The Elasticity of the Migrant Labour Supply: Evidence from Temporary Filipino Migrants

Abstract The effect of immigration on host and origin countries is mediated by the way migrants take their labour supply decisions. We propose a simple way of integrating the traditional random utility maximisation model used to analyse location decisions with a classical labour demand function at destination. Our setup allows us to estimate a general upper bound on the elasticity of the migrant labour supply that we take to the data using the evolution of the numbers and wages of temporary overseas Filipino workers between 1992 and 2009 to different destinations. We find that the migrant labour supply elasticity can be very large. Temporary migrants are very reactive to economic conditions in their potential destinations.


Introduction
As long as country of birth represents the largest source of inequality in the world (Milanovic, 2005), it is only natural that individuals try to improve their living conditions by changing their country of residence. The extent to which they do so is going to affect welfare in general, and the labour market in particular, both at their origin country and at their chosen destinations. 1 Furthermore, the temporary admission of foreign workers, as opposed to permanent immigration, has been advocated by Pritchett (2006) as a way of 'breaking the gridlock' on the mobility of labour across borders, which could contribute both to alleviate poverty and to reduce the inequalities documented by Milanovic (2015).
The objective of our paper is to analyse how such a market for temporary migrant labour reacts to variations in economic conditions at destination through adjustments in the labour supply of migrants. Do foreign workers admitted on a temporary basis earn higher wages in good economic times, or is the labour market equilibrium restored only through an increase in the scale of temporary migration flows? Providing a convincing empirical answer to these questions, which have already been analysed by McKenzie, Theoharides, and Yang (2014), requires dealing with a key analytical challenge, namely the interaction of the labour supply and the labour demand in each possible location. It is now well established in the literature that ignoring the threat posed by correlated variations in the labour market conditions across destinations can produce biassed estimates (Bertoli & Fernández-Huertas Moraga, 2013, a potentially relevant threat for the analysis proposed by McKenzie et al. (2014) given the time and geographical composition of their sample of destinations for temporary Filipino migrants.
The contribution of this paper is to show how to deal with this analytical challenge through the introduction of the random utility maximisation (RUM) model in a canonical analysis of the functioning of the labour market. We reveal how the gravity elasticities derived from the RUM model cannot be directly interpreted as labour supply elasticities since they are affected by the evolution of labour demand. However, as long as the component of labour demand idiosyncratic to each destination country can be empirically isolated, a general upper bound on the migrant labour supply elasticity can be computed by dividing the elasticity of migration flows with respect to labour demand shocks by the elasticity of migrant wages to labour demand shocks. In order to identify destination-specific labour demand shocks, we propose using multifactor error models (Bai, 2009;Pesaran, 2006) which allow us, for example, to clean the estimated effect of the evolution of the GDP in a given country from its spurious correlation with the evolution of the GDP in alternative destinations for the migrants.
We apply this strategy to the computation of the elasticity of the migrant supply of temporary Filipino workers. To this end, we draw on panel data on the number of overseas Filipino workers and on their wages to 54 destination countries between 1992 and 2009 collected by the Philippine Overseas Employment Administration (POEA) and which have been processed by McKenzie et al. (2014).
We estimate that the upper bound on the labour supply elasticity of temporary Filipino workers is as large as 8.57. To our knowledge, this is the largest ever estimated labour supply elasticity and only some of the estimates in Kleven, Landais, Saez, and Schultz (2014) for professional footballers (elasticity of three for top quality players) come anywhere close to it. 2 A common feature of the football market and the migrant labour market that we analyse is the relevance of mobility restrictions, on the side of the demand for football players, and on supply itself in the case of temporary migrant workers. We interpret this large elasticity as proof of the ability of prospective migrants to choose among many alternative competing destinations, which is contrary to the image of temporary workers taking whatever job they are offered.
We show that both the wages and the number of temporary Filipino migrants are pro-cyclical. Dealing with the threat to identification posed by the correlated variations in macroeconomic conditions across destinations proves to be crucial for obtaining an unbiased estimate of the responsiveness of the scale of temporary migration and of the wages of Filipino migrants with respect to real GDP at destination, our source of destination-specific demand shocks. When this threat to identification is not dealt with, the two estimated coefficients are biassed in opposite directions, as predicted by a standard market-clearing model for temporary migrant labour. Furthermore, the bias is larger for the estimated coefficient of real GDP in the migration rather than in the wage equation, a finding that can be accounted for by an elastic labour demand for temporary migrant labour. If we ignore the correlation in GDP shocks across destination countries, which gives rise to what Bertoli and Fernández-Huertas Moraga (2013) have termed multilateral resistance to migration bias, our estimated elasticity goes down to 3.34.
While our labour supply elasticity estimates are large from the point of view of the literature using tax rate changes to estimate labour supply functions, they are very similar to the reduced form findings from the estimation of international migration gravity models (Beine, Bertoli, & Fernández-Huertas Moraga, 2016). With respect to McKenzie et al. (2014), we reproduce their estimate on the migration equation but consider it downward biassed because they ignore the confounding influence of the effect of GDP in alternative destinations. Contrary to them, we find a positive and significant relationship between GDP and migrant wages at destination.
Our paper is also related to the growing literature analysing emigration from the Philippines, one of the main origin countries for emigration in the world. This goes back to the classic papers by Dean Yang (Yang, 2006(Yang, , 2008, whose tradition has recently been continued by the already cited McKenzie et al. (2014), Theoharides (2015), Cortes (2015) or Licuanan, Omar Mahmoud, and Steinmayr (2015).
The rest of the paper is structured as follows: Section 2 discusses the theory that underlies the estimation of the labour supply elasticity, and Section 3 briefly introduces the data. Then, Section 4 summarises the econometric results and Section 5 draws the main conclusions.
The elasticity of the migrant labour supply 1823

