Hello, Alessia Montinaro

Your interpretation is correct, assuming that your linear probability model (LPM) is specified as:

$$y_{it} = \alpha_i + \beta x_{it} + \epsilon_{it}$$

where $y_{it}$ is the binary outcome variable for unit $i$ at time $t$, $\alpha_i$ is the unit fixed effect, $x_{it}$ is the standardized independent variable of interest, and $\epsilon_{it}$ is the error term.

In this case, the coefficient $\beta$ represents the marginal effect of $x_{it}$ on $y_{it}$, holding everything else constant. Since $y_{it}$ is a probability that ranges from 0 to 1, and $x_{it}$ is standardized to have a mean of 0 and a standard deviation of 1, the coefficient $\beta$ can be interpreted as the change in the probability of $y_{it}$ being 1 when $x_{it}$ increases by one standard deviation.

So, if your coefficient is 0.019, it means that a one standard deviation increase in your variable of interest increases the probability of implementing a trade policy by 0.019, or 1.9 percentage points.

However, you should also be aware of some limitations and caveats of using LPM with a binary outcome variable. For example:

- The LPM may predict probabilities that are outside the [0,1] range for some values of $x_{it}$, which violates the logic of probabilities.

- The LPM may not capture the nonlinear relationship between $x_{it}$ and $y_{it}$, which may lead to biased and inconsistent estimates of $\beta$.

- The LPM may not account for heteroskedasticity in the error term $\epsilon_{it}$, which may affect the standard errors and inference of $\beta$.

Therefore, you may want to consider using alternative models for binary outcome variables, such as logistic regression or probit regression, which do not have these problems. However, these models also have their own challenges and assumptions, such as the need to specify a link function and the difficulty of interpreting the coefficients directly as marginal effects.