**Guy Judge and R.I.D. Harris**- University of Portsmouth

When version 3.0 of the program came onto the market in 1991 it already incorporated a procedure for estimating cointegration relationships using Johansen's (1988) maximum likelihood method, as well as an ADF command for augmented D ickey-Fuller unit root tests and many other techniques for estimating and testing linear and non-linear dynamic models (see McAleer and Oxley (1993) and Harris (1994)). However both econometrics and technolog y move on, and many users have been eagerly awaiting the new version 4.0 of the package which, it was promised, would incorporate new developments in univariate and multivariate time series analysis and take advantage of the flexibility of the Windows ope rating environment. The DOS version of the new Microfit 4.0 has now been released, and although users must wait a little longer for the Windows version of the product to appear they can get an idea of what to expect if they download a demo version from the Microfit web site.

The new program comes on a CD-ROM (or diskettes on request) and is easy to install. There is a 500 page manual "Working with Microfit 4.0: Interactive Econometric Analysis" which, as well as containing reference material on the program's menus and command s, includes 76 tutorial lessons using more than 25 different real data sets and this provides an excellent introduction or refresher course on modern time series econometric modelling techniques and methodology. This is a most valuable part of the package - for students perhaps the most valuable part - and it will be a great help both to individual learners and to those who teach applied econometric modelling courses built around the use of Microfit.

New single equation options include LOGIT and PROBIT estimation procedures, the Phillips-Hansen Fully Modified OLS method of estimating cointegrating relations, and a procedure for using model selection criteria to estimate a single cointegrating relation within an Autoregressive-Distributed Lag (ARDL) framework. The approach allows for the inclusion of time trends, seasonal dummies and other deterministic/exogenous regressors in the cointegrating relation. There is a whole raft of maximum likelihood pro cedures for the estimation of models under various conditional heteroskedastic error specifications (likely to be particularly relevant in finance applications). The program also offers new procedures for non-nested tests of linear versus log-linear model s (in level differenced and log-differenced form) and also for some other non-linear specifications of the dependent variable.

The program now has a comprehensive set of options for estimating and testing multiple equation (systems) models covering unrestricted VAR models, cointegrating VAR models and Seemingly Unrelated Regression (SURE) models, in both unrestricted and restrict ed form. Akaike, Schwarz and log-likelihood criteria are available to assist in the selection of a suitable model. There are procedures for new cointegration tests in VAR models and the analysis of identifying and overidentifying restrictions on the lo ng-run cointegrating relations. The computation of orthogonalized and generalized impulse response functions, multivariate dynamic forecasts, and forecast error-variance decomposition is also possible with the Microfit 4.0.

Figure 1 gives an overview of the menus structure of the new program.

Figure 1: A flow chart of the menus in Microfit 4.0

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First, a brief comment about the data. It consists of annual data from 1963 to 1992, taken from the OECD National Accounts. The variables in the file are as follows:

NF = expenditure on food in current prices RF = expenditure on food in constant (1980) prices NTE = total expenditure in current prices RTE = total expenditure in constant (1980) pricesThomas treats RF = Q as a measure of food demand, NTE = X as a measure of total consumers' expenditure, NF/RF = P is an index of the price of food and NTE/RTE = G is a general price index. The computer exercise requires one to begin by estimating a model with log Q as the dependent variable and the logs of X, P and G, together with one period lags of all variables (including the dependent variable) as regressors.

Figure 2: Data Input Menu

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When you run Microfit 4.0, after a brief copyright screen you arrive at the Data Input Menu (see Figure 2). The program positions you over option 3, ready to load up data from a Microfit file, but if you want to use a file in one of the other acceptable f ormats or enter new data at the keyboard you can select one of the other options.

Figure 3: File Selection Box

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Figure 4: Action Menu

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A box opens allowing you to move through the various drives and directories available to you until you locate the file you want (see Figure 3). You are then taken to the Action Menu (Figure 4) where you can either procede directly to another menu and esti mate a single equation or multivariate model, or, as we do here, select option 1 so that we can transform the series in the data file into the ones we want to work with in our analysis.

Figure 5: Data Processing Menu

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Figure 6: Formula and Commands Screen Editor

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Next you are taken to the Data Processing Menu (Figure 5) where we select option 2. A screen editor then appears (see Figure 6) with a box at the bottom where you enter formulae or commands. The variables currently in the memory will be listed at the top. Here you see the screen after the formulae have been entered and computed. You can also see that Help is available by pressing F1 or F2 as required. At this stage you might wish to examine the data graphically and there are commands to produce time serie s plots or scatter diagrams of variables. On leaving this screen editor (by pressing Esc) you are taken back to the Data Processing menu. Note that the program requires you to create your own constant intercept term so you should do this first before movi ng back through the Action Menu and on to the Single Equation Estimation Menu (Figure 7).

