Здесь есть несколько проблем:

1. you sometimes use я and sometimes lag_i, but only я is defined. я changed all to lag_i for consistency
2. if j = 1 is incorrect syntax. You need if j == 1
3. You need to return fit_d so that it persists after your loop

Я сделал это, применив эти изменения

import pandas as pd
import numpy as np
import statsmodels.api as sm

df = pd.DataFrame(np.random.randint(low=0, high=10, size=(100,17)), 
              columns=['Historic Rate', 'Overnight', '1M', '3M', '6M','1Y','2Y','3Y','4Y','5Y','6Y','7Y','8Y','9Y','10Y','12Y','15Y'])

def Simulation(TotalSim,j):
    Super_fit_d = {}
    for lag_i in range(1,TotalSim):
        #Create a introductory loop to run the first set of regressions
        #Each loop produces a univariate regression
        #Each loop has a fixed lag of i

        fit_d = {}  # This will hold all of the fit results and summaries
        for col in [x for x in df.columns if x != 'Historic Rate']:
            Y = df['Historic Rate'] - df['Historic Rate'].shift(1)
            # Need to remove the NaN for fit
            Y = Y[Y.notnull()]

            X = df[col] - df[col].shift(lag_i)
            X = X[X.notnull()]
            #Y now has more observations than X due to lag, drop rows to match
            Y = Y.drop(Y.index[0:lag_i-1])

            if j == 1:
                X = sm.add_constant(X)  # Add a constant to the fit

            fit_d[col] = sm.OLS(Y,X).fit()
        #append the dictionary for each lag onto the super dictionary
      #  return fit_d
            Super_fit_d[lag_i] = fit_d
    return Super_fit_d



test_dict = Simulation(11,1)

Первый лаг

test_dict[1]['Overnight'].summary()

Out[76]: 
<class 'statsmodels.iolib.summary.Summary'>
"""
                            OLS Regression Results                            
==============================================================================
Dep. Variable:          Historic Rate   R-squared:                       0.042
Model:                            OLS   Adj. R-squared:                  0.033
Method:                 Least Squares   F-statistic:                     4.303
Date:                Fri, 28 Sep 2018   Prob (F-statistic):             0.0407
Time:                        11:15:13   Log-Likelihood:                -280.39
No. Observations:                  99   AIC:                             564.8
Df Residuals:                      97   BIC:                             570.0
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         -0.0048      0.417     -0.012      0.991      -0.833       0.823
Overnight      0.2176      0.105      2.074      0.041       0.009       0.426
==============================================================================
Omnibus:                        1.449   Durbin-Watson:                   2.756
Prob(Omnibus):                  0.485   Jarque-Bera (JB):                1.180
Skew:                           0.005   Prob(JB):                        0.554
Kurtosis:                       2.465   Cond. No.                         3.98
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""

Второй отход

test_dict[2]['Overnight'].summary()

Out[77]: 
<class 'statsmodels.iolib.summary.Summary'>
"""
                            OLS Regression Results                            
==============================================================================
Dep. Variable:          Historic Rate   R-squared:                       0.001
Model:                            OLS   Adj. R-squared:                 -0.010
Method:                 Least Squares   F-statistic:                   0.06845
Date:                Fri, 28 Sep 2018   Prob (F-statistic):              0.794
Time:                        11:15:15   Log-Likelihood:                -279.44
No. Observations:                  98   AIC:                             562.9
Df Residuals:                      96   BIC:                             568.0
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.0315      0.428      0.074      0.941      -0.817       0.880
Overnight      0.0291      0.111      0.262      0.794      -0.192       0.250
==============================================================================
Omnibus:                        2.457   Durbin-Watson:                   2.798
Prob(Omnibus):                  0.293   Jarque-Bera (JB):                1.735
Skew:                           0.115   Prob(JB):                        0.420
Kurtosis:                       2.391   Cond. No.                         3.84
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""