Employment Reallocation and Unemployment Revisited: A Quantile Regression Approach

Panagiotidis, Theodore; Pelloni, Gianluigi Working Paper Employment Reallocation and Unemployment Revisited: A Quantile Regression Approach Quaderni - Working Paper DSE, No. 881 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Panagiotidis, Theodore; Pelloni, Gianluigi (2013) : Employment Reallocation and Unemployment Revisited: A Quantile Regression Approach, Quaderni - Working Paper DSE, No. 881, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/3734 This Version is available at: https://hdl.handle.net/10419/159720 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Employment Reallocation and Unemployment Revisited: A Quantile Regression Approach Theodore Panagiotidis Gianluigi Pelloni Quaderni - Working Paper DSE N°881 1 Employment Reallocation and Unemployment Revisited: A Quantile Regression Approach * Theodore Panagiotidis Department of Economics, University of Macedonia, Greece; and Rimini Centre for Economic Analysis, Italy. [email protected] Gianluigi Pelloni Department of Economics, University of Bologna, Italy; Department of Economics, Wilfrid Laurier University, Canada; The Johns Hopkins University, SAIS-Bologna , Italy; and Rimini Centre for Economic Analysis, Italy. [email protected] 14 May 2013 ABSTRACT This study revisits the sectoral shifts hypothesis for the US for the period 1948 to 2011. A quantile regression approach is employed in order to investigate the asymmetric nature of the relationship between sectoral employment and unemployment. Significant asymmetries emerge. Lilien’s dispersion index is significant only for relatively high levels of unemployment and becomes insignificant for low levels suggesting that reallocation affects unemployment only when the latter is high. More job reallocation is associated with higher unemployment. Keywords: unemployment, employment reallocation, sectoral shifts, aggregate shocks, conditional quantile regression model, bootstrapping JEL Classification: C22, C50, E24 * Not to be quoted without authors’ permission. Acknowledgments: We wish to thank Francesco Franceschi, Ramazan Gencay, Angelo Melino, Emmanuel Pikoulakis, Thanasis Stengos. The usual caveat applies. 2 1. Introduction The relevance of intersectoral labor reallocation as a triggering force of aggregate (un) employment fluctuations is at the centre of an ongoing controversy. This debate persists because of the “observational equivalence” problem which is endemic in the sectoral shifts analysis (Lilien 1982b; Abraham and Katz, 1986). Both aggregate and allocative shocks can explain the observed positive correlation between unemployment and intersectoral employment dispersion signals. Discriminating between the impact of these two sources of shocks on unemployment has become one of the major challenges of empirical macroeconomics, and the massive effort aimed at overcoming this identification problem has led to important analytical extensions (e.g. job creation and job destruction analysis) and a vast and growing literature (for a survey c.f. Gallipoli and Pelloni, 2008). Originally the observational equivalence problem emerged in linear regression models which can only identify the conditional mean response of unemployment to changes in the covariates. The linear regression model (LRM) restricts the analysis to responses of the conditional mean and would be misleading as reallocation shocks are asymmetric and non-directional by nature. In the present paper, we adopt a new line of analysis which has novel features. We estimate a reduced form equation for unemployment of the Lilien (1982a) type and draw inferences by implementing a quantile regression (QR) approach to exploit the intrinsic asymmetries of allocative shocks. Quantile regression modelling allows us to quantify the response of each unemployment quantile to covariates. We can analyze not only the conditional central location but also the off-central location responses. In section 2 we put the sectoral shifts issue into the perspective of QR. In section 3 we introduce our QRM (Quantile Regression Model) for sectoral shifts and discuss briefly estimation and inference issues leaving details to an appendix. In section 4 we present results and finally in section 5 we draw conclusions and briefly outline possible developments. 