Long-run economic performance and the labor market.

Tran, Kien C.

1. Introduction

This article studies growth when the economy is not using all its productive resources to establish a bridge among two subdisciplines in economics: growth theory and unemployment theory. The former is dynamic and considers the impact on output of the growth in inputs under the assumption that unemployment is nonexistent. The latter is static and considers the determination of the rate of unemployment under the assumption that the growth of capital is nonexistent. Our goal herein is twofold. On one hand, we want to modify slightly the growth models to include the effects of persistent unemployment on long-run growth. On the other, we want to analyze the role played by the accumulation of capital in determining the unemployment rate.

The underlying assumption in the neoclassical growth model is that, even if we admit sticky wages in the short run, in the long run, the labor market should have time to clear and the economy should return to full employment, understood as the level of employment compatible with frictional unemployment. Therefore, what is relevant when talking about growth is the growth of the labor force, not the growth of the employed labor force. However, if the equilibrium employment level in the labor market persistently differs from the more desirable frictional level, it is conceivable that this persistent deviation will have an impact on long-run growth. The average U.S. unemployment rate during the 1990s was 5.8% while countries such as France and Spain maintained double-digit unemployment rates in the 1980s and 1990s. It seems intuitive that double-digit unemployment during two decades should have long-lasting effects on standards of living. The disparate experiences of some European countries as opposed to the United States in terms of employment rates are due to very different institutional factors in the corresponding labor markets. This article studies the impact of labor market institutional variables on long-ran growth.

Despite a very large literature on both growth and unemployment, few papers have jointly studied these two phenomena. The exceptions are Furuya (1998) and Daveri and Tabellini (2000). Daveri and Tabellini study the implications of an increase in labor taxes on both unemployment and economic growth. The models in these two papers are of the overlapping generation class, but whereas in Furuya's, the labor market does not clear because of the existence of efficiency wages, in Daveri and Tabellini's, the labor market does not clear because of the existence of a union. Our model is a simple variation of the standard Solow model suitable for a first approximation to an empirical investigation of the interrelationship between economic growth and the labor market.

We use a variation of Blanchflower and Oswald's (1995) wage curve, which is more suitable for integration with a growth model. The wage curve shows an empirical inverse relation between unemployment and wage levels. This inverse relation is consistent with models of noncompetitive wage determination. Basically, we use a reduced form of the open-trade-union Layard-Nickell (Layard and Nickell 1985, 1986) model of wage determination to explain why the equilibrium unemployment level differs from the frictional level. A weakness of relying on trade union behavior to explain unemployment is that, in most countries, not all workers are unionized. Union membership varies greatly across countries, but in most countries, a large part of the labor force is nonunionized. However, Blanchard and Summers (1986) argue that the trade union model can be interpreted as describing the behavior of a group of workers that acts as a group even if there is no formal trade union. The fact that both capital intensity and productivity affect the equilibrium unemployment rate is implicit in the Layard-Nickell model. We emphasize the importance of capital intensity in the determination of unemployment and incorporate unemployment into a growth model.

We distinguish between potential growth and feasible growth and describe the potential growth path for a given savings rate as the one that could be followed if all resources were utilized. The feasible growth path for a given savings rate, on the other hand, is that that can be followed given the institutional conditions regarding the labor market. These conditions imply that some labor may not be employed. The first path is a potential one because a different labor market would make this path possible. The feasible growth path, thus, implies some underachievement. We show that both income and capital per worker are lower in the feasible steady state than in the potential steady state. Both income and capital per worker depend positively on labor market flexibility.

The conclusions regarding the effects of the labor market on steady-state variables are no different from the ones of a simpler Solow model in which the production function in period t is [Y.sub.t] = [K.sup.[alpha].sub.t][(1 - [u.sup.*])[[A.sub.t][L.sub.t]].sup.(1-[alpha])], where, as usual, K denotes capital, Y denotes output, L denotes the labor force, A is an indicator of labor efficiency, and [u.sup.*] refers to the natural rate of unemployment. What is different is that our model studies the interrelations between economic growth and the labor market, that is, the effect of variables affecting the steady state, such as capital accumulation, on unemployment. This model also predicts that a decrease in the savings rate, an increase in the rate of growth of the labor force, or an increase in the rate of technical progress increase the rate of unemployment in the steady state. Finally, there is a third and novel prediction of the model: Lack of labor market flexibility slows convergence of the economy toward its steady state. Lack of flexibility implies that the economy produces below its potential every period.

