Barriers to technological adoption in Spain and Portugal

Abstract

Since 1945, both Spain and Portugal have experienced significant market transformations. These countries were both led by dictators for many years until the mid 1970s when each moved toward more democratic governments and more open markets. As a result, each experienced significant changes in output with Spain’s becoming a model for proper market based transformations. Although Portugal’s transformation has been less impressive it experienced improvements too. This paper uses a Parente and Prescott (J Polit Econ 102(2), 298–321, 1994; 2000) type model to investigate the recent transformations in each of these countries and quantify the extent to which barriers to technological adoption may have played for these two development experiences. Our results indicate that from 1945 to 2003 these barriers have fallen considerably but remain high, and are somewhat higher in Portugal than in Spain.

Mathematical appendix

Because of the unusual interpretation that the labor market situation is located at a boundary, it is easiest to think of the social planning problem as a two step problem where in the first step a representative agent makes all the allocation decisions taking prices as given and then in the second step equilibrium rental rates and wage rates are applied. To this end, the Lagrangian for this problem is

$$\begin{array}{rll} \mathcal{L}(\cdot )~ &=&~\sum\limits_{t=0}^{\infty }\beta ^{t}\left\{ \ln (c_{t}-B(1+\gamma )^{t}h_{t}^{\eta })\right. ~ \\ &&\left. +~\lambda _{t}\left[ r_{kt}k_{t}\!+\!r_{zt}z_{t}\!+\!w_{t}h_{t}- c_{t} - k_{t+1}^{\frac{1}{\delta _{k}} }(A_{k})^{\frac{-1}{\delta _{k}}}k_{t}^{\frac{\delta _{k}-1}{\delta _{k}} }-~z_{t+1}^{\frac{1}{\delta _{z}}}(A_{z})^{\frac{-1}{\delta _{z}}}z_{t}^{ \frac{\delta _{z}-1}{\delta _{z}}}\right] \right\} . \end{array}$$

The first order conditions for t = 0,1,... are

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial c_{t}}~~:~~\frac{1}{ c_{t}-B(1+\gamma )^{t}h_{t}^{\eta }}~-~\lambda _{t}~=~0, $$

(10)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial h_{t}}~~:~~\frac{-B(1+\gamma )^{t}\eta h_{t}^{\eta -1}}{c_{t}-B(1+\gamma )^{t}h_{t}^{\eta }}~+~\lambda _{t}w_{t}~=~0, $$

(11)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial k_{t+1}}~~:~~-\lambda _{t}\left( \frac{1}{\delta _{k}}\right) \left( \frac{i_{kt}}{k_{t+1}}\right) ~+~\beta \lambda _{t+1}\left[ r_{kt+1}~-~\left( \frac{\delta _{k}-1}{\delta _{k}}\right) \left( \frac{i_{kt+1}}{k_{t+1}}\right) \right] ~=~0, $$

(12)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial z_{t+1}}~~:~~-\lambda _{t}\left( \frac{1}{\delta _{z}}\right) \left( \frac{i_{zt}}{z_{t+1}}\right) ~+~\beta \lambda _{t+1}\left[ r_{zt+1}~-~\left( \frac{\delta _{z}-1}{\delta _{z}}\right) \left( \frac{i_{zt+1}}{z_{t+1}}\right) \right] ~=~0, $$

(13)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial \lambda _{t}} ~~:~r_{kt}k_{t}+r_{zt}z_{t}+w_{t}h_{t}-c_{t}-i_{kt}-i_{zt}=~0. $$

(14)

Substituting in Eqs. 4, 5 and 6 gives the social planner’s first order conditions for t = 0,1,... of

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial c_{t}}~~:~\frac{1}{ c_{t}-B(1+\gamma )^{t}h_{t}^{\eta }}~-~\lambda _{t}~=~0, $$

(15)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial h_{t}}~~:~~\frac{-B(1+\gamma )^{t}\eta h_{t}^{\eta -1}}{c_{t}-B(1+\gamma )^{t}h_{t}^{\eta }}~+~\lambda _{t}\frac{(1-\theta _{k}-\theta _{z})y_{t}}{h_{t}}~=~0, $$

