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The informational value of unemployment statistics: A note on the time series properties of participation rates
Economics Letters 92 (2006) 428 – 433 www.elsevier.com/locate/econbase
The informational value of unemployment statistics: A note on the time series properties of participation rates ¨ sterholm * Magnus Gustavsson 1, Pa¨r O Department of Economics, Uppsala University, Box 513, 75120 Uppsala, Sweden Received 21 April 2005; received in revised form 10 March 2006; accepted 24 March 2006 Available online 24 July 2006
Abstract Using a battery of unit root tests, we show that labor force participation rates in Australia, Canada and the U.S. are non-stationary. This implies that great care is needed before unemployment rates are used as measures of joblessness. D 2006 Elsevier B.V. All rights reserved. Keywords: Hysteresis; Unit root test JEL classification: C22; E24; J21
1. Introduction Unemployment rates are often the focus of studies of the macroeconomic causes and consequences of joblessness, for example in studies concerning unemployment persistence, the connection between nonemployment and income inequality, and how non-employment affects crime rates.2 The unemployment rate is also often used as a control for the state of the labor market in time series regressions.3 However,
* Corresponding author. Tel.: +46 1 202 378 4135; fax: +46 18 471 1478. ¨ sterholm). E-mail addresses: [email protected] (M. Gustavsson)8 [email protected] (P. O 1 Tel.: +46 18 471 1103; fax: +46 18 471 1478. 2 See e.g. Blinder and Esaki (1978), Song and Wu (1997), and Gould et al. (2002). 3 See e.g. Dee and Sela (2003) and Jacobson (2004). 0165-1765/$ - see front matter D 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2006.03.032
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
429
that the evolution of the unemployment rate need not reflect that of joblessness is neglected in many studies, even though it is well known that individuals’ labor force participation may change over time for market-driven reasons (bdiscouraged workersQ) as well as in response to a partner’s labor market status (badded workersQ).4 Due to important discouraged-worker effects among low-skilled men in the U.S., Murphy and Topel (1997, p. 295) argue that bthe unemployment rate has become progressively less informative about the state of the labor marketQ, a theme which is echoed in the recent debate over whether the decline in the U.S. unemployment rate has been driven by lower participation rates (Krugman, 2004). If this criticism is relevant, focusing on unemployment rates alone could make the state of the labor market appear worse or better than what is actually the case. Whether changes in labor force participation rates are sufficiently persistent to affect the informational value of unemployment rates over a longer time span is, however, unclear. In this paper we will try to answer this question using a new approach; employing recent developments in time series econometrics, we investigate whether participation rates in Australia, Canada and the U.S. are stationary. If participation rates are mean reverting, long-term changes in unemployment rates carry over directly to long-term changes in employment rates. If, on the other hand, participation rates are non-stationary it is unclear what is captured by changes in the unemployment rate. Accordingly, evidence of non-stationarity would question previous research that uses time series of unemployment rates to draw conclusions regarding the behavior of labor markets and the causes of joblessness.
2. Empirical study Monthly data on seasonally adjusted participation rates for Australia, Canada and the U.S. were taken from the EcoWin database.5 The samples begin in February 1978, January 1976 and January 1951 respectively and cover the time period up to November 2004. Data are a compromise considering the trade-off of wanting both a long sample and a high sampling frequency; long series on a high frequency are not available for a large number of countries, but as shown by Choi and Chung (1995) high frequency can be important in order to increase the power of unit root tests. We initially employ a battery of univariate unit root tests: the Augmented Dickey–Fuller test (Said and Dickey, 1984), the Augmented Dickey–Fuller (ADF) test with GLS detrending (Elliott et al., 1996), the KSS test (Kapetanios et al., 2003) and the KPSS test (Kwiatkowski et al., 1992). While the first three tests have a unit root under the null, the burden of proof is reversed in the KPSS test with stationarity under the null. In the ADF test and ADF test with GLS detrending (ADF–GLS) we determine lag length by applying the Hannan–Quinn information criterion. Lag length in the KSS test regressions is set equal to that of the ADF test; as pointed out by Kapetanios et al. (2003), linear dynamics can be seen as a first order approximation if the true augmentations are non-linear in nature.
