# Convergence of per capita income: the case of U.S. metropolitan statistical areas.

1. Introduction

Convergence is defined as poorer regions or countries growing faster than rich regions or countries, so that the gap in relative incomes between the two will become smaller over time. Much empirical work has been done on this concept over the past 25 years. This is due to the fact that data on growth over many countries--has been highly dissimilar over the last 3 decades. The empirical studies have been done to ascertain whether or not the convergence phenomenon is indeed valid, or merely a theoretical prediction of the seminal Solow (1956) model. The study of convergence is also important in order to analyze the determinants of growth, and why certain regions/ countries tend to grow faster than others.

There are numerous empirical works testing the convergence hypothesis, with varying results. The main methodology used in the literature involves fitting cross-country regressions, where convergence is confirmed if there is a negative relationship between the average growth rate and initial income of a specific country, i.e. the higher the initial income, the slower the average growth rate. Studies by the pioneering Baumol (1986), as well as those by Barro and Sala-i-Martin (1991, 1992), and Mankiw et al. (1992) all find that convergence exists among OECD/industrial countries, as well as the regions within them.

For illustration, Barro and Sala-i-Martin (1991) make use of per capita income data for the U.S. states for the time period 1840-1990. They find significant evidence for the existence of convergence across the U.S. states for the time period. They then compare their original results for the U.S. to a cross country sample, using real GDP per capita from 1985-1990 for 85 countries, including industrialized as well as non-industrialized countries. Again they find significant evidence for the convergence of income.

The above mentioned methodology has been criticized for its simplicity, and other techniques applied to the convergence hypothesis. In contrast to the cross-sectional studies above, Quah (1993), making use panel data, and Bernard and Durlauf (1995), using a univariate form of cointegration tests that defines convergence as a stochastic process, cannot confirm convergence across a large sub-section of countries.

Time series methodologies appear to hold weight, as recently the study by Strazicich et al. (2002) makes use of a time series approach, utilizing a minimum Lagrange multiplier unit root test which endogenously determines two structural breaks in level and trend. This approach is not subject to restrictions on the null hypothesis, as many other tests are. Strazicich et al. empirically find that incomes are stochastically converging across 15 OECD countries for the time period 1870-1994. This means that the shocks to each country analyzed are temporary, and do not affect incomes in the long run. They find two structural breaks for all countries, most often around the period of the two World Wars. These results contrast with other time series tests that did not allow for structural breaks, which gives weight to the inclusion of structural breaks in our analysis.

Further evidence of the validity of the inclusion of structural breaks are provided by Carlino and Mills (1996) as well as by Loewy and Papell (1996), who utilize one-break exogenous and endogenous unit root tests, respectively, and find support for convergence among the U.S. regions in the period 1920-1990. Fleissig and Strauss (2001) examine OECD countries with a variety of panel unit root tests and find, in general, support for convergence only in the post-WWII period.

Other methods that find support for convergence include spatial econometrics, which incorporates regional factors into the analysis, as well as Instrument Variable approaches making use of 2SLS. Rey and Montouri (1999) use a spatial econometric approach, in which they incorporate effects specific to their region of study, such as geography, to test convergence of the U.S. region relative incomes. They revealed strong evidence of spatial autocorrelation in the levels of state per capita incomes over the sample period of 1929-1994. They further found that state income growth rates had a high degree of autocorrelation. This implies that, while states may be converging in relative incomes, they do this together, i.e. not independently, but rather tend to display similar movements to that of their regional neighbors.

As far as the IV approach goes, Higgins, Levy and Young (2003) use 2SLS--making use of instrumental variables--to study growth determination and the speed of income convergence across the U.S. They find that the U.S. states are converging, as confirmed by both methodologies. However, they further emphasize that convergence rates are not constant across the U.S., for example, the counties in the Southern states converge at a rate that is more than two and half times faster than the counties located in the New England states. Further, the authors confirm that large presences of finance, insurance, real estate industry, and entertainment industry are positively correlated with growth.

Finally, in line with this papers methodology, Fousekis (2007) makes use of relative stochastic convergence and specifically, stationarity tests on panel data to analyze convergence of per capita incomes for the period 1929-2005 in US state data. This covers the period just before the global crisis of 2008, and gives a good indication of convergence pre-crisis in the U.S. region. The author discovers that not all states were stationary for every sub-period after the 1960s (which is when the data is considered to become free of any deterministic or stochastic trends). This implies that there is some degree of divergence in state per capita income, although more than 80% of the states have converged, or reached their steady-state equilibrium values.

Thus, considering the importance of testing convergence, and in light of the recent turmoil that engulfed the world economy in the form of the global crisis, this paper will investigate the convergence hypothesis for the U.S., using metro regions in the period subsequent to the crisis. Note that, existence of convergence implies that national-level policies will have uniform effects on the regions of the economy, in our case the 384 US metros. Also, convergence implies, if it exists, that shocks originating from one region is likely to spread to other regions over time, i.e., in the long-run. Hence, determining the existence or non-existence of convergence is of paramount information from a policy-makers perspective, as this allows the policy authorities to understand if specific regions require additional attention following the changes in policy.

In order to achieve this, we make use of multivariate tests for stability, and the existence of unit roots, as used in the literature by Abuaf and Jorion (1990), and more recently by Harvey and Bates (2003). The stationarity tests are used to conclude whether the regions have converged, while the unit root tests come in handy to conclude whether the regions are converging. We account for the presence of structural breaks in the series, due to the highly volatile nature of the economy over the period of study, considering our data the recent global crisis, as well as numerous other possible structural breaks. Further accounting for potential breaks in our data, we conclude our empirical analysis with the panel stationarity test that accounts for structural changes, as proposed by Carrion-i-Silvestre, Del Barrio-Castro and LopezBazo [CBL] (2005).

We make use of U.S. data for studying convergence in a post-crisis world, due to the fact that we have a vast resource of data for over 40 years, on what is similar to over 384 separate economies, spread over 50 US states. There is substantial heterogeneity among the U.S. metros, in both terms of wealth, income, regulatory institutions, geographical location, and income per capita. The economies are also very open, which allows for high mobility of capital, labor and technology--all cornerstones of neo-classical models on which the idea of convergence is based. Exchange rate fluctuations are eliminated, as all the regions use the same currency. Price variations in consumer goods across countries also tend to be smaller than in a cross country analysis. We thus use the U.S as a benchmark, for what may be observed across the world. Additionally, due to our methodology, as Bernard and Durlauf (1996) mention "time series tests of convergence are not appropriate for those countries positioned far from the steady state as occurs with developing countries, in this case, the data would not be characterized by well-defined population moments, since the data are far from their limiting distribution."

To the best of our knowledge, this is the first paper that analyzes the convergence of per capita income across the 384 metros of the US economy, using not only standard unit root tests, but also tests of stability, and unit root tests with breaks, which previous studies on this topic, like Drennan et al., (2004), Drennan (2005), ignored, and failed to find evidence of convergence. We also work with data that covers more metros than these studies and also updated data that includes the "Great Recession"--a major structural break for the US economy. Note that many studies at the metro-level have analyzed convergence in prices (Huang et al. (2013) and references cited there in) and house prices (Canarella et al. (2012)), but not extensively income as we do. Most of the literature on convergence in income is only restricted to US states (see Heckelman (2013) and references cited therein), but for policy making, it is important that a more disaggregated analysis is conducted, and hence, the choice of metros in our paper. The rest of the paper is structured as follows: Section 2 discusses the methodology we employ, after which we detail the data we use in section 3. The empirical results are outlined in section 4. Finally we conclude in section 5.

2. Methodology

We study a group of metros, attempting to identify if the metro's income per capita trend is stationary--indicating convergence. For this we make use of multivariate tests for stability. We take cognizance of the fact that there are probable structural breaks in our data, and due to this we make use of the Carrion-i-Silvestre et al.'s (2005) test, which appreciates structural changes. All unit root tests we perform, excluding the KPSS, have a null hypothesis of a unit root, meaning that a rejection of null indicates convergence. The KPSS test has the opposite null of no unit root. The Hadri Lagrange multiplier (LM) test that we make use of has as the null hypothesis that all the panels are (trend) stationary.

2.1 Multivariate tests for stability and unit roots

Multivariate tests are appropriate, if the aim is studying across a group of observations. Let [x.sub.t] be n vector of contrasts between each of the metros, and a benchmark, e.g. [x'.sub.t] = ([y.sup.1.sub.t], [y.sup.2.sub.t], ..., [y.sup.N.sub.t]). The simplest multivariate convergence model is the zero mean VAR(l) process:

[x.sub.t] = [alpha][x.sub.t-1] + [[omega].sub.t]. (3)

where [alpha] is a N x N matrix and [[omega].sub.t] is N dimensional vector of martingale differences innovations with constant variance [summation over [omega]] []. The model is said to be homogeneous if [alpha] = [phi][I.sub.N]. Following Abuaf and Jorion (1990), Harvey and Bates (2003) propose the use of the multivariate unit root test from the homogeneous model. Specifically, they used the Wald-type statistic on [rho] = [phi] - 1, that is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

and referred to as the multivariate homogeneous Dickey-Fuller (MHDF) statistic, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is initially estimated by the sample covariance matrix of first-differenced data and then re-estimated by iterating the estimation of [phi] to convergence. Under the null hypothesis, [H.sub.0]: [rho] = 0,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [W.sub.i](r) are independent standard Brownian motion processes, i=1, ..., N; if N is large, [[psi].sub.0](N) is approximately Gaussian. The null hypothesis is rejected when [[psi].sub.0](N) less than a given critical value [delta].

An interesting feature of the MHDF test is that it is invariant to any nonsingular transformation of [x.sub.t]. Consequently, it is invariant to which country is chosen as benchmark. This feature is lost in case of heterogeneous model in which [alpha] is diagonal.

One can designate a parametric correction of the variance of the errors, through the addition of lagged differenced terms of [x.sub.t]. to cope with serial correlation of the errors. The critical values of the test can be obtained from Harvey and Bates (2003); see also O'Connell (1998).