From the empirical point of view, using OECD data, Furuya shows that a decrease in the savings rate, an increase in the rate of growth of the labor force, or an increase in the rate of technical progress increase the rate of unemployment in the steady state. Using a combination of OECD and World Bank data, the Penn Worm Tables, and data on labor market institutional variables from Blanchard and Wolfers (2001), we show not only that a lower saving rate, a higher growth rate of the labor force, or a higher rate of technical progress results in higher unemployment but also that labor market institutional variables have the predicted effects on steady-state output per worker and that labor market flexibility affects convergence toward the steady state. Although we consider these results somewhat preliminary, partially due to the quality of our data, we regard them as very encouraging. Our results can be viewed as stylized facts that grant further work, mostly at the theoretical level, toward the construction of another model that, preserving the conclusions of this simpler model, has better microeconomic foundations. We believe that more work is needed on the interrelation between economic growth and unemployment.

Section 2 specifies the model. Section 3 tests the implications of the model concerning how technical progress and investment affect long-run employment. Section 4, on the other hand, tests the implications of the model pertaining to the long-run impact of labor market variables. Section 5 tests the implications regarding convergence toward the steady state. Section 6 concludes.

2. The Model

Herein, we abstract from household behavior concerning savings to concentrate on the production side of the growth model. Both the overlapping generations or the infinite-horizon, intertemporally-optimizing, representative-agent frameworks have problems, and their results are similar to those in the simpler Solow model. As Solow (1994, p. 49) phrases it, "... the use made of the intertemporally-optimizing representative agent.... adds little or nothing to the story anyway, while encumbering it with unnecessary implausibilities and complexities." Furthermore, for empirical purposes, it is useful to maintain the assumption of exogenous (and different across-countries) saving rates.

Blanchflower and Oswald (1995) deem the empirical inverse relation between unemployment and the level of wages the wage curve. Our starting point is a variation of Blanchflower and Oswald's (1995) wage curve more suitable for integration with a growth model. By using a wage curve, we are following a tradition in the growth literature of using aggregate functions that replicate stylized facts, such as the Cobb-Douglas production function or the use of the Mincer wage regression to introduce years of schooling into the aggregate production function (e.g., Hall and Jones 1999). We deviate from Blanchflower and Oswald in that they claim the unemployment elasticity of earning to be basically the same all over, while we assume this elasticity to be a function of labor market institutional variables. As Card (1995) points out, this is probably their most contentious claim.

We assume that contracts are negotiated between employers and employees. Workers' bargaining power depends inversely on the unemployment ratio. Rather than modeling the bargaining process, we just assume that, consistent with a wage curve, the real wage [omega] resulting from this negotiation can be expressed as the following function of the rate of employment, [epsilon],

(1) [omega] = [bar.[omega]][[epsilon].sup.[beta]],

where [beta] denotes the elasticity of agreed wages to employment and [bar.[omega]] denotes the real wage demanded at full employment. (1) Workers supply labor infinitely elastically at this wage.

Firms maximize profits and employ workers as long as the marginal product exceeds the real wage. Because workers supply labor elastically at the agreed wage, firms' demand sets the employment level. We assume a Cobb-Douglas production function. Let L denote active population, which we assume insensitive to wages, and N denote employed workers, that is, [epsilon] = N/L. The production function of the representative firm is as follows:

Y = [K.sup.[alpha]] [(L[epsilon]).sup.1-[alpha]].

Equilibrium in the labor market requires the marginal product of the employed labor to equal the real wage sought by workers at this employment rate, that is,

(2) (1 - [alpha])[K.sup.[alpha]][(L[epsilon]).sup.-[alpha]] = [bar.[omega][[epsilon].sup.[beta]].

At the rate of employment implied by this equation, the real wage sought by workers is the real wage that employers are willing to pay.

Note that, for the equilibrium level of employment rate to be less than 1, [bar.[omega]] should be greater than (1 - [alpha])[(K/L).sup.[alpha]], the wage firms would be willing to pay at full employment. Changes in the parameter [bar.[omega]] change the level of the curve. The degree of flexibility of the labor market in this model depends on two factors. The first factor is the degree in which workers' aspirations react to the rate of unemployment or elasticity of agreed wages to employment rate, [beta]. The second is the level of these aspirations, modeled by the real wage demanded at full employment, [bar.[omega]].

By solving for [epsilon] in Equation 2, we obtain the equilibrium level of employment rate

(3) [epsilon] = min (1, [[1 - [alpha]/[bar.[omega]] [(K/L).sup.[alpha]]].sup.1/[alpha]+[beta]],

or

[epsilon] = min (1, [1 - [[alpha]/[bar.[omega]] [k.sup.[alpha]]].sup.1/[alpha]+[beta]]),

where k, throughout the article, denotes capital per active worker (as opposed to capital per employed worker). This expression indicates that the equilibrium rate of employment depends on the level of capital per active worker as well as on the degree of flexibility of the labor market. With the same labor market, an increase in the marginal product of labor shifts its demand. Thus, the quantity demanded increases as well as the real wage: It is easier to meet workers' demand for higher wages.

