How to analyse interaction for specific year and quarters in Stata?

[Ali Zul]

Hi,

I am trying to observe the impact of COVID across industries where my dependent variable is employment. Additionally, my supervisor told me to look at the impact for each quarter in year 2020 (COVID year)

I was advised by my supervisor to run the equation below but as I tried to run the regression but there is error saying varlist required
xi: reg Y i.quarter i.year i.industry i.[2020]*i.quarter

---

Stata Command:
xi: reg lnemp i.qyear i.year i.econsector i.[2020]*i.qyear, r

Stata Result:
i.qyear _Iqyear_220-243 (naturally coded; _Iqyear_220 omitted)
i.year _Iyear_2015-2020 (naturally coded; _Iyear_2015 omitted)
i.econsector _Ieconsecto_1-19 (naturally coded; _Ieconsecto_1 omitted)
varlist required
r(100);

---

I do not fully understand the year and quarter dummy and hope that someone can further guide me on this.

Thank you!

[Clyde Schechter]

The expression i.[2020]*i.qyear is not correct syntax. I assume you are trying to create an interaction between qyear and a dichotomous indicator ("dummy") for year = 2020.

The -xi- command and prefix are now almost entirely obsolete,* having been superceded by factor-variable notation. (See -help fvvarlist-.) Unless you are using an ancient version of Stata you should change that code to:

gen byte year2020 = 2020.year
reg lnemp i.year i.econsector i.year2020##i.qyear, robust

to get what you are looking for.

* Some old commands written early in Stata's history do not allow factor-variable notation, and for these the xi: prefix can be useful. But most of these commands have, themselves, been superseded by more modern commands that perform the same function, and do support factor-variable notation. There also remain a few odd places in modern Stata commands where factor-variable notation is not allowed, but these are few and far between. In general, you should almost, but not quite, forget you ever heard of -xi-.

[Ali Zul]

Hi!

Appreciate your prompt response.

Yes you are correct, thank you so much for your kind guidance! I tried running this but my variable was omitted as below and I dont' know exactly how to interpret the results:

 
reg lnemp i.year i.qyear i.econsector i.year2020##i.qyear, robust
note: 227.qyear omitted because of collinearity
note: 231.qyear omitted because of collinearity
note: 235.qyear omitted because of collinearity
note: 239.qyear omitted because of collinearity
note: 243.qyear omitted because of collinearity
note: 1.year2020 omitted because of collinearity
note: 0b.year2020#240.qyear identifies no observations in the sample
note: 0b.year2020#241.qyear identifies no observations in the sample
note: 0b.year2020#242.qyear identifies no observations in the sample
note: 0b.year2020#243.qyear identifies no observations in the sample
note: 1.year2020#220b.qyear identifies no observations in the sample
note: 1.year2020#221.qyear identifies no observations in the sample
note: 1.year2020#222.qyear identifies no observations in the sample
note: 1.year2020#223.qyear identifies no observations in the sample
note: 1.year2020#224.qyear identifies no observations in the sample
note: 1.year2020#225.qyear identifies no observations in the sample
note: 1.year2020#226.qyear identifies no observations in the sample
note: 1.year2020#227.qyear identifies no observations in the sample
note: 1.year2020#228.qyear identifies no observations in the sample
note: 1.year2020#229.qyear identifies no observations in the sample
note: 1.year2020#230.qyear identifies no observations in the sample
note: 1.year2020#231.qyear identifies no observations in the sample
note: 1.year2020#232.qyear identifies no observations in the sample
note: 1.year2020#233.qyear identifies no observations in the sample
note: 1.year2020#234.qyear identifies no observations in the sample
note: 1.year2020#235.qyear identifies no observations in the sample
note: 1.year2020#236.qyear identifies no observations in the sample
note: 1.year2020#237.qyear identifies no observations in the sample
note: 1.year2020#238.qyear identifies no observations in the sample
note: 1.year2020#239.qyear identifies no observations in the sample
note: 1.year2020#240.qyear omitted because of collinearity
note: 1.year2020#241.qyear omitted because of collinearity
note: 1.year2020#242.qyear omitted because of collinearity
note: 1.year2020#243.qyear omitted because of collinearity

Linear regression                               Number of obs     =        456
                                                F(41, 414)        =   14549.89
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9990
                                                Root MSE          =     .04139

