An SVAR model of fluctuations in U.S. migration flows and state labor market dynamics.

Rickman, Dan S.

1. Introduction

The high degree of geographic labor mobility is often thought to play a key role in the relative flexibility of the U.S. economy (Evans and McCormick 1994; Decressin and Fatas 1995). Regional mobility in the United States has been reported to be at least 3.5 times greater than that of the United Kingdom (Hughes and McCormick 1994) and two to three times higher than most European Union nations (Obstfeld and Peri 1998). Labor migration can equilibrate regional labor markets exposed to asymmetric demand shocks because employed or jobless individuals in areas that are experiencing a relative (to the national average) economic downturn can migrate to areas that are not as adversely affected, reducing the aggregate unemployment rate (Archibald 1969). The resulting net employment gains increase aggregate output. Thus, if migration flows mainly smooth over asymmetric demand shocks, greater regional labor mobility improves macroeconomic performance and enhances the effectiveness of a currency union or monetary policy (Mundell 1961; Bayoumi and Eichengreen 1993; Obsffeld and Peri 1998).

An often-overlooked aspect is there may be shifts in population location unrelated to changing job fortunes, which implies that migration becomes an additional source of labor-market fluctuations. The dramatic modern shift in U.S. population to warmer and amenity-attractive areas in the South and West suggests that migration flows may be key sources of regional economic shocks (Graves 1979; Mueser and Graves 1995; Rappaport 2004). So, if U.S. migration flows are greatly influenced by other factors besides demand shocks, large aggregate migration flows may not be necessarily indicative of a more flexible labor market, and may even work against adjustment to regional demand shocks, which would contrast with prevailing economic wisdom.

A related issue is migration's role in affecting economic development policies such as tax breaks, subsidies, educational support, and infrastructure. In assessing the effectiveness of economic development policies that alter labor demand, Bartik (1991, 1993) finds that migration is the primary supply response, but he also reports that demand shocks induce modest permanent changes in local unemployment and labor-force participation rates. To the extent that migrants take the new jobs, economic development policies are less effective in improving economic outcomes of a region's original residents. Conversely, Eberts and Stone (1992) report that increased labor-force participation is the primary supply response to demand shocks, suggesting that original residents benefit more from employment growth. Decressin and Fatas (1995) similarly find that shifts in labor-force participation are the primary short-run supply responses to demand shocks in Europe.

In short, not only do migration fluctuations reflect responses to asymmetric regional demand shocks, they also reflect supply-side innovations and affect whether local economic development policies are successful in benefiting original residents. Therefore, this paper utilizes a structural vector autoregression (SVAR) approach to carefully examine the fluctuations in U.S. migration from the 1970s through the 1990s for the lower 48 states. In assessing the proportion of migration fluctuations that are responses to labor demand shocks versus being sources of shocks themselves, a primary goal will be to appraise migration's role in facilitating regional and overall U.S. labor-market flexibility in responding to asymmetric shocks. The results have implications for assessing both the transmission mechanism of macroeconomic policies and the effectiveness of state and local economic development policies. Indeed, one of the more interesting findings is that the underlying determinants of a particular state's migration flows can differ from the underlying causes of its employment growth (e.g., Partridge and Rickman 2003). (1)

The next section discusses the theoretical underpinnings of migration fluctuations. Section 3 discusses empirical implementation of the SVAR, with particular emphasis given to separating demand influences on migration from supply influences. Identification follows from imposing long-run restrictions on impulse functions in the spirit of Blanchard and Quah (1989). The long-run restrictions derive from a commonly used regional labor-market framework. Conversely, previous studies of regional labor-market dynamics have generally relied on instrumental-variable methods and more recent reduced-form VAR approaches that contained more stringent contemporaneous exogeneity restrictions. Thus, the SVAR specified in this study extends the literature by avoiding some of the restrictions imposed in previous VAR studies by directly accounting for labor-supply innovations. (2) Section 4 then presents the empirical results, while the final section contains a summary and conclusions.

2. A Regional Migration and Labor-Market Model

Although U.S. regional growth rates over long periods are strongly correlated, the substantial fluctuations in growth around the long-term growth trends indicate the existence of shocks (Blanchard and Katz 1992; Partridge and Rickman 2002, 2003). There are divergent views regarding the regional sources of shocks, including whether migration is simply a response to asymmetric demand shocks or is also a source of shocks.

Consistent with migration equilibrating aggregate and regional labor markets, one commonly held view is that short-term deviations in U.S. migration flows are primarily responses to changes in the spatial distribution of demand. With empirical studies dating back to Blanco (1964), migration is often reported to be the dominant adjustment mechanism, arbitraging away wage and unemployment-rate differentials induced by asymmetric demand shocks (e.g., Marston 1985; Blanchard and Katz 1992; Davis, Loungani, and Mahidhara 1997). There is some question as to how long and how fully migration arbitrages away the effects of demand shocks. Gabriel, Shack-Marquez, and Wascher (1993) conclude that migration alone does not equilibrate shocks to the distribution of regional unemployment rates within periods of less than several years. In questioning Blanchard and Katz's (1992) results, Rowthorn and Glyn (2003) contend that migration does not in itself fully equilibrate regional economies subjected to demand shocks.

With its roots in location theory, an alternative view of migration is that it serves as the primary source of regional growth differentials in employment and population (Borts and Stein 1964; Mueser and Graves 1995). Although amenities such as climate are generally time invariant, their influence can change as income, preferences, or relative prices change. For example, because location-specific amenities are assumed to be normal or superior goods, their derived demand should rise with wealth and income, creating migration-inducing utility differentials. This may not only alter long-term migration trends, but may also generate short-term shocks if the demand for amenities fluctuates (Graves and Mueser 1993). For example, dramatic events such as terrorist attacks or the severe 2004 hurricane season may produce short- and long-term changes in amenity attractiveness of the affected areas. Changing preferences for location-specific amenities is not the only cause for migration innovations because technological advances such as air conditioning have surely altered the relative attractiveness of areas. Moreover, because propensities to migrate differ by age, migration flows covary with changes in the U.S. age structure (Graves 1979). Finally, the immigrant portion of migration also varies over space and time, imparting shocks to local labor markets (Greenwood and Hunt 1996; Card 1997). Although these types of migration flows are consistent with utility maximization, they are not necessarily conducive to greater labor-market flexibility, particularly in cases where migration shocks are negatively related to the demand shocks.

To assess these issues, we use a theoretical model that follows the framework of Partridge and Rickman (2003), which fits in the general mold of the traditional regional labor-market representation (e.g., Bartik 1991, 1993; Blanchard and Katz 1992; Treyz et al. 1993; Bound and Holzer 2000). However, its structure includes additional features to better disentangle short-run innovations from persistent long-run trends in regional labor markets. The model captures long-term persistence in employment growth, wage growth, and net-migration flows, while allowing for contemporaneous labor demand and supply innovations that induce disequilibrium adjustments. Including migration directly contrasts with most recent approaches that only consider it indirectly as a residual of job growth minus responses in labor-force participation and unemployment (or the employment-population ratio). A distinguishing feature of the approach when compared with recent VAR approaches (e.g., Blanchard and Katz 1992) is that contemporaneous shocks in labor supply are allowed (by migrants and the original-resident labor force), which contrasts with simply assuming that all contemporaneous innovations are attributable to labor-demand shocks. (3) Correspondingly, unemployment and employment rates and population rates are not assumed to be long-run stationary processes, which allow some jobless original residents to permanently find employment (Obstfeld and Peri 1998). For now, labor demand is assumed to equal labor supply, which is an assumption that is relaxed later to allow for unemployment responses.

Regional Labor Supply

Regional labor supply growth ([DELTA][l.sup.s]) in time t is composed of growth in the original-resident labor-force ([DELTA][l.sup.so]) plus net labor-force migration (m):

(1) [DELTA][l.sup.s.sub.t] = [m.sub.t] + [DELTA][l.sup.so.sub.t].

