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EC208 – Introductory Econometrics. Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models)

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Presentation on theme: "EC208 – Introductory Econometrics. Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models)"— Presentation transcript:

1 EC208 – Introductory Econometrics

2 Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models)

3 EC208 – Introductory Econometrics Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models) Important topic: - highlights pitfalls of regression analysis - data mining - stresses the importance of careful consideration of the statistical properties of economic time series

4 EC208 – Introductory Econometrics Topic: Spurious/Nonsense Regressions (as part of chapter on Dynamic Models) Important topic: - highlights pitfalls of regression analysis - data mining - stresses the importance of careful consideration of the statistical properties of economic time series Presentation: 1) Motivate the problem empirically 2) Provide simple technical arguments 3) Corroborate with simulation-based example 4) Give practical reccomendations

5 EC208 – Introductory Econometrics Spurious Regressions Telecommunications demand as a function of…

6 EC208 – Introductory Econometrics Spurious Regressions Telecommunications demand as a function of… the price of beef !!!???

7 EC208 – Introductory Econometrics Spurious Regressions Telecommunications demand as a function of… the price of beef !!!??? Argument: improved fit (R-squared)

8 EC208 – Introductory Econometrics Spurious Regressions Telecommunications demand as a function of… the price of beef !!!??? Argument: improved fit (R-squared) Another example: UK government expenditures and Private Consumption in Burkina-Faso (annual data, 1954-1998), regression in logs

9 ============================================================= Dependent Variable: Log(Gov) Method: Least Squares Sample: 1954 1998 Included observations: 45 ============================================================= Variable Coefficient Std. Error t-Statistic Prob. ============================================================= C -10.0400 0.285481 -35.1687 0.0000 Log(Cons) 1.084797 0.023368 46.42229 0.0000 ============================================================= R-squared 0.980437 Mean dependent var 3.142963 Adjusted R-squared 0.979982 S.D. dependent var 1.386575 S.E. of regression 0.196179 Akaike info criteri -0.376149 Sum squared resid 1.654911 Schwarz criterion -0.295853 Log likelihood 10.46336 F-statistic 2155.029 Durbin-Watson stat 0.377805 Prob(F-statistic) 0.000000 ============================================================= 3 EC208 – Introductory Econometrics Spurious Regressions

10 - Both series display a trending pattern, as most macroeconomic time series do

11 - What are the implications of this trending behaviour?

12 EC208 – Introductory Econometrics Spurious Regressions In a regression model is consistent if

13 EC208 – Introductory Econometrics Spurious Regressions In a regression model is consistent if must be well-behaved, so that “good behaviour” means that regressors must be stationary (and ergodic)

14 EC208 – Introductory Econometrics Spurious Regressions Strict stationarity implies that the distribution of a process does not change with time Weak stationarity: first and second moments are constant through time

15 EC208 – Introductory Econometrics Spurious Regressions Strict stationarity implies that the distribution of a process does not change with time Weak stationarity: first and second moments are constant through time Simple example: white noise

16 EC208 – Introductory Econometrics Spurious Regressions Strict stationarity implies that the distribution of a process does not change with time Weak stationarity: first and second moments are constant through time Simple example: white noise Many economic time series seem to be stationary after differencing:

17 EC208 – Introductory Econometrics Spurious Regressions Strict stationarity implies that the distribution of a process does not change with time Weak stationarity: first and second moments are constant through time Simple example: white noise Many economic time series seem to be stationary after differencing: This means that the series in levels is a random walk (or I(1) process):

18 EC208 – Introductory Econometrics Spurious Regressions 1 Random walk with drift and with no drift

19 EC208 – Introductory Econometrics Spurious Regressions Random walks arise from theory (e.g., Hall, 1978) or empirically A random walk is a special case of an autoregression Running an autoregression for each series…

20 ============================================================= Dependent Variable: Log(Gov) Method: Least Squares Sample: 1954 1998 Included observations: 45 ============================================================= Variable Coefficient Std. Error t-Statistic Prob. ============================================================= C0.0986120.0227724.3303230.0001 LOG(GOV(-1))0.9966380.006730148.08750.0000 ============================================================= R-squared0.998088 Mean dependent var3.188173 Adjusted R-squared0.998041 S.D. dependent var1.368644 S.E. of regression0.060547 Akaike info criterion -2.726413 Sum squared resid0.153968 Schwarz criterion -2.645313 Log likelihood61.98100 F-statistic21929.91 Durbin-Watson stat0.618692 Prob(F-statistic)0.000000 ============================================================= 3 EC208 – Introductory Econometrics Spurious Regressions