Theoretical framework
We build on a simple labour market model to discuss the conditions under which it is possible to recover empirically the labour supply elasticity of temporary Filipino migrants. Specifically, we focus on the implications of different distributional assumptions on the unobserved component of the underlying static RUM model describing the location-decision problem faced by potential migrants. 3

The market for temporary migrant labour
Consider a simple setup describing the labour market equilibria for temporary migrants in j ¼ 1; . . . ; N destination countries at different points in time t ¼ 1; . . . ; T . 4 The inverse demand function D j y jt À Á for temporary migrant labour in each destination j at time t depends on the real GDP y jt and on the number of migrants m jt that move on a temporary basis from the origin country to destination country j at time t. Let w t ¼ w 0t ; w 1t ; . . . ; w Nt ð Þ 0 and c t ¼ 0; c 1t ; . . . ; c Nt ð Þ 0 be two vectors that gather migrants' wages and bilateral migration costs at time t. 5 The supply of temporary migrant labour can be derived from an underlying static random utility maximisation model that describes the location-decision problem faced by potential migrants, which represents the standard microfoundation of a gravity equation for migration (Beine et al., 2016). Specifically, the utility attached to each location j at time t can be decomposed into a deterministic component of utility that depends on the logarithm of the wage w jt and on bilateral migration costs c jt , and an individual-specific stochastic component ijt . Assuming that ijt follows an independent and identically distributed Extreme Value Type-1 distribution, it can be shown (see McFadden, 1974) that the expected value of the labour supply m jt depends on the wage w jt , on bilateral migration costs c jt , and on the expected value from the choice situation that potential migrants face at time t (Small & Rosen, 1981), which is a function of w t and c t . Under the assumption that the bilateral migration costs follow an identical time profile, the labour supply for each destination country j at time t depends on a country-specific constant capturing time-invariant shifts in wages and migration costs, and on common shocks that vary only over time but not across destinations. Figure 1 plots the (logarithmic transformation of) the inverse demand function D j y jt À Á and the inverse supply function S j w t ; c t ð Þ for migrant labour in destination j described above in the [ln(m jt ), ln(w jt )] space. It shows that it is possible to recover the labour supply elasticity as long as changes in labour demand independent from changes in labour supply in other destinations can be isolated. This is explored in the next subsection.

Reduced form regressions
From the model sketched above, it is straightforward to derive the following reduced-form equations that allow to identify the scale of migration and the elasticity of migrants' wages with respect to the real GDP at destination 6 : and where w jt in Equation (2) is either the mean or the median wage earned by the m jt migrants and d j and d t are two vectors of destination and time dummies. Destination dummies d j control for the dyadic time-invariant component of migration costs, and for the destination-specific time-invariant level of the demand for temporary migrant labour. Time dummies d t control for the factors that exert a timevarying influence on lnðm jt Þ and lnðw jt Þ for any j ¼ 1; . . . ; N, such as demographic factors at origin or variations in macroeconomic conditions in all potential destinations and at origin. It is then immediate to recover an estimate of the labour supply elasticity parameter as 7 : β ¼ψ m ψ w : (3)