Net migration includes fixed longer-term flows ([g.sub.m]), responses to changes in relative wage rates [[DELTA][w.sub.t](L)], responses to own-lag migration effects, responses to relative expected job opportunities, which is proxied by current and lagged changes in employment [[DELTA][n.sub.t](L)], and own-innovations ([[epsilon].sup.m]):

(2) [m.sub.t] = [f.sup.m][[g.sup.m], [DELTA][w.sub.t](L), [m.sub.t-1](L), [DELTA][n.sub.t](L), [[epsilon].sup.m.sub.t]],

where L is a lag operator to allow for sluggish migration responses. The demand for amenities should increase with wealth and income, establishing long-term migration trends, which are reflected in the [g.sub.m] term (Mueser and Graves 1995; Rappaport 2004). This assumption is consistent with the quality-of-life literature (e.g., Roback 1982) and Greenwood et al.'s (1991) migration findings that relative state wage levels reflect compensating differentials such as amenities. In this case, changes in relative long-run wages reflect demand shocks that produce the deviations in migration flows that are of interest. Thus, relative state wage levels help produce the persistent trend net-migration differences, though we are more interested in wage innovations (or change in wage) that produce migration deviations from long-term trends. Nevertheless, we tested our assumption that relative wage shocks are best captured by changes in relative wages. We conclude that relative wage levels are non-stationary and their use would have produced implausible results (see footnote 7). Lagged migration is included because it can affect current migration through chain migration and return migration. Indeed, empirical studies have found a "self-perpetuating" response where current migration flows induce future flows (Greenwood and Hunt 1984; Davis, Loungani, and Mahidhara 1997).

Several potential sources of migration innovations ([[epsilon].sup.m]) exist. For one, short-term migration shocks result if there are fluctuations in the demand for amenities (Graves and Mueser 1993). Other sources of migration innovations include: technological changes such as improvements in air conditioning (Rappaport 2004); changes in the age structure of the U.S. population (Graves 1979); and changes in regional patterns of foreign immigration, including any offsetting migration by natives (Borjas, Freeman, and Katz 1996; Greenwood and Hunt 1996; Card 1997). Demand and supply innovations in other regions provide a final potential source of own-region migration innovations. For example, downturns in California can induce migration to nearby states such as Oregon and Washington (e.g., during the early 1990s).

Internal labor supply growth ([DELTA][l.sup.so]) includes that attributable to long-term factors such as population growth ([g.sup.so]), responses to current and lagged wage rate changes, responses to expected job opportunities proxied by current and lagged employment growth [[DELTA][n.sub.t](L)], and own-innovations ([[epsilon].sup.n]).

(3) [DELTA][l.sup.so.sub.t] = [f.sup.so]([g.sup.so], [DELTA] [w.sub.t](L), [DELTA][n.sub.t](L), [[epsilon].sup.n.sub.t].

Aside from long-term trends, positive demand shocks increase wages and employment, which increase internal labor supply through greater labor-force participation. Given information lags and liquidity constraints faced by potential migrants in other regions, the response of the original-resident labor force will most likely be faster than the corresponding migration response. Because of increased competition in the labor market and lower wages, positive migration innovations are expected to reduce the labor supply of the original residents. Innovations in the original resident labor supply ([[epsilon].sup.n]) can occur for a variety of reasons such as a change in the reservation wage that might accompany changes in unemployment benefit generosity or welfare reform.

Regional Labor Demand

Firms are assumed to sell their products in local, national, and foreign markets, and are expected to have negative-sloped input demand curves. Changes in demand for the region's goods and services shift labor demand. Thus, labor demand ([L.sup.d]) is related to long-term persistent factors ([g.sup.d]), wage changes induced by supply shifts, and own-innovations.

(4) [DELTA][l.sup.d.sub.t] = [f.sup.d]([g.sup.d], [DELTA][w.sub.t](l), [[epsilon].sup.d.sub.t].

Two general sets of factors are assumed to cause shifts in regional labor demand. First, are persistent factors (or fixed effects) such as secular productivity growth, which can vary across states depending upon industry composition. Closely related are differing regional productivity trends that can arise as a result of differences in public capital and proximity to natural resources and oceans (Rappaport 2004), as well as variations in the state and local business climate (e.g., taxes, regulations, "good" government, etc.). Second, demand innovations such as region-specific productivity shocks and changes in the demand for the region's exports also shift labor demand. For example, Partridge and Rickman (1999b) found regional-productivity changes to be a primary cause for state labor markets to experience labor demand shifts in the 1980s and 1990s. Following convention, we assume constant returns to scale (CRS) in long-run production (Muth 1971; Blanchard and Katz 1992; Balmaseda, Dolado, and Lopez-Salido 2000), which is underpinned by also assuming perfect long-run mobility of capital and labor. Regarding productivity, an implication of assuming CRS is that innovations in labor supply have no long-run effect on wage levels--that is, potential congestion and agglomeration effects offset as population increases. (4)

Regional Labor Market Dynamics

The previous model implies that the only way for the regional wage rate to change in the long run is for productivity to change (or for there to be a permanent shift in the region's terms of trade). Thus, the long-run regional labor demand curve is perfectly elastic. Yet, we allow for short-run deviations from the CRS assumption as households make adjustments in terms of labor-force participation and migration, and firms adjust through relocation or capital stock adjustment. Hence, the short-run labor demand curve is downward sloping, reflecting the current level of demand based on the identified factors. Given the intranation mobility of firms and capital, a region's short-run curve is likely to be more elastic than the corresponding aggregate U.S. labor-demand curve. Deviations between the current wage obtained from the short-run demand curve and the wage that is associated with the long-run demand curve induces an adjustment by firms that shifts short-run labor demand. Long-term shifts in labor productivity (or the region's terms of trade) produce parallel shifts in both short- and long-run labor demand, which alters long-run wages. (5)

The previous discussion also implies different short- and long-run labor supply curves. The long-run labor supply curve is more elastic to primarily reflect the delayed response of migrants to changes in the region's economic conditions. If the short- and long-run labor supply curves intersect at the prevailing wage, there will be no supply-side adjustments. If instead, say, a favorable demand shock results in the prevailing wage rate intersecting the short-run supply curve above the long-run labor supply curve, migrants will be attracted to the region, shifting the short-run labor-supply curve outward until it intersects the long-run labor supply curve at the prevailing wage. On the other hand, a long-run shift in the region's labor supply produces a parallel outward shift in the short-run and long-run supply curves so that they intersect at a higher level of employment.

One difference from most past VAR studies is that this model implies that the wage increase associated with a positive demand shock induces an increase in the labor-force participation of the original residents (unless the region's internal labor-supply curve is perfectly inelastic). Another feature of most previous VAR approaches is that wages are not directly accounted for in the base model, which may influence migration responses. By more realistically allowing the labor supply of original residents to not be perfectly inelastic, it is unlikely that net migration will be the only source of the resulting long-term employment growth differentials. Yet, this model allows for the possibility that continued in-migration over time displaces many of the original residents who initially took a job after the demand shock. A final characteristic of this model is that labor demand shocks are simply identified by a positive covariance between the change in the wage rate and employment, while supply shocks are identified by a negative covariance.

3. Empirical Model and Implementation

The reduced-form VAR approach is popular because of its ease of use and success in explaining the empirical regularities of employment growth (e.g., Blanchard and Katz 1992; Decressin and Fatas 1995; Jimeneo and Bentolila 1998). Its simplicity comes at the expense of imposing some stringent restrictions, which make it unsuitable for our purposes. For one, contemporaneous employment innovations are assumed to only originate from labor-demand innovations. Likewise, because the standard VAR approach does not explicitly consider migration (it is derived only as a residual from employment growth, the employment to population ratio, and unemployment rate), it is not possible to directly examine the importance of migration innovations.

Perhaps most importantly, long-ran stationarity assumptions in the reduced-form VAR approach force migration to fully arbitrage away unemployment and employment-rate differentials induced by demand shocks (Obstfeld and Peri 1998). Along with implicitly assuming no role for supply shocks, the stationarity assumptions of the reduced-form VAR model make it less accurate for structural analysis. This leaves no role for nonemployed original residents to be a source of long-run employment gains and implicitly forces migration to be the sole source of long-run employment growth differentials. Yet, when considering data after the early 1970s, Rowthorn and Glyn (2003) generally could not reject the hypothesis that state employment rates follow a unit-root process. This possible nonstationarity led them to question Blanchard and Katz's (1992) contention that migration is the dominant regional-adjustment mechanism. Thus, to overcome these concerns, we employ an SVAR model that applies economically meaningful long-run restrictions, based on the theoretical model in the previous section, to a reduced-form VAR model to identify the labor-supply and -demand shocks.

