General-to-specific (Gets) modelling consists of a cycle of three steps: formulation (or re-formulation), estimation and evaluation, and model simplification, the last of which PcGets can do automatically. The modelling process takes place within the Model and the Test menus described below. This tutorial will guide you through dynamic model formulation and estimation, based on the M1UK data set. Two main estimation methods for single-equation models will be explained: the first is Ordinary Least Squares (OLS). Next, we examine Instrumental Variables Estimation (IVE).
Chapter 4 will consider alternative methods of model evaluation, before Chapter 5 describes model simplification, which explains how PcGets selects a model from the general unrestricted model (GUM). Then Chapter 6 illustrates model selection for cross-section data. Regular users of PcGive could go directly to Chapter 5.
This tutorial explains the use of PcGets for estimating linear regression equations using time-series data. The background to regression and least squares estimation methods is explained in Chapters 10 and 12. If you are unfamiliar with regression, proceed with this chapter till you feel lost, then read Chapter 12 and return here.
Start PcGets, and load M1UK.IN7 in GiveWin, if you are starting this tutorial afresh.
Start PcGets from inside GiveWin, for example from the workspace window:
Once PcGets has started, you can switch back from GiveWin to PcGets by clicking again on PcGets in the list of modules, or clicking on PcGets in the Windows taskbar.
Select the Formulate command on the Model menu on PcGets.
If you prefer to use the keyboard, you can use Alt+y as the short-cut key (denoting `model the y variable'); or, as a shortcut, click on the first icon on the toolbar (the graphical metaphor is that it involves creating the building blocks for a model).
Any of these three ways initiates the Data selection dialog, shown below.
As this is a much-used dialog, we consider it in detail. It consists of four columns: on the right are the three familiar OK, Cancel and Help buttons, the listbox with special variables, and the lag-length selection options. The number of lags to implement can be set automatically for all database variables to be entered in a model (e.g., 2 lags: highlight and type in a new integer; or click on the arrows to increase or decrease); or by clicking on Query (Alt+q) to set differently for each variable. Moving to the left, we see the variables in the currently-selected database. If more than one database is loaded in GiveWin, you could select any of them, shown in the box at the foot of the column. From the currently-selected database, we select variables for the model. The next list box, labelled Model has the model specification, empty at the moment. Below it is a Recall button, for recalling previously estimated models. Finally, we have a column of buttons which act on variables in the model once it has been specified.
To formulate a model, one marks database variables and adds them to the model. Mark a variable by clicking on it with the mouse. To select several variables, use the Ctrl key with the mouse; to select a range, use Shift plus the mouse, or drag the mouse. Lastly, just using the keyboard: type Alt+b to set focus to the database list box, then select a variable (using the arrow keys), and press Enter each time.
Once variables are selected, the OK button changes to Add (if the wrong selection is marked, use Deselect All to clear). Press Add to add the variables to the model (or just press the Enter key). The marked variable that is highest in the database becomes the dependent variable, because it is the first to enter the model. A two-step procedure might be required to make a lower variable into the dependent variable: first mark and add that dependent variable, then add the remaining variables. Alternatively, just enter the variables in the order that they occur in the database and change the status of the required variables later: the requisite buttons are described below.
The data are denoted m for M1, y for real total final expenditure in 1985 prices, p for its deflator, and R for the opportunity cost of holding money (measured by the 3-month local-authority interest rate minus a learning-adjusted retail sight-deposit rate): lower-case denotes logs. Select all four levels, m, p, y and R, with 1 lag and add these marked variables to the model, as shown in the capture below.
A brief digression on lags is needed. PcGets names lagged variables by appending an underscore and then the lag length. So m_1 is m one period lagged. PcGets uses this naming scheme to keep track of the lag length. Suppose the database holds both an m and an m_1 variable. Then, when formulating a model involving the first lag of m, PcGets will use m to create that lag. So the database m_1 variable is never used. When m_1 is the only m variable in the database, however, PcGets will start using it.
Neither the Constant nor the Trend will be offered for lagging (lagging these would create redundant variables). Seasonals are not used here, but you could add them and delete them if you wish. In that case, you'll see that PcGets automatically adds the correct number of seasonals (three here as the data are quarterly). It takes the constant term into account; without the constant, four seasonals would have been added. Seasonal is always unity in the first period (quarter here). So Seasonal_1 is unity in the second quarter.
The buttons on the left operate on variables in the model, and, as a consequence, only become available when model variables have been selected. As an example, you could try to add the R variable lagged twice to the model, and then delete it: mark Query, then to add R, double click on it in the database and select 2 lags as shown:
To delete R_2 from the model, click on `R_2' in the model, then press the Delete key, or the Delete button. Note that a Constant is automatically added, but can be deleted if the scale of the variables lets a regression through the origin have meaning. m is marked with a Y to show that it is an endogenous (here, the dependent) variable: its status can be cleared by marking it then clicking on the Clear button (and reset by marking and clicking on the Y:Regressand button). Delete the seasonals from the model if you did add them, as the data are seasonally adjusted.
The next button of note is New Model, which deletes every model variable in order to start a new model. If you press it by accident, any earlier model can be recalled by clicking the Recall button at the foot of the dialog. The remaining status buttons on the left assign, or change, the status of model variables. These could be used to change the dependent variable. Otherwise they are mainly relevant for instrumental variables estimation and model selection.
