metadata: authors: 0: author: Fiess,Norbert Matthias
1: author: Fugazza,Marco
2: author: Maloney,William F.
count: Latin America
docna: 0: docna: Exchange rate appreciations, labor market
            rigidities, and informality
docty: Policy Research Working Paper
subtopic: Labor Markets,Capital Markets and Capital Flows,Capital Flows,Inflation,Employment and Unemployment,Rural Labor Markets
teratopic: Finance and Financial Sector Development
abstracts: cdata!: This paper works at the interface of the
            literature exploring the raison d'etre of the informal
            labor market and that explaining the real exchange rate
            appreciations occurring in many Latin American countries
            during periods of reform. The authors first build a small
            country-Australian style model where the informal sector is
            seen as an unregulated non-tradables sector, augmented by
            heterogeneity in entrepreneurial ability and capital
            adjustment costs. They then examine the behavior of the
            model with and without a formal sector rigidity. It shows
            that the co-movements of relative formal/informal incomes,
            formal/informal sector size, and the real exchange rate can
            offer insight into the level of distortion in the labor
            market and the source of exchange rate fluctuations. The
            paper then explores time series data from Brazil, Colombia
            and Mexico using multivariate co-integration techniques to
            establish what "regime" each country is in at
            various periods of time. Mexico appears to be relatively
            undistorted and the 1987-92 appreciation appears to be
            largely a function of a boom in the non-tradables sector
            rather than wage inertia. In spite of a secular expansion of
            the informal sector there is little evidence of dualism or
            of a rigidity driven appreciation of the Real, from
            1993-1996. Post 1995 Colombia corresponds to a classic
            segmented labor market and an appreciation partly driven by
            labor market rigidities. Graphical analysis suggests that
            neither the Argentine appreciation (1988-1992) or the
            celebrated Chilean appreciation (1975-1982) were driven by
            inertial forces
repnme: repnme: Exchange rate appreciations, labor market
            rigidities, and informality
display_title: Exchange rate appreciations, labor
            market rigidities, and informality
listing_relative_url: /research/2002/02/2874378/exchange-rate-appreciations-labor-market-rigidities-informality
topicv3: Informal Sector m1326258 1168,Labor Markets m1326488 855,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Capital Markets m1326967 332,Self-Employment m1504000 2698
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
no_of_pages: 42
author_keys: 0: author_key: 453560
1: author_key: 480260
2: author_key: 93000
model_extractions: WPS2771

**Exchange Rate Appreciations, Labor Market Rigidities, and Informality**<sup>**•**</sup>

Norbert M. Fiess<sup>∗</sup> Marco Fugazza<sup>°</sup> William Maloney<sup>∗</sup> The World Bank February 2002

**Abstract:** This paper works at the interface of the literature exploring the raison d’etre of the informal labor market and that explaining the real exchange rate appreciations occurring in many Latin American countries during periods of reform. We first build a small country-Australian style model where the informal sector is seen as an unregulated non-tradables sector, augmented by heterogeneity in entrepreneurial ability and capital adjustment costs.  We then examine the behavior of the model with and without a formal sector rigidity. We show that the co-movements of relative formal/informal incomes, formal/informal sector size, and the real exchange rate can offer insight into the level of distortion in the labor market and the source of ER fluctuations.  We then explore time series data from Brazil, Colombia and Mexico using multivariate co-integration techniques to establish what “regime” each country is in at various periods of time. Mexico, for instance, appears to be relative undistorted and the 1987-92 appreciation appears to be largely a function of a boom in the non-tradables sector rather than wage inertia.  In spite of a secular expansion of the informal sector and there is little evidence of dualism or of a rigidity driven appreciation of the Real, from 1993-1996.  Post 1995 Colombia corresponds to a classic segmented labor market and an appreciation partly driven by labor market rigidities. Graphical analysis suggests that neither the Argentine appreciation (1988-1992) or the celebrated Chilean appreciation (1975-1982) were driven by inertial forces.

> • This work partially financed by the Regional Studies Program of the Office of the Chief Economist for Latin America and the Caribbean.  The development of the conceptual framework  was supported by the Franco-Italian Foundation for Theoretical Philanthropy.  We are grateful to Rashmi Shankar for early conceptual discussions, to Leonardo Gaspirini for helpful comments, to Norman Loayza and Claudio Montenegro for help with data, and to Gabriel Montes for expert research assistance.  Corresponding author: wmaloney@worldbank.org.

> ∗ The World bank

> ° CERAS, Ecole Nationale des Ponts et Chaussées
# **1.  Introduction**

This paper works at the interface of two literatures. The first debates whether the unregulated or informal self-employed sector that accounts for often over 30% of LDC labor forces should be seen as the disadvantaged segment of a highly segmented labor market, or perhaps simply as an unregulated, largely voluntary, entrepreneurial sector. The issue is particularly important in light of the rise in the importance of the sector in the 1990s. The second literature debates whether the sources of the real exchange rate appreciations that were observed in the 1980 and 90s in many countries of Latin America were due to inertial considerations, such as backward indexation to inflation, or to “real” effects such as productivity shocks or booms in non-tradable demand. The first question we propose can be answered by looking at the time series properties of relative sector sizes and relative remuneration of the formal salaried and informal self-employed sectors. Since the informal self-employed sector is largely non-tradable and unaffected by formal sector rigidities, these same time series properties can also help identify between models of the real exchange rate.

We begin by developing a model that combines Lucas’s (1978) idea of workers having differing levels of entrepreneurial ability, with a small economy trade model of the style most recently elaborated by Obstfeld and Rogoff (1996). In spirit we are similar to Aizenman and Frenkel (1988) in introducing heterogeneous ability, in our case varying entrepreneurial ability, to generate non-stationary behavior in relative tradable (formal) and non-tradable (informal self-employed) earnings.

We also introduce capital adjustment costs consistent with the literature on credit as a barrier to entering self-employment (Evans and Jovanovic 1989) and more generally imperfect capital markets. This corresponds to a more realistic view of barriers to entry into informality, and allows for transitory deviations of all variables from their steady state result without positing nominal wage rigidities in the formal sector (see for example Agenor and Aizenman 1999). It also permits us to view the evolution of self-employed incomes as they are reported - a combination of return to capital and labor ability.

Though the model cannot exhaust all possible patterns of comovements of relative sector sizes and incomes, and the real exchange rate, it does plausibly postulate several 1
core identifying relationships to motivate the empirical analysis that are robust to an array of parameter variables and to the modeled adjustment process. The spirit of the exercise is to see how far we can go explaining the comovements of the three series without recourse to imposing rigidities.

# **1.1 Background**

The traditional “dualistic” view sees the informal sector as the residual of highly distorted LDC labor markets. Unions or government regulation push wages above their equilibrium level, rationing workers into the inferior informal sector where they enjoy no labor protections. However, an emerging literature argues that as a first approximation, this sector should be treated as an unregulated/unprotected entrepreneurial sector that may be desirable to many workers both because of the desire for independence and the misalignment of implicit and explicit labor taxes with perceived benefits. In this case, workers may be choosing to be their own bosses and though becoming unprotected, they reach a higher level of welfare. We argue here that both the “integrated” and “segmented” views should be seen as special cases of the same model: The informal sector may very well be a prosperous non-tradables sector, but one which also contains involuntarily informal workers. The relative shares of voluntary and involuntary worker will reflect the degree of segmentation in the labor market which can vary depending on the shocks to the economy.

