DOCSLIB.ORG

Lectures on Structural Change

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lectures on Structural Change Lectures on Structural Change Eric Zivot Department of Economics, University of Washington April 4, 2001 1 Overview of Testing for and Estimating Struc- tural Change in Econometric Models 2 Some Preliminary Asymptotic Theory Reference: Stock, J.H. (1994) “Unit Roots, Structural Breaks and Trends,” in Handbook of Econometrics, Vol. IV. 3 Tests of Parameter Constancy in Linear Mod- els 3.1 Rolling Regression Reference: Zivot, E. and J. Wang (2002). Modeling Financial Time Series with S-PLUS. Springer-Verlag, New York. For a window of width k<n<T,the rolling linear regression model is yt(n) = Xt(n)βt(n) + εt(n),t= n,...,T (n 1) (n k) (k 1) (n 1) × × × × Observations in yt(n)andXt(n)aren most recent values from times • t n +1tot − OLS estimates are computed for sliding windows of width n and increment • m Poor man’s time varying regression model • 3.1.1 Application: Simulated Data Consider the linear regression model yt = α + βxt + εt,t=1,...,T =200 xt iid N(0, 1) ∼ 2 εt iid N(0,σ ) ∼ 1 No structural change parameterization: α =0,β =1,σ =0.5 Structural change cases Break in intercept: α =1fort>100 • Break in slope: β =3fort>100 • Break in variance: σ =0.25 for t>100 • Random walk in slope: β = βt = βt 1 +ηt,ηt iid N(0, 0.1) and β0 =1. • − ∼ (show simulated data) 3.1.2 Application: Exchange rate regressions References: 1. Bailey, R. and T. Bollerslev (???) 2. Sakoulis, G. and E. Zivot (2001). “Time Variation and Structural Change in the Forward Discount: Implications for the Forward Rate Unbiasedness Hypothesis,” unpublished manuscript, Department of Eco- nomics, University of Washington. Let st = log of spot exchange rate in month t ft = log of forward exchange rate in month t The forward rate unbiased hypothesis is typically investigated using the so-called differences regression ∆st+1 = α + β(ft st)+εt+1 − ft st = forward discount − If the forward rate ft is an unbiased forecast of the future spot rate st+1 then we should find α = 0 and β =1 The forward discount is often modeled as an AR(1) model ft st = δ + φ(ft 1 st 1)+ut − − − − Statistical Issues ∆st+1 is close to random walk with large variance • ft st behaves like highly persistent AR(1) with small variance • − ft st appears to be unstable over time • − Tasks: compute rolling regressions for 24-month windows incremented by 1 month • compute rolling regressions for 48-month windows incremented by 12 months • (insert rolling regression graphs here) 2 3.2 Chow Forecast Test Reference: Chow, G.C. (1960). “Tests of Equality between Sets of Coeffi- cients in Two Linear Regressions,” Econometrica, 52, 211-22. Consider the linear regression model with k variables 2 yt = x0tβ + ut,ut (0,σ ),t=1,...,n ∼ y = Xβ + u Parameter constancy hypothesis H0 : β is constant Chow forecast test intuition If parameters are constant then out-of-sample forecasts should be unbiased • (forecast errors have mean zero) Chow forecast test construction: Split sample into n1 >kand n2 = n n1 observations • − y n X n y = 1 1 , X = 1 1 y2 n2 X2 n2 µ ¶ µ ¶ Fit model using first n1 observations • ˆ 1 β1 =(X10 X1)− X10 y1 ˆ uˆ1 = y1 X1β1 2 − σˆ = uˆ0 uˆ1/(n1 k) 1 1 − Use βˆ and X2 to predict y2 using next n2 observations • 1 ˆ yˆ2 = X2β1 Compute out-of-sample prediction errors • uˆ2 = y2 yˆ = y2 X2βˆ − 2 − 1 Under H0 : β is constant uˆ2 = u2 X2(βˆ β) − 1− and E[uˆ2]=0 2 1 n var(uˆ2)=σ I 2 + X2(X10 X1)− X20 ³ ´ 3 Further, If the errors u are Gaussian then uˆ2 N(0,var(uˆ2)) ∼ 1 2 uˆ20 var(uˆ2)− uˆ2 χ (n2) 2 2 ∼ 2 (n1 k)ˆσ /σ χ (n1 k) − 1 ∼ − This motivates the Chow forecast