A generalization of the KPSS test can be applied to xt to test whether the N metros have converged in the context of stability analysis. Then, the involved statistic is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

where C = [T.summation over (t=1)]([t.summation over (j=1)][x.sub.j])([t.summation over (j=1)][x.sub.j])' and [[??].sup.-1] is a non-parametric estimation of the long run variance of [x.sub.t]. Under the null hypothesis of zero mean stationarity, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with d denoting weak convergence in distribution. Critical values are provided in Nyblom (1989) and Hobijn and Franses (2000). A non-rejection of the null hypothesis would suggest overall evidence of stability, in the sense that the n countries should have converged absolutely.

There may be confusion as to the role that unit root and stationarity tests play in detecting convergence. As described by Busetti et al. (2007), the two types of tests are in fact meant for different purposes and cannot be arbitrarily interchanged. Unit root tests are used for estimating whether series are in the process of converging, dependent on initial conditions. Stationarity tests however, are used for exploring whether series have converged. This implies that the difference between the series is stable. This is again confirmed by Harvey and Carvalho (2002).

It is therefore important to distinguish between convergence and stability. Convergence is analyzed by testing the null hypothesis of unit root, whereas stability is tested by way of the null of stationarity. Thus the unit root tests come in handy to conclude whether the metros are converging, while the stationarity tests are used to conclude whether the metros have converged.

2.2 Panel stationarity test with structural changes: The Carrion-i-Silvestre, Del Barrio-Castro and Lopez-Bazo [CBL] (2005) test

The reasons for taking into account structural breaks in the income per capita series are due to the potential shifts in the data due to shocks--such as the stock market crashes, and more recently the global crisis. It goes without saying the economic system is subject to capricious up and down-swings. Therefore, the income per capita series will be subjected to a number of structural changes. That is why we have taken account of Carrion-i-Silvestre et al.'s (2005) test in the analysis of convergence. In what follows, we briefly describe the CBL (2005) test, which, by design, has the ability to test the null hypothesis of panel stationarity while allowing multiple structural breaks. It will be described as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where [x.sub.i,t] is the logarithm of the series of income per capita, i=1 ..., N represents the number of cross section units and [[epsilon].sub.i,t] is the error term. The dummy variables [Du.sub.i,k,t] and [DT.sup.*.sub.i,k,t] are defined as [DU.sub.i,k,t] = 1 for t > [T.sup.i.sub.b,k] and 0 otherwise, and [DT.sup.*.sub.i,k,t] = t - [T.sup.i.sub.b,k] for t > [T.sup.i.sub.b,j] and 0 wise; and [T.sup.i.sub.b,k] denotes the kth date of the break for the ith individual, k = {1, ... [m.sub.i]}, [m.sub.i] [greater than or equal to] 1.

The model in equation (6) constitutes a generalization of that of Hadri (2000) and it includes individual effects, individual structural break effects (i.e., shift in the mean caused by the structural breaks known as temporal effects where [[beta].sub.i] [not equal to] 0), and temporal structural break effects (i.e., shift in the individual time trend where [[gamma].sub.i] [not equal to] 0). In addition, the specification given by equation (6) considers several structural breaks, which are located on different unidentified dates and where the number of structural breaks is allowed to vary between the members of the panel. The test statistic is constructed by running individual KPSS regressions for each member of the panel, and then taking the average of the N individual statistics. The general expression of the test statistic is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [S.sub.i,t] = [t.summation over (j=1)][[??].sub.i,j] represents the partial sum process that is obtained using the estimated OLS residuals of equation (6), and [[??].sup.2.sub.i] is the consistent estimate of the long-run variance of residual [[epsilon].sub.i,t]; this allows the disturbances to be heteroscedastic across the cross-sectional dimension.

In equation (7), [lambda] is defined as the vector

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The test statistic for the null hypothesis of a stationary panel with multiple shifts is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

As in the case of the univariate KPSS test statistic, the null hypothesis of stationarity in the panel is rejected for large values of Z([lambda]). [bar.[zeta]] and [bar.[zeta]] are the cross-sectional average of the individual mean and variance of [[delta].sub.[down arrow]]i([lambda]) = [[??].sup.-2.sub.i][T.sup.-2] [T.summation over (t=1)][S.sup.2.sub.i,t].

3. Data

We use annual US data, measuring real metro level Income per capita across the U.S. Data incorporating 384 metros from all 50 States is available from 1969-2011, obtained from the Bureau of Economic Analysis regional economic accounts. Note that our metric for the tests of stationarity is the ratio of income per capita of a specific metro relative to the cross-sectional average. So if this ratio shows stationarity, we can conclude of convergence, as this means that the income of the specific metro is moving towards the overall average of the entire country.

We use U.S. data to study convergence, as it represents a unique and vast resource that covers 40 years, and it mimics many separate global "economies;" the states represent over 50 separate economies as the metro areas are dispersed over the states. This allows more in depth analysis and isolation of particular phenomena. Moreover, there is substantial heterogeneity among the U.S. metros, in terms of wealth, income, regulatory institutions, geographical location, and income per capita.

These separate economies are very open due to the fact that they lie in the same country. This allows for unrestricted movement of capital, labor and technology--high mobility of factors is a cornerstone of neo-classical models on which the idea of convergence is based. Fluctuations in exchange rates are all but eliminated, as the regions use the same currency. The effects of inflation and differing consumer prices are also somewhat mitigated, as price variations in consumer goods across countries (i.e. within a country) also tend to be smaller than in a cross country (i.e. between countries) analysis. We make use of the U.S. regions as they act as a benchmark for what may be observed in an analysis that makes use of global data, and to which other studies of this nature may be compared.

All the U.S. metros used are available in the appendix if needed for reference.

4. Empirical Results

Before we proceed with the presentation of our results, we make a note of the specification of our KPSS unit root test. The literature establishes that the KPSS test without a constant has power against a stationary process with a non-zero mean, as well as against a non-stationary process (Busetti and Harvey, 2002). Thus we perform the KPSS test without a constant term, given its increased power when performed in this manner. In this way, we test if the series have converged individually or in groups, and if the involved convergence is absolute.

The Levin-Lin-Chu (2002) and Im-Pesaran-Shin (2003) tests have as the null hypothesis that all the panels contain a unit root. The Hadri (2000) Lagrange multiplier (LM) test has as the null hypothesis that all the panels are (trend) stationary. The KPSS has a null of stationarity, as do the CBL and Hadri LM tests.

With regard to multivariate tests, the cross-section mean was subtracted from each individual series. This can be beneficial in two ways: First, the cross-section mean series can be regarded as a benchmark, and then, the study of all individual series is guaranteed. Second, this subtraction can mitigate the effects of not taking into account the cross-sectional dependence. This assumption reflects reality, as the analysis of macroeconomic time series for different metros may be affected by similar events that could introduce dependency between individuals in the panel data set. We therefore follow Levin et al. (Levin, Lin and Chu [LLC]) (2002), who suggested removing the cross-section mean, which is equivalent to include temporal effects in the panel data. We applied the LLC test to the series to compare its results with those from the other multivariate homogeneous test, including, the MHDF test. Given that the MHDF test does not take account of heterogeneity, we decided to add the Im et al. (Im, Pesaran and Shin [IPS]) (2003) test that has been formulated by allowing for this heterogeneity.

From Table 1 above, we can see that all the tests reject the null of a unit root, both under the homogeneity and heterogeneity assumptions, which indicates that the series are in the process of converging, as they do not have a permanent memory and are heading towards their respective steady states. This does not necessarily imply convergence; however, given the time frame it confirms that in the long run the income of the respective metros should all reach their steady states--we can say that the metros are converging. This is as predicted by contemporary macroeconomic models.

Next, we consider Multivariate tests for stability which, as described, are used to test if the series have converged.

As we see from Table 2, the MKPSS, Hadri and CBL tests all reject the null hypothesis of stationarity. For comparison to the MKPSS test, we used the Bai-Ng (2004) PANIC test for stationarity hypothesis. A specific feature of PANIC is that it tests the data's unobserved co mponents instead of the observed series. From a cursory glance, this procedure is based on the factor structure of the large dimensional panels to reveal the nature of nonstationarity in the data. Using the PANIC test, we failed to reject the null of stationarity.

Due to the fact that the MKPSS test does not take heterogeneity into account, we include the panel stationarity test of Hadri (2000), which allows for heterogeneity. With regards to convergence, this may be advantageous, as the homogeneity assumption restricts every metro to converge at the same rate. The Hadri test that includes structural breaks, as well as Hadri test with individual and temporal effects, both reject the null of stationarity.

Referring in particular to the CBL test, we see that the null hypothesis of stationarity with structural breaks is rejected. A little digression is absolutely essential here. From an econometric point of view, the conflicting results of stationarity and unit root tests may be an indicator of nonlinearity and structural changes. We are therefore justified in using the CBL test.

Based on the results from Table 2, we reject the null of stationarity for the panel as a whole. This would indicate that rather than no convergence, there is actually a divergence of income per capita in the U.S. metros. This result is reasonable within the current investigation, as given the literature, the income per capita in the U.S. metros were typically close together, and have now tended to widen. This divergence terminology is supported by Busetti et al. (2007).

Overall, based on test results from Tables 1 and 2, our finds are that the unit root tests reject the null hypothesis of unit root, and the stationarity tests reject the null hypothesis of stationarity. We can thus conclude from the unit root tests that the series are in the process of converging. However, given the rejection of stationarity hypothesis in the stationarity tests, we can conclude that there is no evidence for overall stability of the income per capita among the U.S. metros, and this implies that the series have diverged.