4
Recent studies lending support for such effects include Benati (2001) and Stephens (2002). Participation rates are defined as the number of people aged 15 and above employed or actively seeking employment, divided by the total number of people in the same age group. 5
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M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
We also test whether participation rates are stationary using two panel unit root tests: the Im et al. (2003) and Johansen (1988) likelihood ratio tests. These tests have been shown to increase power compared to univariate unit root tests even when the cross-sectional dimension of the panel is small; see e.g. Taylor and Sarno (1998) and Im et al. (2003). Because the Im, Pesaran and Shin (IPS) test is based on pooled univariate ADF tests, it seems reasonable to set the lag length in this test to the maximum of the univariate tests. For the Johansen likelihood ratio (JLR) test, the Hannan–Quinn information criterion is applied to the VAR in levels to establish lag length (k); lag length of the vector error-correction model, which forms the base for the test, is then set to k 1. Results from both univariate and panel unit root tests — where mean reversion around a constant level has been tested for — can be found in Table 1. As can be seen from the results in Table 1, the evidence for non-stationarity is overwhelming for all three countries, with complete agreement between all tests. This must be viewed as extremely strong evidence against stationary participation rates and deep cause for concern amongst researchers assuming so. Looking at Fig. 1, some might argue that the complete absence of support for stationarity could be due to a deterministic trend, rather than a stochastic; after all, there appears to be an upward trend in participation rates. While this could potentially be a valid objection, it does on the other hand miss the fact that mean reversion around a deterministic trend in many applications is just as bad as a stochastic trend. In neither case it is possible to infer information about joblessness or the behavior of the labor market solely from unemployment rates. Nevertheless, let us consider the possibility that a temporary deterministic trend is present but the dynamics of the series are unaffected. One argument for such a temporary trend could be the increased female labor force participation; see e.g. OECD (1994). If we furthermore assume that this phenomenon, for some reason, should not be considered a series of shocks instead of a trend, it could be argued that it is relevant to test whether the series are mean reverting around a deterministic trend.
Table 1 Results from unit root tests on participation rates ADF ADF–GLS KSS KPSS Sample
Australia
Canada
U.S.
1.025 0.158 1.357 1.690** 1978:2–2004:11
2.093 1.244 1.790 1.107** 1976:1–2004:11
0.517 1.083 1.199 2.891** 1951:1–2004:11
Panel IPS JLR Sample
1.196 1.267 1978:2–2004:11
Entries in the table are test statistics. ** Significant at the 1% level; * significant at the 5% level.
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433 65 64 63 62 61 60 55
60
65
70
75
80
85
90
95
00
90
95
00
90
95
00
Participation rate Australia 68 67 66 65 64 63 62 61 55
60
65
70
75
80
85
Participation rate Canada 62 60 58 56 54 52 50 55
60
65
70
75
80
85
Participation rate U.S.A
Fig. 1. Time series plots of participation rates.
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M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
Table 2 Results from unit root tests on participation rates allowing for a linear trend ADF ADF–GLS KSS KPSS Sample
Australia
Canada
U.S.
2.116 1.913 1.456 0.251** 1978:2–2004:11
1.770 0.889 0.697 0.397** 1976:1–2004:11
1.447 1.067 2.094 0.347** 1951:1–2004:11
Panel IPS JLR Sample
0.093 1978:2-2004:11
Entries in the table are test statistics. ** significant at the 1% level; * significant at the 5% level.