Once the model formulation is complete, click on OK or press Enter to bring up the Model Settings dialog which we record, but will skip:
Select the default of OK, which is instantly followed by the Estimate Model dialog.
Estimation methods are discussed in more detail in chapter 12. Chapter 4 reviews the statistical output reported after estimation. Here we only need OLS -- the theory of this and other estimation methods is also described in Chapter 12. The short-cut key for model estimation is Alt+l, in which the l stands for least squares.
The present dialog allows you to retain some data for forecasting. The sample period can be adjusted, but the one shown will always be admissible, and will either be the maximum available, or the one used in the previous model. Please verify that the sample size on your screen corresponds to the one shown here, namely the full sample: 1963(2)--1989(2). Retain eight observations for a forecast analysis (H) using the Less forecasts text entry field (the default is none, and the maximum is determined by the sample size). The Options button allows access to the expert settings discussed in Chapter 5, which we skip for the moment. Finally, the number of observations T+H is shown as 105:
The model, the sample or the estimation method can be altered later, either separately or together.
Clicking OK sends the estimation output to the GiveWin results window where further editing is easy.
The estimated equation has the form:
| yt=xt'b+et, t=1,...,T, |
where xt contains a `1' for the intercept, yt-1 for the lagged dependent variable, as well as the other regressors. Assumptions about the error term are that it has mean 0 and a variance which is constant over time:
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Written as an autoregressive-distributed lag (ADL) model:
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The equation estimation results are shown below: we assume that you used the default options settings discussed in Chapters 5 and 15.
GUM( 1) Modelling m by OLS (using M1UK.in7), 1963 (2) - 1987 (2)
Coeff StdError t-value t-prob
Constant -1.17990 0.32957 -3.580 0.0006
m_1 0.90823 0.02159 42.067 0.0000
p 0.28052 0.16511 1.699 0.0928
p_1 -0.19690 0.16614 -1.185 0.2391
y -0.00607 0.10586 -0.057 0.9544
y_1 0.12159 0.10833 1.122 0.2647
R -0.53469 0.11128 -4.805 0.0000
R_1 -0.02415 0.12260 -0.197 0.8443
RSS 0.01759 sigma 0.01406 R^2 0.99963 Radj^2 0.99960
LogLik 417.84256 AIC -8.45036 HQ -8.36450 SC -8.23801
T 103 p 8 FpNull 0.00000 FpConst 0.00000
The reported results include coefficient estimates; standard errors; t -values; the residual sum of squares (RSS); the equation standard error (s^, called sigma); the squared multiple correlation coefficient (denoted R2); and its value adjusted for degrees of freedom (T-p for T observations and p estimated parameters or regressors). The value of s^ is also the residual standard deviation:
| ût=mt-m^t, RSS=åt=1Tût, s^=( |
| )½. |
Since the errors are assumed to be drawn independently from the same distribution with mean zero and constant variance s, an approximate 95%confidence interval for any one error is 0±2s^. That represents the likely interval from the fitted regression line of the observations. When s^=0.014, the 95%interval is 5.6%of m. RSS is the acronym from residual sum of squares, namely åt=1Tût2, which can be useful for hand calculations of tests between different equations for the same variable. The coefficient of multiple correlation squared, R2, measures the correlation between the actual values yt and the fitted values y^t.
The next line shows the log-likelihood value; and the three information criteria, AIC, HQ, SC; then T and p followed by the probability of observing an F value as large or larger for an F-test of R2 equalling zero, denoted FpNull, and a test against a constant denoted FpConst.
The sample period was automatically adjusted for the lags created. Should it be desired, LaTeX equation output can be set in the Test menu. We will consider the evaluation information next, since it has already been reported, and then graphical information in §4.1 below, even though that does not follow the order of the Test menu.
Finally, the output reports the default mis-specification test statistics, which check whether the residuals are indeed consistent with the assumptions in (eq:3.1), and that the parameters are constant.
value prob
Chow(1975:2) 0.4887 0.9912
Chow(1985:1) 0.6349 0.7640
normality test 2.4388 0.2954
AR 1-4 test 3.3130 0.0143
ARCH 1-4 test 0.9343 0.4484
hetero test 1.7929 0.0557
This summary testing sequence on the residuals examines a range of null hypotheses of interest, including: autocorrelation, autoregressive conditional heteroscedasticity (ARCH), the normality of the distribution of the residuals, heteroscedasticity, and functional form mis-specification, as well as parameter constancy.
The evaluation statistics reported commence with two tests of parameter constancy, based on Chow (1960): the first uses a mid-sample split (Chow(1975:2)) whereas the second (Chow(1985:1)) is an end-of-sample test. These are both F-tests, and neither rejects. The normality test is a chi-squared statistic (see Doornik and Hansen, 1994), which again does not reject. The residual autocorrelation test (AR 1--4) rejects at 5%(see Godfrey, 1978), so the first-order lag length in the model may not have been adequate to capture the dynamics. The ARCH 1--4 test is for fourth-order autoregressive conditional heteroscedasticity (see Engle, 1982a), and the hetero test is for unconditional heteroscedasticity (see White, 1980): neither of these rejects. Note how easy these tests were calculated; and how informative they are about the match of model and evidence. The theory of model evaluation is discussed in Chapter 13.