Correlated variations in real GDP across destinations
The evolution of macroeconomic conditions across alternative destinations might be (positively or negatively) correlated; specifically, a pattern of predominantly positive correlations entails that a rightward shift of the curve D j y jt À Á would be associated with a leftward shift of the curve S j w t ; c t ð Þ, as potential migrants would face higher wages in alternative destinations. This would produce an upward bias in the induced variation in migrants' wages, and a downward bias in the effect on the scale of migration flows to j, if the correlated shift in the migrant labour supply is not controlled for, as depicted in Figure 2. This, in turn, would imply that b β would be downward biassed.
However, this does not pose a serious threat to identification under the distributional assumptions à la McFadden (1974), as these entail that the inverse supply curves for different destinations are The elasticity of the migrant labour supply 1825 identical up to a constant. Hence, this confounding effect is fully controlled for in the estimation of Equation (1) and Equation (2) through the inclusion of time dummies d t . 8 This also applies under the distributional assumptions of Ortega and Peri (2013), which allow for unobserved individual heterogeneity in the preferences for migration, as the function that describes the influence of the attractiveness of alternative destinations on the migrant labour supply is still invariant across destinations.
Correlated variations in macroeconomic conditions across destinations pose a more serious threat to identification under more general distributional assumptions, which allow for differences in the elasticities of substitution across different pairs of destination countries (Bertoli & Fernández-Huertas Moraga, 2013, and that can be motivated by an incomplete specification of the deterministic component of location-specific utility. 9 Imagine, for instance, that potential Filipino migrants perceive South Korea (j) and Malaysia (h) as close substitutes, while the United States (k) represent a distant substitute for both destinations: an increase in the attractiveness of Malaysia induces a proportional reduction in the supply of Filipino migrants to South Korea at the contracted wage w jt that exceeds the corresponding proportional reduction in the supply of Filipino migrants to the United States at the contracted wage w kt . In other terms, the inverse supply functions S j w t ; c t ð Þand S k w t ; c t ð Þ do not follow an identical time profile over time, and the use of time dummies d t no longer suffices to control for the shifts over time of the inverse supply functions.
If this threat is not adequately controlled for, then the error terms of Equation (1) and Equation (2) will be serially correlated, as the attractiveness of alternative destinations is likely to evolve slowly over time, and correlated across destinations if some destination countries have similar sets of destinations that are perceived as close substitutes to each of them, for example, Malaysia might be a close substitute for both South Korea and Indonesia. The non-spherical nature of the error term can produce inconsistently estimated standard errors, and, more importantly, it gives rise to an endogeneity problem for ln(y jt ) when the economic shocks in destination j are correlated with the economic shocks in other destinations that are close substitutes to j. This can create a serious threat to identification, as shifts in the labour demand curve in destination j can be correlated with shifts in the labour supply due to changes in the attractiveness of other destinations. Specifically, if there is a positive correlation in the evolution of economic conditions in destinations that are regarded as close substitutes, then a rightward shift in the labour demand curve is associated with a leftward shift in the supply curve, leading to a downward bias in the estimate of ψ m and to an upward bias in the estimate of ψ w . This situation is depicted in Figure 2. The relative importance of the bias on the two coefficients of interest depends on the elasticity of the labour demand schedule. If the labour demand is flatter, and hence more elastic, then the correlation in macroeconomic shocks across destinations will induce a larger bias in the estimate of ψ m than of ψ w . 10 The opposite pattern of correlation would reverse the direction of the bias in the estimation of ψ m and ψ w .

Dealing with the threat to identification
Bertoli and Fernández-Huertas Moraga (2013) demonstrate that the Common Correlated Effects, CCE, estimator proposed by Pesaran (2006) allows us to control for the threat to identification posed by the dependence of the migrant labour supply on the attractiveness of alternative destinations. 11 The CCE estimator calls for adding a set of auxiliary regressors corresponding to destination-specific effects of the cross-sectional averages of the dependent variable and of all the independent variables in the model. In the case of the reduced-form migration regression, this amounts to estimating: where 12 : Similarly, for the wage regression we can estimate: We can observe that Equation (4) reduces to Equation (1) if we impose the restriction that ϕ mj ¼ ϕ m for any j, 13 and that Equation (5) reduces to Equation (2) if ϕ wj ¼ ϕ w . In this sense, the fixed effects models in Equation (1) and Equation (2) are nested in the CCE estimator. Hence, we will refer to Equation (4) and Equation (5) as the unrestricted specifications and to Equation (1) and Equation (2) as the restricted specifications. In terms of the interpretation of the estimates, this is the difference between assuming that all destination countries are equally substitutable for potential migrants, as in Ortega and Peri (2013), and assuming different patterns of substitution across destinations for potential countries, as in Bertoli & Fernández-Huertas Moraga (2013. The more complicated error structure would also affect the computation of the labour supply elasticity in Equation (3). Still, it would not change the interpretation of the parameterβ ¼ψ m =ψ w as an upper bound on the true elasticity.

