Reserve Bank of New Zealand Analytical Notes

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1 Reserve Bank of New Zealand Analytical Notes Developing a labour utilisation composite index for New Zealand AN6/4 Jed Armstrong, Güneş Kamber, and Özer Karagedikli April 6 Reserve Bank of New Zealand Analytical Note Series ISSN -555 Reserve Bank of New Zealand Po Box 498 Wellington NEW ZEALAND The Analytical Note series encompasses a range of types of background papers prepared by Reserve Bank staff. Unless otherwise stated, views expressed are those of the authors, and do not necessarily represent the views of the Reserve Bank.

2 Reserve Bank of New Zealand Analytical Note Series - - NON-TECHNICAL SUMMARY A wide range of variables are available for assessing labour market conditions, most of which have some useful information content for labour market analysis. Interpreting the information content in all variables can be difficult. This is particularly the case when different labour market variables show contradictory movements, or when a single variable has a large movement that does not necessarily reflect true labour market conditions. In these situations, it is useful to combine a range of labour market indicators into a summary measure. In this paper we present such a measure for New Zealand, which we call a labour utilisation composite index (). We combine seventeen labour market variables into a single composite index using a statistical technique called principal component analysis. The evolution of the resulting index is in line with the broad features of the New Zealand business cycle. We also show that the index doesn t change much if it is estimated using a different set of labour market variables, or if it is estimated over different sample periods.

3 Reserve Bank of New Zealand Analytical Note Series - - INTRODUCTION Rich and wide-ranging data are available for labour market analysis in New Zealand. A researcher or policy maker has access to stock variables and flow variables, covering both labour market quantities and prices (i.e. wages), from a wide range of sources. Interpreting the information content in all of these variables can be difficult. Different variables may sometimes give contradictory signals about the overall state of the labour market. The signal extraction problem may be further complicated by the idiosyncrasies that individual series can contain. Therefore relying on a single measure may be misleading in assessing labour market conditions. For this reason, many policy makers have argued that it is useful to combine a range of labour market variables into a summary measure, which provides a broader view on labour market conditions (Yellen, 4). Various statistical models exist to combine series and summarise the information contained in large number of indicators. In this Note, we propose an index that summarises labour market conditions in New Zealand. We present a labour utilisation composite index () that combines seventeen labour market variables into a summary indicator using principal component analysis. Our index is similar to the labour market conditions indices developed and used by the Federal Reserve System (see Chung et al. (5) and Willis and Hakkio (4)). We show that the evolution of the is in line with the broad characteristics of the New Zealand business cycle over the last 5 years. Further, the index is robust to variable choice and estimation period, does not suffer large revisions in real-time estimation, and improves the forecast of individual labour market indicators. The remainder of this Note is structured as follows: Section describes the labour market data and the methodology used to construct the. Section presents the resulting index and its cyclical properties. In section 4, we undertake some robustness exercises and show that the baseline is stable over time and its dynamics are not affected by the choice of input variables. Section 5 presents an evaluation of the index based on out-of-sample forecasting. Section 6 concludes. We thank Adam Richardson, Benjamin Wong, Gina Williamson, and Yuong Ha for useful comments.

4 Reserve Bank of New Zealand Analytical Note Series DATA AND METHODOLOGY The presented in this Note is based on seventeen input variables. The variables, their data sources, and the transformations used, are shown in table. Table : Variables used in the Variable Source Transformation Number unemployed HLFS APC Number underemployed HLFS APC Number employed HLFS APC Number short-term unemployed (<7 weeks) HLFS APC Total hours worked HLFS APC Transitions from U to E HLFS Level (% of unemployed) Transitions from N to E HLFS Level (% of NILF) Transitions from E to U HLFS Level (% of employed) Working age population HLFS APC Filled jobs QES APC Average hourly earnings QES APC Employment intentions QSBO Level (index) Difficulty finding unskilled labour QSBO Level (index) Labour as a limiting factor QSBO Level (index) Job ads posted ANZ Level (number) Registered job seekers WINZ APC Unit labour costs LCI APC HLFS: Household Labour Force Survey; QES: Quarterly Employment Survey; QSBO: Quarterly Survey of Business Opinion; ANZ: ANZ Bank; WINZ: Work and Income New Zealand; LCI: Labour Cost ; NILF: Not in labour force; APC: Annual percent change. These variables capture a comprehensive set of labour market indicators. The variables come from a range of sources, and represent different aspects of labour markets, such as quantities, wages, and flows. However, this list is not exhaustive; there are other variables that could See Appendix A for a full description of the input data.