3 2. Quantile Regression and Employment Reallocation Lilien (1982a) claims that intersectoral shifts in demand composition could operate as the driving force of unemployment fluctuations. Idiosyncratic shocks can bring about a process of workers reallocation (from declining to expanding sectors) which could be slow enough to require prolonged unemployment spells. Periods of relatively higher aggregate unemployment would be then associated with periods of relatively higher dispersion in employment demand. Lilien’s outcomes emerged from the estimation of a dynamic reduced form equation for the U.S. unemployment rate of the general form: [ ] () ,(),() tttt uFALUBLzCL σ = (1) where ut is the unemployment rate, zt is a vector of aggregate demand variables and A(L), B(L) and C(L) are polynomials in the lag operator L. The covariate σt, often called the Lilien dispersion proxy, is the weighted standard deviation of cross-sectoral employment growth rates: 2/1 2 ,, )lnln)(/( ⎥ ⎦ ⎤ ⎢ ⎣ ⎡Δ−Δ= ∑ jttjttjt NNNN σ (2) where Njt is employment in sector j at time t for j= 1,2…, K, Nt is aggregate employment at time t, and ( Njt /Nt ) are weights defined by the relative size of each sector. Lilien's empirical evidence suggests that σt is significantly and positively correlated with ut over the period 1948-1980 and that much of US unemployment in the 1970's, contrary to that of the early 1960's, can be explained by sectoral shifts. Figure 1 shows that over time in the US, there has been a large amount of workers reallocation, as characterized by σt, and that peaks in σt often coincide with peaks in unemployment.. Figure 1 Here Earlier analysis of these phenomena (Lilien 1982b; Abraham and Katz 1986, 1987; Weiss 1986) showed that the positive unemployment-sectoral dispersion (u-σ) correlation (as measured by using Lilien’s proxy) could instead capture the effects of aggregate shocks if cyclical responsiveness varies across sectors. Thus two alternative theories of unemployment fluctuations could yield observationally equivalent predictions. Subsequent research has been moving in 4 disparate directions and has seen a flourishing of empirical studies but at the same time no unifying analytical framework has obtained a widespread consensus1. Explorations of the (u-σ) correlation have in most cases borne out Abraham and Katz’s (1986) skeptical views about sectoral shifts2. These results, rooted in the LRM, reflect the response of the conditional mean function to a change in the covariates. They ignore the asymmetric and non-directional nature of allocative shocks. Aggregate shocks are directional (positive/negative), and, through the relevant propagation mechanism, could bring about large unemployment oscillations even when they are small. In principle these effects are reflected in each quantile of the unemployment distribution and would imply essentially a central location change. Reallocation shocks are disturbances unfavourable to the existing allocation of resources: a sectoral shock should bring about a reallocation process which is followed by an oscillation in aggregate unemployment. Some sectors will be affected positively and others negatively. At the macro level, this change in demand composition is reflected in the ensuing reallocation of workers which, for given search technology, would bring about an increase in unemployment consistent with