In many situations, it is not legitimate to treat all regressors as valid conditioning variables, hence instrumental variables (IV) (which for extraneous reasons are known to be valid) must be used.
Formulate a model consisting of mp=m-p on the Constant, mp_1, Dp, R and y_1. Skip the Model Settings dialog. Move to the Estimate model dialog, accept OLS (ordinary least squares), and set the maximum possible estimation sample, keeping no observations for forecasting. Press OK to send the full-sample estimates to the Results window in GiveWin.
Now re-select Model/Formulate as a first step towards the IVE option. To compute instrumental variables, PcGets needs to know the status (dependent -- or normalized -- variable, endogenous, and exogenous or lagged) that you wish to assign to each variable. Given the present model, with a predefined dependent variable (mp), known lags (mp_1, and y_1) and a known status for the Constant (exogenous, as it is deterministic), only Dp and R need a status. Thus, make both of them endogenous (mark, then press the E: endogenous button).
Next, we must assign instruments: these form part of the model specification, but are not included in the fitted model. Crucially, the instruments must be sufficient in number to identify the equation: i.e., at least as many as right-hand side endogenous variables. Moreover, the instruments should be independent of (or at least uncorrelated with) the error on the equation, yet be sufficiently correlated with the endogenous regressors to ensure reasonably-precise estimates. Add the first lags of Dp and R to the model. Highlight both lagged values in the model column, and press the A: instrument button (the A denotes autonomous). The screen should show:
OK to accept and bring up the Estimation dialog, switch to instrumental variables, and press OK again.
The structural estimates appear as usual in the GiveWin Results window:
GUM( 2) Modelling mp by IVE (using M1UK.in7), 1963 (3) - 1989 (2)
Coeff StdError t-value t-prob
Constant -0.89414 0.09484 -9.428 0.0000
mp_1 0.91617 0.01290 71.015 0.0000
y_1 0.08329 0.00844 9.873 0.0000
R -0.61700 0.08624 -7.154 0.0000
Dp -0.40548 0.18784 -2.159 0.0333
RSS 0.01887 sigma 0.01381 R^2 0.99505 Radj^2 0.99485
LogLik 447.94916 AIC -8.51825 HQ -8.46675 SC -8.39112
T 104 p 5 FpNull 0.00000 FpConst 0.00000
Endogenous variables: R, Dp.
Additional instrument variables: Dp_1, R_1.
value prob
normality test 5.1095 0.0777
AR 1-4 test 4.0797 0.0043
ARCH 1-4 test 0.6657 0.6175
hetero test 1.1625 0.3306
Note the significant residual autocorrelation, invalidating most of the inferences you may have been tempted to make. The use of IVs may correct a simultaneity or measurement-error problem, but the basic model specification must be sound before their use adds value.
Nevertheless, the estimated coefficients on the first three variables are almost identical to those delivered by OLS, whereas the relative magnitudes of the last two have switched.
All the usual graphical and recursive evaluation options are available.
We have now estimated three models, together with one that was the same model by a different estimator. Nevertheless, that is a sufficient list to examine our progress: access via the Model menu, and Progress. Select these choices to see the following screen.
There are three columns: the far right lists the available operations; the center shows the specification of the model currently highlighted in the leftmost column; and that in turn lists all the estimated models. Scrolling down that left column shows each model's specification in turn. The `=' sign is a mark, and the batch code for all marked models can be written to the Results window (and saved via a batch file -- see Ch. 7). The `up/down' bent arrows scroll and mark simultaneously.
Alternatively, by pressing Find Results, PcGets jumps straight to the output of the highlighted equation.
This concludes the tutorial on model formulation and model estimation; we now turn to a more detailed consideration of model evaluation, before discussing the automatic Gets procedure.
Akaike, A. (1973). "Information theory and an extension of the maximum likelihood principle" In Petrov, B. N., and Saki, F. L.(eds.), Second International Symposium of Information Theory. Budapest.
Akaike, H. (1985). "Prediction and entropy" In Atkinson, A. C., and Fienberg, S. E.(eds.), A Celebration of Statistics, pp. 1--24. New York: Springer-Verlag.
Akerlof, G. A. (1979). "Irving Fisher on his head: The consequences of constant target-threshold monitoring of money holdings" Quarterly Journal of Economics, 93, 169--188.
Amemiya, T. (1980). "Selection of regressors" International Economic Review, 21, 331--354.
Anderson, T. W. (1971). The Statistical Analysis of Time Series. New York: John Wiley & Sons.
Andrews, D. W. K. (1991). "Heteroskedasticity and autocorrelation consistent covariance matrix estimation" Econometrica, 59, 817--858.
Banerjee, A., Dolado, J. J., Galbraith, J. W., and Hendry, D. F. (1993). Co-integration, Error Correction and the Econometric Analysis of Non-Stationary Data. Oxford: Oxford University Press.
Bårdsen, G. (1989). "The estimation of long run coefficients from error correction models" Oxford Bulletin of Economics and Statistics, 50.
Bean, C. R. (1977). "More consumers' expenditure equations" Academic panel paper (77)35, H.M. Treasury, London.