Potential reasons for this divergence of income per capita in the U.S. metros are outlined by Ganong and Shoag (2012). They argue that migration of labor can account for all of the observed change in convergence. In their study, it is shown that the relationship between migration and housing prices has changed in the recent past. Even though housing prices have always been higher in richer areas, housing prices now capitalize a far greater proportion of the income differences across states. Due to the fact that housing prices are now a bigger divider between income groups, labor markets no longer clear through migration, but rather by skill-sorting. Thus, the divergence in income per capita may be attributed to a divergence in the skill-specific returns to productive places, a redirection of low-skilled migration, diminished human capital convergence, and continued convergence among places with unconstrained housing supply.

Consequently, the reason that convergence of income per capita has ceased, can be answered by a divergence in workers with tertiary education across places--where high-skilled workers are becoming relatively more concentrated. As argued by the authors, there is an increase in consumers' desire to live in places that are highly educated, as well as an increase in firms' desire for highly skilled labor. The fact that they are willing to pay increasingly large amounts to live in their place of choosing, drives up the price of housing in these areas.

From the firm side, the rise of the so-called information economy and a bias towards highly skilled technological change cause an upsurge in the demand for skilled labor, due to their higher productivity levels. This means that firms in highly-skilled areas may pay higher wages, however, due to the fact that migration of labor has been prevented by the excessive housing prices, only a select few highly-skilled individuals can take advantage of the higher wages in these areas. The fact that housing prices constrain the movement of labor means that workers from poorer regions are not able to move to regions where their remuneration may be higher, and this is due to the upsurge of housing prices in the areas that offer higher wages. Further, because low-workers are no longer able to move to well-educated regions, there is a slowdown of human capital convergence--which may be due to diminished learning by doing and skills-sharing, all caused by increased housing prices.

5. Conclusion

The confirmation of convergence is of utmost importance to policy makers and economists, since it is necessary to find out what impact certain policies might have on growth, as well as to test to see if model predictions hold in the real world--which would indicate the validity of certain macroeconomic models. Having recently undergone a major global crisis which may have affected the distribution of income, we test the convergence hypothesis across the U.S metros for the time period 1969-2011.

Firstly, we make use of multivariate tests for existence of unit roots. Given that the series are likely to contain structural breaks, and that these breaks must be accounted for, we proceed with the analysis using the panel stationarity test accounting for structural changes as proposed by Carrion-i-Silvestre et al. (2005).

Overall, our results indicate that while the U.S metros are indeed converging, they have not converged but have indeed diverged. So, just like earlier studies, allowing for more sophisticated techniques with breaks and updated data, cannot reverse the evidence of divergences of US metros. Potential reasons for this are vast, and to be sure a full study needs to be undertaken to determine probably causes. However, given the increase in housing prices in rich areas, migration of labor may be constrained, which limits the convergence of human capital and productive returns to specific skills. This may limit the "catch up" factor that drives convergence of income per capita.

Given the finding in this paper, future studies may test for convergence over a large sample of countries, both developed and potentially developing. A limitation of this study, which may be rectified in future work, is that a more in-depth study focusing on the reasons for the divergence found in the U.S. metros could be carried out.

Our findings have important implications for literature related to macroeconomic modeling, but also policy regarding land-ownership. Literature may need to take into account the role of the price of land, and how it affects labor, in modeling economic growth, while policy makers should take note of the fact that increases in house prices may limit the migration of labor, and ultimately affect productivity. Policy that encourages the continued migration of labor by way of ensuring realistic housing prices for the working class may ensure future convergence.

GHASSEN EL-MONTASSER

University of Manouba

RANGAN GUPTA

rangan.gupta@up.ac.za

University of Pretoria

DEVON SMITHERS

University of Pretoria

Received 26 August 2015 * Received in revised form 2 October 2015

Accepted 3 October 2015 * Available online 25 January 2016

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Strazicich, M. C., J. Lee, and E. Day (2002), "Are Incomes Converging among OECD Countries? Time Series Evidence with Two Structural Breaks," Journal of Macroeconomics 26: 131-145.

Convergence is defined as poorer regions or countries growing faster than rich regions or countries, so that the gap in relative incomes between the two will become smaller over time. Much empirical work has been done on this concept over the past 25 years. This is due to the fact that data on growth over many countries--has been highly dissimilar over the last 3 decades. The empirical studies have been done to ascertain whether or not the convergence phenomenon is indeed valid, or merely a theoretical prediction of the seminal Solow (1956) model. The study of convergence is also important in order to analyze the determinants of growth, and why certain regions/ countries tend to grow faster than others.

There are numerous empirical works testing the convergence hypothesis, with varying results. The main methodology used in the literature involves fitting cross-country regressions, where convergence is confirmed if there is a negative relationship between the average growth rate and initial income of a specific country, i.e. the higher the initial income, the slower the average growth rate. Studies by the pioneering Baumol (1986), as well as those by Barro and Sala-i-Martin (1991, 1992), and Mankiw et al. (1992) all find that convergence exists among OECD/industrial countries, as well as the regions within them.

For illustration, Barro and Sala-i-Martin (1991) make use of per capita income data for the U.S. states for the time period 1840-1990. They find significant evidence for the existence of convergence across the U.S. states for the time period. They then compare their original results for the U.S. to a cross country sample, using real GDP per capita from 1985-1990 for 85 countries, including industrialized as well as non-industrialized countries. Again they find significant evidence for the convergence of income.

The above mentioned methodology has been criticized for its simplicity, and other techniques applied to the convergence hypothesis. In contrast to the cross-sectional studies above, Quah (1993), making use panel data, and Bernard and Durlauf (1995), using a univariate form of cointegration tests that defines convergence as a stochastic process, cannot confirm convergence across a large sub-section of countries.

Time series methodologies appear to hold weight, as recently the study by Strazicich et al. (2002) makes use of a time series approach, utilizing a minimum Lagrange multiplier unit root test which endogenously determines two structural breaks in level and trend. This approach is not subject to restrictions on the null hypothesis, as many other tests are. Strazicich et al. empirically find that incomes are stochastically converging across 15 OECD countries for the time period 1870-1994. This means that the shocks to each country analyzed are temporary, and do not affect incomes in the long run. They find two structural breaks for all countries, most often around the period of the two World Wars. These results contrast with other time series tests that did not allow for structural breaks, which gives weight to the inclusion of structural breaks in our analysis.

Further evidence of the validity of the inclusion of structural breaks are provided by Carlino and Mills (1996) as well as by Loewy and Papell (1996), who utilize one-break exogenous and endogenous unit root tests, respectively, and find support for convergence among the U.S. regions in the period 1920-1990. Fleissig and Strauss (2001) examine OECD countries with a variety of panel unit root tests and find, in general, support for convergence only in the post-WWII period.

Other methods that find support for convergence include spatial econometrics, which incorporates regional factors into the analysis, as well as Instrument Variable approaches making use of 2SLS. Rey and Montouri (1999) use a spatial econometric approach, in which they incorporate effects specific to their region of study, such as geography, to test convergence of the U.S. region relative incomes. They revealed strong evidence of spatial autocorrelation in the levels of state per capita incomes over the sample period of 1929-1994. They further found that state income growth rates had a high degree of autocorrelation. This implies that, while states may be converging in relative incomes, they do this together, i.e. not independently, but rather tend to display similar movements to that of their regional neighbors.

As far as the IV approach goes, Higgins, Levy and Young (2003) use 2SLS--making use of instrumental variables--to study growth determination and the speed of income convergence across the U.S. They find that the U.S. states are converging, as confirmed by both methodologies. However, they further emphasize that convergence rates are not constant across the U.S., for example, the counties in the Southern states converge at a rate that is more than two and half times faster than the counties located in the New England states. Further, the authors confirm that large presences of finance, insurance, real estate industry, and entertainment industry are positively correlated with growth.

Finally, in line with this papers methodology, Fousekis (2007) makes use of relative stochastic convergence and specifically, stationarity tests on panel data to analyze convergence of per capita incomes for the period 1929-2005 in US state data. This covers the period just before the global crisis of 2008, and gives a good indication of convergence pre-crisis in the U.S. region. The author discovers that not all states were stationary for every sub-period after the 1960s (which is when the data is considered to become free of any deterministic or stochastic trends). This implies that there is some degree of divergence in state per capita income, although more than 80% of the states have converged, or reached their steady-state equilibrium values.

Thus, considering the importance of testing convergence, and in light of the recent turmoil that engulfed the world economy in the form of the global crisis, this paper will investigate the convergence hypothesis for the U.S., using metro regions in the period subsequent to the crisis. Note that, existence of convergence implies that national-level policies will have uniform effects on the regions of the economy, in our case the 384 US metros. Also, convergence implies, if it exists, that shocks originating from one region is likely to spread to other regions over time, i.e., in the long-run. Hence, determining the existence or non-existence of convergence is of paramount information from a policy-makers perspective, as this allows the policy authorities to understand if specific regions require additional attention following the changes in policy.

In order to achieve this, we make use of multivariate tests for stability, and the existence of unit roots, as used in the literature by Abuaf and Jorion (1990), and more recently by Harvey and Bates (2003). The stationarity tests are used to conclude whether the regions have converged, while the unit root tests come in handy to conclude whether the regions are converging. We account for the presence of structural breaks in the series, due to the highly volatile nature of the economy over the period of study, considering our data the recent global crisis, as well as numerous other possible structural breaks. Further accounting for potential breaks in our data, we conclude our empirical analysis with the panel stationarity test that accounts for structural changes, as proposed by Carrion-i-Silvestre, Del Barrio-Castro and LopezBazo [CBL] (2005).

We make use of U.S. data for studying convergence in a post-crisis world, due to the fact that we have a vast resource of data for over 40 years, on what is similar to over 384 separate economies, spread over 50 US states. There is substantial heterogeneity among the U.S. metros, in both terms of wealth, income, regulatory institutions, geographical location, and income per capita. The economies are also very open, which allows for high mobility of capital, labor and technology--all cornerstones of neo-classical models on which the idea of convergence is based. Exchange rate fluctuations are eliminated, as all the regions use the same currency. Price variations in consumer goods across countries also tend to be smaller than in a cross country analysis. We thus use the U.S as a benchmark, for what may be observed across the world. Additionally, due to our methodology, as Bernard and Durlauf (1996) mention "time series tests of convergence are not appropriate for those countries positioned far from the steady state as occurs with developing countries, in this case, the data would not be characterized by well-defined population moments, since the data are far from their limiting distribution."