By substituting [epsilon], the equilibrium level of employment, in the production function, we obtain

(4) Y = [K.sup.[alpha][L.sup.1-[alpha]] [1 - [alpha]/[bar.[omega]] [(K/L).sup.[alpha]]].sup.1-[alpha]/[alpha]+ [beta]] = C[K.sup.[alpha](1+[beta])/[alpha]+[beta] [L.sup.(1-[alpha])[beta]/[alpha]+[beta]],

where C = [((1 - [alpha]/[bar.[omega]).sup.1-[alpha]/[alpha]+[beta]]. Equation 4 states the feasible production function that determines the amount of production attainable with the available amounts of capital and labor given the institutional characteristics of the labor market.

The feasible production function looks similar to the usual production function. As the latter, it exhibits constant returns to scale in capital and active population. However, note that the efficiency parameter in this function C depends on the conditions of the labor market; specifically, positively on [beta] and negatively on [bar.[omega]]. The interpretation is straightforward. If either [bar.[omega]] increases or [beta] decreases, employment decreases, and thus product, at the same level of capital and active population, decreases. Thus, we can specify the feasible production function as the relationship between product and active worker at the equilibrium rate of employment. The feasible production function, then, incorporates two aspects: first, the technical ones usually covered by the production function, and second, institutional considerations. These institutional aspects have an impact on the production function to the degree that labor remains persistently unemployed.

We can write the feasible production function in its intensive form,

y = min([k.sup.[alpha]], [Ck.sup.[alpha](1+[beta]/[alpha]-[beta]]),

where y is feasible product per active worker. The feasible product per worker lies below the potential product per worker, [k.sup.[alpha]], as a consequence of the degree of unused labor.

An increase in active population increases production only if the increase in population results in an increase in the number of employed workers. With a completely flexible labor market, [beta] = [infinity], real wages decrease until all active population is employed. An increase in active population is translated one by one into an increase in employed workers. With a semirigid labor market, the first effect of an increase in active population is a decrease in the employment rate, which reduces the wage sought by workers. Lower wages imply an increase in the number of employed workers and, thus, an increase in production. However, an increase in active population is not translated one by one into an increase in employed workers.

On the other hand, with a completely rigid labor market ([beta] = 0), an increase in active population does not affect the wage sought by workers and, therefore, does not affect the absolute level of employment. In this case, the feasible production function turns into Y = CK: Feasible production can increase only if capital increases.

As usual, the change in the capital stock per worker is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

where s denotes the saving rate. (2) In the feasible steady state,

(5) [k.sup.*] = [(sC/n+[delta]).sup.[alpha]+[beta]/[beta](1-[alpha])],

where [k.sup.*] denotes capital per active worker in this steady state. Capital per worker is lower in the feasible steady state than in the potential steady state because the feasible production function lies below the potential production function. Therefore, the economy approaches a lower steady state.

If [beta] = [infinity], so that the labor market is completely flexible, the model returns to the usual Solow model, potential and feasible growth are equal, and the economy realizes its potential. If, on the other hand, [beta] = 0, there is absolute wage rigidity and the model resembles the Harrod-Domar model, today often referred to as the AK model. Depending on the level of aspirations, [bar.[omega]], there is only one savings rate that guarantees a steady state.

Because the employment rate is different for each level of capital per worker, there is an e that corresponds to the steady-state capital per worker, that is, there is a steady-state equilibrium employment rate, [[epsilon].sup.*]. By substituting Equation 5 into Equation 3,

[[epsilon].sup.*] = min [(1, ((1 - [alpha])/[bar.[omega]]).sup.1/[alpha]+[beta]] [(sC/n+[delta]).sup.[alpha]/[beta](1- [alpha])]).

The steady-state unemployment rate, [u.sup.*], can be calculated by substituting the value of C into the expression

[u.sup.*] = 1 - [[epsilon].sup.*] = max (0, 1 - [(1 - [alpha]/[bar.[omega]]).sup.1/[beta]] (s/n+ [delta]).sup.[alpha]/[beta](1-[alpha]).

The steady-state unemployment rate depends positively on the rate of population growth, n; negatively on the savings rate, s; and positively on the level of workers' expectations, [bar.[omega]]. In the usual neoclassical model, with a flexible labor market, an increase in active population growth implies a lower wage in the new steady state but, of course, has no influence on unemployment rates in the long run. With a less flexible labor market that does not absorb all the active population, an increase in active population growth not only affects wages in the long ran, but it also affects the rate of employment in the steady state. In a similar way, a decrease in the saving rate implies less capital per worker in the long run. With a flexible market, the savings rate does not affect employment rates in the long run. Only wages adjust. With less flexible wages, the unemployment rate will increase.

Compare income per worker in the feasible steady state to income per worker in the potential steady state. Clearly, the former is smaller for two masons. First, unemployment exists in the feasible steady state, but all resources are employed in the potential steady state. Second, the level of capital per active worker is lower in the feasible steady state, as explained above. Unemployment means that the economy is investing less than it would otherwise and, therefore, income per capita is lower in the long run.