test statistic 1 uˆ20 In2 + X2(X10 X1)− X20 uˆ2 ChowFCST(n2)= 2 F (n2,n1 k) ³ n2σˆ1 ´ ∼ − Remarks: Test is a general specification test for unbiased forecasts • Implementation requires apriorisplitting of data into fitandforecast • samples 3.2.1 Application: Exchange rate regression cont’d (show Eviews output for Chow forecast test) 3.3 CUSUM and CUSUMSQ Tests Reference: Brown, R.L., J. Durbin and J.M. Evans (1975). “Techniques for Testing the Constancy of Regression Relationships over Time,” Journal of the Royal Statistical Society, Series B, 35, 149-192. 3.3.1 Recursive least squares estimation The recursive least squares (RLS) estimates of β are based on estimating yt = βt0 xt + ξt,t=1,...,n by least squares recursively for t = k +1,...,ngiving n k least squares (RLS) ˆ ˆ − estimates (βk+1,...,βT ). RLS estimates may be efficiently computed using the Kalman Filter • If β is constant over time then βˆt should quickly settle down near a com- • mon value. If some of the elements in β are not constant then the corresponding RLS • estimates should show instability. Hence, a simple graphical technique for uncovering parameter instability is to plot the RLS estimates βˆit (i =1, 2) and look for instability in the plots. 4 3.3.2 Recursive residuals Formal tests for structural stability of the regression coefficients may be com- puted from the standardized 1 step ahead recursive residuals − ˆ0 vt yt βt 1xt wt = = − − √ft √ft 2 1 ft =ˆσ 1+x0t(Xt0 Xt)− xt h i Intuition: If β changes in the next period then the forecast error will not have mean • zero 3.3.3 CUSUM statistic The CUSUM statistic of Brown, Durbin and Evans (1975) is t wˆj CUSUMt = σˆw j=k+1 X n 2 1 2 σˆ = (wt w¯) w n k t=1 − − X Under the null hypothesis that β is constant, CUSUMt has mean zero and variance that is proportional to t k 1. − − 3.3.4 Application: Simulated Data (insert graphs here) Remarks Ploberger and Kramer (1990) show the CUSUM test can be constructed • with OLS residuals instead of recursive residuals CUSUM Test is essentially a test to detect instability in intercept alone • CUSUM Test has power only in direction of the mean regressors • CUSUMSQ test does not have good power for changing coefficients but • has power for changing variance 3.3.5 Application: Exchange Rate Regression cont’d (show recursive estimates, CUSUM and CUSUMSQ plots) 5 3.4 Nyblom’s Parameter Stability Test Reference:Nyblom, J. (1989). “Testing for the Constancy of Parameters Over Time,” Journal of the American Statistical Association, 84 (405), 223-230. Consider the linear regression model with k variables yt = x0tβ + εt The time varying parameter (TVP) model assumes 2 β = βt = βt 1 + ηt, ηt (0,ση) − ∼ Note: the TVP model nests the single break model by setting ηt = γ, t = r +1 and ηt =0otherwise. The hypotheses of interest are then 2 H0 : β is constant ση =0 ⇔ 2 H1 : ση > 0 Nyblom (1989) derives the locally best invariant test as the Lagrange multiplier test n n n 1 2 L = tr S−n ˆεkxk ˆεkx0k /σˆε >c j=1 k=j k=j X X X 1 ˆεt = yt x0tβˆ, βˆ =(X0X)− X0y −1 Sn = n− X0X Under mild assumptions regarding the behavior of the regressors, the limiting distribution of L under the null is a Camer-von Mises distribution: 1 µ µ L Bk (λ)Bk (λ)dλ ⇒ 0 µ Z Bk (λ)=Wk(λ) λWk(1) − Wk(λ) = k dimensional Brownian motion Remarks: Test statistic is a sum of cumulative sums of weighted full sample residuals • Test is for constancy of all parameters • Test is applicable for models estimated by methods other than OLS • Distribution of L is different if xt is non-stationary (unit root, determin- • istic trend) 6 3.4.1 Application: Simulated Data Nyblom Test Model Lc No SC .332 Mean shift 13.14∗∗∗ Slope shift 14.13∗∗∗ var shift .351 RW slop e 9.77∗∗∗ 3.4.2 Application: Exchange rate regression cont’d Nyblom Test Model Lc AR(1) 1.27∗∗∗ Diff reg .413 3.5 Hansen’s Parameter Stability Tests References 1. Hansen, B.E. (1992). “Testing for Parameter Instability in Linear Mod- els ”Journal of Policy Modeling, 14(4), 517-533. 