To the best of our knowledge, this is the first paper that analyzes the convergence of per capita income across the 384 metros of the US economy, using not only standard unit root tests, but also tests of stability, and unit root tests with breaks, which previous studies on this topic, like Drennan et al., (2004), Drennan (2005), ignored, and failed to find evidence of convergence. We also work with data that covers more metros than these studies and also updated data that includes the "Great Recession"--a major structural break for the US economy. Note that many studies at the metro-level have analyzed convergence in prices (Huang et al. (2013) and references cited there in) and house prices (Canarella et al. (2012)), but not extensively income as we do. Most of the literature on convergence in income is only restricted to US states (see Heckelman (2013) and references cited therein), but for policy making, it is important that a more disaggregated analysis is conducted, and hence, the choice of metros in our paper. The rest of the paper is structured as follows: Section 2 discusses the methodology we employ, after which we detail the data we use in section 3. The empirical results are outlined in section 4. Finally we conclude in section 5.

2. Methodology

We study a group of metros, attempting to identify if the metro's income per capita trend is stationary--indicating convergence. For this we make use of multivariate tests for stability. We take cognizance of the fact that there are probable structural breaks in our data, and due to this we make use of the Carrion-i-Silvestre et al.'s (2005) test, which appreciates structural changes. All unit root tests we perform, excluding the KPSS, have a null hypothesis of a unit root, meaning that a rejection of null indicates convergence. The KPSS test has the opposite null of no unit root. The Hadri Lagrange multiplier (LM) test that we make use of has as the null hypothesis that all the panels are (trend) stationary.

2.1 Multivariate tests for stability and unit roots

Multivariate tests are appropriate, if the aim is studying across a group of observations. Let [x.sub.t] be n vector of contrasts between each of the metros, and a benchmark, e.g. [x'.sub.t] = ([y.sup.1.sub.t], [y.sup.2.sub.t], ..., [y.sup.N.sub.t]). The simplest multivariate convergence model is the zero mean VAR(l) process:

[x.sub.t] = [alpha][x.sub.t-1] + [[omega].sub.t]. (3)

where [alpha] is a N x N matrix and [[omega].sub.t] is N dimensional vector of martingale differences innovations with constant variance [summation over [omega]] []. The model is said to be homogeneous if [alpha] = [phi][I.sub.N]. Following Abuaf and Jorion (1990), Harvey and Bates (2003) propose the use of the multivariate unit root test from the homogeneous model. Specifically, they used the Wald-type statistic on [rho] = [phi] - 1, that is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

and referred to as the multivariate homogeneous Dickey-Fuller (MHDF) statistic, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is initially estimated by the sample covariance matrix of first-differenced data and then re-estimated by iterating the estimation of [phi] to convergence. Under the null hypothesis, [H.sub.0]: [rho] = 0,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [W.sub.i](r) are independent standard Brownian motion processes, i=1, ..., N; if N is large, [[psi].sub.0](N) is approximately Gaussian. The null hypothesis is rejected when [[psi].sub.0](N) less than a given critical value [delta].

An interesting feature of the MHDF test is that it is invariant to any nonsingular transformation of [x.sub.t]. Consequently, it is invariant to which country is chosen as benchmark. This feature is lost in case of heterogeneous model in which [alpha] is diagonal.

One can designate a parametric correction of the variance of the errors, through the addition of lagged differenced terms of [x.sub.t]. to cope with serial correlation of the errors. The critical values of the test can be obtained from Harvey and Bates (2003); see also O'Connell (1998).

A generalization of the KPSS test can be applied to xt to test whether the N metros have converged in the context of stability analysis. Then, the involved statistic is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

where C = [T.summation over (t=1)]([t.summation over (j=1)][x.sub.j])([t.summation over (j=1)][x.sub.j])' and [[??].sup.-1] is a non-parametric estimation of the long run variance of [x.sub.t]. Under the null hypothesis of zero mean stationarity, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with d denoting weak convergence in distribution. Critical values are provided in Nyblom (1989) and Hobijn and Franses (2000). A non-rejection of the null hypothesis would suggest overall evidence of stability, in the sense that the n countries should have converged absolutely.

There may be confusion as to the role that unit root and stationarity tests play in detecting convergence. As described by Busetti et al. (2007), the two types of tests are in fact meant for different purposes and cannot be arbitrarily interchanged. Unit root tests are used for estimating whether series are in the process of converging, dependent on initial conditions. Stationarity tests however, are used for exploring whether series have converged. This implies that the difference between the series is stable. This is again confirmed by Harvey and Carvalho (2002).

It is therefore important to distinguish between convergence and stability. Convergence is analyzed by testing the null hypothesis of unit root, whereas stability is tested by way of the null of stationarity. Thus the unit root tests come in handy to conclude whether the metros are converging, while the stationarity tests are used to conclude whether the metros have converged.

2.2 Panel stationarity test with structural changes: The Carrion-i-Silvestre, Del Barrio-Castro and Lopez-Bazo [CBL] (2005) test

The reasons for taking into account structural breaks in the income per capita series are due to the potential shifts in the data due to shocks--such as the stock market crashes, and more recently the global crisis. It goes without saying the economic system is subject to capricious up and down-swings. Therefore, the income per capita series will be subjected to a number of structural changes. That is why we have taken account of Carrion-i-Silvestre et al.'s (2005) test in the analysis of convergence. In what follows, we briefly describe the CBL (2005) test, which, by design, has the ability to test the null hypothesis of panel stationarity while allowing multiple structural breaks. It will be described as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where [x.sub.i,t] is the logarithm of the series of income per capita, i=1 ..., N represents the number of cross section units and [[epsilon].sub.i,t] is the error term. The dummy variables [Du.sub.i,k,t] and [DT.sup.*.sub.i,k,t] are defined as [DU.sub.i,k,t] = 1 for t > [T.sup.i.sub.b,k] and 0 otherwise, and [DT.sup.*.sub.i,k,t] = t - [T.sup.i.sub.b,k] for t > [T.sup.i.sub.b,j] and 0 wise; and [T.sup.i.sub.b,k] denotes the kth date of the break for the ith individual, k = {1, ... [m.sub.i]}, [m.sub.i] [greater than or equal to] 1.

The model in equation (6) constitutes a generalization of that of Hadri (2000) and it includes individual effects, individual structural break effects (i.e., shift in the mean caused by the structural breaks known as temporal effects where [[beta].sub.i] [not equal to] 0), and temporal structural break effects (i.e., shift in the individual time trend where [[gamma].sub.i] [not equal to] 0). In addition, the specification given by equation (6) considers several structural breaks, which are located on different unidentified dates and where the number of structural breaks is allowed to vary between the members of the panel. The test statistic is constructed by running individual KPSS regressions for each member of the panel, and then taking the average of the N individual statistics. The general expression of the test statistic is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [S.sub.i,t] = [t.summation over (j=1)][[??].sub.i,j] represents the partial sum process that is obtained using the estimated OLS residuals of equation (6), and [[??].sup.2.sub.i] is the consistent estimate of the long-run variance of residual [[epsilon].sub.i,t]; this allows the disturbances to be heteroscedastic across the cross-sectional dimension.

In equation (7), [lambda] is defined as the vector

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The test statistic for the null hypothesis of a stationary panel with multiple shifts is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

As in the case of the univariate KPSS test statistic, the null hypothesis of stationarity in the panel is rejected for large values of Z([lambda]). [bar.[zeta]] and [bar.[zeta]] are the cross-sectional average of the individual mean and variance of [[delta].sub.[down arrow]]i([lambda]) = [[??].sup.-2.sub.i][T.sup.-2] [T.summation over (t=1)][S.sup.2.sub.i,t].

3. Data

We use annual US data, measuring real metro level Income per capita across the U.S. Data incorporating 384 metros from all 50 States is available from 1969-2011, obtained from the Bureau of Economic Analysis regional economic accounts. Note that our metric for the tests of stationarity is the ratio of income per capita of a specific metro relative to the cross-sectional average. So if this ratio shows stationarity, we can conclude of convergence, as this means that the income of the specific metro is moving towards the overall average of the entire country.

We use U.S. data to study convergence, as it represents a unique and vast resource that covers 40 years, and it mimics many separate global "economies;" the states represent over 50 separate economies as the metro areas are dispersed over the states. This allows more in depth analysis and isolation of particular phenomena. Moreover, there is substantial heterogeneity among the U.S. metros, in terms of wealth, income, regulatory institutions, geographical location, and income per capita.

These separate economies are very open due to the fact that they lie in the same country. This allows for unrestricted movement of capital, labor and technology--high mobility of factors is a cornerstone of neo-classical models on which the idea of convergence is based. Fluctuations in exchange rates are all but eliminated, as the regions use the same currency. The effects of inflation and differing consumer prices are also somewhat mitigated, as price variations in consumer goods across countries (i.e. within a country) also tend to be smaller than in a cross country (i.e. between countries) analysis. We make use of the U.S. regions as they act as a benchmark for what may be observed in an analysis that makes use of global data, and to which other studies of this nature may be compared.

All the U.S. metros used are available in the appendix if needed for reference.

4. Empirical Results

Before we proceed with the presentation of our results, we make a note of the specification of our KPSS unit root test. The literature establishes that the KPSS test without a constant has power against a stationary process with a non-zero mean, as well as against a non-stationary process (Busetti and Harvey, 2002). Thus we perform the KPSS test without a constant term, given its increased power when performed in this manner. In this way, we test if the series have converged individually or in groups, and if the involved convergence is absolute.

