# R&D DID framework

## Model1
$$
\begin{equation}
\begin{split}
Y_{ijt}=&\alpha+R_{t}+\lambda_j+\beta_1(R_{t} \times T_{ijt})+\beta_2(Age)_{ijt}+\beta_3(Size)_{ijt}+\beta_4(Export){ijt}\\
&+\beta_5(Foreign\_ownership)_{ijt}+\beta_6(raw\_material\_import)_{ijt}\\
&+\beta_7(Royalty)+\beta_8(Real\_importe\_tech)_{ijt}\\
\end{split}
\end{equation}$$

## Model2
$$
\begin{equation}
\begin{split}
Y_{ijt}=&\alpha+\gamma_t+\lambda_j+\beta_1(R_{t} \times T_{ijt})+\beta_2(Age)_{ijt}+\beta_3(Size)_{ijt}+\beta_4(Export){ijt}\\
&+\beta_5(Foreign\_ownership)_{ijt}+\beta_6(raw\_material\_import)_{ijt}\\
&+\beta_7(Royalty)+\beta_8(Real\_importe\_tech)_{ijt}\\
\end{split}
\end{equation}$$

## Calculation

### Model 1: baseline OLS

$$log(TFP)_{Dijt}=\beta_0 +\beta_1(DSIR)_{Dijt}+\beta_{2}(Reform)_{t}+\beta_{3}(DSIR_{Dijt} \times Reform_{t})+\theta X_{Dijt}+\epsilon_{Dijt}$$

reg logtfp dsir reform dsir*reform, vce(cluster industry)

### Model 2: OLS with year and industry fixed effects
$$log(TFP)_{Dijt}=\beta_0 +\alpha_j+\gamma_t+\beta_1(DSIR)_{Dijt}+\beta_{2}(DSIR_{Dijt} \times Reform_{t})+\theta X_{Dijt}+\epsilon_{Dijt}$$

reg logtfp dsir dsir*reform i.year i.industry, vce(cluster industry)

### Model 3: OLS with year, industry fixed effects and industry-time trend
$$log(TFP)_{Dijt}=\beta_0 +\alpha_j+\gamma_t+\lambda_{jt}+\beta_1(DSIR)_{Dijt}+\beta_{2}(Reform)_{t}+\beta_{3}(DSIR_{Dijt} \times Reform_{t})+\theta X_{Dijt}+\epsilon_{Dijt}$$

reg logtfp dsir dsir*reform c.year##i.industry , vce(cluster industry)

### Model 4: OLS with year, firm fixed effects and industry-time trend
$$log(TFP)_{Dijt}=\beta_0 +\alpha_i+\gamma_t+\lambda(industry \times t)+\beta_1(DSIR)_{Dijt}+\beta_{2}(Reform)_{t}+\beta_{3}(DSIR_{Dijt} \times Reform_{t})+\theta X_{Dijt}+\epsilon_{Dijt}$$

reg logtfp dsir dsir*reform i.year i.firm c.year#i.industry, vce(cluster industry)

### Model 5: OLS with year, firm fixed effects and firm-time trend
$$log(TFP)_{Dijt}=\beta_0 +\alpha_i+\gamma_t+\lambda(firm \times t)+\beta_1(DSIR)_{Dijt}+\beta_{2}(Reform)_{t}+\beta_{3}(DSIR_{Dijt} \times Reform_{t})+\theta X_{Dijt}+\epsilon_{Dijt}$$

reg logtfp dsir dsir*reform i.year i.firm c.year#i.firm, vce(cluster industry)

## Explanation of coefficients
Control group: Non-DSIR firms; Treament group: DSIR frims
Reform period: post: 2010-2016; Pre-reform period: 2003-2009

- $\beta_{0}:$ Average log(TFP) of non-DSIR firms in the pre-reform period.
$$E(Y_0|X=0)=\beta_0$$

- $\beta_{1}:$ Difference in average log(TFP) between DSIR and non-DSIR firms in the pre-reform period.
$$E(Y_0|X=1)-E(Y_0|X=0)=\beta_1$$

- $\beta_{2}:$ The change in average log(TFP) in control group in the post-treatment.
$$E(Y_1|X=0)-E(Y_0|X=0)=\beta_2$$

- $\beta_{3}:$ Difference in difference between in average log(TFP) between DSIR and non-DSIR firms in the post-reform period.
$$[E(Y_1|X=1)-E(Y_0|X=1)]-[E(Y_1|X=0)-E(Y_0|X=0)]=\beta_3$$

## Tranformations

$$\begin{equation}
\begin{split}
\beta_1+\beta_3=&E(Y_0|X=1)-E(Y_0|X=0)\\
&+[E(Y_1|X=1)-E(Y_0|X=1)]-[E(Y_1|X=0)-E(Y_0|X=0)]\\
=&E(Y_1|X=1)-E(Y_1|X=0)\\
\end{split}
\end{equation}
$$

- $\beta_1+\beta_3:$ The difference in average log(TFP) for DSIR firms and non-DSIR firms in the post-reform period.

$$Mutiliplicative \ treatment=\frac{e^{\beta_1+\beta_3}}{e^{\beta_1}}=e^{\beta_3}$$

$$Actual \ treatment=(e^{\beta_3}-1)\times 100$$

## Paper definition:

The results of this statistically more demanding specification imply that compared to the average R&D expenditure in the control group of non- DSIR-registered firms, the average R&D expenditure in the treatment group of DSIR-registered firms was exp(0.674) = 1.96 times greater in the pre-reform years and exp(0.674 + 0.552) = 3.41 times greater in the post-reform years. The estimate of the multiplicative treatment effect thus equals exp(0.552) = 3.41/1.96 = 1.74. It implies that the impact of DSIR registration on firm R&D expenditure has increased by 1.74 times after the reform. In other words, the treatment effect of the reform equals [exp(0.552)− 1]100 = 74%.