Empirically, in the absence of segmentation, we demonstrate that we should expect relative sector size and relative remuneration to move together across time. However, should formal sector rigidities become very binding, perhaps due to a negative shock to formal sector productivity, the overall composition of the sector can be shifted such that it behaves in the more traditional dualistic way: relative earnings move against relative sector size as workers rationed into the informal self-employed sector drive down their relative earnings.

The difference of these two views also has the potential to shed light on the puzzling behavior of real exchange rates following liberalization in many Latin American countries. In the southern cone in the 1970s and in particular Chile, from 1979 to 1982, Mexico from 1988-1995, Argentina 1990-1995, and Brazil beginning in 1992, the 2
exchange rate appreciated, often dramatically following stabilization policies that fixed the nominal exchange rate and liberalized capital markets.<sup>1</sup> Loosely extending Calvo and Vegh’s (1994) typology, two types of explanations have emerged, those relying on backward-looking price and wage behavior (Rodriguez 1982, Dornbusch 1982, Edward and Cox- Edwards 1987, Calvo and Vegh 1994)<sup>2</sup> and those focusing on “real” phenomena arising from credibility problems (Calvo 1986, Calvo and Vegh 1993) wealth effects do either to falling inflation or expected productivity effects (Helpman and Razin 1987 Schmidt Hebbel 1988, Conley and Maloney 1995) or removing inflationary distortions (De Gregorio, Guidotti, and Vegh 1998, Roldos 1997, Uribe 1997). Central to the Chilean post-mortems of the early 1980s, this dichotomy between “inertial” (Dornbusch and Werner 1995, Edwards 1996) vs “real” (Carstens and Gil-Diaz 1996) explanations remained salient in the discussions of the Mexican peso appreciation of the early 1990s, and Rebelo and Vegh’s (1995) efforts to nest and evaluate competing theories of post-stabilization behavior.

The nature of the labor market data we work with here offers the potential to inform these debates. First, the informal self-employed are concentrated in nontradables: Argentina 87%, Brazil 92%, Chile 86%, Colombia 87%, Mexico 83%. Second, almost by definition, their incomes are less affected by official regulations. These two characteristics make them ideal for analyzing exchange rate movements in the context of a small economy model, and the relative movement of relative informal/formal wages and sectors sizes and help identify the presence of formal sector rigidities, and inertial forces in exchange rate movements.

As an example, returning to the canonical Chilean case, figure 1, shows that in the 1960s and early 1970s, relative sector sizes and relative incomes moved oppositely, suggesting that under the progressive Christian Democratic government and later under the Socialist government of Salvador Allende, nominal rigidities in formal sector wage

> 1 The exchange rate is defined as the price of non-tradables relative to tradables Pn/Pt  which can be shown to map into the more standard exchange rate adjusted ratio of price indices EP*/P under most conditions. The real exchange rates for Argentina, Brazil, Colombia and Mexico are displayed in Figure 1 in the Appendix A.

> 2 It should be noted that  Calvo and Vegh  show that backward looking price behavior can explain the stylized facts only if the intra-temporal  elasticity of substitution between traded and non traded goods is smaller than the intertemporal rate elasticity of substitution which they find implausible.

3
setting did, in fact, lead to a segmented labor market. However, during the period of exchange rate appreciation of 1975-1982, the two series move together, suggesting that the currency movements were not driven by backward indexing of formal sector wages. Further, the fact that the formal sector was expanding during this period suggests that a strong productivity shock to the formal sector may have been driving both labor force and exchange rate variables in a Balassa-type effect.

For two other important cases, Mexico and Argentina, the appreciations in 19881993 and 1988-94 respectively occur simultaneously with increases in informal nontradables sector and relative wages suggesting a largely desirable expansion of the informal non-tradables sector and hence a “real” appreciation of the exchange rate.<sup>3</sup> In these cases, possibly increases in demand for non-tradables may have provided the initial impetus to appreciation. The nascent negative co-movements after 1991 in Mexico offer potential evidence that after the first four years of appreciation, there were formal sector rigidities that were only resolved with the nominal depreciation. At this point, the still negative but now inverted comovements of relative wages and sector sizes suggests the recovery from a period of significant segmentation. The behavior in Argentina seems less clear cut although it suggests a similar story- the appreciation of the ER is accompanied by positive wage/sector size comovement suggesting, again, a boom to the non-tradables sector. The secular increase in informal work in Brazil (figure 1d) after 1987 concomitant with a secular rise in the relative wage in the sector also suggests that this evolution was desirable for many workers and this seems broadly concomitant with the real exchange rate appreciation across the latter half of the period, again consistent with a non-tradable demand led view.

Finally, very sharp negative co-movements in Colombia at the end of the 1990s suggest strong rigidities in the labor market leading to very large rationing out of workers from the formal sector. The sharp real exchange rate beginning in 1995 may reflect this inertial behavior which the nominal depreciation at the end of the period helped offset.

For the countries where the data permit, Brazil and to a lesser extent Mexico and Colombia, the more systematic empirical work of the second half of the paper confirms these initial views.

> 3 See Maloney (1998)

4
# **2. A  Model**

We consider the case of a small economy that produces two composite goods, tradables and non-tradables. The formal sector is assumed to produce tradables (T), the numeraire, while the production of non-tradables is concentrated in the informal sector (N). All workers are homogenous when salaried in the formal sector. However, workers in the informal sector are self-employed and following Lucas, individuals (j) differ in terms of entrepreneurial capability, φ j distributed uniformly on [0,1]. For simplicity, we also normalized the labor force to unity so that, provided that the economy is not in a corner solution, the value of entrepreneurial ability of individual m, who is indifferent between salaried work and self-employment, also corresponds to the size of formal labor _*_ force. We set _φ m = φ_ . Then, _φ * = LT._ . This effectively maintains the usual labor supply constraint, but builds in a decrease in marginal entrepreneurial ability as labor shifts toward self-employment.

Formal output _YT_ is given by constant-returns production functions of the capital _K T_ and labor _LT_ employed in sector _T_ , Production of individual _j_ in the self-employment sector is given by We assume that capital is mobile both internationally and across sectors but not instantaneously. Capital markets are not perfect for the informal and, as Evans and Jovanovic demonstrated for the US, entrepreneurs are often credit constrained. Those entering self-employment must install some capital the period before producing and pay a _<u>χ</u>_  _I_<sup>2</sup> _j_  deadweight installation cost (paid in terms of tradables) of , where _Ij_ 2 <sup></sup> _h_ ~~(~~ _k j_ ~~)~~ <sup></sup>   represents the change in capital stock between two successive periods for self-employed 5
individual _j_ and χ is inversely related to the speed of adjustment. _h_ (<sup>_k_</sup> _j_ ) is a linear function of capital accumulated by the individual self-employed _j_ . We further assume that individuals willing to leave self-employment must dispose of all the capital they have in place before they become employed in the formal sector. However, due to imperfect capital markets, they face symmetrical adjustment costs. This specification ensures that (de)installation costs are always finite. Further, since marginal costs of capital installation are increasing, capital adjustment will not happen instantaneously. Labor is allocated only mobile between the two sectors and as will be shown, since the entrepreneur must install capital before moving, labor also does not adjust fully within one period and differentials in net remuneration among sectors are not instantly arbitraged by labor flows. This permits us to analyze both steady state movements in relative wages, relative sector sizes and exchange rates, but, also transitional dynamics.<sup>4</sup> As to labor, it can migrate only between sectors within the economy.