Bean, C. R. (1978). "The determination of consumers' expenditure in the UK" Government economic service working paper 4, H.M. Treasury, London.
Bontemps, C., and Mizon, G. E. (2001). "Congruence and encompassing" In Stigum, B.(ed.), Studies in Economic Methodology. Cambridge, Mass.: MIT Press.
Boswijk, H. P. (1992). Cointegration, Identification and Exogeneity, Vol. 37 of Tinbergen Institute Research Series. Amsterdam: Thesis Publishers.
Bowman, K. O., and Shenton, L. R. (1975). "Omnibus test contours for departures from normality based on Öb1 and b2" Biometrika, 62, 243--250.
Box, G. E. P., and Jenkins, G. M. (1976). Time Series Analysis, Forecasting and Control. San Francisco: Holden-Day. First published, 1970.
Box, G. E. P., and Pierce, D. A. (1970). "Distribution of residual autocorrelations in autoregressive-integrated moving average time series models" Journal of the American Statistical Association, 65, 1509--1526.
Breusch, T. S. (1990). "Simplified extreme bounds" in Granger 1990, pp. 72--81.
Brown, R. L., Durbin, J., and Evans, J. M. (1975). "Techniques for testing the constancy of regression relationships over time (with discussion)" Journal of the Royal Statistical Society B, 37, 149--192.
Burns, A. F., and Mitchell, W. C. (1946). Measuring Business Cycles. New York: NBER.
Campos, J., and Ericsson, N. R. (1999). "Constructive data mining: Modeling consumers' expenditure in Venezuela" Econometrics Journal, 2, 226--240.
Carruth, A., and Henley, A. (1990). "Can existing consumption functions forecast consumer spending in the late 1980s?" Oxford Bulletin of Economics and Statistics, 52, 211--222.
Chatfield, C. (1995). "Model uncertainty, data mining and statistical inference" Journal of the Royal Statistical Society, A, 158, 419--466. With discussion.
Chow, G. C. (1960). "Tests of equality between sets of coefficients in two linear regressions" Econometrica, 28, 591--605.
Chow, G. C. (1981). "Selection of econometric models by the information criteria" In Charatsis, E. G.(ed.), Proceedings of the Econometric Society European Meeting 1979, Ch. 8. Amsterdam: North-Holland.
Clayton, M. K., Geisser, S., and Jennings, D. E. (1986). "A comparison of several model selection procedures" In Goel, P., and Zellner, A.(eds.), Bayesian Inference and Decision Techniques: Elsevier Science.
Clements, M. P., and Hendry, D. F. (1998). Forecasting Economic Time Series. Cambridge: Cambridge University Press.
Clements, M. P., and Hendry, D. F. (1999a). Forecasting Non-stationary Economic Time Series. Cambridge, Mass.: MIT Press.
Clements, M. P., and Hendry, D. F. (1999b). "Modelling methodology and forecast failure" Unpublished typescript, Economics Department, University of Oxford.
Coen, P. G., Gomme, E. D., and Kendall, M. G. (1969). "Lagged relationships in economic forecasting" Journal of the Royal Statistical Society A, 132, 133--163.
Cox, D. R. (1961). "Tests of separate families of hypotheses" In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 105--123 Berkeley: University of California Press.
Cox, D. R. (1962). "Further results on tests of separate families of hypotheses" Journal of the Royal Statistical Society B, 24, 406--424.
Cran, G. W., Martin, K. J., and Thomas, G. E. (1977). "A remark on algorithms. AS 63: The incomplete beta integral. AS 64: Inverse of the incomplete beta function ratio" Applied Statistics, 26, 111--112.
D'Agostino, R. B. (1970). "Transformation to normality of the null distribution of g1" Biometrika, 57, 679--681.
Davidson, J. E. H., and Hendry, D. F. (1981). "Interpreting econometric evidence: The behaviour of consumers' expenditure in the UK" European Economic Review, 16, 177--192. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Davidson, J. E. H., Hendry, D. F., Srba, F., and Yeo, J. S. (1978). "Econometric modelling of the aggregate time-series relationship between consumers' expenditure and income in the United Kingdom" Economic Journal, 88, 661--692. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Deaton, A. S. (1982). "Model selection procedures or, does the consumption function exist" In Chow, G. C., and Corsi, P.(eds.), Evaluating the Reliability of Macro-Economic Models, Ch. 5. New York: John Wiley.
Doan, T., Litterman, R., and Sims, C. A. (1984). "Forecasting and conditional projection using realistic prior distributions" Econometric Reviews, 3, 1--100.
Doornik, J. A. (1999). Object-Oriented Matrix Programming using Ox 3rd ed. London: Timberlake Consultants Press.
Doornik, J. A., and Hansen, H. (1994). "A practical test for univariate and multivariate normality" Discussion paper, Nuffield College.
Doornik, J. A., and Hendry, D. F. (1996). GiveWin: An Interactive Empirical Modelling Program. London: Timberlake Consultants Press.
Doornik, J. A., and Hendry, D. F. (2001a). Econometric Modelling using PcGive 10, Volume II. London: Timberlake Consultants Press.
Doornik, J. A., and Hendry, D. F. (2001b). Interactive Monte Carlo Experimentation in Econometrics using PcNaive. London: Timberlake Consultants Press.