The Levin-Lin-Chu (2002) and Im-Pesaran-Shin (2003) tests have as the null hypothesis that all the panels contain a unit root. The Hadri (2000) Lagrange multiplier (LM) test has as the null hypothesis that all the panels are (trend) stationary. The KPSS has a null of stationarity, as do the CBL and Hadri LM tests.

With regard to multivariate tests, the cross-section mean was subtracted from each individual series. This can be beneficial in two ways: First, the cross-section mean series can be regarded as a benchmark, and then, the study of all individual series is guaranteed. Second, this subtraction can mitigate the effects of not taking into account the cross-sectional dependence. This assumption reflects reality, as the analysis of macroeconomic time series for different metros may be affected by similar events that could introduce dependency between individuals in the panel data set. We therefore follow Levin et al. (Levin, Lin and Chu [LLC]) (2002), who suggested removing the cross-section mean, which is equivalent to include temporal effects in the panel data. We applied the LLC test to the series to compare its results with those from the other multivariate homogeneous test, including, the MHDF test. Given that the MHDF test does not take account of heterogeneity, we decided to add the Im et al. (Im, Pesaran and Shin [IPS]) (2003) test that has been formulated by allowing for this heterogeneity.

From Table 1 above, we can see that all the tests reject the null of a unit root, both under the homogeneity and heterogeneity assumptions, which indicates that the series are in the process of converging, as they do not have a permanent memory and are heading towards their respective steady states. This does not necessarily imply convergence; however, given the time frame it confirms that in the long run the income of the respective metros should all reach their steady states--we can say that the metros are converging. This is as predicted by contemporary macroeconomic models.

Next, we consider Multivariate tests for stability which, as described, are used to test if the series have converged.

As we see from Table 2, the MKPSS, Hadri and CBL tests all reject the null hypothesis of stationarity. For comparison to the MKPSS test, we used the Bai-Ng (2004) PANIC test for stationarity hypothesis. A specific feature of PANIC is that it tests the data's unobserved co mponents instead of the observed series. From a cursory glance, this procedure is based on the factor structure of the large dimensional panels to reveal the nature of nonstationarity in the data. Using the PANIC test, we failed to reject the null of stationarity.

Due to the fact that the MKPSS test does not take heterogeneity into account, we include the panel stationarity test of Hadri (2000), which allows for heterogeneity. With regards to convergence, this may be advantageous, as the homogeneity assumption restricts every metro to converge at the same rate. The Hadri test that includes structural breaks, as well as Hadri test with individual and temporal effects, both reject the null of stationarity.

Referring in particular to the CBL test, we see that the null hypothesis of stationarity with structural breaks is rejected. A little digression is absolutely essential here. From an econometric point of view, the conflicting results of stationarity and unit root tests may be an indicator of nonlinearity and structural changes. We are therefore justified in using the CBL test.

Based on the results from Table 2, we reject the null of stationarity for the panel as a whole. This would indicate that rather than no convergence, there is actually a divergence of income per capita in the U.S. metros. This result is reasonable within the current investigation, as given the literature, the income per capita in the U.S. metros were typically close together, and have now tended to widen. This divergence terminology is supported by Busetti et al. (2007).

Overall, based on test results from Tables 1 and 2, our finds are that the unit root tests reject the null hypothesis of unit root, and the stationarity tests reject the null hypothesis of stationarity. We can thus conclude from the unit root tests that the series are in the process of converging. However, given the rejection of stationarity hypothesis in the stationarity tests, we can conclude that there is no evidence for overall stability of the income per capita among the U.S. metros, and this implies that the series have diverged.

Potential reasons for this divergence of income per capita in the U.S. metros are outlined by Ganong and Shoag (2012). They argue that migration of labor can account for all of the observed change in convergence. In their study, it is shown that the relationship between migration and housing prices has changed in the recent past. Even though housing prices have always been higher in richer areas, housing prices now capitalize a far greater proportion of the income differences across states. Due to the fact that housing prices are now a bigger divider between income groups, labor markets no longer clear through migration, but rather by skill-sorting. Thus, the divergence in income per capita may be attributed to a divergence in the skill-specific returns to productive places, a redirection of low-skilled migration, diminished human capital convergence, and continued convergence among places with unconstrained housing supply.

Consequently, the reason that convergence of income per capita has ceased, can be answered by a divergence in workers with tertiary education across places--where high-skilled workers are becoming relatively more concentrated. As argued by the authors, there is an increase in consumers' desire to live in places that are highly educated, as well as an increase in firms' desire for highly skilled labor. The fact that they are willing to pay increasingly large amounts to live in their place of choosing, drives up the price of housing in these areas.

From the firm side, the rise of the so-called information economy and a bias towards highly skilled technological change cause an upsurge in the demand for skilled labor, due to their higher productivity levels. This means that firms in highly-skilled areas may pay higher wages, however, due to the fact that migration of labor has been prevented by the excessive housing prices, only a select few highly-skilled individuals can take advantage of the higher wages in these areas. The fact that housing prices constrain the movement of labor means that workers from poorer regions are not able to move to regions where their remuneration may be higher, and this is due to the upsurge of housing prices in the areas that offer higher wages. Further, because low-workers are no longer able to move to well-educated regions, there is a slowdown of human capital convergence--which may be due to diminished learning by doing and skills-sharing, all caused by increased housing prices.

5. Conclusion

The confirmation of convergence is of utmost importance to policy makers and economists, since it is necessary to find out what impact certain policies might have on growth, as well as to test to see if model predictions hold in the real world--which would indicate the validity of certain macroeconomic models. Having recently undergone a major global crisis which may have affected the distribution of income, we test the convergence hypothesis across the U.S metros for the time period 1969-2011.

Firstly, we make use of multivariate tests for existence of unit roots. Given that the series are likely to contain structural breaks, and that these breaks must be accounted for, we proceed with the analysis using the panel stationarity test accounting for structural changes as proposed by Carrion-i-Silvestre et al. (2005).

Overall, our results indicate that while the U.S metros are indeed converging, they have not converged but have indeed diverged. So, just like earlier studies, allowing for more sophisticated techniques with breaks and updated data, cannot reverse the evidence of divergences of US metros. Potential reasons for this are vast, and to be sure a full study needs to be undertaken to determine probably causes. However, given the increase in housing prices in rich areas, migration of labor may be constrained, which limits the convergence of human capital and productive returns to specific skills. This may limit the "catch up" factor that drives convergence of income per capita.

Given the finding in this paper, future studies may test for convergence over a large sample of countries, both developed and potentially developing. A limitation of this study, which may be rectified in future work, is that a more in-depth study focusing on the reasons for the divergence found in the U.S. metros could be carried out.

Our findings have important implications for literature related to macroeconomic modeling, but also policy regarding land-ownership. Literature may need to take into account the role of the price of land, and how it affects labor, in modeling economic growth, while policy makers should take note of the fact that increases in house prices may limit the migration of labor, and ultimately affect productivity. Policy that encourages the continued migration of labor by way of ensuring realistic housing prices for the working class may ensure future convergence.