# **2.1 The firm**

The representative formal sector firm maximizes where _wT,s_ is the wage (gross) prevailing in the tradables sector at time t=s. The world interest rate _r_ , expressed in terms of tradables, is assumed to be constant.

Let us define the capital-labor ratios in traded goods production as _k T = KT /LT_ , and rewrite outputs per employed worker as _yT =AT f(kT)_ . The first order conditions are given by:

> 4 As usually assumed, one unit of tradables can be transformed into a unit of capital at no cost. The reverse is also true. Non tradables can be used only for consumption. Capital can be used for production and then consumed (as a tradable) at the end of the same period.

6
Because _r_ is the world interest rate expressed in terms of tradables, it must correspond to the marginal product of capital in the formal sector as indicated by equation (1). Equation (2) simply states that the wage prevailing in the sector equals labor marginal productivity. Because both factors do not shift instantaneously across sectors, equations (1) and (2) may fail to hold ex-post in the event of unanticipated shocks.

In the informal sector, individual _j_ maximizes The first order condition is given by where _q_ denotes the shadow price of installed capital in non-tradables and _p_ denotes the price of non-tradables relative to the price of tradables. In other words, _p_ is simply the inverse of the real exchange rate defined as the relative price of traded goods in terms of non-traded goods. Equation (3) indicates that investment is positive only for values of _q_ larger than 1. Equation (4) is a standard investment Euler equation. It must also be true in the long run for all self-employed individuals that returns to capital equal the market rate of interest _pAN φ j α N k α j N_ − 1 = _r_ (4’) and that the pivotal individual is indifferent between wage work and self-employment, we have 7
# **2.2 The Consumer**

As is standard, we assume that the economy is inhabited by an infinitely-lived representative consumer whose demands and asset holdings are identified with aggregate national counterparts and who maximizes a lifetime utility function of the form Where _CT_ and _C N_ stand for consumption in the tradables and non-tradables sectors, respectively, Φ( _CT_ ,<sup>_C_</sup> _N_ ) is a linear homogenous function of its arguments and _u(.)_ is isoelastic with intertemporal substitution elasticity σ . The representative consumer faces a lifetime budget constraint where national financial wealth _Qt_ = _Bt_ + _K N_ , _t_<sup>+</sup> _KT_ , _t_ is measured in terms of tradables and _B_ stands for net aggregate holdings of foreign assets. _φ *_ is the ability of the individual who is indifferent between self-employment and wage work. We will be more precise about the latter definition below. IN,s represents total investment and KN,s total capital accumulated in the informal sector at date s.

For the general case of a CES utility function<sup>5</sup> relative intratemporal consumption depends only on the relative price _p_ and not upon consumer's spending level where _γ_ indicates the weight of the tradable good in the utility function. Moreover,

> 5 See Obsfeld and Rogoff (1996, pp 226-235) for a full derivation.

8
A rise in non-tradables relative price induces a rise in tradables consumption growth relative to non-tradables consumption growth. Note that if _σ = θ_ , tradables consumption remains constant along the perfect foresight paths.

Since, by assumption non-tradables can only be consumed, in equilibrium consumption equals production in the informal sector. Substitution and combination of the Euler equation for tradables consumption with the lifetime budget constraint of the representative consumer yields an expression for the optimal consumption of tradables where P is the price index P = [ _γ_ + 1( − _γ_ ) _p_ 1 − _θ_ ]1 /1 − _θ_ ] which is increasing in p.

# **2.3 Responses to Productivity and Demand Shocks**

Before turning to the dynamics of the economy, we first describe its steady state equilibrium and assess the impact of permanent productivity and consumption shocks. We then introduce a wage rigidity in the formal sector. The results of all exercises are tabulated in Table 1.

# **2.3.1 Shocks in the Long Run**

Productivity shocks are represented by a permanent variation in the _A_ productivity scale coefficients and demand shocks by a permanent variation in the _γ_ parameter. In the 9
> ^ ∆ _x_ following, variables with hats refer to rates of change ( _x_ = ). Log differentiation _x_

leads to the following results, assuming that initially _p = 1_ and initial _γ_ is equal to one half.

**_The real exchange rate:_** Differentiating (4’) and aggregating across all j gives

_p_ ˆ + _A_ ˆ _N_ + _φ_ ˆ * −( 1 − _α N_ ) _k_ ˆ* = _r_ ˆ = 0 ˆ Although individual ability remains constant by assumption, _φ j_ = 0 and hence the capital growth rate is the same for everyone, the labor reallocation after a shock results in a change in the pivotal individual so that _φ_ ˆ * is no longer equal to zero for the labor force as a whole. By the same logic _p_ ˆ + _A_ ˆ _N_ + _φ_ ˆ * + _α N k_ ˆ*<sup>=</sup> _w_ ˆ _T_ where _k_ ˆ*<sup>=</sup><sup>_k_</sup> ˆ _j_ and is given by equation (4’). Defining _η L_ , _T_ = _wT LT_ , labors’ share in _YT_ This simply restates the Balassa-Samuelson result that, for values of 1 − _α N_ close to 1, _η LT_ the real exchange rate is determined by the relative rates of productivity growth.

**_Relative Sector Size:_** Demand for tradables and non-tradables can be re-written as, respectively

In order to simplify the analysis we assume that total financial wealth remains constant across steady state. We implicitly assume that any variation in the total level of physical 10
capital is fully offset by an equal variation of opposite sign in foreign assets holdings. This allows us to write Changes in non tradables consumption can be written as ^ ^ ˆ ˆ _C N_ = − _γ_ + _Z_ − ( _θγ_ + ( 1 − _γ_ )) _p_ and changes in total production in the informal sector by ˆ ˆ Since non tradable goods market equilibrium requires that _C N_ = _YN_ , the entrepreneurial ability of the pivotal worker, and implicitly, the share of the workforce in tradables, can be written as

**_Relative Earnings:_** The change in  informal production expressed in tradables units is now

the relative variation in entrepreneurs earnings _(denoted by wNj thereafter)_ as the latter is a constant proportion of the former.

11
The change in average informal production (entrepreneurs earnings) expressed in terms of tradables units can be written as:

# **Productivity Shock to the Formal/Tradables Sector**

^ ^ ^ In the case where _AT_ > 0 , _A N_ = 0 and _γ_ = 0 , consistent with BalassaSamuelson, the real exchange rate appreciates - non-tradables become more expensive relative to tradables. Both sectors become relatively more capital intensive and as a consequence net earnings are higher. The direction of change of the employment share of self-employment depends on the sign of [ _φ LT_ + _φ se_ − 1 + ( 1 − _α N_ )( _γ_ ( 1 − _θ_ ) − 1 )] . It is unambiguously negative when _θ ≥ 1_ and labor flows toward the formal sector and<sup>ˆ</sup> * _φ_ > 0 . However, for smaller values of _θ_ , the wealth effect may prevail over the substitution effect and both consumption of non-tradables and employment in the<sup>ˆ</sup> * informal sector may increase in levels. A sufficient condition for observing _φ_ > 0 for any _θ > 0_ is given by As by definition γ is smaller than 1 then, condition (8) is always satisfied. Total informal production, measured in tradables units, depends on the sign of 12
In the case of Cobb-Douglas preferences, it is straightforward to see that 0 < 1 − Ω 2 [ 1 − _φ LT_ − _φ se_ + ( 1 − _α N_ ) _γ_ ] < 1 for values of Ω 2 close enough to unity, and the total value of informal production increases. Since Ω 3 < Ω 2 , this is also true for average production and thus average entrepreneurs earnings. The reason is twofold. First the price of non-tradables increases and second, only the most able entrepreneurs remain in the informal sector. For larger values of Ω 2 and Ω 3 and or γ then the expression into ˆ brackets is likely to become negative. Since _w_ ˆ _T_ = _AT_ , on average self-employed _η LT_ earnings fall relative to workers earnings in the formal sector for any value of Ω 2 , Ω 3 and _θ_ .