Judging by the results in Table 2, it is clear that allowing for a linear trend in the data does not weaken the evidence for non-stationarity; all tests still unanimously conclude that participation rates are generated by unit root processes.6
3. Conclusion To conclude, this paper finds that participation rates in Australia, Canada, and the U.S. are not stationary — not even around a deterministic trend. One field where this finding is especially relevant is for studies of unemployment hysteresis. For example, Camarero and Tamarit (2004) test for hysteresis in nineteen OECD countries and reject the hypothesis of a unit root in the unemployment rates for the three countries studied in this paper. However, as we have established that the corresponding participation rates are non-stationary, the results of Camarero and Tamarit are uninformative about the state as well as the functioning of these labor markets. ¨ sterholm (2006), who confirm that This claim is further strengthened by Gustavsson and O unemployment rates appear to be stationary in these countries but present overwhelming evidence for employment rates being generated by unit root processes. Hence, there is employment hysteresis and this certainly affects how one should look at the functioning of the labor markets in these countries in terms of one-time shocks to employment. This discrepancy between employment and unemployment rates is a direct result of the non-stationary participation rates. Based on the results in this paper, we recommend that the time series properties of participation rates should be investigated carefully before using unemployment rates as a measure of joblessness. If participation rates are non-stationary, unemployment rates should — at a minimum — be combined with other labor market statistics before conclusions are drawn. 6 The JLR test has, to our knowledge, never been empirically employed allowing for mean reversion around a trend and this fact — together with the absence of Monte Carlo evidence — means that little is known about the finite-sample properties of the test in such a setting. Proceeding nevertheless, it turns out that the null cannot be rejected.
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
433
Acknowledgements Financial support from Jan Wallander’s and Tom Hedelius’ foundation is gratefully acknowledged.
References Benati, L., 2001. Some empirical evidence on the ddiscouraged workerT effectQ. Economics Letters 70, 387 – 395. Blinder, A., Esaki, H., 1978. Macroeconomic activity and income distribution in the postwar United States. Review of Economics and Statistics 60, 604 – 609. Camarero, M., Tamarit, C., 2004. Hysteresis vs. natural rate of unemployment: new evidence for OECD countries. Economics Letters 84, 413 – 417. Choi, I., Chung, B.S., 1995. Sampling frequency and the power of tests for a unit root: a simulation study. Economics Letters 49, 131 – 136. Dee, T.S., Sela, R.J., 2003. The fatality effects of highway speed limits by gender and age. Economics Letters 79, 401 – 408. Elliott, G., Rothenberg, T.J., Stock, J.H., 1996. Efficient tests for an autoregressive unit root. Econometrica 64, 813 – 836. Gould, E.D., Weinberg, B.A., Mustard, D.B., 2002. Crime rates and local labor market opportunities in the United States: 1979– 1997. Review of Economics and Statistics 84, 45 – 61. ¨ sterholm, P., 2006. Does Unemployment Hysteresis Equal Employment Hysteresis? Working Paper. Gustavsson, M., O Department of Economics, Uppsala University. Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, 53 – 74. Jacobson, M., 2004. Baby booms and drug busts: trends in youth drug use in the United States, 1975–2000. Quarterly Journal of Economics 119, 1481 – 1512. Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231 – 254. Kapetanios, G., Shin, Y., Snell, A., 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359 – 379. Krugman, P.R., 2004. Checking the Facts, in Advance. New York Times. October 12. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?Q Journal of Econometrics 54, 159 – 178. Murphy, K.M., Topel, R., 1997. Unemployment and nonemployment. American Economic Review 87, 295 – 300. OECD, 1994. Employment Outlook. OECD, Paris. Said, S.E., Dickey, D.A., 1984. Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71, 599 – 607. Song, F.M., Wu, Y., 1997. Hysteresis in unemployment: evidence from 48 US States. Economic Inquiry 35, 235 – 243. Stephens, M., 2002. Worker displacement and the added worker effect. Journal of Labor Economics 20, 504 – 537. Taylor, M.P., Sarno, L., 1998. The behaviour of real exchange rates during the Post-Bretton Woods period. Journal of International Economics 46, 281 – 312.