GHASSEN EL-MONTASSER

University of Manouba

RANGAN GUPTA

rangan.gupta@up.ac.za

University of Pretoria

DEVON SMITHERS

University of Pretoria

Received 26 August 2015 * Received in revised form 2 October 2015

Accepted 3 October 2015 * Available online 25 January 2016

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APPENDIX a) List of all Metro's 1 hp10180 Abilene, TX (Metropolitan Statistical Area) 2 hp10420 Akron, OH (Metropolitan Statistical Area) 3 hp10500 Albany, GA (Metropolitan Statistical Area) 4 hp10580 Albany-Schenectady-Troy, NY (Metropolitan Statistical Area) 5 hp10740 Albuquerque, NM (Metropolitan Statistical Area) 6 hp10780 Alexandria, LA (Metropolitan Statistical Area) 7 hp10900 Allentown-Bethlehem-Easton, PA-NJ (Metropolitan Statistical Area) 8 hp11020 Altoona, PA (Metropolitan Statistical Area) 9 hp11100 Amarillo, TX (Metropolitan Statistical Area) 10 hp11180 Ames, IA (Metropolitan Statistical Area) 11 hp11260 Anchorage, AK (Metropolitan Statistical Area) 12 hp11300 Anderson, IN (Metropolitan Statistical Area) 13 hp11340 Anderson, SC (Metropolitan Statistical Area) 14 hp11460 Ann Arbor, MI (Metropolitan Statistical Area) 15 hp11500 Anniston-Oxford, AL (Metropolitan Statistical Area) 16 hp11540 Appleton, WI (Metropolitan Statistical Area) 17 hp11700 Asheville, NC (Metropolitan Statistical Area) 18 hp12020 Athens-Clarke County, GA (Metropolitan Statistical Area) 19 hp12060 Atlanta-Sandy Springs-Marietta, GA (Metropolitan Statistical Area) 20 hp12100 Atlantic City-Hammonton, NJ (Metropolitan Statistical Area) 21 hp12220 Auburn-Opelika, AL (Metropolitan Statistical Area) 22 hp12260 Augusta-Richmond County, GA-SC (Metropolitan Statistical Area) 23 hp12420 Austin-Round Rock-San Marcos, TX (Metropolitan Statistical Area) 24 hp12540 Bakersfield-Delano, CA (Metropolitan Statistical Area) 25 hp12580 Baltimore-Towson, MD (Metropolitan Statistical Area) 26 hp12620 Bangor, ME (Metropolitan Statistical Area) 27 hp12700 Barnstable Town, MA (Metropolitan Statistical Area) 28 hp12940 Baton Rouge, LA (Metropolitan Statistical Area) 29 hp12980 Battle Creek, MI (Metropolitan Statistical Area) 30 hp13020 Bay City, MI (Metropolitan Statistical Area) 31 hp13140 Beaumont-Port Arthur, TX (Metropolitan Statistical Area) 32 hp13380 Bellingham, WA (Metropolitan Statistical Area) 33 hp13460 Bend, OR (Metropolitan Statistical Area) 34 hp13644 Bethesda-Rockville-Frederick, MD (MSAD) 35 hp13740 Billings, MT (Metropolitan Statistical Area) 36 hp13780 Binghamton, NY (Metropolitan Statistical Area) 37 hp13820 Birmingham-Hoover, AL (Metropolitan Statistical Area) 38 hp13900 Bismarck, ND (Metropolitan Statistical Area) 39 hp13980 Blacksburg-Christiansburg-Radford, VA (Metropolitan Statistical Area) 40 hp14020 Bloomington, IN (Metropolitan Statistical Area) 41 hp14060 Bloomington-Normal, IL (Metropolitan Statistical Area) 42 hp14260 Boise City-Nampa, ID (Metropolitan Statistical Area) 43 hp14484 Boston-Cambridge-Quincy, MA-NH (Metropolitan Statistical Area) 44 hp14500 Boulder, CO (Metropolitan Statistical Area) 45 hp14540 Bowling Green, KY (Metropolitan Statistical Area) 46 hp14740 Bremerton-Silverdale, WA (Metropolitan Statistical Area) 47 hp14860 Bridgeport-Stamford-Norwalk, CT (Metropolitan Statistical Area) 48 hp15180 Brownsville-Harlingen, TX (Metropolitan Statistical Area) 49 hp15260 Brunswick, GA (Metropolitan Statistical Area) 50 hp15380 Buffalo-Niagara Falls, NY (Metropolitan Statistical Area) 51 hp15500 Burlington, NC (Metropolitan Statistical Area) 52 hp15540 Burlington-South Burlington, VT (Metropolitan Statistical Area) 53 hp15764 Cambridge-Newton-Framingham, MA (MSAD) 54 hp15804 Camden, NJ (MSAD) 55 hp15940 Canton-Massillon, OH (Metropolitan Statistical Area) 56 hp15980 Cape Coral-Fort Myers, FL (Metropolitan Statistical Area) 57 hp16020 Cape Girardeau-Jackson, MO-IL (Metropolitan Statistical Area) 58 hp16180 Carson City, NV (Metropolitan Statistical Area) 59 hp16220 Casper, WY (Metropolitan Statistical Area) 60 hp16300 Cedar Rapids, IA (Metropolitan Statistical Area) 61 hp16580 Champaign-Urbana, IL (Metropolitan Statistical Area) 62 hp16620 Charleston, WV (Metropolitan Statistical Area) 63 hp16700 Charleston-North Charleston-Summerville, SC (Metropolitan Statistical Area) 64 hp16740 Charlotte-Gastonia-Rock Hill, NC-SC (Metropolitan Statistical Area) 65 hp16820 Charlottesville, VA (Metropolitan Statistical Area) 66 hp16860 Chattanooga, TN-GA (Metropolitan Statistical Area) 67 hp16940 Cheyenne, WY (Metropolitan Statistical Area) 68 hp16974 Chicago-Joliet-Naperville, IL-IN-WI (Metropolitan Statistical Area) 69 hp17020 Chico, CA (Metropolitan Statistical Area) 70 hp17140 Cincinnati-Middletown, OH-KY-IN (Metropolitan Statistical Area) 71 hp17300 Clarksville, TN-KY (Metropolitan Statistical Area) 72 hp17420 Cleveland, TN (Metropolitan Statistical Area) 73 hp17460 Cleveland-Elyria-Mentor, OH (Metropolitan Statistical Area) 74 hp17660 Coeur d'Alene, ID (Metropolitan Statistical Area) 75 hp17780 College Station-Bryan, TX (Metropolitan Statistical Area) 76 hp17820 Colorado Springs, CO (Metropolitan Statistical Area) 77 hp17860 Columbia, MO (Metropolitan Statistical Area) 78 hp17900 Columbia, SC (Metropolitan Statistical Area) 79 hp17980 Columbus, GA-AL (Metropolitan Statistical Area) 80 hp18020 Columbus, IN (Metropolitan Statistical Area) 81 hp18140 Columbus, OH (Metropolitan Statistical Area) 82 hp18580 Corpus Christi, TX (Metropolitan Statistical Area) 83 hp18700 Corvallis, OR (Metropolitan Statistical Area) 84 hp18880 Crestview-Fort Walton Beach-Destin, FL (Metropolitan Statistical Area) 85 hp19060 Cumberland, MD-WV (Metropolitan Statistical Area) 86 hp19124 Dallas-Fort Worth-Arlington, TX (Metropolitan Statistical Area) 87 hp19140 Dalton, GA (Metropolitan Statistical Area) 88 hp19180 Danville, IL (Metropolitan Statistical Area) 89 hp19260 Danville, VA (Metropolitan Statistical Area) 90 hp19340 Davenport-Moline-Rock Island, IA-IL (Metropolitan Statistical Area) 91 hp19380 Dayton, OH (Metropolitan Statistical Area) 92 hp19460 Decatur, AL (Metropolitan Statistical Area) 93 hp19500 Decatur, IL (Metropolitan Statistical Area) 94 hp19660 Deltona-Daytona Beach-Ormond Beach, FL (Metropolitan Statistical Area) 95 hp19740 Denver-Aurora-Broomfield, CO (Metropolitan Statistical Area) 96 hp19780 Des Moines-West Des Moines, IA (Metropolitan Statistical Area) 97 hp19804 Detroit-Warren-Livonia, MI (Metropolitan Statistical Area) 98 hp20020 Dothan, AL (Metropolitan Statistical Area) 99 hp20100 Dover, DE (Metropolitan Statistical Area) 100 hp20220 Dubuque, IA (Metropolitan Statistical Area) 101 hp20260 Duluth, MN-WI (Metropolitan Statistical Area) 102 hp20500 Durham-Chapel Hill, NC (Metropolitan Statistical Area) 103 hp20740 Eau Claire, WI (Metropolitan Statistical Area) 104 hp20764 Edison-New Brunswick, NJ (MSAD) 105 hp20940 El Centro, CA (Metropolitan Statistical Area) 106 hp21060 Elizabethtown, KY (Metropolitan Statistical Area) 107 hp21140 Elkhart-Goshen, IN (Metropolitan Statistical Area) 108 hp21300 Elmira, NY (Metropolitan Statistical Area) 109 hp21340 El Paso, TX (Metropolitan Statistical Area) 110 hp21500 Erie, PA (Metropolitan Statistical Area) 111 hp21660 Eugene-Springfield, OR (Metropolitan Statistical Area) 112 hp21780 Evansville, IN-KY (Metropolitan Statistical Area) 113 hp21820 Fairbanks, AK (Metropolitan Statistical Area) 114 hp22020 Fargo, ND-MN (Metropolitan Statistical Area) 115 hp22140 Farmington, NM (Metropolitan Statistical Area) 116 hp22180 Fayetteville, NC (Metropolitan Statistical Area) 117 hp22220 Fayetteville-Springdale-Rogers, AR-MO (Metropolitan Statistical Area) 118 hp22380 Flagstaff, AZ (Metropolitan Statistical Area) 119 hp22420 Flint, MI (Metropolitan Statistical Area) 120 hp22500 Florence, SC (Metropolitan Statistical Area) 121 hp22520 Florence-Muscle Shoals, AL (Metropolitan Statistical Area) 122 hp22540 Fond du Lac, WI (Metropolitan Statistical Area) 123 hp22660 Fort Collins-Loveland, CO (Metropolitan Statistical Area) 124 hp22744 Fort Smith, AR-OK (Metropolitan Statistical Area) 125 hp22900 Fort Smith, AR-OK 126 hp23060 Fort Wayne, IN (Metropolitan Statistical Area) 127 hp23104 Fort Worth-Arlington, TX (MSAD) 128 hp23420 Fresno, CA (Metropolitan Statistical Area) 129 hp23460 Gadsden, AL (Metropolitan Statistical Area) 130 hp23540 Gainesville, FL (Metropolitan Statistical Area) 131 hp23580 Gainesville, GA (Metropolitan Statistical Area) 132 hp23844 Gary, IN (MSAD) 133 hp24020 Glens Falls, NY (Metropolitan Statistical Area) 134 hp24140 Goldsboro, NC (Metropolitan Statistical Area) 135 hp24220 Grand Forks, ND-MN (Metropolitan Statistical Area) 136 hp24300 Grand Junction, CO (Metropolitan Statistical Area) 137 hp24340 Grand Rapids-Wyoming, MI (Metropolitan Statistical Area) 138 hp24500 Great Falls, MT (Metropolitan Statistical Area) 139 hp24540 Greeley, CO (Metropolitan Statistical Area) 140 hp24580 Green Bay, WI (Metropolitan Statistical Area) 141 hp24660 Greensboro-High Point, NC (Metropolitan Statistical Area) 142 hp24780 Greenville, NC (Metropolitan Statistical Area) 143 hp24860 Greenville-Mauldin-Easley, SC (Metropolitan Statistical Area) 144 hp25060 Gulfport-Biloxi, MS (Metropolitan Statistical Area) 145 hp25180 Hagerstown-Martinsburg, MD-WV (Metropolitan Statistical Area) 146 hp25260 Hanford-Corcoran, CA (Metropolitan Statistical Area) 147 hp25420 Harrisburg-Carlisle, PA (Metropolitan Statistical Area) 148 hp25500 Harrisonburg, VA (Metropolitan Statistical Area) 149 hp25540 Hartford-West Hartford-East Hartford, CT (Metropolitan Statistical Area) 150 hp25620 Hattiesburg, MS (Metropolitan Statistical Area) 151 hp25860 Hickory-Lenoir-Morganton, NC (Metropolitan Statistical Area) 152 hp25980 Hinesville-Fort Stewart, GA (Metropolitan Statistical Area) 153 hp26100 Holland-Grand Haven, MI (Metropolitan Statistical Area) 154 hp26180 Honolulu, HI (Metropolitan Statistical Area) 155 hp26300 Hot Springs, AR (Metropolitan Statistical Area) 156 hp26380 Houma-Bayou Cane-Thibodaux, LA (Metropolitan Statistical Area) 157 hp26420 Houston-Sugar Land-Baytown, TX (Metropolitan Statistical Area) 158 hp26580 Huntington-Ashland, WV-KY-OH (Metropolitan Statistical Area) 159 hp26620 Huntsville, AL (Metropolitan Statistical Area) 160 hp26820 Idaho Falls, ID (Metropolitan Statistical Area) 161 hp26900 Indianapolis-Carmel, IN (Metropolitan Statistical Area) 162 hp26980 Iowa City, IA (Metropolitan Statistical Area) 163 hp27060 Ithaca, NY (Metropolitan Statistical Area) 164 hp27100 Jackson, MI (Metropolitan Statistical Area) 165 hp27140 Jackson, MS (Metropolitan Statistical Area) 166 hp27180 Jackson, TN (Metropolitan Statistical Area) 167 hp27260 Jacksonville, FL (Metropolitan Statistical Area) 168 hp27340 Jacksonville, NC (Metropolitan Statistical Area) 169 hp27500 Janesville, WI (Metropolitan Statistical Area) 170 hp27620 Jefferson City, MO (Metropolitan Statistical Area) 171 hp27740 Johnson City, TN (Metropolitan Statistical Area) 172 hp27780 Johnstown, PA (Metropolitan Statistical Area) 173 hp27860 Jonesboro, AR (Metropolitan Statistical Area) 174 hp27900 Joplin, MO (Metropolitan Statistical Area) 175 hp28020 Kalamazoo-Portage, MI (Metropolitan Statistical Area) 176 hp28100 Kankakee-Bradley, IL (Metropolitan Statistical Area) 177 hp28140 Kansas City, MO-KS (Metropolitan Statistical Area) 178 hp28420 Kennewick-Pasco-Richland, WA (Metropolitan Statistical Area) 179 hp28660 Killeen-Temple-Fort Hood, TX (Metropolitan Statistical Area) 180 hp28700 Kingsport-Bristol-Bristol, TN-VA (Metropolitan Statistical Area) 181 hp28740 Kingston, NY (Metropolitan Statistical Area) 182 hp28940 Knoxville, TN (Metropolitan Statistical Area) 183 hp29020 Kokomo, IN (Metropolitan Statistical Area) 184 hp29100 La Crosse, WI-MN (Metropolitan Statistical Area) 185 hp29140 Lafayette, IN (Metropolitan Statistical Area) 186 hp29180 Lafayette, LA (Metropolitan Statistical Area) 187 hp29340 Lake Charles, LA (Metropolitan Statistical Area) 188 hp29404 Lake County-Kenosha County, IL-WI (MSAD) 189 hp29420 Lake Havasu City-Kingman, AZ (Metropolitan Statistical Area) 190 hp29460 Lakeland-Winter Haven, FL (Metropolitan Statistical Area) 191 hp29540 Lancaster, PA (Metropolitan Statistical Area) 192 hp29620 Lansing-East Lansing, MI (Metropolitan Statistical Area) 193 hp29700 Laredo, TX (Metropolitan Statistical Area) 194 hp29740 Las Cruces, NM (Metropolitan Statistical Area) 195 hp29820 Las Vegas-Paradise, NV (Metropolitan Statistical Area) 196 hp29940 Lawrence, KS (Metropolitan Statistical Area) 197 hp30020 Lawton, OK (Metropolitan Statistical Area) 198 hp30140 Lebanon, PA (Metropolitan Statistical Area) 199 hp30300 Lewiston, ID-WA (Metropolitan Statistical Area) 200 hp30340 Lewiston-Auburn, ME (Metropolitan Statistical Area) 201 hp30460 Lexington-Fayette, KY (Metropolitan Statistical Area) 202 hp30620 Lima, OH (Metropolitan Statistical Area) 203 hp30700 Lincoln, NE (Metropolitan Statistical Area) 204 hp30780 Little Rock-North Little Rock-Conway, AR (Metropolitan Statistical Area) 205 hp30860 Logan, UT-ID (Metropolitan Statistical Area) 206 hp30980 Longview, TX (Metropolitan Statistical Area) 207 hp31020 Longview, WA (Metropolitan Statistical Area) 208 hp31084 Los Angeles-Long Beach-Santa Ana, CA (Metropolitan Statistical Area) 209 hp31140 Louisville-Jefferson County, KY-IN (Metropolitan Statistical Area) 210 hp31180 Lubbock, TX (Metropolitan Statistical Area) 211 hp31340 Lynchburg, VA (Metropolitan Statistical Area) 212 hp31420 Macon, GA (Metropolitan Statistical Area) 213 hp31460 Madera-Chowchilla, CA (Metropolitan Statistical Area) 214 hp31540 Madison, WI (Metropolitan Statistical Area) 215 hp31700 Manchester-Nashua, NH (Metropolitan Statistical Area) 216 hp31740 Manhattan, KS (Metropolitan Statistical Area) 217 hp31860 Mankato-North Mankato, MN (Metropolitan Statistical Area) 218 hp31900 Mansfield, OH (Metropolitan Statistical Area) 219 hp32580 McAllen-Edinburg-Mission, TX (Metropolitan Statistical Area) 220 hp32780 Medford, OR (Metropolitan Statistical Area) 221 hp32820 Memphis, TN-MS-AR (Metropolitan Statistical Area) 222 hp32900 Merced, CA (Metropolitan Statistical Area) 223 hp33124 Miami-Fort Lauderdale-Pompano Beach, FL (Metropolitan Statistical Area) 224 hp33140 Michigan City-La Porte, IN (Metropolitan Statistical Area) 225 hp33260 Midland, TX (Metropolitan Statistical Area) 226 hp33340 Milwaukee-Waukesha-West Allis, WI (Metropolitan Statistical Area) 227 hp33460 Minneapolis-St. Paul-Bloomington, MN-WI (Metropolitan Statistical Area) 228 hp33540 Missoula, MT (Metropolitan Statistical Area) 229 hp33660 Mobile, AL (Metropolitan Statistical Area) 230 hp33700 Modesto, CA (Metropolitan Statistical Area) 231 hp33740 Monroe, LA (Metropolitan Statistical Area) 232 hp33780 Monroe, MI (Metropolitan Statistical Area) 233 hp33860 Montgomery, AL (Metropolitan Statistical Area) 234 hp34060 Morgantown, WV (Metropolitan Statistical Area) 235 hp34100 Morristown, TN (Metropolitan Statistical Area) 236 hp34580 Mount Vernon-Anacortes, WA (Metropolitan Statistical Area) 237 hp34620 Muncie, IN (Metropolitan Statistical Area) 238 hp34740 Muskegon-Norton Shores, MI (Metropolitan Statistical Area) 239 hp34820 Myrtle Beach-North Myrtle Beach-Conway, SC (Metropolitan Statistical Area) 240 hp34900 Napa, CA (Metropolitan Statistical Area) 241 hp34940 Naples-Marco Island, FL (Metropolitan Statistical Area) 242 hp34980 Nashville-Davidson-Murfreesboro-Franklin, TN (Metropolitan Statistical Area) 243 hp35004 Nassau-Suffolk, NY (MSAD) 244 hp35084 Newark-Union, NJ-PA (MSAD) 245 hp35300 New Haven-Milford, CT (Metropolitan Statistical Area) 246 hp35380 New Orleans-Metairie-Kenner, LA (Metropolitan Statistical Area) 247 hp35644 New York-Northern New Jersey-Long Island, NY-NJ-PA (Metropolitan Statistical Area) 248 hp35660 Niles-Benton Harbor, MI (Metropolitan Statistical Area) 249 hp35840 North Port-Bradenton-Sarasota, FL (Metropolitan Statistical Area) 250 hp35980 Norwich-New London, CT (Metropolitan Statistical Area) 251 hp36084 Oakland-Fremont-Hayward, CA (MSAD) 252 hp36100 Ocala, FL (Metropolitan Statistical Area) 253 hp36140 Ocean City, NJ (Metropolitan Statistical Area) 254 hp36220 Odessa, TX (Metropolitan Statistical Area) 255 hp36260 Ogden-Clearfield, UT (Metropolitan Statistical Area) 256 hp36420 Oklahoma City, OK (Metropolitan Statistical Area) 257 hp36500 Olympia, WA (Metropolitan Statistical Area) 258 hp36540 Omaha-Council Bluffs, NE-IA (Metropolitan Statistical Area) 259 hp36740 Orlando-Kissimmee-Sanford, FL (Metropolitan Statistical Area) 260 hp36780 Oshkosh-Neenah, WI (Metropolitan Statistical Area) 261 hp36980 Owensboro, KY (Metropolitan Statistical Area) 262 hp37100 Oxnard-Thousand Oaks-Ventura, CA (Metropolitan Statistical Area) 263 hp37340 Palm Bay-Melbourne-Titusville, FL (Metropolitan Statistical Area) 264 hp37380 Palm Coast, FL (Metropolitan Statistical Area) 265 hp37460 Panama City-Lynn Haven-Panama City Beach, FL (Metropolitan Statistical Area) 266 hp37620 