In sum, for any positive value of _θ_ , we expect to observe relative earnings and relative sector sizes to positively co-move. In addition they move with the real exchange rate.

# **Productivity Shock to the Informal/Non-Tradables Sector**

^ ^ ^ In the case where _AT_ = 0 , _AN_ > 0 , and _γ_ = 0 the real exchange rate decreases in proportion to the productivity shock in non tradables and neither capital intensity nor self-employed earnings are affected. The impact on informal employment is determined by the sign of ( 1 − _γ_ ( 1 − _θ_ )) , which is positive for any positive value of the intra-temporal elasticity of substitution. In all situations average earnings and participation rate in the informal sector increase relative to their counterpart in the tradables sector and move together although they move against the real exchange rate.

However, it is hard to identify a case with a _negative_ non-tradables productivity shock against the mainstream case of a strong positive shock to tradables, for instance, in the case of Chile 1979-82 although the boom in real estate and construction across that period (see Conley and Maloney 1995) weighs in favor of the latter.

13
# **Shift in Preferences toward Non-Tradables**

^ A shift in preferences, for example, towards non-tradables consumption _AT_ = 0 , ^ ^ _A N_ = 0 and _γ_ < 0 increases self-employment as well as absolute and relative consumption of non-tradables. Absolute and relative average earnings of the selfemployed increase while wages in the formal sector remain at their initial level. Again, we observe co-movements in relative sector sizes and returns. In the long run, there is no change in the real exchange rate although, as we discuss below, this is not true in the short run.

# **Negative Formal/Tradables Productivity Shock  with Formal Sector Wage Rigidities**

Unions or mandatory minimum wages may introduce downward wage rigidities in the formal sector that can reverse many of the findings above. A negative shock to productivity in the tradables sector translates into wage downward pressures in the formal sector. However, as this cannot occur, labor must migrate to the informal sector. Because capital returns are tied to the world interest rate, the outflow of labor in the formal sector is more pronounced than in the flexible case. This outflow corresponds to Equilibrium of the demand and supply conditions in the non-tradables sector and gives 14
which is negative for any _θ > 0_ as is As labor migrates towards the informal sector, production rises, the real exchange rate depreciates, and average earnings in the informal sector fall. Moreover, as workers cannot migrate back to the formal sector, those whose entrepreneurial ability is relatively low earn less than what they would get in the formal sector. For those workers “trapped” in the informal sector earnings performance has worsened relative to those employed in the formal sector as earnings in the formal sector are preserved by institutional rigidities. With the exception of the implausible case where _θ_ < ( _φ se_ − _γ_ /) _γ_ , the two labor force series move against each other. Critically, the same result would hold in the case where indexation of wages to past inflation forces formal sector wages above equilibrium: we should see relative sector sizes and incomes move against each other.

# **2.3.2 Short Run Equilibrium and Dynamics**

The adjustment to the steady state may depend on the relative values of _σ_ and _θ_ although the previous section showed that long run properties of the economy are exclusively dictated by the absolute value of _θ._ To simplify, we start with the case where _θ = σ =1_ and then refer to alternative parameterizations. To refresh, _σ_ > _θ_ implies that tradables consumption reacts more to variations in the gross real interest rate<sup>6</sup> induced by a variation in the relative price of non-tradables than to the variation in the relative price itself.

Linearizing equations (3) and (4) around the steady state _~~q~~_ = 1, _k j_ we obtain 15
The equations _∆ kj = 0_ and _∆ qj = 0_ are depicted in a two-equation phase diagram in _q_ and _kj_ that shows the dynamics of self-employed individuals investment decisions (figure 2). The perfect foresight path is indicated by the line denoted by SS.

As the steady level of investment chosen by each individual is not identical, we expect to observe that a common shock affects differently heterogeneous individuals differently. Should a shock lead to contraction of the self-employment sector, those whose entrepreneurial ability falls below the threshold steady state value of _φ *_ (those who would be better off in the wage work sector), the perfect foresight path leads to zero capital and a zero capital shadow value at steady state as depicted in figure 3. Should − _r_ self-employment expand, new-entrants invest initially _I_ 0 =<sup>1</sup> _a_ independently of the _r χ_ wage prevailing in the formal sector since the initial shadow value of their capital is above one ( _q0=1/r_ ).

Inter-sectoral worker movements are not expected to be simultaneous because of entrepreneurial ability heterogeneity across individuals. More able individuals are the first to enter self-employment and the last to leave it. A sketch proof of these results is presented in appendix A.

# **Productivity Shock to the Formal/Tradables Sector**

Production of tradables increases and so do labor and capital returns, leading to increased demand for both types of goods and causing _p_ to rise to clear the non-tradables market. Along the perfect foresight transition path, some self-employed find it more profitable to move to the formal sector. As a consequence the shadow value of the capital they use at the end of the period following the shock falls short below 1 and tends to zero in the long run, and they decumulate capital. Those whose sequence of returns from selfemployment remains above that of the formal wage face _q>1_ and they accumulate more capital.

16
On impact, no adjustment can take place because formal firms must wait for the following period to adjust their capital and self-employed can migrate only once the capital they have in place at the moment of the shock has been completely dismantled, that is not before the following period. Then, prices are the only adjustment element. On ^ _<u>φ</u> LT_ <u>(</u> 1 − _α N_ <u>)</u> ˆ impact, _E_ ( _pYN_ ) = _AT_ , which corresponds to the initial rise in ( 1 − _α N_ )( _θγ_ + ( 1 − _γ_ )) − _φ se α N_ _p_ . It can be shown that average self-employed earnings at steady state are lower than the level they reach on impact while the opposite is true for the formal wage. Then along the perfect foresight transition path, average earnings in the informal sector are expected to fall relative to wage changes in the formal sector. As condition (8) is always satisfied, the informal share is also expected to fall, as indicated in the previous section. Moreover, along the adjustment path, both sectors become more capital intensive, production in tradables increases unambiguously and the real exchange rate appreciates. Then, towards the long run _wT / wN_ increases, _LT / LN_ falls and _p_ rises relative to its initial level. Price overshooting and opposite movements of earnings and participation in the informal sector could never be observed. The relative ranking of _σ_ and _θ_ may affect the length of adjustment but preserve dynamics and long run properties. Indeed, _CT,t_ is given by (7) which suggests that the level of tradables consumption along the saddle path is affected by variations in _p_ in a manner that could either reinforce or offset the impact of a shock.

The impact of a rise in _p_ on consumption bundles is dampened by consumers’ inter-temporal considerations in the case where _σ_ > _θ_ and amplified in the opposite case. In the former case, consumption of non-tradables falls less rapidly relative to consumption in the tradables than in the case where _σ_ < _θ_ . This implies that migration occurs over a longer period of time when inter-temporal substitution considerations prevail over intra-temporal substitution considerations.

