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ECSTAT(tm) An instructional econometrics package Version 1.1 Manual and Program by Robert S. Dohner Fletcher School Tufts University Medford, MA, 02155 (Copyright (C) 1984. All rights reserved.) NOTICE Disclaimer: This program is distributed AS IS, and is not guaranteed to be free of errors or defects, nor is it guaranteed to do the specific task of the user. In no event will the author of this program be liable to you for any damages, including any lost profits, lost savings, or other incidental or consequential damages arising out of the use of or inability to use this program, even if the author of this program has been advised of the possibility of such damages, or for any claim by any other party. User Supported Software: This program is distributed as User Supported Software. If you find this program to be of value, you are encouraged to make a contribution of $25 to the author at the address below. An invoice is provided on the next page for your convenience. Whether you contribute or not, you are encouraged to copy and distribute this program, subject to the restrictions below: A limited license is granted to all users of this program to make copies of this program, and of this manual and distribute them to other users subject to the following conditions: 1. Neither this program nor this manual is to be distributed to others in modified form. 2. No more than $10.00 may be charged to cover copying costs, costs of media, and costs of distribution. 3. The notice displayed at the beginning of the program is not to altered, bypassed, or removed. Finally, although this program has been tested extensively, there may still be a few remaining errors. The author would appreciate hearing about them IN WRITING ONLY. Please report documented errors to: Robert S. Dohner Fletcher School Tufts University Medford, MA 02155 ------- INVOICE ------- Purchased from: Robert S. Dohner Fletcher School Tufts University Medford, MA 02155 DATE: / / INVOICE # 00127 ----------------------------------------------------------------- QTY PRICE ECSTAT Econometrics Program 1 $25 Sales Tax 0 ------------------ PLEASE PAY THIS AMOUNT $25 TOTAL ----------------------------------------------------------------- Make check payable to: Robert S. Dohner You may retain this invoice for your records PAGE 3 ECSTAT(tm) Econometrics Program ECSTAT(tm) Manual (Manual and Program by Robert S. Dohner, copyright (C) 1984) Introduction This is a simple econometrics program, designed for instructional use. It allows the user to: 1. Enter, edit, and display data 2. Save data files on disks, and retrieve them from disks. 3. Create new variables as functions of existing variables, including logarithms, exponentials, square roots, and trigonometric functions. 4. Perform multiple linear regression, and linear regression corrected for first order autocorrelation. It also allows the user to forecast regression equations out of sample. 5. Create time plots and scatter plots of data 6. Use sub-ranges of the data for graphing and regression, and easily incorporate lags and leads in variables. The program relies on menus and prompts the user for information at most points. Thus the program is relatively easy to learn. At present, the program has very few frills. This version is written for the IBM Personal computer using advanced basic. A version also exists for the Zenith Z-100 personal computer. Some Preliminaries 1. Format a new disk and transfer the operating system to it, using the FORMAT /S command under DOS. Next copy the file BASICA.COM (or BASIC.COM if you have the monochrome monitor and do not intend to do graphics) onto the formatted disk. Finally copy the files ECSTAT.BAT and ECSTAT.BAS onto the disk, as well as the file SAMPLE.DAT. To start the program under DOS type in (at the A> prompt) ECSTAT . 2. DO NOT write-protect the disk, as the program needs to write on the disk during its operation. 3. USE CAPITAL LETTERS... The program expects that the user will be using capital letters, so make sure that the Caps Lock key on the computer is pressed down. PAGE 4 ECSTAT(tm) Econometrics Program 4. The operation of the program revolves around a menu of some 16 different operations that the user may perform. If you are in the midst of some operation and decide that you have made a mistake and want to start over, then responding to a question by hitting the Enter key (Return key) alone will get you back to the main menu. Starting Out - Selecting the Data Range and Entering Data The first thing that the program will ask you is: DO YOU WISH TO LOAD DATA FROM A DISK FILE (Y/N)?