5 Reserve Bank of New Zealand Analytical Note Series conceivably be included in the index. Some variables were excluded on the available data sample all variables here are available from 999 at the latest, meaning that we can construct the index for more than 5 years. Others were excluded because the data aren t widely available all variables included are available free-of-charge, and most are publicly accessible online. This choice was made to ensure that our index is transparent and replicable by other researchers. There are a range of approaches available to combine a large number of series into a single summary measure. For the index presented in this paper, we use principal component analysis (PCA). PCA is a dimensionality-reduction technique, in which the extracted series (that is, the first principal component) captures the largest amount of variance in the underlying input series. 4 Stock and Watson () show that principal component analysis consistently estimates the true latent factors, and as such our index should properly capture the underlying labour market movements. 5 Principal component analysis provides a more sophisticated approach to combination than a simple average, as some series are weighted more highly than others. At the same time, the weights on the series are determined entirely by the data PCA does not rely on any prior judgement to be made by the researcher. As with the data choices, this should ensure that our methodology is replicable. Prior to the computation of the principal components all variables are transformed to be stationary, and are standardised. The variable transformations we use to achieve stationarity are simple and intuitive any clearly non-stationary variable is transformed by an annual percentage change, while any stationary variable is used in levels terms. We extract only the first principal component this first principal component is the. As such, the is a linear combination of the individual input series which explains more of the variation in the labour market data than any other linear combination. Once extracted, the index is standardised. Thus, by construction, the has a mean of zero and will (on average) lie between and - 68 percent of the time, between and - 95 percent of the time, and and percent of the time. We have undertaken preliminary work looking at constructing a monthly using experimental data from the Employer Monthly Schedule, with promising results. 4 See Appendix B for technical details of how to extract the. Malysheva and Sarte (9) also provides a comprehensive technical summary of PCA in a labour market application. 5 See Stock and Watson () for a detailed discussion of principal component analysis and of this point.

6 Reserve Bank of New Zealand Analytical Note Series RESULTS Figure shows the extracted from all seventeen variables over the full period 999Q to 5Q4 (the period for which all data are available). Figure : Labour utilisation composite index Roughly speaking, composite labour market indices used by policy-makers tend to fall into two broad categories: those showing the state of the labour market (i.e. how far above or below average labour market conditions are), and those showing the change in labour market conditions (i.e. how rapidly conditions are evolving). 6 We classify the as a state indicator, based on the fact that it has higher correlation with state variables than change variables. 7 As such, we interpret an value greater than zero as indicating higher labour market tightness than usual and a value less than zero as indicating lower labour market tightness than usual. Visually, the evolution of the is in line with the broad features of the New Zealand business cycle. The New Zealand economy experienced a strong expansion in the s followed by 6 For more on the distinction between a state indicator and a change indicator, see Hakkio and Willis (). 7 The result that the is a state indicator rather than a change indicator is not a conscious choice that we made prior to estimation. The is produced by a completely data-driven modelling approach (as opposed to an approach relying on researcher judgement), and so it was not clear ex-ante whether the resulting index would be a state indicator or a change indicator.