In what follows, we assume that the labor market institutional constraints are binding when talking about feasible growth.

Technical Progress

Let the production function for period t be

(6) [Y.sub.t] = [K.sup.[alpha].sub.t][([L.sub.t][[epsilon].sub.t][A.sub.t]).sup.1-[alpha]]

in which [Y.sub.t], [K.sub.t], [L.sub.t], and at refer to product, capital, active population, and employment (respectively) in period t, and [A.sub.t] is an indicator of labor efficiency that we assume increases at an annual rate g. Let us call [y'.sub.t] = [Y.sub.y]/([L.sub.t][A.sub.t]) output per efficiency worker and rewrite Equation 6 in intensive form,

[y'.sub.t] = [k'.sup.[alpha].sub.t][[epsilon].sup.1-[alpha].sub.t],

where [k'.sub.t] = [K.sub.t]/([L.sub.t][A.sub.t]) denotes capital per efficiency worker.

In period t, the real wage [[omega].sub.t] sought by workers can be expressed as the following function of the level of employment

[[omega].sub.t] = [[bar.[omega].sub.t][[epsilon].sup.[beta].sub.t].

Because [A.sub.t] grows at a rate g to allow for the existence of a steady state, we assume that [[bar.[omega]].sub.t], the wage that workers would demand at full employment, grows at the same rate. Blanchard and Katz (1997) provide some explanations about why workers' aspirations increase with productivity. Insofar as aspirations are linked to reservation wages, and these are linked to household productivity, we just need to assume that productivity grows at the same rate in both sectors. Reservation wages are also linked to unemployment insurance and other income support programs, which are in their turn linked to wages.

The labor market equilibrium condition for period t is

(1 - [alpha])[K.sup.[alpha].sub.t][(L[[epsilon].sub.t]).sup.-[alpha]] A[(t).sup.1-[alpha]] = [[bar.[omega]].sub.t][[epsilon].sup.[beta].sub.t].

By dividing both sides by [A.sub.t] and by calling [[bar.[omega]].sup.'.sub.t] = [[bar.[omega]].sub.t]/[A.sub.t], we obtain

(1 - [alpha])[k'.sub.t.sup.[alpha]].sub.t][[epsilon].sup.-[alpha].sub.t] [[bar.[omega]]'.sub.t][[epsilon].sup.[beta].sub.t],

the labor market equilibrium condition in terms of efficiency worker. [[bar.[omega]]'.sub.t] denotes the wage per efficiency worker sought by workers at full employment. For the rest of the section, we will eliminate the subindex t.

By solving for [epsilon] in the labor market equilibrium condition,

(7) [epsilon] = [[1 - [alpha]/[[bar.[omega]']] [k'.sup.[alpha]] 1/[alpha]+[beta]]

and substituting the value of [epsilon] in the production function, we obtain the feasible product per efficiency worker,

(8) y' = [k'.sup.[alpha]] [[1 - [alpha]/[bar.[omega]'] [k'.sup.[alpha]].sup.1-[alpha]/[alpha] + [beta]] = [Bk'.sup.(1+[beta])[alpha]/[alpha]+[beta]],

where B = ((1 - [alpha])/[[bar.[omega]]').sup.1-[alpha]/[alpha]+[beta]].

To determine the unemployment rate in the steady state, first, we determine the level of capital per efficiency worker in the feasible steady state [k'.sup.*], where

(9) [k'.sup.*] = [(sB/n + g + [delta]).sup.[alpha]+[beta]/[beta](1-[alpha])].

By calling the unemployment rate in the steady state [u.sup.*] and substituting the value of [k'.sup.*],

[u.sup.*] = 1 - [[epsilon].sup.*] = 1 - [(1 - [alpha]/[bar.[omega]']).sup.1/[alpha]+[beta]] [(sB/n + g + [delta]).sup.[alpha]/[beta](1-[alpha])]

or, substituting B by its value,

[u.sup.*] = 1 - [(1 - [alpha]/[bar.[omega]']).sup.1/[beta]] [(s/n + g + [delta]]).sup.[alpha]/[beta](1-[alpha])].

It is now evident that the value of the steady-state unemployment rate depends negatively on the marginal propensity to save, s; positively on the population growth rate, n; positively on the productivity growth rate, g; and positively on the level of workers' salary expectations, [bar.[omega]].

