S3 Predict method for IV object

[zhizhongpu]

Problem: predict() yields 0 for IV objects

> library(fixest)
> library(dplyr)
> iv = feols(mpg ~ 1 | hp ~ cyl, data = mtcars)
> iv |> summary(stage = 2)
TSLS estimation - Dep. Var.: mpg
                  Endo.    : hp
                  Instr.   : cyl
Second stage: Dep. Var.: mpg
Observations: 32
Standard-errors: IID 
             Estimate Std. Error  t value   Pr(>|t|)    
(Intercept) 33.290411   2.051284 16.22906  < 2.2e-16 ***
fit_hp      -0.089986   0.013059 -6.89063 1.1934e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 4.01816   Adj. R2: 0.52588
F-test (1st stage), hp: stat = 67.7, p = 3.478e-9, on 1 and 30 DoF.
            Wu-Hausman: stat = 15.5, p = 4.804e-4, on 1 and 29 DoF.
> dt_test = mtcars  |> 
+ select(mpg, hp, cyl) |> 
+ mutate(fit_hp = hp)
> dt_test$mpg_hat = predict(iv, newdata = dt_test)
> dt_test |> head(5)
                   mpg  hp cyl fit_hp mpg_hat
Mazda RX4         21.0 110   6    110       0
Mazda RX4 Wag     21.0 110   6    110       0
Datsun 710        22.8  93   4     93       0
Hornet 4 Drive    21.4 110   6    110       0
Hornet Sportabout 18.7 175   8    175       0

Expected behavior: either of

1. Raise an error to alert the user that this is not supported
2. support it (including the se.fit argument)

[kylebutts]

What do you think the output should be of predict(iv, newdata = dt_test)?

My opinion is that this should error because the goal of IV is to estimate the slope parameter, not to make forecasts

[zhizhongpu]

What do you think the output should be of predict(iv, newdata = dt_test)?

My opinion is that this should error because the goal of IV is to estimate the slope parameter, not to make forecasts

Thanks @kylebutts

In my personal use case (where I use IV 2ns stage coefficients for some counterfactual analyses), there's value in allowing prediction using the 2nd stage model - even adding the se.fit parameter.

However, your claim makes sense too.

Overall, I suggest that there be a short term PR that raises an error in the spirit of "predicting using IV isn't allowed - join #596 for more discussions." Then we could discuss the long term solution.

[kylebutts]

there's value in allowing prediction using the 2nd stage model - even adding the se.fit parameter.

Could you describe a bit more? I'm open to hearing use cases

[zhizhongpu]

there's value in allowing prediction using the 2nd stage model - even adding the se.fit parameter.

Could you describe a bit more? I'm open to hearing use cases

Thanks @kylebutts

Suppose we're interested in the research question of, what would happen to some output $Y$ if we were to change input $X$ from $x$ to $x'$. Suppose that one of the approaches to this question is to specify a cross sectional linear production model of

$$ Y_i = \beta X_i + e_i $$

where the RHS essentially specifies a (homogeneous) linear production function.

If this is the correct model, then the counterfactual CEF for each unit $i$ can be derived by the following procedure:

1. estimate $\hat \beta$ on data using OLS (e.g. feols)
2. modify data by changing the realized values of $X_i$ (e.g. from $x_i$ to $x_i'$)
3. compute fitted $\hat y$ using $\hat\beta$ and $x'$ (e.g. predict() method for feols objects)
4. calculate fitted value uncertainty based on e.g. coefficient uncertainty via se.fit= argument (or we can bootstrap, of course)

Now, suppose that $X$ is endogenous such that the OLS estimates of $\beta$ is not consistent, but we still want to model the process as a homogenous linear model and suppose that we happen to have valid instruments $Z$, which we can use to derive a 2SLS estimate of $\hat\beta$ that is consistent. Then we are justified to modify our procedure:

1. estimate $\hat \beta_{2SLS}$ on data using 2SLS (e.g. via feols() with instruments)
2. modify data by changing the realized values of $X_i$ (e.g. from $x_i$ to $x_i'$)
   • note that here there could be scenarios in which we'd like to alter $Z$ instead of / in addition to $X$, but that's not my use case so I shall say no more.
3. compute fitted $\hat y$ using $\hat\beta_{2SLS}$ and $x'$ (where I encounter the issue of predict() returning 0
4. calculate fitted value uncertainty based on e.g. coefficient uncertainty via se.fit= argument (or we can bootstrap, of course)

[zhizhongpu]

@kylebutts now that I've outlined my use case in #596 (comment), if you happen to see a quick workaround I could adopt, I'd be grateful if you let me know.