> If you are just starting out, or if you are starting a new problem, the answer to this question will be N (for no.) You will immediately be asked: NUMBER OF OBSERVATIONS> The basic unit of data in this program is the variable, which is given a name (e.g. GNP), and consists of a column of numbers that are the observations for that variable. The observations are numbered from 1 to however many observations you have, and you are being asked here to specify the size of the largest variable. Once you supply a number of observations, you are limited to variables of this size or smaller, in the normal operation of the program. However, the user can at a later point extend the size of the sample range using the Extend Sample Range command, listed under the Housekeeping Operations . Next you will be presented with the following menu of choices: 1. CATALOG DATA IN MEMORY 2. CATALOG FILES ON DISK 3. DISPLAY DATA 4. PRINT DATA 5. ENTER DATA 6. EDIT DATA 7. SAVE DATA TO DISK 8. RETRIEVE DATA FROM DISK 9. CHANGE SAMPLE RANGE 10. COMPUTE A NEW VARIABLE 11. MEANS, VARIANCES, AND CORRELATIONS 12. ORDINARY LEAST SQUARES REGRESSION 13. REGRESSION - AUTOCORRELATION 14. TWO STAGE LEAST SQUARES 15. OUT OF SAMPLE REGRESSION FIT 16. OUTLIERS AND INFLUENCE 17. SCATTER PLOT 18. TIME PLOT 19. LOAD DATA FROM AN ASCII FILE 20. HOUSEKEEPING OPERATIONS 21. RESTART PROGRAM 22. EXIT PROGRAM PAGE 5 ECSTAT(tm) Econometrics Program If you are using the program for the first time, or if you are starting a new problem, then you will want to enter data, so enter a 5 and then hit the Enter key (carriage return). Data may be entered for one or more variables at a time. You first supply a name for each of the variables you are entering data for. ONLY LETTERS AND NUMBERS MAY BE USED FOR VARIABLE NAMES, AND THE FIRST CHARACTER OF THE NAME MUST BE A LETTER. Also, you should NOT use any of the following names, each of which has a special meaning for the program: CONST RESID SRESID LOG EXP SQR ABS SIN COS TAN You will next be prompted to enter the data for each variable in turn, one observation at a time. Decimal points are fine in numbers, but DO NOT USE ANY COMMAS. (Numbers may also be entered using scientific notation. Enter the mantissa, an E, and a two digit exponent. E.G. 1.23E02 = 123.) If you just hit the enter key, the program will supply a zero and skip to the next observation (or if you have backed up to the current observation, hitting return will maintain the previous value and advance to the next variable.) Aside from entering numbers, there are two special commands that you can use during data entry. These are: B (Backup) - move back one variable and re-enter data. If used repeatedly, this will allow you to space back and correct a mis-entry. E (End) - stop data entry. The program will supply zeroes for the remaining observations on the variables. Displaying Data Once you have entered data, you will often want to see what you have entered. Data can be displayed on the screen (using option #3 on the Main menu), or the data can be printed out on the printer (option #4). In each case, the program will ask you for the names of the variables to be displayed. These can be the names of variables that you have entered data for, or variables that you have created, using the procedure described in a later paragraph. You can enter as many names as you want, but the computer will display the data four variables at a time, doing the first four, and then the second four, etc. (if you forget what the names of the variables are, you can find out the names from option #1, Catalog data, described below.) If you have chosen to print the data out, make sure that a printer is connected to the computer, that it is turned on, and that it has paper. PAGE 6 ECSTAT(tm) Econometrics Program Editing Data If you need to change the values of observations in a variable (because you have revised data, or because you made a mistake in entering the data), you can do so with Option #6, Edit Data. Editing is done one variable at a time. The program will then ask: OBSERVATION NUMBER TO BE CHANGED > Here you can do one of three things. You can: 1. Supply an observation number (its place in line, NOT its value.) The program will then allow you to change the value of that observation. 2. Enter an N (for Next), and the program will move to the next observation. 3. Hit the Return key only, and the program will take you back to the Main Menu. If you have supplied an observation number (or the next observation) the program will print the current value of that observation and ask: NEW VALUE?> Here you can do several things: 1. If you enter a new number, the program will print the old and the new values of that observation and then ask for the next observation. 2. If you simply hit the return key, the program will leave the observation unchanged, and ask you for the next observation you want to change. 3. If you enter D (for Drop), the program will delete the current value of this observation, and move all succeeding values back one place in line. The last observation of the variable becomes zero. This is useful if you copy something twice. 4. If you enter I (for Insert), the program will move all the values one place forward in line, starting with the current observation. This will open up a hole at the current observation, and the program will then ask you for a value to put in there. This is useful if you leave something out in copying a series of numbers. (Remember that the process of moving numbers ahead will cause the original value of the last observation of the variable to be dropped.) After each of these observations, the program will ask you for the number of the next observation to work with. To get back to the main menu, just hit the Return key alone. PAGE 7 ECSTAT(tm) Econometrics Program Cataloging the Variables To find the names of all the variables that the computer is currently storing, do Option 1 at the Main Menu. The computer will then tell you the number of observations that are