We have assumed that [[bar.[omega]].sub.t] changes at the productivity growth rate, g. What happens if workers' claims are not synchronized with their productivity? Obviously, if workers claim salary increases consistently higher (or lower) than productivity increases, we do not have a steady state. But suppose that the deviation happens just once, so the economy will move to a different steady state. As we have said, an increase in [bar.[omega]'] means a decrease in the efficiency parameter B. Thus, both the product curve and the savings per efficiency worker curve shift down, so in the new steady state, the level of capital per efficient worker will be lower. On the other hand, with a greater [bar.[omega]], the equilibrium employment rate curve shifts down as well. The combined effect of a lower level of capital at the new steady state and a lower employment rate at each level of capital is a greater unemployment rate at the new steady state.

The lack of flexibility in the labor market implies not only a greater unemployment rate and a lower product in the short run but also a greater unemployment rate and a lower product in the long run.

Rate of Convergence

According to the standard neoclassical model, income converges to its steady state as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

or the rate of convergence is (1 - [alpha])(n + g + [delta]). According to our model, income converges to its steady state as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

Because ([beta](1 - [alpha]))/([alpha] + [beta]) [less than or equal to] 1 - [alpha], the predicted rate of convergence, [beta](1 - [alpha])(n + g + [delta])/([alpha] + [beta]), is smaller than the one predicted by the standard growth model. Lack of labor market flexibility implies that the economy produces below its potential every period. This underachievement slows down the rate at which the economy approaches its steady state.

3. Impact of Growth Variables on Persistent Unemployment

Our model, like Furuya's (1998), predicts a higher rate of long-run or persistent unemployment due to a lower savings rate, a higher growth rate of the labor force, or faster technological progress. As he does, we test these predictions of the model using OECD data, more specifically from the Economic Outlook. (3) Data on unemployment rates are taken directly from the database. The growth rate of the labor force is calculated using Total Labor Force. Saving rate is, in fact, the investment rate: Total Investment (excluding Stockbuilding) as percentage of Gross Domestic Product (GDP). To measure the rate of technological progress, we have calculated the growth rate of the Productivity Index in the data; that is, we assume that countries are indeed at their steady states, and thus, output per worker and capital per worker grow at the same rate. Furuya performs both a cross-sectional analysis and a time-series analysis; (4) we use a pooled-ordinary least-squares (OLS) regression with five-year averages. (5) We use data for the period 1960-1999 (i.e., 8 five-year periods) and 29 countries (all OECD countries except for the Slovak Republic). The pooled-OLS regression confirms Furuya's results: Lower savings rate, higher growth of the labor force, or faster technological progress result in a higher rate of unemployment in the long run (Table 1).

Savings rate, labor force growth, and technical progress have a long-run effect on unemployment because of the positive relation between the equilibrium rate of employment and the level of capital per efficient worker predicted by the model. To corroborate this channel, we test Equation 7 by using the same OECD data on unemployment. The detrended capital per worker series was constructed using the Capital Stock, Business (1995 PPP dollars) series plus the Productivity Index and Total Labor Force series abovementioned. A pooled-OLS regression shows that an increase in capital per efficient worker of 1000 1995 PPP dollars decreases employment by 0.13% (t = 2.79, 1% significance). In its log form, the coefficient equals 0.0163, equal to [alpha]/([alpha] + [beta]), according to the model.

4. Long-Run Effects of Labor Market Variables

Our model also implies that labor market institutions that affect unemployment will affect both the steady state and convergence toward the steady state. We capture labor market institutions by two parameters, [bar.[omega]] and [beta]. We have explained above the effects of a change in [bar.[omega]] on income and employment in the long run. A decrease in [bar.[omega]] means an increase in efficiency of production. The savings per worker curve shifts upward, with the final effect being that the level of capital and therefore of income per worker is greater in the new steady state. A lower [bar.[omega]] shifts upward the nonaccelerating rate of employment curve as well. The combined effect of a greater level of capital at the new steady state and a higher employment rate at each level of capital is a lower unemployment rate at the new steady state.

The other parameter that encompasses labor market semirigidity in our model is [beta], elasticity of sought wage with respect to the employment rate. A more flexible labor market increases the coefficient [beta]. The effects of a change in [beta] on income and employment in the long run are similar to those of a change in [bar.[omega]]. An increase in [beta] shifts the nonaccelerating rate of employment curve upward. An increase in [beta] also increases the efficiency in production. Therefore, the savings per worker curve shifts upward in this case as well. Both capital and income per worker are greater in the new steady state. As is the case with a decrease in [bar.[omega]], the combined effect of a greater level of capital and a higher employment rate at each level of capital is a lower unemployment rate at the new steady state.

However, in this case, there exists an added effect. An increase in [beta] increases the rate of convergence, [beta](1 - [alpha])(n + [delta])/([alpha] + [beta])/([beta] + [beta]), to steady state. Graphically, an increase in [beta] increases the curvature of the savings rate per worker. Therefore, the new steady state is reached sooner than if there were a decrease in workers' salary expectations.

By substituting Equation 9 and the value of B into Equation 5, we obtain the following equation:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

where [??] = s/(n + g + [delta]).