Data and descriptive statistics
We use the bilateral data on the scale of temporary Filipino migration and on migrants' wages between 1992 and 2009 collected by the Philippines Overseas Employment Administration (POEA). 14 Our analysis draws on the replication files by McKenzie et al. (2014), which include information on the (total and gender-specific) number of new hires and on the median and mean hiring wages to 54 destination countries. 15 New hires are defined as all the instances in which land-based overseas Filipino workers sign a temporary contract with a new employer; this definition thus includes both first-time migrants and migrants that change their job at destination. 16 The destination countries included in the sample recorded a positive number of new hires in each year, and accounted for no less than 85 per cent of the total number of new hires of Filipino workers in the world for every year between 1992 and 2009.  Table 1 reports the number of total new hires over our period of analysis for each of the 54 countries in The elasticity of the migrant labour supply 1827 our sample. Saudi Arabia represents the main destination country, accounting for 30.02 per cent of the total number of new hires over our period of analysis, followed by Japan, Taiwan and the United Arab Emirates, with each of these three countries representing more than 10 per cent of the total number of new hires. 17 The data reveal that temporary migration represents the mainat times, nearly the uniqueentry door for Filipino migrants in a number of destination countries: for instance, 98.2 per cent of Filipinos residing in Saudi Arabia in December 2009 were temporary migrants, and the median share of temporary migrants over our sample of destination countries stands at 69.3 per cent. 18,19 The geographically diverse set of destination countries in our sample clearly experienced a different evolution in their macroeconomic conditions over our period of analysis, but it is important to observe that business cycle conditions of destination countries located in the same region display a remarkable degree of (positive) correlation, which might pose a threat to identification, as discussed in Section 2. For instance, Figure 4 plots the evolution of real GDP growth between 1993 and 2009 for South Korea and Malaysia, to give a visual feeling of the extent of the correlation in the evolution of macroeconomic conditions in relevant destinations for Filipino migrants.
Overall, the average correlation of GDP growth across the 54 countries in the sample is actually 0.24 but this goes up to 0.41 when we confine ourselves to the 10 main destinations (see Table 1), and even to 0.75 if we concentrate on the six East Asian countries, namely Japan, Taiwan, Hong Kong, South Korea, Singapore and Malaysia, which account for more than 40 per cent of new hires. 20 This implies that the concern about the threat to identification posed by correlated variations in macroeconomic conditions across destinations has a strong empirical relevance in this case.

Econometric analysis
We present here the results from the estimation of the restricted and unrestricted versions of the wage and of the migration equations, and the ensuing values for the elasticity of the migrant labour supply. 21 All our results are robust when we rely on median rather than mean wages as the dependent variable in the wage equation, and when we estimate the wage equation separately on the sub-sample of male and female Filipino migrants; Online Appendix A2 reports these additional specifications. 22 Table 2 presents three different ways of estimating the relationship between mean wages of overseas Filipino workers and contemporaneous GDP shocks. 23 In Column (1), we present the estimate of the  Notes: *** p < 0.01, ** p < 0.05, * p < 0.10; standard errors clustered at the country level in brackets for specifications (1) and (2); specification (1) corresponds to  (2) and (3)  restricted version of Equation (5), that is, we estimate Equation (2), and we assign an equal weight to each observation. The elasticity of the mean wage with respect to GDP per capita is statistically zero in an unweighted estimation with destination and year fixed effects. However, things change drastically in Column (2), where we weight the observations corresponding to each destination-year by the corresponding total number m jt of overseas Filipino workers. This practise is common in the migration literature (see, for instance, Borjas, 2003;Mishra, 2007), and it prevents results from being driven by observations with a limited number of migrants, where measurement error in migrants' wages might be a severe concern. 24 Once we weight the observations, the elasticity of mean wages with respect to GDP shocks is estimated at 0.46, and it is significant at the 5 per cent confidence level. 25 Column (3) presents the results of estimating the unrestricted version of Equation (5). The F-test, which is conducted on the null hypothesis that φ wj ¼ φ w , reveals that the coefficients of the auxiliary regressors added by the CCE procedure vary across destinations, thus validating the need to lift the restriction upon which the estimation of Equation (2) reported in Column (2) is based. The estimated elasticity in Column (3), which is significant at the 1 per cent confidence level, is very similar in magnitude to the one observed in Column (2). The elasticity decreases, as predicted by the theory in the empirically relevant scenario of a predominantly positive correlation in macroeconomic conditions across destinations, but only from 0.46 to 0.39, an insignificant difference at conventional levels. This result suggests that labour demand is elastic enough so that substitutability patterns across destinations do not affect migrant wages much. Table 3 presents two alternative estimations for Equation (4), which give us an estimate of the elasticity of the number of new hires of overseas Filipino workers with respect to real GDP at destination. Column (1) contains the results from the estimation of the restricted version of Equation (4), that is, Equation (1). The estimated coefficient on log GDP implies an elasticity of 1.52 in the relationship between GDP shocks and number of overseas Filipino workers. 26 Column (2) shows the results of running the unrestricted version of the same equation, thus allowing for a richer structure of the error term that allows for different substitution patterns across destinations for Notes: *** p < 0.01, ** p < 0.05, * p < 0.10; standard errors clustered at the country level in brackets for specification (1); specification (1) corresponds to  (1) and (2)  migrants by using the CCE estimator. The test on the significance of the destination-specific auxiliary regressors added by the CCE estimator confirms the need to control for a richer substitution pattern across destinations and the test for the equality of coefficients between both models rejects the null at a 5 per cent significance level (p-value = 0.03), despite the large clustered standard errors implied by the base specification. This suggests the need for a more complicated structure of the error term in Equation (1) that cannot be controlled for just by adding destination and year fixed effects. The estimated coefficient for GDP increases from 1.52 to 3.38. The elasticity estimated in Column (1) is downward biassed, as expected with a positive correlation in the evolution of macroeconomic conditions across destinations (see Section 3), the case depicted in Figure 2. The intuition for the difference is straightforward. For each destination and year, the 1.52 coefficient was picking up both the direct positive effect of GDP shocks on migration to that destination and that year and the indirect negative effect of correlated shocks in alternative destinations or in the same destination in different years.