2. Hansen, B.E. (1992). “Tests for Parameter Instability in Regressions with I(1) Processes,” Journal of Business and Economic Statistics,10, 321-336. Same set-up as Nyblom’s LM test. Under the null of constant parameters, the score vector from the linear model with Gaussian errors is based on the normal equations n xitˆεt =0,i=1,...,k t=1 X 2 2 (ˆεt σˆ )=0 − X ˆεt = yt x0tβˆ − n 2 1 2 σˆ = n− ˆεt t=1 X Define xitˆεt i =1,...k fit = 2 2 ˆεt σˆ i = k +1 ½t − Sit = fij ,i=1,...,k+1 j=1 X 7 Note that n fit =0,i=1,...,k+1 i=1 X Hansen’s LM test for H0 : βi is constant, i =1,...,k and for 2 H0 : σ is constant is n 1 2 Li = Sit,i=1,...,k nVi t=1 n X 2 Vi = fit t=1 X Under the null of no structural change 1 µ µ Li B (λ)B (λ)dλ ⇒ 1 1 Z0 For testing the joint hypothesis 2 H0 : β and σ are constant define the (k +1) 1 vectors × ft =(f1t,...,fk+1,t)0 St =(S1t,...,Sk+1,t)0 Hansen’s LM statistic for testing the constancy of all parameters is n n 1 1 1 1 Lc = S V St = tr V StS n 0t − n − 0t t=1 à t=1 ! nX X V = ftft0 t=1 X Under the null of no-structural change 1 µ µ Lc Bk (λ)Bk (λ)dλ ⇒ +1 +1 Z0 Remarks Tests are very easy to compute and are robust to heteroskedasticity • 8 Null distribution is non-standard and depends upon number of parameters • tested for stability 5% critical value for individual tests is 0.470 • Tests are not informative about the date of structural change • Hansen’s L1 test for constancy of intercept is analogous to the CUSUM • test Hansen’s Lk+1 test for constancy of variance is analogous to CUSUMSQ • test Hansen’s Lc test for constancy of all parameters is similar to Nybolom’s • test Distribution of tests is different if data are nonstationary (unit root, de- • terministic trend) - see Hansen (1992), JBES.
Load more

Recommended publications
  • Lecture 7: Common Factor Tests and Stability Tests
    Lecture 7: Common Factor Tests and Stability Tests R.G. Pierse 1 Common factor Tests Consider again the regression model with first order autoregressive errors from lecture 4: Yt = β1 + β2X2t + ··· + βkXkt + ut ; t = 1; ··· ;T (1.1) and ut = ρut−1 + "t ; t = 1; ··· ;T (1.2) where −1 < ρ < 1 : The transformed version of this equation is Yt − ρYt−1 = (1 − ρ)β1 + β2(X2t − ρX2;t−1) + ··· + βk(Xkt − ρXk;t−1) + "t (1.3) where "t obeys all the assumptions of the classical model. Note that this model has k + 1 parameters. Compare this with the unrestricted dynamic model: Yt = γ1 + ρYt−1 + β2X2t + ··· + βkXkt + γ2X2;t−1 + ··· + γkXk;t−1 + "t : (1.4) which has 2k parameters. Equation (1.3) is a special case of equation (1.4) that satisfies the k − 1 nonlinear restrictions γj = −ρβj ; j = 2; ··· ; k : This suggests that the autoregressive model can be viewed as a restricted form of a dynamic model, satisfying a particular type of parameter restriction known as common factor restrictions. Evidence of serial correlation from the residuals from estimating equation (1.1) may indicate omission of any or all of the variables Yt−1, X2;t−1, ··· , Xk;t−1 rather than indicating the AR(1) model (1.3). 1 Sargan (1964) and Hendry and Mizon (1978) suggest a test of common factor restrictions in the model (1.4). This test is based on the statistic RSS T log r RSSu where RSSu is the residual sum of squares from the unrestricted model (1.4) and RSSr is the residual sum of squares from the restricted model (1.3).