-------------------------------------------------------------------------------------------------------------------------------
                                                              |               Robust
                                                        lnemp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------------------------------------------------+----------------------------------------------------------------
                                                         year |
                                                        2016  |   .0122363   .0120782     1.01   0.312     -.011506    .0359786
                                                        2017  |   .0349866   .0127105     2.75   0.006     .0100015    .0599717
                                                        2018  |   .0557209    .013849     4.02   0.000     .0284978    .0829439
                                                        2019  |   .0777262   .0156626     4.96   0.000     .0469381    .1085143
                                                        2020  |   .0640603   .0181217     3.54   0.000     .0284383    .0996823
                                                              |
                                                        qyear |
                                                         221  |  -.0142433   .0172781    -0.82   0.410    -.0482071    .0197206
                                                         222  |  -.0080162   .0177444    -0.45   0.652    -.0428966    .0268642
                                                         223  |   .0118375   .0159729     0.74   0.459    -.0195607    .0432356
                                                         224  |  -.0192117   .0119972    -1.60   0.110    -.0427947    .0043714
                                                         225  |  -.0132797   .0087317    -1.52   0.129    -.0304438    .0038843
                                                         226  |  -.0111836    .008248    -1.36   0.176    -.0273969    .0050296
                                                         227  |          0  (omitted)
                                                         228  |  -.0141376   .0115449    -1.22   0.221    -.0368314    .0085563
                                                         229  |  -.0193802   .0104065    -1.86   0.063    -.0398364    .0010759
                                                         230  |  -.0087175    .009862    -0.88   0.377    -.0281034    .0106684
                                                         231  |          0  (omitted)
                                                         232  |  -.0159169   .0106268    -1.50   0.135    -.0368061    .0049723
                                                         233  |  -.0138531   .0097805    -1.42   0.157    -.0330788    .0053725
                                                         234  |  -.0079864   .0096311    -0.83   0.407    -.0269184    .0109456
                                                         235  |          0  (omitted)
                                                         236  |  -.0162748   .0136448    -1.19   0.234    -.0430966     .010547
                                                         237  |  -.0126599   .0137209    -0.92   0.357    -.0396312    .0143114
                                                         238  |  -.0091156   .0135357    -0.67   0.501    -.0357228    .0174916
                                                         239  |          0  (omitted)
                                                         240  |   .0114722   .0183731     0.62   0.533    -.0246441    .0475884
                                                         241  |  -.0196264    .018816    -1.04   0.298    -.0566132    .0173604
                                                         242  |  -.0054675   .0185237    -0.30   0.768    -.0418798    .0309447
                                                         243  |          0  (omitted)
                                                              |
                                                   econsector |
                              Beverages and tobacco products  |  -4.612658   .0121923  -378.33   0.000    -4.636625   -4.588692
                                                Construction  |  -.2202465   .0139249   -15.82   0.000    -.2476188   -.1928742
                 Electrical, electronic and optical products  |  -1.202312   .0082211  -146.25   0.000    -1.218473   -1.186152
                                       Finance and insurance  |  -1.624887   .0084612  -192.04   0.000    -1.641519   -1.608255
                          Food & beverages and accommodation  |  -.2266071   .0150524   -15.05   0.000    -.2561957   -.1970185
                               Information and communication  |  -2.124689   .0140898  -150.80   0.000    -2.152386   -2.096993
                                        Mining and quarrying  |  -3.181292   .0179931  -176.81   0.000    -3.216661   -3.145922
Non-metallic mineral products, basic metal and fabricated ..  |  -1.663272    .009022  -184.36   0.000    -1.681006   -1.645537
                                              Other Services  |   .3432047   .0096607    35.53   0.000     .3242145    .3621948
            Petroleum, chemical, rubber and plastic products  |  -1.548084   .0083286  -185.87   0.000    -1.564455   -1.531712
                           Real estate and business services  |  -.5474867   .0107437   -50.96   0.000    -.5686057   -.5263676
              Textiles, wearing apparel and leather products  |  -2.061269   .0107523  -191.71   0.000    -2.082405   -2.040133
         Transport equipment, other manufacturing and repair  |  -2.254839   .0136497  -165.19   0.000     -2.28167   -2.228007
                                  Transportation and storage  |  -1.265602   .0098355  -128.68   0.000    -1.284935   -1.246268
                                                   Utilities  |  -2.908234    .008827  -329.47   0.000    -2.925585   -2.890883
        Vegetable and animal oils & fats and food processing  |  -1.480373   .0100459  -147.36   0.000     -1.50012   -1.460625
                                  Wholesale and retail trade  |   .2554544    .011867    21.53   0.000     .2321273    .2787815
       Wood products, furniture, paper products and printing  |  -1.799917   .0115868  -155.34   0.000    -1.822693   -1.777141
                                                              |
                                                   1.year2020 |          0  (omitted)
                                                              |
                                               year2020#qyear |
                                                       0 240  |          0  (empty)
                                                       0 241  |          0  (empty)
                                                       0 242  |          0  (empty)
                                                       0 243  |          0  (empty)
                                                       1 220  |          0  (empty)
                                                       1 221  |          0  (empty)
                                                       1 222  |          0  (empty)
                                                       1 223  |          0  (empty)
                                                       1 224  |          0  (empty)
                                                       1 225  |          0  (empty)
                                                       1 226  |          0  (empty)
                                                       1 227  |          0  (empty)
                                                       1 228  |          0  (empty)
                                                       1 229  |          0  (empty)
                                                       1 230  |          0  (empty)
                                                       1 231  |          0  (empty)
                                                       1 232  |          0  (empty)
                                                       1 233  |          0  (empty)
                                                       1 234  |          0  (empty)
                                                       1 235  |          0  (empty)
                                                       1 236  |          0  (empty)
                                                       1 237  |          0  (empty)
                                                       1 238  |          0  (empty)
                                                       1 239  |          0  (empty)
                                                       1 240  |          0  (omitted)
                                                       1 241  |          0  (omitted)
                                                       1 242  |          0  (omitted)
                                                       1 243  |          0  (omitted)
                                                              |
                                                        _cons |   7.487014   .0131916   567.56   0.000     7.461083    7.512944
-------------------------------------------------------------------------------------------------------------------------------