the size of the required job reallocation. It is the magnitude of the engendered reallocations which determines the aggregate response in terms of higher unemployment. As reallocation shocks affect unemployment to the extent they are unfavorable to the current allocation of resources, small shocks generate a small unemployment increase while large shocks generate a large rise in unemployment. In analytical terms, it is the size of the shock and its asymmetric structure that count. Thus, the conditional unemployment distribution would be skewed to the left and the effects of employment reallocations on the lower quantiles will be small and insignificant. Asymmetry and/or the non-directional nature of idiosyncratic shocks have received a relatively small and restricted attention in testing the “job reallocation hypothesis” (e.g. Davis and Haltiwanger, 1999; Pelloni and Polasek, 1999; Pelloni and Polasek, 2003; Panagiotidis et al 2003 and for nonlinearity Panagiotidis and Pelloni, 2007). In the context of Lilien-type approach, equations (1) and (2) above, asymmetry has played no role and most of the focus has been on the mean response and / or the volatility3. In this paper, we take a different view and suggest that modelling the conditional mean of unemployment is not an appropriate strategy as it fails to take into account the fundamental intrinsic asymmetries of allocative shocks. If the conditional distribution of unemployment is skewed to the left, the mean will be smaller than the median and would be representative of lower tail behavior. Even as a measure of central location the conditional mean would be potentially distorting. Furthermore, given the intrinsic skewness of the conditional unemployment distribution under the employment reallocation assumption, researchers would be interested in measuring and testing off-central location responses and changes in the shape of the conditional unemployment distribution in response to changes in the covariates. Clearly, the LRM 5 would not be able to provide the necessary information. Preceding analyses were all based on the LRM and so all of them suffered of the shortcomings just illustrated. In summary in this paper we argue that two main characteristics characterize unemployment fluctuations brought about by allocative shocks: - The size of the shock; - The asymmetric response of unemployment. The first of these traits could be handled within the LRM through a polynomial representation of the dispersion proxy which would capture the non-linearity of the allocative shocks4. However such a framework would capture only the shock size effect on the conditional mean. The second feature could hardly be captured within a LRM. We suggest handling the analysis of equations like (1) and (2) by using quantile regression. In fact the QRM would provide an approach capable of overcoming some of these shortcomings. It would identify variations in the conditional quantile in response to changes in the covariates and gives us the possibility to focus on different segments of the distribution.5 Our approach is not embedded within a tight theoretical framework. However, no fully developed theoretical model of sectoral shifts has been developed up to now. Thus our line of attack, like others in the past, is based on fundamental features of sectoral shifts. Though it may not provide a final assessment on sectoral shifts (this would have to wait for the missing theory), we maintain that it can provide important and useful clues and leads. . 