stored for each variable (this is the same for all variables), the number of variables that you have defined, and the number of remaining variables that the computer can hold. Then it will tell you the names of the variables that it is storing. The first name on this list will always be CONST . CONST is a variable that the computer defines for you, and is equal to 1 in each of its observations. You cannot alter this variable, and you should not try to define another variable with the same name. This variable is included to employ a constant term in a regression. The catalog will also tell you the current sample range, which is described in the section "About Variables" below. Storing and Retrieving Data from Disks Data can be stored on disks, and later retrieved from them, so you don't have to re-enter data each time you use the program. When you use this program, put your program disk in drive A: . You can store files on this disk (there should be plenty of room), or for extra space you can store files on a second disk in drive B: . When storing or retrieving files from a drive other than the default drive, make sure you include the device prefix. E.g. B:SAMPLE.DAT . Storing files If you choose Option 7, "Save Data to Disk", the computer will ask you for a filename. Give the computer the file name and press Return, and it will store the file for you. Retrieving Files If you choose Option 8, "Retrieve Data from Disk", the computer will go to the appropriate drive and look for the file. If it is there, and if the file was created by this program, it will read the data into its memory and record the variable names. If the file is not there, the program will tell you. If you don't happen to remember the name of the file that you want, you can have the program give you the names of the files stored on the disk in either drive, by replying with a question mark "?" to the name of file question (don't type the quotation marks.) The program will then ask you for the appropriate drive. It is possible to combine data from two or more saved files. Retrieve one file using Option 8. Then use the add data procedure under Option #20 (Housekeeping Operations), which is described below. PAGE 8 ECSTAT(tm) Econometrics Program Displaying the Names of Files Stored on Disks If you want to find out the names of all the files that you have stored on a disk, you can do so using Option #2 of the Main menu, "Catalog Files Stored on Disk". The program will ask you: WHICH DRIVE?> to which you should respond A or B (use capital letters, as always.) The program will then print out the names of the files stored on the disk in that drive. (The program will accept drive designations A through H.) About Variables The remaining sections require you to know something about the way the program stores and manipulates variables. Once a variable is created and given a name, that name refers to the variable as a whole, in other words, the whole column of numbers (observations) that make up the variable. When you work with variables, as in regressions, finding means, or doing plots, the program will work with all the observations of that variable. If you add two variables together to form a third, or multiply two variables together to form a third (described below), the computer will add (or multiply) the two variables observation by observation to form the observations of the third. Sample Range There is a way to restrict the observations that the program works with when it does regressions, finds means, does plots, or computes new variables. This is known as setting the "sample range". When you first create variables, you are asked the number of observations, and this sets the maximum range for all variables. This maximum remains constant as long as you use a particular data set, and is stored along with the variables when you store data on a disk. When you first start the program, or when you retrieve data from a disk, the sample range is set equal to this maximum range. However, you can change the sample range to use only a portion of the total number of observations, and you can also choose the sample range so that certain observations within the variable are dropped. This is done by choosing Option #9 "Change Sample Range", on the Main Menu. To make the examples clearer, suppose that each variable has 20 observations in all; the maximum range is 1 to 20, and the sample range is initially set equal to this. Suppose you want to use only observations 1 to 15. You choose Option #9, and the program will ask you: ENTER SAMPLE RANGE(S): You respond by typing in 1, a space, 15, and then Enter, so the screen looks like this: ENTER SAMPLE RANGE(S): 1 15 PAGE 9 ECSTAT(tm) Econometrics Program The program will return you to the main menu, and all regressions, means, plots, and computed new variables will use only observations 1 to 15 of any variable. To change the sample range, you have to use Option #9 again. To find out what the current sample range is, use Option #1 "Catalog Data in Memory". Other options for specifying the sample range include: ENTER SAMPLE RANGE(S): 2 10 13 20 this forces the program to use only observations 2 to 10 and 13 to 20, dropping observations 1, 11, and 12. The numbers that you supply the program must be in ascending order, must fall within the maximum range of the observations (1 to 20 in this example), and up to ten pairs may be used. You can also select individual observations like so: ENTER SAMPLE RANGE(S): 8 8 10 20 which forces the computer to use observation 8 and observations 10 to 20. Note that the 8 must be entered twice here (always maintain pairs.) The following ranges are invalid: 1 25 takes sample range beyond maximum number of observations (20 in this example.) 