7 Reserve Bank of New Zealand Analytical Note Series a deep contraction from 8. The economic recovery started in 9Q according to the dating by Hall and McDermott (), and the matches these dates closely. However, the recovery has been slow, with an acceleration in late and a slow-down in late 4. The picks up these patterns well. The phases and the magnitudes of the cycle are also very similar to the output gap estimates published by the Reserve Bank of New Zealand. The raw contemporaneous correlations of the with each input variable (and with the output gap published in the Bank s March 6 Monetary Policy Statement) are shown in table. 8 Again, it is clear that the moves closely with the variables that represent labour-market (and economic) slack. Table : Raw contemporaneous correlations Variable r Number unemployed.78 Number underemployed.54 Number employed.84 Number short-term unemployed (<7 weeks).65 Total hours worked.68 Transitions from U to E.65 Transitions from N to E.9 Transitions from E to U.79 Working age population.49 Filled jobs.86 Average hourly earnings.7 9 Employment intentions.65 Difficulty finding unskilled labour.95 Labour as a limiting factor.8 Job ads posted.8 Registered job seekers.9 Unit labour costs.4 9 Output gap.8 8 Appendix C has plots of the with each input series.

8 Reserve Bank of New Zealand Analytical Note Series An advantage of PCA as a combination technique is that it allows us to compute how much of the total variance in the underlying dataset is explained by each extracted component. The (i.e. the first principal component) explains 48 percent of the total variation in the input labour-market dataset. The second principal component extracted from the data explains about 5 percent of the variability, with subsequent components explaining much less (figure ). The high share of variability captured by the suggests that it is sufficient to explain underlying movements in the labour market. Figure : Share of total variability explained by each component (scree plot) % % Component 4 ROBUSTNESS In this section we test the robustness of the against two potential issues. First, we check against the choice of input variables. We vary the number of variables from our data set to understand the sensitivities of the. Second, we estimate the in real time and analyse its real-time revision properties. 9 This correlation is low because the is a leading indicator of wage inflation. The correlation between the and both average hourly earnings and unit labour costs one year ahead is.66. It is possible that forecasting exercises using the could also benefit from use of the second component. This is particularly the case for wage forecasting the two wage series have high loadings in the second principal component.

9 Reserve Bank of New Zealand Analytical Note Series ROBUSTNESS TO CHOICE OF INPUT VARIABLES Given the relatively small number of variables in our data set, it is necessary to establish whether the estimated is driven by a subset of variables included in the analysis. We test the robustness of the to variable choice in two ways. Firstly, to test the sensitivity of the to each individual variable, we estimate the seventeen times, each time with one variable excluded from the input data set. This approach is very similar to the more formal bootstrapping proposed by Gospodinov and Ng (). The resulting subset s are shown in figure. All of the estimates are similar, suggesting that the is not being driven by any single input variable. Figure : Indices calculated without one variable 6 variable subsets All variables Secondly, we test robustness by estimating the principal component of a large number of smaller subsets of the input variables. In particular, we estimate s based on all possible -variable subsets of the seventeen input variables. Looking at the distribution of the To test this similarity formally, we form a distribution of the subset s at each point in time, and compare the variance of these distributions to the variance of the aggregate (which is by construction). In order to conclude that the subset s are similar, the variance at each point in time should be lower than the variance of the aggregate. We find that the subset variance is between and.4, which shows that the subset s are similar the variability introduced by omitting variables is less than one th of the variability of the.

10 Reserve Bank of New Zealand Analytical Note Series - - estimated s allows us to construct the - and -standard deviation range around our point estimate (figure 4). Again, the appears to be reasonably robust to variable choice different subsets of variables produce very similar results to the baseline. Figure 4: Distribution of s estimated from -variables subsets s.d. s.d. Point estimate REAL-TIME REVISION PROPERTIES Most of the input series in the are not revised over time, and those that are (such as HLFS series after population rebases) tend to be revised only a small amount. Moreover, the technique used to extract the (principal component analysis) is a relatively stable approach. That is, as additional data points are introduced to the sample, there does not tend to be large revisions to the estimated model and to the historical values. In order to test revision properties, we estimate the in pseudo-real time between Q and 5Q4. We use these estimates to construct a (pseudo-)real time (figure 5). We find that the is not heavily revised over time. During the Global Financial Crisis there As above, we compare the variance of the subset s at each point in time to that of the aggregate. We find that the subset variance is between and.5, which again shows that the subset s are similar the variability introduced by omitting variables is about one third of the variability of the. Pseudo-real time means that the final data vintage is used at each point in time, but only data up to that point in time.