3. A Benchmark QRM of Unemployment. We estimate linear versions of equation (1), which provide representations of how each conditional quantile of unemployment depends on a (purged) Lilien’s dispersion measure and a vector of aggregate covariates. We start by providing a brief overview of the econometric methodology adopted here. Let U represent a random variable, in our case the unemployment rate, the conditional quantile function (CQF) at quantile τ given a vector of regressors, Xi: can be defined as )()( 1iU i iXFXUQ τ τ − = where )( iU XF τ is the distribution function for Yi at Y, conditional on Xi. When τ=0.5, )( i iXUQ τ would give us the conditional mean, while τ=0.9 provides the upper decile of U given Xi. The following minimisation problem is solved by the CQF: 6 [ ] ))((minarg)( ii i ii XqUEXUQ −= τ ρ where ))0(1()( ≤−= ww τ ρ τ is the absolute value check function. When τ=0.5, we have the least absolute deviations (LAD) estimator, so that when )( i ii XUQ is the conditional median. The check function puts negative and positive weights in an asymmetric way: wwwww )1)(0()0(1)( ττρτ −≤+>= Within the quantile regression framework, we set: [ ] argmin ( ' ) i EUXb ττ βρ ≡− and ˆ τ β is the quantile regression estimator. This minimisation can be considered as a linear programming problem. We would like to keep our experiment as close as possible to Lilien (1982a). However, we cannot ignore lessons which have been emerging since the publication of Lilien’s article. Thus our specification of the unemployment equation is somehow closer to the specification in Mills et al (1995). As dependent variable, following Wallis (1987), we employ the logistic transformation of unemployment rate. Although the discussion on the stationarity properties of the unemployment rate is extensive, we treat it here as a mean reverting process. We have employed a number of unit root tests such as the ADF, Phillips-Perron, the Zivot-Andrews (1992) with a break and the nonlinear one proposed by Kapetanios et al (2003). All of them reject the unit root either at the 5% or at the 1% significance level (results available upon request). The summary statistics of the unemployment and its logistic transformation are presented in Table 1. It emerges that the mean is greater than the median and there is some positive skewness. Figure 2 presents the kernel density together with the histogram for the two series. It is worth mentioning that the right tail of the distribution of the unemployment seems longer than its left tail and the one of its logistic transformation. We interpret it as a potential signal of asymmetry. Table 1 Here Figure 2 Here The unemployment rate is modelled as a linear function of money growth (m), the dispersion index (s), the natural logarithm of the US public deficit (d ), the growth rate of energy prices (e ) and so for the τth quantile vector x = ( s, m, d, e) 7 Our covariate, s, is Lilien’s dispersion measure purged of aggregate effects (Lilien’s sigma was constructed using data from the Bureau of Labor Statistics using four sectors: Construction, Finance, Manufacturing and Trade). Because of potential aggregate influences on the weighted cross-sectoral variance of employment growth rates, we have purged the Lilien’s proxy in (2) by regressing it on the current value of the aggregate variables appearing on the right hand side of (1). As the state of the art dictated in 1982, Lilien’s monetary policy covariate was a measure of unanticipated monetary growth. Since in the interim period empirical evidence has not borne out the importance of unperceived money changes as a potential triggering force of cycles, we can cast aside the separation between perceived and unperceived money growth. In our model we use the growth rate of M2 as a measure of monetary policy. The natural logarithm of the US public deficit is introduced to capture the effects of fiscal policy while the growth rate of energy prices, e, enters as another potential source of aggregate real shocks The inclusion of energy prices as an aggregate source of fluctuations might be controversial. Early important work on energy costs, Loungani (1986), Hamilton (1988), Keane (1991), Keane (1993) and Keane