The theoretical model outlined in Equations 1-4 implies that wage rates, employment growth, and migration are simultaneously determined. An SVAR representation of the relationship between the three variables can be written as

(5) [B.sub.0][x.sub.t] = D + B(L)[x.sub.t-1] + [[epsilon].sub.t],

where [x.sub.t] = the column vector ([DELTA][w.sub.t], [m.sub.t], [DELTA][n.sub.t])',

D = a vector of constant terms, capturing persistent trends in x over the period ([g.sup.d], [g.sup.m], [g.sup.so])',

[B.sub.0] = a 3 x 3 matrix of coefficients, reflecting contemporaneous relationships among the three variables,

[[epsilon].sub.t] = the column vector of structural error terms from Equations 2-4 ([[epsilon].sup.d.sub.t], [[epsilon].sup.m.sub.t], [[epsilon].sup.n.sub.t])',

B(L) = a 3 x 3 matrix with elements equal to the polynomials [B.sub.ij](L),

L = a lag operator.

Premultiplying all terms in Equation 5 by [B.sup.-1.sub.0] yields the following reduced-form VAR representation:

(6) [x.sub.t] = C + A(L)[x.sub.t-1] + [e.sub.t],

where C = [B.sup.-1.sub.0]D, A(L) = [B.sup.-1.sub.0]B(L), and [e.sub.t] -- [B.sup.-1.sub.0][[epsilon].sub.t].

Each constant term in C is a composite of the long-term growth terms (g) in Equations 2-4. Correspondingly, the x variables are influenced by composites of the structural shocks in the dynamic system with each reduced-form residual being contemporaneously influenced by structural demand ([[epsilon].sup.d]), migration ([[epsilon].sup.m]), and original-resident labor-supply shocks ([[epsilon].sup.n]).

Letting [A.sub.0] denote [B.sup.-1.sub.0], [A.sub.0] represents the matrix of contemporaneous responses of [x.sub.t] to the structural shocks. Thus, knowledge of [A.sub.0] is the key to untangling the structural sources of migration (labor market) fluctuations:

(7) [[epsilon].sub.t] = [A.sup.-1.sub.0][e.sub.t].

Equation 7 shows that given [A.sup.-1.sub.0] the structural shocks can be obtained from the reduced-form VAR residuals. Yet [A.sub.0] is not known and the SVAR process of identifying its elements typically involves utilizing the derived expression for the variance-covariance matrix of the reduced-form VAR residuals ([[summation].sub.e]):

(8) [[summation].sub.e] = E([e.sub.t][e.sub.t]') = [A.sub.0]E ([[epsilon].sub.t][[epsilon].sub.t]')[A.sub.0] = [A.sub.0][[summation].sub.[epsilon]][A.sub.0]'.

The right-hand side of Equation 8 contains 18 (2[n.sup.2]) unknown parameters. Assuming orthogonality of the shocks, normalizing the diagonal elements of [A.sub.0] to equal unity, combined with the estimated variance-covariance matrix of the reduced-form VAR ([[summation].sub.e]), leaves Equation 8 short three [n(n - 1)]2] restrictions for identification of the unknown parameters.

Two restrictions follow from the long-run CRS assumption in the theoretical model. Because only labor-demand innovations affect relative long-run wages, each supply innovation is restricted to have no long-run effect on the wage rate. This implies that any wage trends from congestion or agglomeration economies would be gradual and occur over periods greatly in excess of those under consideration. Such long-run trends are captured in the constant term ([g.sup.d]) of the SVAR wage equation. Thus, the assumption only means that the innovations are not substantial enough to produce significant congestion or agglomeration economies during the time span under study (see footnote 4). Moreover, Blanchard and Quah (1989) show that in cases where in reality there are small long-run effects from variables whose innovations are constrained to have no long-run influence, the identifying SVAR restrictions still recover approximately correct results. Hence, regarding the CRS restriction, the results will be approximately correct if demand innovations such as productivity shocks are close to being the sole source of all long-run wage changes.

The final identifying restriction derives from assuming that the sum of migration responses to internal labor-supply shocks equals zero, which implies that labor-demand innovations and own-innovations are solely responsible for cumulative long-run migration fluctuations. In other words, the cumulative impulse response function of migration to internal labor supply shocks equals zero, while the cumulative impulse responses functions of migration to the other two sources of shocks are unconstrained (for mathematical formulations of SVAR long-run restrictions, see Enders 1995, p. 335; Partridge and Rickman 2003).

The third restriction does not fall from the theoretical model but follows from the observation that migration flows are generally persistent and are not affected in the long run by transitory shifts in a state's unemployment or labor-force participation rate. The restriction could lead to an understatement of the role of internal labor-supply innovations, and an offsetting overstatement of the role of migration innovations, if somehow there was some sort of permanent change in the labor-market attachment of the original labor force not captured in the long-run trend [g.sup.so]; i.e., changes in migration could be credited with such a change. However, short-run responses of migration to internal labor-supply innovations are not restricted. Also, if the long-run restriction is only slightly binding, in that there are actually small long-run impacts on migration, then as described above, the understatement of the role of original-resident labor-supply innovations is likely very small (which our results later suggest). This assumption is much less restrictive than Blanchard and Katz's (1992) short-run exogeneity restriction that all contemporaneous employment shocks equate with labor-demand shocks, and their stationarity restrictions on employment and unemployment rates, which imply that the internal labor supply of the original residents plays no long-run role in satisfying demand-induced employment growth or in arbitraging economic differentials.

The SVAR model is separately implemented for each of the lower 48 states for 1970-1998. (6) Responses are allowed to vary across states to avoid heterogeneity bias associated with erroneously imposing uniform responses. As with the related VAR literature, a possible concern is that there are only 29 years of data for each model. Yet, we will employ an averaging across all states or functional groups of states to mitigate any abnormal influence from an outlying observation. Because the focus is on the relative state fluctuations in migration, the variables in Equation 6 are defined relative to the nation. Defining the variables relative to the nation differences out common national productivity and cyclical effects. Construction of the variables and the list of data sources are discussed in the Appendix.

Restricting the sum of the three respective impulse responses over time to equal zero imposes the long-run restrictions: two restrictions derived from both sources of supply shocks having no long-run impact on wage rates, and a third restriction derived from assuming internal labor-supply shocks have no long-run impact on migration. These include cumulative impulse responses of migration to each of the supply shocks, and the cumulative response of migration to internal labor supply. Imposition of the restrictions in Equation 8 yields [A.sub.0], which can be used to calculate impulse response functions and variance decompositions (Enders 1995, pp. 305-312). For the impulses to approach zero in the long run, stationarity of the variables is required. Based on augmented Dickey-Fuller (ADF) tests, unit roots in each of the variables were rejected for all states except for relative migration in Ohio. (7) Since the long-run-restrictions SVAR approach is an alternative to cointegration for capturing long-run equilibrium relationships (Quah 1995; Hansson 1999), cointegration tests were not performed.

The number of lags included in each equation is based on the optimum Schwarz Bayesian information criterion (BIC) statistic, with the maximum number of lags specified as four years. Although they can differ by state, the number of lags is restricted to be equal across equations for each state. For all but four states, the optimum lag length based on the Schwarz BIC is equal to one year. (8) The Schwarz BIC criterion is chosen because it tends to yield shorter lag structures than other alternatives, where a shorter lag length has been suggested as one approach to improving the reliability of inferences drawn from SVAR models (Faust and Leeper 1997). The robustness to alternative lag-setting criteria is discussed in the next section.

4. Results

Empirical implementation of the SVAR provides the desired insights into the underlying determinants of fluctuations in aggregate migration flows and the functioning of state labor markets. Specifically, we examine the SVAR results in the form of estimated impulse responses, structural shocks, and variance decompositions. In addition to state-specific statistics, we also report some arithmetic averages for Census regions and aggregations of states into functional groupings of Sunbelt, Rustbelt, Energy, and Farm states. (9)

First, the estimated impulse responses and structural shocks are checked to assess the efficacy of the identification scheme. We find strong empirical support for the identification assumptions applied in our SVAR. Second, we calculate and compare demand-induced employment and migration impulse responses to estimate the proportion of demand-induced jobs that are satisfied by migrants versus original residents. Overall, we estimate that migrants fill most of the (demand-induced) newly created jobs, but there is significant heterogeneity across regions in which the role played by original residents nearly equals that of migration in some regions. Third, we report variance decompositions of the migration forecasts. We find that relative (reduced-form) fluctuations in migration flows ([e.sup.m]) are primarily composed of exogenous labor-supply shocks in the short run ([[epsilon].sup.m]), with asymmetric regional labor-demand shocks ([[epsilon].sup.d]) being slightly more important in the long run. This indicates that migration fluctuations should not be simply viewed as evidence of a flexible labor market smoothing out regional cyclic asymmetries. Indeed, migration fluctuations also may be the sources of regional cyclic asymmetries. Finally, we examine the impulse responses regarding the time required for regional labor markets to equilibrate, providing additional insight into migration's role in the flexibility of the U.S. economy.

