Interpreting results

[Fran Zayn]

Hello,

I was running a panel data regression with a time dummy but I am having difficulties to interpret the results.
My regression:

Liq_i,t = a + b1 *spread_i,t +b2 * volume_i,t + b3 * D_t * spread_i,t * b4 * D_t * volume_i,t

b1 would be interpreted like if the spread goes up by 1 than liquidity should also go up 1 (same for volume right?)
Dt is a time dummy which is 1 for everything from march and later, 0 for everything for the period before.
So how can I interpret b3 and b4 regarding liqudity?
Also if the coefficents are different than for b1 and b2 what does that mean?

thank you for your help!

[Clyde Schechter]

The model you show is mis-specified and cannot be interpreted at all. The problem is that you have Dt*spread and Dt*volume interaction terms, but the Dt variable does not appear alone. Its appearance is mandatory.

You give your regression in terms of an abstract equation, so I don't know what your Stata variables actually are. But what you want will be like this (with your real variable names substituted):

regress liq i.time##c.(spread volume)

This assumes that spread and volume are continuous variables.

Now, by using an interaction model, you are stipulating that there is no such thing as the marginal effect of spread or volume. Rather you are saying that each of these variables has two, typically different, marginal effects: one that applies before March, and the other that applies after. To find these marginal effects, follow your -regress- command with:

margins time, dydx(spread volume)

If you wish to test whether the marginal effect of spread is differs between the before and after periods, that test is in the regression output (not the margins output) in the row headed by time#spread. The coefficient in that row is the estimated difference between the before and after marginal effects, and the rest of the row gives you a test of the null hypothesis that the difference is zero. Similarly, the row headed by time#volume will give you the test of whether the marginal effect of volume is different before vs during and after March.

[Fran Zayn]

thank you for your advise!

so giving you some background information:

I have 12 securities with weekly observations regarding spread and volume.
There was a certain law which I want to test if it significantly influenced liquidity once it got implemented.(liquidity independent variable)
Hence, I am testing whether the spread increased or the volume declined after the implementation compared to the period before..
Consequently, I am doing an event window period for the time before the law and the time after.

So your suggested regression tells me whether liquidity declined after the law implementation by using both codes?

[Clyde Schechter]

The code I have written will give you a difference-in-differences estimate of the effect of the law implementation. The validity of that approach, of course, depends on many other factors about which I have no information. Among these are the validity of the measures you are using, the linearity of the spread-liquidity and volume-liquidity relationships, the adequacy of your sample, and the issue of whether something other than this particular law might have coincidentally happened in March that actually accounts for any observed differences.

There is one issue related to sampling and statistics. For this model, or anything even like it, to work, you need observations before and after March and you also need observations on firms that were and firms that were not subject to the law implementation in March, and you need all four combinations of those. If you have the same firms being observed both before and after, then this is panel data and you must use a panel data estimator such as -xtreg-, not -regress-, to fit your model. If, however, the firms that were observed after March are different from the firms that were observed before, then -regress- is fine.

[Fran Zayn]

I have observations for the period before and for the period after. The number of firms is constant for all observations and there is no change in firms for the whole data set.
For my data set I only have firms that were subject to the law. That is why I created the time dummy variable to measure if the event lead to a significant change in liquidity. But appearently that is not possible to measure like this. Does your code work for my data set too? Or do I need to find a different approach? Since I don't have observations regarding firms not subject to the law the difference-in-differences estimate can not be applied.

[Clyde Schechter]

So, if all of your firms were subject to the law, this is not a difference in differences design. The code will still work, but it's a pre-post design, which is far weaker support for causal inference. In interpreting your findings you must be far more cautious about claiming causality. You can say only that things changed by a certain amount (or not!) after implementation of the law--which may just be coincidental.

[Fran Zayn]

I tried to use that code but stata gives me the error code
( invalid name
is there something i am missing?

Maybe another approcach will do it too:

I try to write a regression that gives me the answer to the question whether liquidity changed after law

[Clyde Schechter]

I tried to use that code but stata gives me the error code
( invalid name
is there something i am missing?

Which code? Please show the exact code you ran and the exact output, including error messages, Stata gave you.

[Fran Zayn]

Sorry for replying that late. I was at holidays.

so thats what Stata gives me

maybe if it helps that is how my dataset looks like:



Dummies are already multiplied by 1 or 0
liquidity is the dependent variable

thank you agaib for your help!

[Martyn Sherriff]

I think that you have an extraneous space. Try:

xtreg liquidity i.Time##c.(BAS NOC)

[Fran Zayn]

thanks alot, that worked!

now i am wondering how I can interpret the two given coefficents

does that mean that illiquidity actually decreased during the period of the ban?
since both coeffiecients are negative?
I created an extra column for the dummy now (Dummy1); where it is just 1 or 0; not already multilplied like in the dataset i gave you before

[Clyde Schechter]

The names of your variables, other than illiquidity, are uninformative, so only you know what these results mean, and nobody else knows which of them, if any, refers to "the period of the ban."