# **Productivity Shock to the Informal/Non-Tradables Sector**

Again dynamics are driven by the importance of inter-temporal relative to that of intra-temporal considerations. On impact the real exchange rate is expected to fall to offset the positive productivity shock in order to keep the non-tradables market in equilibrium. However, the expected fall in _p_ leads to a rise in demand for non-tradables.

17
This rise in demand increases as _θ_ takes higher values relative to _σ_ . That is, for _σ < θ_ we observe some undershooting of _p_ along the transition path. Undershooting describes the fact that _p_ falls to the level that offsets the impact of the productivity shock only when the economy reaches its new steady state. Whenever, _σ > θ_ consumption of tradables increases as _p_ falls. The positive impact on the demand for non-tradables is smaller than in the previous case. This implies that the real exchange rate undershooting is less pronounced during the transition to the steady state than in the previous case. In other words, when _σ < θ_ adjustment is expected to take place over a shorter period than in any other situation.

From previous section findings we have that at steady state, neither capital intensity nor self-employed earnings are affected on an individual basis. This implies that selfemployed individuals already in place at the occurrence of the shock, do not modify their capital stock as indicated by equations (3’) and (4’). Nevertheless, they increase their production as the initial real effect of the technological shock is positive. They return progressively to their pre-shock level of production as migration takes place.

# **Shift in Preferences toward Non-Tradables**

On impact, the real exchange rate appreciates, relative informal earnings rise, and the shadow value of capital increases. This attracts new entrepreneurs to the sector, expanding non-tradables supply and the relative price of non-tradables begins to return to its initial, relative productivity determined level. Again the adjustment is more rapid when _σ > θ_ and slowed in the opposite case. This represents an important case where both _wT / wN_ and _LT / LN_ fall concomitant with an exchange rate depreciation, and then an appreciation.

# **Negative Formal/Tradables Productivity Shock with Formal Sector Wage Rigidities**

Because of downward wages rigidity, consumption levels are not affected on impact and _p_ is not affected. However, released labor from the formal sector now flows to the non-tradable sector increasing its production, driving down _p,_ and reducing average self-employed earnings. At the end of the first period, the tradables labor market is reequilibrated and outflow of capital again equalizes the marginal productivity of capital to 18
the world interest rate. For those self-employed already in place, the fall in _p_ observed along the transition path, leads to capital decumulation. This effect is stronger in the case where _σ > θ_ and _θ_ > _<u>φ</u> se_ − _<u>γ</u>_ . In the symmetric case, we would still observe capital _γ_ withdrawal from the informal sector but of a smaller size. Indeed, the non-tradables’ relative price can rise on impact<sup>7</sup> , which slows down the path of capital decumulation in that sector. As a consequence, average earnings in the self-employment sector increase in the long run.

Nevertheless this result should be regarded as a particular case. In the general case, those workers “forced” to become self-employed, even when on their optimal production path, are stuck in a position with earnings below the formal wage. Along the transition towards steady state, average earnings in the informal sector have fallen relative to the formal salary while the size of self-employment has increased.

# **3. Methodology and Empirical Results:**

The analysis above makes two important points. First, using very standard models, it is clear that theory implies relationships between our labor market variables and the real exchange rate. Second, independent of skill heterogeneity and adjustment costs, under no conditions can we generate a counter movement of relative sector sizes and earnings in the absence of a wage rigidity. This implies that any appreciation attributed to inertia or rigidities in the formal sector must be associated with opposing movements in sector size and earnings. Third, even in the absence of wage rigidities, the correlations between the real exchange rate and labor market variables will depend on the relative magnitudes of intra and intertemporal elasticities.

In this section, we use the multivariate Johansen approach (1988) to explore possible cointegration relationship in these three variables with the aim of establishing the degree of dualism in the labor market and driving force behind exchange rate

> 7 This is verified if _α N_ > 1 − _<u>γ</u>_ 1 − _γ_ − _φ se_

19
movements Mexico, Brazil and Colombia.<sup>8,9</sup> Although cointegration is sometimes given the economic interpretation of capturing “long run” relations, fundamentally it is a statistical relationship existing among non-stationary series. In our case, both relative sector sizes and the real exchange rate can plausibly be posited as I(1) and they always appear to be so in the analysis. Changing aggregate skill levels postulated in section 2 suggest no reason to assume the wages ex ante to be I(0) and even if they were, a slow adjustment process could lead to apparent non-stationary behavior within the sample analyzed.<sup>10</sup> We then use recursive cointegration estimation techniques to explore the stability of the cointegration space over time and we apply LR-test to test hypotheses on the coefficients of the cointegration vectors in order to provide empirical evidence to test the various predictions of the model and to extract some conclusions about labor market rigidities and the source of appreciations in the three countries.

# **3.1 Data**

We use quarterly data for Mexico, Brazil and Colombia on the log-transformed real exchange rate, _p_ , the wage ratio of formal over self-employed workers, _WT/WN_ , and the ratio of the absolute size of formal over the self-employed sector, _nT/nN_ . Real exchange rates where taken from IFS, all labor market data were derived from national labor force surveys ( _Pesquisa Mensual do Empreg_ o for Brazil, _Encuesta Nacional de Empleo Urbano_ for Mexico and _Encuesta Nacional de Hogares_ , Colombia). The work force was defined as only the active male population. Because we are interested in informal workers and not educated workers opening consulting firms, all workers with more than 12 years of education were dropped from the sample.

We use as a definition of informal self-employment either that size is under 6 total workers, or that the worker is not registered with social security. We might also,

> 8 The statistical concept of a long-run equilibrium underlying cointegration analysis refers to the existence of a _stationary_ relationship among two or more _non-stationary_ time series.

> 9 Appendix B contains a brief overview of the multivariate cointegration approach of Johansen (1988). 10   Theoretically, however, it is legitimate to include an I(0) variable in the cointegrating relationship, although we would expect at least one cointegrating vector to emerge that captures simply the stationary series.  In practice, these series were never stationary across our sample and the problem was moot.

20
following Loayza (1995) focus on evasion of taxes or other regulations although in practice these different dimensions of “informality” are highly correlated and would probably change the analysis little.<sup>11</sup> In viewing the data, it is worth mentioning that even if remuneration between the two sectors were equilibrated, these would include all monetary and non-monetary remuneration (independence, benefits foregone, taxes avoided, implicit returns to capital, etc.). Thus, even though in most of the countries the informal self-employed appear on average to earn higher incomes this does not account for unobservable types of remuneration.<sup>12</sup>

# **3.2 Empirical Analysis**

We estimate separate VAR models for Mexico, Brazil and Colombia. The VAR models include a constant in the cointegration space, different lags for _p_ , _WT/WN_ and _nT/nN_ as well as country specific dummies and these specifications prove sufficient to produce random errors.<sup>13</sup> The λ trace tests indicate one significant cointegrating vector in all three models (Table 2). Normalizing the cointegration vectors on the 1<sup>st</sup> element, yields the following estimates for the β s (Table 3) and _α_ s (Table 4)<sup>14</sup> : The adjustment coefficient of ∆ _nT/nN_ is strongly insignificant for Mexico and borderline significant in the case of Brazil and Colombia. This indicates weak exogeneity of _nT/nN_ and thus provides evidence that _nT/nN_ is driving the system, while _WT/WN_ and _p_ are adjusting to disturbances in the long-run equilibrium.