    [Show full text]
  • Econometrics-I-11.Pdf
    Econometrics I Professor William Greene Stern School of Business Department of Economics 11-1/78 Part 11: Hypothesis Testing - 2 Econometrics I Part 11 – Hypothesis Testing 11-2/78 Part 11: Hypothesis Testing - 2 Classical Hypothesis Testing We are interested in using the linear regression to support or cast doubt on the validity of a theory about the real world counterpart to our statistical model. The model is used to test hypotheses about the underlying data generating process. 11-3/78 Part 11: Hypothesis Testing - 2 Types of Tests Nested Models: Restriction on the parameters of a particular model y = 1 + 2x + 3T + , 3 = 0 (The “treatment” works; 3 0 .) Nonnested models: E.g., different RHS variables yt = 1 + 2xt + 3xt-1 + t yt = 1 + 2xt + 3yt-1 + wt (Lagged effects occur immediately or spread over time.) Specification tests: ~ N[0,2] vs. some other distribution (The “null” spec. is true or some other spec. is true.) 11-4/78 Part 11: Hypothesis Testing - 2 Hypothesis Testing Nested vs. nonnested specifications y=b1x+e vs. y=b1x+b2z+e: Nested y=bx+e vs. y=cz+u: Not nested y=bx+e vs. logy=clogx: Not nested y=bx+e; e ~ Normal vs. e ~ t[.]: Not nested Fixed vs. random effects: Not nested Logit vs. probit: Not nested x is (not) endogenous: Maybe nested. We’ll see … Parametric restrictions Linear: R-q = 0, R is JxK, J < K, full row rank General: r(,q) = 0, r = a vector of J functions, R(,q) = r(,q)/’. Use r(,q)=0 for linear and nonlinear cases 11-5/78 Part 11: Hypothesis Testing - 2 Broad Approaches Bayesian: Does not reach a firm conclusion.
    [Show full text]
  • Permutation Methods for Chow Test Analysis an Alternative for Detecting Structural Break in Linear Models
    Advances in Science, Technology and Engineering Systems Journal Vol. 4, No. 4, 12-20 (2019) ASTESJ www.astesj.com ISSN: 2415-6698 Permutation Methods for Chow Test Analysis an Alternative for Detecting Structural Break in Linear Models Aronu, Charles Okechukwu1,*, Nworuh, Godwin Emeka2 1Chukwuemeka Odumegwu Ojukwu University (COOU), Department of Statistics, Uli, Campus, 431124, Nigeria 2Federal University of Technology Owerri (FUTO), Department of Statistics,460114, Nigeria A R T I C L E I N F O A B S T R A C T Article history: This study examined the performance of two proposed permutation methods for Chow test Received:22 February, 2019 analysis and the Milek permutation method for testing structural break in linear models. Accepted:19 June, 2019 The proposed permutation methods are: (1) permute object of dependent variable and (2) Online: 09 July, 2019 permute object of the predicted dependent variable. Simulation from gamma distribution and standard normal distribution were used to evaluate the performance of the methods. Keywords: Also, secondary data were used to illustrate a real-life application of the methods. The Chow Test findings of the study showed that method 1(permute object of dependent variable) and Economic Growth Method2 (permute object of the predicted dependent variable) performed better than the Structural Break traditional Chow test analysis while the Chow test analysis was found to perform better Permutation Method than the Milek permutation for structural break. The methods were used to test whether the introduction of Nigeria Electricity Regulatory Commission (NERC) in the year 2005 has significant impact on economic growth in Nigeria.