Identification Check

Although long-run restrictions are imposed on three impulse response functions, all short-run impulses are unconstrained and can be checked for consistency with economic theory. Hence, the estimated short-run responses can serve the same purpose as standard over-identification tests (Bayoumi and Eichengreen 1993). The state-specific impulses (not shown) reveal that the short-run responses consistently follow expectations, suggesting that the identifying restrictions correspond to actual economic behavior. (10) For example, regarding migration responses to other shocks, by the second period, 47 states have a cumulative positive migration response to a labor-demand shock, while 46 states have a cumulative negative migration response to a shock in internal labor supply. Likewise, employment and wage responses almost universally fit a priori expectations regarding demand and supply shocks. (11)

In further analysis of the efficacy of the identification scheme, the calculated demand shocks and migration shocks are regressed on a demand-shift variable that has been used as an instrument for job growth in previous studies (Bartik 1991; Blanchard and Katz 1992). The variable is the employment growth that would occur in a state if all its industries grew at their national rates, less the overall national rate of growth. The variable is positive (negative) when a state has disproportionate shares of fast (slow) growing industries nationally. The measure is calculated beginning in 1979 because of data availability.

For ease of summary, pooled regressions for 1979-1998 are run with a common intercept. As expected, a positive and significant relationship is found between the exogenous demand shift measure and the demand shocks derived from the SVAR (t = 4.29). (12) Likewise, there is not any significant relationship between the calculated migration shocks and the demand shift variable (t = 0.49). Along with the negative short-run impulses of wage rates to migration shocks, this provides strong evidence that the calculated migration shocks are missing a demand component and are indeed supply shocks. Similarly, the corresponding t-statistic only equals 1.44 when regressing the internal labor supply shocks on the industry-mix demand-shock variable.

Unfortunately, a corresponding exogenous time-varying supply-side instrument does not exist to further consider the validity of the model, although the tact that the supply shocks appear to be unrelated to the exogenous demand instrument is encouraging. Of course, if such a supply instrument existed, the SVAR approach would possess less advantage over the instrumental-variable regression approach.

In another test of the long-run restriction that internal labor shocks have no cumulative long-run effect on migration flows, the current-period state (relative) net-migration rates were regressed on the estimated internal labor-supply shocks in a pooled model. A Wald test failed to reject the null hypothesis that the sum of the regression coefficients on the contemporaneous and lagged internal-labor supply shocks equaled zero (e.g., in the fixed effects model, p = 0.31 with three lags and p = 0.62 with four lags). This supports the restriction that internal labor supply innovations have no long-run effect on migration.

Migrant Responses to Demand Shocks

One of the key questions in the interregional migration literature is how jobs created by a demand shock are distributed between original residents and new migrants (e.g., Bartik 1991, 1993; Blanchard and Katz 1992; Decressin and Fatas 1995; Jimeneo and Bentolila 1998). Besides its implications for aggregate and regional labor-market flexibility, this question relates to whether a successful economic development strategy creates jobs tot the original residents or for migrants. The answer can be obtained by comparing the employment and migration impulse responses to a labor-demand shock.

The previously described migrant responses, defined as proportions of population, have to be scaled for comparability to employment because economic migrants that respond to labor-demand shocks are more likely to be employed in the new location than the rest of the population--at least after they had time to obtain employment. Thus, our "base" migration-impulse responses to demand are scaled up 1.461 by assuming all new households relocate for economic reasons. As described in the Appendix, we believe that scaling up by almost one-half is defensible, though we acknowledge that some of the assumptions could produce an overstatement of the employed-migration response. (13) Thus, we also produce a "lower bound" estimate that scales up the migration response by 1.076. As noted in the Appendix, this is calculated by comparing migrant labor-force participation to the general population. Yet, this is likely a significant understatement because economic migrants would likely have a much higher labor-force participation rate than the universe of all migrants, which includes retirees.

As shown in Figure 1, the average employment response (of the 48 separately estimated models) to a positive one standard-deviation labor-demand shock is generally consistent with past VAR studies. In the first year, the employment growth response exceeds 0.6%, while the migration response equals approximately 0.2%. Total employment growth exceeds the initial response, peaking in the sixth year before slightly declining. In both the base and lower-bound cases, internal sources are initially the primary supply of workers for the newly created jobs, while migrants fill most of the jobs in the longer run. Cumulative migration flows, on average, peak in about the ninth year before stabilizing. After the third year, migrants begin crowding out some of the original-resident employment gains, in which migrants eventually crowd out more than one-half of the newly employed native workers.

[FIGURE 1 OMITTED]

In the base case, the ratio of the migrant response to the employment response in the first two years is 0.29 and 0.43, which falls within the range of 0.3 to 0.5 found by Bartik (1993) in his literature survey. In fact, the initial migration response falls between that reported by Blanchard and Katz (1992) for the United States and Decressin and Fatas (1995) for the European Union. The base migration to employment ratio of 0.79 in the later years falls in the range of long-run responses of 0.6 to 0.9 reported by Bartik. The lower bound estimates are about three-fourths the size of the base case. Yet, in the long run, economic migrants still fill almost 60% of the newly created jobs. Especially in the base case, migration eventually arbitrages away much of the original-resident employment-rate gains induced by asymmetric demand and productivity shocks. However, higher wages associated with the demand shock still produce a long-run increase in the employment rate as nonemployed original residents fill many of the new jobs. This pattern runs counter to the employment rate stationarity assumption of reduced-form VAR approaches (e.g., Blanchard and Katz 1992). (14)

These results suggest that U.S. labor-market flexibility is enhanced in the short run by labor-force participation changes of the original residents (and changes in unemployment), while migration plays the dominant role in equilibrating asymmetric demand shocks in the medium to long run. The results also imply that state and local economic development policies on average can significantly raise employment prospects for jobless original residents in the short run and even have modest effects in the long run. Economic development policies more likely improve original-resident outcomes when migration is less of a factor in facilitating regional adjustment to demand shocks.

The average supply responses nationally mask significant regional heterogeneity. Illustration of regional heterogeneity is provided in Figure 2, which shows the proportion of newly created jobs taken by migrants for several regional groupings of states. Only the proportions for the base case scaling of migration are provided, but the comparison across regions is invariant to scaling. Migration plays its strongest role in enhancing Sunbelt labor-market flexibility with approximately 51% of newly created jobs being taken by migrants in the second year (in the base case), stabilizing at approximately 87% in the fifteenth year. Regarding migration's overall role in the Sunbelt, Partridge and Rickman (2003) found that Sunbelt employment fluctuations were primarily caused by supply responses, consistent with their amenity attractiveness. Thus, while migration fluctuations drive employment fluctuations, Sunbelt migration itself is quite responsive to regional demand disparities.

[FIGURE 2 OMITTED]

Likewise, migration is the primary supply response in the energy producing states, with 46% of newly created jobs taken by migrants in the second year and 76% in the fifteenth year. Rustbelt adjustment to demand shocks is more attributable to changes in labor-force participation and unemployment, especially in the short term. Only 30% of new jobs in the second year, and 45% of new jobs in the fifteenth year, are taken by migrants in the Rustbelt (including Pennsylvania). This pattern supports Greenwood and Hunt's (1984) earlier finding that the migrant attractiveness of a new job was less in the North and Northeast Census regions. One possible reason for the lower migration response to demand shocks is the Rustbelt's perceived lack of amenities.

Farmbelt patterns are similar to the Rustbelt. For example, migrants fill 31% of new jobs in the second year, increasing to 55% in the fifteenth year. Farmbelt states also likely experienced reallocation between the farm and nonfarm sectors, providing an additional source of internal labor supply. For the top-third of fast-growing states over the sample period, 45% of new jobs were taken by migrants by the second year and 70% by the fifteenth year, which is slightly below the average across all states. (15) Overall, differences in the role of migration appear to be more attributable to functional categorization, such as industrial specialization, or geographic location, rather than whether a state is fast-growing or not.