> 11   Levenson and Maloney (1998) argue that formality, conceived as participation in social institutions (social security, judicial, taxes payment, etc)  itself may be largely incidental- social participation in general can be seen as a normal good in the production function that is more desired as firms grow.  With growth firms may embrace

> 12 See Maloney (1999) for more detail.

> 13 The model specifications for the three models are presented in Tables 8 and 9 in the Appendix along with tests for long-run exclusion, stationarity and weak-exogeneity (Table 7). All variables appear to be nonstationary and the diagnostics on the residuals of the system show the absence of autocorrelation and indicate normality. A sensitivity analysis for different lag lengths and with and without dummies further indicated robustness of the findings.

> 14 Figures 14 to 16 display the recursive trace statistics and indicate stability of the unrestricted cointegration space.

21
# **3.3.1 Identifying the Cointegration Space**

Identifying the cointegration space in the present case translates to sequentially impose restrictions on the cointegration vectors guided by the theoretical considerations of the previous sections. We begin by putting no restrictions on the exchange rate, but focus purely on the evolution of the two labor market variables. Effectively, referring to Table 1, we are testing between the first division between markets with or without wage rigidities. A test that a rise in relative formal employment is accompanied by a rise in relative formal wages ( _integrated sector size/wage movement_ ), is implemented by restricting the coefficient of the relative formal wage to –1. A hypothesis test that a relative rise in formal employment is accompanied by a decline in relative formal wages ( _segmented sector size/wage movement_ ), is implemented by restricting the coefficient of _WT/WN_ to 1.

Table 5 presents the results for the whole sample. For Mexico, the test of integrated markets can be strongly rejected while the test for segmentation cannot be rejected. For Brazil, the hypothesis of integration cannot be rejected and the hypothesis of segmentation is rejected at the 1% level. In Colombia, the hypothesis of segmentation can borderline not be rejected but a hypothesis of integration across the whole period can be.

However, recursive cointegration tests of the stability of the cointegration space suggest in all cases the possibility of different relationships for subperiods, consistent with the idea that nominal rigidities may bind in some periods and not in others. Operationally, the trace statistics are calculated initially over a base period and then recalculated for every new observation added until the end of the sample is reached.

**_Mexico:_** Figures 4 and 6 show, for Mexico, the test of the hypothesis that the full sample estimate of<sup>_β_</sup> , with the over-identifying restrictions (1, 1, *, *)<sup>15</sup> imposed, is in the space spanned by _β i_ in each sub-sample. The test-statistics have been scaled by the 2 _χ_ 95% quintile in the distribution such that unity corresponds to the 5% significance level. Since the plot of the test statistics is above unity prior to roughly 1995,  the hypothesis of segmentation is only accepted from 1995 onwards.  A recursive test of the hypothesis of integration (expressed in vector form as (1,-1, *, *)) is plotted in Figures 5

> 15 A * indicates that a variable has been left unrestricted.

22
and 7 and, as Figure 1 suggested, cannot be rejected prior to 1995. These tests confirm that in the recovery period leading up to 1995, the rise in the informal sector was largely due to greater attractions of the sector itself, and not to labor market rigidities.

**_Brazil:_** For Brazil, the data cannot reject integration across the entire period although there are some sub-periods where it is difficult to reject segmentation as suggested by  Figure 9.

**_Colombia:_** The recursive stability test for Colombia strongly supports the hypothesis of a segmented labor market post 1995 onwards and never supports the view of integration for any subsample.  This supports the view that the Colombian labor market does have some formal sector rigidities which were intensified in the post 1995 period.  In particular, the  rise of the real minimum wage across the period, concomitant with a collapse in formal sector activity due, among other factors, a financial crisis would correspond very well to the story that emerges.

# **3.3.2 Further Restrictions on the Cointegration Space**

In the previous section we have left the real exchange rate unrestricted. As our theoretical model shows that a real exchange rate appreciation (depreciation) can be accompanied by an increase (decrease) in the relative informal sector size as well as an increase (decrease) in relative informal wages, further empirical support for our model would be to identify a vector of (1, -1, -1, *) in the cointegration space. We limit our analysis to the cases of Mexico and Brazil since we cannot reject segmentation in the labor market.

For Mexico, we limit our estimation period in this section from the post 1987 recession to the pre Peso crises (1988:01 to 1994:03). We cannot reject the hypothesis test of (1, -1, -1, *) at a conventional level of significance, that is, the real exchange rate appreciation in Mexico prior to the Peso crisis was accompanied by an increase in the relative informal sector size and an increase in relative wages. (Table 6). This is consistent with a positive demand shock to non-tradables, perhaps the boom in construction during the period, driving the exchange rate in the short to medium term, and is inconsistent with the inertial view. Although the cointegration relationship only falls apart after 1995, the cumulative nature of the statistics may hide an earlier 23
disequilibrium and the relationship does become less stable as we approach the crisis, consistent with the graphical evidence of segmentation appearing in 1992. In this sense, Carstens and Gil-Diaz were correct that the appreciation was caused by real factors, but Dornbusch and Werner were correct that a nominal depreciation was in order in 1994.

For Brazil we could not reject positive comovement of the relative sector size and the relative wages over the whole sample (see Table 5), though this relationship appears to be stable only from around 1990 onwards (see Figure 8). A test of a coefficient vector of (1, -1, -1, *) being part in the cointegration space is accepted at the 5 % level of significance for the whole sample. We cannot therefore reject the hypothesis that the real exchange rate in Brazil is, again, driven perhaps by a positive demand shock to nontradables. A recursive plot of the cointegration tests of (1,-1,-1,*) with the less restrictive test of (1, -1, *,*) of the last section superimposed is shown for the case of Brazil in Figures 12 and 13. Interestingly, both coefficient restrictions are stable from around 1990 onwards although the increasing instability of the identified cointegration relationship and, visually, the divergence of the two labor series starting in 1995-96 may suggest a scenario similar to that for Mexico.

# **4. Conclusion:**

This paper has offered an integrated view of LDC labor market and exchange rate behavior. Modifying the Rogoff-Obstfeld small economy model to include heterogeneous entrepreneurial ability and credit constraints to entering self-employment, it first generates a set of hypotheses about the comovement of relative sector sizes and earnings and the real exchange rate.

These patterns of comovement are then tested in a cointegration framework and we find two provocative results. First, there is strong evidence in favor of the formal and informal sectors being integrated, rather than dual labor markets as customarily envisaged: there is often strong comovement between relative sector sizes and earnings. This offers strong evidence in favor of the idea of viewing informal self employment primarily as a voluntary non-regulated non-tradable entrepreneurial sector. Much of the 24
increase in informality across the 1990s appears explainable by an increase in the relative attractiveness of the sector.

Second, we can explain the appreciations of the peso in Mexico from 1988-1991 and the Brazilian Real from 1993-1996 without recourse to inertial stories. Put differently, in both cases, a positive demand shock to non-tradables appears as a more likely explanation than one based on labor market rigidities. Graphical evidence suggests that similar “equilibrium” phenomena drove the initial appreciations of the Chilean Peso from 1978-1992 and Argentine Peso from 1988-1994. Colombia is the only case where there is evidence of labor market rigidities that may contribute to exchange rate appreciation. That said, in almost all cases, there is a suggestion that, although the initial appreciations were not driven by rigidities, they were nonetheless unsustainable and that the nominal adjustments were eventually required.