The informational value of unemployment statistics: A note on the time series properties of participation rates ¨ sterholm * Magnus Gustavsson 1, Pa¨r O Department of Economics, Uppsala University, Box 513, 75120 Uppsala, Sweden Received 21 April 2005; received in revised form 10 March 2006; accepted 24 March 2006 Available online 24 July 2006
Abstract Using a battery of unit root tests, we show that labor force participation rates in Australia, Canada and the U.S. are non-stationary. This implies that great care is needed before unemployment rates are used as measures of joblessness. D 2006 Elsevier B.V. All rights reserved. Keywords: Hysteresis; Unit root test JEL classification: C22; E24; J21
1. Introduction Unemployment rates are often the focus of studies of the macroeconomic causes and consequences of joblessness, for example in studies concerning unemployment persistence, the connection between nonemployment and income inequality, and how non-employment affects crime rates.2 The unemployment rate is also often used as a control for the state of the labor market in time series regressions.3 However,
* Corresponding author. Tel.: +46 1 202 378 4135; fax: +46 18 471 1478. ¨ sterholm). E-mail addresses: [email protected] (M. Gustavsson)8 [email protected] (P. O 1 Tel.: +46 18 471 1103; fax: +46 18 471 1478. 2 See e.g. Blinder and Esaki (1978), Song and Wu (1997), and Gould et al. (2002). 3 See e.g. Dee and Sela (2003) and Jacobson (2004). 0165-1765/$ - see front matter D 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2006.03.032
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
429
that the evolution of the unemployment rate need not reflect that of joblessness is neglected in many studies, even though it is well known that individuals’ labor force participation may change over time for market-driven reasons (bdiscouraged workersQ) as well as in response to a partner’s labor market status (badded workersQ).4 Due to important discouraged-worker effects among low-skilled men in the U.S., Murphy and Topel (1997, p. 295) argue that bthe unemployment rate has become progressively less informative about the state of the labor marketQ, a theme which is echoed in the recent debate over whether the decline in the U.S. unemployment rate has been driven by lower participation rates (Krugman, 2004). If this criticism is relevant, focusing on unemployment rates alone could make the state of the labor market appear worse or better than what is actually the case. Whether changes in labor force participation rates are sufficiently persistent to affect the informational value of unemployment rates over a longer time span is, however, unclear. In this paper we will try to answer this question using a new approach; employing recent developments in time series econometrics, we investigate whether participation rates in Australia, Canada and the U.S. are stationary. If participation rates are mean reverting, long-term changes in unemployment rates carry over directly to long-term changes in employment rates. If, on the other hand, participation rates are non-stationary it is unclear what is captured by changes in the unemployment rate. Accordingly, evidence of non-stationarity would question previous research that uses time series of unemployment rates to draw conclusions regarding the behavior of labor markets and the causes of joblessness.
2. Empirical study Monthly data on seasonally adjusted participation rates for Australia, Canada and the U.S. were taken from the EcoWin database.5 The samples begin in February 1978, January 1976 and January 1951 respectively and cover the time period up to November 2004. Data are a compromise considering the trade-off of wanting both a long sample and a high sampling frequency; long series on a high frequency are not available for a large number of countries, but as shown by Choi and Chung (1995) high frequency can be important in order to increase the power of unit root tests. We initially employ a battery of univariate unit root tests: the Augmented Dickey–Fuller test (Said and Dickey, 1984), the Augmented Dickey–Fuller (ADF) test with GLS detrending (Elliott et al., 1996), the KSS test (Kapetanios et al., 2003) and the KPSS test (Kwiatkowski et al., 1992). While the first three tests have a unit root under the null, the burden of proof is reversed in the KPSS test with stationarity under the null. In the ADF test and ADF test with GLS detrending (ADF–GLS) we determine lag length by applying the Hannan–Quinn information criterion. Lag length in the KSS test regressions is set equal to that of the ADF test; as pointed out by Kapetanios et al. (2003), linear dynamics can be seen as a first order approximation if the true augmentations are non-linear in nature.