Engle, R. F. (1982a). "Autoregressive conditional heteroscedasticity, with estimates of the variance of United Kingdom inflation" Econometrica, 50, 987--1007.
Engle, R. F. (1982b). "Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation". 50, 987--1008.
Engle, R. F., Hendry, D. F., and Richard, J.-F. (1983). "Exogeneity" Econometrica, 51, 277--304. Reprinted in Hendry, D. F., Econometrics: Alchemy or Science? Oxford: Blackwell Publishers, 1993, and Oxford University Press, 2000; and in Ericsson, N. R. and Irons, J. S. (eds.) Testing Exogeneity, Oxford: Oxford University Press, 1994.
Engle, R. F., Hendry, D. F., and Trumbull, D. (1985). "Small sample properties of ARCH estimators and tests" Canadian Journal of Economics, 43, 66--93.
Engle, R. F., and White, H.(eds.)(1999). Cointegration, Causality and Forecasting. Oxford: Oxford University Press.
Ericsson, N. R. (1983). "Asymptotic properties of instrumental variables statistics for testing non-nested hypotheses" Review of Economic Studies, 50, 287--303.
Ericsson, N. R., Campos, J., and Tran, H.-A. (1990). "PC-GIVE and David Hendry's econometric methodology" Revista De Econometria, 10, 7--117.
Ericsson, N. R., Hendry, D. F., and Prestwich, K. M. (1998). "The demand for broad money in the United Kingdom, 1878--1993" Scandinavian Journal of Economics, 100, 289--324.
Ericsson, N. R., and Irons, J. S.(eds.)(1994). Testing Exogeneity. Oxford: Oxford University Press.
Faust, J., and Whiteman, C. H. (1997). "General-to-specific procedures for fitting a data-admissible, theory-inspired, congruent, parsimonious, encompassing, weakly-exogenous, identified, structural model of the DGP: A translation and critique" Carnegie--Rochester Conference Series on Public Policy, 47, 121--161.
Friedman, M., and Schwartz, A. J. (1982). Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates, 1867--1975. Chicago: University of Chicago Press.
Frisch, R., and Waugh, F. V. (1933). "Partial time regression as compared with individual trends" Econometrica, 1, 221--223.
Gilbert, C. L. (1986). "Professor Hendry's econometric methodology" Oxford Bulletin of Economics and Statistics, 48, 283--307. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press.
Godfrey, L. G. (1978). "Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables" Econometrica, 46, 1303--1313.
Godfrey, L. G., and Orme, C. D. (1994). "The sensitivity of some general checks to omitted variables in the linear model" International Economic Review, 35, 489--506.
Godfrey, L. G., and Veale, M. R. (1999). "Alternative approaches to testing by variable addition" Mimeo, York University, UK.
Gourieroux, C., and Monfort, A. (1995). "Testing, encompassing, and simulating dynamic econometric models" Econometric Theory, 11, 195--228.
Granger, C. W. J. (1969). "Investigating causal relations by econometric models and cross-spectral methods" Econometrica, 37, 424--438.
Granger, C. W. J.(ed.)(1990). Modelling Economic Series. Oxford: Clarendon Press.
Haavelmo, T. (1944). "The probability approach in econometrics" Econometrica, 12, 1--118. Supplement.
Hannan, E. J., and Quinn, B. G. (1979). "The determination of the order of an autoregression" Journal of the Royal Statistical Society, B, 41, 190--195.
Harris, R. I. D. (1995). Using Cointegration Analysis in Econometric Modelling. London: Prentice Hall.
Harvey, A. C. (1981). The Econometric Analysis of Time Series. Deddington: Philip Allan.
Harvey, A. C. (1990). The Econometric Analysis of Time Series, 2nd ed. Hemel Hempstead: Philip Allan.
Hendry, D. F. (1976). "The structure of simultaneous equations estimators" Journal of Econometrics, 4, 51--88. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Hendry, D. F. (1979). "Predictive failure and econometric modelling in macro-economics: The transactions demand for money" In Ormerod, P.(ed.), Economic Modelling, pp. 217--242. London: Heinemann. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Hendry, D. F. (1980). "Econometrics: Alchemy or science?" Economica, 47, 387--406. Reprinted in Hendry, D. F., Econometrics: Alchemy or Science? Oxford: Blackwell Publishers, 1993, and Oxford University Press, 2000.
Hendry, D. F. (1985). "Monetary economic myth and econometric reality" Oxford Review of Economic Policy, 1, 72--84. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Hendry, D. F. (1994). "HUS revisited" Oxford Review of Economic Policy, 10, 86--106.
Hendry, D. F. (1995a). Dynamic Econometrics. Oxford: Oxford University Press.
Hendry, D. F. (1995b). "Econometrics and business cycle empirics" Economic Journal, 105, 1622--1636.
Hendry, D. F. (1996). "On the constancy of time-series econometric equations" Economic and Social Review, 27, 401--422.
Hendry, D. F. (1997). "On congruent econometric relations: A comment" Carnegie--Rochester Conference Series on Public Policy, 47, 163--190.
Hendry, D. F. (1999). "An econometric analysis of US food expenditure, 1931--1989" in Magnus, and Morgan 1999, pp. 341--361.