I could write several paragraphs about what these results say, just in terms of the names of the variables, but much of that may be of little or no interest to you. So please clarify your request. I also recommend that you run the following commands after the regression, as their output is likely to be easier to understand than the regression output itself.

margins Dummy1, dydx(BAS NOC)

Next, pick some interesting, meaningful values of BAS and NOC and run

margins Dummy1, at(BAS = (interesting values of BAS) NOC = (interesting values of NOC))
marginsplot

margins Dummy1, dydx(BAS NOC) at(BAS = (interesting values of BAS) NOC = (interesting values of NOC))

[Fran Zayn]

So my regression looks and dataset looks like this

illiq_i,t = a + b1 *BAS_i,t +b2 * _NOCi,t + b3 * D_t * BAS_i,t * b4 * D_t * NOC_i,t

illiq = stands for illiquidity at time t for security i
BAS = bid-ask-spread in time t for security i
NOC = is the amount of traders willing to trade security i at time t
Dt = is the dummy variable taking the value 0 before the ban and 1 for every time after the ban

The results have shown:

as the coefficent of BAS is positive it means that illiquidty increases for "b1 units" if we have an increase in BAS (makes sense since an increase in spreads should decrease liquidity)
as the coefficent of NOC is negative it means that illiquidty decreases for "b2 units" if we have an increase in NOC (also makes sense since more market participants increase liquidity)

so now what do the negative interaction terms mean for the bid-ask-spread and number of traders in paricular their influence on illiquidty,
but more imorptantly did illiquidity increase after the ban? >> which is my main question

the margin command has given me this:

for BAS the coeeficients even switched after the ban.
Does it mean that illiquidity decreased after the ban instead of increasing?

and what do you mean with some interesting values?
I am not sure about that.

Thank you alot for your help.
Hope it is clear what I want to test now.

[Clyde Schechter]

as the coefficent of BAS is positive it means that illiquidty increases for "b1 units" if we have an increase in BAS (makes sense since an increase in spreads should decrease liquidity)
as the coefficent of NOC is negative it means that illiquidty decreases for "b2 units" if we have an increase in NOC (also makes sense since more market participants increase liquidity)

No, these syllogisms are false. The first one doesn't even reach a correct conclusion. The second one does, but the reasoning is still wrong.

The positive coefficient of BAS means that illiquidity increases by b1 (= .1797173) units per unit increase in BAS when Dummy1 = 0. But that is not the case when Dummy1 = 1. When Dummy1 = 1, illiquidity decreases by 0.2286858 units per unit increase in BAS. You can find that in the output of the -margins Dummy1, dydx(BAS NOC)-. Or, the hard way, you could calculate that from the regression output as 0,1797173 + (-0.4084032) (= cofficient of BAS + coefficient of Dummy1#BAS).

The effects of NOC when Dummy1 = 0 are similarly readable from the regression table.. When Dummy1 = 1, the effect must either be calculated by adding the NOC and Dummy1#NOC coefficients, or, more easily, by reading from the -margins- output.

so now what do the negative interaction terms mean for the bid-ask-spread and number of traders in paricular their influence on illiquidty,

The interaction term is, in each case, the difference between the effect of BAS (respectively, NOC), when Dummy1 = 1 and the effect of BAS (respectively NOD) when Dummy = 0. That is, since these interaction coefficients are negative it means that the effects of BAS and NOC are both reduced when Dummy = 1. (Reduced here can mean more negative, as is the case with NOC, or changed from positive to negative, as with BAS, or a smaller positive effect, which doesn't occur in your study.)

but more imorptantly did illiquidity increase after the ban? >> which is my main question

The analyses shown cannot answer this question. It depends on the distributions of BAS and NOC both before and after the ban. You can estimate average illiquidity both before and after the ban, adjusted for those distributions, by running:

margins Dummy1

You can estimate (and test a null hypothesis about, if you wish) the change in illiquidity after the ban with

margins, dydx(Dummy1)

[Fran Zayn]

The analyses shown cannot answer this question. It depends on the distributions of BAS and NOC both before and after the ban. You can estimate average illiquidity both before and after the ban, adjusted for those distributions, by running:

margins Dummy1

so stata gives me this if I run that code

this means that average illiquidty is about 0.096014 higher after the ban?
do the t-statistics respectively z-statistics matter here?
Does it give me information about significance? Or just additional information?

You can estimate (and test a null hypothesis about, if you wish) the change in illiquidity after the ban with

margins, dydx(Dummy1)

so this means that the increase in illiquidty after the ban is not significant?
meaning that there is no change in illiquidty after the ban?
But if it were significant, would it mean that illiqduity increased about 0.906014 after the ban?

PS: I changed the Name of the Variable "Dummy1" to "TimeDummy" (so I hope you dont get confused)

Thank you so much you are a real help!