4
Recent studies lending support for such effects include Benati (2001) and Stephens (2002). Participation rates are defined as the number of people aged 15 and above employed or actively seeking employment, divided by the total number of people in the same age group. 5
430
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
We also test whether participation rates are stationary using two panel unit root tests: the Im et al. (2003) and Johansen (1988) likelihood ratio tests. These tests have been shown to increase power compared to univariate unit root tests even when the cross-sectional dimension of the panel is small; see e.g. Taylor and Sarno (1998) and Im et al. (2003). Because the Im, Pesaran and Shin (IPS) test is based on pooled univariate ADF tests, it seems reasonable to set the lag length in this test to the maximum of the univariate tests. For the Johansen likelihood ratio (JLR) test, the Hannan–Quinn information criterion is applied to the VAR in levels to establish lag length (k); lag length of the vector error-correction model, which forms the base for the test, is then set to k 1. Results from both univariate and panel unit root tests — where mean reversion around a constant level has been tested for — can be found in Table 1. As can be seen from the results in Table 1, the evidence for non-stationarity is overwhelming for all three countries, with complete agreement between all tests. This must be viewed as extremely strong evidence against stationary participation rates and deep cause for concern amongst researchers assuming so. Looking at Fig. 1, some might argue that the complete absence of support for stationarity could be due to a deterministic trend, rather than a stochastic; after all, there appears to be an upward trend in participation rates. While this could potentially be a valid objection, it does on the other hand miss the fact that mean reversion around a deterministic trend in many applications is just as bad as a stochastic trend. In neither case it is possible to infer information about joblessness or the behavior of the labor market solely from unemployment rates. Nevertheless, let us consider the possibility that a temporary deterministic trend is present but the dynamics of the series are unaffected. One argument for such a temporary trend could be the increased female labor force participation; see e.g. OECD (1994). If we furthermore assume that this phenomenon, for some reason, should not be considered a series of shocks instead of a trend, it could be argued that it is relevant to test whether the series are mean reverting around a deterministic trend.
Table 1 Results from unit root tests on participation rates ADF ADF–GLS KSS KPSS Sample
Australia
Canada
U.S.
1.025 0.158 1.357 1.690** 1978:2–2004:11
2.093 1.244 1.790 1.107** 1976:1–2004:11
0.517 1.083 1.199 2.891** 1951:1–2004:11
Panel IPS JLR Sample
1.196 1.267 1978:2–2004:11
Entries in the table are test statistics. ** Significant at the 1% level; * significant at the 5% level.
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433 65 64 63 62 61 60 55
60
65
70
75
80
85
90
95
00
90
95
00
90
95
00
Participation rate Australia 68 67 66 65 64 63 62 61 55
60
65
70
75
80
85
Participation rate Canada 62 60 58 56 54 52 50 55
60
65
70
75
80
85
Participation rate U.S.A
Fig. 1. Time series plots of participation rates.
431
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M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
Table 2 Results from unit root tests on participation rates allowing for a linear trend ADF ADF–GLS KSS KPSS Sample
Australia
Canada
U.S.
2.116 1.913 1.456 0.251** 1978:2–2004:11
1.770 0.889 0.697 0.397** 1976:1–2004:11
1.447 1.067 2.094 0.347** 1951:1–2004:11
Panel IPS JLR Sample
0.093 1978:2-2004:11
Entries in the table are test statistics. ** significant at the 1% level; * significant at the 5% level.