In sum, because original residents on average satisfy significant portions of newly created demand-induced jobs, original residents benefit from economic development efforts that stimulate demand. This contrasts with the implications of the reduced-form VAR result by Blanchard and Katz (1992), in which, by assumption, original residents never benefit in the long run from increased regional labor demand. Compared to the Sunbelt and Energy states, adjustments to a demand shock in Farm and Rustbelt states were more likely satisfied by internal-labor sources rather than migrants, suggesting migration's role in facilitating labor-market adjustment or flexibility varies across regions. Hence, successful economic development policies will be more likely to raise employment rates of original residents in the Farmbelt and the Rustbelt, and more likely to increase population in other states. In particular, for communities experiencing lower out-migration in reaction to negative demand shocks, such as from the existence of strong ties to the community (Irwin et al. 2002), successful economic development would benefit adversely affected original residents.

Variance Decomposition

Table 1 reports the variance decomposition of forecasts for migration fluctuations. The entries are the proportions of the migration-forecast variance attributable to relative labor-demand shocks (D), relative migration labor-supply shocks (M), and relative internal (original-resident) labor-supply shocks (IS) over forecast horizons of 1, 2, and 15 years. The variance decomposition is first reported for states and then by averages for the nation and some regional aggregations.

For the short-term forecast horizons, migration fluctuations are, on average, primarily attributable to own-shocks. For example, on average about 28% of the first-year variance is due to labor-demand shocks, while about 46% is due to own-innovations in migration. Consistent with other applied VAR studies (Enders 1995, pp. 311-2), only in the long run, as lagged migration responses to demand accumulate, do labor-demand (other) shocks slightly overtake migration (own) shocks in importance. Internal labor supply shocks fall below the other two sources of shocks in importance, particularly after the first year.

The results indicate that migration innovations result from a combination of factors, and cannot be entirely characterized as simply responses to asymmetric demand shocks, or as primarily own shocks. One potential contributing factor to migration shocks explaining nearly one-half of the variation in U.S. migration innovations is the availability of a range of amenity options across locations (e.g., mountains, oceans, climate) within the possibility set (defined by factors such as common culture and language). Because persistent long-term patterns are likely amenity driven (Blanchard and Katz 1992; Treyz et al. 1993), and more than one-half of migration fluctuations (around the trend) are not responses to demand shocks, the observed higher rates of migration in the United States do not necessarily indicate a more flexible labor market. So, for example, high rates of U.S. migration should not necessarily be viewed as primary evidence of an optimal currency area because much of it is driven by shifts in household location choices unrelated to labor demand shifts. (For a related discussion, see Rowthorn and Glyn 2003.)

The relative importance of the shocks varies greatly across areas and generally corresponds to widely held views of regional growth. Demand shocks play their greatest role in Energy states, accounting for over 73% of the 15-year-ahead forecast variance for migration. Likewise, demand shocks dominate in the long run in the Farm states, although South Dakota is an exception. Hence, migration played the primary role in labor-market adjustment to asymmetric demand shocks in the states that were most likely to be affected by those shocks. In Sunbelt states, structural shocks to migration account for about twice the migration-forecast variance as do asymmetric demand shocks. Thus, what most likely accounts for deviations from the trend rate of Sunbelt migration are factors that underlie innovations in migration such as changing demand for amenities. For Census regions, demand shocks dominate in the West South Central and Mountain states. Migration shocks dominate in the New England, West North Central, and South Atlantic regions.

Perhaps surprisingly, Rustbelt migration patterns are generally more attributable to own-migration shocks. Yet, because Rustbelt states are part of the Frostbelt, changing demand for warmer climates may underlie the result. These findings differ from previous findings for employment. Partridge and Rickman (2003) found that Rustbelt employment variations were more strongly influenced by demand shocks, consistent with one's underlying expectations given the region's reliance on goods production.

Standard Deviation of Labor-Market Shocks

We also calculated the standard deviation of the realized shocks across states for each year. A comparison of the year-by-year standard deviations (not shown) reveals the primary source of variability in state labor markets. (16) The standard deviations also reveal whether the primary source of shocks changed over time.

The mean standard deviation of demand shocks across states was three times greater than that of migration shocks over the entire period. Generally, variability in demand and supply shocks declined over time. Demand shocks produced the greatest variability across state economies in the 1970s and 1980s when the U.S. economy was experiencing dramatic shocks, such as in energy. Hence, migration's relative role in facilitating regional adjustments to differential demand shocks would have also been greater in the 1970s and 1980s. Likewise, compared to migration, the standard deviation of demand shocks varies significantly more over time. The relatively smaller changes in the cross-state variation of migration innovations is consistent with these innovations being primarily caused by factors that are more stable over time such as gradual changes in preferences.

The correlation between the state demand-shock standard deviation rankings and the corresponding state migration labor-supply rankings is 0.30. The comparable correlation for demand with internal labor supply is 0.29, while the correlation between the standard deviation rankings for the two labor-supply variables is 0.26. Low correlation coefficients suggest that for most states, there is likely one key underlying factor that primarily explains their relative variability over the period. In regressing the standard deviation of migration shocks on a time trend and the standard deviation of demand shocks, the time trend was significant at the 10% level (t = 1.93), while the demand shock standard deviation was insignificant (slope = 0.07, t = 1.42). The absence of a relationship between the standard deviations indicates that demand shocks in neighboring states were not a dominant source of relative supply shocks for most states, further supporting the view that changing preferences underlie the supply shocks.

Speed of Migration and Labor-Market Adjustment

Because the variance decomposition in Table 1 suggested that large fluctuations in migration flows are insufficient to ensure flexible labor markets, we also examine the speed of labor-market adjustment to the shocks. The response speeds provide information on whether the flexibility provided by migration occurs in the short run, or takes longer to achieve, and how this varies geographically. State and regional calculations regarding the speed of labor-market adjustments are given in Table 2. For each variable, Panel A reports the number of years required for 95% of the maximum response to a structural shock to occur, with states receiving equal weighting in calculating the regional averages. Panel B displays the 10 states with the quickest and slowest responses for each shock.

Panel A shows that labor markets almost fully adjust to shocks within five to eight years on average, which is consistent with the five to seven years found by Blanchard and Katz (1992). (17) Employment responds most quickly to all shocks. Not surprisingly, given potential sticky wages and costly migration, wage rates take longer to adjust, with migration taking nearly as long. The relatively slow seven- to eight-year average response of net-migration to labor-market shocks shows that migration's interregional equilibration role occurs in the long run. Indeed, the faster responsiveness of employment further illustrates that continued migration flows offset some of the initial participation-rate changes of original residents.

There is considerable variation across regions in adjustment lags. New England (5.63) and the South Atlantic (5.73) regions have the fastest response times when averaged across all nine possible cases. New England has the quickest average migration and employment response to shocks. This confirms unemployment research that suggested New England's more-mobile educated workforce contributed to reducing its unemployment rate (Partridge and Rickman 1997). Contrarily, West Virginia ranks in the bottom 10 states in terms of sluggishness of migration responses to labor-supply shocks, which might be explained by its lower education levels and the strong place attachment of its native population (Partridge and Rickman 1997). The South Atlantic region has the fastest average wage-rate response, and the second fastest average employment response, which may be related to its low unionization rate.

At the other extreme, the Mountain states (8.23) and Farm states (8.11) have the slowest response times when averaged over the nine cases. They have the most sluggish migration and employment responses, and very slow wage responses as well. Many Mountain states also are Energy states, with Energy states all appearing in the bottom 10 for at least one response. One reason may be that energy shocks are typically national in scope, leaving little incentive for cross-state migration of energy-sector workers to other parts of the nation where that sector would be faring better (Partridge and Rickman 1999a). For example, in his study of the construction of the Alaskan oil pipeline in the 1970s, Carrington (1996) found that a limited interindustry elasticity of labor supply was mostly responsible for containing the largest wage responses to only the most directly impacted industries. A similar rationale may be given for sluggish Farm state adjustment. Hence, limited interindustry elasticities likely reduce the effectiveness of migration in facilitating regional labor-market adjustment to asymmetric shocks.

5. Summary and Conclusion

This study examined migration's role in facilitating interregional labor-market flexibility and adjustment. By enhancing U.S. labor-market flexibility, migration helps fill employment adjustments caused by asymmetric regional demand shocks. Yet, factors such as changes in household amenity preferences may underlie significant migration innovations, which only under fortuitous circumstances would they facilitate adjustment to labor-demand shocks. Thus, large interregional migration flows do not necessarily ensure labor-market flexibility and may even in some instances disrupt the adjustment to regional-asymmetric demand shocks.