11 Reserve Bank of New Zealand Analytical Note Series - - was a divergence of about one index point between the real-time realisation and the ex-post estimate, but this quickly closed. 4 For most of the sample, the real-time and ex-post estimates are almost identical. In particular, the real-time properties of the compare very favourably with the real-time properties of output gap estimates (Armstrong, 5). Figure 5: estimated in pseudo-real time Ex post Pseudo real time OUT-OF-SAMPLE FORECAST EVALUATION The strong correlation with the output gap and favourable real-time properties suggest that the forms a useful tool for nowcasting the current state of the economy and the labour market. Another way to test the usefulness of the is to evaluate its ability to forecast individual labour market variables. In order to test this, we estimate two out-of-sample forecasting models for each input variable and look at the root mean square forecast error (RMSFE). The first model is a simple AR() model, representing the baseline. The second model is an AR() augmented with the. Comparing the RMSEs of the two models allows us to determine if the aids predictive power (i.e. reduces the forecast error) or worsens predictive power. 4 This divergence probably reflects the short data sample pre-gfc with which to estimate the model parameters, rather than a genuine failure of the model to pick up large cyclical movements.

12 Reserve Bank of New Zealand Analytical Note Series - - We forecast up to 8 quarters ahead (i.e., over horizons typically considered to be relevant for monetary policy), using an expanding estimation window with a minimum window of quarters. 5 A summary of the forecast improvements is shown in table. The improves forecasts of all variables for at least one horizon, and improves forecasts at all horizons for 4 variables. Table : Does the improve forecasts for a given variable? Variable At least one horizon All horizons Number unemployed Number underemployed Number employed Number short-term unemployed (<7 weeks) Total hours worked Transitions from U to E Transitions from N to E Transitions from E to U Working age population Filled jobs Average hourly earnings Employment intentions Difficulty finding unskilled labour Labour as a limiting factor Job ads posted Registered job seekers Unit labour costs 5 Due to the small sample size, the number of observations in our out-of-sample forecasting exercise is small (as few as 9 forecast observations). Thus, these results are only indicative, and should be treated with caution.

13 Reserve Bank of New Zealand Analytical Note Series CONCLUSION We have presented a composite index that summarises labour market utilisation in New Zealand. The index is robust to the choice of variables and has stable real-time properties. Our measure explains the overall characteristics of the New Zealand business cycle well. An out-of-sample forecasting analysis suggests that the adds predictive power to labour market forecasts over policy-relevant horizons.

14 Reserve Bank of New Zealand Analytical Note Series REFERENCES Armstrong, J. (5). The Reserve Bank of New Zealand s output gap indicator suite and its real-time properties. Reserve Bank of New Zealand Analytical Notes series AN/8, Reserve Bank of New Zealand. Chung, H., Fallick, B. C., Nekarda, C. J., and Ratner, D. (5). Assessing the Change in Labor Market Conditions. Working Paper 48, Federal Reserve Bank of Cleveland. Gospodinov, N. and Ng, S. (). Commodity Prices, Convenience Yields, and Inflation. The Review of Economics and Statistics, 95():6 9. Hakkio, C. S. and Willis, J. L. (). Assessing labor market conditions: the level of activity and the speed of improvement. Macro Bulletin, pages. Hall, V. B. and McDermott, C. J. (). A quarterly post-second World War real GDP series for New Zealand. New Zealand Economic Papers, 45():7 98. Malysheva, N. and Sarte, P.-D. G. (9). Heterogeneity in sectoral employment and the business cycle. Economic Quarterly, (Fall):5 55. Silverstone, B. and Bell, W. (). Gross Labour Market Flows in New Zealand: Some Questions and Answers. Working Papers in Economics /5, University of Waikato, Department of Economics. Stock, J. H. and Watson, M. (). Forecasting Using Principal Components From a Large Number of Predictors. Journal of the American Statistical Association, 97: Willis, J. L. and Hakkio, C. S. (4). Kansas City Fed s Labor Market Conditions Indicators (LMCI). Macro Bulletin, pages. Yellen, J. L. (4). Labor Market Dynamics and Monetary Policy: a speech at the Federal Reserve Bank of Kansas City Economic Symposium, Jackson Hole, Wyoming, August, 4. Speech 85, Board of Governors of the Federal Reserve System (U.S.).