    [Show full text]
  • Econometrics - 2011/12
    ECONOMETRICS - 2011/12 Giorgio Calzolari Lecture 1 Introduction. Complements of linear algebra, idempotent matrices, projection matrices, trace of the projection matrix Mx. The idempotent matrix that produces deviations from the arithmetical average. Linear regression model, compact notation using vectors and matrices, algebraic assumptions that lead to ordinary least squares estimation (OLS). X'X is a positive definite matrix. Minimization of the sum of squared errors, estimated coefficients, residuals. Orthogonality between OLS residuals and explanatory variables. Sum of residuals is zero for a model with intercept. R^2 in a model with intercept. Limitations of the R^2 concept. Lecture 2 Inequality between positive semidefinite matrices. Statistical assumptions for the classical linear regression model. Expectation and variance-covariance matrix of OLS coefficients. Unbiasedness of OLS estimator. Constructing other linear unbiased estimators of coefficients. Gauss-Markov theorem, with 2 different proofs: traditional textbook proof and proof based on Schwarz inequality. Unbiased estimation of sigma^2, with proof. Forecast (conditional) and variance of the forecast error. The additional assumption of normality of the error terms. Standardization of a random variable; standard normal distribution. Test of a simple hypothesis on a coefficient using the standard normal (supposing Sigma^2 known). “Operational” introduction to the “t-test” (two-sided and one-sided), without proofs involving the multivariate normal and the chi^2 distribution (that will be explained in the third lesson on Statistics next week) Lecture 3 Some properties of eigenvalues and eigenvectors of symmetric matrices and idempotent matrices; the orthogonal matrix containing the normalized eigenvectors; the spectral decomposition of a symmetric matrix. Distributions of linear and quadratic forms, when the vectors have a multivariate normal distribution, with proofs.
    [Show full text]
  • Package 'Strucchange'
    Package ‘strucchange’ October 12, 2019 Version 1.5-2 Date 2019-10-12 Title Testing, Monitoring, and Dating Structural Changes Description Testing, monitoring and dating structural changes in (linear) regression models. strucchange features tests/methods from the generalized fluctuation test framework as well as from the F test (Chow test) framework. This includes methods to fit, plot and test fluctuation processes (e.g., CUSUM, MOSUM, recursive/moving estimates) and F statistics, respectively. It is possible to monitor incoming data online using fluctuation processes. Finally, the breakpoints in regression models with structural changes can be estimated together with confidence intervals. Emphasis is always given to methods for visualizing the data. LazyData yes Depends R (>= 2.10.0), zoo, sandwich Suggests stats4, car, dynlm, e1071, foreach, lmtest, mvtnorm, tseries Imports graphics, stats, utils License GPL-2 | GPL-3 NeedsCompilation yes Author Achim Zeileis [aut, cre] (<https://orcid.org/0000-0003-0918-3766>), Friedrich Leisch [aut], Kurt Hornik [aut], Christian Kleiber [aut], Bruce Hansen [ctb], Edgar C. Merkle [ctb] Maintainer Achim Zeileis <[email protected]> Repository CRAN Date/Publication 2019-10-12 18:35:49 UTC 1 2 R topics documented: R topics documented: BostonHomicide . .3 boundary . .4 boundary.efp . .5 boundary.Fstats . .6 boundary.mefp . .7 breakdates . .8 breakfactor . .9 breakpoints . 10 catL2BB . 15 confint.breakpointsfull . 17 DJIA............................................. 19 durab . 20 efp.............................................. 21 efpFunctional . 24 Fstats . 27 gefp............................................. 29 GermanM1 . 31 Grossarl . 33 logLik.breakpoints . 36 mefp............................................. 37 PhillipsCurve . 39 plot.efp . 41 plot.Fstats . 43 plot.mefp . 45 RealInt . 46 recresid . 47 root.matrix . 48 scPublications . 49 sctest . 50 sctest.default .
    [Show full text]
  • An Asymptotically F-Distributed Chow Test in the Presence of Heteroscedasticity and Autocorrelation∗
    An Asymptotically F-Distributed Chow Test in the Presence of Heteroscedasticity and Autocorrelation∗ Yixiao Sun Xuexin Wang Department of Economics School of Economics and WISE UC San Diego, USA Xiamen University, China October 25, 2019 Abstract This study proposes a simple, trustworthy Chow test in the presence of heteroscedasticity and autocorrelation. The test is based on a series heteroscedasticity and autocorrelation robust variance estimator with judiciously crafted basis functions. Like the Chow test in a classical normal linear regression, the proposed test employs the standard F distribution as the reference distribution, which is justified under fixed-smoothing asymptotics. Monte Carlo simulations show that the null rejection probability of the asymptotic F test is closer to the nominal level than that of the chi-square test. Keywords: Chow Test, F Distribution, Heteroscedasticity and Autocorrelation, Structural Break. 1 Introduction For predictive modeling and policy analysis using time series data, it is important to check whether a structural relationship is stable over time. The Chow (1960) test is designed to test whether a break takes place at a given period in an otherwise stable relationship. The test is widely used in empirical applications and has been included in standard econometric textbooks. This paper considers the Chow test in the presence of heteroscedasticity and autocorrelation. There is ample evidence that the Chow test can have very large size distortions if heteroscedasticity and autocorrelation are not accounted for (e.g., Kr¨amer(1989) and Giles and Scott (1992)). Even if we account for them using heteroscedasticity and autocorrelation robust (HAR) variance estimators (e.g., Newey and West (1987) and Andrews (1991)), the test can still over-reject the null hypothesis by a large margin if chi-square critical values are used1.