Judging by the results in Table 2, it is clear that allowing for a linear trend in the data does not weaken the evidence for non-stationarity; all tests still unanimously conclude that participation rates are generated by unit root processes.6
3. Conclusion To conclude, this paper finds that participation rates in Australia, Canada, and the U.S. are not stationary — not even around a deterministic trend. One field where this finding is especially relevant is for studies of unemployment hysteresis. For example, Camarero and Tamarit (2004) test for hysteresis in nineteen OECD countries and reject the hypothesis of a unit root in the unemployment rates for the three countries studied in this paper. However, as we have established that the corresponding participation rates are non-stationary, the results of Camarero and Tamarit are uninformative about the state as well as the functioning of these labor markets. ¨ sterholm (2006), who confirm that This claim is further strengthened by Gustavsson and O unemployment rates appear to be stationary in these countries but present overwhelming evidence for employment rates being generated by unit root processes. Hence, there is employment hysteresis and this certainly affects how one should look at the functioning of the labor markets in these countries in terms of one-time shocks to employment. This discrepancy between employment and unemployment rates is a direct result of the non-stationary participation rates. Based on the results in this paper, we recommend that the time series properties of participation rates should be investigated carefully before using unemployment rates as a measure of joblessness. If participation rates are non-stationary, unemployment rates should — at a minimum — be combined with other labor market statistics before conclusions are drawn. 6 The JLR test has, to our knowledge, never been empirically employed allowing for mean reversion around a trend and this fact — together with the absence of Monte Carlo evidence — means that little is known about the finite-sample properties of the test in such a setting. Proceeding nevertheless, it turns out that the null cannot be rejected.
M. Gustavsson, P. O¨sterholm / Economics Letters 92 (2006) 428–433
433
Acknowledgements Financial support from Jan Wallander’s and Tom Hedelius’ foundation is gratefully acknowledged.
References Benati, L., 2001. Some empirical evidence on the ddiscouraged workerT effectQ. Economics Letters 70, 387 – 395. Blinder, A., Esaki, H., 1978. Macroeconomic activity and income distribution in the postwar United States. Review of Economics and Statistics 60, 604 – 609. Camarero, M., Tamarit, C., 2004. Hysteresis vs. natural rate of unemployment: new evidence for OECD countries. Economics Letters 84, 413 – 417. Choi, I., Chung, B.S., 1995. Sampling frequency and the power of tests for a unit root: a simulation study. Economics Letters 49, 131 – 136. Dee, T.S., Sela, R.J., 2003. The fatality effects of highway speed limits by gender and age. Economics Letters 79, 401 – 408. Elliott, G., Rothenberg, T.J., Stock, J.H., 1996. Efficient tests for an autoregressive unit root. Econometrica 64, 813 – 836. Gould, E.D., Weinberg, B.A., Mustard, D.B., 2002. Crime rates and local labor market opportunities in the United States: 1979– 1997. Review of Economics and Statistics 84, 45 – 61. ¨ sterholm, P., 2006. Does Unemployment Hysteresis Equal Employment Hysteresis? Working Paper. Gustavsson, M., O Department of Economics, Uppsala University. Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, 53 – 74. Jacobson, M., 2004. Baby booms and drug busts: trends in youth drug use in the United States, 1975–2000. Quarterly Journal of Economics 119, 1481 – 1512. Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231 – 254. Kapetanios, G., Shin, Y., Snell, A., 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359 – 379. Krugman, P.R., 2004. Checking the Facts, in Advance. New York Times. October 12. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?Q Journal of Econometrics 54, 159 – 178. Murphy, K.M., Topel, R., 1997. Unemployment and nonemployment. American Economic Review 87, 295 – 300. OECD, 1994. Employment Outlook. OECD, Paris. Said, S.E., Dickey, D.A., 1984. Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71, 599 – 607. Song, F.M., Wu, Y., 1997. Hysteresis in unemployment: evidence from 48 US States. Economic Inquiry 35, 235 – 243. Stephens, M., 2002. Worker displacement and the added worker effect. Journal of Labor Economics 20, 504 – 537. Taylor, M.P., Sarno, L., 1998. The behaviour of real exchange rates during the Post-Bretton Woods period. Journal of International Economics 46, 281 – 312.