The implied elasticity of the migrant labour supply
The tests conducted on the estimates of the reduced form wage and migration equations presented in Tables 2 and 3 reject the restrictions upon which Equations (2) and (1) are based. Thus, the unrestricted versions of the two reduced form equationswith weights included in the wage equationrepresent our preferred specifications. When we take the ratio betweenψ m = 3.38 from Column (2) of Table 3 andψ w = 0.39 from Column (3) of Table 2, we obtain an implied labour supply elasticityβ of temporary Filipino migrants which stands at 8.57 (s.e. = 2.91). 27 As the estimation of the restricted versions of the two equations deliver a downward biassed estimate of ψ m and an upward biassed ψ w , following the prediction of our simple theoretical model, then they result in a significant underestimation of β, which stands at 3.34 (s.e. = 1.50). Dealing with the threats to identification in the reduced form regressions proves to be crucial for a sound measurement of the elasticity of migrant labour supply.

Concluding remarks
The reaction of international migrants to wage differences across countries depends on the interaction of the labour supply decisions of the workers and the labour demand situation in every potential destination. This simple observation has implications on how we should interpret the reduced form estimates from gravity models of international migration. In particular, gravity equation parameters on economic conditions are not equivalent to labour supply elasticities.
In this paper, we explicitly show the relationship between the estimates from a gravity model of migration and the labour supply elasticity. We then go on to provide an example by estimating an upper bound on the elasticity of the labour supply of temporary Filipino migrant workers between 1992 and 2009. We find that the labour supply elasticity of this subset of workers is as high as 8.57, which implies that temporary Filipino migrants are very responsive to wages offered by employers at different destinations. Summing up, they retain a very high ability to choose among competing offers by changing their destination.
From the point of view of host countries, this high responsiveness means that labour-importing countries should not take temporary workers for granted. They will not be willing to come if conditions become too harsh. A different issue, for future research, is the ability of host countries to substitute unwilling Filipino workers with workers from other origins. It would be interesting to understand whether the high labour supply elasticity of Filipino migrants is matched by other countries of origin for temporary workers. (Theoharides, 2015). The estimates are also robust to the exclusion of the main destination (Saudi Arabia) from the sample; results are available from the authors upon request. 23. Wage data are missing for 5 out of 972 observations. 24. Weighting also allows us to recover the estimates that we would have obtained running the model on micro instead of on aggregate data (Angrist & Pischke, 2009). 25. In addition, the explanatory power of the model increases substantially: the adjusted R 2 goes up from 0.74 to 0.97 in Table 2. 26. This and subsequent elasticities on migration regressions should be interpreted as an upper bound on the true elasticity in a RUM-based model (Bertoli & Fernández-Huertas Moraga, 2015). 27. Bootstrapped standard errors from resampling 100 times with replacement.