Using a long-run restrictions SVAR model that allows for both contemporaneous labor demand and labor supply shocks, we find that less than one-half of migration fluctuations were responses to asymmetric regional demand shocks. The result challenges the way that migration flows are often used to assess labor-market dynamics. For example, migration's role in facilitating U.S. macroeconomic adjustment may have been overemphasized. It questions whether simple cross-country comparisons of aggregate migration flows (e.g., the United States to Europe) should be used to assess the relative degree of labor flexibility within a country, or its predisposition to being an optimal currency area.

We find that in response to a demand shock, it is not until the third period that most newly created jobs are taken by migrants, which indicates that the short-run employment rate significantly changes. Even in the long run, labor-demand shocks induce a modest change in the employment rate, which is precluded in reduced-form VAR models that assume long-run stationarity in employment rates. In contrast, by utilizing the positive wage response that follows from a favorable labor-demand shock, the SVAR approach captures the positive labor-supply responses of original residents.

Like migration, employment-rate responses through changes in unemployment and labor-force participation are important, especially in the short run. This means that economic development policies are most effective in the short-run, but even in the long run, they likely have favorable effects in improving the prospects of jobless original residents. In the spatial dimension, migration plays a larger role in facilitating regional adjustment to cyclical and structural demand shocks in Sunbelt and Energy states compared with Farm and Rustbelt states. This suggests that effective economic development policies will most likely lift the employment prospects of original residents in the Rustbelt and Farmbelt.

Examination of labor market adjustment speeds to exogenous shocks allowed further assessment of the role of migration in labor-market flexibility. Labor markets were found to almost fully adjust within about five to eight years on average. Besides geographically varying responses to demand shocks, it was also found that migration adjustments do not occur quickly, in which labor-supply responses of the original residents dominated in the short run.

In summary, comparisons of aggregate migration flows and examination of reduced-form VAR dynamics have been useful in establishing empirical regularities of regional labor markets. However, this study found that a full assessment of labor-market flexibility requires going beyond examination of empirical regularities by incorporating structural features. To further understand the structural relationships, future analysts should utilize micro data integrated with well-known theoretical constructs such as those found in regional-location theory. In examining these constructs, more examination of workforce expectations of future trends, the possibility of "sticky" wage adjustment, and possible asymmetry in responses may be needed to better explain regional adjustment to economic shocks.

Appendix

Relative wage rate growth is based on total wages and salaries from the U.S. Department of Commerce REIS 1969-1998 CD-ROM and is defined as state wage rate growth minus national wage growth. Although the wages of farm workers are included, only 900,000 out of a U.S. total of 133 million wage and salary workers were farm workers in 1998. Those engaged in fanning occupations are primarily proprietors. The use of annual wages allows for capturing the effect of relative demand shocks on the already employed that would alter average weekly hours and average weeks worked per year, even if average hourly wages are sticky in the short term. Yet, as a check of the model's robustness, we substituted average weekly earnings for annual earnings and found that the results were little affected. The national job growth rate is subtracted from the state job growth rate using nonfarm payroll data from the U.S. Department of Labor to produce relative employment growth. Finally, there are no official state-level price indexes, which may introduce a modest amount of measurement error if there are transitory state-level price shocks. Yet, any errors should be smoothed over because we primarily report results averaged across major regions and the nation.

The relative net-migration rate is calculated by subtracting U.S. net migration (mostly immigration) as a share of U.S. population from state net migration as a share of state population. Census migration estimates are used for the 1980s and 1990s. Net migration for the 1990s is defined as the sum of net-international migration, net-domestic migration, and net-federal movement (U.S. Census Bureau, 1999). Net-federal movement is defined by the U.S. Census Bureau as "... the difference between the movement of federal employees (both military and civilian) and their dependents into and out of the United States (excluding Puerto Rico) during the period." Net migration in the 1980s is obtained from the U.S. Census Bureau residual series, which implicitly contains the sum of the 1990s components (U.S. Census Bureau, 1995). In the absence of Census Bureau estimates for the 1970s, we use the residual method, which follows the general Census methodology used for the 1980s. Births and deaths are estimated each year to obtain the natural increase in state population. The total change in population less the natural increase yields a residual that is interpreted as the sum of the net-migration components. Birth and death rates from Vital Statistics of the United States are used in the calculations.

The "upper-bound" 1.461-employed net-migrant share of total employment was obtained as follows. First, it was assumed that migrants attracted by new employment opportunities would be from households with at least one worker. So taking 1990 as a representative year, the U.S. Census Bureau publication Geographical Mobility: March 1987 to March 1990 suggests that about 24.7% of the population that moved across states between 1989 and 1990 were children under 18 years old, who we assume do not work. If anything, this may understate the share of children and overstate the share of workers because economic-migrant households tend to be younger than the typical migrant household, which would include retirees. The U.S. Census Bureau publication Social and Economic Characteristics, CP-2-1 from the 1990 Census suggests about 10.5% of workers over the age of 17 are from married-couple families with only one employed worker. Therefore, of the remaining 75.3% share (over the age of 17), about 68.1% will be in the labor force and about 7.2% will be nonworking spouses.

The 1990 unemployment rate of 5.6% (U.S. Bureau of Labor Statistics, http://www.bls.gov/cps/cpsaatl.pdf) suggests that about 5.6% of the 68.1% share will be unemployed, which leads to the 64.3% employed figure. In the short-run, this may be an overstatement if new migrants experience greater difficulty in finding work in the new location, but in the long mn, migrants should have unemployment rates near the overall average. The 64.3% figure would also be overstated if there are trailing migrants such as elderly parents and other relatives who are not in the labor force, although this would be somewhat offset because some of the migrating 15 to 17 year olds would take employment. Finally, as described in footnote 13, because 44% of the population was employed in nonfarm employment, taking 64.3/44 produces 1.461. While we view the underlying assumptions as defensible, we generally believe the 64.3% figure is near the upper bound of the new migrant population that would be working, especially since only 44% of the general population is employed.

The "lower bound" 1.076 migration-employment scaling is derived following Bartik (1993, p. 307). Essentially, he reports that "'long-term" migrants (more than five years) have labor-force participation ratios that are 7.6% higher than the general population. Assuming that unemployment rates are about the same between long-term migrants and the general population would imply a 7.6% higher employment rate. However, the 7.6% figure is likely an understatement in our case because Bartik was considering the entire population of migrants such as those that moved for family or amenity reasons including retirees. We would expect economic migrants to be much more likely to participate in the labor market than the general migrant population.

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(1) Partridge and Rickman (2003) assess state employment fluctuations using the same SVAR approach. This companion paper assessed whether employment growth is more affected by labor-demand or labor-supply shocks in investigating the jobs versus people "chicken and egg" question. Rather than employment innovations, the present paper greatly differs by examining migration's role in labor-market fluctuations as either a force that smoothes over asymmetric demand shocks, or one that may be destabilizing. Another key distinction is that this study investigates whether migrants eventually take all of the newly created jobs after a demand shock, which is critical in assessing whether original residents are beneficiaries of state and local economic development policies.

(2) The SVAR approach has the advantage over traditional instrumental-variable estimation in that the latter produces consistent estimates of responses to identifiable portions of the shocks, but only portions of the labor market innovations are identified (e.g., regional labor-supply innovations are exceedingly difficult to identify).

(3) Long-run VAR restrictions are in general considered to be less restrictive than short-ran exogeneity restrictions (Stock and Watson 2001). Thus, reduced-form VARs are more effective for establishing or examining empirical regularities in the data, not for analysis of the underlying structure of the economy. Also, because the change in employment, migration, and the employment rate, which captures both changes in the unemployment rate and labor force participation, is an identity, we must exclude one of the variables. Because it is our focus, migration is not assumed as the residual, which allows us to report migration impulse functions and variance decompositions.

(4) Previous studies suggest the CRS assumption approximately reflects reality in terms of annual changes. For instance, Ciccone and Hall (1996) found relatively modest agglomeration economies, in which a doubling of employment density yielded a 6% increase in productivity (also see Glaeser et al. 1992). Over the decades that it takes the typical region's employment to double, the average annual productivity gain due to agglomeration is almost inconsequential, while any agglomeration influence by labor demand and supply innovations would be even smaller. Agglomeration economies can also be offset by congestion costs (Blanchard and Katz 1992). Perhaps reflecting the offsetting effects, Glaeser, Scheinkman, and Shleifer (1995) and Glaeser and Shapiro (2003) essentially find no association between initial city population and subsequent population growth.