Thank you

[Clyde Schechter]

All of these omissions are completely correct and nothing to be concerned about.

Because you are including variables both for quarters and for years, there is invariably redundancy here. The messages

note: 227.qyear omitted because of collinearity
note: 231.qyear omitted because of collinearity
note: 235.qyear omitted because of collinearity
note: 239.qyear omitted because of collinearity
note: 243.qyear omitted because of collinearity

are telling you that the fourth quarter of each year is being omitted as a variable--that makes sense because there are only 4 quarters in each year, so, given that there is already a variable for year, you only need three indicators, not four, to completely identify the quarter. (The fourth quarter of a year is the quarter in which the indicators for the first three quarters are all zero.)

The variable 1.year2020 is omitted because it is evidently colinear with i.year: it is equal to 1*2020.year + 0*(all other values of year).

The messages
[code]
note: 0b.year2020#240.qyear identifies no observations in the sample
note: 0b.year2020#241.qyear identifies no observations in the sample
note: 0b.year2020#242.qyear identifies no observations in the sample
note: 0b.year2020#243.qyear identifies no observations in the sample[
/code]
are just telling you that the four quarters of year 2020 never occur in observations where year != 2020, so interactions between those quarters and 0.year2020 are non-existent.

The next block of messages are telling you that quarters for years other than 2020 never occur in observations where year == 2020, so really the flip side of the last ones.

The final four messages are telling you that it is always year2020 in quarters 2020q1, 2020q2, 2020q3, and 2020q4--so year2020 is redundant for these observations, as it can be inferred based on the quarters. That's more collinearity.

So what happened is that the model over-specified the information, and what you are looking for was diffused among many other variables.

Depending on what exactly you are looking for, there are a few way you can revise the model that will appear more sensible to you.

1. What is the point of the qyear variables? Are you trying to pick up seasonality here? If so, you shouldn't use a quarterly date variable: you should use a variable that takes on values 1, 2, 3, and 4 in the corresponding quarters of the year. You can get that variable with -gen quarter = quarter(dofq(qyear))- and then use i.quarter instead of i.qyear in your model.

2. If you really want independent shocks of each quarter of each year on the outcome represented, as opposed to just wanting to pick up seasonality, then keep year qyear, but get rid of i.year: it is completely redundant and it is absorbing the effect you are actually interested in seeing.

[Ali Zul]

Thank you so much Mr Clyde Schechter for your kind help and prompt response,

I have tried to apply your feedback and obtained results as below.