For the first of our empirical models, we test the logarithmic form of Equation 10, assuming [beta] to be the same across countries,

(11) ln y' = 1/[beta] ln(1 - [alpha]) - 1/[beta] ln [bar.[omega]] + (1 + [beta])[alpha]/[beta](1 - [alpha]) ln [??].

As said above, institutional variables may affect the parameter [beta], and therefore, [beta] may not necessarily be the same across countries. However, because the relation between the parameters [beta] and [bar.[omega]], as implied by the model, is highly nonlinear, estimating this equation without further information or assumptions is an almost impossible task. (6) Therefore, the simplifying assumption of a same [beta] should be construed just as a first approach to the problem. The problems we encounter are similar to the ones described in the debate between Lee, Pesaran, and Smith (1998) and Islam (1998) concerning the econometrics of growth and convergence and the need to impose slope homogeneity in certain cases.

In Equation 11, the first term is a constant, the second depends on wage aspirations, and the third depends on the redefined saving rate. If we knew [bar.[omega]], we could run the regression to estimate the implied [alpha] and [beta]. Because we do not know [bar.[omega]], we assume that [bar.[omega]] depends on the institutional variables in an exponential form; that is,

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

where [x.sub.j] refer to the institutional variables. These institutional variables are from Blanchard and Wolfers (2001) and are time invariant. (7)

Our pooled regression is

ln [y.sub.it] = c + [8.summation over (j=1] [a.sub.j] ln [x.sub.jt] + [a.sub.0] ln [[??].sub.it],

where y and [??] refer to five-year averages. Data for these two variables are from World Bank's World Development Indicators 2001. We have data for 35 years, that is, t = 1, 7, and 19 countries, that is, i = 1, 19. (8) Investment rates refer to Gross Capital Formation (as percentage of GDP) in the data. The labor growth rate is calculated from Total Labor Force. The depreciation rate is set equal to 5% and the rate of technological progress is set equal to 2.5%. We construct a measure of detrended output per worker by dividing GDP in 1995 US$ by the Total Labor Force and detrending assuming g = 2.5%. The institutional variables are the benefit replacement rate in case of unemployment (rrate in Blanchard and Wolfers 2001) and its duration (benefit); a measure of employment protection (empro); union density (uden); union contract coverage (union); and a measure of employer and union coordination in wage bargaining (coordd); a measure of spending on active labor market assistance per unemployed person (almphatt); and, finally, the tax wedge (t).

Because of their effects on unemployment, we expected replacement rate, duration, employment protection, union density, and union coverage to have a negative impact; coordination and active labor market policies to have a positive impact; and the tax wedge to have no impact. Table 2 depicts the results of the regression. As expected, the tax wedge is not significant; neither is employment protection, although in this case, we expected it to be significant. All the other variables are significant and have the expected sign, except for unemployment benefit duration, which we expected to have a negative effect. The discrepancy may be explained by the fact that a longer duration allows for a better job-worker match, increasing productivity in the long run, and thus, overcoming the short-run negative effects. (9)

The coefficient for s (adjusted saving in the tables) is consistent with our expectations as well: the coefficient, 0.4922, equals (1 + [beta])a/([beta](1 - [alpha])), according to the model. As stated in section 3, the coefficient of the log-linear regression of employment on capital per efficient unit of labor, 0.0163, equals [alpha]/([alpha] + [beta]), according to the model. These two coefficients jointly imply an [alpha] = 0.32 and a [beta] = 19.29.

To test whether labor market institutional variables in the regression are picking up the effect of a more general institutional quality, we include Hall and Jones' (1999) measure of government antidiversionary policy, GADP, as an additional control variable in the regression. (10) The variable turns out to be nonsignificant in this case, although it is significant in Hall and Jones' analysis of 127 countries, probably reflecting the fact that general institutional quality is fairly similar for OECD countries.

Both this regression and the model assume savings rate to be exogenous. A Hausman's test using financial market development indicators as instrumental variables rejects endogeneity of savings: the value of the test statistic is 2.396, which is nonsignificant ([[chi square].sub.(1)]) = 3.84 at 5%). (11)

Finally, we test the implication that labor market institutional variables have an effect on steady-state capital per worker. By substituting the value of B into Equation 9, we obtain

k' = [[1 - [alpha]/[bar.[omega]].sup.1/[beta]] [[??].sup.[alpha]+[beta]/[beta](1-[alpha]).

We test the logarithmic form of this Equation 10, assuming [beta] to be the same across countries,

(13) ln k' = 1/[beta] ln(1 - [alpha]) - 1/[beta] ln [bar.[omega]] + [alpha] + [beta]/[beta](1 - [alpha] ln [??],

in which the first term is a constant, the second depends on wage aspirations, and the third depends on the redefined savings rate. We assume again that [bar.[omega]] depends on the institutional variables in an exponential form. Therefore, our regression is

ln [k.sub.it] = c + [8.summation over (j=1)] [[alpha].sub.j] ln [x.sub.jt] + [[alpha].sub.0] ln [[??].sub.it],

where k and [??] refer to five-year averages.

