1c2 to assess the dependency of the choice of technology on preferences, volatility, and costs. we wIll Ident lfy cl rcumstances where there Is a conf llct of Interest between the Inputs, and we will address the role of policies In these circumstances. Notice tttat whenever the expected pro exceeds the productivity gain (p). Henceforth we will assume that p -k exp(-e) The right hand side of (20) is the utility in the traditional sector, whet~ u = 1. The left t'land siae ls the expected utility with the new technology, oelng an average of the bad states wliere unemployment occurs ( u = u0) and the good states where - 18a - p s· • FIGURE 2 - 19- u = exp{p+h}). Equation (20) allows us an assessment of tne potential role of volatility. Assuming tttat tne conditions for a binding minimum wage In bad states hold (i.e. p < h), it can be shown that if e(I- u0) > In 2 then the new technology Is undesirable for any v(e'}· This Is be<:ause a high enough degree of risk aversion (e) and low enough non-market productivity ( u0) Imply that with the new technology the drop in ut IItty In bad states is too large to be compensated for In gOOd states. If, however, e(l- u0) < In 2, then for large enough p+ h labOr will benefit from the new tectmology. Higher volatility enhances the relative attractiveness of the new teChnology because a rise In h has the effect of raising utility In gOOd states, without a corresponding drop In bad states. The same result can be derived for a case of a continuous distribution of e·. This result s!ems from the fact that the minimum wage truncates the distribution of the effective prOductivity of labor In bad states. In generaL for truncated distributions a mean preserving spread of tne underlying variable (£' in our case) puts greater weight on the tails, resulting In a hlgner expected vatue of the effective productivity. curve G G In Figure Two plots 1 2 configurations of (V(e'); p ) that leave taf)or indifferent between the two 10 technologies. The area above G1G2 defines the region where labor expects to benefit from the new technology. The curve is downward sloping because a rise In volatilHy raises expected utility with tne new technology, allowing a drop In the ·reservation" value of prO(Juctlvlty gain. p. It can be shown that a drop in the degree of risk aversion shifts G1G2 downwards. The entrepreneur will benefit from the new technology if the expected Income exceeds the cost of capita I, or if - 20- (21) .5((1- e<- S)/e<)J e)(p{p+ h} > l(l+r). As In the f le)( lb le labor market case, volat Ill ty enhances the reI at lve attract lveness of the new technology from the entrepreneur's point of view. curve F F In Figure 12 ·Two plots configurations of combinations of (V(E'); p ) that leave the entrepreneur indifferent with respect to the new technology. The area above F F def lnes the 1 2 region where entrepreneurs expect to benefit from the new technology. A comparison between the flex,ole wage case (curves A A and 1 2 c1c2) and the minimum wage case (curves G1G2 and F1F2) reveals that while higher volatility of foreign shocks enhances the possibility of conflicts between Inputs with flexible wages, it works In the opposite direction with mtnlmum wages. Note that because the presence of minimum wages diminishes the chance of adopting the new technoi¢9Y, there Is a greater potential role for labor market institutions of the type elaborated in section 3.3. For example, a point likes· (Figure 2) corresponds to an economy that adopts the new technology In a flexible wage equltiDrlum, but adopts ttle traditional technology In the presence of the minimum wage. Notice that a contract that will fix wages and employment at w=l and L=l wfll preempt the effect of the minimum wage, enac11ng the attainment of an efficient equilibrium. If such contracts are not credible, a minimum wage policy will generate a greater demand for protection. The role of protect lve measures is to overcome the potential adverse consequences of the minimum wage oo the employment level associated with the new technology In bad states. While sUCh policies can achieve their goaL they are dominated by alternative policies that deal directly with marln see Azariadis 0975) ana Bai Jy (1974). 5. Tt1e key assumption is that inputs differ in their attitude towards risk and their excess to the capital market. For exposition purposes we consider a special case where entrepreneurs are risk neutr aI. The d 1scuss ion can oe E~xtended for the case where beth laDor an