21 ============================================================= Dependent Variable: Log(Cons) Method: Least Squares Sample: 1954 1998 Included observations: 45 ============================================================= Variable Coefficient Std. Error t-Statistic Prob. ============================================================= C0.0501900.1456840.3445100.7322 LOG(Cons(-1)) 1.0032770.01197483.790650.0000 ============================================================= R-squared0.994053 Mean dependent var12.19506 Adjusted R-squared0.993912 S.D. dependent var1.247209 S.E. of regression0.097316 Akaike info criterion -1.777324 Sum squared resid0.397754 Schwarz criterion -1.696225 Log likelihood41.10113 F-statistic7020.873 Durbin-Watson stat2.282059 Prob(F-statistic)0.000000 ============================================================= 3 EC208 – Introductory Econometrics Spurious Regressions

22 However, random walks are not stationary!

23 EC208 – Introductory Econometrics Spurious Regressions However, random walks are not stationary! - consider - substituting back, we get - substituting recursively, we get

24 EC208 – Introductory Econometrics Spurious Regressions However, random walks are not stationary! - consider - substituting back, we get - substituting recursively, we get The process has a deterministic trend component,, and a stochastic trend

25 EC208 – Introductory Econometrics Spurious Regressions However, random walks are not stationary! - consider - substituting back, we get - substituting recursively, we get The process has a deterministic trend component,, and a stochastic trend Shocks have permanent effects, long memory process

26 EC208 – Introductory Econometrics Spurious Regressions However, random walks are not stationary! - consider - substituting back, we get - substituting recursively, we get The process has a deterministic trend component,, and a stochastic trend Shocks have permanent effects, long memory process Taking expectations, we have

27 EC208 – Introductory Econometrics Spurious Regressions However, random walks are not stationary! - consider - substituting back, we get - substituting recursively, we get The process has a deterministic trend component,, and a stochastic trend Shocks have permanent effects, long memory process Taking expectations, we have Calculating the variance

28 EC208 – Introductory Econometrics Spurious Regressions Mean and variance vary with time! Random walks are non-stationary processes

29 EC208 – Introductory Econometrics Spurious Regressions Mean and variance vary with time! Random walks are non-stationary processes Back to OLS: non-stationary regressors means that does not converge to a finite matrix

30 EC208 – Introductory Econometrics Spurious Regressions Mean and variance vary with time! Random walks are non-stationary processes Back to OLS: non-stationary regressors means that does not converge to a finite matrix Hence, OLS is not consistent Nor asymptotically normal

31 EC208 – Introductory Econometrics Spurious Regressions Simple Monte Carlo experiment (Monte Carlo corresponds to a lab experiment in Econometrics…) - Generate n.i.d. variables - Construct independent random walks (no drift) - Regress - Compute - Repeat the process 10 000 times

32 Tt-ratio rejection frequency (5%) 500.74480.3063 1000.82490.5404 2500.88830.7229 5000.92390.8115 10000.94250.8672 - Conventional t-tests reject the null of no relationship more often than it should (sample size worsens the problem) - R-squared converges to a non-degenerate distribution - DW statistic converges to 0 - This suggests informal way of recognizing spurious regressions - This experiment closely follows Granger & Newbold (1974), whose results were later confirmed analitically by Phillips (1986)

33 EC208 – Introductory Econometrics Spurious Regressions Practical implications Standard inference does not apply Importance of distinguishing between I(0) and I(1) What should we do to avoid nonsense regressions - regressions in differences: non-stationarity solved, but long run information (in levels) is lost -Cointegration: some economic variables share a common stochastic trend, implying a long run relationship (regression in levels makes sense, under certain conditions)

34 EC208 – Introductory Econometrics Spurious Regressions Students were introduced to new concepts: - Spurious/Nonsense regressions - stationary time series - Random walks/I(1) processes - Monte Carlo simulation - Hints for cointegration While making use of acquired ideas: -Regression/Large sample properties of OLS -Hypothesis testing -Fit of a regression -Autocorrelation (testing for…) -Dynamic modelling

35 EC208 – Introductory Econometrics Spurious Regressions The End

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