8 3 sample must be given in ascending order 1 18 20 not an even number of entries. 1 8 8 20 a single observation number cannot end one pair and start another. Lags and Leads Suppose you were running a regression model and wanted to regress the current level of investment (I) on last year's level of GNP. The program allows you to pair one observation of I with the previous observation of GDP by specifying GNP in the regression as GNP[-1] . The figure in square brackets is the lag. It says that observation number 5 of GNP[-1] is really observation number 4 of GNP. You can lag a variable for as many periods as you wish (subject to the warning below); thus if you have monthly data on car sales, CARS , then CARS[-12] would be the sales of the corresponding month of the previous year. The number in square brackets can also be positive, thus GNP[1] and GNP[+1] (it doesn't matter which you use) refer to GNP in the next period. PAGE 10 ECSTAT(tm) Econometrics Program Restrictions on using lags are: 1. The sample range must be adjusted so that the lag or lead does not take the variable outside the range of available data. In our previous example, if you had 20 observations and were using GNP[-1] then you would set the sample range at 2 20 . 2. Lagged variables can generally be used anywhere on the right hand side of an equation, but not the left hand side. Thus you can regress an unlagged variable on a lagged variable, but you can't use a lagged variable as your dependent (LHS) variable. Similarly, you can create an unlagged variable as a function of lagged variables, but you must use an unlagged name in creating a new variable. Lagged variables can be used in scatter plots and time plots, and can be included when you calculate means, variances and covariances. 3. Don't use variables with zero lag, and avoid embedded spaces in lags. Thus DON'T use GNP[0] use GNP DON'T use GNP[ -1] use GNP[-1] Make sure no space comes between the variable name and the open brackets, ie don't use GNP [-1]. Computing New Variables The program will do the tedious work of taking logarithms of variables, or adding two variables together to form a third. Use Option #10, "Compute a New Variable" to form new variables (with new names). When you choose option 10, the program will ask you: ENTER FORMULA FOR VARIABLE TO BE COMPUTED > You then give the program a name for the new variable that you are creating, and an equation that defines it. For example you might define consumption (CONS) as the difference between GNP and investment: > CONS = GNP - I The program will compute CONS by subtracting I from GNP observation by observation. PAGE 11 ECSTAT(tm) Econometrics Program The functions that are available to you are: + addition - subtraction * multiplication (an asterix) (DONT use X) / division ^ exponentiation (ie W^5 is W to the fifth power) LOG() take the natural logarithm of what is in parentheses EXP() raise e to the power of what is in parentheses SQR() take the square root of what is in parentheses ABS() absolute value SIN() , COS() , TAN() sine, cosine, tangent You can form fairly complicated formulas by combining the operations above, and by using parentheses. However there are a few things you must be careful of. When several operations are included in a formula, the program does them in a particular order. The order is: 1. The functions LOG EXP SQR ABS SIN COS TAN are calculated first 2. exponentiation is done second. 3. multiplication and divison are done third. 4. addition and subtraction are done last. Thus: 5+3*2 = 11 (not 16) 2^2*3 = 12 (not 64) if you are in doubt about the order of calculation, use parentheses: (5+3)*2 = 16 2^(2*3) = 64 For the most part you will be working with variables that already exist. Some examples: LGNP = LOG(GNP) calculates the log of GNP PCGNP = 100*(GNP/GNP[-1] - 1) calculates the percentage change in GNP. PAGE 12 ECSTAT(tm) Econometrics Program Some things to remember: 1. In calculating the new variable, the program needs to be able to write on the program disk. DO NOT WRITE-PROTECT YOUR PROGRAM DISK! 2. Don't try to take the square root of a negative number, the logarithm of zero or of a negative number, and don't divide by zero. 3. When squaring a variable W, use W*W and not W^2 . The first method is faster, and more accurate. 