# Persistence and Cycles in US Hours Worked

## Summary (2 min read)

### 1. Introduction

- This paper proposes a modelling approach for US hours worked, specifically average weekly hours in manufacturing.
- Both types of studies use similar empirical (VAR) frameworks, the crucial difference between them being in the treatment of the hours worked variable.
- The reason for choosing this specification is that the periodogram of the hours worked series is found not to exhibit a peak at the zero 1 Section 2 briefly describes the different types of long range dependence or long memory models used here.
- Section 4 discusses the empirical results and their implications for the debate on the relationship between hours worked and technology shocks, while Section 5 contains some concluding remarks.

### 2. A cyclical I(d) model

- This includes a wide range of model specifications such as the white noise case, the stationary autoregression (AR), moving average (MA), and stationary ARMA models.
- For this case specifications with stochastic trends have usually been adopted, under the assumption that the first differenced process is stationary I(0), and thus valid statistical inference can be drawn after differencing once.
- For an alternative definition (Type I) see Marinucci and Robinson (1999).
- Most of the empirical literature has focused on the case when the singularity or pole in the spectrum occurs at the zero frequency (λ * = 0).

### 3. The dataset

- The series examined here is the average number of hours worked per week by production workers in US manufacturing industries, monthly, over the sample period 1939m1 – 2011m10; the source is the Current Employment Statistics (CES) monthly survey of the US Bureau of Labor Statistics.
- The authors analyse both seasonally adjusted and unadjusted data (HWSA11 and HWNSA11 respectively) for the whole sample period and also for a shorter sample ending in 2007m4 (HWSA07 and HWNSA07) in order to establish whether the 2007/8 crisis had an impact on hours worked.
- It also shows the correlograms, which exhibit a clearly cyclical pattern.
- The periodograms, also displayed in the same figure, have the highest peak at frequency 7, as opposed to the zero frequency, which suggests that the I(d) and I(1) specifications estimated by other authors are not appropriate, and also that cycles have a length of approximately T/7 = 124.85 months, i.e. around ten and a half years.
- 4 3 LRD also admits processes with multiple poles or singularities in the spectrum (k-factor Gegenbauer processes - see Giraitis and Leipus, 1995; Woodward et al., 1998; etc.) but these are beyond the scope of the present study.

### 4. Empirical results

- As a first step the authors estimate the order of integration of the series using a standard I(d) model, i.e. assuming that the peak of the spectrum occurs at the long run or zero frequency.
- The latter is a non-parametric approach to modelling the I(0) disturbances that approximates ARMA structures with a small number of parameters and has been widely employed in the context of fractional integration (see GilAlana, 2004).
- On the basis of the above evidence that supports the cyclically I(d) specification for hours worked, 7 Box-Pierce Q-statistics indicate that the models including AR(1) disturbances (see Table 3) are free of additional serial correlation.
- The estimated value of c (not reported) is 38 in all cases, consistently with the periodograms displayed in Figure 4, whilst the estimated values of d are in all cases in the interval (0, 1) but smaller than for the seasonally unadjusted data (in Table 7), implying long memory and mean reverting behaviour.
- Next the authors investigate which of the potential models for the disturbances is the most adequate for the two series examined.

### 5. Conclusions

- This paper analyses monthly hours worked in the US over the sample period 1939m1 – 2011m10 using a cyclical I(d) model based on Gegenbauer processes, which are characterised by a spectral density function unbounded at a non-zero frequency.
- For the seasonally unadjusted data, the estimated values of d range between 0.123 and 0.272, whilst for the seasonally adjusted ones the variability is much higher, the values ranging between 0.068 and 0.705.
- This is in contrast to the models normally found in the literature (e.g., Gali, 1999; Christiano, Eichenbaum and Vigfusson, 2003; Gil-Alana and Moreno, 2009) that, although differing in the degree of integration assumed for hours worked, are all based on hours worked being a highly persistent series with a peak at the zero frequency in the spectrum.
- When including productivity as a weakly exogenous variable further evidence is obtained supporting the Gegenbauer model, the order of integration again being in the interval (0, 0.5).
- Moreover, hours worked are found to increase on impact in response to a technology shock (although its effects disappear after two years).

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### Cites background from "Persistence and Cycles in US Hours ..."