    [Show full text]
  • Evidence on Structural Changes in U.S. Time Series
    Economic Modelling 22 (2005) 391–422 www.elsevier.com/locate/econbase Evidence on structural changes in U.S. time series Jamel Jouini*, Mohamed Boutahar1 GREQAM, Universite´delaMe´diterrane´e, 2 rue de la Charite´, 13002 Marseille, France Accepted 18 June 2004 Abstract Some developments in the analysis of structural change models are presented to explore the empirical evidence of the instability by uncovering structural breaks in some U.S. time series. Indeed, the unstable series may be subjected to a meticulous examination allowing to determine changes present in their structure. To that effect, we pursue a methodology composed of different steps and we propose a modelling strategy so as to detect the break dates that can exist in the series. Once the breaks are selected, we attempt to find economic explanations showing why in the chosen dates there are changes in the series. The results indicate that the time series relations have been altered by various important facts and international economic events such as the two Oil-Price Shocks and changes in the International Monetary System. They also show that the presence of high correlation in the data greatly affects the estimation precision of some procedures. D 2004 Elsevier B.V. All rights reserved. JEL classification: C20 Keywords: Structural change; Break dates; Hypothesis testing; Model selection 1. Introduction The econometrics and statistics literature holds an important volume of works related to the problem of structural change. For linear regression models, there exist the works of * Corresponding author. Tel.: +33 4 91 14 07 23; fax: +33 4 91 90 02 27.
    [Show full text]
  • Heteroskedasticity-Robust Tests for Structural Change
    Q ED Queen’s Economics Department Working Paper No. 717 Heteroskedasticity-Robust Tests for Structural Change James G. MacKinnon Queen’s University Department of Economics Queen’s University 94 University Avenue Kingston, Ontario, Canada K7L 3N6 5-1988 Heteroskedasticity-Robust Tests for Structural Change James G. MacKinnon Department of Economics Queen’s University Kingston, Ontario, Canada K7L 3N6 Abstract It is remarkably easy to test for structural change, of the type that the classic F or “Chow” test is designed to detect, in a manner that is robust to heteroskedasticity of possibly unknown form. This paper first discusses how to test for structural change in nonlinear regression models by using a variant of the Gauss-Newton regression. It then shows how to make these tests robust to heteroskedasticity of unknown form and discusses several related procedures for doing so. Finally, it presents the results of a number of Monte Carlo experiments designed to see how well the new tests perform in finite samples. This research was supported, in part, by the Social Sciences and Humanities Research Council of Canada. I am grateful to Allan Gregory and Simon Power for helpful comments on an earlier draft. This paper was published in the Empirical Economics, 14, 1989, 77–92. May, 1988 1. Introduction A classic problem in econometrics is testing whether the coefficients of a regression model are the same in two or more separate subsamples. In the case of time-series data, where the subsamples generally correspond to different economic environments, such as different exchange-rate or policy regimes, such tests are generally referred to as tests for structural change.