Hendry, D. F. (2000a). Econometrics: Alchemy or Science? Oxford: Oxford University Press. New Edition.
Hendry, D. F. (2000b). "Epilogue: The success of general-to-specific model selection" In Econometrics: Alchemy or Science?, pp. 467--490. Oxford: Oxford University Press. New Edition.
Hendry, D. F., and Doornik, J. A. (1994). "Modelling linear dynamic econometric systems" Scottish Journal of Political Economy, 41, 1--33.
Hendry, D. F., and Doornik, J. A. (1999). "The impact of computational tools on time-series econometrics" In Coppock, T.(ed.), Information Technology and Scholarship, pp. 257--269. Oxford: Oxford University Press.
Hendry, D. F., and Doornik, J. A. (2001). Econometric Modelling using PcGive 10: Volume I. London: Timberlake Consultants Press.
Hendry, D. F., and Ericsson, N. R. (1991a). "An econometric analysis of UK money demand in `Monetary Trends in the United States and the United Kingdom' by Milton Friedman and Anna J. Schwartz" American Economic Review, 81, 8--38.
Hendry, D. F., and Ericsson, N. R. (1991b). "Modeling the demand for narrow money in the United Kingdom and the United States" European Economic Review, 35, 833--886.
Hendry, D. F., and Krolzig, H.-M. (1999a). "General-to-specific model selection using PcGets for Ox" Unpublished paper, Economics Department, Oxford University.
Hendry, D. F., and Krolzig, H.-M. (1999b). "Improving on `Data mining reconsidered' by K.D. Hoover and S.J. Perez" Econometrics Journal, 2, 202--219.
Hendry, D. F., and Krolzig, H.-M. (2000). "The econometrics of general-to-simple modelling" Mimeo, Economics Department, Oxford University.
Hendry, D. F., Leamer, E. E., and Poirier, D. J. (1990). "A conversation on econometric methodology" Econometric Theory, 6, 171--261.
Hendry, D. F., and Mizon, G. E. (1978). "Serial correlation as a convenient simplification, not a nuisance: A comment on a study of the demand for money by the Bank of England" Economic Journal, 88, 549--563. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Hendry, D. F., and Mizon, G. E. (1990). "Procrustean econometrics: or stretching and squeezing data" in Granger 1990, pp. 121--136.
Hendry, D. F., and Mizon, G. E. (1993). "Evaluating dynamic econometric models by encompassing the VAR" In Phillips, P. C. B.(ed.), Models, Methods and Applications of Econometrics, pp. 272--300. Oxford: Basil Blackwell.
Hendry, D. F., and Mizon, G. E. (1999). "The pervasiveness of Granger causality in econometrics" in Engle, and White 1999.
Hendry, D. F., and Mizon, G. E. (2000). "Reformulating empirical macro-econometric modelling" Oxford Review of Economic Policy, 16, 138--159.
Hendry, D. F., and Morgan, M. S. (1995). The Foundations of Econometric Analysis. Cambridge: Cambridge University Press.
Hendry, D. F., Muellbauer, J. N. J., and Murphy, T. A. (1990). "The econometrics of DHSY" In Hey, J. D., and Winch, D.(eds.), A Century of Economics, pp. 298--334. Oxford: Basil Blackwell.
Hendry, D. F., and Neale, A. J. (1987). "Monte Carlo experimentation using PC-NAIVE" In Fomby, T., and Rhodes, G. F.(eds.), Advances in Econometrics, Vol. 6, pp. 91--125. Greenwich, Connecticut: Jai Press Inc.
Hendry, D. F., and Richard, J.-F. (1982). "On the formulation of empirical models in dynamic econometrics" Journal of Econometrics, 20, 3--33. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press and in Hendry D. F., op. cit., (1993) and (2000).
Hendry, D. F., and Richard, J.-F. (1989). "Recent developments in the theory of encompassing" In Cornet, B., and Tulkens, H.(eds.), Contributions to Operations Research and Economics. The XXth Anniversary of CORE, pp. 393--440. Cambridge, MA: MIT Press.
Hendry, D. F., and von Ungern-Sternberg, T. (1981). "Liquidity and inflation effects on consumers' expenditure" In Deaton, A. S.(ed.), Essays in the Theory and Measurement of Consumers' Behaviour, pp. 237--261. Cambridge: Cambridge University Press. Reprinted in Hendry, D. F., op. cit., (1993) and (2000).
Hendry, D. F., and Wallis, K. F.(eds.)(1984). Econometrics and Quantitative Economics. Oxford: Basil Blackwell.
Hoover, K. D., and Perez, S. J. (1999). "Data mining reconsidered: Encompassing and the general-to-specific approach to specification search" Econometrics Journal, 2, 167--191.
Jarque, C. M., and Bera, A. K. (1980). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals" Economics Letters, 6, 255--259.
Johansen, S. (1988). "Statistical analysis of cointegration vectors" Journal of Economic Dynamics and Control, 12, 231--254. Reprinted in R.F. Engle and C.W.J. Granger (eds), Long-Run Economic Relationships, Oxford: Oxford University Press, 1991, 131--52.
Johansen, S. (1992). "Testing weak exogeneity and the order of cointegration in UK money demand" Journal of Policy Modeling, 14, 313--334.