Just a little overview of what my supervisor advised me to do are as as below:

The regression I mentioned below is motivated by the following observation: you code covid =1 all quarters in 2020. That means that your covid period is going to be compared to the other years in levels. But you could try to see if there are relative differences across quarters in 2020 to understand the impact of covid once you take into account seasonality, and also see the dynamics of the covid impact (maybe very negative in the first two quarters, and positive or nhil later… )

Hence, I assumed I only would like to see the seasonal impact of covid in year 2020. I have tried to regress your suggestion as below:

reg lnemp i.year i.quarter i.econsector i.year2020##i.quarter, robust baselevels
note: 1.year2020 omitted because of collinearity

Linear regression                               Number of obs     =        456
                                                F(29, 426)        =   20508.97
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9990
                                                Root MSE          =      .0409

-------------------------------------------------------------------------------------------------------------------------------
                                                              |               Robust
                                                        lnemp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------------------------------------------------+----------------------------------------------------------------
                                                         year |
                                                        2015  |          0  (base)
                                                        2016  |    .003923   .0072839     0.54   0.590    -.0103938    .0182398
                                                        2017  |   .0270333   .0073604     3.67   0.000     .0125661    .0415004
                                                        2018  |   .0488873   .0069441     7.04   0.000     .0352383    .0625362
                                                        2019  |   .0708191   .0075697     9.36   0.000     .0559405    .0856978
                                                        2020  |   .0826392   .0129425     6.39   0.000     .0572001    .1080783
                                                              |
                                                      quarter |
                                                           1  |          0  (base)
                                                           2  |  -.0015751   .0055157    -0.29   0.775    -.0124164    .0092663
                                                           3  |   .0041043   .0054712     0.75   0.454    -.0066496    .0148583
                                                           4  |   .0154757   .0057033     2.71   0.007     .0042656    .0266858
                                                              |
                                                   econsector |
                                                 Agriculture  |          0  (base)
                              Beverages and tobacco products  |  -4.612658   .0119773  -385.12   0.000    -4.636201   -4.589116
                                                Construction  |  -.2202465   .0135458   -16.26   0.000    -.2468715   -.1936216
                 Electrical, electronic and optical products  |  -1.202312   .0079389  -151.45   0.000    -1.217917   -1.186708
                                       Finance and insurance  |  -1.624887   .0082719  -196.44   0.000    -1.641146   -1.608628
                          Food & beverages and accommodation  |  -.2266071   .0147845   -15.33   0.000    -.2556667   -.1975475
                               Information and communication  |  -2.124689   .0138741  -153.14   0.000    -2.151959   -2.097419
                                        Mining and quarrying  |  -3.181292   .0177644  -179.08   0.000    -3.216208   -3.146375
Non-metallic mineral products, basic metal and fabricated ..  |  -1.663272   .0087264  -190.60   0.000    -1.680424   -1.646119
                                              Other Services  |   .3432047   .0093382    36.75   0.000     .3248501    .3615593
            Petroleum, chemical, rubber and plastic products  |  -1.548084   .0080544  -192.20   0.000    -1.563915   -1.532252
                           Real estate and business services  |  -.5474867   .0105206   -52.04   0.000    -.5681654    -.526808
              Textiles, wearing apparel and leather products  |  -2.061269   .0104389  -197.46   0.000    -2.081787   -2.040751
         Transport equipment, other manufacturing and repair  |  -2.254839   .0132868  -169.70   0.000    -2.280954   -2.228723
                                  Transportation and storage  |  -1.265602   .0095314  -132.78   0.000    -1.284336   -1.246867
                                                   Utilities  |  -2.908234   .0085586  -339.80   0.000    -2.925056   -2.891412
        Vegetable and animal oils & fats and food processing  |  -1.480373   .0098265  -150.65   0.000    -1.499687   -1.461058
                                  Wholesale and retail trade  |   .2554544   .0116923    21.85   0.000     .2324726    .2784362
       Wood products, furniture, paper products and printing  |  -1.799917   .0113165  -159.05   0.000     -1.82216   -1.777674
                                                              |
                                                     year2020 |
                                                           0  |          0  (base)
                                                           1  |          0  (omitted)
                                                              |
                                             year2020#quarter |
                                                         1 2  |  -.0295235   .0169669    -1.74   0.083    -.0628729    .0038258
                                                         1 3  |   -.021044   .0166368    -1.26   0.207    -.0537444    .0116564
                                                         1 4  |  -.0269479   .0189892    -1.42   0.157    -.0642721    .0103764
                                                              |
                                                        _cons |   7.479907   .0105554   708.64   0.000      7.45916    7.500654
-------------------------------------------------------------------------------------------------------------------------------

Additionally, my supervisor also told me to use fixed effects for this where I have used command

xtset econsector

and obtained following regression

xtreg lnemp i.year i.quarter i.year2020##i.quarter, fe baselevels
note: 1.year2020 omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        456
Group variable: econsector                      Number of groups  =         19

