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  • Interpretation of coefficients

    Dear Statalist,

    I would like to know how to interpret the results of a regression that I'm running. I'm regressing the monthly returns of a portfolio given in decimal form on the monthly change in the TED spread (which is also given in decimal form).
    Y = portfolio1
    X = changeted

    Changeted is generated by taking the first difference of the monthly TED spread as in:
    Code:
    gen changeted = D.ted

    I'm getting the following results from the regression
    Code:
     reg portfolio1 changeted
    portfolio1 Coefficient Std. Err. t
    changeted 1.722623 0.6577956 2.62
    _cons 0.0046564 0.0012223 3.81
    Now what is the correct way to interpret these results?

    1. A 1 percentage point increase in the monthly change of the TED spread increases the returns of the portfolio by 172 percentage points

    2. A 1% increase in the monthly change in the TED spread increases the returns of the portfolio by 172%

    Here's a subset of my data below so you can see how the relevant variables are depicted:

    Code:
    * Example generated by -dataex-. To install: ssc install dataex
    clear
    input float mdate double portfolio1 float(changeted ted)
    358   .00849232634736   -.0028476184  .008680953
    359    .0196473443785    .0002295738 .0089105265
    360   .00908474893664   -.0018010028  .007109524
    361  -.00789620730366   -.0008674185  .006242105
    362    .0195815621909   -.0003057416  .005936364
    363     .027590637801    .0020110048  .007947369
    364  .000916804789517   -.0005902257  .007357143
    365    .0158492072062   -.0011095237  .006247619
    366    .0228994165542   -.0002857144  .005961905
    367    .0160825575945    .0005199136  .006481818
    368    .0436228907427     .001891866  .008373684
    369    .0429131154968     .001658134  .010031818
    370  -.00697735981956    .0010681814       .0111
    371    .0216892669748    .0005894741  .011689474
    372   -.0095828701076   -.0005085217  .011180952
    373   -.0324055587067    -.003454636  .007726316
    374   -.0063345531009   -.0010813158     .006645
    375  .000701541869713   -.0008307146  .005814285
    376  -.00404627954966    .0001476193  .005961905
    377    .0240512142543   .00038309535     .006345
    378  .000794257469344   -.0007313639  .005613636
    379 -.000107101605566   -.0011945884  .004419048
    380   -.0114348075008   -.0004490479      .00397
    381  -.00761210352102    .0008163638  .004786364
    382     .033791962529    .0004188996  .005205263
    383    .0174744570914 -.000015263446      .00519
    384    -.042712548086   -.0014185715 .0037714285
    385   -.0115241663969   -.0004714285       .0033
    386    .0120620200275   .00022727274  .003527273
    387    .0114044506298    .0006477272     .004175
    388   .00235680516069   -.0008907893 .0032842106
    389    .0115165324735    .0000976075  .003381818
    390    .0113243855309   -.0003318181      .00305
    391    .0333249198916        .000215     .003265
    392   .00759933642572    .0005016667 .0037666666
    393    .0144097172053    .0019904762  .005757143
    394   -.0133345697828    .0008902256  .006647368
    395  -.00943171681865    -.002456892  .004190476
    396   -.0373814303009   -.0007220551  .003468421
    397   -.0157087963392    -.000368421       .0031
    398   -.0125583788066  -.00021304353 .0028869566
    399   -.0254557869421    .0006980435     .003585
    400  -.00886132794598   -.0007586842  .002826316
    401   -.0211462904909  -.00016722502  .002659091
    402   -.0127728666938  -.00007813843 .0025809524
    403   -.0047867762325  -.00015714276 .0024238096
    404  -.00181247685364   .00023333333  .002657143
    405  -.00387143948895    .0010778571     .003735
    406    .0147179584594   .00010499987      .00384
    407   .00182382931063   -.0006299999      .00321
    408   -.0242212731622  -.00020473683  .003005263
    409    .0272000913751   -.0000526316 .0029526316
    410    .0155942011949    .0008038902  .003756522
    411   .00510120234059    .0006879228 .0044444446
    412  -.00116494962791   .00049555534      .00494
    413    .0144875169313   .00004636357  .004986363
    414  -.00659186811291   .00025863666     .005245
    415    .0186325126031   -.0008086367 .0044363635
    416    .0160257094466    .0006493507  .005085714
    417    .0309753274867     .001664286      .00675
    418    .0274654193376   -.0008300003      .00592
    419   .00460671756132        .001935     .007855
    420   .00574407730955        -.00152     .006335
    421  -.00290292902279   -.0014139474  .004921053
    422    .0126022717027    .0004702518  .005391304
    423 -.000910747414227    .0004198067  .005811111
    424  -.00232210454743   -.0012634918 .0045476193
    425  -.00376991614283    .0007887445  .005336364
    426  -.00587224952977   -.0006363639       .0047
    427   -.0215626957343    .0003181817  .005018182
    428   .00919582327103    .0008318182      .00585
    429    .0431705338809    .0007642857  .006614286
    430  -.00230383648953    -.001385714  .005228572
    431  -.00833769362855    .0008293232  .006057895
    432   -.0160017915454    -.000600752  .005457143
    433   .00873168041384   -.0009671426      .00449
    434  -.00758796582581  -.00017095264 .0043190476
    435   .00613113205471    .0011609523      .00548
    436   .00637332670668   -.0006799996       .0048
    437    .0182696639881   -.0000400003      .00476
    438    .0235125729808    .0001718183  .004931818
    end
    format %tm mdate
    Last edited by Bob Ferguson; 28 Nov 2020, 09:34.

  • #2
    Both 1 and 2 are wrong.

    1) is at least on the right track. A 1 percentage point difference in the value of changeted, since changeted is given "in decimal form" means changeted increases by 0.01. The associated difference in portfolio1 is then 1.72*0.01 = 0.0172, which, in percentage points is 1.72 percentage points. 2) is completely off base: percentage increases are multiplicative, and in a linear model the relationship between proportional change in y and proportional change in x (known as the elasticity) is not constant; it depends on the starting value of x.

    Also, apart from the calculation and modeling issues, using the verb "increases" implies a causal effect that cannot be inferred from observational data in this way. It is better to say "an unit increase in x is associated with a b unit increase in y."

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