Judge, G. G., and Bock, M. E. (1978). The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics. Amsterdam: North Holland Publishing Company.
Judge, G. G., Griffiths, W. E., Hill, R. C., Lütkepohl, H., and Lee, T.-C. (1985). The Theory and Practice of Econometrics, 2nd ed. New York: John Wiley.
Kent, J. T. (1986). "The underlying nature of nonnested hypothesis tests" Biometrika, 73, 333--343.
Keynes, J. M. (1939). "Professor Tinbergen's method" Economic Journal, 44, 558--568.
Keynes, J. M. (1940). "Comment" Economic Journal, 50, 154--156.
Kiviet, J. F. (1985). "Model selection test procedures in a single linear equation of a dynamic simultaneous system and their defects in small samples" Journal of Econometrics, 28, 327--362.
Kiviet, J. F. (1986). "On the rigor of some mis-specification tests for modelling dynamic relationships" Review of Economic Studies, 53, 241--261.
Koopmans, T. C. (1947). "Measurement without theory" Review of Economics and Statistics, 29, 161--179.
Koopmans, T. C., Rubin, H., and Leipnik, R. B. (1950). "Measuring the equation systems of dynamic economics" In Koopmans, T. C.(ed.), Statistical Inference in Dynamic Economic Models, No. 10 in Cowles Commission Monograph, Ch. 2. New York: John Wiley & Sons.
Krolzig, H.-M. (2001). "General-to-specific reductions of vector autoregressive processes" Economics discussion paper 2000-W34, Nuffield College, Oxford.
Krolzig, H.-M., and Hendry, D. F. (2001). "Computer automation of general-to-specific model selection procedures" Journal of Economic Dynamics and Control, 25, 831--866.
Leamer, E. E. (1978). Specification Searches. Ad-Hoc Inference with Non-Experimental Data. New York: John Wiley.
Leamer, E. E. (1983a). "Let's take the con out of econometrics" American Economic Review, 73, 31--43. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press.
Leamer, E. E. (1983b). "Model choice and specification analysis" In Griliches, Z., and Intriligator, M. D.(eds.), Handbook of Econometrics, Vol. 1, Ch. 5. Amsterdam: North-Holland.
Leamer, E. E. (1984). "Global sensitivity results for generalized least squares estimates" Journal of the American Statistical Association, 79, 867--870.
Leamer, E. E. (1990). "Sensitivity analyses would help" in Granger 1990, pp. 88--96.
Ljung, G. M., and Box, G. E. P. (1978). "On a measure of lack of fit in time series models" Biometrika, 65, 297--303.
Lovell, M. C. (1983). "Data mining" Review of Economics and Statistics, 65, 1--12.
Lütkepohl, H. (1991). Introduction to Multiple Time Series Analysis. Berlin: Springer.
Magnus, J. R., and Morgan, M. S.(eds.)(1999). Methodology and Tacit Knowledge: Two Experiments in Econometrics. Chichester: John Wiley and Sons.
Majunder, K. L., and Bhattacharjee, G. P. (1973a). "Algorithm AS 63. The incomplete beta integral" Applied Statistics, 22, 409--411.
Majunder, K. L., and Bhattacharjee, G. P. (1973b). "Algorithm AS 64. Inverse of the incomplete beta function ratio" Applied Statistics, 22, 411--414.
Mayo, D. (1981). "Testing statistical testing" In Pitt, J. C.(ed.), Philosophy in Economics, pp. 175--230: D. Reidel Publishing Co. Reprinted as pp. 45--73 in Caldwell B. J. (1993), The Philosophy and Methodology of Economics, Vol. 2, Aldershot: Edward Elgar.
McAleer, M., Pagan, A. R., and Volker, P. A. (1985). "What will take the con out of econometrics?" American Economic Review, 95, 293--301. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press.
Mizon, G. E. (1977a). "Inferential procedures in nonlinear models: An application in a UK industrial cross section study of factor substitution and returns to scale" Econometrica, 45, 1221--1242.
Mizon, G. E. (1977b). "Model selection procedures" In Artis, M. J., and Nobay, A. R.(eds.), Studies in Modern Economic Analysis, pp. P97--120. Oxford: Basil Blackwell.
Mizon, G. E. (1984). "The encompassing approach in econometrics" in Hendry, and Wallis 1984, pp. 135--172.
Mizon, G. E. (1995). "Progressive modelling of macroeconomic time series: the LSE methodology" In Hoover, K. D.(ed.), Macroeconometrics: Developments, Tensions and Prospects, pp. 107--169. Dordrecht: Kluwer Academic Press.
Mizon, G. E., and Richard, J.-F. (1986). "The encompassing principle and its application to non-nested hypothesis tests" Econometrica, 54, 657--678.
Moore, H. L. (1914). Economic Cycles -- Their Law and Cause. New York: MacMillan.
Muellbauer, J. N. J. (1994). "The assessment: Consumer expenditure" Oxford Review of Economic Policy, 10, 1--41.
Nicholls, D. F., and Pagan, A. R. (1983). "Heteroscedasticity in models with lagged dependent variables" Econometrica, 51, 1233--1242.
Pagan, A. R. (1984). "Model evaluation by variable addition" in Hendry, and Wallis 1984, pp. 103--135.