R-sq:                                           Obs per group:
     within  = 0.3419                                         min =         24
     between = 0.0000                                         avg =       24.0
     overall = 0.0005                                         max =         24

                                                F(11,426)         =      20.12
corr(u_i, Xb)  = 0.0000                         Prob > F          =     0.0000

----------------------------------------------------------------------------------
           lnemp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
            year |
           2015  |          0  (base)
           2016  |    .003923   .0066356     0.59   0.555    -.0091196    .0169657
           2017  |   .0270333   .0066356     4.07   0.000     .0139906    .0400759
           2018  |   .0488873   .0066356     7.37   0.000     .0358446    .0619299
           2019  |   .0708191   .0066356    10.67   0.000     .0577765    .0838618
           2020  |   .0826392   .0111035     7.44   0.000     .0608146    .1044638
                 |
         quarter |
              1  |          0  (base)
              2  |  -.0015751   .0059351    -0.27   0.791    -.0132408    .0100907
              3  |   .0041043   .0059351     0.69   0.490    -.0075614      .01577
              4  |   .0154757   .0059351     2.61   0.009       .00381    .0271414
                 |
        year2020 |
              0  |          0  (base)
              1  |          0  (omitted)
                 |
year2020#quarter |
            1 2  |  -.0295235    .014538    -2.03   0.043    -.0580986   -.0009485
            1 3  |   -.021044    .014538    -1.45   0.148    -.0496191     .007531
            1 4  |  -.0269479    .014538    -1.85   0.064    -.0555229    .0016272
                 |
           _cons |   5.999743   .0059351  1010.89   0.000     5.988078    6.011409
-----------------+----------------------------------------------------------------
         sigma_u |  1.2679848
         sigma_e |  .04090481
             rho |  .99896039   (fraction of variance due to u_i)
----------------------------------------------------------------------------------
F test that all u_i=0: F(18, 426) = 23061.66                 Prob > F = 0.0000

Are these the correct ways and I am still not sure about which one is better.

Also, sorry to ask this but I have a question to clarify with you on interpreting this data. I am a bit confuse on interpreting the the data especially the main effects for quarter, year and the econsectors.

In terms of analysis wise, do I need to talk about the main effects as well or is it okay to just mention the interaction, because the interaction term looks like a feasible explanation on the covid situation as it employement decreases -0.0295 in Q2 due to lockdown and picked up again in Q3 -0.0210 and due to another lockdown decreases again to -0.0269. Also, do I need to worry about the significancy as only quarter 2 is significant.

Thank you!

[Clyde Schechter]

The last results you show in #5 look like they are an appropriate model for what your supervisor asked you to do. Your interpretation in the last paragraph before "Thank you!" is not, however correct. The -0.0295 is not the dip in employment from 2020Q21 to 2020Q2. It is the difference between the seasonal effect (Q2 vs Q1) in 2020 and the seasonal effect (Q2 vs Q1) in years other than 2020. To see what is going on I would follow that regression with:

margins year2020#quarter

This will show you the model's expected value of lnemp in each quarter of 2020 and in the average over other years in each quarter. If you want to specifically contrast those, run -margins- again, adding the -pwcompare- option.

Let me also caution you about attributing the changes from one season to the next in 2020 to specific aspects of the pandemic or the response to the pandemic. The pandemic has been a very complicated phenomenon, with lots of moving parts, and positive and negative feedback loops. So I think it is even more unwise than usual to draw conclusions about cause and effect from observational studies in this context.

Also, do I need to worry about the significancy as only quarter 2 is significant.

The American Statistical Association has recommended that the concept of statistical significance be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the "executive summary" and https://www.tandfonline.com/toc/utas20/73/sup1 for all 43 supporting articles. Or https://www.nature.com/articles/d41586-019-00857-9 for the tl;dr. So I hardly ever concern myself with the significance of anything. I look at the effect sizes and confidence intervals and judge whether these represent a difference that is meaningful in a real world sense or not.

[Ali Zul]

Noted on the explanation. Thank you so much!