25
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# **Appendix A: Migration Timing**

Because we assume that the self-employed individual, who is willing to move to the wage-work sector, has to disinstall the capital she borrowed before moving, migration occurs whenever, Labor could adjust within the first period following the shock. However, because individuals are non homogenous when producing in the informal sector, the optimal time for leaving the latter may differ across workers.

The Left Hand Side of the above expression is increasing with entrepreneurial ability. Namely, more able individuals earn more than less able ones. Then the opportunity cost of migrating to the formal sector at time t, without considering the direct migration costs corresponding to capital disinstallation, is increasing in the level of entrepreneurial capability. The last term of the RHS, which represents the present value of labor earnings in the formal sector is identical for all individuals at time t. However, the first term of the RHS is likely to be different. The sign of the partial derivative of the latter with respect to _φ_<sup>_j_</sup> is given by If the above expression appears to be positive, that would imply that the cost of migrating to the formal sector at time is increasing with the level of entrepreneurial capability. If this is the case, then the total cost of migration is unambiguously increasing with _φ_<sup>_j_</sup> . As a consequence we may expect more able entrepreneurs to postpone their migration towards the wage sector with respect to less able ones.

In the case of a shock leading to an expansion of the informal sector, migration can occur within the first period following the shock, even though capital accumulation may take more than a period because of installation costs. Individuals migrate at the end of period _s_ whenever 29
Following arguments similar to those presented above, we can infer that more able entrepreneurs will leave the formal sector first, in order to "cash in" the expected earnings differential the soonest.

30
# **Appendix B: The Multivariate Cointegration Analysis of Johansen**

The Johansen procedure allows us to test for cointegration in a multivariate system./ Starting from an unrestricted vector autoregressive model (VAR), the hypothesis of cointegration is formulated as a hypothesis of reduced rank of the long run impact matrix Π (Johansen, 1988, Johansen and Juselius, 1990). The VAR is generated by the vector zt, which defines the potential endogenous variables of the model. Taking first differences of the variables, the VAR can be transformed into an error correction model ∆ z t = Γ ∆ 1 z t − 1 + ... +Γ k − 1 ∆ z t − k = 1 + Π z t − k + ψ Dt + ε t , ε t ~ IN(0, Σ ) where the estimates of Γ _i_ = − ( _I_ − _A_ 1 − ... − _Ai_ ), ( _i_ = 1,..., _k_ − )1 describe the short run dynamics to changes in zt and Π = − ( _I_ − _A_ 1 −− ... _Ai_ ) captures the long run adjustments and _D_ contains deterministic terms.

Cointegration occurs in the case of reduced rank of Π . Only if the rank is reduced (r<n) is it possible to factorize Π into Π ( = αβ ') where _α_ denotes the adjustment coefficients and _β_ the cointegration vectors. The cointegration vectors _β_ have the property that _β_ ' zt is stationary even though _zt_ itself is non-stationary.

If the rank is reduced it is possible to interpret the VAR in first differences as a vector error correction model and to obtain estimates of _α_ and _β_ via the reduced rank regression. Since the rank of Π is equal to the number of independent cointegration vectors and the rank of Π is also equal to the number of non-zero eigenvalues, the test of cointegration thus amounts to a test for the number of non-zero eigenvalues. The trace statistics, λ trace, is a non-standard distributed likelihood-ratio test, which is commonly used to determine the number of cointegration vectors, (Johansen, 1988). The trace statistic tests the null hypothesis that there are at most _r_ cointegration vectors: _H0:_<sup>_λ_</sup> _i_<sup>=0, for i = r+1,..n</sup> where only the first _r_ eigenvalues, _λ_ , are non-zero against the unrestricted hypothesis that r = n.<sup>16</sup>

> 16 The null hypothesis of at most _r_ cointegration vectors implies that there are _n-r_ unit roots and, theoretically, _n-r_ zero eigenvalues. This is because the hypothesis of cointegration is formulated as the ' ' reduced rank of Π = _αβ_ and the full rank of _α_ ⊥<sup>Γ</sup><sup>_β_</sup> ⊥ , where _α_ and _β_ are _n_ × _r_ matrices and _α_ ⊥ and

31
It is now common practice to try to identify the cointegration space and we follow the approach outlined in Johansen (1992) and Johansen and Juselius (1994). In their approach, a system is exactly or just identified if _k = r_ - 1 restrictions are placed on each cointegration vector and the rank condition for generic identification is satisfied.<sup>17</sup> _β_ ⊥ are n × _(n-r)_ matrices orthogonal to _α_ and _β_ . This allows us then to distinguish between _r_ cointegrating I(0) relations and n _-r_ non-cointegrating I(1) relations.

> 17 In the case of two cointegration vectors generic identification requires that the rank condition _rank(Ri' Hj)_ ≥ 1 for _i_ , _j_ = 1, 2 and _i_ ≠ _j_ is fulfilled. Where _Ri_ is the orthogonal complement of _Hi_ , such that _Ri_ and _Hi_ are both of full rank and satisfy the conditions _Ri 'Hi_ =0, _Ri' β_ i = 0 and _β_ i = _Hi_ φ i . _Ri_ are _p ∗ k_ matrices and _Hi_ are _p ∗ s_ matrices with _k + s_ = _p_ .

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# **Table 1**

|**Short /**<br>**Medium Run**||**_∆ ( wT / wN ) _**|**_∆( LT / LN ) _**|**_∆p _**|
|---|---|---|---|---|
|**_∆AT > 0_**||> 0|> 0|> 0|
|**_Flexible Wage_**<br>**_∆AN > 0_**||< 0|< 0|< 0<br>(undersh.)|
|**_∆γ< 0_**||< 0|< 0|0 ><br>(oversh.)|
|**_Wage Rigidities_**<br>**_∆AT < 0_**|_A_<br>><br>_θ_|> 0|< 0|< 0|
||_A_<br><<br>_θ_|< 0|< 0|< 0, > 0|
|**Long Run**|||||
|**_∆AT > 0_**||> 0|> 0|> 0|
|**_Flexible Wage_**<br>**_∆AN > 0_**||< 0|< 0|< 0|
|**_∆γ< 0_**||< 0|< 0|0|
|**_Wage Rigidities_**<br>**_∆AT < 0_**|_A_<br>><br>_θ_|> 0|< 0|< 0|
||_A_<br><<br>_θ_|< 0|< 0|< 0|
|_γ_<br>_γ_<br>_φ_<br>−<br>=<br>_se_<br>_A_|||||

33
# **Table 2**

|||Mexico|Brazil|Colombia|||
|---|---|---|---|---|---|---|
|Null|Alternative|Lag: 4|Lag: 4|Lag: 2|95%|90%|
|Hypothesis|Hypothesis|With Constant|With Constant|With Constant|Critical Value|Critical Value|
|λ tracetest|||||||
|r = 0|r > 0|55.80<sup>*</sup>|40.56<sup>*</sup>|36.45<sup>*</sup>|35.10|31.88|
|r≤1|r > 1|12.08|19.68|6.43|20.17|17.79|
|r≤2<br>|r > 2<br>|4.04<br>|6.05|1.69|9.10|7.50|

<u>*Rejection at the 5% level of significance 18</u>

# **Table 3**

||**Mexico**|**Brazil**|**Colombia**|
|---|---|---|---|
||_β_|_β_|_β_|
|nT/nN|1.000|1.000|1.000|
|WT/WN|0.969|-0.637|2.846|
|P|0.976|-0.356|-2.776|
|Constant|-2.803|0.101|-4.811|

# **Table 4**

||**México**||**Brazil**||**Colombia**||
|---|---|---|---|---|---|---|
||_~~α~~_|t-stat.|_~~α~~_|t-stat.|_~~α~~_|t-stat.|
|∆nT/nN|0.028|0.531|-0.012|-0.212|-0.213|-1.750|
|∆WT/WN|-0.088|-3.393|0.572|3.841|-0.057|-1.961|
|∆p|-0.250|-6.457|0.281|2.381|0.088|6.009|

_Note:_ ∆ indicates a variable in first differences.