(5) Like this model, Roback (1982) assumed CRS and perfectly mobile capital. However, a key difference is that her focus on cities forced her to fix the supply of land. Thus, an increase in labor would drive down the marginal product of labor, and in turn, the wage rate. Conversely, given the larger geographic scope of our study (states), the issue of land supply is not a central issue and is implicitly assumed to be elastically supplied.

(6) The RATS econometric software was used with an SVAR RATS procedure written by Norman Morin.

(7) This finding is not unexpected since the variables are defined as rates of change relative to the nation. Where rejected, the p-value was less than or equal to 0.01, except for wage rates in New Jersey, in which the null was rejected at the 0.05 level. The number of lags included in the ADF tests was derived from the optimums for the VAR equation system for each state. Conversely, we also tested our assumption that relative wage levels are nonstationary, including allowing for the possibility of relative wage levels following a deterministic trend. To examine this possibility, we utilized the DF-GLS test. Yet, there was only one state (New York) for which the null hypothesis of a unit root could be rejected at the 0.05 level, indicating that relative wages were not trend stationary and permanent changes in relative wages occurred. To further assess this issue, we also estimated our model using relative wage levels rather than relative wage changes, in which we allow relative wage levels to have a trend component. However, the results often were implausible with shocks sometimes producing explosive results, or even worse, results such as positive demand shocks inducing long-ran out-migration. We thank a referee for suggesting that we test the ramifications of using relative wage levels.

(8) The optimal lag length equals 3 in Connecticut, and 2 in California, Massachusetts, and South Dakota.

(9) Sunbelt states include Arizona, California, Florida, and Nevada. Rustbelt states are sometimes narrowly classified as East North Central region states (Michigan, Illinois, Indiana, Ohio, and Wisconsin). We usually report a broader Rustbelt grouping that adds Pennsylvania. The Energy states are Colorado, Louisiana, Montana, Oklahoma, Texas, West Virginia, and Wyoming. Based on 1980 shares of civilian employment in farm occupations (U.S. Department of Labor, Geographical Profile of Employment and Unemployment), Farm states include Iowa, Montana, Nebraska, North Dakota, and South Dakota. Note: Montana is considered both a Farm and Energy state.

(10) To improve identification, we reestimated six states using optimal lag lengths based on the Akaike information criterion (AIC). The resulting AIC lag lengths, which were longer, generally improved identification for these states: 4 for Louisiana, Ohio, and New York; 3 for Delaware and Wyoming; and 2 for Kansas. See Partridge and Rickman (2003) for more details.

(11) In sensitivity analysis, replacing the annual wage rate with the weekly rate for workers covered by unemployment insurance (and using the same lag structure) produced comparable results.

(12) Use of calculated shocks as demand variables introduces heteroskedasticity. Thus, White heteroskedasticity--consistent t-statistics are reported. Adding fixed effects does not appreciably change the results in both regressions.

(13) We estimate that about 64.3% of the new "economic" migrant population will be employed (see the Appendix). Conversely, the 1990 average nonfarm-employment share of the population was about 44% of the 1990 population, or 1.461 = 64.3/44.0 (U.S. Bureau of Labor Statistics, ftp://ftp.bls.gov/pub/suppl/empsit.ceseebl.txt, U.S. Census Bureau, Statistical Abstract of the United States 1996).

(14) In sensitivity analysis, we changed the restriction from internal labor supply having no long-run impact on migration, to migration having no long-run impact on internal labor supply. We do this by changing the ordering of our variables from wage, migration, and employment, to wage. employment, and migration. We restrict ourselves though to the primary assumption of our theoretical model that supply has no long-run effect on wage rates (i.e., keeping wage first in the ordering). We only alter the assumption regarding how the two supply sources affect one another in the long run--an assumption for which we are on less solid theoretical ground. The base case results are very close to those reported above: Migration satisfies 30% of the one-year change in employment, 43% of the two-year change in employment, and 78% of the predicted 15-year change in employment.

(15) In alphabetical order, and using Table 1 abbreviations, the 16 fastest-growing states in terms of largest average relative employment growth rates are AZ, CO, FL, GA, ID, NC, NH, NM, NV, OR, SC, TX, UT, VA, WA, WY.

(16) Because the constant terms in Equation 6 capture the persistent trends in these variables over the sample period, the standard deviations reflect variation around the long-run trend for each state (with the variables measured as relative growth rates). Conforming to expectations, Energy states had the largest variability in demand shocks on average, and Sunbelt states experienced the greatest variability in migration shocks. Reflecting reallocation between the farm and nonfarm sectors, Farm states experienced the largest internal labor-supply shocks. For instance, with nonfarm jobs being the employment measure, farm to nonfarm employment reallocations during an agricultural downturn would appear as a positive internal labor-supply shock.

(17) As described above, adjustment dynamics in this model somewhat differ from those in Blanchard and Katz (1992). Decressin and Fatas (1995) also find that the overall adjustment lag in the European Union is about the same as the United States using a VAR model. Yet, they find that EU migration initially responds somewhat slower, in which changes in EU labor-force participation bear more of the initial response. Also using a VAR approach, Jimeneo and Bentolila (1998) find Spanish adjustments to be more sluggish than those in the European Union and the United States. However, as noted above, there are key differences in how VAR studies identify demand and supply shocks compared with the SVAR approach. See Obsffeld and Peri (1998) for an assessment of migration's influence on U.S. and EU labor-market flexibility.

Mark D. Patridge * and Dan S. Rickman ([dagger])

* Department of Agricultural Economics, University of Saskatchewan, 51 Campus Drive, Saskatoon, SK S7N 5A8 Canada; E-mail mark.partridge@usask.ca.

([dagger]) 338 College of Business, Oklahoma State University, Stillwater, OK 74078 USA; E-mail dan.rickman@okstate.edu; corresponding author.

Earlier versions of this paper were presented at the 49th North American Regional Science Association Meetings, San Juan, Puerto Rico, and in seminar series at the University of Oklahoma and Oklahoma State University.

Received December 2003; accepted January 2005.

Table 1. Variance Decomposition of Migration (a)

 1 year 2 year

 D M IS D M IS

AL 0.005 0.531 0.464 0.045 0.639 0.316
AR 0.244 0.214 0.542 0.477 0.168 0.355
AZ 0.066 0.545 0.388 0.260 0.550 0.190
CA 0.617 0.364 0.019 0.757 0.217 0.026
CO 0.134 0.633 0.233 0.358 0.510 0.132
CT 0.480 0.007 0.512 0.612 0.233 0.155
DE 0.048 0.880 0.073 0.020 0.878 0.102
FL 0.004 0.673 0.323 0.146 0.685 0.169
GA 0.101 0.690 0.208 0.316 0.551 0.133
ID 0.595 0.167 0.237 0.677 0.203 0.119
IL 0.242 0.367 0.391 0.385 0.381 0.234
IN 0.516 0.198 0.287 0.488 0.344 0.168
IA 0.552 0.175 0.273 0.624 0.192 0.184
KS 0.283 0.638 0.079 0.237 0.675 0.088
KY 0.711 0.135 0.154 0.817 0.086 0.098
LA 0.690 0.065 0.245 0.905 0.024 0.071
MA 0.011 0.875 0.114 0.170 0.750 0.079
MD 0.760 0.194 0.047 0.818 0.153 0.029
ME 0.443 0.339 0.218 0.585 0.264 0.151
MI 0.139 0.443 0.418 0.290 0.528 0.182
MN 0.094 0.898 0.008 0.080 0.913 0.006
MO 0.000 0.780 0.220 0.038 0.822 0.140
MS 0.179 0.436 0.385 0.309 0.437 0.255
MT 0.064 0.591 0.346 0.256 0.536 0.207
NE 0.472 0.445 0.084 0.550 0.392 0.058
NH 0.290 0.438 0.272 0.274 0.586 0.140
NV 0.180 0.457 0.363 0.272 0.496 0.233
NJ 0.299 0.380 0.320 0.313 0.463 0.224
NM 0.084 0.222 0.694 0.507 0.108 0.385
NY 0.547 0.034 0.419 0.757 0.018 0.225
NC 0.041 0.849 0.110 0.045 0.864 0.090
ND 0.098 0.703 0.199 0.368 0.524 0.109
OH 0.002 0.938 0.060 0.097 0.664 0.239
OK 0.493 0.117 0.390 0.682 0.139 0.179
OR 0.567 0.155 0.278 0.761 0.109 0.129
PA 0.132 0.825 0.043 0.164 0.797 0.040
RI 0.135 0.802 0.063 0.168 0.773 0.060
SC 0.144 0.453 0.403 0.228 0.496 0.277
SD 0.011 0.872 0.118 0.025 0.890 0.086
TN 0.068 0.699 0.232 0.299 0.568 0.133
TX 0.109 0.822 0.068 0.492 0.471 0.037
UT 0.419 0.127 0.454 0.616 0.137 0.247
VT 0.023 0.778 0.199 0.050 0.813 0.137
VA 0.007 0.987 0.006 0.114 0.866 0.020
WA 0.104 0.511 0.385 0.189 0.581 0.230
WV 0.678 0.053 0.27 0.790 0.110 0.101
W1 0.193 0.600 0.207 0.443 0.424 0.133
WY 0.583 0.314 0.104 0.801 0.127 0.073
Average 0.283 0.456 0.262 0.402 0.442 0.157
New Engl. 0.230 0.540 0.230 0.310 0.570 0.120
Mid Atl. 0.326 0.413 0.261 0.411 0.426 0.163
ENC 0.218 0.510 0.273 0.341 0.468 0.191
WNC 0.216 0.644 0.140 0.275 0.630 0.096
S. Atl. 0.223 0.597 0.180 0.310 0.575 0.115
ESC 0.241 0.450 0.309 0.368 0.433 0.201
WSC 0.384 0.305 0.311 0.639 0.201 0.161
Mountain 0.266 0.382 0.352 0.468 0.333 0.198
Pacific 0.429 0.343 0.227 0.569 0.302 0.128
Sunbelt 0.217 0.510 0.273 0.359 0.487 0.155
Energy 0.393 0.371 0.237 0.612 0.274 0.114
Farm 0.296 0.513 0.191 0.391 0.487 0.122
Rustbelt 0.204 0.562 0.234 0.311 0.523 0.166