and Prasad (1996) suggest that relative productivity changes associated with oil price changes could lead to significant variations in frictional unemployment as labour is reallocated across sectors. We prefer to interpret oil price changes as aggregate shocks, because we wish to present a lower bound estimation for the hypothesis of sectoral shifts (c.f. Mills et al., 1995). The gist of our experiment is linked to the different nature of allocative and aggregate shocks. Allocative shocks being compositional and not directional induce only movements of the unemployment rate above its long run steady state value (LRSSV). For instance, if the LRSSV is 5% when an allocative shock hits the economy, unemployment will increase temporarily above its 5% LRSSV, to converge back to it in due course when reallocations have been completed. This characteristic entails that a Lilien’s proxy, if properly designed to capture sectoral shocks, would only affect significantly values of the unemployment rate above the LRSSV of unemployment. Furthermore the compositional nature of allocative shocks implies that only size matters. Directional shock could affect the economy even when they are small through the magnifying effect of a propagation mechanism while allocative shock effects depend on the size of change in demand composition. Thus we postulate that the effect of our Lilien proxy will be non-significant for the lower quantiles of a skewed conditional distribution of the unemployment rate . On the other end, aggregate shock, though necessarily symmetric, must capture variations above and below the unemployment LRSSV and would moderately affect the shape of the distribution and would tend to look like central location shifts (conditional means effects). Our experiment claims that a unit change of one of the aggregate covariates should cause every quantile to change 14 Lilien, D. M. (1982b), A sectoral model of business cycle, MRG WP no. 8231, University of Southern California. Loungani, P. (1986), Oil Price Shocks and the Dispersion Hypothesis, The Review of Economics and Statistics, Vol. 68 (3), 536-539. Mills T.C., Pelloni G. and Zervoyianni A. (1995), Fluctuations in the US : Further Tests of the Sectoral Shifts Hypothesis, The Review of Economics and Statistics, 77 (2), 294-304. Panagiotidis, T. and Pelloni, G., (2007), Nonlinearity in The Canadian And U.S. Labor Markets: Univariate And Multivariate Evidence From A Battery Of Tests, Macroeconomic Dynamics, 11(05), 613-637. Panagiotidis, T., Pelloni, G. and Polasek, W. (2003), Macroeconomic effects of reallocation shocks: A generalised Impulse Response Function analysis for three European Countries, Journal of Economic Integration, 18, 794-816. Pelloni G. and Polasek W., (2003), Macroeconomic effects of sectoral shocks in Germany, the U.K., U.S.: a VAR-GARCH-M approach, Computational Economics, 21 (1&2), 65-85. Phillips, P.C.B and Perron P. (1988), Testing for a Unit Root in Time Series Regression, Biometrika, 75 (2), 335–346 Wallis, K.F. (1987), Time series analysis of bounded economic variables, Journal of Time Series Analysis, 8(1), 115-123. Weiss, L. (1986), Asymmetric Adjustment Costs and Sectoral Shifts, in “Equilibrium Analysis: Essays in Honor of Kenneth J. Arrow”, ed. by R. S. W. P. Heller, and D. Starret, CUP, Cambridge. Zivot, E. and Andrews, D. W. K. (1992), Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis, Journal of Business & Economic Statistics, 10 (3), 251-270. 