4. The program will tell you if it has successfully calculated your formula, but it won't tell you if that was really what you wanted to calculate. Be careful, and display and check your data occasionally. Calculating Means, Variances, and Correlations Option #11 allows you to calculate the means, standard deviations, and variances of a group of variables, and the correlations among them. If you choose option 11 the program will ask: ENTER VARIABLE NAME(S) SEPARATED BY A SPACE> Up to 20 variable names may be entered. The program will use only the observations specified in the current sample range, and will calculate means, variances and standard deviations, as well as correlation coefficients for the variables. You will be given an opportunity to print the results if you wish to. Make sure the printer is on and has paper if you do want to print out results. It is perfectly all right to include lagged variables in the list of names, but make sure that the sample range is adjusted so that you do not go outside the available data. Multiple Regression Option #12 allows you to run an ordinary least squares regression of one dependent variable on up to 20 right hand side variables (including the constant.) The regression will be calculated using the current sample range. When you choose option 12, the program will ask for the name of the dependent (left hand side) variable, and then will ask for the independent (right hand side) variables. CONST There is a variable that is internal to the program, called CONST that consists entirely of 1's. You must include this variable in your list of right hand side variables in order to get a constant term in the regression. PAGE 13 ECSTAT(tm) Econometrics Program For example, if you wanted to regress the level of consumption expenditures (CONS) on a constant, its own lagged value, the level of GNP and the interest rate (R), you would respond so the screen looks like this: ENTER DEPENDENT VARIABLE VARIABLE NAME IS?> CONS ENTER INDEPENDENT VARIABLES ENTER VARIABLE NAMES SEPARATED BY A SPACE> CONST CONS[-1] GNP R The program will then calculate the regression for you, and print on the screen the estimated coefficients, along with their estimated standard errors and T-statistics. The program will also display several summary statistics concerning the regression, and give you the option of showing the estimated variance-covariance matrix of the estimated coefficients. You will also be given the option to repeat the output on the screen, and to print either the coefficient estimates, the variance covariance matrix, or both. RESID The program contains an internal variable called RESID which contains the residuals from the last regression that was performed. You can save these residuals by moving them to another variable, through the computation procedure in Option #10. Thus you might use option 10 and respond: > RES = RESID The fitted value of the variable may be found by subtracting RESID (or RES in this example) from the actual value of the dependent variable (CONS in this example.) > FIT = CONS - RESID These new variables, RES and FIT could be examined later, or plotted on the screen. Correction for First-Order Autocorrelation (Cochrane-Orcutt) The program allows regression estimates corrected for first order autocorrelation using the Cochrane-Orcutt method. The method involves using quasi-differences of the variable data (eg CONS - RHO*CONS(-1)). The procedure works the same way as in ordinary least squares; you are asked for the dependent variable, and then for a list of independent variables. In addition, you will be asked if you want to choose a starting value for the autocorrelation coefficient, RHO . If you reply NO , or simply use a carriage return, the program will start with an initial value of zero. PAGE 14 ECSTAT(tm) Econometrics Program The procedure iterates to get a progressively better value for RHO, and proceeds until the successive changes in RHO are small. The procedure is slow, so wait for it. It will tell you if anything is wrong. The program will print the final value of RHO , the estimated coefficients, and their estimated standard errors and T-statistics, and give you the option of seeing the variance-covariance matrix. You can repeat the screen output, or have it printed out. The program also makes available the residuals from the estimation procedure, and these are available in the variable RESID . WARNING: In the current version of the program, the sample range for the estimation must be continuous. Two Stage Least Squares Option #14 allows you to estimate an equation using instrumental variables (two-stage least squares). If you choose option 14 the program will first ask you for the dependent variable, then the explanatory variables, just as in ordinary least squares. Finally the program will ask you for the names of the variables that you wish to include as instruments. Here you should include the names of all of the variables you specified as explanatory variables that are exogenous (including the constant) and at least one instrumental variable for each endogenous variable included in the list of explanatory variables. Thus there must be at least as many instruments in total as there are explanatory variables in the equation. For example, suppose that you are estimating consumption (CONSUMP) as a function of income (Y) and the interest rate (R). You consider income and consumption to be endogenous, while you assume that the interest rate is exogenous (given by world interest rates.) You also consider exports (X) and government expenditure (G) to be exogenous variables, and so available for use as instruments. To estimate a comsumption function using two stage least squares you would respond: DEPENDENT VARIABLE VARIABLE NAME IS? > CONSUMP EXPLANATORY VARIABLES ENTER VARIABLE NAMES SEPARATED BY A SPACE > CONST Y R INSTRUMENTS ENTER VARIABLE NAMES SEPARATED BY A SPACE > CONST R X G The program