Our data are from the Penn World Tables because the World Development Indicators do not report data on capital. Capital per worker refers to Capital Stock per Worker (1985 International Prices) and Investment Rates refer to Investment Share of GDP percentage (1985 International Prices) in the data. (12) The institutional variables, depreciation rate, and rate of technological progress are the same, as is the labor force growth rate (because the Penn World Tables report data on population but not on labor). Finally, capital per worker is detrended in the same way.

If we were to consider only their effects through the chain unemployment--income-savings (the subject of this article), we would expect replacement rate, duration, employment protection, union density, and union coverage to have a negative impact; coordination and active labor market policies to have a positive impact; and the tax wedge to have no impact. However, this model is too stylized to take into account other effects such as substitution, etc. For this reason, we expect the results to be less clear cut in this case. Table 3 reports the empirical results of the regression.

As it turns out, the unemployment benefit replacement rate, union coverage, and union density have no significant effects; coordination and active labor market policies have the expected positive effects; and employment protection shows the expected negative effect. However, both the tax wedge and unemployment benefit duration show positive effects, contrary to expectations. In the case of the tax wedge, a higher tax wedge may encourage substitution toward capital and away from labor. The effect of benefit duration is consistent with that on productivity in Table 2.

5. Testing for Convergence Effects

The model predicts that the lower the labor market flexibility, the slower the convergence to the steady state: Income or capital per capita approaches its steady-state level at the rate [beta](1 - [alpha])(n + g + [delta])/([alpha] + [beta]). At this point, and to test this implication of the model, we abandon our simplifying assumption of a same [beta] and return to the idea of institutional variables affecting this parameter and, thus, convergence.

In the previous sections, we test steady-state relations. In this section, we perform a convergence (transitional dynamics) analysis. The OECD countries are likely at or near the steady state, with small changes in steady states due to small changes in savings or population growth rates. We take advantage of their vicinity to the steady state in the two previous sections, but in this section, we take the stand that small deviations around the steady state are enough to test for convergence.

We calculate convergence rates using the following formula (equation 14 in Mankiw, Romer, and Weil 1992) to solve for [[lambda].sub.i]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

where output per worker refers to Real GDP per Worker (1985 International Prices) in the Penn World Tables. The initial year is 1960 and the final one is 1990.

The steady state value, [y.sup.*i], is calculated using Investment Share of GDP percentage (1985 International Prices), and the same depreciation rate, rate of technological progress, and labor force growth rate as above. Capital intensity, [alpha], is set equal to 1/3. The steady-state value is calculated as follows:

[y.sup.*i] = [([[??].sub.i]/[[??].sub.US]).sup.[alpha]/(1-[alpha])][y.sup.US.sub.t],

where, again, [??].sub.i] = [s.sub.i]/([n.sub.i] + g + [delta]). Investment shares and labor force growth rates refer to averages for the period. This method assumes that the United States is at the steady state, and therefore, we cannot calculate a convergence rate for the States. Equivalently, we calculate convergence rates using the United States as a yardstick.

Table 4 shows the results expressed as percentage. As explained in section 4, we do not expect all institutional variables to affect the curvature. The variables we find to affect convergence are unemployment benefit duration and, of the ones pertaining to union power, coordination. More surprising, we find the tax wedge to have a small but positive impact, consistent with the effect of the tax wedge on capital accumulation in Table 4. Table 5 depicts the results of the regression with the significant variables.

6. Conclusions

Our model is a simple variation of Solow's model that adjusts from the fact that employed labor differs from active labor, period by period, due to the lack of flexibility in the labor market--a simple variation of the Solow model suitable for a first approximation to an empirical investigation of the interrelationship between economic growth and the labor market.

The model predicts, first, that both income and capital per worker depend positively on flexibility of the labor market; second, that the steady-state unemployment rate depends positively on the rate of population growth and the rate of technological progress and negatively on the savings rate and on flexibility of the labor market; and third, that labor market flexibility also impinges on the convergence of an economy toward its steady state: The less flexible the labor market, the slower the convergence.

We use a pooled-OLS regression to show that, in fact, lower savings rate, higher growth of the labor force, or faster technological progress results in higher unemployment. Our pooled regression shows that most of the labor market institutional variables have the predicted effects on steady-state output per worker. Finally, we construct convergence rates and regress them against the same labor market institutional variables. We find that three of these variables affect convergence toward the steady state.

We find these first results encouraging enough to grant further work, both at the theoretical and empirical levels, on the interactions between unemployment and economic growth.