I have regress the fe equation in #5 and include -margin- command but I obtained the command below:

margins year2020#quarter

Predictive margins                              Number of obs     =        456
Model VCE    : Robust

Expression   : Linear prediction, predict()

----------------------------------------------------------------------------------
                 |            Delta-method
                 |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
year2020#quarter |
            0 1  |          .  (not estimable)
            0 2  |          .  (not estimable)
            0 3  |          .  (not estimable)
            0 4  |          .  (not estimable)
            1 1  |          .  (not estimable)
            1 2  |          .  (not estimable)
            1 3  |          .  (not estimable)
            1 4  |          .  (not estimable)
----------------------------------------------------------------------------------

However, for the -pwcompare- I obtained below:

pwcompare year2020#quarter

Pairwise comparisons of marginal linear predictions

Margins      : asbalanced

------------------------------------------------------------------
                 |                                 Unadjusted
                 |   Contrast   Std. Err.     [95% Conf. Interval]
-----------------+------------------------------------------------
year2020#quarter |
 (0 2) vs (0 1)  |  -.0015751   .0059351     -.0132408    .0100907
 (0 3) vs (0 1)  |   .0041043   .0059351     -.0075614      .01577
 (0 4) vs (0 1)  |   .0154757   .0059351        .00381    .0271414
 (1 1) vs (0 1)  |          .  (not estimable)
 (1 2) vs (0 1)  |          .  (not estimable)
 (1 3) vs (0 1)  |          .  (not estimable)
 (1 4) vs (0 1)  |          .  (not estimable)
 (0 3) vs (0 2)  |   .0056794   .0059351     -.0059863    .0173451
 (0 4) vs (0 2)  |   .0170507   .0059351       .005385    .0287164
 (1 1) vs (0 2)  |          .  (not estimable)
 (1 2) vs (0 2)  |          .  (not estimable)
 (1 3) vs (0 2)  |          .  (not estimable)
 (1 4) vs (0 2)  |          .  (not estimable)
 (0 4) vs (0 3)  |   .0113714   .0059351     -.0002944    .0230371
 (1 1) vs (0 3)  |          .  (not estimable)
 (1 2) vs (0 3)  |          .  (not estimable)
 (1 3) vs (0 3)  |          .  (not estimable)
 (1 4) vs (0 3)  |          .  (not estimable)
 (1 1) vs (0 4)  |          .  (not estimable)
 (1 2) vs (0 4)  |          .  (not estimable)
 (1 3) vs (0 4)  |          .  (not estimable)
 (1 4) vs (0 4)  |          .  (not estimable)
 (1 2) vs (1 1)  |  -.0310986   .0132713     -.0571839   -.0050132
 (1 3) vs (1 1)  |  -.0169397   .0132713      -.043025    .0091456
 (1 4) vs (1 1)  |  -.0114722   .0132713     -.0375575    .0146132
 (1 3) vs (1 2)  |   .0141589   .0132713     -.0119265    .0402442
 (1 4) vs (1 2)  |   .0196264   .0132713     -.0064589    .0457117
 (1 4) vs (1 3)  |   .0054675   .0132713     -.0206178    .0315528
------------------------------------------------------------------

Interpretation wise, should I focus on the last 6 row of variables, for example for (1 2) vs (1 1), in 2020, there is a 0.03 decrease in employment from in Q2 as compared to Q1?

Let me also caution you about attributing the changes from one season to the next in 2020 to specific aspects of the pandemic or the response to the pandemic. The pandemic has been a very complicated phenomenon, with lots of moving parts, and positive and negative feedback loops. So I think it is even more unwise than usual to draw conclusions about cause and effect from observational studies in this context.

My apologies, I do not fully follow this, do you mean something like this. For example, in Malaysia the government started lockdown in Q2. Hence, this might not be a strong conclusion to why the data is as such. There might be other factors attributing to the seasonal change across quarters.

Thank you!

[Clyde Schechter]

Interpretation wise, should I focus on the last 6 row of variables, for example for (1 2) vs (1 1), in 2020, there is a 0.03 decrease in employment from in Q2 as compared to Q1?

Yes, those are the comparisons you are most interested in.

There might be other factors attributing to the seasonal change across quarters.

Yes. There are many things influencing the pandemic. Here in the US, there was considerable variation among the states about what kind of lockdown, if any, they imposed, and when they imposed them, and how they enforced them. Making matters even more complicated, analysis of mobility data gathered from tracking the locations of cell phones suggests that the correlation between what was mandated by government was not only weakly related to what people actually did. The weather also influences the transmissibility of the virus, and that varies over both time and space. The amount of travel from one area to another also affects the epidemic in each area. There are just too many things going on to draw any clear conclusions about anything causing anything else related to this pandemic. Maybe in a decade or two we'll eventually get it sorted out, but not any time soon.

[Ali Zul]

Noted with much thanks. Appreciate your kind feedback and insight on this. I will definitely discuss this with my supervisor. Thank you so much again Professor.