Parkersburg-Marietta-Vienna, WV-OH (Metropolitan Statistical Area) 267 hp37700 Pascagoula, MS (Metropolitan Statistical Area) 268 hp37764 Peabody, MA (MSAD) 269 hp37860 Pensacola-Ferry Pass-Brent, FL (Metropolitan Statistical Area) 270 hp37900 Peoria, IL (Metropolitan Statistical Area) 271 hp37964 Philadelphia-Camden-Wilmington, PA-NJ-DE-MD (Metropolitan Statistical Area) 272 hp38060 Phoenix-Mesa-Glendale, AZ (Metropolitan Statistical Area) 273 hp38220 Pine Bluff, AR (Metropolitan Statistical Area) 274 hp38300 Pittsburgh, PA (Metropolitan Statistical Area) 275 hp38340 Pittsfield, MA (Metropolitan Statistical Area) 276 hp38540 Pocatello, ID (Metropolitan Statistical Area) 277 hp38860 Portland-South Portland-Biddeford, ME (Metropolitan Statistical Area) 278 hp38900 Portland-Vancouver-Hillsboro, OR-WA (Metropolitan Statistical Area) 279 hp38940 Port St. Lucie, FL (Metropolitan Statistical Area) 280 hp39100 Poughkeepsie-Newburgh-Middletown, NY (Metropolitan Statistical Area) 281 hp39140 Prescott, AZ (Metropolitan Statistical Area) 282 hp39300 Providence-New Bedford-Fall River, RI-MA (Metropolitan Statistical Area) 283 hp39340 Provo-Orem, UT (Metropolitan Statistical Area) 284 hp39380 Pueblo, CO (Metropolitan Statistical Area) 285 hp39460 Punta Gorda, FL (Metropolitan Statistical Area) 286 hp39540 Racine, WI (Metropolitan Statistical Area) 287 hp39580 Raleigh-Cary, NC (Metropolitan Statistical Area) 288 hp39660 Rapid City, SD (Metropolitan Statistical Area) 289 hp39740 Reading, PA (Metropolitan Statistical Area) 290 hp39820 Redding, CA (Metropolitan Statistical Area) 291 hp39900 Reno-Sparks, NV (Metropolitan Statistical Area) 292 hp40060 Richmond, VA (Metropolitan Statistical Area) 293 hp40140 Riverside-San Bernardino-Ontario, CA (Metropolitan Statistical Area) 294 hp40220 Roanoke, VA (Metropolitan Statistical Area) 295 hp40340 Rochester, MN (Metropolitan Statistical Area) 296 hp40380 Rochester, NY (Metropolitan Statistical Area) 297 hp40420 Rockford, IL (Metropolitan Statistical Area) 298 hp40484 Rockingham County-Strafford County, NH (MSAD) 299 hp40580 Rocky Mount, NC (Metropolitan Statistical Area) 300 hp40660 Rome, GA (Metropolitan Statistical Area) 301 hp40900 Sacramento-Arden-Arcade-Roseville, CA (Metropolitan Statistical Area) 302 hp40980 Saginaw-Saginaw Township North, MI (Metropolitan Statistical Area) 303 hp41060 St. Cloud, MN (Metropolitan Statistical Area) 304 hp41100 St. George, UT (Metropolitan Statistical Area) 305 hp41140 St. Joseph, MO-KS (Metropolitan Statistical Area) 306 hp41180 St. Louis, MO-IL (Metropolitan Statistical Area) 307 hp41420 Salem, OR (Metropolitan Statistical Area) 308 hp41500 Salinas, CA (Metropolitan Statistical Area) 309 hp41540 Salisbury, MD (Metropolitan Statistical Area) 310 hp41620 Salt Lake City, UT (Metropolitan Statistical Area) 311 hp41660 San Angelo, TX (Metropolitan Statistical Area) 312 hp41700 San Antonio-New Braunfels, TX (Metropolitan Statistical Area) 313 hp41740 San Diego-Carlsbad-San Marcos, CA (Metropolitan Statistical Area) 314 hp41780 Sandusky, OH (Metropolitan Statistical Area) 315 hp41884 San Francisco-Oakland-Fremont, CA (Metropolitan Statistical Area) 316 hp41940 San Jose-Sunnyvale-Santa Clara, CA (Metropolitan Statistical Area) 317 hp42020 San Luis Obispo-Paso Robles, CA (Metropolitan Statistical Area) 318 hp42044 Santa Ana-Anaheim-Irvine, CA (MSAD) 319 hp42060 Santa Barbara-Santa Maria-Goleta, CA (Metropolitan Statistical Area) 320 hp42100 Santa Cruz-Watsonville, CA (Metropolitan Statistical Area) 321 hp42140 Santa Fe, NM (Metropolitan Statistical Area) 322 hp42220 Santa Rosa-Petaluma, CA (Metropolitan Statistical Area) 323 hp42340 Savannah, GA (Metropolitan Statistical Area) 324 hp42540 Scranton-Wilkes-Barre, PA (Metropolitan Statistical Area) 325 hp42644 Seattle-Tacoma-Bellevue, WA (Metropolitan Statistical Area) 326 hp42680 Sebastian-Vero Beach, FL (Metropolitan Statistical Area) 327 hp43100 Sheboygan, WI (Metropolitan Statistical Area) 328 hp43300 Sherman-Denison, TX (Metropolitan Statistical Area) 329 hp43340 Shreveport-Bossier City, LA (Metropolitan Statistical Area) 330 hp43580 Sioux City, IA-NE-SD (Metropolitan Statistical Area) 331 hp43620 Sioux Falls, SD (Metropolitan Statistical Area) 332 hp43780 South Bend-Mishawaka, IN-MI (Metropolitan Statistical Area) 333 hp43900 Spartanburg, SC (Metropolitan Statistical Area) 334 hp44060 Spokane, WA (Metropolitan Statistical Area) 335 hp44100 Springfield, IL (Metropolitan Statistical Area) 336 hp44140 Springfield, MA (Metropolitan Statistical Area) 337 hp44180 Springfield, MO (Metropolitan Statistical Area) 338 hp44220 Springfield, OH (Metropolitan Statistical Area) 339 hp44300 State College, PA (Metropolitan Statistical Area) 340 hp44600 Steubenville-Weirton, OH-WV (Metropolitan Statistical Area) 341 hp44700 Stockton, CA (Metropolitan Statistical Area) 342 hp44940 Sumter, SC (Metropolitan Statistical Area) 343 hp45060 Syracuse, NY (Metropolitan Statistical Area) 344 hp45104 Tacoma, WA (MSAD) 345 hp45220 Tallahassee, FL (Metropolitan Statistical Area) 346 hp45300 Tampa-St. Petersburg-Clearwater, FL (Metropolitan Statistical Area) 347 hp45460 Terre Haute, IN (Metropolitan Statistical Area) 348 hp45500 Texarkana, TX-Texarkana, AR (Metropolitan Statistical Area) 349 hp45780 Toledo, OH (Metropolitan Statistical Area) 350 hp45820 Topeka, KS (Metropolitan Statistical Area) 351 hp45940 Trenton-Ewing, NJ (Metropolitan Statistical Area) 352 hp46060 Tucson, AZ (Metropolitan Statistical Area) 353 hp46140 Tulsa, OK (Metropolitan Statistical Area) 354 hp46220 Tuscaloosa, AL (Metropolitan Statistical Area) 355 hp46340 Tyler, TX (Metropolitan Statistical Area) 356 hp46540 Utica-Rome, NY (Metropolitan Statistical Area) 357 hp46660 Valdosta, GA (Metropolitan Statistical Area) 358 hp46700 Vallejo-Fairfield, CA (Metropolitan Statistical Area) 359 hp47020 Victoria, TX (Metropolitan Statistical Area) 360 hp47220 Vineland-Millville-Bridgeton, NJ (Metropolitan Statistical Area) 361 hp47260 Virginia Beach-Norfolk-Newport News, VA-NC (Metropolitan Statistical Area) 362 hp47300 Visalia-Porterville, CA (Metropolitan Statistical Area) 363 hp47380 Waco, TX (Metropolitan Statistical Area) 364 hp47580 Warner Robins, GA (Metropolitan Statistical Area) 365 hp47644 Warren-Troy-Farmington Hills, MI (MSAD) 366 hp47894 Washington-Arlington-Alexandria, DC-VA-MD-WV (MSAD) 367 hp47940 Waterloo-Cedar Falls, IA (Metropolitan Statistical Area) 368 hp48140 Wausau, WI (Metropolitan Statistical Area) 369 hp48300 Wenatchee-East Wenatchee, WA (Metropolitan Statistical Area) 370 hp48424 West Palm Beach-Boca Raton-Boynton Beach, FL (MSAD) 371 hp48540 Wheeling, WV-OH (Metropolitan Statistical Area) 372 hp48620 Wichita, KS (Metropolitan Statistical Area) 373 hp48660 Wichita Falls, TX (Metropolitan Statistical Area) 374 hp48700 Williamsport, PA (Metropolitan Statistical Area) 375 hp48864 Wilmington, DE-MD-NJ (MSAD) 376 hp48900 Wilmington, NC (Metropolitan Statistical Area) 377 hp49020 Winchester, VA-WV (Metropolitan Statistical Area) 378 hp49180 Winston-Salem, NC (Metropolitan Statistical Area) 379 hp49340 Worcester, MA (Metropolitan Statistical Area) 380 hp49420 Yakima, WA (Metropolitan Statistical Area) 381 hp49620 York-Hanover, PA (Metropolitan Statistical Area) 382 hp49660 Youngstown-Warren-Boardman, OH-PA (Metropolitan Statistical Area) 383 hp49700 Yuba City, CA (Metropolitan Statistical Area) 384 hp49740 Yuma, AZ (Metropolitan Statistical Area) Table 1 Summary of the results of the tests for unit roots Test Statistic p-value Decision Multivariate homogeneous -29.0945 0.0000 Reject [H.sub.o] of Dickey-Fuller (MHDF) a unit root Levin Lin Chu (LLC) -3.6540 0.0000 Reject [H.sub.o] of a unit root In, Pesaran and Shin (IPS) -3.5929 0.0000 Reject [H.sub.o] of a unit root Table 2 Summary of the results of the panel and multivariate test for stationarity Test Statistic p-value Decision MKPSS 46668 0.000 Reject [H.sub.o] of stationarity Bai-Ng Panic test 1611.134 0.144 Cannot Reject [H.sub.o] for stationarity of stationarity Hadri LM Test 15.794725 0.0000 Reject the [H.sub.o] of stationarity CBL Test 77.181 0.000 Reject the [H.sub.o] of stationarity

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Author: | Montasser, Ghassen El-; Gupta, Rangan; Smithers, Devon |
---|---|

Publication: | Economics, Management, and Financial Markets |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Dec 1, 2016 |

Words: | 8752 |

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