Table 1. Unemployment as Dependent Variable

Variable Coefficient t-Statistic

Saving -0.48 * -3.71
Labor force growth 0.84 ** 2.02
Technical progress 1.74 * 3.52

Adjusted [R.sup.2] 0.621
Included observations 187

* Refers to 1% significance and ** to 5%.

Table 2. ln(y) as Dependent Variable

Variable Coefficient t-Statistic

ln(replacement rate) -0.11 *** -1.78
ln(duration) 0.18 * 4.28
ln(active policies) 0.18 * 3.17
ln(union coverage) -0.79 * -3.44
ln(union density) -0.17 ** -2.42
ln(tax wedge) -0.00 -0.03
ln(coordination) 0.47 * 3.84
ln(employment protection) -0.10 -1.38
ln(adjusted saving) 0.49 ** 2.49
Constant 8.26 5.74

Adjusted [R.sup.2] 0.408
Included observations 120

* Refers to 1% significance; ** to 5%, and *** to 10%.

Table 3. ln(k) as Dependent Variable

Variable Coefficient t-Statistic

ln(replacement rate) -0.13 -1.49
ln(duration) 0.10 *** 1.81
ln(active policies) 0.15 ** 1.96
ln(union coverage) 0.13 0.40
ln(union density) -0.11 -1.12
ln(tax wedge) 0.49 * 2.66
ln(coordination) 0.34 ** 2.22
ln(employment protection) -0.46 * -4.57
ln(adjusted saving) 0.78 * 3.62
Constant 4.35 2.70

Adjusted [R.sup.2] 0.393
Included observations 120

* Refers to 1% significance; ** to 5%, and *** to 10%.

Table 4. Convergence Rates (as Percentage)

Australia 3.06
Austria 3.44
Belgium 4.50
Canada 6.54
Denmark 2.34
Finland 3.01
France 3.87
Germany 3.37
Ireland 3.56
Italy 4.36
Japan 3.64
Netherlands 4.19
Norway 3.31
New Zealand 1.16
Portugal 2.98
Spain 4.16
Sweden 2.98
Switzerland 3.12
United Kingdom 3.60

Table 5. Convergence Rate as Dependent Variable

Variable Coefficient t-Statistic

Duration -0.0027 *** -1.80
Tax wedge 0.0005 ** 2.12
Coordination -0.0054 ** -2.92
Constant 0.0424 4.20
[R.sup.2] 0.410
Observations 19

* Refers to 1% significance; ** to 5%, and *** to 10%.

We are most grateful to one of the referees of this journal for invaluable suggestions. We also thank Francesco Daveri, German Echecopar, Mobinul Huq, Charles Leung, Huw Lloyd-Ellis, Robert F. Lucas, Fernando Perera, Huntley Schaller, and Christian Zimmermann for comments on an earlier version; Ayokunle Dina and Morteza Haghiri for their research assistance; Olivier Blanchard and Justin Wolfers for the use of their data; and the Social Sciences and Humanities Research Council of Canada (410-99-0862) for financial support.

(1) Arguably [bar.[omega]], the level of workers' aspirations, should evolve over time with productivity. We introduce this tie later on.

(2) Presumably, the savings rate could depend on the unemployment rate. However, this variation will only make the model more cumbersome without producing any new insights.

(3) OECD data were downloaded from the OecdSource webpage in November 2001.

(4) We replicated his analyses with basically the same results (not reported in this article).

(5) Analysis for this and the next section were also conducted for seven-year averages to test robustness. Results are basically the same.

(6) We tried to find other variables to use as instrumental variables without much success.

(7) These variables were downloaded from Blanchard's webpage in November 1999.

(8) The countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Ireland, Italy, Japan, Netherlands, Norway, New Zealand, Portugal, Spain, Sweden, Switzerland, United Kingdom, and the United States. We did not have institutional data for the other members of the OECD. Germany was excluded because the institutional data referred to Western Germany and the saving data to the unified Germany.

(9) We obtain similar results by using the Penn Worm Tables.

(10) The variable was downloaded from www.standford.edu/~chadj.

(11) The financial market development indicators were downloaded from www.worldbank.org/research/projects/finstructure/ database.htm.

(12) Variables downloaded in November 2001.

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Alberto Alonso, * Cristina Echevarria, ([dagger]) and Kien C. Tran ([double dagger])

* Universidad Complutense, Economia Aplicada III. Fac. CC. Economicas, Somosaguas 28223 Madrid, Spain; E-mail [email protected].

([dagger]) University of Saskatchewan, Department of Economics, 9 Campus Drive, Saskatoon SK S7N 5A5, Canada; E-mail [email protected]; corresponding author.

([double dagger]) University of Saskatchewan, Department of Economics, 9 Campus Drive, Saskatoon S75 5A5, Canada; E-mail [email protected].

Received May 2002; accepted July 2003.