15 Figure 1: Unemployment rate and Lilien’s σt for the USA .02 .04 .06 .08 .10 .12 .00 0 .00 5 .01 0 .01 5 .02 0 .02 5 .03 0 50 55 60 65 70 75 80 85 90 95 00 05 10 Unemployment rate σ Figure 2: Kernel Density for Unemployment and its Logistic Transformation 0 10 20 30 40 50 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 Density Unemplo y men t Ra t e 0.0 0.5 1.0 1.5 2.0 2.5 -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 Kernel Histogram Density Logis t ic T r ans f r oma t ion 16 Figure 3 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile C -40 -20 0 20 40 60 80 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile SIGMA_PURGED2 -13 -12 -11 -10 -9 -8 -7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile FEDERALDEFICIT -6 -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile DLAMBSL -5 -4 -3 -2 -1 0 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile DLCPI_ENERGY Quantile Process Estimates (95% CI) 17 Figure 4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile C -20 0 20 40 60 80 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile SIGMA_PURGED2(-6) -11 -10 -9 -8 -7 -6 -5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile FEDERALDEFICIT(-6) -2 -1 0 1 2 3 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile DLAMBSL(-6) -3 -2 -1 0 1 2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile DLCPI_ENERGY(-6) Quantile Process Estimates (95% CI) 18 Figure 5 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile C -20 -10 0 10 20 30 40 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile SIGMA_PURGED2(-12) -12 -10 -8 -6 -4 -2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile FEDERALDEFICIT(-12) -2 0 2 4 6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile DLAMBSL(-12) -1 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile DLCPI_ENERGY(-12) Quantile Process Estimates (95% CI) 19 Figure 6 -.20 -.15 -.10 -.05 .00 .05 .10 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile C -8 -4 0 4 8 12 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile SIGMA_PURGED2 -.6 -.4 -.2 .0 .2 .4 .6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile FEDERALDEFICIT -.4 -.2 .0 .2 .4 .6 .8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile DLAMBSL -.3 -.2 -.1 .0 .1 .2 .3 .4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile DLCPI_ENERGY 0.94 0.96 0.98 1.00 1.02 1.04 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile LOGISUNRATE(-1) Quantile Process Estimates (95% CI) 20 Figure 7 -.16 -.12 -.08 -.04 .00 .04 .08 .12 .16 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile C -6 -4 -2 0 2 4 6 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile SIGMA_PURGED2(-6) -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile FEDERALDEFICIT(-6) -.2 .0 .2 .4 .6 .8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile DLAMBSL(-6) -.2 -.1 .0 .1 .2 .3 .4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Quantile DLCPI_ENERGY(-6) 0.96 0.98 1.00 1.02 1.04 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0 Quantile LOGISUNRATE(-1) Quantile Process Estimates (95% CI) 21 Table 1: Summary Statistics Unemployment Rate Lo g istic Transformation of Unemployment rate Mean 0.057312 -2.839907 Median 0.056000 -2.824774 Maximum 0.108000 -2.111335 Minimum 0.025000 -3.663562 Std. Dev. 0.016304 0.300950 Skewness 0.666020 -0.048311 Kurtosis 3.297517 2.838616 Table 2: OLS Estimates of the model (t-stats below each coef) Model 1 Contamporaneous Model 2: 6 lags Model 3: 12 lags C -2.9907 -2.9703 -2.9436 -126.98 -108.74 -94.13 SIGMA_PURGED2 13.0201 14.9764 11.9904 2.48 2.133 1.817 FEDERALDEFICIT -8.8452 -7.8625 -6.5078 -14.17 -13.03 -8.605 DLAMBSL 0.2692 1.6661 2.5287 0.925 3.87 3.622 DLCPI_ENERGY -0.3362 0.0003 1.0646 -1.02 0.0007 1.451 Adjusted R^2 0.555 0.447 0.306 F-stat 202.271 130.841 71.246 Pr(F-stat) 0.000 0.000 0.000 Serial Correlation LM Test Pr(12 lags) 0.000 0.000 0.000 HAC standard errors & covariance (Bartlett kernel, Newey-West fixed bandwidth 7) 22 Table 3: Quantile Process Estimates Specification: LOGISUNRATE C SIGMA_PURGED2 FEDERALDEFICIT DLAMBSL DLCPI_ENERGY Model 1 Contamporaneous Model 2: 6 lags Model 3: 12 lags Quantile Coefficient t-Statistic Coefficient t-Statistic Coefficient t-Statistic C 0.1 -3.23 -137.42 -3.24 -178.27 -3.26 -262.38 0.2 -3.13 -165.27 -3.13 -191.74 -3.13 -229.83 0.3 -3.05 -215.23 -3.06 -274.23 -3.08 -302.68 0.4 -3.00 -344.63 -3.02 -318.36 -3.02 -223.53 0.5 -2.97 -400.81 -2.99 -235.62 -2.97 -229.21 0.6 -2.95 -359.39 -2.94 -148.04 -2.92 -200.57 0.7 -2.92 -288.12 -2.88 -140.53 -2.84 -153.12 0.8 -2.88 -158.32 -2.80 -115.26 -2.75 -153.30 0.9 -2.77 -89.62 -2.68 -148.70 -2.61 -100.60 SIGMA_PURGED2 0.1 -15.81 -1.68 -0.52 -0.06 3.16 0.31 0.2 11.00 1.51 1.55 0.32 7.70 1.71 0.3 8.65 1.61 7.26 1.55 10.94 1.75 0.4 12.09 3.61 8.32 2.21 16.76 2.91 0.5 14.23 5.01 13.77 2.99 17.68 3.54 0.6 17.09 3.09 14.67 2.51 14.87 2.91 0.7 24.03 4.72 23.66 3.06 16.75 2.55 0.8 27.74 4.68 31.48 3.85 15.36 2.16 0.9 37.37 3.27 49.46 4.57 22.11 2.02 FEDERALDEFICIT 0.1 -9.54 -20.17 -10.13 -35.95 -9.92 -16.62 0.2 -8.88 -19.64 -8.62 -20.21 -8.01 -17.92 0.3 -8.55 -27.39 -8.32 -39.79 -8.07 -23.95 0.4 -8.57 -42.34 -8.20 -30.82 -7.68 -27.52 0.5 -8.48 -48.96 -8.26 -23.23 -7.11 -21.20 0.6 -8.52 -49.13 -7.78 -18.43 -6.43 -17.45 0.7 -8.88 -27.06 -7.35 -17.84 -5.66 -13.04 0.8 -9.34 -16.82 -6.76 -14.48 -5.07 -12.26 0.9 -10.08 -10.07 -6.60 -9.78 -4.23 -6.42 DLAMBSL 0.1 0.82 1.14 0.13 0.20 0.46 0.48 0.2 0.70 1.16 0.81 1.10 1.46 2.06 0.3 0.25 0.65 0.54 0.74 0.64 0.76 0.4 0.12 0.31 1.72 2.20 0.72 0.76 0.5 0.03 0.06 1.74 2.33 1.25 1.24 0.6 -0.13 -0.23 1.81 3.23 2.99 2.92 0.7 -0.12 -0.15 1.43 2.26 2.81 2.69 0.8 -0.77 -0.71 1.00 1.16 2.76 2.66 0.9 -2.27 -1.72 0.38 0.46 2.98 3.39 DLCPI_ENERGY 0.1 0.25 0.76 0.00 0.01 0.00 0.01 0.2 -0.21 -0.58 -0.15 -0.23 0.06 0.17 0.3 -0.68 -2.57 -0.26 -0.41 0.02 0.05 0.4 -0.40 -1.17 -0.22 -0.47 0.56 1.02 0.5 -0.38 -1.16 -0.04 -0.10 1.05 1.44 0.6 -0.47 -1.37 0.22 0.63 1.36 1.75 0.7 -0.29 -0.65 -0.02 -0.03 1.36 1.50 0.8 -0.77 -1.13 -0.48 -0.56 1.68 1.71 0.9 -2.05 -1.98 -0.51 -0.75 2.53 3.14 Table 4: Goodness of fit for Quantile Regressions Model 1 Model 2 Model 3 Pseudo R-squared 0.386 0.305 0.202 Adjusted R-squared 0.382 0.301 0.197 Quasi-LR statistic 665.011 428.219 237.933 Prob(Quasi-LR stat) 0.000 0.000 0.000 Note: Pseudo R-squared are from Koenker and Machado (1999). 23 Table 5: Quantile Process Estimates Model 4 Contamporaneous Model 5: 6 lags Quantile Coefficient t-Statistic Coefficient t-Statistic C 0.1 -0.069 -1.552 -0.064 -1.562 0.2 -0.078 -2.216 -0.026 -0.694 0.3 -0.009 -0.207 0.015 0.456 0.4 -0.056 -1.748 -0.019 -0.754 0.5 0.000 0.000 0.000 0.044 0.6 0.002 0.097 0.019 0.738 0.7 -0.023 -0.557 0.053 1.274 0.8 -0.028 -0.756 0.077 2.117 0.9 0.006 0.157 0.080 2.567 SIGMA_PURGED2 0.1 -2.106 -1.622 -1.128 -0.775 0.2 -1.330 -0.845 -0.962 -0.848 0.3 -0.018 -0.014 -0.472 -0.694 0.4 1.118 1.112 -1.395 -1.777 0.5 0.000 0.000 -0.129 -0.201 0.6 1.354 1.197 -0.013 -0.014 0.7 0.372 0.208 -0.439 -0.684 0.8 5.341 2.295 -0.677 -0.506 0.9 7.756 5.808 2.345 1.119 FEDERALDEFICIT 0.1 -0.165 -0.896 -0.034 -0.221 0.2 -0.203 -1.456 0.022 0.190 0.3 -0.078 -0.571 0.077 0.725 0.4 -0.093 -0.715 0.079 0.920 0.5 0.000 0.000 0.023 0.368 0.6 -0.003 -0.039 0.165 1.233 0.7 0.010 0.090 0.360 2.574 0.8 -0.067 -0.589 0.444 3.183 0.9 0.105 0.701 0.580 4.219 DLAMBSL 0.1 0.361 1.695 0.474 4.621 0.2 0.293 1.652 0.361 4.671 0.3 0.231 1.394 0.279 3.637 0.4 0.286 1.716 0.268 2.952 0.5 0.000 0.000 0.114 1.145 0.6 0.126 1.086 0.233 2.323 0.7 0.061 0.545 0.209 2.215 0.8 0.140 1.380 0.158 1.662 0.9 0.016 0.161 0.197 2.106 DLCPI_ENERGY 0.1 0.113 1.196 0.113 1.131 0.2 0.082 0.866 0.065 0.840 0.3 0.049 0.496 0.014 0.236 0.4 0.158 1.743 0.044 0.589 0.5 0.000 0.000 0.007 0.114 0.6 0.013 0.169 0.120 1.085 0.7 -0.001 -0.007 0.135 1.436 0.8 -0.036 -0.411 0.050 0.551 0.9 -0.051 -0.676 0.157 1.502 LOGISUNRATE(-1) 0.1 0.992 66.650 0.992 70.647 0.2 0.983 86.602 1.000 82.590 0.3 1.004 65.066 1.012 90.271 0.4 0.984 106.718 0.995 110.891 0.5 1.000 584.689 1.000 561.182 0.6 1.000 117.149 1.005 130.977 0.7 0.985 69.708 1.011 71.433 0.8 0.981 77.853 1.016 84.621 0.9 0.984 79.838 1.009 96.409