will then perform the two-stage regression, print out estimated coefficients and standard errors, and the estimated variance- covariance matrix. Residuals are made availble in the variable RESID, and the equation can be estimated out of sample using the following procedure. PAGE 15 ECSTAT(tm) Econometrics Program Forecasting a Regression Equation Beyond the Sample Option #15 allows you to project an equation estimated by any of the regression options outside the sample upon which the equation was originally estimated. Suppose, for example, that you had estimated the consumption equation described above, using observations 1 to 15 (sample range 1 15). The forecast option allows you to see how well the equation does at predicting the values of consumption in periods 16 or later, using the right hand side variables for those periods, and the estimated regression model from the earlier observations. First, you must run the regression on the sample range of 1 to 15. Immediately after you run the regression, choose option 15 from the main menu. The program will ask you for the sample range for the forecast, and if you wanted to use the remaining observations, you would respond 16 20 . However the program also allows you to include observations within the original estimation period, so you can see how the equation was doing at the point at which it started forecasting. In this case, you might reply 12 20 , to see the last four observations in the estimation period, and the five observations of the forecast period. The program will display actual values of the left hand side variable, the fitted value from the regression equation, and the prediction error for each observation. Some summary statistics are calculated for the forecast period and displayed. (These only apply to the observations outside the original estimation period.) The program will also ask you if you want to see a graph of the results. If you respond Y (yes), then the program will prepare a time plot of the actual and fitted values, and separate the estimation from the forecast period by a dashed vertical line. If you exit this option here, the sample range will remain that of the forecast, and this sample range will apply to all operations you do after the forecast. The program will automatically tell you the current sample range, and will ask you if you want to change the sample range. Either enter the desired sample range, or hit Return to retain the current range. (A technical note: If the original equation was estimated using a correction for serial correlation of the error term, the out of sample forecast will add in a fraction of the error term of the last observation of the estimation period. That fraction is RHO raised to the power of the current observation number minus the number of the last observation of the sample period. Forecast errors within the forecast period are NOT used to improve the next period forecast. For correct results, the forecast range must be continuous.) PAGE 16 ECSTAT(tm) Econometrics Program Outliers and Influence As an aid to regression diagnostics, Option #16 will allow you to retrieve corrected (Studentized) residuals, and to determine the Cook's Distance for each data point, a mesure of the influence of that data point on the regression results. The studentized residuals are scaled to have unit variance, and are calculated by using the following matrix: M = (I - X(X'X) X') which produces the residuals from the error term in the regression model. Option #16 calculates the Studentized residuals from the last regression that was performed, prints them out, and also stores them in an internal variable SRESID , where they can be retrieved using option #10 and plotted. The program also prints out the (uncorrected) residual, the diagonal elements from the M matrix, Mii , and the Cook's Distance for the data point. The last is a measure of the extent to which the regression coefficients would have changed, had that particular data point been deleted from the sample. Although the Cook's Distance measure is not distributed as an F distribution, the F table does provide an approximate scale by which to judge the significance of the measure. For further information on Cook's Distance, and on the studentized residuals, see Weisberg, Sanford, Applied Linear Regression (New York; Wiley, 1980) Chapter 5. NOTE: The outliers and influence procedure is only available following an ordinary least squares regression. Graphics The program makes some rudimentary graphics available to you. The program will produce time plots of up to four variables (plots of the variables by observation), and will produce scatter plots of one variable against another. Note: On the IBM Personal Computer, the use of either of these options requires that you be using advanced basic, and that the results be displayed on a screen connected to the Color/Graphics Adapter. Scatter Plot Option #17 allows you to produce a scatter plot of values of one variable against the corresponding values of another variable. When you choose this option, you will be asked for the name of the variable to put on the X-axis and the variable to put on the Y-axis . The program will then draw the scatter plot. The axes are labelled, but the units are not marked. The axes will shift to indicate where zero is for each variable, if