...and Marmol (2004), Morana (2007), and Caporale and Gil-Alana (2014). It is, however,...

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..., Cazelles et al. (2007). In contrast, in their examples with economic data Aguiar-Conraria and Soares (2014) consider a parametric approach and generate new samples by bootstrapping ARMA models for the analyzed data, for instance the cycles....

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### Cites background from "Persistence and Cycles in US Hours ..."

...…(or employment) has been a controversial issue in the literature (see Francis and Ramey (2005), Chang and Hong (2006), Francis and Ramey (2009), and Caporalea and Gil-Alana (2014) among others) because it provides a direct empirical test on the validity of the existing business cycle theories....

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##### References

1,463 citations

### "Persistence and Cycles in US Hours ..." refers result in this paper

...This is in contrast to the models normally found in the literature (e.g., Gali, 1999; Christiano, Eichenbaum and Vigfusson, 2003; Gil-Alana and Moreno, 2009) that, although differing in the degree of integration assumed for hours worked, are all based on hours worked being a highly persistent…...

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...Gali (1999), Francis and Ramey (2005) and Gali and Rabanal (2004 - GR) found that, contrary to the implications of Real Business Cycle (RBC) models, they decline in response to a technology shock....

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...Gali (1999), Francis and Ramey (2005) and Gali and Rabanal (2004 - GR) found that, contrary to the implications of Real Business Cycle (RBC) models, they decline in response to a technology shock. These results were challenged, among others, by Christiano, Eichenbaum and Vigfusson (2003 - CEV) who presented evidence that instead hours worked increase following a technology shock.(1) Both types of studies use similar empirical (VAR) frameworks, the crucial difference between them being in the treatment of the hours worked variable. In particular, the former authors model it as a nonstationary I(1) variable whilst the latter assume that it is a stationary I(0) process. More recently, Gil-Alana and Moreno (2009) allow the order of integration of hours worked to be fractional, i....

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1,308 citations

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### "Persistence and Cycles in US Hours ..." refers methods in this paper

...…and also employ a testing procedure developed by 4 Burn and Mitchell (1946), Romer (1986, 1994), Stock and Watson (1998), Diebold and Rudebusch (1992), Canova (1998), Baxter and King (1999), King and Rebelo (1999) among others showed that the average length of the cycle is approximately six years....

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1,023 citations

### "Persistence and Cycles in US Hours ..." refers methods in this paper

...…and also employ a testing procedure developed by 4 Burn and Mitchell (1946), Romer (1986, 1994), Stock and Watson (1998), Diebold and Rudebusch (1992), Canova (1998), Baxter and King (1999), King and Rebelo (1999) among others showed that the average length of the cycle is approximately six years....

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892 citations

### "Persistence and Cycles in US Hours ..." refers background or methods in this paper

...Robinson (1994), which has been shown to be the most efficient one in the context of fractional integration....

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...Finally, it is the most efficient method in the Pitman sense against local departures from the null (see Robinson, 1994).5 [Insert Table 1 about here] Table 1 displays the (Whittle) estimates of d (and the 95% confidence bands corresponding to the non-rejection values of d using Robinson’s (1994)…...

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...We further investigate this issue by employing the parametric approach of Robinson (1994) described above assuming that the disturbances are white noise and autocorrelated in turn....

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...7 Robinson (1994), which has been shown to be the most efficient one in the context of fractional integration. This method, based on the Lagrange Multiplier (LM) principle, tests the null hypothesis Ho: d = do in (2) and (5) for any real value do and has several advantages over other approaches. First, it allows to test for any real value of do, therefore encompassing both the stationary (d < 0.5) and nonstationary (d ≥ 0.5) hypotheses. Moreover, the limiting distribution is N(0, 1) and this standard behaviour holds independently of the regressors used in the regression model (5) and the type of model for the I(0) disturbances ut in (2). Finally, it is the most efficient method in the Pitman sense against local departures from the null (see Robinson, 1994).(5) [Insert Table 1 about here] Table 1 displays the (Whittle) estimates of d (and the 95% confidence bands corresponding to the non-rejection values of d using Robinson’s (1994) method) in the model given by equations (2) and (5) with zt in (5) equal to ( 1, t), t ≥ 1, 0 otherwise, i....

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...7 Robinson (1994), which has been shown to be the most efficient one in the context of fractional integration....

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