 15 year

 D M IS

AL 0.152 0.585 0.263
AR 0.556 0.159 0.285
AZ 0.278 0.563 0.159
CA 0.354 0.637 0.009
CO 0.588 0.328 0.084
CT 0.670 0.256 0.074
DE 0.021 0.926 0.053
FL 0.280 0.581 0.139
GA 0.362 0.500 0.138
ID 0.725 0.203 0.072
IL 0.415 0.367 0.218
IN 0.361 0.496 0.143
IA 0.629 0.248 0.123
KS 0.255 0.638 0.107
KY 0.827 0.107 0.067
LA 0.956 0.016 0.028
MA 0.551 0.389 0.060
MD 0.822 0.157 0.021
ME 0.605 0.250 0.145
MI 0.364 0.488 0.148
MN 0.074 0.919 0.007
MO 0.045 0.815 0.140
MS 0.376 0.389 0.235
MT 0.526 0.336 0.138
NE 0.607 0.350 0.043
NH 0.222 0.677 0.101
NV 0.299 0.501 0.200
NJ 0.248 0.584 0.168
NM 0.591 0.112 0.297
NY 0.820 0.020 0.160
NC 0.055 0.859 0.086
ND 0.602 0.319 0.078
OH 0.261 0.477 0.263
OK 0.731 0.142 0.127
OR 0.806 0.098 0.096
PA 0.212 0.748 0.040
RI 0.162 0.780 0.059
SC 0.188 0.572 0.240
SD 0.176 0.737 0.088
TN 0.354 0.524 0.122
TX 0.714 0.262 0.024
UT 0.725 0.127 0.148
VT 0.074 0.779 0.147
VA 0.218 0.762 0.020
WA 0.190 0.600 0.211
WV 0.727 0.208 0.065
W1 0.564 0.333 0.104
WY 0.900 0.041 0.059
Average 0.451 0.423 0.125
New Engl. 0.381 0.522 0.099
Mid Atl. 0.427 0.451 0.123
ENC 0.393 0.432 0.175
WNC 0.341 0.575 0.084
S. Atl. 0.334 0.571 0.095
ESC 0.427 0.401 0.172
WSC 0.739 0.145 0.116
Mountain 0.579 0.276 0.145
Pacific 0.450 0.445 0.105
Sunbelt 0.303 0.571 0.127
Energy 0.735 0.190 0.075
Farm 0.503 0.404 0.093
Rustbelt 0.363 0.485 0.153

(a) The variance decomposition of 1, 2, and 15 year-ahead forecasts for
relative net migration rates in terms of labor demand (D), migration
labor supply (M), and internal labor-supply shocks of original
residents (IS). Average is the unweighted average over the 48 states.
The Rustbelt includes the East North Central BEA region plus
Pennsylvania.

Table 2. Speed of Adjustment (a)

 Wage Response Speed to Migration Response
 Shock in Speed to Shock in

Region

Panel A: Average Years of Adjustment to Shocks

 D M IS D M IS

New Eng 5.5 7.5 6.7 4.7 6.2 7.0
Mid Atl 7.3 8.0 8.3 6.3 6.7 8.7
E.N. Cen 5.6 8.2 9.0 7.0 7.8 6.4
W.N.Cen 6.6 7.9 8.6 5.7 5.9 8.9
South Atl 4.5 6.6 5.4 6.9 6.5 8.4
E.S. Cen 6.3 6.3 9.5 6.5 6.8 9.5
W.S. Cen 7.8 10.5 10.8 8.0 7.3 9.0
Mountain 7.6 8.1 10.4 8.8 7.3 9.9
Pacific 6.0 10.7 8.0 7.7 8.7 5.3
Rustbelt 6.0 8.7 9.5 7.3 7.3 6.5
Sunbelt 4.5 8.0 6.0 7.8 8.5 5.5
Farm 8.2 9.4 10.4 8.4 6.4 10.2
Energy 7.6 8.7 9.1 8.1 6.6 9.6
Average 6.3 7.9 8.4 6.8 6.9 8.3

Panel B: Top/Bottom Ten States Ranking by Speed of Adjustment

 1 DE NY CT KS TX CA
 2 MN NC DE MN ND OH
 3 AZ AL NJ IN SD GA
 4 GA FL WV RI GA FL
 5 IN MN AZ SC KS IL
 6 MO MO MO VT MA MA
 7 NC WY NC GA MO MI
 8 SC AZ CA MO MT MO
 9 FL GA FL WA AL NC
10 MI KS GA CT FL ND
39 TX OH WA TX WV WV
40 WI PA WI VA MD WY
41 ID TX MD CO CT ID
42 NM WV NM MD IA TX
43 OK IA PA NM NE WI
44 IA KY OK UT UT MD
45 KY OK IA DE KY IA
46 MD NE NE NE LA UT
47 NE UT KY CA CA KY
48 UT CA UT OH OH NE

 Employment Response
 Speed to Shock in

Region

Panel A: Average Years of Adjustment to Shocks

 D M IS

New Eng 2.7 4.7 5.7
Mid Atl 5.3 5.7 7.3
E.N. Cen 4.0 6.6 5.2
W.N.Cen 6.4 5.1 5.3
South Atl 4.3 4.0 5.0
E.S. Cen 5.3 4.0 6.5
W.S. Cen 5.8 3.8 5.5
Mountain 7.8 6.3 7.9
Pacific 3.3 7.7 4.7
Rustbelt 4.8 6.5 5.0
Sunbelt 4.8 7.5 5.0
Farm 7.6 6.0 6.4
Energy 6.4 4.4 7.3
Average 5.1 5.2 5.9

Panel B: Top/Bottom Ten States Ranking by Speed of Adjustment

 1 RI NC CA
 2 SC LA RI
 3 IN MN GA
 4 VT ND LA
 5 CA TX MD
 6 CT AL MN
 7 GA FL NC
 8 KY GA ND
 9 MA IL IL
10 NH KS MI
39 DE ID ID
40 MT KY IA
41 TX UT MT
42 CO WI NJ
43 NM NM NM
44 PA CT DE
45 TN IA KY
46 IA NE NY
47 UT CA CT
48 NE OH WY

Speed of adjustment reflects the number of years before 95% of
the maximum response has occurred. The "fastest"
responding state receives a value of 1 with the "slowest" responding
state receiving a value of 48. The Rustbelt includes
the East North Central BEA region plus Pennsylvania. See Bayoumi
and Eichengreen (1993) for a similar responsiveness
measure.