zero is included in the values within the sample range of either variable. PAGE 17 ECSTAT(tm) Econometrics Program Time Plot Option #18 will plot up to four variables by observation, drawing lines between successive values of the variables. The actual values for each observation are indicated by, successively, a + , an X, a box, and a diamond. The units are not given on the axes, but the X-axis will shift to indicate where zero is, if it falls within the range of values of the variables. Before the program draws the time-plot, it will ask you whether you want the variables scaled by means. If you say no, the program will plot the actual value of the variables on the screen. If you say yes, the program will divide the values of each variable by the sample average of the variable. This puts the variables in the same range, and is useful if the variables differ greatly in size. Loading Data from Non-ECSTAT Files Option #19 allows the user to enter data from ASCII files. This allows transfer of data from spreadsheet programs such as VisiCalc (using xxxxxx.PRF files) or SuperCalc or 1-2-3 (using xxxxxx.PRN files). It also allows the user to prepare a data file using a word-processing or editing program. The program expects certain things of the ASCII file that it is reading in, and care should be taken to produce files that meet these requirements. One or more initial lines of the file may be blank, these will be ignored by the program. The first line of information in the file may optionally be a list of the variable names to which the data corresponds. Note that these names must all appear on a single line, separated by spaces. The rest of the file must consist only of data (numbers), separated by spaces. The data may either be given as values for each of the variables in turn for a single observation, followed by data for the variables for the next observation (ordering by observation). Or the data may be given as all the observations for a single variable, followed by all the observations for the next variable, etc. (ordering by variable). ALL THE VARIABLES MUST HAVE THE SAME NUMBER OF OBSERVATIONS OF DATA. Ordering the data by observation is preferable if it can be done. In a spreadsheet program this would correspond to a Print file with the data for each variable in columns. Thus a data file with odd numbers, even numbers, and powers of two would look like: ODDS EVENS TWOS 1 2 2 3 4 4 5 6 8 7 8 16 PAGE 18 ECSTAT(tm) Econometrics Program When you load a file using option 19, the program will first ask you for the name of the file that contains the data. Next it will ask for the number of observations (data points) for each variable, and the number of variables. It will next ask if variable names are included in the file. If variable names are not given in the file, you will be asked to supply them. Finally, you will be asked whether the data is ordered by observation or by variable. Loading data from an external file is by its nature much trickier than loading data from a file created by the program. After you load the data you should check the variables currently held in memory, and display the values for the first and the last variable loaded. Housekeeping Operations Choosing option #20 produces the following menu: 1 RENAME A VARIABLE 2 DELETE VARIABLE(S) 3 EXTEND DATA RANGE 4 ADD DATA FROM A DISK FILE 5 RETURN TO MAIN MENU Option #1 allows you to change the name of a variable currently being held in memory. The program will display a list of the current variable names, ask you for the old name, and then for the new name. Option #2 allows you to delete one or more variable to free up space. The program will display a list of the current variable names, and ask you for the names of one or more variables to be deleted. Option #3 allows you to increase the maximum range of variables to include new observations. You will be told the current maximum observation number, and asked to specify a new maximum. The program will supply zeroes for the added observations. Data values can be supplied using the Edit operation from the main menu. Option #4 allows you to read in data from a disk file, and add it to the data that is currently being stored in memory. In this way, data from two or more data files can be combined. The length of stored variables in memory is determined by the current maximum range. If the number of observations on the variables stored in the second disk file is greater than this range, the final observations on the added variable will be dropped when they are read in. If the current maximum data range is longer than the variables that are being read in from the second disk file, the remaining observations will be set to zero. In using Option #4, you must take particular care to assure that the observation numbers on the original data in memory and the observation numbers on the data being read in correspond. The program assumes that they match up correctly. PAGE 19 ECSTAT(tm) Econometrics Program Remaining Options The remaining options are Option #21, which allows you to start the program over from the beginning, so as to use a new data set. Option #22 allows you to quit the program. You should be careful using either of these options, because you will lose the values of the current variables, unless you have saved them on the disk.