**Table 5: Summary of Hypothesis Tests (whole sample)**

||**Mexico**|**Brazil**|**Colombia**|
|---|---|---|---|
|**Integrated**|2<br>_χ_ (1) = 15.42|2<br>_χ_ (1) = 1.87|2<br>_χ_ (1) = 16.96|
|**(1,-1,*,*)**|p=0.00|p = 0.17|p = 0.00|
|**Segmented**|2<br>_χ_ (1) = 0.04|2<br>_χ_ (1) = 7.26|2<br>_χ_ (1) = 5.13|
|**(1, 1,*,*)**|p=0.84|p=0.01|p = 0.02|

**Table 6:** Test of (1,-1,-1,*) being part of the cointegration space in different subsamples

||México|Brazil|
|---|---|---|
|Sample:|**1988:01– 1993:04:**|**1982:01 – 1998:02:**|
||2<br>_χ_ (2) = 4.35 , p=0.11|2<br>_χ_ (2) = 5.06, p = 0.08|

18 The Reinsel-Ahn small sample corrected critical value at the 10% level is 43.13 for Mexico, 39.53 for Brazil and 36.32 for Colombia).

34
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**Figure 2:** Self-employment and gradual capital adjustment

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**Figure 12: Brazil   (1,-1,*,*) versus (1,-1,-1,*) restrictions**

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**Figure 13: Brazil   (1,-1,*,*) versus (1,-1,-1,*) restrictions [without dummies]**

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38
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# **Model Specification Tests for the VAR models:**

**Table 7: Tests for Long-Run Exclusion, Stationarity and Weak Exogeneity**

|||Méxic|o:||Brazil|||Colom|bia||
|---|---|---|---|---|---|---|---|---|---|---|
|Model Specification:||Lag len|gth: 4||Lag Le|ngth: 4||Lag Le|ngth: 2||
|||Dumm|ies: 1994Q4|(Peso Crises)|Dumm|ies: 1994Q|2|Dummi|es: 1992Q2||
||||||(Curre<br>Cruzer|ncy conver<br>io Real to R|sion from<br>eal)|(large a<br>betwee|dverse mo<br>n 1992Q1 a|vements in nT/nN<br>nd 1992Q3)|
|Test for Long-Run E|xclusion:|LR-Test|(<br>)<br>(<br>2 _r_<br>_χ_<br>)||||||||
|R<br>dgf|)5<br>(<br>2<br>_χ_|nT/nN|_WT/WN_|_P_<br>_C._|_nT/nN_|_WT/WN_|_p_<br>_C._|_nT/nN_|_WT/WN_|_p_<br>_C._|
|1<br>1|3.84|16.97|10.54|26.06<br>12.6|<br>7.44|6.87|4.51<br>0.3|<br>21.58|11.25|12.81<br>20.6|
|2<br>2|5.99|18.67|12.11|27.82<br>14.4|<br>13.27|10.16|4.85<br>1.1|<br>23.38|13.13|15.27<br>23.1|
|Test for Stationarity:<br>|LR-Test|(<br>(<br>2<br>_p_−<br>_χ_<br>|)<br>_r_<br>)<br>||||||||
|r<br>dgf|)5<br>(<br>2<br>_χ_|nT/nN|WT/WN|P|nT/nN|WT/WN|p|nT/nN|WT/WN|p|
|1<br>3|7.81|37.96|38.52|35.22|11.61|11.85|8.35|28.18|27.76|28.96|
|2<br>2|5.99|2.74|3.28|2.87|3.65|4.28|0.77|2.91|2.50|4.10|
|Test for Weak-Exoge<br>|neity: L|R-Test (<br>_χ_<br>|)<br>(<br>2 _r_<br><br>)<br>||||||||
|r<br>dgf|)5<br>(<br>2<br>_χ_|nT/nN|WT/WN|P|nT/nN|WT/WN|p|nT/nN|WT/WN|p|
|1<br>1|3.84|0.57|12.06|21.22|0.28|6.29|2.48|2.83|3.33|24.83|
|2<br>2<br>**Table 8**|5.99<br>**: Mult**|1.92<br>**ivariate**<br>|12.49<br>**Statistic**<br>|22.03<br>**s (Residual**|7.90<br>**Analysi**<br>|11.97<br>**s)**|2.50|3.00<br>|5.48<br>|25.95|
|||**Méxic**|**o:**||**Brazil**|||**Colomb**|**ia**||
|_Information Criteria:_|||||||||||
|SC||-15.90|||-15.40|||-13.37|||
|HQ||-16.95|||-16.21|||-13.85|||
|**Autocorrelation**|||||||||||
|Ljung-Box:||2<br>_χ_<br>(63)|= 74.3, p -v|alue = 0.16|2<br>_χ_<br>(11)|= 140.8, p-|val. = 0.01|2<br>_χ_<br>(99)|= 129.5, p-|value = 0.02|
|LM(1)||2<br>_χ_<br>(9)|= 7.09, p-va|lue = 0.63|2<br>_χ_<br>(9) =|16.9, p-va|lue = 0.05|2<br>_χ_<br>(9) =|7.6, p –val|ue = 0.58|
|LM(4)||2<br>_χ_<br>(9)|= 9.7, p-val|ue = 0.38|2<br>_χ_<br>(9) =|4.4, p-val|ue = 0.88|2<br>_χ_<br>(9) =|7.9, p –val|ue = 0.54|
|_Normality_||2<br>_χ_<br>(6)|= 9.14, p-va|lue = 0.17|2<br>_χ_<br>(6) =|10.1, p-va|lue = 0.12|2<br>_χ_<br>(6) =|31.5, p-val|ue = 0.00|

**Table 9: Univariate Test Statistics (Residual Analysis)**

||**Mexico**|||**Brazil**|||**Colom**|**bia**||
|---|---|---|---|---|---|---|---|---|---|
||nT/nN|WT/WN|<sup>p</sup>|nT/nN|WT/WN|<sup>p</sup>|nT/nN|WT/WN|<sup>p</sup>|
|**Skewness**|0.8483|-0.4627|0.0814|-0.3984|0.1036|0.7109|0.2750|-0.1402|-0.014|
|_Kurtosis_|4.1049|3.3300|3.2463|2.6781|2.2688|3.4843|5.8000|4.3100|3.8161|
|_ARCH_|2.4730|0.8230|9.9090|11.1260|1.2360|2.9560|4.3170|2.7780|3.3060|
|_Normality_<br>|5.7730|2.2730|1.4720|2.4550|1.2400|5.6900|19.6240|7.6740|4.4030|
|_R_<sup>_2_</sup>|0.2330|0.5250|0.8130|0.3760|0.4470|0.4980|0.4050|0.3840|0.4110|

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