If you have access to data on sectoral GDP contributions over time, you could consider using a fixed-effects panel regression to estimate the relationship between the number of COVID cases and deaths and sectoral GDP. Fixed-effects models can control for unobserved time-invariant differences between sectors, which can be an important consideration in a cross-sectional analysis

Muneeb Shah thank you for the answer. does that mean fixed effect model consider that both COVID cases and deaths are common to the each sector, but using the GDP contribution of each sector it can identify how COVID cases and deaths affect each sector?

The very important to note that, the fixed effects model does not assume that COVID cases and deaths are common to each sector, but rather, it accounts for differences in the levels of COVID cases and deaths between sectors by using sector-specific variables.

Muneeb Shah I applied Hausman test to the dataset and it resulted that random effect model is appropriate. But still I have to fit fixed effect model due to the limited data. is it?

if the Hausman test indicates that a random effects model is appropriate, you should generally use that model. However, if you have limited data, a fixed effects model may be more appropriate due to the reduced ability to estimate the individual-specific effects in the random effects model

I will suggest to dig in more into the literature, because within the literature, these are broader study areas. Thoroughly you have to get a better n clear idea about your methodology

Muneeb Shah Thank you for the clarification

Your hypothesis is that sector GDP is a function of Covid cases and deaths in these sectors. As you have no Covid data for the sectors, I see no chance to find-out, how the sectors' production is influenced by Covid. If by sector you mean (groups o) industries like agriculture, manufacturing, construction, services etc. and you have regional Covid data, you could try to find out, whether sectors with a high or low share of a sector and high or low Covid data have special GDP developments.But I fear that there is no promising way to find out.

Include 6 dummy variables to separate the sectors.

I think that Antonio's proposal does not make sense, because it would lead to an over-identivication.

If you want to measure the impact of Covid-19 on different sectors of India like agriculture, manufacturing and Service sector and have taken sector-wise GVA as a dependent variable then you can investigate the impact on unemployment rate, sector-wise export & import, pricing, wages/salaries of employees, with time dummy variable. You can check the database of RBI and Indiastat for more variables. You can also do a state-wise comparative analysis using panel regression. As per the data you can choose which panel regression model will be applied – pooled reg, fixed and random effect. First do more literature survey and try to find what exactly you want to investigate before jumping into modelling.

Dr Anusuya Biswas I'm doing the analysis for Sri Lankan sectors. can you suggest me some methods?

It seems that I was in error about the aim of your inquiry, when I first answered your question. I now understand, that you want to find-out the effect of the country wide covid infections and deaths on the development of the value-added of seven sectors. For that, you need no panel regression, but simply 7 time-series regressions for the seven sectors. First, I would look at the correlations between %change of GDP sector i and number of covid cases and deaths, respectively (i.e. 14 correlograms) with different lags (lagged covid data).

Anton Rainer can I apply the VAR model considering the GDP share of each sector as dependent variable and COVID data as independent variables?

Why do you want to apply Var? Before choosing a method, you should think-over why and how covid influeances value-added. For example, more infections will likely lead to an increase of medical services, because there are more treatments. More deaths mean an increase of VA of undertakers. The effects on other sectors are not that clear. If the number of infections is extremely high, this could lead to shortages of active employees and restrict VA. In this respect, the effect of deaths is likely to be low (because it is mainly old people who die from covid). Of course, it also depends on policy measures. A decision for a lock-down will, of course, strong economic effects.

If you find plausible hypotheses, you should first use the simplest possible statistidal methods to test correlations, OLS). I think,you should not use the sectors' shares. Even if VA of a sector is not affected by covid, its share would change because of a change in other sectors.

Finally, I think, that for VAR you have much to few data. I assume that for sectoral GDP, there are quarterly data. For covid, you cannot; I assume, get data for more than two years. That means, you have common time series of

8 quarters (if you include, say, the preceding two years, with zeros for covid, then you have 16), a number which is by far to low to apply VAR.

Anton Rainer I collected data from 2014 to 2021. After 2020, I considered the pandemic period; before 2014, it was my pre-COVID period. I want to see, in the presence of COVID cases and deaths, how the performance of sectors varies w.r.t its share of GDP. In this case can you suggest me some methods to do my analysis?

It is impossible to replace lack of data, common sense and thinking by a statistical method. What conserns data: I assume you have quarterly sector GDP data (i.e. 32 values for every sector. Apart from that quarterly data are, in gerneral. not as good as annual GDP data, I think, that you have not got any covid data before spring 2020 and the first of them were certainly not complete. Therefore, the common time span of reliable GDP and covid data is only 7 quarters. In principle, it is possible to produce monthly or even daily data from quarterly data such that there are more common data (I think your covid data are daily - but with a strong weekly pattern), but this procedure will, in fact, bring not additional information. If you assume lags between covid and value added (which is implicit when you apply VAR), the common period is father shortened. Of course, the GDP data 2014-2020 include some information, but the value of this information is minor to that of the common period.

Covid has changed over time (in the beginning, the death rate was rather high). That means that restrictive measures (which are likely to have reduced economic activity) against might have been released or reduced.

Therefore, I recommend, that you think over the reasons, why and how covid may affect sectors' value added and to apply the most simplest methods on your data, first (looking at diagrams, correlations, OLS).

The problem with the shares is, that it is open, whether an estimated positive (negative) effect is due to a direct effect on this sector or to negative (positive) effects on other sectors.