15 Reserve Bank of New Zealand Analytical Note Series APPENDIX A DATA DESCRIPTION Variable Description Notes Number unemployed Seasonally adjusted by Statistics New Zealand. Number underemployed Prior to 4 we use the sum of Statistics New Zealand Part-time workers preferring more hours and Part-time workers preferring full-time work. The series are spliced using least-squares regression. We seasonally adjust these data ourselves using an X seasonal-adjustment programme. Number employed Seasonally adjusted by Statistics New Zealand. Short-term number unemployed (<7 weeks) Total unemployed less those unemployed 5+ Seasonally adjusted by Statistics New Zealand. weeks and those unemployed 7-5 weeks. Total hours worked Total number of actual hours worked each week. Transitions from U to E The probability of an unemployed person (U) becoming employed (E) in a quarter. Transitions from N to E The probability of an unemployed person (U) becoming employed (E) in a quarter. Transitions from E to U The probability of an unemployed person (U) becoming employed (E) in a quarter. Sourced from HLFS gross flows data. We seasonally adjust these data ourselves using an X seasonal-adjustment programme. See Silverstone and Bell () for a comprehensive discussion of these flows and their cyclical properties. Working age population Seasonally adjusted by Statistics New Zealand. Filled jobs Total, all industries. We seasonally adjust these data ourselves using an X seasonal-adjustment programme. Average hourly earnings Ordinary time, private sector. Seasonally adjusted by Statistics New Zealand. Employment intentions QSBO Numbers employed, next three months We seasonally adjust these data ourselves using an X seasonal-adjustment programme. Difficulty finding unskilled labour Seasonally adjusted by NZIER. Labour as a limiting factor Seasonally adjusted by NZIER. Job ads posted From ANZ Bank s NZ Job Ads publication. Newspaper and internet. We sum the quarterly newspaper and quarterly internet series prior to 4, and use an aggregated monthly series after 4. The series are spliced using leastsquares regression. Registered job seekers Seasonally adjusted by WINZ. Unit labour costs Salary and wage rates, private sector. Seasonally adjusted by Statistics New Zealand.

16 Reserve Bank of New Zealand Analytical Note Series APPENDIX B HOW TO CONSTRUCT THE Step : Collect the 7 labour market variables (denote here by y i, and standardise each into a z-score over the common date range for which all variables are available. This is done by subtracting the series mean and dividing by the series standard deviation (both calculated over the common date range). Step : Arrange these standardised variables in a T 7 matrix (where T is the number of time periods for which all data are available) of the form M = [y y... y 7 ] Step : Form the 7 7 variance-covariance matrix (Ω) by Ω = M M Step 4: Extract all eigenvalues (e i ) and eigenvectors (v i ) from Ω using a statistical package (e.g. R, MATLAB, EViews). Denote the eigenvalues by e as the largest eigenvalue (which corresponds to v ) through to e 7 for the smallest eigenvector (which corresponds to v 7 ). Sort the eigenvectors by descending value of their corresponding eigenvalue to form a 7 7 loadings matrix λ = [v v... v 7 ] Step 5: Find all components by forming the T 7 matrix F = Mλ Step 6: Take the first column of the matrix F, and standardise it by subtracting the series mean and dividing by the series standard deviation. The resulting series is the.

17 APPENDIX C PLOTS OF THE AND EACH INPUT VARIABLE Number unemployed (inverted) Number underemployed (inverted) Number employed Short term number unemployed (<7 weeks) (inverted) Total hours worked Transitions from U to E

18 4 4 Transitions from N to E Transitions from E to U (inverted) Working age population Filled jobs Average hourly earnings Employment intentions

19 Difficulty finding unskilled labour Labour as a limiting factor Job ads posted Registered job seekers (inverted) Unit labour costs