    [Show full text]
  • Testing for Unit Roots and Structural Breaks
    Testing for unit roots and structural breaks Prepared by Ziyodullo Parpiev, PhD for Regional Summer School September 21, 2016 Unit Root Tests • Traditionally, Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests are used to assess the order of integration of the variables. • Uniform outcomes of both tests are necessary for the final conclusion about the stationarity properties of each series. • Usually, all variables are tested with a linear trend and/or intercept or none. Structural Breaks • A well-known weakness of the ADF and PP unit root tests is their potential confusion of structural breaks in the series as evidence of non-stationarity. • In other words, they may fail to reject the unit root hypothesis if the series have a structural break. • In other words, for the series that are found to be I(1), there may be a possibility that they are in fact stationary around the structural break(s), I(0), but are erroneously classified as I(1). Nonstationarity: Structural Breaks The coefficients of the model might not be constant over the full sample. Clearly, it is a problem for forecasting if the model describing the historical data differs from the current model – you want the current model for your forecasts! So we will: • Go over the way to detect changes in coefficients: tests for a break • Work through an example: the U.S. labor productivity Case I: Break date is known A series of data can often contain a structural break, due to a change in policy or sudden shock to the economy, i.e. 1987 stock market crash.
    [Show full text]
  • Theory and Practice of Testing for a Single Structural Break in Stata
    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Majune, Socrates Kraido Preprint Theory and Practice of Testing for a Single Structural Break in Stata Suggested Citation: Majune, Socrates Kraido (2018) : Theory and Practice of Testing for a Single Structural Break in Stata, ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften, Leibniz-Informationszentrum Wirtschaft, Kiel und Hamburg This Version is available at: http://hdl.handle.net/10419/172517 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Theory and Practice of Testing for a Single Structural Break in Stata Socrates Kraido Majune* January, 2018 Abstract The major objective of this paper is to demonstrate, theoretically and empirically, the test of a single structural break/change.
    [Show full text]
  • Chapter 12 Tests for Structural Change and Stability
    Chapter 12 Tests for Structural Change and Stability A fundamental assumption in regression modeling is that the pattern of data on dependent and independent variables remains the same throughout the period over which the data is collected. Under such an assumption, a single linear regression model is fitted over the entire data set. The regression model is estimated and used for prediction assuming that the parameters remain same over the entire time period of estimation and prediction. When it is suspected that there exists a change in the pattern of data, then the fitting of single linear regression model may not be appropriate, and more than one regression models may be required to be fitted. Before taking such a decision to fit a single or more than one regression models, a question arises how to test and decide if there is a change in the structure or pattern of data. Such changes can be characterized by the change in the parameters of the model and are termed as structural change. Now we consider some examples to understand the problem of structural change in the data. Suppose the data on the consumption pattern is available for several years and suppose there was a war in between the years over which the consumption data is available. Obviously, the consumption pattern before and after the war does not remain the same as the economy of the country gets disturbed. So if a model yiikiki011XXin ... , 1,2,..., is fitted then the regression coefficients before and after the war period will change. Such a change is referred to as a structural break or structural change in the data.
    [Show full text]
  • Testing for Structural Breaks in the Evaluation of Programs
    TESTING FOR STRUCTURAL BREAKS IN THE EVALUATION OF PROGRAMS Suzanne J. Cooper John F. Kennedy School of Government, Harvard University Anne Morrison Piehl John F. Kennedy School of Government, Harvard University and NBER Anthony A. Braga John F. Kennedy School of Government, Harvard University David M. Kennedy John F. Kennedy School of Government, Harvard University April 2001 Keywords: parameter stability, program evaluation, youth homicide JEL No. C22, K42, I12 The Boston Gun Project was supported under award #904-IJ-CX-0056 from the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice. Piehl appreciates the support of the Robert Wood Johnson Foundation. Points of view in this document are those of the authors and do not necessarily represent the official position of the U.S. Department of Justice. The authors appreciate the helpful comments of two anonymous referees and the editor, as well as Christopher Avery, Richard Blundell, Kristin Butcher, David Card, James Stock, and seminar participants at the University of California, Berkeley, Harvard University, Yale University, and the NBER. Please address correspondence to Anne Piehl, 79 JFK Street, Cambridge, MA 02138, [email protected]. TESTING FOR STRUCTURAL BREAKS IN THE EVALUATION OF PROGRAMS Abstract A youth homicide reduction initiative in Boston in the mid-1990s poses particular difficulties for program evaluation because it did not have a control group and the exact implementation date is unknown. A standard methodology in program evaluation is to use time series variation to compare pre- and post-program outcomes. Such an approach is not valid, however, when the timing of a potential break is unknown.
    [Show full text]