Figure 7: Single Equation Estimation Menu

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Figure 8: Model Specification Screen Editor

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Here we select option 1 and this takes us on to the model specification screen editor. Figure 8 shows how you specify the equation to be estimated. If you forget the names of any of the variables you can press the Home key to get a drop down menu with a full variable list, as shown here. On leaving this box you will be prompted for the estimation period to use. Just pressing

Figure 9: Estimation Menu (Linear Regression)

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Figure 10a: OLS Results

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Figure 10b: Regression Diagnostics

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Next you select the estimation method (see Figure 9) and the results will then appear on the screen as shown in Figures 10a and 10b. The main results table is very similar to that produced by Microfit 3.0, except that it now includes the Akaike Informatio n Criterion (AIC) and Schwarz Bayesian Criterion statistics.

Figure 11: Post Regression Menu

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Figure 12: Hypothesis Testing Menu

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At this stage the results may either be printed or saved to disk, after which you are taken to the Post Regression Menu (see Figure 11). Moving to the Hypothesis Testing Menu you can choose from a variety of specification and misspecification tests (see F igure 12). Moving via the Post Regression Menu you can then go to a menu (Figure 13) where you can examine the residuals or fitted values graphically, or save them to disk.

Figure 13: Display/Save Results and Fitted Values Menu

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Figure 14: Residuals Histogram

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Figure 14 shows what the histogram of the residuals looks like in this case. The screen display is in colour, but before saving the graphic image (in one of a number of different formats) you can switch to a monochrome version by just pressing any key on the keyboard. This a very quick and convenient feature.

We will leave this example at this point as it should be enough to illustrate the look and feel of the program and to show how the program operates. Thomas's example goes on to test the suitability of various restricted formulations nested within the orig inal model and this is easily accomplished within Microfit. Alternatively, in this case one could have made use of the new ARDL procedure described below

Where there is likely to be more than one cointegrating vector it is necessary to approach the analysis from a system or multiple equation perspective and Microfit 4.0 implements a generalization of the Johansen Maximum Likelihood procedure within the fra mework of a vector error correction model (VECM). The model allows for the inclusion of a number of I(1) exogenous variables and intercept and deterministic trend terms. The endogenous and exogenous variables are separated by an ampersand sign (&) i n the list entered into the cointegration analysis editing box, but the user must choose from a menu the combination of intercept and deterministic trends to allow for.

Figure 15: Cointegration Results showing Maximal Eigenvalues

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A set of results for each endogenous variable is then presented, giving the trace and maximum eigenvalue statistics for testing hypotheses concerning the rank of the long-run matrix, together with critical values at the 90 and 95% levels. (See Figure 15. Note: these are based on those computed by Pesaran et al. 1996, rather than the original Johansen-Juselius or Osterwald-Lenum values.) The program also gives you the maximized values of the log-likelihood function of the cointegrat ing VAR model, Akaike, Schwarz, and Hannan-Quinn model selection criteria for the different values of r.

Before you can proceed you must choose a value of r. Sometimes the criteria all point to the same value for r but in other cases (including the example used in the tutorial) there may be a conflict and it will be necessary to turn to relevant economic th eory for assistance. One this is done you can view the cointegrating vectors and the matrix of long run multipliers (but not, unfortunately, the speed of adjustment coefficients ). You can then go on to test restrictions on the cointegrating vectors i.e. the long-run parameters (but again it is not possible to test restrictions on and hence weak exogeneity). If the identifying or over-identifying restr ictions are applied the program presents the (normalized) cointegrating vectors with the standard errors. Restictions to be tested are entered in simple form in a dialog box and can be saved in a file for later use.

Johansen, S. (1988) Statistical Analysis of Cointegration Vectors. *Journal of Economic Dynamics and Control*, Vol 12 pp 231-254.

McAleer, M. and Oxley L. (1993) Microfit 3.0. An Interactive Econometric Software Package. *The Economic Journal*, Vol 103 pp767-774.

Pesaran, M.H., Shin, Y. and Smith, R.. (1996) *Structural Analysis of Vector Error Correction Models with Exogenous I(1) variables*. Unpublished manuscript, University of Cambridge.

Phillips, P.C.B and Hansen B.E. (1990) Statistical Inference in Instrumental Variables Regression with I(1) processes. *Review of Economic Studies*, Vol 57 pp99-125.

- at least 4Mb free RAM (8Mb recommended)
- DOS 3.0 or higher
- at least 12 Mb of free hard disk space
- VGA or SVGA monitor

For further information, or to order the software contact either *Oxford University Press* (United Kingom and the rest of the world except USA, Canada and Mexico) or *Camfit Data Limited* (USA, Canada and Mexico) at the addresses below:

Janet Caldwell,

Customer Service Department, Electronic Publishing, Oxford University Press, Walton Street, Oxford OX2 6DP; United KingdomTelephone +44 1865 267979

Fax +44 1865 267990

Mrs Marian Swainston,

Camfit Data Limited, 283 Hills Road, Cambridge CB2 2RP, United KingdomTelephone +44 1223 500639

Fax +44 1223 564 379

Alternatively go the Microfit World-Wide Web site from where order forms can be downloaded.

*Editor's Note: Just as this issue of CHEER was going to press we received a copy of the Windows version of Microfit 4.0 We will provide an update review in a future issue.*