Pagan, A. R. (1987). "Three econometric methodologies: A critical appraisal" Journal of Economic Surveys, 1, 3--24. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press.
Paroulo, P. (1996). "On the determination of integration indices in I(2) systems" Journal of Econometrics, 72, 313--356.
Pesaran, M. H. (1974). "On the general problem of model selection" Review of Economic Studies, 41, 153--171.
Pesaran, M. H.(ed.)(1987). The Limits of Rational Expectations. Oxford: Basil Blackwell.
Pike, M. C., and Hill, I. D. (1966). "Logarithm of the gamma function" Communications of the ACM, 9, 684.
Rahbek, A., Kongsted, H. C., and Jørgensen, C. (1999). "Trend-stationarity in the I(2) cointegration model" Journal of Econometrics, 90, 265--289.
Sargan, J. D. (1964). "Wages and prices in the United Kingdom: A study in econometric methodology (with discussion)" In Hart, P. E., Mills, G., and Whitaker, J. K.(eds.), Econometric Analysis for National Economic Planning, Vol. 16 of Colston Papers, pp. 25--63. London: Butterworth Co. Reprinted as pp. 275--314 in Hendry D. F. and Wallis K. F. (eds.) (1984). Econometrics and Quantitative Economics. Oxford: Basil Blackwell, and as pp. 124--169 in Sargan J. D. (1988), Contributions to Econometrics, Vol. 1, Cambridge: Cambridge University Press.
Sargan, J. D. (1973). "Model building and data mining" Discussion paper, London School of Economics. Presented to the Association of University Teachers of Economics, Meeting, Manchester, April 1973.
Sargan, J. D. (1980). "Some tests of dynamic specification for a single equation" Econometrica, 48, 879--897. Reprinted as pp. 191--212 in Sargan J. D. (1988), Contributions to Econometrics, Vol. 1, Cambridge: Cambridge University Press.
Sargan, J. D. (1981). "The choice between sets of regressors" Mimeo, Economics Department, London School of Economics.
Savin, N. E. (1984). "Multiple hypothesis testing" In Griliches, Z., and Intriligator, M. D.(eds.), Handbook of Econometrics, Vol. 2--3, Ch. 14. Amsterdam: North-Holland.
Sawa, T. (1978). "Information criteria for discriminating among alternative regression models" Econometrica, 46, 1273--1292.
Schwarz, G. (1978). "Estimating the dimension of a model" Annals of Statistics, 6, 461--464.
Shea, B. L. (1988). "Algorithm AS 239: Chi-squared and incomplete gamma integral" Applied Statistics, 37, 466--473.
Shenton, L. R., and Bowman, K. O. (1977). "A bivariate model for the distribution of Öb1 and b2" Journal of the American Statistical Association, 72, 206--211.
Shibata, R. (1980). "Asymptotically efficient selection of the order of the model for estimating parameters of a linear process" Annals of Statistics, 8, 147--164.
Sims, C. A. (1980). "Macroeconomics and reality" Econometrica, 48, 1--48. Reprinted in Granger, C. W. J. (ed.) (1990), Modelling Economic Series. Oxford: Clarendon Press.
Sims, C. A., Stock, J. H., and Watson, M. W. (1990). "Inference in linear time series models with some unit roots" Econometrica, 58, 113--144.
Smith, G. W. (1986). "A dynamic Baumol-Tobin model of money demand" Review of Economic Studies, 53, 465--469.
Spanos, A. (1989). "On re-reading Haavelmo: A retrospective view of econometric modeling" Econometric Theory, 5, 405--429.
Sullivan, R., Timmermann, A., and White, H. (1998). "Dangers of data-driven inference: The case of calendar effects in stock returns" Mimeo, Economics Department, University of California at San Diego.
Summers, L. H. (1991). "The scientific illusion in empirical macroeconomics" Scandinavian Journal of Economics, 93, 129--148.
Teräsvirta, T. (1976). "Effect of feedback on the distribution of the portmanteau statistic" Manuscript, London School of Economics.
Theil, H. (1971). Principles of Econometrics. London: John Wiley.
Tinbergen, J. (1940a). Statistical Testing of Business-Cycle Theories. Geneva: League of Nations. Vol. I: A Method and its application to Investment Activity.
Tinbergen, J. (1940b). Statistical Testing of Business-Cycle Theories. Geneva: League of Nations. Vol. II: Business Cycles in the United States of America, 1919--1932.
Vuong, Q. H. (1989). "Likelihood ratio tests for model selection and nonnested hypotheses" Econometrica, 50, 1--25.
White, H. (1980). "A heteroskedastic-consistent covariance matrix estimator and a direct test for heteroskedasticity" Econometrica, 48, 817--838.
White, H. (1984). Asymptotic Theory for Econometricians. London: Academic Press.
White, H. (1990). "A consistent model selection" in Granger 1990, pp. 369--383.
Wooldridge, J. M. (1999). "Asymptotic properties of some specification tests in linear models with integrated processes" in Engle, and White 1999, pp. 366--384.
Wright, P. G. (1915). "Moore's economic cycles" Quarterly Journal of Economics, 29, 631--641.
Yancey, T. A., and Judge, G. G. (1976). "A Monte Carlo comparison of traditional and stein-rule estimators under squared error loss" Journal of Econometrics, 4, 285--294.