(16)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial k_{t+1}}~~:~~-\lambda _{t}\left( \frac{1}{\delta _{k}}\right) \left( \frac{i_{kt}}{k_{t+1}}\right) ~+~\beta \lambda _{t+1}\left[ \theta _{k}\frac{y_{t+1}}{k_{t+1}}~-~\left( \frac{\delta _{k}-1}{\delta _{k}}\right) \left( \frac{i_{kt+1}}{k_{t+1}} \right) \right] ~=~0, $$

(17)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial z_{t+1}}~~:~~-\lambda _{t}\left( \frac{1}{\delta _{z}}\right) \left( \frac{i_{zt}}{z_{t+1}}\right) ~+~\beta \lambda _{t+1}\left[ \theta _{z}\frac{y_{t+1}}{z_{t+1}}-~\left( \frac{\delta _{z}-1}{\delta _{z}}\right) \left( \frac{i_{zt+1}}{z_{t+1}} \right) \right] ~=~0, $$

(18)

$$ \frac{\partial \mathcal{L}(\cdot )}{\partial \lambda _{t}} ~~:~y_{t}-c_{t}-i_{kt}-i_{zt}=~0. $$

(19)

To find the decision rules we use the method of undetermined coefficients. We guess the functional forms

$$ i_{kt}~=~a_{k}y_{t}, $$

(20)

$$ i_{zt}~=~a_{z}y_{t}, $$

(21)

$$ \frac{1}{\lambda _{t}}~=~a_{\lambda }y_{t}, $$

(22)

where a _k , a _z and a _λ are constants to be determined. Substituting these into Eq. 17 and solving for a _k gives

$$ a_{k}~=~\frac{\beta \delta _{k}\theta _{k}}{1-\beta (1-\delta _{k})}. $$

Substituting these into Eq. 18 and solving for a _z gives

$$ a_{z}~=~\frac{\beta \delta _{z}\theta _{z}}{1-\beta (1-\delta _{z})}. $$

To find the consumption decision rule substitute Eq. 20 and Eq. 21 into Eq. 19 and solve for c _t to get

$$ c_{t}~=~(1-a_{k}-a_{z})y_{t}. $$

(23)

We can interpret (1 − a _k  − a _z ) as the marginal propensity to consume out of income. Note, this is simply the decision rule from the Solow model. To find the labor decision rule we substitute Eq. 15 into Eq. 16 and using Eq. 1 gives get

$$ B(1+\gamma )^{t}\eta h_{t}^{\eta }~=(1-\theta _{k}-\theta _{z})y_{t}=(1-\theta _{k}-\theta _{z})A(\pi )h_{t}(1+\gamma )^{(1-\theta _{z}-\theta _{k})t}k_{t}^{\theta _{k}}z_{t}{}^{\theta _{z}}. $$

Now solving for h _t gives

$$ h_{t}~=~\left[ \frac{(1-\theta _{k}-\theta _{z})A(\pi )k_{t}^{\theta _{k}}z_{t}{}^{\theta _{z}}}{B\eta (1+\gamma )^{(\theta _{z}+\theta _{k})t}} \right] ^{\frac{1}{\eta -1}}. $$

Finally, we need to verify that our guess was correct by verifying that a _λ is a constant. To do this, substitute Eq. 15 into Eq. 16) to get

$$ B(1+\gamma )^{t}\eta h_{t}^{\eta }~=(1-\theta _{k}-\theta _{z})y_{t}. $$

(24)

Next, substitute Eq. 22 into Eq. 15 to get

$$ c_{t}-B(1+\gamma )^{t}h_{t}^{\eta }~=~a_{\lambda }y_{t}. $$

Now substituting in Eqs. 23 and 24 and solving for a _λ gives

$$ a_{\lambda }=(1-a_{k}-a_{z})-~\frac{1-\theta _{k}-\theta _{z}}{\eta }. $$

which is a constant and thus confirms our guess.